.—-_1 r‘ufi-‘v'~’ rr‘v 1...“, MICHmAN STATE UNWERSITY 0F AGR'LU‘HSRI MD wPHLD SCUENCE " LANSMG. MICHIGAN Emu EWICU OF WWW-A KINE'HC STUDY By- Horatio 8. 8151110 LTHIBIS Submitted to the School or Advanced Graduate Studies or Wan State University of Agriculture and Applid Science in partial mum of the remix-cunts for the degree of DOCTOR OF PMOPHY Department of Gheldatny 1959 ACKNOWLEDW 1' It is with sincere appreciation that I acknowledge the assistance and valnable counsel of Professor James C. Sternberg under whose direction this investigation was con- ducted. I also wish to express my gratitude to the staff of the menistry Department for assistance and advice on many matters. In particular, I gratemny acknowledge the sugb gesticmn offered by Professor Richard H. Schwendeman that pertained to the comtationa‘l. analytical procedure. I an indebted to Mr. N. H. C. Sham of Glaxo Laboratories, Ltd., Qreezfl‘ord, hgland, for his kind furnishing of samples and spectral data. Acknowledgment is also due the National Institutes of Health for their grants supporting this work. Last, but by no means least, I wish to thank Irene, IV wife, for her patience and understanding, and for her willingness to leave a secure and comfortable station in order that I lidlt conplete this phase of aw education. W PHOWGAL ISOMEIRIZATIQI OF ERGOSTEROIr-“A UNETIC STUDY By Horatio S. Stillo AN ABSTRACT Submitted to the School of Advanced Graduate Studies of Hichigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR 0F PHJHBOPHI Department of Chemistry Year 1959 Approved W \F ABSTRACT ”A kinetic investigation of the photochemical isomerization of ergosterol has been carried out. The kinetic data have been obtained in solvents with a range of viscosity, but fixed chemical nature, at dif- ferent wavelengths in a stirred reaction cell. A spectrophotometric analytical procedure based on a least-squares curve-fitting technique has been developed, verified, and employed to determine the requisite concentration vs. time data. A novel photometric technique has also been developed and actinometrically calibrated to make possible the absolute determination of the absorbed light intensity as a function of time of irradiation. Cambination of these data with the spectrOphotometric analytical results has furnished the absorbed light intensity for each component as a function of time, making possible the elimination of the "inner filter' effect and the use of a new type of photochemical kinetic expression; Stereochemical information and considerations of the excited states ' of the components of the irradiation mixture have been utilized to formulate a kinetic mechanism expressed in general and in specific terms. The general formulation is a special photochemical application of general- _ ised first order series and parallel reaction kinetics, and has been shown to lead to expressions for concentrations of the components as linear combinations of definite integrals representing the amounts of radiation absorbed by the individual components during a given irradiation iv interval. In the specific cases of interest, the expressions reduce to simple linear relationships between individual concentrations and single integrals. ' A.comparison of the results of the kinetic runs with the derived rate expressions furnishes values for the quantum;yield, ¢E, for the conversion of ergosterol to total products, the quantum yield, ¢PT, for the conversion of precalciferolz.toptachysterolz, and the quantum yield, égL, for the conversion of ergosterol to lumisterolg. The values of the quantum yields have been found as functions of wavelength and viscosity. The value of $3 is in accord with bioassay results and the value of ¢PT supports recent data of Havinga Obtained by direct irradiation of precalciferolz. This agreement with the results of investigations based on other analytical techniques substantiates both the novel photometric technique and the validity of the analytical scheme. The results also indicate that the solvent effect is truly a'viscosity effect and show the direction of the viscosity dependence for ¢pT to be Opposite to that obtained for ¢E and ¢EL' In addition, an appreciable wavelength dependence for ¢E and ¢PT’ entirely apart from inner filter effect, is demonstrated. An interpretation or description of the prOposed mechanism has been made'with the following features: (a) the optical excited state is a singlet state, (b) the Optical excited state for ergosterol differs from that for precalciferolz, (c) conversions occur through cross-overs of potential energy surfaces along coordinates corresponding to internal rotations, (d) the solvent exerts an effect through its viscous resist- ance to internal rotation, and (e) the excess energ per quantum of radiation at shorter wavelengths helps overcome the barrier to internal rotatim. An alternative non-mechanistic interpretation has been presented but is ruled out on thebasis of the available data. The results of this investigation have been utilized to suggest other studies which would help further to establish the complete mechanism . vi TABLE OF CONTENTS Page I. mmmImOOCOOOOOOOOCOOOQOOOOOCOOOOOOOOOOOOOOOOOOO0.00... II. mmTMJOOO...OOOOOOOOOSOO0.0000000000000000000000GOO... A. PreparativeOOOOOOOOOOODOD...OOOOOOOOOOOOOOOOOO00...... l. Irradiation Procedure and Apparatus . . . . . . . . . . . . . 2 . Preparation of Irradiated Solution for 'Chroma-s ’ tOgraphic Separation......................... 3 . Chromatographic Separation ‘and Preparation ‘of ‘ Derivatives............... ................... B. Kinetic StudiBSOOOOOOOOOOOOOOOOOOOOOOO0.00.00.00.00... 1. Apparatus....................................... a. Source and Monochromator.................. b. The Photometer Section.................... (1) Optics for Splitting the Radiation _ into Sample and Reference Beams.... (2) The Sample Beam.................... (3) The Reference Beam................. (’4) The alOpper...........o............ (S) Principle of Operation ‘of the PhOtometereeeeeeeeeeeeeeeeeeeeee (6) The Detector, Amlifier,‘ and Rscorder........................ (7) Detector, Anplifier, and Recorder Operating Procedure............. 2. Calibration of the Photometer................... a. Principle of the Actinometric Procedure... b . Causes of Non-Linearity of the Photometer. c . Experimental Verification of 'Non-‘Linearity Of PhOtOtUbe Response...............'...’ d. Actinometer Conpounds..................... (1) Uranyl Oxalate..................... (2) Malachite Green Leucocyanide PreparationOOOOOOO...0.0.0.0.... (3) Photolysis of Malachite Green Leucocymideeeeeeeedeeeeeeeeeeee Ce mmration maultSOOOOOOOOOOOOOOOOO0.0... vii 1 WWW '5 TABLE OF CONTENTS - Continued ._: Page 3. Irradiation Procedure........................... a. Preparation of Solutions.................. b. The Irradiation Process..................'. 0. SpectrOphotometric Analysis of the Samples d. Summary of Irradiation Conditions Employed h. Materials and Purification Procedures........... 5. ViscometIV-OOOOOOOOOOOOOOO0.0.0.0000...0.0.0.0... III. DMSSIONJOF PMMTIVEWOMOOOO0.0000000000000000000COO... A. GeneralOOOOOOOOOOOOOOOO. ..... 0.00....OOOOOOOOOOOOOOOOO. BO ResultSOOOOO0.0...OOOOOOOOOOOOOOOOOOOOOOOO0.0.0.0000... C. Miscellaneous Observations............................. 1. Stability of Irradiation Mixture................. 2. Yellow Component of Irradiation Product.......... De verification Of Beer-Lambert-Bouger LaWeeeeeeeeoeoeeeee IV. SPECTROPHOI‘OMETRIC ANALYSIS OF I‘MLTICOMPONENT SYSTEIB USING“ TEMT 80.1% &m MODOOOOOOOOOOOOOOOOOOOOOOOO... A e LeaSt-Sq'llares Treatment‘“MatriX MethOd e e o e e e o e e e e e e e e e e B. Application of the Method to the Ergosterol Irradiation systeInOOOIO0.00.00.00.00...0.00.000...00.000.000.000 it ProcedureOOOOOOOOOOOO00.00.00.00000.00.000.000... 2 . Verification of the Beer-Lambert-Bouger Law. . . . . . 3. Specific Modifications of the Method for the system StudiedOCCCCOC.C‘COOCOOOOCO0.0...0...... h. Calculations of the Matrix M =- . [(3 g)‘1:fi_] S . Applicability of the Calculated Matrices . . . . . . . . . viii h8 148 148 h? 50 50 5b 55 SS 58 62 62 6h 6h 66 66 72 72 72 73 77 81 TABLE OF CONTENTS - Continued Page V. IRRADIATION RESULTS.......................................... 90 A. Application of the Matrix Mbthod to Sharpe's Data...... 90 B. Irradiation Results--Kinetic Study... 113 VI.DEVELOPMENT OF KINETICEIPRESSIOI‘E........................... 130 A. Survey of Recent Considerations on the Reaction‘ MeChanismOOOOOO0......OOOOOOOOOOOOOOCOOO0.0...0.0... 130 B. Stereochemical Considerations.......................... 132 l. Tachysterol...................................... 133 2. Precalciferol.................................... 13h 3. Calciferol....................................... 136 C. Electronic Changes During the Reaction........... ..... . 137 D. Derivation of Kinetic Expressions...................... lh3 1. Introductory Discussion.......................... lh3 2. Some General Considerations of the Reaction' Mechanism and Kinetic Treatment. . . . . . . . . . . . . lhh 3. Glossary of Symbols Used in Specificherivations. 151 14. Case of Equivalence of Optical and Derived moi-ted States.00......0.00.00.00.0000000...... 153 5. Case of Non-Equivalent Optical and Derived‘ F‘XCj-ted StateSOOOOOOOIOOOOIIOOOOOCCCOOIOOOO... 15? VII 0 PESULTS OF Tm KIMTI C STIJDY O O O O O O O O O O O 000000000 O O 0 O I O O O O O O O O 161 A 0 Treatment Of the Data- 0 O O O O O O 0 O O O O O O O O O O O O O O O O O O O O O O O O O I 1-61 B. ResultSOOOOOO0.0000000000000000000000000000000000000000 166 1. Case of Equivalence of Optical and Derived ECCited StateSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. 166 TABLE OF CONTENTS - Continued Page 2. Case of Non-Equivalent Optical and Derived EXCitedStates.0.00.00...OOOOOOOOOOIOOOOOOO0..177 VIII. INTERPRETATION OF KINETIC RESULTS........................... 193 II. SUGGESTIONS FOR FURTHER WORK................................ 209 .I. SUMMARY..................................................... 212 LITERATURE CITED.................................................. 218 APPEIQDILTESOOOOOOOOOOOOOIOOUOOOOOOOOOOOOOOOOOO 0000000 0.00.00.00.00. 221 II III IV VI VII VIII II III XIII XIVa XIVb IIVc IIVd IIVe IV XVI LIST OF TABLES _ Page Ultraviolet Absorption of Aqueous Copper Sulfate Solutions . l2 Spectral Response of lP28 Photomltiplier lube . . . . . . . . . . . . . 32 Non-Linearity of Photomultiplier Response . . . . . . . . . . . . . . . . . . 3h Absorbancy of Irradiated Malachite Green Leucocyanide ‘in' 95% EthanOleeeeeeeeeeeoeeeeeeeeeeeeeeeeeeeeeeeeeeeeoeeeeeoe AA2 Calibration of Detector Assembly........................... h? Stability of the Irradiation Mixtures...................... 63 Verification of the Beer-Lambert-Bouger Law-—Additivity of Absorbancies of Pure Components in Synthetic Mixtures...... 7).; Ultraviolet Absorption of Ergosterol and Irradiation PrOduCtSeeeeeeeeeeeeoeeeoeeeeeeoeeeeeeeeoeeeooeeeeeoeeeeeee 78 Matrices g and Determinants |@’_E_:)'J1 82 Calculated Compositions of Synthetic Mixtures . . . . . . . . . . . . . . 85 Standard Deviations Obtained for Each 14 Matrix. . . . . . . . . . . . . 86 Calculated Compositions of Synthetic Mixtures . . . . . . . . . . . . . . 88 Standard Deviation of Individual Components . . . . . . . . . . . . . . . . 89 Composition of Irradiation Mixtures--2537 A0. . . . . . . . . . . . . . . 92 Composition of Irradiation Mixtures--26Sh A0 . . . . . . . . . . . . . . . 93 Composition of Irradiation Mixtures-4801; Ao . . . . . . . . . . . . . . . 9h Composition of Irradiation Mixtures--2967 Ao . . . . . . . . . . . . . . . 9S Composition of Irradiation Mixtures-~3132 A0. . . . . . . . . . . . . . . 96 Solvent Effect on Rate of Disappearance of Ergosterol. . . . . . llO Solvent and Wavelength Effect on Product Composition . . . . . . . lll LIST OF TABLES - Continued TABLE XVIIa JIVIIb XVIIc XVIII XII .IXII Page Composition of Irradiation Mixtures--Kinetic Study--2537 A0 Composition of Irradiation Mixtures-~Kinetic Study-4801; A° Composition of Irradiation Mixtures--Kinetic Study-~2967 A0 Solvent Viscosities........................................ Molar Absorbancies at Irradiating”Wavelengths.............. Kinetic Data............................................... The Results of the Kinetic Treatment, Equivalent Excited StateSOOIOOCOOOO0.0.000...0..COO...OOOOOOOOOOOOOOOOOOOOOOOO Results of the Kinetic Treatment, Non-Equivalent Excited Sta-13880090000000.0000.0.000000000000000000000000000000.0000 xii 115 117 119 129 165 169 177 192 8. 9. 10. ll. 12. LIST OF FIGURES Page Stmctural fornulae of the components of the irradiation mixtureOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOODOOOOOOO0.0.0.0.... Ultraviolet absorption spectra of the components of the 3 60, ergosterol irradiation mixture in absolute ethanol......... 7 Preparative irradiation apparatus.......................... 10 Irradiation apparatus for kinetic studies--optical compmentSOOOOOOOOOOOOOOOO000.00.....OOOOOOOOOOOOOOOOOOOOOO 18 Actinometer recorder pattern............................... 22 Irradiation apparatus for kinetic studies-schematic repre- sentation of assembly of electrical components............. 2h Irradiation apparatus for kinetic studies--electrical ctmitW....OOOOOOOOOOOOOOO0.000.0.0000000000000000COOOOOO 25 Ultraviolet emission of medium pressure mercury lamp....... 27 Ultraviolet absorption spectrum of malachite green leuco- cymide in 95% 91311811010000.0000.oeoooooooooooooooto...coco. 38 calibration curve-~absorbanqy of irradiated maladhite green leucoqyanide in 95% ethanol (acidified).................... no calibration 0f phOtometer--2967 Aoooooeoo0.0000000000000000 ’46 “Chromatogram” of methanol soluble fraction........... ..... l351“]. to lBe-h. Composition of irradiation mixtures--Sharpe's data.0.00.00...COO...0..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 97-106 115‘‘1 to 1140-5. Composition of irradiation mixtures-~kinetic Study.0.00000...0.000.000.0000.0.00.0.0...COO0.0.0.0... 121-127 1.5 . Planar rotational conformers of precalciferol. . . . . . . . . . . . . . 135 16. Valence bond structures of the ionic excited state of ergosterOlOOOOOOO0.0000000000000000COOOOOOOOOOOOOOOOOOOOOOO lho xiii LIST OF FIGURES - Continued FIGURE ’ Page 17. Typical kinetic plots, case of equivalent optical and 3derj-v.w ”Cited statSSOOOOOOOOOOOOOOOOOOOOOOOOO00.00.00I... 168 18-30. Kinetic plots, case of non-equivalent Optical and derived GXCited States.00.000000000000000...00000000000000.0000 179-192 31a-3ld. Potential energy curves.............................. 200-201 xiv I . INTRODUCTION A kinetic study of the photochemical isomerization of ergosterol to calciferolz is of interest,since this reaction affords the only practical synthesis of the biologically important compound, calciferolz. From a fundamental point of view, this reaction is representative of a very important class of photochemical reacticms of excited molecules. Despite the expendiimre of a vast amount of effort in the study of the photochemical isomerization of ergosterol over the past thirty years, an extensive kinetic investigation capable of quantitative treatment had not been made until. the present study. Sebrell and Harris (35) have summarized the results of these investigations up to the year 1952. More recent work has been summarized by Sharpe (37). In view of the pub- lication of these works, the historical discussion of the topic will be limited. The early workers in this field, 1.6., A. Windans, O. Rosenheim, J. Weddell, and others, established ergosterol as an important provitamin that could be activated to calciferola by ultraviolet irradiation. Uindaus 1783 one of the principal investigators and did mch of the work that “salted in the characterization of a number of the irradiation products (’1‘ ergosterol. As a result of this early work a mechanism was proposed 111 which the irradiatim reacticn proceeded irreversibly throng: the identified intermediates as follows: ergosterol 113-» lumisterol, —h-Y-> tachysterol, 33—9 calciferol, fl» overirradiation products. In 19h8-h9 Vellum (hZ) and his associates announced the charactexh inaticn of a hitherto overlooked intermediate which they called precalciferola. They observed that the newly discovered compound was transformed to calciferola by a thermal reaction. An equilibrinn exists between the two camounds in which increasing temeralmre favors calciterolg. Precalciferol, had escaped detection became the l”'itorking up. or the irradiated provitanin or resin was quite involved and re- quired the during which precalciferol, was largely converted to calciferolg. me comments of the ergosterol irradiatim sequence are isomers; and their structural formulae showing generally accepted stereochemical details are presented in Figure 1. The stereochemical details are quite inortant with respect to the development. or this thesis and will be discussed in the body of the text. the discovery of prooaloii'orof by Venus and his associates has “insisted a great deal of interest in this field; in the decade follow- in; this inpartant discovery, three grmps working in Europe have made Mire contribution directly in the study or the photochemical “main a ergosterol. mess groups have been under the direction ‘_ *l'or convenience, the subscript 2 will not be mloyed from this Point'in the tut. All of the work of this investigationwas performed With ergosterol as the starting material, and consequently discussion to this investigation will refer to the irradiatim products ‘1‘th subscript 2—i.e., the products derived from ergosterol. me Pertinent chemistry of the products derived from ergosterol is identical ‘ With that out the products derived from 7-dehydrocholesterol (subscript 3) , lid general discussicn will be equally applicable to both the ergosterol ‘d 7-demdrocholesterol irradiatiai sequences . Figure 1. Structural Formulae of the Components of the Irradiation Mixture. 3 1‘2 18 ERGOSTEROL LUMISTEROL { 2 f/ HO PRECALCIFEROL Proposed Nonplanar Structure 19 1“\ R R __ 1 / '— 5 \N HO E \ 9 CALCIFEROL Tamwmpm. Of V0111m (h2,h3.hh. and 1:5). .Havinsa (ll-3.19.20.27.33.3h,h6,h7.h8.h9,50). em Morten (22 ,23 ,2h,25,26). mess groups have reported the results of investigatims on the mechanism, stereochenistry, and general. chancel details of the photochemical isomerization of ergosterol. In additicn the studies of this reaction have stimulated other investigations on related reactius of other comounds containing similar structural details. For exalple, Buchi and lung (6) have reported their results er photochemical. isosarization of certain dienemes. Also typical of related work is the investigation or the irradiation of dehydroergoeterol by Berton end [ems (2). Investigations are also being made of the reectims of the consulate of the ergosterol irradiation sequence. 1 meat contribution (11) has been the elucidation of the structure of Ilpresterol II, one of the over-irradiation products of the photo- chelieel isomerisetion of ergosterol. Brande and Wheeler (1;) have uplored new synthetic routes to simple analogues that contain the cllz‘aophores of. the comments of the ergosterol irradiaticn mixture. 1!:th contributions with respect to analytical procedures applicable to this field have been nade by Shaw and his associates (39). Hevinge. and his essociates have re-exanined the early nechanisn POItuleted for the photochemical isonerizetim of ergosterol and have cited evidence that refutes the original fomlatim of the reaction 'Oepence. hsentislly their contribution has been to demonstrate that 11.16901 .6 We]. are not essential inter-stint“ in the tom-nation of calciferol. They have also reportedwconcurrently with the results of this investigation—that precalciferol is the primary Product or the reactiml. lite o! :9: iii 8 h! h a in: he Kinetic Mine of the reaction have been quite limited. Dealer (10) had rqorted a kinetic study in which only the concentration of ergosterol was followed as a function of tine. More recently, results of linited kinetic studies have been reported and interpreted in the 11th of recent knowledge of the reaction (33 ,3h). However, an extensive kinetic investigatim which is capable of explaining such observations es the wsvelength and specific solvent effects had not been made . rer exauple, in a given solvent, the short wavelengths (about 2500 1°) favor e rapid conversion of ergosterol and fast formation of tachysterol. Irradiation with wavelengths at the longer wavelength Mt of the deception bend (about 3000 1°) results in a slower rate of conversion at ergosterol and favors the formation of lnnisterol. In addition, a Specific solvent effect has been observed in which the minus obtainable m of calciferol is apparently greater in other than in alcohol. The neior obstacle to a successful conpletion of a kinetic study he. been the lack of a suitable analytical procedure. Recent advances have been acne in analysis of the couple: irradiation mixtures through coebination of chromatographic and colorieetric procedures (3h,39), hi it eeued desirable to find a more rapid analysis which could be °ln'ried out et tine intervals during the irradiation without disturbing the irradiation nixture. The possibility of carrying out the analysis Ntirely on the basis of ultraviolet spectrophotometry was therefore I‘D-examined. he irradiation litture nay contain the following principal cen- M: ergosterol, lunisterol, tachysterol, precalciferol, end hair. t’ spec moi 111:1: oalciferol, and possible over-irradiation products . hosterol and the far other naJor comments are isomers and have very similar ultra- violet absorptiat spectra (of. Figure 2), complicating the utilization of spectrophotuetric techniques. Past attempts for obtaining the cmitiut of the irradiation mixture, based upon the direct appli- catiul of the Beer-Lebert-Bouger Law to the ultraviolet absorption spectra of the fixtures, failed because the system of five siniltaneous linear fiction obtained lacked sufficimt independence. his failure has generally been attributed to the lack of accuracy with which the spectra of the commute were known. It appeared that it night be possible to obtain with reasonable accuracy the eoepoeitions of the irradiation mixtures by application of curve-fitting techniques to the spectra, utilizing the available spectral data for the commute. Sharpe (3 7) employed a curve fitting technique, Ihich involved a comarison of experimental absolption spectra with eres calculated a the basis of the Beer-Lashert-Bouger Law, and utiliz~ 1n; m punched card naohines for performing the calculations and °~arisons3 this nethod proved partially successful. However, the pro- °Nhre yielded several compositions that would smelly well satisfy the °°Iditius for the camel-ism. In addition, one of the major comments °t the irradiation nixture, precalciferol, was neglected in nking the NW, since the existence of precalciferol in appreciable quanti- “es in the irradiation nixture was not generally recognised at the the the calculations were initiated. min omission has invalidated the results of the calculations, althle the method appears souni. 333 Figure 2. Ultraviolet Absorption Spectra of the Components of the Ergosterol Irradiation Mixture in Absolute Ethanol (ha) . i? I T I I I I L - mmisterol '1' 700 1‘ - Iachysterol "" P - Precalciferol D - Calciferol E - Ergosterol 300 200..— 0 I -l ‘l 1 I 2300 21:00 2500 2600 2700 2800 2900 3000 wavelength , A0 mmmflitydmrenmnmotthemcu- pm (39AM, an: the no of I. nor. conflict statistical W3 Woummbutloutemntdtho calculatedmltl ”Wan-duo data, hmmndoit ponible to Media- taotory duly-a otthe mummbymmum W. -Mth13 investigation“: initiated, platinum-dot. mmeqmm'mnotnlflfilemordorto obtain-m mmmmummmmmmwmn— mmdthe omutianpmtothemdlmhetiodx- hr... Mathiaworkminprom, mama. 0,8huotaluo W, Ltd" Word, W, tinny finished the necessary spectral mm "ml. at the comments,“ the prep-ruthenium 4mm. Fm: the dwelopnnt at the emtetiaul nautical procedure, it n- mm. to «have the objective or this etudy, 1..., :- «to-1n Moetudyuhichmemuihobuh fez-ammo: the phonon-1011 13th at mandrel. TABLE OF CONTENTS II. mWLOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO00.0.0000...O.CO... A. PreparativeOOOOCOOOOOOOOOOOOOOOOOOOCOOOOO...0.0.0.0....0. 9 l. Irradiation Procedure and Apparatus................ 9 2. Preparation of Irradiated'Solution'for'ChromeH ' tographic Separation............................... 12 3. Chromatographic Separation and Preparation of Derivatives........................................ 13 B. xmtic StudieSOOOOOCOOOO0.00000000000000000000.00.0.0... 16 1. Apparatus.......................................... 16 a. Source and Mbnochromator..................... 17 b. The Photometer Section....................... I? (1) Optics for Splitting the Radiation into Sample and Reference Beams....... 1? (2) The Sample Beam....................... 1? (3) The Reference Beam.................... 20 (h) The Chapper........................... 20 (S) Principle of Operation of the Photom- eter.................................. 21 (6) The Detector, Amplifier, and Recorder. 23 (7) Detector, Amplifier, and Recorder‘ - Operating Procedure................... 28 2. Calflbration of the Photometer...................... 29 a. Principle of the Actinometric Procedure...... 29 b. Causes of Noaninearity of the Photometer.... 30 c. Experimental Verification of Noaninearity of Phototube Response........................... 33 d..Actinometer Compounds........................ 35 (l) Uranyl Oxalate........................ 35 (2) Malachite Green.Leucocyanide Prepara- - timOCOOOOOOOOCOOOOOOCOC.CCCOOOCOOOOCO 35' (3) Photolysis of Maladhite Green LeucocymMGOOCOOOOOCOOCOCOCCOOOOOO... 37‘ e. Calibration Results.......................... DB 3. Irradiatim ProcedurBOOOOCOOOOOOOOCCCOOOOOOOOCOOOO. ’48 a. Preparation of Solutions..................... h8 b. The Irradiation.Process...................... ha 0. Spectrophotometric Analysis of the Samples... h9 d. Summary of Irradiation Conditions Employed... 50 h. Materials and Purification Procedures.............. 50 5. ViacometWOOOOOOOOOOOOOCOOOOOOOOOOOCOOCCOOO00...... 5h II. EIPERIHHIAL A. Preparative l. Irradiation Procedure and Apparatus Solutions of ergosterol in isopropyl alcohol were subjected to ultraviolet radiation in a flow system illustrated in near- 3. Lcylindricellowpmsurenercurylanpwas «played as thescurce of radiation. Ihenercurylamwasplaced inthe centerofthreeccn- centric cylindrical (parts chebers. Tap water was circulated thrmgh the inner cheater—next to the lam—to cool the system; a copper sulfate solution was circulated througl the niddle chadier to filter out ultra- violet radiation and provide further cooling of the systen. Adjustment of the concatration of the copper sulfate solntion permitted a vari- ation of the wavelength of cut-off of the radiatialx this factor willhe discussed further in a succeeding paragraph.- nle ergosterol schtion that use to he irradiated was circulated thrcudl the ontencst chateau the irradiated ergosterol solution and the copper sulfate collation were cooled by passing than through heat exchangers throng idlich ice water was circulated. Centrifugal punps were emloyed to circulate the cell solnticn and the filter solntion. A packing comisting of reflon shavings and Silicate grease was mloyed in the pulp in the irradiation circuit. With the exception of the steel pup, the irradiation circuit consisted entirely of «arts, glass, and Teflon tubing, which was mlqed to Join the conpmente of the systen. 10 Figure 3 Preparative Irradiation Apparatus Tap water 3-way stopcock to To cooling 00118 9 facilitate filling ‘- ouso, E (9 g E . 4—7.1?111 by gravity 7—23— ‘ Gas fl from reservoir _. escape F :55? d) J r3: {3 x - A ‘- l I (Eu—SO4 4 Tap water xi ---- *1? L1.— Vess’el to increase capacity of system Ice water -- F The capacity of the irradiation system was increased from sbcnt 500 ml. to approximately 900 ml. by the inclusion of the vessel indicated in Figure 3. me thickness of the chamber containing the solution being irradiated was 0.50 on. Prior to filling the system with ergosterol solu- tion, nitrogen was passed through the irradiation circuit. The solvent was also purged with nitrogen prior to the preparation of the ergosterol solution. The course of the irradiation was followed by detenunation of the ultraviolet absorption spectrum of the irradiated solution. Samples of the cell solution were withdrawn periodically through the sampling port, of. Figure 3. A suitable dilution was made and the spectrum determined on a Beclman DK-2 spectrophotometer. it the time the experimental work was started, it was believed that. radiation of wave length greater than 296 mp. would favor the formation of precalcifercl,which was the product to be prepared initially. be reasons for this belief will be discussed in a later section. In order to achieve this condition, the bulk of ultraviolet radiation of short wave length was filtered out by an aqueous copper sulfate solution of appro- priate concentration which was chosen from the data summarised in Table I; the absorption spectra of aqueous copper sulfate solutions were determined at varying concentrations. The wave length at which the percent transmission was reduced to 10% was considered as the lower wave length cut-off. 12 min I alumna incomes or heinous corpse scum sown-s PathLength-lmcn. Concentration Wavelength at Which Percent ngOO :1. water framnission - 10,; 20 .0 318 10.0 312 6.7 309 5.0 307 2.5 298 1.25 290 0.625 279 0.312 265 2. Preparation of Irradiated Solution for Giro-atomic Separatim mil-radiated soluticnwas evaporated tcdryness insvacuun» evaporatia apparatus thatutilised sdryicebnthas sheet-sink» Liquid inthe evaporatorwasetirredhynenn cfsnapeticstirrisgharto increasetheruteefevaporationanitcpsevent'huping' ofthelimid. newumnqsicisthewsporstorsummu 0" c. hythevepcrisetim process. he resin (the residue in the evaporator) ens dissolved in nethauels- about 25 n1. cf’solvent per gre- os crude irreiistios protect-«an mmtommtstaatfc. theuirturewaspleoedinaa ice-seltbethfor several hours: themeected ergosterclwas separated 13“ from the soluble irradiation product by filtration. The filtrate was evaporated to dryness in the vacuum evaporation apparatus described “Me 3 . (In-untographic Separation and Preparation of Derivatives the subsement treatnmt of the resin was that of Shaw gt 3;. (39). the resin was taken up in patrolman ether and chromatographed on as alanine column with a height of 50 on. and diameter of 3 on. and exploying a sitters consisting of 6S acetone in petrolema ether (v/v) as shout. the colnn was filled with petroleum ether to a height of no on. and alumina was poured thrmgh the solvent to for. a 50 on. column. Alanine with an activity of III on the Brocknann scale (5,52) was gland in the chromatographic procedure. the activity of. alanine. is , determined by its behavior toward binary mixtures of certain aso dyes. A test solution consisting of Sudan red and Sudan yellow 0.01.: w/v of each dye—is a solvent with a oompositim of 20$ banana and 801 petrol” ether v/v, is «played in the test for Grade III activity. m :1. or thetestsohtionareintroduoed intoanahsinaoohwns on. inlen‘th a with a diaseter of 1.5 on. The oolnln is developed with 20 ll. oi’ solvent. in aotixity of Grade 111 is indicated if the Sudan yellow band, which is the lower band, is still held on the oolm about 3-1; on. 11-. the tep. he alanine «played—Huck lease-1t Grade, marked suitable for chro-etopaphio absorption—possessed; an activity of III witth nrther treat-ant. The oolsnwas eluted attherate oi'B-hal. per ninteand 15-1. fractions were collected. Each fraction was checked with autism trichloiide reagent in order to detect the appearance out buds in the elnent. A 0.05 ml. portion of each fraction was evaporated to dryness and 0.5 ll. of the antinow trichloride reagent was added to the residue. A yellowish-pink or bronze color is developed which reaches uni-us intusity within 30 seconds and is stable for h—5 sinstes. he relative intensity of the anti-ow trichloride color that is developed by the commute of the irradiatim nixtnre (on the basis or the color of calciferol as 1001) is as follows (39): Anti-my triohloride Color M < 13 yellow Lanistecrol < 11 yellow Precalciferol 1001 orange tachysterol 96-1001 orange Calciterol 100$ arena laness am mackewnsh have reported siailar observations with regard to a. anti-ow triohloride color (23). _. . Slings. (39)“ereportedthattheooapmute otthe irradiation m:- are resolved into three basds as follows: W Precaloiferol uninterol Masterel II brooaleiterol 15 Second Band Calciferol Tachysterol Saprasterol V hirdBand Ergosterol Isopyrocalc iferol moprocedarooraieidgg. (31)waselployed forthepreparatian of the antisony trichloride reagent. Herck's reagent chloroform was washed seven tiles with equal portions of distilled water and then shaken with an excess of phosphorus pentoxide, followed by a rapid filtratim throng: filter paper. The chlorofor- was distilled throng: a fractimat- in; colnm and the appropriate fractims were used to prepare the reagent. hen 15-22 gram of antinony trichloride (Hallinckrodt Analytical hagent grade) were dissolved per 100 ml. of the purified chloroform, and the litters was warned to 35-450 to facilitate rapid sohtion of the salt. he litters was filtered and 2.0 d. of freshly distilled acetyl chloride were added to every 100 :1. of the filtrate. he reagent-m stored in loo .1. glass-stoppered dark bottles. he limid of the band that contained precalciferol was evaporated — to dryness in vanno, am the 3,5 dinitrobenzoate was prepared by reacting the residue with freshly prepared 3,5 dinitrobemoyl chloride in a solvent couistingotBPartsbemmandlpartpyridine. hereactionwas allowedtoproceedsttapwatertemerameforabmtonehoer,andthen thereactimflnskwas allowed tostand inanicebath for farhoure. 16 he reaction nirhare was poured into water, sodinn carbonate was added, ad the lq'ers were separated. me aqueous layer was attracted with beans, and the combined benzene extracts were added to the original basses layer. The benzene solution was dried over sodinn sulfate and evaportted to dryness in vacuo. A recrystallization solvent sitters esployed by void” 129%) was utilized. The crude product was dis- solved in a solvent consisting of 3 parts absolute ethanol and 1 part 2-but-ue. Part of the solvent was evaporated in vacuo at 0° 0. until crystallisatiea began. the precipitate was filtered by section and' wasbedwith theooldsolvent. moperertionswere carried outwith the apparwtus insured in n ice bath. 3. MOW law thetwobuictypesofdataregiredforthekineticstadywerethe amid» otthe components ofthe irradiationdxtareas aftnotiai ottiaeandtheaseast ozfradiatim absorbedbythesamle solstice daring the period of irradiation. me concentration-tine datawere Mained by the spectrophoto-stris mflytical procedure described in another section, stilising data taken with a Beck-n DI-Z Decca-din; spectrophotosster. Sinoethisisastandardccnercial instment, it will not be described here. the irradiatim ocf the solntiais with none- dn'onstisedli‘htregiredasoameandsonoohrosator, andtheasasaresents oi absorbed light intemity daring the irradiation required construction of a photo-star desiged for that purpose. base portion of the 1? appara'bls will now be considered in detail. me optical conpments of the apparatus are shown in Figure 1;. a. Source and Honochronator A file source of ultraviolet light for the irradiations of the kinetic studywas anflanoriaSnnBurner Type Sfiuamdinnpressnre serouryarc. honoraryarcwasnsed in condunctionwith aBansch andlouh crating sonochronetorehiohhad afocallength orzso sillineters, alinear dispersim of 66 A0 per millimeter and an effective aperture of f/h.h. he grating, which was blazed for first-order in the range 2000-th 1°, oontainedéOOJJnespersillineteronasurfaoeSOISOnillilsters. he slit widths were adjustable and were maintained at 1.5 ud 2.0,1111- m as indicated in the presentation of the data. imartslensattheaxitslitoftheamoohronatorinagedthap‘at- in; atapoint about 60 n. in front of the sonochrosator housing.. A carts collecting law was placed about 50 as. beyond the point at which the grating was issued; the collecting lens possessed a focal length of about 50-. the result of this goo-etryeae a slowly cmvergingbeas of radiatim emulating from the collecting lam. b. The Photoeleter Section (1) Optics for Splitting the Radiation into Sasple and Reference Beans. 1m platewas placed inthe path ofthe radiation at a distenceofSO-.beyondthecollacting lens, and inclinedat anangle ofabmth5°tothebeam rho incidentbeanwas divided into abeaw which was slightly reduced in intensity and slightly deflected tron the Irradiation Apparatus for Kinetic Studies-- Condensing Mbnochromator \\ 1/, 9 ‘Hhrcury lamp l _J Figure h. Optical Components lens Solvent or cell 18 Plate ChOpper ‘ To power supply and amplifier *0 /{—a—> C D 1P28 Photomultiplier A tube A ""—{:} Solution Plate cell / Mirror 19 original direction, and a second beam, with a fraction of the intensity out the incident bean, which was reflected to a direction appruinateiy perpendicular to the original direction of propagation. (2) The Samle Beam. The scintion to be irradiated was contained in a Becknan spectrophotometer (partz cell with a path length of 1.00 on. me irradiation cell was placed in the path of the najor portion of the incident bean about 16 on. beyord the quartz plate; this placed the irradiaticn cell slifitly in front of the focal point of the bean. he image incident on the front side of the cell was nctangulnr in shape with the dilusicns 0:! 21:20.3 -. at a slit width of 1.50 I. mess dimims were increased to about 2120.5 m. when an exit slit width of 2.00 III. was employed. Stirring in the irradiation cell was achieved by a mystic stirrer which consisted of a coil constructed from the fine alloy steel wire enployed for cloning hapodennic needles. he “0151c stirrernotorwaslountedbeneatthanaimmtrackwhichservedae a hunting for a cell holder of the type employed with the Beck-n Model DU Spectrophotometer. The solution spectrophotometer cell was placed in the cell holder. he radiation that passed through the scintion being irradiated was reflectedtronanaluimfront-enrracednirrorplaced inthe path of thebean, aboutls cn.beyondtheirradiation celland inclinedatan an. at 15° to the directim a: propagatim. nus reflected beanwas againdiwidedbyagarte plateplaced abut 10 on. fronthenirrorand inclinedatanangleefhsotofiienewdirectimofthebean. mango;- portionoi‘thinbeanpassed thread: the quartz plate andwas absorbedby 20 the walls or cover of the apparatus; the renaining portion was reflected to a photoultiplier tube (D28). The tube was nounted in a housing which was emippedwithmeperturemdshutter. (3) he Reference Beam. me radiation absorbed by the solntion'is secured by comarison of the intensities of the radiation striking the photohbetronthebeanjustdescribed and fronabeanwhich travels an identical path except for the contents or, the cell (solvent ratherthan sciatica). be second bean W as the reflected portim or the radiation which strikes the first quarts plate beyond the collecting lens, ghflgareB. mmrmticnisageinrefleotedbyenalm mimmmmntftoncdmmuuommm omtron the quarts plate. A Becknn spectrophotonster cell with a. path lugth or 1.00 on. and containing solvent is placed in the path of the bean slightly in front of the focal point or the been. The solvent cell ianountedinthe'opticalpathinanamersindinrtotha'tdeacribed. ‘ above for the scintion cell. the solvent_bean is divided by the quarts plateinfrentotthe phototube intoaretleotedportimandatruadtted fraction which strikes the phototube. (14) he Chopper. 1 semicircular chopper with a period or about five mei- was placed in a plane perpMicIlar to the direction or the solvent and solution bee- and betseen solvent m solution cells and thsplateuddrrorttcandbtoalternatslynaskthesolnntandsoln- tion bea- tren the detector. illcoqpautswererigidlynounted cnopticalbenches,wbich in turawerebolted to one another rm. .m ntri'a. no apparatus 21 was covered with a box which had been painted with a flat black paint on both the anterior mid interior sides. (5) Principle of Operation of the Photometer. It is apparent that the path of the solution beam, ABGD, is equivalent to that of the solvent bean, 1360, with the exception that the latter bean traverses a cell containing solvent only, while the solution beam traverses a cell contain- ing solution. Therefore the difference between the amounts of radiaticn striking the detector from the two beam is a neasure of the anoint. of radiation absorbed by the solution. file signal fron the phototube is amplified and fed continuously to a recorder (the electrical conpments are described nore fully in a succeeding parapaph) . me recorder pattern produced by the alternate signals from the solvent and solution beam is shown in Fix!” 5. The difference between the scale deflection produced by the reference bean anthatofthesolventbeanatanyglreninstmtis aneasureof the rate that radiation is being absorbed; the area between the curves con- necting the iniividual deflections provides an integration in tins and is a neasure of the anount of radiation absorbed during a giren interval of tine. In order to obtain an absolute neasure of the radiaticn absorbed, it is necessary to relcte the area between the curves to an absolute snount of radiation; this was achieved by calibration with a chancel actinonster as described in the next section. two thicknesses of final natal wire screen, no nesh, were placed directly in frmt out the detector to reduce the intensity of the bean striking the detector: this will also be discussed further in the next section. 22 . Figure 5 Actinometer~Recorder Pattern Recorder Scale -20 -lO 1\ 10 20 30 no 50 60 7O 80 ”##— I ' Solvent I trace I Solution ' fine trace 1 . I 5 Min. 1 J 1 ,1- 1 ’\ { - 0--“ 7 -oo nan—s- . - - m- 0...“... 9......- t E I',‘ TV ..——-"’ “Base line» (No radiation striking detector.) Area ABCD is a measure of the radiation absorbed by the solution during the interval t-to. Actual trace of the recorder. - - - - Interpolated trace. 23 (6) The Detector, Amplifier, and Recorder. The detector, anplifier, md recorder system were assailed from components of The rarrand Electron Multiplier Photoneter and the Leeds and Northrup Electro- (henograph. me former consisted of a photomltiplier tube (1P28) and a power supply of 30 batteries of 30 volts each. The components of the nectro-Qienograph that were utilized were a Leeds and Northrup No. 7673 Thernionic imlifier, the Polarizing Unit, and a Leeds and Northrup morons: Recorder, nodal S h0000 Series. The assemly of the comments is shown schenatically in Figure 6. The output of the photomltiplier systen is passed on to the thermionic amplifier to amplify the current in order “that it may be utilized in the measuring circuit of the recorder. The measuring circuit consists of a potentiometer which is automatically balanced by means of a mechanically operated slidewire which is calibrated for the rage -h0 to #4160 millivolts-.? The recorder scale is divided into 100 emal divisiais which cover the ranges ~20 to 0 to +80. This arrange- nent provided for a current reversal which was useful for polarographic deterninations . For this work the circuitry was arranged to emloy the range 0 to +80. A portion of the circuitry of the Polarizer Unit was utilized. to facilitate use of the recorder without further nodification._ niecircuitryisshowninde‘tailinliaum'f, andthedetails ofoperation of the electrical comments are presented in the next section. The apparatus was enployed to obtain a plot of recorder scale de- flection vs. wave length for the nercury are used in the irradiation etudiss, of. figure 8. The slitwidth of the nonochronetorwas setat 1.00 n. for this determination. 2h Figure 6 Irradiation Apparatus for Kinetic Studies 7-Schematic Representation of Assembly of Electrical Components C \ Recorder. Wire Color Code Hire No. Color Code 21 Red 22 Green 23 Grey 2h Red-yellow ' 25 Green-yellow 26 Black-yellow 27 Red-Green 28 Yellow 29 white ot ot 1 2 3 1. s p- 3 j 1> 0 0 <9 2967 > 2537 A0. This order is the result of the intensity of the source with reSpect to wave length, (of. , Figure 8), the slit widths, and the fact that two layers of ho mesh Monel metal screen were placed immediately in front of the detector for the irradiation at 2967 and 2537 A0. The order of deviationnwith respect to wave length of irradiation-~of the constancy of g for a variation of T4 is also 2801; > 2967 > 2537 A0 as evidenced by the value of the lepe, ’7’ . This is further proof that the deviation from a constant value for; at a particular wave length is due to a non-linear response of the detector with respect to intensity of the radiation striking the detector. he data of Table V were utilized to calculate the total quanta absorbed during an interval of irradiation of the ergosterol solutions from the area between the solution and solvent curves recorded during the irradiation. 11.8 3. Irradiation Procedure a. Preparation of Solutions Stock solutions of ergosterol in isopropyl alcohol and in n-hexane were prepared from a sample of purified ergosterol which was generously furnished by U. H. C. Shaw of Glaxo Laboratories, Ltd. , Greenford, England. The stock solutions were prepared from about ten milligrams of ergosterol (weighed to 0.1 milligram) diluted to 100 ml. with the appr0priate solvent which had been flushed with nitrogen for at least one hour ilmediately before preparation of the solution. Aliquots of the stock solutions were diluted with several solvents to produce a series of solutions of varying viscosity. The solutions were prepared as follows: (a) 5 m1. of the isoprOpyl alcohol stock solution were diluted to 25 ml. with isopropyl alcohol. (b) 5 m1. of isoprOpyl alcohol stock solution plus 15 ml. isoprOpyl alcohol were diluted to 25 ml. with glycerol; designated as 20% glycerol. (0) 5 ml. of n-hexane stock solution were diluted to 25 ml. with n-hecxane. (d) 5 ml. of n-hexane stock solution plus 15 ml. of n-hexane were diluted to 25 ml. with mineral oil; designated as 20% mineral oil. (e) 5 m1. of n-hexane stock solution plus 10 m1. of n-hexane were diluted to 25 ml. with mineral oil; designated as 110% mineral oil. b. The Irradiation Process Three m1. of a given solution were placed in the Beckman spectro- photometer cell and the cell was positioned in the irradiation apparatus. 119 A cell containing solvent was placed in the other beam of the apparatus. Stirring was effected during irradiation by the magnetic stirring device discussed in a previous section. Irradiations were conducted in an air- conditioned room which was maintained at about 22° C. The mercury arc was turned on, but a shutter was placed in the beam in front of the mono- chromator to allow the intensity of the beam to stabilize. The shutter was then removed and the irradiation of the cell was started. The light intensities transmitted by the solvent and solution cells were recorded by means of the photometer arrangement described in an earlier section. The irradiation was interrupted periodically for spectrophotometric analysis of the solution. c. 'SpectrOphotometric Analysis of the Samples The ultraviolet absorption spectra of the irradiated materials were determined in the range 31400-2200 A0 on the Beckman DK-2 spectrophotometer; three spectrophotometer cells were employed for the determination of the spectra. Two cells containing solvent were utilized to balance the two beams and to determine the zero absorption line. The cell in the sample beam of the spectrOphotometer was replaced with the cell containing the irradiated solution, and the spectrum was determined. A small correction (less than .01 absorbency unit) was applied to the spectrum to correct for the difference in transmission of the cells used in the solvent beam. A further correction was made for the error in calibration of the chart paper; the wave length on the instrument indicator dial differed (generally less than 10 AC) from the value on the chart. A corrected calibration scale was obtained by st0pping the instrument when the wave 50 length indicator recorded the desired wave lengths and marking this position on the chart paper. This scale was aligned with a reference wave length on each Spectral determination and the desired wave lengths were marked off on the Spectrum. The spectrophotometric analysis yielded the concentrations of the components of the mixture as a function of time of irradiation . d. Summary of Irradiation Conditions Employed The conditions of irradiation were as follows: Hav e Length 00 Irradiation Slit Width A I‘ m. 2537 1-50 28014 2 .00 2967 1.50 The solvents employed are summarized below: 2531 A0 - one run with each of the solvents, i.e., n-hexane, 20% mineral oil, isopropyl alcohol, and 20% glycerol. 280;; A0 - same as 2537 A0 2261 A0 - same as 2537 A0 with the addition of a duplicate run with n~hexane and an additional run with 110% mineral 1;. Materials and Purification Procedures Ergosterol, Lumisterol, Calciferol. Purified samples of ergosterol, lumisterol, and calciferol--which were generously furnished by V. H. C. Shaw of Glaxo Laboratories, Ltd. , Greenford, England-«were utilized for the kinetic studies and for the verification of the analytical procedure. 51 ISOpropyl Alchol. Commercial grades of alcohol were purified by shaking with sodium hydroxide, separating the aqueous layer and fractionally distilling the alcohol layer. The ultraviolet absorption spectra of the fractions were determined in the range 3400-2200 A0 in the Beckman DK-2 spectrOphotometer employing distilled water as the reference. The suitable fractions were tranSparent to about 2500 A0 (greater than 95% transmission); a general absorption began at 2500 A0, but the transmission was still larger than 80% at 2300 A0. During the latter stages of the preparative work, Analytical Reagent Grade material was obtained from Mallianrodt; this material was almost as transparent as the purified alcohol and was employed without further treatment for the preparative work. However, for the kinetic studies and the verification of the analytical procedure, it was also purified as described above. Ethanol. A commercial grade of 95% ethanol was refluxed for several hours with 10 grams of silver nitrate and 1 gram of potassium hydroxide per liter of solvent; the liquid was decanted and fractionally distilled. The ultraviolet absorption spectra of the fractions were determined as described for iSOprOpyl alcohol; the transparency in the ultraviolet was similar to that of isoprOpyl alcohol. Glycerol. Mallinckrodt Analytical Reagent Grade glycerol was employed without further purification. In the region 2500-3uoo A0, the material exhibits a minimim transmittancy of 75% with distilled water as reference. A large fraction of the apparent absorption may be attributed to the dif- ference in refractive indices of water and glycerol. Attempted vacuum distillation of this product was not successml, as the transmittancy of 52 the distilled material was lower than that of the untreated glycerol. n-Hexane. A commercial grade of n~hexane was passed through an activated silica gel column with an internal diameter of h.0 cm. and a height of 75 cm. A flow rate of about 2 ml. per minute was employed. The silica gel was obtained from The Davison Chemical Co. , Baltimore, Md. , and was designated as a desiccant (activated) commercial grade. The purified n-hexane was completely transparent up to 2500 A0 where a general absorption started; the transmittancy decreased to about 75-85% transmission at 2300 A0. Distilled water was employed as a reference. Mineral Oil. U.S.P. grade mineral oil was passed through a silica gel column with a diameter of 14.0 cm. and a height of 110 cm. NitrOgen was employed to apply a pressure of about 15 lbs. per sq. in (gauge); a flow rate of about 20 ml. per hour was achieved urxier these conditions. The ultraviolet absorption spectra of the fractions were determined employing distilled water as a reference. In the range 2500-31400 A0, the minimum percent transmission decreased from about 85% for the first fractions to about 70% for the later fractions. The fractions were conbined and passed through another silica gel column with a diameter of 3.0 cm. and a height of 75 cm. A flow rate of about 20 ml. per hour was again achieved by apply- ing pressure with nitrogen at a pressure of 15 lbs. per sq. in. (gauge). In the range 2500-3h00.A°, the minimum transparency of the fractions varied from 95-901 transmission. A general absorption began at 2500 A0 and the transmittancy decreased to 20-355 transmission at 2300 A0. The purified material did not fluoresce when subjected to ultraviolet radiation. 53 Miscellaneous Materials. Solvents and other materials employed were of C.P., Spectral Grade, or Reagent Grade purity, and were used without further treatment. Stability of Irradiation Solvents. The solvents employed in the irradiation work were examined for stability to ultraviolet radiation by subjecting each of the solvents to radiation at 28014 A0 with a slit width of 2.00 mm. for periods of at least one hour. The ultraviolet absorption spectra of the solvents were not altered by this treatment. Storage and Handling Procedures. The ergosterol, lumisterol, and calciferol which were received from W. H. 0. Shaw in sealed glass ampules were stored in a small desiccator which was refrigerated at temperatures lower than -h0° C. The necks of the ampules were cut and material was withdrawn; nitrogen was passed through the ampule before sealing with a tightly fitting rubber serum bottle cap. 'me opened ampules were immediately placed in the desiccator and refrigerated. Stock solutions of the materials in glass stOppered reagent bottles were stored in a large desiccator which was refrigerated at 5° 0.; the desiccator was flushed with nitrogen before sealing. Solutions of ergos- terol and lumisterol were stable for a period of at least three months when stored under these conditions; the ultraviolet absorption spectra were employed as the criteria of stability. Calciferol did not exhibit this stability over the three month period; the absorbancy of the stored solution increased appreciably in the range 2200-2600 A0. SpectrOphotometric determinations employed for verification of the analytical procedure were conducted on solutions which had been stored Sh under the above conditions for not more than several days. The stock solutions of ergosterol employed for the kinetic studies were stored under the above conditions; the ultraviolet absorption spectrum was always determined prior to each irradiation run. Dilutions for the kinetic runs were made immediately prior to the run and the diluted solutions were not stored. 5. Viscometry The viscosities of the solvent and solvent mixtures were determined with Ostwald viscometers in a thermostated bath maintained at 25 i 0.10 C. Absolute viscosity was calculated from the two parameter equation d ‘n a Rdt w St where 'q = absolute viscosity in centipoise d a density of the liquid in grams cm‘3 t = time of flow of liquid between calibrated marks of the viscometer R, S e empirically determined constants. Densities of the liquids were determined with pycnometers calibrated with distilled water. The constants, R and S, were determined empirically by utilization of liquids of known viscosity ~i.e., distilled water and a water-glycerol mixture. The composition of the latter was determined from its specific gravity and the composition-specific gravity data of aqueous glycerol mixtures which have been reported by Bosart and Snoddy (3). The viscosity data employed for the determination of the empirical constants were those of Sheely (38). TABLE OF CONTENTS Page III. DISCUSSION OF PREPARATIVE WORK 55 A. General................................................. 55 B. Results................................................. 58 C. Miscellaneous 0bservations.............................. 62 1. Stability of the Irradiation Mixture.............. 62 2. Yellow Component of Irradiation Product........... 6h D. Verification of Beer-Lambert-Bouger Law................. 6h 55 III. DISQJSSION OF PREPARATIVE WORK A. General The objectives of the preparative work were to obtain the components of the irradiation mixture, to obtain preliminary kinetic data to check the qualitative conclusions of Sharpe (37), and to acquire a familiarity with the experimental techniques that have been employed in the investir gation of the photochemical isomerization of ergosterol. The components of the irradiation mixture were desired in order to directly verify the analytical curve fitting technique developed by Sternberg and Sharpe (37), and to Obtain the ultraviolet absorption spectra Of the components. It was believed that the results obtained from the analytical curve fitting technique could be improved by more reliable spectral data. Another Objective of the preparative work was to obtain verification that there were no Specific interactions among the components of the irradiation mixture and that the mixtures obtained Obeyed the Beer-Lambert-Bouger Law. ‘Hhile the preparative work was in progress, W3 H. 0. Shaw of Glaxo Laboratories, Ltd., furnished us with tabulated spectral data and with purified samples of ergosterol, lumisterol, calciferol, and precalciferol 3,5 dinitrObenzoate. The preparative work was discontinued upon receipt of these materials and data, since the other Objectives of the preparative work had by that time been achieved. Up to the time of receipt of the materials, the preparative runs were directed towards the preparation of precalciferol in a pure state. 56 The results obtained by Sharpe (37) indicated that precalciferol should be most suitably prepared in hydroxylic solvents with irradiation at comparatively long wave lengths. Although the results of Sharpe were invalidated, with respect to quantitative interpretation, by the omission of precalciferol from the calculations, it was believed that the quali- tative conclusions with respect to, precalciferol formation were valid. These conclusions were also rationalized on the basis of the ultraviolet absorption spectra of the components of the irradiation mixture and on previously reported data. These data have been summarized by Havinga and Bots (18) in the following manner: Wavelength of Irradiation, A0 Product Composition > 2810 Calciferol + lumisterol < 28h0 Calciferol + large amount of ' tachysterol {- small amount of lumisterol < 25140 Larger amounts of tachysterol 0 smaller amounts of calciferol > 2900 Reduced yields of calciferol Although precalciferol is not listed in the above tabulation, the indicated calciferol would actually be precalciferol if the temperature of the irradiation mixture were maintained at room temperature or below. On the basis of Sharpe's experimental results and his proposed mechanism, a hydroxylic solvent or a solvent of high viscosity should suppress the formation of lumisterol. Therefore, irradiation of ergosterol at low temperatures with radiation of wavelength greater than 28140 AC, and in a hydroxylic solvent should yield a product consisting largely of 57 precalciferol and unreacted ergosterol. It was considered necessary to limit the extent of conversion of ergosterol in order to minimize the formation of overirradiation products. In order to fulfill the wavelength requirements, the radiation of the low pressure mercury arc was filtered by aqueous capper sulfate solu- tions at concentrations of 5.00 grams/100 ml. water and 1.25 g./lOO ml. 'water; the thickness of the filter solution chamber was 0.5 cm. Under these conditions, the more concentrated solution absorbed 90% of the radiation of wavelength less than 2900 A0, while the more dilute solution absorbed 90% of the radiation of wavelength less than 2790 A0. The more dilute solution was employed for the later preparative runs to decrease the reaction time and thus minimize the thermal conversion of precalciferol to calciferol. Since the solubility of ergosterol in 95% ethanol is quite limited, this solvent is not suitable for the preparative work. Crude solubility determinations were made at room temperature to find a more suitable hydroxylic solvent. Saturated solutions of ergosterol in absolute ethanol and in iSOpropyl alcohol were prepared at room temperature. The solutions were filtered, aliquots of the filtrate were evaporated to dryness in vacuo, and the weights of the residues were obtained. The solubility of ergosterol in iSOpropyl alcohol.was found to be 10.7 grams per liter as compared with 3.9 grams per liter found in absolute ethanol. The solu- bility in isopropyl alcohol is adequate and this solvent was employed in all of the preparative work. 58 B . Results In general, observation of the ultraviolet absorption spectra of the irradiation mixture and of the chromatographic fractions indicated that precalciferol was the major product. 0n the basis of the intensity of the antimony trichloride color produced by the fractions from the chromatographic separation, one fairly narrow band was observed during the early portion of the elution procedure of the methanol soluble fraction of the irradiation product. However, during one run in which the ergosterol solution being irradiated was not cooled efficiently, two bands were clearly detected. The first band did not contain mch product while the second bend contained the bulk of the material. Apparently most of the precalciferol hadribeen converted to calciferol during the irradiation andthe "working up“ of the resin. A particular run will be discussed in detail. A solution containing 7.6? gram of ergosterol dissolved in 900ml. of isoprOpyl alcohol was irradiated for 914 minutes. After evaporating the solvent in vacuo, the resin was taken up in methanol and 2.51 gram of precipitate (ergosterol) were separated by filtration. The ultraviolet absorption spectrum of the filtrate was determined after suitable dilution of a small aliquot cf the filtrate with methanol; the reference solution consisted of methanol that was saturated with ergosterol at the same temperature as the smle solution, so that the contribution of ergosterol to the BPOctrum would be nullified. The reference solution was prepared by filtration of a. saturated solution of ergosterol in methanol (at the S9 temperature of the methanol extraction of the irradiation resin) and dilution of the filtrate with methanol in the same manner as the sample solution. The absorption spectrum was very similar to that of precalci- ferol with an absorption maximm at 2600 A0. However, the extinction coefficient, Elzcm.’ at the maximum had a value of only 16).; based on the total solute, while the extinction coefficient of precalciferol is equal to 230 at 2600 A0. The discrepancy is partly due to the ergosterol that was in solution, which acted essentially as a spectroscopically. inactive diluent, since its absorption was balanced by the ergosterol in the reference solutim. The methanol solution was evaporated in vacuo and about h.5 grams of resin were recovered. The residue was taken up in the petroleum ether-acetone mixture and chromatographed on alumina employing petroleum other as eluent. About 75 ml. of liquid that was first eluted was dis- carded; this liquid gave a negative test with antimony trichloride reagent. Ten ml. fractions were then collected at an eluticn rate of 3 ml./min. The fractions were imediately imersed in an ice bath, and the autism trichloride reagent test was applied to each fraction. The results of the tests are summarised in Figure 12. On the basis of the color test it is apparent that only one major band is present, and this band is quickly eluted from the column. he behavior is characteristic of precalciferol. Fractions lO-27 were combined (the upper limit of the band was somewhat arbitrary)g.1ami.theoiolvmrrwae evaporated in vacuo. About two grams of residue were recovered. The remaining fractions were arbitrarily conbined and solvent was evaporated as follows: Color Intensity, Visual Estimation on Relative Basis Figure 12 "Chromatogram" of Methanol Soluble Fraction ‘-pink orange-red red- orange 20 to 60 80 160 120 Fraction Nuber‘ 61 Residue Recovered F. _r.a.C'o,;g;}~=: {App 1‘ animate} 28-h? 2 grams h8'87 .h grams 88-135 .3 grams 'Heighed amounts of the crude residues were dissolved in iSOpropyl alcoholjand the ultraviolet absorption spectra were determined with isopr0pyl alcohol as the reference on the Beckman DK-2 Spectrophotometer. The Spectrum of the "precalciferol band? fractions 10-27, was quite similar to that of precalciferol; the absorption maximum was at 2615 A0 with Elzcm equal to 202 as compared to a value of 230 for precalciferol (,gnimmtatzzoooufi. The discrepancy could reasonably be attributed to small amounts of less absorbing contaminant, since the crude resins were employed for the spectral determination. The spectrum of fractions 28-h? was quite similar to that of fractions 10-27, and it is reasonable to conclude that fractions lO-h? consisted largely of precalciferol. The spectrum of fractions h8-87 indicated that this portion consisted essentially of a mixture of precalciferol and calciferol; it should be noted that these fractions contained a very small amount of solute (about .h grams). Ergosterol was clearly indicated by the spectrum of fractions 88-135 (maxima were obtained at about 2950, 2820, 2720, and 2620 i°), although an additional maximum at about 2520 i° indicated the presence of other irradiation products. The above analysis confirms the belief that the prescribed conditions of irradiation should produce precalciferol relatively free of other irradiation products. 62 About 0.8 grams of the 3 ,5 dinitrobenZoate of precalciferol were prepared from the residue of fractions 10-27. The procedure of Velluz gt a_l.. (h2), as described in the experimental section, was utilized. The preparative experimental work was discontinued at this point since U. H. 0. Shaw furnished complete spectral data and purified samples of the required materials. 0. Miscellaneous Observations 1. Stability of the Irradiation mixture The ultraviolet absorption spectra of samples withdrawn at intervals from the irradiation apparatus were determined after storage for six days at 5° 0. and compared with the spectra determined immediately at the time of withdrawal from the system. These data were obtained for the run that was described in detail in the preceding section and are summarized in Table VI. me absorption spectrum of ergosterol (zero time of irradiation) does not change significantly during the storage period. However, the absorb- ancy of the stored irradiation mixtures consistently increases during storage. The change in absorbancy may be attributed to a slow thermal conversion of precalciferol to calciferol, since the absorption spectrum of the latter is more intense than that of precalciferol, of. Figure 2. TABLE VI STABILITY OF THE IRRADIATION MIXTURES 63 Concentration of Irradiation Mixture 0.0026 g./100 ml. Time of Irradiation Wavelength Absorbancy (Minutes) A S 0 O 29h0 .h2h .h20 2900 .383 .378 2820 .772 .769 2765 .612 .605 2635 .503 .h97 26 2930 .358 .3h0 2900 .3h7 .328 2820 .636 .615 2765 .5h3 .520 2710 .632 .612 2630 .u89 .h6o 62 2920 .278 .259 2820 .h98 .h63 2765 -hh9 .h13 2710 .516 .h75 2630 .h26 .390 914 2920 .279 .263 2765 .h69 .h32 2710 .533 .h9h 2630 -.h28 .391 S - After storage for 6 days at 5° C. O - Immediately after withdrawal from irradiation system 6h 2. Yellow Component of Irradiation Product The irradiated ergosterol solution sometimes took on a yellow color. Ergosterol itself becomes slightly yellow on standing. It has not been ascertained whether the yellow color is an oxidative degradation product or an irradiation product. This component appeared as a yellow band on the alumina chromatographic column and was eluted off the column during the last portion of the precalciferol band and the first portion of the calciferol band. These yellow chromatographic fractions were combined, the solvent was evaporated in vacuo, and a weighed amount of the residue was dissolved in isOprOpyl alcohol, and the ultraviolet absorption spectra was determined in the range 5000 to 2300 A0. ISOprOpyl alcohol was employed as a reference and the percent transmittancy scale of the Beckman DK-2 spectrOphotometer was utilized. The absorpticn due to the yellow component begins at about 5000 A0 - and appears to reach a maximm at about 3300 A0. However, the cosmonauts of the irradiation mixture start to absorb in this region and the maximm of the yellow component is masked since the latter is probably present as a minor constituent of the mixture. The value of the extinction co- orricient, a? at 3300 A0 calculated on the basis of total solute is cm’ about 5. D. Verification of Beer-Lashert-Bouger Law Since the analytical method employed in the kinetic studies utilizes the Beer-Lanbert-Bouger Law, it was first necessary to establish the amildlcability of this law to the ergosterol irradiation mixture. .65 The linearity of absorbancy vs. concentration for single components has been established for several components of the irradiation mixture (21,51). Because of the possibility of specific interactions among com- ponents, it was deemed necessary to obtain verification of the applicabil- ity of this law to solutions containing mixtures of the components. This further verification was obtained in two additional respects: (1) for irradiation mixialres, the linearity of the absorbancy vs . overall concentration of the entire mixture was established, and (2) for synthetic mixtures prepared from pure components, the additivity of absorbancies of the pure components to give the absorbancy of the mixture was verified. The latter verification will be discussed in the next section; spectral data obtained during the preparative runs were utilized for (l). . The spectra of the irradiated solutions were determined periodically during the irradiation; in addition, several dilutions were made of the irradiated solutions and their spectra were determined. Plots of absorb- ancy at various wavelengths (in the region 3000-2300 A0) were obtained from these spectra. A linear relationship was found between absorbancy and overall concentration of the irradiation mixture. The standard deviation from linearity was found to be only i 0.012 absorbancy units. This value was obtained on the basis that the plots were constrained to pass through the origin; the standard deviation was calculated from 71 experimental values which comprised 19 separate plots. The absorbancies of the samples employed covered the complete range from about .025 to 1.50. TABLE OF CONTENTS Page IV. SPECTROPHOTOHETRIC.ANALISIS OF MULTICOMPONENT SYSTEMS USING THE M! Sww mm WHQDOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO A. Least-Squares Treatment-Hatrix Method.................... B. Application of the Method to the Ergosterol-Irradiation' systemOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOO 1. Procedure........................................... 2. Verification of the Beer-Lambert-Bouger Law......... 3. Specific Modifications of the Method for the System Studied................;,................. u. Calculations of the Matrix 35 - [(3 _E_)-1 film"... 5. Applicability of the Calculated-Matrices............ 66 66 72 12" 3'2 733‘ 7.7. 81 IV. SPECTROPHOTOMETRIC ANALYSIS OF MILTICOMPONENT SISTEI‘S USING ' THE LEAST SQJAREB MATRIX METHOD Because of the general applicability of the least squares matrix method to spectrophotometric data, the method will first be presented in general form, and then applied to the ergosterol irradiation system. A. Least-Squares Treatment--Matrix Method The calculation of concentrations of n components in Spectrophoto- metric analyses has been generally regarded as a process of solving a set of n simltaneous linear equations (obtained by selecting absorbancies at n wavelengths) in the n unknowns (concentrations). As 11 becomes large, this method exhibits great sensitivity to small errors in the experimental data. An alternative viewpoint is to regard the calculation as a curve- fitting process, in which the experimental absorbancy curve is to be matched, as well as possible, by an absorbancy curve calculated by combin- ing the extinction curves of the individual components with selected weighting factors (the concentrations); the best possible matching is to be determined by the usual least squares criterion. The curve fitting may be based on any desired mater of wavelengths greater than n, and may be performed in a mmber of different ways. One method of curve fitting is to prepare a library of calculated curves for different compo- sitions and select from the library the calculated curve most nearly matching the experimental curve. "The same goal can be achieved, however, by an analytic method which can be conveniently developed in terms of a matrix notation. The application of the matrix analytic method to -1 6? spectral data was suggested by Professor Richard H. Schwendeman. The treatment presented here assumes applicability of the Beer- Lambert-Bouger Law to the absorption spectrum of the system. For a system of n components, then, the absorbancy A1 at wavelength /\1 is given by n A1 - Z, aijcjb (IV-l) J '- 1 where 31:) is the absorptivity of component :1 at wavelength A 1, c: is the concentration of component 3, and b is the cell thickness, usually in cm. The units of all of these quantities must be compatible, such that if 03 is the molar concentration, an will be the molar absorptivity/.while if 03 is the concentration of component 3 in gm./lOO ml. of solution, am will be the absorptivity of a 1% (w./v.) solution, usually designated gmfi Since the cell thickness is usually constant in an experimental applicatial, it is convenient to work with n ti E Di-—- a c (IV-2) b 3.1 133 . where Di is than the absorbancy per unit length of cell. In practice it sometimes proves convenient to work with equations of the form of (IV-2) in which the synbols Bi! 8.13, and c3 represent functions derived from the absorbancies per unit length, the absorptivities, and the concentrations 3 the relationships which follow apply to the mathematical form of equation (IV-2) and are not restricted to the usual definitions of the symbols. If data are available at m different wavelengths, A1, A a . . . , [\m, equation (IV-2) becomes a set of m sinultaneous linear equations. 68 Such equations can be written in matrix notation as .12 - as (IV-3) where the underlined symbols represent the matrices appearing in expanded form as —- T. l.— .. D2 321 8.22 e e ‘ e o 8211 C2 D3 a3]. ' ° ' ° aan c3 0 : e e e e e e e (Iv-h) LDm_ Lam}. amz e e e 0 am On Note that in the matrices it is not required that m - fir-that is, the number of wavelengths need not be the same as the nunber of components. However, if m - n, the matrix a is square and has an inverse 3.1 (unless its characteristic determinant is equal to zero). If the matrix a is known and non-singular, its inverse can be found (30), and we can obtain a“ P. - 2'1 a .9. (IV-5) or 2 - a“ .12. (IV-6) which is the solution for the concentrations (knowledge of the matrix 3 implies knowledge of each of its elements, the concentrations of the 69 individual components). This is the usual method of treatment of spectro- photometric data. If m < n (fewer wavelengths than components) no solutions for the 3 matrix can be obtained (fewer equations than unknowns). However, if m > n (more wavelengths observed than the number of components), we have more equations than unknowns and can obtain a variety of solutions for the 3 matrix by using different sets of equations. In the presence of experimental errors in both the a and 2 matrices, it will not ordinarily be possible to satisfy equation (IV-3) or (IV-h) exactly. However, it is possible to obtain the‘matrix g which will minimize the quantity m 2 g 2 A I E (Di " Di) (IV-7) i I l where the D1 come from the experimental absorbancies and the Di are values computed using equation (IV-3) with the 3 matrix and the 2 matrix 2 obtained. A is the sum of the squares of the individual deviations. Equation (7) can also be written in matrix notation as A2 - (D' - D) (D' - D) (IV-8) in which the matrix (M) is the transpose of the matrix (M)--i.e., it is obtained from the original matrix merely by interchange of rows and columns. A 2 is a single number, so is not underlined in the matrix equation (IV-8). Selection of _c_:_ to minimize A3 is the familiar least squares criterion for obtaining the best set of concentration values, 70 and can be seen to correspond to obtaining the closest fit of a calcu- lated absorbancy curve to the experimental absorbancy curve. It can be shown (12) that the least squares criterion is satisfied by solving equation (IV-3) in the following manner. First, multiply both sides of (IV—3) by the transpose of the matrix 3 (generally non-square). Then a 2 (IV-9) Iml In} 2 . The matrix g5 will be a square matrix, with dimensions n x n, since it results from mltiplication of the n x m matrix’gI by the m x n matrix a. The matrix 25:}; will be n x 1 since it results from nultiplication of the n x 1: matrix 3’ by the m x 1 matrix _I_)_. file multiplication by the tranSpose matrix to obtain the best least squares fit is a consequence of the form of equation (IV-8), in which A2 is itself a product of a matrix with its tranSpose. The matrix equation (IV-9) may be regarded as a new set of n simil- taneous linear equations in the n unknown concentrations. This may be solved by the usual methods of solution of simultaneous linear equations, where the nunber of equations is equal to the number of unknowns. Unfortunately, the solution of a set of simultaneous linear equations would be necessary for each sample analyzed if equation (IV-9) were to be used. The matrix inversion method described below requires a more difficult operation than solving a set of simultaneous linear equations, but the difficult step needs to be performed only once, and the result can be used in all subsequent analyses. 'u-AOI were. firs” ‘0‘... i ‘ 3. ‘8": 71 . . N Since the square matrix _a a will (if non-singular) have an inverse, both sides of equation (IV-9) may be multiplied by this inverse, (gm-1. Then N _l (a 2Y1 €5.12 = (Es) (.2972) .C. - _C. (IV-10) This is the solution to the matrix equation (IV-3), for it prescribes how to obtain from it the concentrations 3 best satisfying (by the least squares criterion) the experimental data. It is convenient to define a new matrix, 3, by M 3. ii - (earl (IV-11) where M is an n x in matrix which can be obtained directly, by suitable computations, from the known matrix _a. M will be a matrix character- istic of the system studied and the wavelengths selected, and will facili- tate calculation of the concentrations _g by' s-ia own) The individual concentrations than are given by m 0i " E Mij D3 (IV-l3) J - 1 in which each concentration is expressible as a linear combination of the absorbancy values at the set of wavelengths selected. 72 B. Application of the Method to the Ergosterol Irradiation System 1. Procedure The matrix method was applied to solutions of known composition and the calculated values of the concentrations of the components were compared to the true values. The applicability of the Beer-Lambert-Bouger Law was verified further with respect to the additivity of the absorbancies of the components in a mixture. Solutions of known composition consisting of ergosterol, lumisterol, and calciferol in varying prOportions were prepared from the pure com- ponents employing purified iSOprOpyl alcohol as the solvent. Stock solu- tions of each of the components were prepared as follows: about ten milli- grams of material were weighed to 0.1 of a milligram and diluted to 100 ml. The solutions were then prepared by dilution of aliquots of the stock solutions-~employing l, 2, 3, and 5 ml. volumetric pipets--to 25 ml. The ultraviolet absorption Spectra of the synthetic mixtures and of the pure components were determined employing the Beckman Model DKeZ SpectrOphotometer and a path length of 1.00 cm. In general, the spectra of the pure components in isoprOpyl alcohol were in good agreement with values reported by Shaw, Jefferies, and Holt (39,h0). 2. Verification of the Beer-Lambert-Bouger Law In addition to the verification for irradiation mixtures as described in the preparative section, the applicability of the Beer-Lambert-Bouger Law was verified for synthetic mixtures prepared from pure components; 73 the additivity of absorbancies of the pure components to give the absorb- ancy of the mixture was verified. The spectra of synthetic mixtures of known compositions were compared with absorbancies calculated from the spectra of the individual components and the conposition of the solution to establish the additivity of absorb- ancies of the pure comonents. This comparison was made at intervals of five millimicrons in the wavelength range 230 to 300 millimicrons and a standard deviation, S.D., was calculated for each synthetic mixture. The standard deviation was calculated on the following basis: S D . ¢ JSOI‘banCl 0f Mixture-Calculated Absorbancy)‘2 o o > n (”.m) where n is the number of wavelengths at which the comparisons were made. The values of the absorbancies of the solutions were about 0.15 to 0.70:. at the maxima. The data are presented in Table VII. The data verify the additivity of absorbancies of components in a mixture within the limits of experimental error. It was believed that deviations from the Beer-Lambert-Bouger Lav: would be most likely to occur in solutions containing calciferol and lumisterol, since these compounds form a crystalline molecular addition con:pound--i.e., the old Vitamin 1),. However, the data indicate the absence of such an interaction in solution, at least at the concentrations employed . 3. Specific Modifications of the Method for the System Studied In the ergosterol irradiation system, all four of the products are isomeric, so that the initial concentration of starting material (ergosterol) 714 TABLE VII VERIFICATION OF THE BEER-LAMBERT-BOUGER LAW--ADDITIVITY OF ABSORBANCIE‘S OF PURE CDMPONENTS IN SYNTHETIC MIXTURES Composition of Solution S.D.* _ nger 100 ml. of solution) Absorbancy Ergosterol Lumisterol Calciferol Units 0.“)1380 0.000hhh 0 i 0.006 0.000920 0.000888 0 i: 0.009 0.0001460 0.001332 0 i 0.009 0.001380 0 0.000392 i 0.005 0.000920 0 0.0007824 i 0.005 0.0001460 0 0.001176 i 0.008 0 0.000hhh 0.001176 i 0.008 0 0.000888 0.000781; i 0.010 0 0.001332 0.000392 i 0.007 0.001380 0.000hhh 0.000392 i 0.015 0.000920 0.000888 0.000781; i 0.006 SOD. - (Absorbancy of Mixture - Calculated Absorbancy)2 n 75 is always the total concentration of the five species present in the system. Designating ergosterol as component I, we have 5 5 C10 3 8:;1 cj a el + :2"_J cj (IV-15) J = 1 - 2 or 5 0 cl - cl - :E:J Cj (IV-l6) J a 2 Substitution of the value' for c1 from equation (IV-l6) into equation (Ivel), gives 5 5 A1 - ail clO b - aiib E- cj e E aijcjb (IV-l7) j . 2 j . 2 or o 5 A1 - ailcl b e E (aid - ail) cj b (IV-18) 3-2 Because of the practical difficulty in making dilute solutions accurately up to known concentration by weighing, it is convenient to normalize the results to put them on the basis of the initially observed ergosterol concentration, as determined spectrOphotometrically. Equation (IV-l8) is therefore divided by equation (IV-l9), which applies to the initial condition, before irradiation. O 76 The division gives 1‘3. —5_ 8‘0 - " a‘l C. J: ._. 1 + ‘ --l 2.7.1.... {)1 (IV-20) A0 «_J 611 C1 1 j a 2 or . 5 . 5-1. 2(33 403-1 (Iv—21) Equation (IV-21) is put into the form of equation (IV-2) by defining Di= i}. - 1 (IV-22) 0 Ai E13 I .2321. .. 1 (IV-23) ail and c.- 5.2L °J (IV-2h) J'-1 03 is seen to be the fraction of component 3 in the irradiation products. Then 5 Di - Z Eij cJ (Iv-25) 3-2 When m wavelengths are considered, we obtain a set of m simultaneous equations in the four unknown concentrations. The resultant set of equations has the matrix form of equation (IV-3) 2 " .15 .9 (IV-26) 77 The best values for the concentrations by the least squares criterion are then given by equation (IV-10) or (IV-12), which here have the form .9 - (3.12)“ 3’2 (Iv-27> or .9 a 11 1.3 (IV-28) with a . (E’s-2)" E. (xv-29) The matrix _lj can now be calculated from available data on the absorptivi- ties of the components at whatever set of wavelengths is selected for the analysis. This calculation requires setting up the {:3 matrix, elements of which are defined by equation (IV-23), multiplying this matrix by its transpose 35’, obtained by interchanging the rows and columns of 23.: and then finding the inverse (ngl, of the square product matrix, E5. The matrix inversion is the only tedious step, and here involves inversion of a h x )4 matrix. When the inverse matrix, (:3: _E.)'1, is obtained, it is to be mlti- plied by Etc give the desired 31 matrix. 1;. Calculations of the Matrix 35 [(59435]. The data used were those of Shaw gt _a_l. (39,10) and are tabulated in Table VIII. The matrix inversion was performed for several different combinations of wavelengths in an attempt to find the matrix [gm-1 3] - g which would give the best results in the calculation of the compositions of synthetic mixtures. The following choices of wavelength were carried through the matrix inversion: (continued on p. 81) TTBLE VIII ULTRAVIOLET ABSORPTION 0F ERGOSTEROL AND IRRADIATION PRODUCTS Elfin Values in Absolute Ethanol A; Ergosterol Lumisterol Tachysterol Calciferol Precalciferol 2300 1111.7 32 .3 217 156 2320 33 .1 260 2 3110 311.8 2350 1.5.2 282 151. 2360 37 .7 2370 298 2380 111.11 21100 51.1. 146.11 136 3214 169 21120 53 .0 339 211110 60 .1 2150 65.8 172 361 189 21160 69 .5 21170 377 21180 80.3 21190 88 .8 2500 97 -l 96 .9 229 399 210 2510 101.8 2520 111 .0 107 .6 258 .2 1.12 217 2530 116.2 251.0 121.8 121.3 2550 128 .5 128 .3 303 1431; 225 2560 136.6 136.2 320.0 199 .5 226.7 2570 1118 .0 11115 2580 152 .11 2590 175 .8 2600 189 .5 169 .7 396 1.63 230 2610 197 .11 2620 202 .5 1811 .3 1170 2630 203 .5 189 .0 151 .5 172 .3 227 .3 2610 2011.5 1911.9 1169 .6 1171; .0 225.8 2650 208.2 200.2 11911 1175 2211 2660 216.7 205.3 2663 220.5 207 .5 525 1173 .8 220 .5 2670 551 2680 21.6.1 218 .5 583 .6 869 211; .9 2690 590 Continued TABLE VIII - Continued o A ,A Ergosterol Lumisterol Tachysterol Calciferol Precalciferol 2700 281.5 232 .3 602 1158 207 2710 290 .2 235 .6 609 2715 290.5 237 .0 611 11117 .1 199 .5 2720 289 .2 238 .0 611 11111. 197 .1 2730 280.0 236.1 620 271:0 265.5 233 .1 631 2750 252 .7 231.0 1112 182 2760 215 .6 226.9 668 397 .5 176.8 2770 21.7 .o 221. .7 381 2780 258 .1 223 .7 718 2790 272 .2 22 3 .7 737 353 158 .8 2800 288.2 223.7 7h5 3h0 152 2810 301.5 222 .5 7112 2820 306 .0 219 .3 728 306 .o 137 .2 2830 296.1 213.5 290 2839 27S .5 203 .7 679 .5 275 .5 1211.2 2810 271 .7 202 .5 677 273 .9 123 .6 2850 21.0. 3 2 58 117 . 2860 209 .0 177 .9 631 2870 617 227 2880 165 .9 152 .1; 609 210.1 98 .1 2890 157 .7 608 2895 157 .2 137 .2 608 188 .7 89 .o 2900 158 .3 133 .3 608 181 86 2910 162 .9 607 2912 1611.0 125.8 606 1611.0 79 2920 168 .11 121 .3 599 153 .5 711.3 2930 172.6 2935 17h.0 112.8 572.5 13h.6 66.0 291.0 173 .6 110 .1 561 2950 167 .0 119 58 .5 2960 188.1 92.3 h81 107.7 53.2 2980 89 .3 69 .1 386 3000 112 .5 116 .h 307 70 37 .S 3010 29 .8 3030 8 .2 3050 12 .0 177 38 22 3070 2 .6 3100 0.8 11.1 118 18 12.5 3125 3 .3 98 3150 2 .9 82 The above values were obtained from large scale plots drawn from tabu- lated data that were kindly furnished by Shaw (110), and were used for the calculation of the matrix 11 in cases l—h. Continued TABLE VIII - Continued o )\,A Ergosterol Lumisterol Tachysterol Calciferol Precalciferol 80 2500 2600 2650 2700 2750 2800 2850 2900 97 .0 186 .0 213 .o 276 .0 257 .5 282 .5 250.0 159.0 95 .0 170 .0 200.0 231.0 228 .5 2211.5 189 .0 133 .5 225.0 398 .0 1:92 .5 601.0 655 .0 7113 .0 657 .5 607 .0 399 .0 1461.0 1:75 .0 1159 .0 1108 .o 3110 .0 257 .5 182 .5 209.0 230.0 223.0 208.0 181.0 153.0 ll8 .0 85 .0 The values listed above were obtained from enlarged plots of the figures presented in the paper by Shaw _e_t_ _a_l_. (39) and were utilized for the calculation of the matrix 15 in Case (0). 81 (0) Eight wavelengths - 2500, 2600, 2650, 2700, 2750, 2800, 2850, and 2900 2. Data for this case were taken directly from enlarged plots of the figures from Shaw .e_t_ 31. (39). For Cases l-h, data were taken from large scale plots drawn from tabulated data furnished by Shaw (110) . (1) Twelve wavelengths at intervals of no 2 from 2520 to 2960 2. (2) Twelve wavelengths including the maxina and minima of the components of the mixture, i.e., 2500, 2600, 2630, 2650, 2715, . 2720, 2760, 2790, 2800, 2820, 2895, and 2935 X. H (3) Twelve wavelengths including points of intersection of the ergosterol curve with those of the other components and maxima and minima of the other components, i.e., 2500, 2550, 2600, 2650, 2663, 2720, 2790, 2800, 2820, 2839, 2895, and 3000 R. (1;) Twelve wavelengths including the maxima and minima of ergosterol and points of intersection of the ergosterol absorption curve with curves of the other components, 1.0. , 2500, 2550, 2630, 2663, 2715, 2760, 2820, 2839, 2895, 2912, 2935, and 3000 R. The matrices _15 and the determinants (E _E_)"1 are presented in Table 113’ 5. Applicability of the Calculated Matrices The calculated matrices g were checked by applying them to spectral data obtained on synthetic mixtures consisting of ergosterol, lumisterol, *The matrix inversions were, with the exception of case (0), carried out on the HISTIC Computer at Richigan State University; the author is indebted to Hiss Susann Brimer for carrying out the calculations on the conputer. 82 ooseaecoo $897 a 13. @ eo ecmfiseoeon memes.ou mmemm.o- amnmo.o mammo.o ooaeo.o memmm.o ammom.o meHeN.o Hesom.o mmebm.o ommea.o acmea.o- Hoeoeaoamo emsea.a Hanan.o meeao.o- mmomH.o- membm.o- Hmebe.o- emmbb.o- meemb.o- emcee.o- asmam.o- sombH.o- msemo.a Hoaoeaoamooaa emeba.o demos.o amoaa.o- absmo.o- waaao.o aeoeo.o samaa.o- camea.ou beemo.o- mambo.o- smamo.o- Hamma.o Hohoemaeoes oammm.m- ambmm.e damwe.av mammn.o- mesm~.o abebw.a emmaa.o- meme~.o- hemnn.a occab.o mooae.o- Hmmmm.a- Hoaoemessa amen mama onN 00mm ommw awa oNeN mafia omom anew comm comm “my ones mesons .. 13. ma so cassette sesam.o- omabm.o- wmamm.o- bemaa.o comba.o Nsmsm.o monas.o anaem.o 0e60m.o mamm~.o- amaoo.o smeea.o- Hoceeaoamo nommm.o cabba.o mmama.o mmaan.o- mmams.ou caeee.ov monm.ou mmaae.ou Hmmbb.o- owmmm.o- snoom.o mammm.o Hoeoeaoamooem beaeo.o easmm.o cambm.o msmmH.o- mammo.o- o~aao.o ammsm.o- memaa.o- oeaao.o- momma.o- msmao.o ewwoa.o Housemaeoea besae.m- memob.o- aceea.m emmme.o- cmemm.o- emwnm.fl mess~.o- flames.o commons mamae.o- neoeo.o Hecao.av Hoeoemassq 1|.Obmm swam chem onmm 66mm 66am Omen ombm oebm coca comm cams aav ease Nmmweé .. ends. we no esmfiseoeoq. modem.o- oemem.o- emoao.o- mmmmm.o seawm.o benea.o msmmm.o memom.o- Hoaoeaoamo bsqflm.o semmm.o msmsm.o monem.fln mmmea.o- anaem.au baomm.o- unmas.a Hocoeaoamooee HHaOb.o emnmo.o- 40:60.6- msbeo.o- bemam.o- eowmo.ou webma.o- Nemea.o Hoaoemaeoee momma.a bmmbo.m- mmamJ.N- ceoms.m Nbbbo.a- Nomem.s Hmmmm.o o-ma.~- Hoeoemassq comm omen 00mm ommm ooau ombu comm oomu peosoesoo is as a £35353 1 I 1.3..an 824ng 8,2 w. 963.22 N4. 33434. 83 8366 a law. my no 88538 8:39 @3136. 8696: 3806 b586 $086 $336 coming. 3806 6886 $686 0336.. 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Each of the matrices described above was applied to six synthetic mixtures j and the calculated compositions were compared with the known values for the composition. The application of the matrices _lg to spectral. data of the synthetic mixtures requires the value a: (of. Equations IV-l9 to IV-25); this is the value of the absorbancy of an ergosterol solution of concentration equivalent to the sum of the concentrations of the individual ccnponents of the given synthetic mixture. A value of A: was calculated from the sum of the concentrations of the given synthetic mixture and the fig” values for ergosterol that were furnished by Shaw gt _a_l_., cf. Table VIII. he results are summarized in Table I. It is to be noted that although all five components were not present in the synthetic mixtures, the matrix 3; was calculated from ultraviolet absorption data for the five components. Therefore, compositions for components at zero concentration also serve to establish the validity of the computational procedure. in “over all” standard deviation defined as 2:2 [( Calculated fraction of _ (known fraction of component 3 c i - component i in mixture) 1 in mixture) 1 i' 30 "where the index 1 refers to a summation over the five components, c refers to a summatim over the six mixtures and the value 30 is the total master of 'determinations'--was employed as a basis for selecting the best matrix 15. The values for the standard deviation are given in Table XI. .J...dds]..... na] sagas—.333. . . . l 85 TABLE.X CALCULATED COI-QI‘OS ITIONS 0F SYNTHETIC IkiIZ'I‘URES Matrix.fl Calculated Known Component Percent Composition of Synthetic Mixture Percent 70) (1) (21 (3) (1.) Composition Mixture l Lumisterol 80.5 79.3 83.h 80.0 81.3 77.3 Tachysterol -0.9 -0.h -0.2 -0.7 -0.8 0 Precalciferol -8.1 -5.7 -7.2 -7.8 -8.3 0 calciferol 26.7 25.7 25.7 26.2 26.h 22.7 Ergosterol 1.7 1.2 -1.7 2.3 1.h O ygxture 2 Lumisterol 61.0 56 h 57.h 60.1 50.9 53.1 Tachysterol 2 5 -2 1 2.0 -h.h -3.9 0 Precalciferol -7.1 -h 9 ~h.0 -l2.6 -7.7 0 Calciferol 50.0 h9 u h8.1 52.1 50.1 h6.9 Ergosterol -l 1 1.2 0.5 3.9 10.5 0 Mixture 3 Lumisterol h5.3 32.6 35.0 51.h 33.0 27.h Tachysterol -1.7 0.1 -0.8 -2.2 -1.5 0 Precalciferol -15.l -h.3 -8.7 -18.1 -10.h O Calciferol 80.2 76.5 77.0 81.3 78.2 72.6 Ergosterol -8.7 -5.0 -2.6 -12.h 0.7 0 Mixture g Lumisterol 73.9 78 8 82.5 8h.3 81.8 7h.3 Tachysterol -2.2 -l.0 -1.1 -1.1 -1.0 0 Precalciferol -8.2 -6.5 -8.2 -9.1 -8.0 0 Calciferol 3.0 2.1 2.2 2.6 2.2 O Ergosterol 33.5 26.5 ‘ 2h.6 23 2 25.0 25.7 Mixture 5 Lumisterol h2.2 53.8 50.2 h7.6 50.2 h9.l Tachysterol -O.7 -l.6 -O.8 -0.5 -0.6 0 Precalciferol 1.0 -h.5 -2.2 -0.h -l.5 0 Calciferol -O.5 2.1 ~O.5 -0.3 0.2 O Ergosterol 58.0 50.2 53.3 53.3 51.7 50.9 Mixture 6 Lumisterol 8 .3 31.6 31.1 21.6 31.2 2h.3 Tachysterol -1.7 -0.6 -0.7 ~O.1 -O.5 O Precalciferol -2.7 -9.1 -7.6 -h.9 -7.5 0 Calciferol 1.9 3.2 3.0 1.8 2.9 0 ErSosterol 9h-3 75 0 7h 2 78-7 73-9 75-7 86 TABLEIXI STANDARD DEVIATIONS OBTAINED FOR EACH fl MATRIX (Standard deviation in percent of Matrix 5 component in mixture) :wNHO H- p- tr The results demonstrate the effectiveness of employing a larger number of wavelengths, (i.e., utilizing more experimental data), since with the exception of the results obtained from matrix 3, the results obtained from the matrices based on twelve wavelengths were superior to those obtained from the eight wavelength matrix. Of the twelve wavelength matrices, matrix l--which was based on equally spaced wavelength inter- vals-~yielded the best results. It was originally believed that more significant information would be obtained by use of wavelengths at which the absorptivities of other components intersected that of ergosterol, since at these intersections the difference from the initial ergosterol absorption is attributable entirely to the non-intersecting components . However, matrices 3 and h, which were based on the intersection points (plus other wavelengths) yielded results inferior to those obtained from matrix 1 (equal wave- length intervals) and matrix 2 (based on the maxima and minima of cosmonauts). Apparently, any advantage gained by the elimination of a 8? given component at the point of intersection with the ergosterol curve was offset by the zero value introduced into the calculations. Matrix 1, vmich was based on equal intervals of wavelength in the significant region of the spectrum was selected as the matrix capable of yielding the best results on the basis of the above comparison. This matrix was applied to five more synthetic mixtures to further establish the validity of the procedure. Results obtained with matrix 0 are also included for comparison purposes and the results are presented in Table III. An "overall" standard deviation was calculated for matrices 0 and 1 utilizing the data for eleven mixtures or 55 determinations. The values for the standard deviation are: (Standard Deviation in Percent Matrix 1’! of Component in Mixture) (0) 7.6 (l) L..o These results are comparable to those obtained by the use of the values from only six mixtures. In addition, a standard deviation for individual components defined as 2 ,(Calculated fraction of component _ Known fraction of 2 c in mixture component in mixture) H- 1.1 «where the index c refers to a summation over the eleven mixtures for a given component--was calculated for matrices O and 1. The data are summarized in Table XIII. 88 TABLE XII CALGJLATED COMPOSITIONS OF SYNTHETIC MIXTURES 0°“? ”ant Calculated Percent Composition Matrix_M; Lumisterol Tachysterol. Precalciferol Calciferol .Ergosterol Mflxture 1 True Comp. 0 O O 22.1 77.9 (0) -8.9 » -0.6 1.7 22.3 85.6 (1) 8.2 -1.0 -5.7 25.1 73.h Mixture 8 True Comp. 0 O 0 h6.0 5h.0 (0) 1.8 -l.2 -h .8 h8.9 55.2 (1) 0.9 -0.5 ~3.2 h8.h 5h.5 Mixture 2 True Comp. 0 O O 71.9 28.1 (0) 1h.3 -2.h -13.0 79.1 22.1 (1) hol "los -601] 77 0].]. 2605 Mixture 10 True Comp. 3h.3 O O 30.2 35.5 (0 22 02 -3 .0 -6 09 3].} 03 53 oh (1 37-2 -1.8 -7~7 3h-3 37.9 gfliéure 11 3 w o 20 0° 0 0 ‘17}? 62 03 (0; 11803 -2 03 -602 19 CO 7502 (l 1506 -008 '3 01 17 06 7008 89 TABLE XIII STANDARD DEVIATION 0F INDIVIDUAL COMPWENTS Matrix _M Standard Deviation in Percent Component of Goa onent in Mixture (0) (1) Lumisterol i 10.3 i: 11.8 Tachysterol i: 1.9 i 1.2 Precalciferol i: 8.0 i' 5.8 Calciferol i h.0 i: 3.2 Ergosterol i' 10.1 i 3.14 The data presented in Table XIII demonstrate mrther the improvement affected by the utilization of data from a large mnber of wavelengths. As one would expect, higher deviations were obtained for lumisterol, precalciferol, and ergosterol than for tachysterol and calciferoleince tine absorption curves of the former are quite similar. It would not be reasonable to attribute the low deviation obtained for tachysterol to the absence of tachysterol in the synthetic mixtures, since precalciferol was also absent and it shows a high deviation which may more reasonably be attributed to similarity in spectra. Matrix l--the twelve wavelength matrix which was based on equally 8piilced wavelength intervals--was employed in the kinetic studies. TABLE OF CONTENTS Page V. MMION WLTSOOOOOOD0.0000000000000000000000.000000000000000 9o 1. Application of the Matrix Method to Sharpe's Data........ 90 Be Irradiation R68u1t8--Kinetic Studyooooo.eoloooeoooeeooooeoeo 113 90 V. IRRADIATION RESULTS A. Application of the Matrix Method to Sharpe's Data Neglect of precalciferol as a component of the irradiation mixture in the original treatment of Sharpe' 8 data invalidated the results of his calculations. The matrix method, employing matrix (0), was applied to Sharpe's data to obtain further verification for the computational analytical procedure on actual irradiation mixtures and to re-evaluate the irradiation data. Matrix (0) is based on absorbancy data at the same wavelengths employed by Sharpe in his curve fitting treatment. Several calculations were also made from the utilization of matrix (1), but the results were inferior to those obtained with matrix (0) since it was necessary to use interpolated values of the absorbancy data. Sharpe had not reported absorbancy data at wavelengths which coincided with the wavelengths employed by matrix (1). Compositions were calculated as functions of time of irradiation from Sharpe' a data for irradiated solutions at five wavelengths of irradiation-42537, 26514, 2801., 2967, and 3132 i°--and employing four solvents--n-hexane, cyclohexane, diethyl ether, and 95‘ ethanol. The source and monochromator employed by Sharpe were identical to the com- ponents employed in this investigation; a slit width of 2.50 mm. was used for all his irradiation runs. The thickness of the irradiation cell was 0.57 mm. and the initial concentrations of ergosterol were approximately equal in the various solvents (about 0.02 gnu/100 ml. , film-.3341“... a 91 so that the absorbancy was roughly 0.3 at 2710 A0). The results are reported as weight percentages and are summarized in Tables IIVa-XIVe. Plots of concentration vs. time were made for the recalculated compo- sitions, cf. Figures 13a-1 to l3e-h. m evaluation of the recalculated results was necessarily limited to qualitative interpretation because of the absence of sufficient actinometric data and the high standard deviation of the results obtained with matrix (0). The application of the matrix method to Sharpe's data demonstrated that the computational procedure could be applied to actual irradiation mixtures as well as synthetic mixtures. Reasonable values were obtained for the decay of ergosterol and build-up of irradiation products. he compositions obtained by the matrix method are in general accord with other analyses of irradiation mixtures as will be discussed below. Negative values which consistently became more negative with increas- ing irradiation time were obtained for the concentration of calciferol]. However, the differences between the negative concentrations of calciferol and a value of taro were generally less than the value of the standard deviation for calciferol, except for irradiation mixtures for which the percent conversion of ergosterol was quite high. The consistent growth of negative values might be attributed to the formation of a spectro- scopically active substance which was neglected in the matrix formulation. It is evident from the results that under Sharpe's experimental conditions, ergosterol was converted at a rapid rate and over-irradiation products may have beal formed; his use of very thin unstirred cells would tend to a {41413143 u TABLE XIVa* consortium or IRRADIATION MlITURES--2537 A0 92 Time, Calculated Coupes ition, Percent Min. E I. T P D Ethyl Ether-Rm Code 21.1 S 76 05 501‘ 208 1502 -100 10 60.6 [[09 80].]. 2601 '3 05 20 38 .0 1].; .h 19 oh 311 .7 -6.h 30 23 09 11301 27 07 M01 -9 08 95} Ethanol--fh1n Code 221 5 81.8 -3 .6 13.1 19 .3 -1.7 10 61.5 3.6 12 .1 25 .5 -2 .7 20 115 .3 0.8 27 .3 31.2 44.6 30 29 02 608 39 07 29 03 ‘5 01 1.5 15 .h 7 .8 52 .6 32 .h -8 .2 60 7 07 10 05 58 06 33 00 -9 08 90 609 3 02 63 00 13002 -13 03 n-Hexane--Rnn Code 231 5 7h.8 5.9 3.8 18 .1. -3.0 10 58 01 606 1.1 .0 27 08 -3 0h 20 32 05 10 0].} 23 08 3909 -606 30 23 .3 1.6 30 .1 58 .6 -1.3 .5 Elohexaneufinn Code 33*; 5 79.9 5.1. 1.1. 111.2 -o.§ 10 66 0].] 608 7 0].} 20 09 -101; 20 SO 07 2 03 18 09 32 07 -1]. 06 30 3609 “003 27 01‘ 16308 -8 01 *Glossary of Symbols in Table: 8 - Ergosterol; L - Lumisterol; T - Tachysterol; P - Precalciferol; D - Calciferol (Vitamin D2). 93‘ TABLE mm COMPOSITION OF IRRADIATION MIXTURES-46511 1° J fl Time, Calculated 001993 ition. Per cent Min . E L T P 1 D Ethzl Ether-Run Code 211 5 7108 1‘05 305 22 09 ‘2 07 1° 51‘01 5 05 1105 3102 ‘2 03 20 29 .3 17 .6 19 .2 39 .8 -5.9 30 17 07 1.108 3800 38 01 -5 05 60 5.8 29.0 23.8 110.1 1.1.; 251 Ethanol-diam Code 32; 73 00 205 £600 2108 -1018 10 5h .1 5 .5 11 .5 31 .2 -.2 .3 30 17 07 11.8 38 00 3801 .505 n-Hexane-—Rnn Code 331 S 68 07 605 1‘03 22 03 '108 1.0 1605 11401 1108 3102 -206 20 20.1; 18 .7 211.9 130.7 '44.? 3o 15 .5 2 .1 30.8 63 .9 ~12 .3 gzglohexaneumn Code 291 S 7605 006 301‘ 2102 “108 10 S9 08 2 08 9 07 29 09 -2 02 20 39 .5 0 .8 22 .9 341.11 44.6 30 3008 ‘1002 32 02 5609 -9 07 TABLE XIV c 8081906111011 OF mmmxon MIXTURES-4801. 1° 9h Time, Calculated Congo; ition1 regent _ Kin. E L T P D Ethll Ether-mu Code 1111 5 83 .1 -0.3 1.0 15 .5 0.8 10 79 .8 -3 .8 -3 .h 28 .1 -0.7 20 5002 “006 9 05 ’43 02 -2 02 30 3302 300 1508 5008 -208 w 1209 -109 280,4 '6? 00 -601], 252 Ethanolumm Code 1421 5 8a.). -O.2 0.9 16.6 -o.8 10 7002 100' 301 2608 -101 20 I42 .3 13 .3 8.6 37 .3 -1.6 t 30 36.9 5.6 13 .6 146.6 -2 .7 60 16 03 9 09 25 05 51 .9 -3 06 9o 9 .3 14.0 38.8 57 .5 -5.6 120 601‘ 000 11.002 won -7 .0 n-HexanenRun’ Code 311 5 81.8 1.9 0.6 16.2 -o.5 10 63 .5 6.9 3.1 27 .2 -0.7 20 I40 09 ll 03 9 01 39 06 '1 .0 30 26 0h 11 07 1507 148 03 ’2 01 60 11 .0 “'1 .0 27 06 69 03 “'5 09 wlohm-Rnn Code My]: 5 82 00 602 001 1009 008 10 68.1 8.2 2.0 21.3 0.1; 20 1180).} 807 703 3606 -101 30 33 .0 10.6 13 .1 1411.7 -1.h 60 1602 108 25 07 $09 “’40 95 TABLE IIVd COMPOSITION OF IRRADIATION MIXTURES--2967 1° Time , Calculated 00111903 it ion, Percent Min . E L T P ‘ D Ethxl Ether-Run Code 511 5 811.1; 2 .6 0.5 13.11 --0 .9 10 80.7 —l6.9 11.1 37 .5 -5.11 20 55.2 8.1 11.5 33 .8 -1.7 30 143 .3 8.2 7 .7 1414-7 44.0 115 31.9 6.8 10 .9 511.0 -3 .6 60 16.6 13 .2 13.9 60.8 -11.5 75 15 .1 6.9 15.6 68 .3 -5.9 90 9 .6 -1J,.S 19 .11 86 .5 ~11.1 95} Ethanol--Run Code 521 s 88.0 -h.9 1.1 17.8 -1.9 10 77 .11 ~11.0 2 .0 26 .11 -1.8 20 59 05 ‘3 05 6 00 1.1101 ‘3 00 30 38 .7 11.7 10 .11 50 .1 ~3 .9 115 29 .7 -2 .1 15 .3 62 .5 -5.11 60 18 .9 2.2 18 .3 66.9 -6.3 90 10.1 -1.0 22 .0 77 .11 -8 .6 n-Hexane--Run Code 531 S 78 .5 10.7 0.6 10 .5 -0.2 10 611.8 11.11 2 .l 22 .5 -O.9 20 113 .1 19 .6 11 .9 32 .3 0.1 30 29 .9 2O .0 8 .6 112 .1 -O .6 as 17.2 18.0 13.1 53.8 -2.1 60 7 .11 111.7 16.7 65.2 -11.1 75 h.h 8.6 18.6 78.0 -5.6 90 3 .8 0.5 19 .7 83 .5 -7 .11 cyclohexaneuRun Code 517,1 5 85.9 0.1 0.5 111.2 -0.8 10 71.3 3 .8 2.0 211.0 -1.0 20 57 .3 1.3 11.8 37 .6 -1.0 30 39 01 5 07 9 0’4 118 0h '2 06 115 22.0 7 .7 111.6 59 .2 3.6 60 16.5 11.6 17 .6 65.7 -h.h 75 10.2 h 3 19.8 70.8 -s.1 90 9 .5 -1.9 21.2 78.1 -6.9 TABLE XIVe COMPOSITION OF IRRADIATION MIXTURES--3132 A9 Time, Calculated CompositionL_Percent Min. E L T P D Ethyl Ether-~Run Code 611 10 90.1 0.2 0.0 2.6 -l.0 30 96.h -3.1 0.2 9.3 -2.8 60 85.3 h.l O.h 18.0 -h.2 120 73.3 9.3 -0.h 25.0 —7.5 95% Ethanol--Run Code 621 5 101.6 -h.5 0.1 3.8 -O.8 20 9605 -008 001.1 1.107 -007 60 86.5 -3.2 6.8 11.0 -l.5 90 88.h -3.5 1.5 15.0 -l.7 120 83.9 -2.7 2.1 18.7 -2.1 180 78.8 -2.5 2.6 23.9 -2.7 200 72.0 -1.3 3.5 29.5 -3.7 300 67.2 1.8 3.2 31.1 -3.3 360 6h.1 -1.2 h.l 38.1 -5.2 1180 S9 .9 -3 .5 11.5 116 .1 -7 .0 nrHexane--Run Code 631 15 93.5 3.8 0.3 3.0 -o.6 30 9h.8 -0.6 0.3 7.0 ~1.5 60 86.0 2.1 0.7 13.8 -3.0 90 81.7 1.8 0.9 20.0 -h.5 120 77.1 1.5 1.2 26.2 -6.0 180 65.3 3.7 2.1 38.6 -9.8 Cyclohexane--Run Code 681 5 98.8 0.5 -0.1 1.3 -0.h 10 97.3 1.8 -0.h 1.2 0.0 20 95.1 1.0 0.0 11.8 -0.9 30 9502 003 -0 03 505 .006 16 92 07 "O 0]. .0 01 8 09 -1014 60 89.5 -O.2 0.7 13.7 -2.6 90 80.2 3.5 1.0 19.0 -3.7 120 79 06 .008 103 21406 ’1407 150 70.7 3.0 1.9 30.9 -6.6 180 68 014 002 2 06 3607 -7 09 2h0 57.6 2.7 3.2 h7.7 -11.2 Di-ethyl Etheg 211 2537 A l I I 97 80 .... 2... Figures 130~1 and 13a-2 . Composition of Irradiation fixtures-- 6O _- . __ Sharpe'e Data E 3110 ‘ 8 . *5 r A . 3 . 'r , g 20 .. . __ %® 7 r- , F? . I n I 10 2O 30 110 Time, Min. 1 0-2 I I I {g} T I I I I 95% Ethanol o 221 2537 A O +3 8 ""0 " g I . '3 D I o h how-— A —‘ . P o .1 0 n 20 —- .0 o n 0 n .1 0. I A I I I _ I __ 1.- I I I 10 20 30 140 50 7O 80 90 Time, Min. Percent Comonent P ercent Comp oncnt n--Hex an \ 231 2-37 A U1 10 20 30 110 Time , Min . Figures 130-3 and 13a-11 Composition of Irradiation Mixtures-- Sharpe's Data 1383-17 .._...1.__.-’. --.-. 1 ‘ 1‘ [ Cyclohcxane 211 2537 1° 80... .1 ../." (”LU I M1- . 1--...- .. a) 10 2O 30 1; Time , I'inn . 98 1311-1 ‘7 I " I I i I Di-ethyl Etheg 311 265k A 80 *5 60... a) 0 £3 0 g- E o P o no— 1 -—---------1 +3 5 T O . ’3 $4 _- g / :1: 20— . , .. . ® 0 I I I I I I 10 20 30 no 50 60 Figures 13b-1 and 13b-2 Time, Min. Composition of Irradiation Mixtures-~Sharpe's Data Percent Conponent 100 I 13b-fi 95% Ethanol o 321 26511 A 80 ‘1 O E q 99 Percent Component Figures 13b-3 and 130-8 Composition of Irradiation Mixtures--Sharpe's Data Percent Component 13b'3 3‘11‘3256 1'10 \ 331 2651 1° I 100 80 00 20 Time, Min. l3b-h ‘ I I I Cyclohexane o 301 26Sh A O -—- E ___ P . __ T ‘III 10 20 30 Time, mun. 100 (I‘llahnv.nl=.u~ In .AA....s\..N lanai-.11». .Ous..L......um . . Mn , . 1. . U n. .u P ercent Comment 100 20 101 130-1 100 1 I 1 I | | Ethyl Ether o 011 2800 A 80 _.. 6) _— E .p 60 —— P -—e c (D c O I g. 0 <3 00 __ _fi +3 .5 o o A 1'4 (1) a. 20-—- - T 0‘ 1 I J I l J 10 .20 30 00 . 50 6O ' Time, Min. Figures l3c-l and 130-2 Composition of Irradiation Mixtures--Sharpe's Data l3c-2 - I I I I I I I 1 I I I 95% Ethanol o . 021 2800 A CD I“ P O A It T . III ‘5 an —— -I \ A 0 \©\ Wm H I fifl 10 20 3O 00 50 60 70 80 90 100 110 120 _ m2 100 -. 1. 13°‘3 1 -1 l 1 I I n-Hedcane ' 031 2800 1° Percent Couponentx 8 .. I to '0 I . T 20 - . -- O L . o ' I I I I " 10 20 3O 00.. 50 60 Time, ML. Figures 130-3 and 130-0 . Cmoaitim of Irrfldhtion Mixturee--8harp0'a Data 130-1: 7 I l I 1 I Cyclohonno I 001 2800 1° 100 .p 8 g A .p 8 o 0.0—- M Q) ‘14 —-I 1o 20 30 00 so 60 Time, Min. fi.§afilflfi§~!fifl . J 103 13d-1 100 I I I I I I I I I Ethyl Ether o 511 2967 A - 80— <9 — E P A .p g 60— A ‘— 5 o A A g o 4: I40 —— —-j 8 A O 4. 8 in (D 20 —— n --I 2 o c. a T 9 o I L J I I .I l, . 10 20 30 no so 60 7o 80 90 Time, Min. Figures 13d-1 and 13d—2 . Composition of Irradiation Mixtures--Sharpe's Data 13d-2 W A I I I I 7 . 95% Ethanol o 521 2967 A 80 __. .— no... Percent Component 20-—-. 100 E? 8; Percent Component t’ O 13d-3 10h I I II I I I n~ Hexane 531 2967 A0 U TUE,Mhh Figures 13d-3 and 13d-h Composition of Irradiation fixtures-~5harpe's Data .100 le-h I I I I I I I I I Cyclohexane 5&1 2967 11" 80 ‘ _. P '4» 1% E A 5 6° '1 8‘ . 8 .p § 1;: . ._ tn :2. 20 __ o 1 I -I I, I I I .| 10 20 30 no I so 60 7o 80 90 Time, Min. 105 100 in.-- I. I .. 138‘1 I‘m-XL ‘ O I I I I I ’ -~- «1&3 Ethyl Ether O "‘“rQ. 611 3132 A 80 _~— .p 60 -1. c C) c O E“ O *c’: d) O I ”If": Ii) Ms" " o I», I - I I m. 20 M) 60 80 100 120 Time, Kin. Figures 139-1 and 13e~2 Composition of Irradiation Mixtures-~Sharpe's Data 10° I I I3 I I I " 95% Ethanol o 621 3132 A 80«q-- ___l. m 60“.".u 8 EL 0 :3 +3 0:; I40 _-' /—- 94 /A P I /6"/6 . T ‘ ;/) . L1 EU'—_——iP-__—_i3—_ “13 50 100 150 200 250 300 350 hOO hSO SOO . 106 100 13""3 I I I I J I :I I I n-Hexane * o 8 631 3132 A o... 1'": -I (D 5 SI 8 60.... _I I I; . " ho .._— .— P. 20— d .r T . A 0 V M I ' I” I '20 140 «50 «no "100120 114 160 150 200 rm, tun. Figaro: 139-3 and 1361-1; Composition of Irradiation murmur-Sharpe's Data Jae-II f I I-II. II ”I I II Cyclohexane o 6&1 3132 A q—d .- ants-u- , I '1' I I I W 4'1 I ' ' l J I 20 no _ 80 100 1201:. no 160 180 200 220 2ho Time, Min. 107 maximize over-irradiation effects. However, regardless of the cause of the build up of apparent negative concentrations, the occurrence of such values does not detract from the validity of the results, since the negative values were generally less than the value of the standard deviation except for very high percentages of conversion of ergosterol. Small negative values were also Obtained for tachysterol in a few in- stances. In all such cases the concentration of the component was considered to be zero. A remarkable result indicated by the calculations is that calciferol is not formed in appreciable quantities during the irradiation, although precalciferol is always the predominant product, except in some instances of high percentage conversion of ergosterol. The other products of the irradiation mixture, tachysterol and lumisterol, are formed in minor amounts and their relative abundancies are dependent on the conditions of irradiation. It would appear that nature has designed a reaction, which is remarkably free of major side reactions, to produce the desired physio- logically active material, calciferol. The absence of calciferol in irradiation mixtures which have been formed at room temperature may be attributed to the slowness of’the thermal conversion of precalciferol to calciferol at room temperature. This observation with respect to calciferol formation substantiates the hypothe- sis that calciferol is not a.primary photochemical product of the irradi- ation of ergosterol. Further substantiation of this hypothesis is afforded by evidence reported by Havinga and co-workers (h7); they have observed that calciferol was not formed during irradiation of ergosterol at ~180° C. 108 At this low temperature, the thermal reaction undoubtedly would have been suppressed. The recalculated Sharpe data are also in accord with compositions of irradiation mixtures which have been reported by Havinga's group (33,3h). In more limited kinetic studies, they have irradiated ergosterol in ethanol at 2537 A0. The concentrations of ergosterol, tachysterol, and precalciferol were obtained as functions of time of irradiation. Ergosterol was determined by digitonin precipitation; tachysterol and precalciferol were determined by the antimony trichloride colorimetric procedure (29). They have reported that ergosterol is converted to precalci- ferol in a yield of 85% and the remainder of the conversion product consists of tachysterOl. In addition they report that irradiation of precalciferol results in the formation of tachysterol in almost quantitative yield. The latter Observation is in accord with Sharpe's data Obtained at low irradiating wavelength, i.e., 2537 and 26514 A°,°in which tachysterol was Obtained in relatively high abundance during the latter stages of the irradiation, after a build up of precalciferol had occurred. The compositions of the irradiation mixtures Obtained by the applica- tion of the matrix method of Spectral data are also in general accord with data reported by Shaw and co-workers (39),which were Obtained by application of the antimony trichloride colorimetric procedure and a direct spectro- photometric technique to the chromatographic fractions of irradiation mix- tures. They chromatographed the irradiated mixture on alumina employing the procedure described in the experimental section. 109 Qialitative conclusions have been drawn with respect to the effect of wavelength of irradiation and solvent on the relative abundances of the products of the reaction and the rate of disappearance of starting material. Since lumisterol was formed only in minor amounts and the standard deviation for lumisterol was i 10.3%, it was not possible to determine the effect of solvent and wavelength on lumisterol formation with any degree of certainty, except in the case of long wavelength irradiation-- i.e., 2967 A0" when appreciable amounts of the compound were formed. Because of the above consideration and the scatter of the calculated lumisterol concentration, plots of concentration vs. time were only drawn for lumisterol when appreciable amounts of the compound were found or when the scatter was not present. In order to facilitate the deduction of solvent and wavelength effect, comparison of the compositions of the irradiated solutions were made at 50% conversion of ergosterol. The results are summarized in Tables IV and XVI. In general, for a given wavelength of irradiation (with the exception of the very longest wavelength of 3132 11°) the reaction proceeds most rapidly in n-hexane. It is not possible to draw further conclusions; from the data of Table IV, since the time for 50% conversion does not vary sig- nificantly for the other solvents. Precalciferol abundance was relatively independent of solvent at a given wavelength of irradiation, with the exception of irradiation at 2967 A0; there is a particularly large difference between theamounts of precalciferol in 955 ethanol 047.5%) and in n-hexane 110 TABLE IV SOLVENT EFFECT ON RATE OF DISAPPEARANCE 0F ERGOSTEROL Wavelength Relative Time for 50}? Convegsion'x' Solvent 2537 A0 zésh A0 280h A0 2967 A0 3132 A°** Diethyl Ether 1.00 1.00 1.00 1.00 1.00 95% Ethanol 1.25 1.0IJ, 0.87 1.06 2.51; n-Hexane 0.89 0.76 0.71; 0.63 1.10 Cyclohexane 1.36 1.21 0.87 0.91 1.23 *Based on avalue of 1.00 for the 50% conversion of ergosterol in diethyl ether at the given wavelength. fiTime for to; conversion; extrapolated in some cases. (28.23). At the shorter wavelengths of irradiation, 2537 and zest 1°, the formation of tachysterol is clearly greater in 95% ethanol and cycle- hemane than in diethyl ether or n-hexane. The latter distinction is not as discernible at the longer wavelengths. Because of the limitations of the analytical data with respect to the concentration of lumisterol,/the effect of solvent on the abundance of this component cannot be deduced with a reasonable degree of certainty. However it should be noted that lumisterol was formed in significant amounts only in n-hexane and diethyl ether. The detailed interpretation of these results will be presented in a later section. Batever, it should be pointed out that, as reported by Sharpe (37), the solvent effect appears to correlate with solvent viscosity. The viscosities of the solvents employed in Sharpe's work are listed on p.132 (53): 111 TABLE XVI SOLVENT AND WAVEENGTH EFFECT ON PmDU CT (IJMPOSITION ‘Havelength Composition,Percent* Product 2537 11° 2651; 11° 2801; A0 2967 11° 3132 A° Diethyl Ether L 9 OS 7 0.0 "" -- -- T 11 .9 11.3 10 .5 6 .0 -- 95% Ethanol L -- 5.2 -- -- -- T 22.2 13.1 7.2 8.6 5.9 P 30.5 32.0 36.2 h7.5 h3.7 n-Hexane L -"’ 12 00 9 .8 l7 .2 -- T 13.7 10.7 7.8 h.0 2.2 P 31.1 29.5 3h.5 28.2 h3.0 chlohexane L .. .. .. .. _- T 17 .0 15.6 6.9 6.0 3.0 P 31 .7 35 .9 33 .9 II0 .5 IIS -0 “Composition at 50% conversion of ergosterol except for irradiations at 3132 A in which case the compositions are given for to; conversion of ergosterol. Temp grature , Vis cos ity, Solvent 0. Centipoise Diethyl ether 25 0.222 n-Hexane 25 0.291;, Cyclohexane 17 l .02 95% Ethanol 25 2.35 The rate of disappearance of ergosterol was generally most rapid in n-hexane and in diethyl ether, solvents of low viscosity; however, the data are not consistent for diethyl ether, showing good agreement at 2537,2691, and 3132 A°., but slower disappearance of ergosterol than in higher viscosity solvents at 280).; and 2967 A0. Lumisterol was formed in significant quantities only in the solvents of low viscosity, n—hexane and diethyl ether, while tachysterol abundance was greatest in solvents of high viscosity, cyclohexane and 95% ethanol. Attributing the solvent effect in Sharpe's results exclusively to viscosity is open to criticism, however, since the solvents used also differed structurally. Functional groups such as the hydroxyl group of ethanol may have caused certain specific effects by interaction with the components of the irradiation mixture. The observed wavelength effect can be attributed largely to the relative wavelength variations of the absorption spectra of the components, leading to operation of the "inner-filter effect." This effect can be evaluated and the results compared independently of it by means of quantum yield calculations based on a kinetic study, as reported in a later section of the present work. 113 B. Irradiation Results--Kinetic Study The present investigation of the photochemical isomerization of ergosterol was undertaken to obtain data from which a quantitative kinetic analysis could be made. Sharpe's recalculated results were utilized in the planning of this experimental work. Before presentation of the quantitative treatment, the results of this investigation will be dis- cussed in a qualitative manner. Sharpe's results indicated the occurrence of a solvent effect which might be attributed to the viscosity of the solvents, but the observed effect could also be attributed to a specific polar interaction, since the solvent of highest viscosity, 95$ ethanol, was also a polar solvent. Still another possible explanation of the solvent effect in Sharpe's results is that the use of thin, unstirred cells may have led to aIdiffusion controlled process, in which the same molecules tended to remain in the more intense portion of the beam to umiergo successive radiational changes. This would lead to greater tachysterol build-up in more viscous solvents, where the initially formed precalciferol would absorb another quantum of light to undergo the next step without diffusing out of the most, intense portion of the beam. It was noted by Sharpe, however, that the solvent effect can not be attributed solely to such factors, since it has been observed by other investigators irradiating refluxing solutions . The uncertainty of interpretation of the solvent effect was resolved in this study by enploying structurally similar solvents to obtain a variation of viscosity, and by carrying out the kinetic studies in stirred cells of 1.0 cm. thickness. Under Sharpe's conditions of irradiation, the reaction proceeded rapidly and the probability of occurrence of over- iJrradiation products was increased. The rate of the reaction was decreased in this study by employing narrower slit widths and a larger volume of solution in the cell. The use of narrow slit widths also increased the degree of monochromaticity of the radiation, which yielded more definitive results on the effect of wavelength. Concentrations of the irradiation mixtures of the current study were calculated by application of matrix (1) to the ultraviolet absorption spectra of the irradiated mixtures.* The data are presented in Tables IVIIa:IVIIc, and in Figures lha-l to lhc-S. The results are expressed as weight percentages; although results are presented to the third decimal place, the figures do not possess this significance. It was convenient in.the computational work to carry out the calculations as presented in the tables; the values employed in the kinetic calculations are those tabulated. Results were appropriately rounded off.at later stages of the calculations. The application of matrix (1) to the data of this investigation yielded results quite similar to those Obtained by application of matrix (0) to Sharpe's data. However, in the calculations based on the present study, the consistent growth of negative values for calciferol was not Observed. The negative values that were obtained were generally of smaller magnitude, and the values were more uniformly scattered about the zero concentration level. it . . I. The absorbanc1es of the irradiated solutions are tabulated in.Appendix II. TABLE XVIIa COMPOSITION OF IRRADIATION MIXTURES-~KINETIC STUDY-~2537 A° (Slit Width 1.50 mm.) 115 fl Time, Calculated Coup os itionLP ercent Min. E L T P D IsoprOpyl alcohol--Run No. III-10 Initial Cone. of_§rgcsterol 0.002g2_gms5/100 ml. 20 92 .518 2 .555 0 .710 5 .310 -1 .093 he 89.887 1.7h8 1.082 8.6h7 -l.36h 90 80-830 ho6h5 2-h99 lh.917 '2oh91 120 76.655 b.922 2.983 16.578 -1.138 185 7h.233 1.012 5.h87 20.797 -1.529 2h5 62.61h h.7h9 9.0h2 26.158 -2.563 305 58.802 5.h13 11.356 25.8h5 -l.hl6 365 55.186 3.072 lh.752 29.136 -2.1h6 th h8.88h 5.585 17.386 30.789 -2.6hh 20$ Glycer01--Run No. III-1h Initial Conc. of Ergpsterol 0.002h2_gms./100 ml. 20 92.908 1.9h8 0.5h9 5.975 -1.380 1.0 90 .805 1.559 1 .071 7 .h13 -0.8h8 6o 89 .810 -2 mt 1 .876 12 .h76 -1 .h21 90 85.700 -1.166 2.356 13.819 -0.709 120 81.557 -0 .266 3 cm; 16 .968 -1.353 180 76 0395 -0 0550 S ems 20 .269 -1 e209 2h0 6h.0h8 1.608 9.712 28.539 -3.907 330 59.865 1.h21 12.8h9 29.066 -3.201 h20 57.h65 -3.703 16.890 31.370 -2.022 n-Hexane--Run III-22 Initial Conc. of Ergosterol 0.002l6ggmgg/100 ml. 20 92.h76 5.222 -0.372 2.730 -0.056 to 90.116 3.698 -0.309 7 .587 -1.h18 60 88.165 2.891 0.276 10.621 -l.953 90 8h.206 2.250 1.038 15.087 -2.581 120 81.90h 1.932 l.h79 17.369 -2.68h 185 7h.562 1.782 3.702 23.528 -3.57h 2h0 67.128 2.262 6.797 28.539 -h.726 330 57 .782 b.101 10.16LI 33 .520 -5 .527 h20 1,7 .752 5.205 15.261 38.395 -6.613 ¥ Continued TABLE IVIIa ." Contimed 116 Tine, eases. —; I 201 Mineral Oil-Run III-18 Initi‘l Gone. 0! lrxoater01.0900216 52201100 ml. 20 he so 90 120 185 2nd 330 hot 95-71h 93-773 88.661 85-753 800078 75-397 67.822 60.2h7 51.300 0.6h6 ‘10388 O .707 '0-977 2.106 'ho9h8 '3o7h1 ”hoh26 “0072u -o.313 0.535 0.832 1.716 2.315 5.5h0 8.209 12.623 15.911 Calculated Cogposition, Percent L T a! T 5.616 9.007 12.188 15.683 l7.h72 27.19h 32.255 38.753 h0.7h2 ”10663 -1-927 -20388 “20125 '10971 -30183 “I4 05115 -7.197 “70229 TABLE XVII‘b COMPOSITION OF IRRADIATION MEITURESwKINETIC STUDY-~2801; 1° (Slit Width 2.00 mm.) 117 Time, Calculated ConpositionLPercent Min. E L T P D IsoprOpyl alcohol-dim No. II-ll; lpitial Conc. of Ergosterol 0.002h2_gms,/100 ml. 11; 93 .156 0 .819 0 .558 7 .650 -2 .183 29 91 .051 -l .1402 0 .519 ll .1;31 -1 .1;99 19 81; .698 o .330 0 .016 15 .733 -c.777 58 78 .528 0.510 1.580 21.11;3 -1.791 88 71 .398 -2 .315 3 .1170 30 .1;22 -2 .975 118 67 .989 - 5 .637 5 .155 31; .206 -2 .013 213 51 .396 -7 .070 10 .1;88 1;? .010 -l.821; 273 39 5732 -3 JM 111 .9146 50 507 '1-961 318 35.789 -l.816 16.993 51.190 -2.116 20% Glycerol--Run No. II-9 Initial Cone. of Ergosterol 0.002172 flan/100 ml. 15 92 .806 -0 .852 1 .231; 9 .81;8 -3 .036 30 81; .627 2 .61;6 0 .763 13 .389 -1 .1425 15 83.653 -1.521; 1.177 18.370 -1.676 60 72 .629 3 .918 2 .523 23 .1702 -2 .1;72 90 73 .372 -3 .753 3 .082 28 .791; -1 MS 120 65 .81;3 -2 .1;71; 3 .702 33 .350 -0 .1;21 150 58 .1;32 -1; .218 6 .550 I40 .633 -1 .397 210 16 1:90 -6 .II68 12 .910 50 392 -2 .557 305 38 .730 -9 .038 16 .038 53 .372 0 .898 365 38 .157 -10 .959 16 .381; 58 .533 -2 .115 n-HeccaneuRnn No. II-18 Initial Cone. of Ergosterol 0.00216 gms./100 ml. 15 97 .185 -2 .031; -0 .611; 5 .31;6 O .117 30 88 .917 l .5111; -0 .51;5 0 .930 9 .151; IIS 714.761; 9.511; 0.188 9.011 6.1163 60 77 .792 1; .196 -0 .121; ll .1;31; 6 .702 90 62 .559 7 .958 -0.863 23 .678 6.668 150 55 .01;2 -3 .733 6 .082 37 .508 5 .101 230 38 .21;0 -1 .817 11 .101 1;3 .566 8 .910 290 25 .970 2 .070 16 .062 1.;8 .776 7 .122 350 19 .289 1.310. 19 .861; Sh .257 5 .6II9 #1.: Continued TIBLE.IVIIb - Continued 118 Time, Calculated Composition, Percent Min. E L T P D 20% Mineral 0il--Run No. II-2h Initial Cone. of Ergosterol 0.00216ggmsg/100 ml. 15 89.968 2.373 1.1h6 7.983 -1.h70 30 86 .051; 1.116 1 .091 12 .863 -l .15I; 11; 81.969 1 .9I;1 l .897 21 .271 -3 .196 59 77 .892 -I; .912 2 .952 26 .5118 -2 .I;80 89 61.939 1.697 3.910 31.883 -2.h§9 119 60 .600 -2 .315 S .382 39 .6II7 -3 .311; 189 h8.133 -3.337 9.552 18.178 -2.522 29 In .921; -7 .962 13 .781 56.338 -5.081 32h 26.2h9 1.237 17.833 56.hh7 ~h.766 TABLE XVIIC 119 COMPOSITION OF IRRADIATION MIXTURES--KINETIC STUDY--2967 1° (Slit Width 1.50 mm.) Time, Calculated CompositionLPercent __ Min. E p: T P n ISOpropyl Alcohol-Jinn No. II-6l .Initial Cone. of Ergosterol.0.002h2flgms,/100 ml. 30 92.185 -0.650 0.975 9.628 -2.h38 60 89.6h0 2.887 0.705 1h.h87 -1.915 90 79.750 3.513 0.271 16.6h1 -0.178 120 75.518 1.523 1.119 23.60h -2.06h 195 62.853 2.081 3.129 33.318 -1.68h 285 5h.086 -1.956 6.27h h3.817 -2.221 375 81.699 2.297 8.760 h8.9l6 -1.672 20$ Glycerol--Rim No. III-61; _I_nitial Conc. of Ergosterol 0.002172 ins ./100 ml. 30 89.691 0.768 1.217 10.16h -1.870 60 86.890 -2.7h9 2.073 16.771 -2.985 90 82.933 -h.071 2.115 22.010 -2.987 120 72.932 0.797 3.005 25.281 -2.015 290 53.780 -2.720 7.397 h3.926 -2.383 380 uh.807 -h.2hl 10.h88 51.857 -2.911 n-HemaneuRun No . III-53 ‘Initial Cone. of Erggsterol 0.00216 5E84/100 ml. 30 92.776 1.298 0.233 8.657 -2.97h 60 85.702 1.680 0.886 15.389 -3.657 90 76.85u 6.030 1.169 19.510 ~3.593 120 73 .855 IIJIIO 1.500 21;.I411I 44.109 180 62 .81;o 8 .127 2 .1;69 29 .151 -2 .587 270 50 .031; 10 .1;50 I; .81;7 36.812 -2 .11;3 330 h0.798 1h.638 6.58h h0.258 -2.278 375 39.796 9-8hh 7.980 ht~781 -2.h01 n-Hexane--Rnn No. II-67 gpltial Conc. of arggsterol,0.00216_gns,/100 m1. 330* h3-939 10.385 6.290 38.071 1.355 330 h2.368 12.192 6.837 39.16h ~- 375*7 10.993 6.132 7.881 hh.270 0.721 375 10.391 7.988 7.932 ht.526 -- 135 33.783 9.886 8.985 b5.822 1.52h 195 25.u32 1h.613 10.558 17.177 2.220 560 22.626 11.u69 11.863 52.hhh 1.598 *Average compositions, Ill-53, II-67. TABLE IVIIc - Continued 120 Time, Calculated CompositionL¥Percent Min. E L T P’ D 20% Mineral 011--Run II-57 Initial Cone. of Ergosterol 0.00216 gm54/100 ml. 30 91.111 3.175 -0.711 6.156 -2.731 60 89 .528 -1.719 -0 .036 11 .872 -2 .615 90 80.131 2.733 0.858 19.712 -3.167 120 71.658 2.309 1.167 21.582 -2.716 180 63.755 3.703 2.989 32.896 -3.313 285 51 .076 3 .018 6 .071 13 .919 -1 .117 360 11 .216 1.616 7 .698 16.378 -2 .908 120 37 .181 3.567 10.211 51.019 -1.981 10% Mineral Gila-Run N0. II-70 Initia1390nc. of Ezgggterol 0.00216 gps.[lOO ml. 31 89 .956 1 .897 0 .831 8 .551 —1.211 61 80 .991 3 .216 1 .572 16 .735 -2 .517 91 76 .026 3 .596 1.709 20.071 -l.102 121 73.001 -0.109 2.591 26.917 -2.103 211 56.920 2.221 5.139 38.126 -2.109 301 16 .318 o .950 8 .205 17 .519 -3 .022 391 36.658 3.322 10.611 51.809 -2.103 100 Percent Coup onent 8 . l Figures 11a-1 and 1121-2 1121-1 1 l I— I I I l ISOpropyl Alcoho1 III-10 2537 A f' l 1 L. A. _I 7_ -l I l 100 150 200 250 - 300 350 Time, mm. Composition of Irradiation Mixtures--Kin_etic Study 113-2 100 | I > I I - l l l I '. 20$ Glycerol‘ o . III-11 2537 A 80- O E ' E E 60. . a. W 20 _ 1 I l . l l l 100 150 200 250 300 350 100 Time,Hin. 121 11a-3 10° 3 I I I I I I I Eng n-Hexane o III-22 2537 A 801- G) *5: 8 3' 60" r3 ‘3 o o to o a. 50 100 150 .200 250 300 350 100 Time, Min. Figures 113-3 and 11a-1 Composition of Irradiation Mxturesuxinotio Study 118-1 10° I F I r I I I 7 ' 20$ Mineral 011 o ' , III-18 2537 A 80 1 , .p g t a) E g 60 __ . 8 . *3 ~ 8 . 8 3.. l 1 50100 150 200 250 300 350 100 Time, Min. 11b-1 123 100 r I I r I I I ISGpropyl Alcohgl II-11 2801 A 80.. +3 :3 \Q 0 g 60_ \E\ 9' \ '3 o ' A 8 p “ 8 10— ° 0 A a. A 20«— A A a A T n l 0 n _n U u L I I I 10 80 120 160 200 210 280 Figures 118-1 and 11b-2 Time: “in' Composition of Irradiation Mixtures-4Kinetic Study 11b-2 100 I I I I I I I - I I ' ' 20% Glycerol o " a G G o C) +3 - p a £3 10L a a in 20I— III T O o ' . I I I l l | l . 10 80 '120 160 200 210 280 320 360 Time, Min. 121 ‘ lhb-3 100 .6) I I [m I I T T I n—Hexane 0 Q II-18 2801 A \_ +2 9 8 8 E E" __ ®\\, r. ‘8 \w A/A Q) g /"M/ W 10 "' A/-/' ” ‘\ o A P A G) 20 r- H w T n 3.- X ‘ - n O. ' H u__- I; u\ VI L \(1 IX l 10 80 120 160 200 210 280 320 Figures 110-3 and 11b-1 Time, Min. Composition of Irradiation thuresuKinetic Study 11b-h 10° 7 T I l I I I I II-21 2801 1° 80 _. E I? \., g 60 I. G) ‘ \1 9‘ \O\ a ,A/x/d 43 \ g P II 10 I- G “I. . A 20 .. A O . I I I J I L 10 80 120 160 200 210 280 320 Time, Min. 125 110-1 100 I I I ‘ I . I I I I I . G IsoprOpyl Alcohgl II-6l 2967 A 80 _.. .1 .5 a 6 . d) g E 8 60 _ 0 _. 3 I10 I- A O P A 20 A .1 I—- A A A T I 0 D -.D_...__II‘ I . I I I I _ 10 80 120 160 200 210 280 320 360 Figures 110-1 and 110-2 Time, Min. Composition of Irradiation MixturesnKinetic Study 100 110-2 . ' I I I I I T I I I o 205 Glycerol o 9 113-61 2967 A 80 __ . 0 *5 ° E Q o 9: 6° 1- 8 0 2 I o I w — a a. P A 20 _. A .. A ' . L r M —--17' 0 ...n____n n I ' '1” I - - I I J 10 80 120 160 200 210 280 320‘ 360 Time, Min. 126' 110-3 100 I I I I I 'I I I I I I n-Hexane 0 11-53, 67 2967 A 80.. I? E. 605—— 13 8 10-—- I: n. 201-— A X A _. A L V 11 U . '1' a 0 411‘?» D. II D 'I I I I A I. I I 50 100 150 200 250 300 350 100 150 500 550 Figures 110-3 and 11c-1 Composition of Irradiation Mixtures--Kinetic Study Percent Component Time, Min. 11c-1 10° I T I I I I I I ° 0 20$!!inera10110 IIz-57 2967‘ mg... 0 O E 0 60.— o A. P .. 3 10— o 20— .. 'r n n a 0.7.61.4: “ -I I I- I- 50 100 150 200 250 300' 350 100 Tine, run. Percent Component 127 110-5 . 10% Mineral OilO . II-70 2967 A 80—— C) E 60... 10~— P 20-—- 0‘ . , .- I I ' I I I I 10 80 120 160 200 210 280 320 360 Time, Min. Figure 110-5 Composition of Irradiation Mixtures-Kinetic Study 128 A quantitative kinetic treatment of these data was made, and will be presented in a later section. However, it is appropriate to point out certain facts revealed by qualitative examination of the data. In general, there are no gross differences between the results of this investigation and the recalculated Sharpe data. Again, calciferol was not formed in significant quantities throughout any of the irradiation runs, and lumis- terol was found in significant quantities only when n-hexane was employed as a solvent. Although lumisterol was found in significant quantities in n-hexane at 2801 AD, the data are not too conclusive, since there are only a few values that are larger than the standard deviation for lumisterol by matrix (1), :t 1.8% However, the formation of lumisterol was definitely established in n-hexane at 2967 1°; a consistent build-up (although scatter was present) of the compound was obtained, of. Figure 110-3. In addition, the run was repeated without interruption during the first 330 minutes of irradiation, and continued in the usual manner with periodic interruption for the determination of the absorption spectra until about 801 of the ergosterol was converted. The two mns were coupled at the common points, 330 and 375 minutes, and one plot was made of the two runs employing the average values at the common points. The calculated compositions were well within the standard deviations for all conponents at the common points, the quanta absorbed up to 330 and 375 minutes were equivalmt within experimental error in both runs. The repetition of the irradiations in n-hexane at 2967 1° also established the general reproducibility of the results. In addition, the uninterrupted run served to prove that interruption of the irradiation did not appreciably affect the course of the reaction. 129 The results of the present investigation lend further support to the hypothesis that the solvent effect is primarily due to a variance of viscosity rather than the polarity differences, for in a structurally similar solvent of viscosity higher than n-hexane (20% mineral oil in n-hexane) lumisterol was not found in significant quantities. The viscosities of the solvents employed in this study were determined as described in the experimental section and are tabulated in Table XVIII. TABLE XVIII SOLVENT VISC$ITIE§ (Temperature 25 i 0.1 C.) Solvent Viscosity, Centipoise Isopropyl alcohol 2.068 20% Glycerol 7.135 n-Hexane O .301 2076 Mineral Oil 0.561 10% Mineral Oil 1.192 It is apparent that the viscosity effect is quite sensitive, since only a two-fold increase in viscosity (from n-hexane to 20% mineral oil) is sufficient to prevent the formation of lumisterol within the limits of ' "detection of the analytical Procedure-“1'6" about 5%o TABLE OF CONTENTS Page VI. DEVmaOPME-NT OF KINETIC mmSIONSOOOOOOOO'OOOOOOOIOOOOOO00.00. A. Survey of Recent Considerations on the Reaction MGChanismOOOOOOOOOOOOOOOOO00.000.00.00.00000000000000 B. Stereochemical Considerations........................... 1 I TaChySterOl O O O O O O O O O O O O O O O 0 O O O O O O O O O C O 0 O O O I O O O O O O C 2 O PrecalCiferOl O O o O O O O O O O O O O O O O O O O O O O O O O O O O O 0 O O O O O O O 3. calcjferOlOOO0.000.000.000000COOOOOOOUCOOCO'OCOOO. C. Electronic Changes During the Reaction.................. Do Derivation 0f Kinetic ExprGBSionSooeooee0000000000000... lo IntrOduCtory DiSCUSSionco000.000.000.00...oeeeoeee 2. Some General Considerations of the Reaction Mechanism and Kinetic Treatment................ 3. Glossary of Symbols Used in Specific Kinetic Derivations.................................... 1. Case of Equivalence of Optical and Derived Excited States................................. 5. Case of Non-Equivalent Optical and Derived Excited States.00.......00...00......OOIOOOCOOOOOOOOOOO 130 130 132 133 131 136 137 113 113 111 151 153 157 130 VI. DEVELOPMENT OF KINETIC EXPRESSIONS A quantitative kinetic treatment has been made of the data obtained in this investigation. The kinetic expressions have been developed on the bases of recent considerations of the reaction mechanism, stereo- chemical aspects of the components of the irradiation mixture, and the electronic changes that occur during the photochemical reaction. The kinetic treatment is also to a large part based on the qualitative con- clusions drawn from the recalculated irradiation results of Sharpe's thesis and the calculations of the irradiation results of this study, both presented in Section V. The derivation of the kinetic expressions will be presented after a survey of pertinent material. A. Survey of Recent Considerations on the Reaction Mechanism The early mechanism postulated for the irradiation of ergosterol, i.e., ergosterol -h-Y-> lumisterol £9 tachysterol 193—9 calciferol ill-a over-irradiation products has been modified during the past decade. After the discovery of pre- calciferol by Velluz and his co-workers (12) , the traditional mechanism was re-examined by Havinga's group (19,20). They have concluded from the results of experiments with ergosterol and 7-dehydrocholesterol which were labeled with carbon-l1 that lumisterol and tachysterol are not necessary intermediates in the sequence leading to calciferol. 131 Their tracer experiments involved the irradiation of mixtures con- taining approximately equal amounts of labelled ergosterol and inactive lumisterol; similar experiments were performed with mixtures of labelled 7-dehydrocholesterol and inactive lunisterols. The irradiation resin was treated with digitonin to precipitate the provitamins the rest of the products were separated on the basis of their reactivities with maleic anhydride--i.e., tachysterol > calciferol >‘ lumisterol. From the specific radio-activities of the separated products, it was concluded that neither lumisterol nor tachysterol play a part in the main route of the conversion of provitamin D to calciferol. However, the authors stated that this conclusicn was less definite with respect tettachyst'erflzthan' lunisterol. Other reasons for discarding the traditional reaction sequence were also cited by Havinga's group. They have reasoned that it is difficult to explain the magnitude‘of the quantum yield of calciferol formation which they state is about 0.3, even at the beginning of the irradiation when the percentage of provitamin that is converted is quite small and the concentrations of lumisterol and tachysterol are quite low. In addition, Havinga states that the angular (methyl group, 019113, is not likely to move into another position without the bond between C, and C10 or 010 and Cs being broken. In order to overcome these objections, Havinga's group had proposed the following reaction scheme: ’ Frecalciferol £3129: calciferol -—e‘ over- irradiation 1 Ihv products ergosterol ___hv activated —--‘> lumisterol F ergosterol )0 HM tachysterol 132 Mere recent work of Havinga's group (33) has yielded results from which it was concluded that precalciferol is a direct product of the irradiation and that lumisterol and tachysterol are secondary products. In addition, they have shown that the irradiation of precalciferol yields ‘tachysterol almost quantitatively; only about one percent of the pre- calciferol is converted to ergosterol and over-irradiation products. On the basis of their observed quantum yield of 0.1 for the conversion of precalciferol to tachysterol and the Observations previously cited, they concluded that the excited states of ergosterol and precalciferol cannot be equivalent. They argue that since 855 of the conversion product in the irradiation of ergosterol consists of precalciferol, the quantumeield for the conversion of precalciferol to tachysterol should be less than 0.15 if the excited states of ergosterol and precalciferol are identical; this is not compatible with the experimental quantum yield of 0.1. Independently of the latter conclusion, the experimental facts of the conversion of ergosterol.primarily to precalciferol and the almost quanti- tative conversion of precalciferol to tachysterol appear quite definite. These experimental facts are in complete accord with the results of this investigation. B. Stereochemical Considerations The structural formulae showing stereochemical details that are most generally accepted (with the exception oprrecalciferol) are presented in Figure 1. Most structural and stereochemical details have been established for quite some time for ergosterol and lumisterol. The steroid structure 133 is preserved for these materials, and the rigidity of the fused ring. system excludes many complicating stereochemical configurations and con- formations. However, such is not the case for tachysterol, precalciferol, and calciferol; these compounds possess structures in which the B ring is broken. I. Tachysterol Important contributions to the determination of the structural f0rmula and stereochemical details of tachysterol were made by Grundmann (15), and the groups under the direction of Havinga (27,17) and Inhoffen.(21,25). Tachysterol is represented as a structure which permits a planar relation- ship to exist between all three double bonds, with a trans configuration of the 11-6, 7 bond. The evidence for this configuration is based on infrared spectra, relative reactivity with maleic anhydride, and the observation of an iodine catalyzed cis-trans isomerization of precalciferol to tachysterol. The latter point will be discussed in conJunction'with the structure of precalciferol. A strong absorption band is found for tachysterol at 957 cm‘ls this band is ascribed to a trans configuration of the A -6, 7 bond. The deduction of a trans configuration on the basis of reactivity toward maleic anhydride is based on the existence of an inverse relationship between the rate of reaction and the number of cis substituents of the most reactive dienoic system of calciferol and related compounds in the s-cisoid conformation (1,8,27). 1314 20 Precalciferol The structure for precalciferol that is presented in Figure l is based on evidence similar to that given for establishing the tachysterol structure, some stereochemical relations, and consideration of the ultra- violet absorption spectra of the components of the irradiation mixture- The infrared spectrum of precalciferol does not possess the trans band at 957 cm”1 which has been interpreted by Havinga's group as evidence for a cis ¢§.-6, 7 relationship. The reactivity of precalciferol with maleic anhydride indicates a sterically interfering system which is consistent with the assignment of a cis 43 -6, 7 structure. The transformation of precalciferol into tachysterol.by iodine--a reagent which is known to effect cis to trans isomerization-~proceeds quite readily. The structure is further substantiated by the absence of an absorption band at 900 cmfls this band characterizes a terminal methylene group. Precalciferol could exist in various rotational conformations de- rivable from rotation about the S-5, 6 or S—7, 8 bonds. Two planar conformations formed by rotation about the S-S, 6 bond are shown in Figure 15. Both of the planar conformations are sterically hindered, but the cis S-5, 6 conformer is much more hindered. However, even the trans 8-5, 6 conformation will be hindered by the mutual repulsion of the hydrOgen atoms on C4 and CS. The structure in Figure l was proposed by Sharpe on.the basis of the inability of all three double bonds to exist in one plane and still satisfy the evidence that indicates that precalciferol is a £3 ~6, 7 cis isomer of tachysterol. According to Sharpe, the favored conformation is one in which (3 -6, 7 and [X -8, 9 exist in a 135 Figure 15 Planar Rotational Conformers of Precalciferol 12 136 cisoid relation in a plane perpendicular to the plane of the substituents on :1 *5. 10. Since this structure has only two conjugated double bonds capable of resonance, and these are in a constrained cisoid relationship, the ultraviolet extinctions are much lower for precalciferol than for tachysterol, because of the shorter length of the chromOphoric group. In general the spectrum of precalciferol is much like that of the closed ring structures of ergosterol and lumisterol. A very important feature of this proposed structure is that it is the first sterically favorable conformation which would result upon rupture of the Cg-C10 bond. This is consistent with the experimental fact that precalciferol is the most abundant product of the irradiation of ergosterol. At this point it is pertinent to bring out another feature of the structure postulated for precalciferol by Sharpe. The structure has CD and the hydrOgens on 619 in close proximity making the thermal transfer of a proton or hydrOgen atom (which is presumed to be necessary to form calciferol) sterically plausible. 3. Calciferol Although calciferol was not formed in significant quantities during the irradiation of ergosterol and was not included in the kinetic treat- ment, its structural features will be surveyed for the sake of complete- ness. As stated by Havinga (h?) the only controversial point is the question of the most favorable conformation at the S-6, 7 bond. Evidence for the S-6, 7 form is supplied by Crowfoot and Dunitz (9), 137 who found that, in the solid state, calciferol 3-nitro h-iodobenzoate has the S-6, 7 trans form. Additional evidence for the trans S-6, 7 conformation is afforded 'by the stereochemical consideration that the planar cis-6, 7 conformation would have strong steric interference. Inhoffen (23,26) had argued for the (213-6, 7 structure on the basis or the low extinction of the ultraviolet absorption band and on the stabilization that would occur (as the result of a 6 fi-electron system) if the molecule possessed the planar cis S-6, 7 conformation. However, Havinga's group (b?) has‘presented the reSults of approximate quantum mechanical calculations that are consistent with the assumption of the trans S-6, 7 conformation for calciferol. However, it should be noted that even the trans S-6, 7 conformation will prevent the-molecule from achieving a conpletely planar structure. The results of these calculations are also consistent with“ the accepted assumtion of a trans S-5, 63 trans A--6, 7; and cis S-7, 8 structure for tachysterol. 0. Electronic Changes During the Reaction From an examination of the components of the irradiation mixture it is apparent that all changes that take place during the irradiation of ergosterol occur in ring B. A detailed mechanism mat explain how the changes are effected. The interpretation of the reaction in terms of changes in the excited states of the components as presented by Sharpe will be utilized as a working hypothesis for the development of the kinetic expressions . 138 The initial step surely involves absorption of radiant energy by ergosterol, since the reaction is initiated bylight. A detailed‘deSCrip-" tion of the excited state of the ergosterol molecule that has absorbed ultraviolet radiation cannot be given at the present time. However, plausible arguments are given in Sharpe's thesis for considering that the excited molecule is best described as an ionic excited state. These arguments, together with the interpretation of changes in the excited state that could lead to the products of the irradiation, will be only brieflyksurveyed in view of the extensive discussion available in Sharpe's thesis. The seat of the absorption of radiation of maxima between 21.00 and 2930 A0 by all of the components is undoubtedly in the conjugated double bond network in ringB. The excited moiecule mustinitially be in a singlet excited state, since the high value of the molar absorbanCy indicates an allowed transition from the singlet ground state. Several possibilities exist, however, with regard to the detailed nature of this singlet state and the subsequent processes it may undergo within its normally expected lifetime of about 10.8 seconds. Excited states in conjugated systems often can be described best by the language of valence bond theory, in which ionic resonance forms make a principal contribution to the lowest lying excited states; application of this description leads to the suggestion that the excited state of ergosterol can best be described as an “ionic" excited state, with charge separation in ring B. Some of the structures contributing to this state 139 are represented in Figure 16. Contributing structures include several in which the (lg-Clo bond is cleaved heterolytically. Such structures facilitate the necessary rearrangements to the irradiation products, since the chain composed of Ce, C7, Ca, and C; can undergo rotational motion, the energy barrier to which has been lowered considerably by the absorption of radiation. is shown in Sharpe's thesis, the products can all be derived readily from rotations possible with the labile bond system in the 'ionic' excited state. Alternatively, a description of the excited state based primarily on molecular orbital consideration, would not suggest charge separation, but would, rather, suggest a general 'loosening' of the bond structure and an enhanced chemical reactivity associated with two electrons in different molecular orbitals but with spins paired. such a state is, in a sense, a 'diradical,‘ since the electrons are in different orbitals, although the total spin is zero. A set ’of diradical structures, analogous to the ionic structures shown in Figure 16, can be written to describe the excited state. Rearrangements are again facilitated by the lability of the double bond network, and plausible routes to products can be postulated, again analogous to those described for the ”ionic. excited state. . . In either case, it would appear that the rearrangements met take place within the approximately 10"8 sec. lifetime expected for an excited singlet state. It is also probable that the rearrangements require longer than 10.13-10.“ sec. (the period of a molecular vibration), since vibrational fine structure is clearly evident in the absorption spectrum lhO Figure 16 Valence Bond Structures of the Ionic Excited State of Ergosterol (37) of ergosterol. There seems to be little basis for choice between the two descriptions of the excited state, the differences between which are largely the property of the attempt to approach the description from the two extreme views of valence-bond and molecular-orbital theory. However, one shred of evidence seems to favor the ”ionic“ excited state; the lack of formation of calciferol in the photochemicalsequence sug- gests that a diradical state is not involved in this sequence, since the later thermal isomerization of precalciferol to calciferol can plausibly be attributed to the presence of a low-lying thermally-accessible diradical triplet state of precalciferol (Ill). The other alternatives seem more clearly ruled out. A transition to an excited singlet state above the dissociation limit of the 09-010 bond (leading to dissociation in 10.13-10.14 sec.) appears unlikely in view of the vibrational fine structure on the spectrum. A transition directly to a diradical triplet excited state is ruled out by the high value of the molar absorbancy. A transition directly to an excited singlet state followed by a radiationless transition to an excited trip- let state seems inprobable in view of the high quantum yield (of the order of magniimde of unity) of the conversion from ergosterol to pre- calciferol. It seems fairly definite, then, that an excited singlet state is formed ani rearranges within perhaps lOJ-lO-lz seconds to the structure characteristic of precalciferol and possibly other products . The re- arrangement can be pictured as a cross-over from a potential enerey surface of the qatically excited state of ergosterol to a potential 11:2 energy surface of some state of the product. The cross-over involves rotational motion of bulky portions of the large steroid molecules through the solvent, and may well be expected to be influenced by the viscosity of the medium, in accord with the qualitative results presented in Section III. The period of rotational motion is of the order of 10.3-10-10 sec. and will be viscosity dependent, so that the probability of rearrangement within the lifetime of the excited species (prior to fluorescence or collisional deactivation), and hence quantum yields of products, may be solvent dependent. Furthermore, the heights of rotational barriers will be somewhat altered by viscosity. These concepts have guided the interpretation of the kinetic data. may focus interest on the effect of solvent and irradiating wavelength on the various quantum yields of individual steps. They also suggest a question as to whether the excited state of a given product that results from rotational movements of the excited ergosterol molecule is identical to the excited state that is attained by direct irradiation of the particular product of the irradiation mixture. It was initially believed that the Optically attained excited state was equivalent to that derived from the excited ergosterol molecule. However, as will be shown, application of kinetic expressions derived on the assumption of equi- valence of the excited states leads to a discrepancy which can be resolved only by abandming this assumticn. As was discussed earlier, this conclusion is in agreement with the recent work of the Havinga group. D. Derivation of Kinetic hcpressions 1. Introductory Discussion One cannot deduce the order of the formation of the products from the. qualitative considerations that are described above. However, this treatment has been utilized as a working hypothesis which has served as a basis for. the choice of reactim sequences in the kinetic treatment. Appropriate kinetic expressions have been derived and applied to the data. Cowliance of the data with the kinetic expressions then sub- stantiated the original hypothesis. is discussed above, the kinetic expressions are depenient m the relationship between the optically attained excited states of the irradiation products and those derived from the excited ergosterol mole- cule. Kinetic expressions were first derived on the basis that the two types of excited state were equivalent. Application of these expressions to the data of the runs in which lumisterol was not formed yielded seemingly satisfactory results. However, a discrepancy between certain quantum yields obtained from this treatment and other reported values led to a re-eacamination of the kinetic derivation. A second treatmmt was developed in which the assumption of equivalence of excited states was abandoned. me discrepancy in regard to quantum yields was resolved 'by the latter treatment. In addition, it was also possible to apply the treatment based on non-equivalent excited states to runs in which lumisterol was formed. Attempts to extend the first kinetic treathent to such mns had not been successful. Both kinetic treatments will be 1m; presented.since the discrepancy brought out by equivalent excited state treatment affords evidence that the optically excited states of the irradiation products are not identical to the excited state derived from excited ergosterol. IDuring the application of these kinetic treatments--which were based on certain.simplifying assumptions--to the kinetic data, it became apparent that a general mathematical pattern existed for the system. It is pertinent to present these general kinetic concepts before proceeding with the derivation of the kinetic expressions which are specifically designed for application to the available data. 2. Some General Considerations of the Reaction Mechanism and Kinetic Treatment Many types of information point to the fact that the normal reaction in ergosterol irradiation consists of a sequence of steps including Optical excitation, and molecular rearrangement and deactivation of excited species. There is no indication that any reactions between.pairs of molecules are important; each step of~the~mechanism must be considered to be first-order. Certain generalizations can be made for any combination of series or parallel first-order reactions (1h). In this case the mathematics becomes further simplified by the fact that the stable com- ponents can be formed only from short-lived intermediates. Furthermore, analytical concentration-time data are available on all of the long-lived components of the irradiation mixture; these data, coupled with the actir nometric and spectrOphotometric data, make possible the calculation also of the quanta absorbed by each component during each time interval. 11:5 With these data available, it will be shown that any proposed mechanism can be reduced to solutions of the form where Ci is the concentration of component i at time t and $3 is the ' th integrated absorption for the j—: component from time 0 to t 33 - f 1.1 Addt (VI-2) _ o N Experimental data on all of the Ci and 13 are available as fimctions of time. The 513 are constants which are collections of ratios of rate constants and maybe expressed as’products of ”quantum yields' for particular conversions, where each "quantum yield. represents the fraction of a particular excited species converted to a particular component. Since each of the components of the irradiation mixture absorbs light in the same wavelength region, it seems plausible to consider a general mechanism with the following features: a) Each of the components can exist either in its ground state or in an excited state. b) The excited state of any component can be reached by optical excitation of its ground state, or by rearrangement of the excited state of any of the other components. c) The ground state of any component can be altered only by optical excitation, and can be formed from the excited state of any component . 1his set of conditions can be restricted to special cases of interest by liniiting the transformations which can occur among the excited species, 1116 and limiting the formation of particular ground state components from excited states of other components. Furthermore, this general case includes situations. in which an additional excited state exists for each component, accessible only from excited states of certain other compon- ents, and capable only of passing on to its own corresponding ground state, since any process A —> B --> C, where B is short-lived, is kinetically indistinguishable from the direct process A -—5 C. The only type of situation not included within this mechanism which seems at all plausible at the present time might be one in which optically non- accessible excited states exist for each of the components and can be reached from both Optically accessible and non-accessible excited states of the other components. The. addition of these possibilities will not invalidate the conclusions reached from the mechanism considered, and incorporation of such steps could be made with only slight additional complication of the algebra. 'me umber of steps included in. the mechanism makes it inconvenient to write out the reaction scheme on a single diagram with arrows indicat- ing the individual steps. It is more convenient to systematize the designation of the components and the writing of kinetic steps as follows : Long-liv ed . :Shortrlived _ Com onent Designation Cog on'ent Desiggtion Ergosterol E 1 3* 1' Precalciferol r 2 4 r* 2' Lumisterol L 3' L* 3' Tachysterol . T h 13* h' 1117 Rate constants for individual steps will be designated K13 where the step is i —-> J. For each intermediate,» 1, the summation of rate constants for disappearance is designated 01' (Ti - E I Kij (VI-3) 3+ 1 , - The ratio of the rate constant for a particular step to the summation of rate constants of the disappearing species is formally similar to a quantum yield and is designated ¢1J where ¢1j " xii/Oi 01‘; K13 " 0'1 F513 (VI-h) The complete mechanism is E Eli-93* 3 Rate-IaAE-IE (VI-S) 3* Ell-ks ;z*§iLz_,r,E*EiLa_, Mfg-33L» 'r 3*Emgr*;s*§ilaL+L*;E*£lLtL-er* r3119 r*; Rate--IgAP-Ip r*§.a'_L, E; P*£§L§_, r; Vic-ELL, L5 fight; 2 {533.12, 13*; 3 r*E£L-'£.,. L*;P*§.§.'.ab.'r* LEI—a L*;Rate-IaAL-IL - filial—a. E 3 L*§-33-2-e r; L*§.-1'.2.,L 3L*§3.LL, 'r fig-3., E*; fiaifiig P*3 . 31f ____’K3t‘t 1* T 211—e 13'; Rate-IaAT-Lr {5313—5 E 3 T*§_‘_'_E_, p; T*E_3_.>L3T*;£-‘-:L’T * . . . .1. [4.111 3*; T* Ka'a' P* 5 T* K113: L* 3 From the mechanism, application of the steady state approximation to the short-lived intermediates leads to the following set of simltaneous 1&8 linear equations a * 2&1 . o. . In - c1.(z*) «- K8'1'(P*) +.K3I1I(L*) e x“ 142*) (V356) -, IE - O',.(E*) «t t2. 1. O;:(r*) e ¢e'i' 0;.(13‘) «t - ' ' - - . ¢4I1I 02' (1*) *- '9.§§_1. o . Ir‘ K1I2I(E* ) - 0'2'(P* ) r Ksude ) * 34'2“?) (v n 7) n I, ¢¢112€013(E*)- 0.33“”. )‘OI ¢3' '3‘ 0—3'(L* ) '. ¢4'2' ‘ ' em a * . 2é%_1 _ o . IL ¢ K113»! (3*) t K2'3'(P*) "' (BIO-f) I. Kuadr‘u’.) (VI 8) .- II. t ¢1I3I0'1(E*) e ?3I3I03I(P*) - O§I (If ) t ¢‘lat '(TW {- ? - O - IT «I K1I4I(E*) e K284I(P*) e Kat‘l(L*) - 021““) ' . . , (VI-9) "' Lt" *¢1'4'0-1'(E* )_ " ¢2'4'0-2'(P* ) * ¢3I4NO§WL ) "' ' ~ ‘ ,_ - O-I(T* ). Rewriting these in matrix form, ‘ r 1 2 '¢2' '1' ‘¢3! 1! 44'1' 03.1 (E *y :3 41.2. 1 ' ’ 4:5,; 415,; O',§(P*) I, ., - , y, , , _ * - (VI-10) 41'3'4’2'3' l 403' 03'“) II. J -¢1'4"¢8'4' "Pain 1 ’ ‘ 02;(T*) L5 .. L- _..L L It is readily seen that these equations can be solved for O'1I(E*), O" “I ), . O'3I(I.* ) andO1I(T) in terns of constants and the absorbed .1.th 1&9 quantities IE, 11,, IL, IT. Each expression will be a linear combination, such that 01I(01')- 324cm I3 (VI-11> where the 0.in are each ratios of suns of products of ¢'s. The expressions for rate of change of stable species can now be expressed as follows: 2Q). .. .. IE . K1I1(E* } a K2110?” ) e K3I1(L* ) e K‘11(T) (VI-'12) dt ' (:1 ¢i‘1ai'1'l)IE.7 T; ¢i'1“itx 1!! 13.1! K'21'-1 (VI-13) Integrating between t - 0 and t - t, (3)0 '(E) " (1" Z‘; ¢1I1a1I1)IE ’51 TJ ¢i’l i'a-l' . - K n 2 1I. 1! - 615K Ii (VI-1h) Similarly, . 1‘ a I 4' (P) " (: ¢1t2a132 "' 1) If *1; *,' Z¢i‘z°1'xil{ i'-1' - K ,I a ih-gv - - - - - (VI-15) 1,2,4 (L) - 1. - (¢1I3¢1I3'1)IL* E f, 2, he. '1' K+a i'I-i G1: K Ix (VI‘I6) (T)' 2:1, (¢1I4“14‘1)IT‘ : :1, $1M {LI-11 XI; i"- (1111; 1K (VI-17) 150 or, in general, 4' A a: (ch-<03)“ Z (Mam - 1) ’i’, . 7‘ 7‘ In, 1'. 1' - ‘ _ K+J 1'. 1' Ci'x ’i’x (VI-18) . where (OJ) is the concentration of component 3 at time t and (Gj)° is the‘initial concentration of component 3 . Thus each concentration is see: to be expressible as a linear cominatim of the integrated absorbed quanta. The complexity is considerably reduced when certain less general cases are treated. Two such cases of interest are: (1) formation of products only through their correspording excited states (equivalent to Optically excited states, and (2) non-interconversion of optically excited states, with products formed in ground states (or optically inaccessible excited states) from optically excited states of other species. The first case mathematically is expressed by 45.3 - 0 except for 1 nj Hence ' (V1-19) (+1.1) ¢2' 2, ¢3Iap ¢41‘ + 0, 311 others 20130). a- - ’ ‘ mic leads to simplified concentration expressions as follows: “394%” " wJ'J‘J'J ' 1) 3’3 ‘ x273 ¢3'J “ J'K iI: (VI-2°) The second case mathematically is expressed by 151 ¢i'J' " 0: ¢itj + 0 (VI-21) Eris eliminates all off-diagonal terms in the matrix. (NI-10),:ran'd. leader)". simply to * 01' (E ) ' IE em - I, GENT-f) " IL 0;..(T*) " ITS “43.4 " 0131- 3G1IJIOforj+l. be be ‘uziz 3 11sz - 0 for j III 2. (VI 22) - Va 1 l oata'u l 5 aaIJ -0for,jI|-3. l he a4‘J-Ofor3+h. The concentration expressions then become: 0 N ~ (cJ)-(c3) .. (chm-1) 13¢ K2... '3 ¢KIJ 1K (VI-23) Further simplification can result from specific assumptions about relative magnitudes of particular rate constants or "quantum yields.” TIm particularly pertinent special cases related to the two Just dis- cussed will be presented in detail. Because of the simplicity in obtain- ing the kinetic expressions directly in these cases, their treatment will be individually derived, rather than deveIOped from this general derivation . 3. Glossary of Symbols Used in Specific Kinetic Derivations The symbols employed in the derivation are defined as follows: E, T, P. I. - ergosterol, tackvsterol, precalciferol, and lumisterol, respectively. (E), (T), (P), (1.) - concentration of the indicated component: in' this study, moles per liter of solution. 152 (20°, (10°, (13°, (1.)° - initial (zero time) concentration of the indicated component; in this study, all components but ergosterol were initially at zero concentration. E“, Ti. Pf, If - indicated component in its Optically accessible excited state. (E*), ('1’), (PI) , (If) - concentration of the iidicated component in its excited state. I P* - an excited state of precalciferol which is Optically inaccess- ible and is derived from if. t n time of irradiation. ‘ k3 - kinetic rate constant, ,1 denoting the reaction step considered. Ia - rate of absorption of radiation per unit volume by all Of the components of the irradiatim mixture, i.e., total moles of quanta (Einsteins) absorbed per unit time per liter. ‘8’ A1,, AT, ‘1. - fraction Of the radiation that is absorbed by the component indicated by the subscript. "1’3, ’i}, 3:21., "I; - the value of the definite integral,f Iaaidt, where the subscript i denotes a given conponent. The value of this integral is the total number of moles of quanta per liter that are absorbed by the indicated component during the interval of irradiation O to t. 153 14. Case of Equivalence of Optical and Derived Excited States In the following development it is assumed that lumisterol and calciferol are not formed in significant quantities during the irradiation. The stereochemical and electronic considerations suggest the following sequence for the irradiation of ergosterol: I k 3(- k 41. ”F, Fe Fe " ‘ (VI-21») P ‘1' This reaction scheme may be considerably sinplified by certain assum- tions that are based on experimental Observation. The rate constants k3 and k6 mist be very small, since the irradiation of precalciferol results in the almost quantitative conversion of precalciferol to tachysterol (33). It is therefore assumed that k3 and k6 are essentially equal to zero. In the kinetic development the excited states of the components of the irradiation mixture are considered to be reactive intermediates, and the steady state approximation is applied to these species, i.e., the rate of change of the concentration of the active species is set equal to zero. The law of photochemical equivalence is applied to the absorption of radiant energy for each of the components. From the steady state relations, expressions are Obtained for the concentrations of the active species in terms of experimental quantities; these expressions are substituted into the apprOpriate rate equations, and the differential equations are integrated . 15h The modified reaction scheme may be written as: I all; 217—: 13* _a, P*-§-§—> T* (VI-25) ‘ «its first I T i The rate equations for the reactive intermediates, applying the steady state approximation, are: * %E_l . o - IaAE - (1:1 «I kg) (13*) (VI-26) .§é§:).- 0 ' IaAP * k2(E*) ‘ (k4 T‘ks) P* (VI'27) d(1‘*) . o - 13% o k5(p* ) - k7(t* ) (VI-28) dt The concentrations of the active species are obtained by solution of the resulting three simultaneous equations (VI-26, VI-27, and VI-28). The results are: * I A I E . a E '- ( _) *kl'tkz (‘71 29’ , k (r*) . as ‘kvkz’ W “1'3” 1c4 «I. k5 (T*) - Ia” ‘ (m) Ia? ‘ {kt—LR ‘ kzxk‘k ‘ kala-E-I A (vie-31) The rate expressions for the components of the irradiation mixture in their normal ground states may be written: it? - not“) - res (”'32) 155 Substituting the value of (13*) from equation (VI-29): 2Q). " "’ £32.... IaAE " " ‘t’EIaAE (VI-33) dt k1 «t k2 where the quantity ¢E - has been introduced. This is the .132— R1 + k2 quantum yield for ergosterol conversion, since it represents the fraction of the excited ergosterol converted to other products. 9%; - k.(P*) - 1.1aP (VI-3t) Shibstituting the value of (19*) from equation (VI-30): dt " k4 + k5 ¢EIaAE " k, .. k5 IaAp (VI-35) " (1 ‘ ¢p) ¢EIaAE " ¢PIaAP (”’36) Where the quantity 4)}. - Elf-5:}- has been introduced. This is the 4 5 quantum yield for precalciferol conversion, since it represents the fraction of the excited precalciferol converted to other products. The quantity 1 - 4)}, - 1 - H133}; - W is the fraction of excited precalciferol returning to the ground state. It is important to note here that there is a nmdamehtai difference in the nature of (b; and #1,, since 3* is formed only through Optical excitation of ergosterol, while 2* is formed both by optical excitation of precalciferol and by rearrangement of excited ergosterol, E*. Equation (VI-36) was left in this form for future algebraic manipulaticn. 156 dd: " k7(T*) ‘ IaAT (VI-37) Substituting the value of (T*) from equation (VI-31): dd: " ¢P (IaAP * ¢EIaAE) (VI-38) Integration of equation (VI-33) between the limits of O and t yields a linear relationship between the amount of ergosterol that has reacted and the amount of radiation absorbed by ergosterol, with a slope equal to the quantum yield, (113; the integrated form of (VI-:33) is written: 1’. o N (E) - (E) a 43E 5 IaAEdt - ¢EIE (VI-39) 0 Integration of equation (VI-36) between the limits of O and t yields (P)-(P)° = (l - 4);.) (>332; - 4),,”1} (VI-he) Since (P)O - O at t - O, and ¢ETE . (E)°- (E), equation (VI-hO) becomes A r N (r) - (1 - h) M)" - (3)1 - 4:, II, (VI-t1) In runs where no lumisterol or calciferol is formed, we may substitute (T) for the quantity (E)o - (E) - (P). The following relationship is obtained after this substitution and rearrangement of terms. (T) =- 52 [(1’) fig (VI-M.) 1‘4 Equation (VI-142) shows that a plot of the indicated experimental quantities should be linear with a slope equal to the ratio of We rate constants . 157 Again, an integration of (VI-38) between the limits of O and t yields a linear relation between mmerimental quantities, (r) - m° - 45 (f1', . m.) - (VI-t3) Since (T)° - O and (JET; - (E)? - (E), equation (VI-1&3) becomes r. 4» [(E)° - (E) #11,] (vi-uh) The slope of a plot of the apprOpriate experimental quantities is equal to $1,, the quantum yield for the process P -—-> T. 5. Case of Non-Equivalent Optical and Derived Excited States i Incorporation of the non-equivalency of P* and P? results in the following modification of expression (VI-2h): s IaAE E* k3 L F— - _ 1‘1 1“? (vi-ts) I P* 'l 1*? *— 1“ Excited states of tachysterol and lumisterol which might be con- sidered as derived from P* and 13* are not shown in expression (VI-15), since inclusion of such excited states results in kinetic expressions which incorporate effects that the enerimental data are not capable of detecting. Harv additional steps could also be included showing that the products of the irradiation could be converted to ergosterol; however, such steps again lead to expressions which require more accurate data than are available. These considerations will be discussed further. 15 8 The rate equations for the reactive intermediates, incorporating the steady state approximation, are: * 9&1 - IaAE -.(k1 a kg 15 ka) (3*) - o (VI-hé) *- fldiil . 13A? - (k, . k5) (r*) - o (VI-h?) *1 iii-*1 - k2(E*) - k2'(P*') - 0 (VI-’48) These equations can be solved directly for (3*), (15*), and (PM), giving: 3* . 185E _ ( ) “1.1%..“ (V119) 0*) - 5232.... (VI-so) k4+k5 314.5; *.kzlaA g") 1.2:“) Wife n+2?) W's“ a A The rate expressions for the components in their normal ground states may be written: (1(3) _ _ 1:2 4. kg “ . dt k1 ’ k2 ¢ k8 ISLE - ‘ ¢E18AE (VI-52) The quantum yield $3 is defined as(k3 o k3),(k1 o k, 4» he); this definition is. consistent with the expression for (PE in the previous section, and represents the fraction. of excited ergosterol which is converted to other products. 93;). . 3.3M— .. ksla‘l’ dt k1 t k; «0 k, k. , k5 (VI-53) - 159 '39:) " in IaAE " WT Ia‘r _ (VI-Sh) _lSa___ 1:1 «5 k3’+ k, . excited ergosterol which is-converted to precalciferol, and QPT is __l£a'_t k4 *’k5 where ¢EP is defined as and represents the fraction of defined as and represents the fraction of optically excited precalciferol converted to tachysterol. 1&1 " Mair (VI-55) Q _ k IaAa dt 1:: t kz‘o k8 (VI-'56) % '. inla‘z‘ (VI-57) k.- * k,,o»k3 c kg excited ergosterol converted to iumisterol. where ¢EL is defined as and represents the fraction of Integration of equations (VI-52, VI-Sh, VI-SS, and V1457) between the limits of zero and t yields: of - (n) - «b3 ‘1’ - (be + twin (VI-58) (P) ' ¢zpfz - 4515p ' (VI-59) (r) - $.13, (VI-so) (1.) - buff, (VI-61) Equations (VI-59, VI-60, and VI-6l) are derived on the basis that the concentrations of,P, T, and L are zero at t equal to zero. 160 ‘The equations (VI-58, v1-59, VI-60, and v1-61) are linearly related through the material balance equation (E)o . (E) e (L) o (P) e (1'); —' Since the material balance equation has been used in obtaining the] concur- trations in the analytical procedure, only equations (VI-58,. VIC-60, and v1-61) aroused in the kinetic treatment. The reaction scheme (VI-16) is mathematically identical to the - 3 simplified reaction scheme in which If is deleted, i.e., k:1 l ' (VI-'52) k2 ' l’ 1311: P* kg T # F— 1‘4. The expressions derived from reaction scheme (VI-62) are identical to equations (VI-58, v1-59, VI-oo and v1-61). ' ' g . As in.the caseof equivalent excited states, simple linear relation- ships are obtained. In general, considerations of other reactionsteps in (VI-hS) or (VI-62) will lead to expressions in which a quantity such as (I) is a linear combination of products of quantum yields and the integrals ii" These would introduce a curvatureto the linear relatims (VI-.58, VI-60, and VI-61).‘ However, the values of the secondary‘terms are quite small, and more accurate data than are available would be required to detect the curvature. The equations derived frm reaction schemes (VI-1:5 and VII-62) were found to yield the most plausible fit of the data'within the uperimental limits of accuracy of the data. TABLE<0F CONTENTS Page VII. RESULIS OF THE KINETIC(STUDY}................................ 161 A, Treatment of the Data..................;............... 161 B. Results of Kinetic Treatment........................... 166 1. Case of Equivalence of Optical and Derived ' Excited States................................ 166 2. Case of Noanquivalent Optical and Derived meitGd StatBSOOOOOOOOOOOOOOOO0.00.00.00.00... 177 161 VII. RESJLTS OF THE KINETIC STUDY A. Treatment of the Data It is evident from the kinetic equations that in addition to the concentrations 'of the components , the kinetic procedure requires the knowledge of the nunber of moles of quanta per liter absorbed by a given component during the interval of irradiation from time 0 to t, i.e., the value of the integral 5t Isaidt. its total nunbers of quanta agsorbed by all of the cowonents of the irradiation mixture were directly available from the experimental data for any interval of irradiation. his average rate of absorption of radiation, 1'” was calculated from these data for small. intervals of irradiation and covering the entire irradiation run; these data are tabulated in Appendix III. It was assumed that the average value I. could be substituted for the instantaneous rate Ia for. small intervals ‘ of irradiation. By means of this assumption, the definite integral whose value is equal to the matter of quanta absorbed tythe 1E2 component during the interval t - O to t - t; can be'iritten as. t t(1) t(3) f Igaidt - Ia“) S Aidt e 1(3) Aidt e O O N (1) tn or t1 0 e e 0 * fa(n) f Aidt 1"(n-1) (VII-l) 162 where the numerical subscripts in parentheses denote the subdivisions of the irradiation intervals for which the values of la have been calculated. The use of an average value of the rate of absorption of radiation is justified, since the rate of absorption changes gradually during the irradiation. The integral faidt was evaluated (between the limits corresponding to the intervals for which Ia was calculated) from the concentration-time data, using the known ultraviolet molar absorbancies of the components of the irradiation mixture. The fraction of radiation absorbed by a given component of a mixture for which the Beer-Lambert-Bouger Law is valid is given by the following expression (32): ciéi 0161. 0262‘ "" ‘ CInEm 11 - (VII-2) where Ci - concentration? of the. indicated component i, and 61 - molar absorbancy of component i. Since the radiation emanating from the monochromator was not purely monochromatic, average values of the molar absorbancies were employed to evaluate ‘1- The calculations involved the assumption that the distribution of intensity of radiation with respect to wavelength was that afforded by a triangular slit function. An expression for the average molar absorbancy was derived on the basis of this assumption and the dispersion of the monochromator, i.e., 66 A0 (or 6.6 up.) per mm. The derivation for a ' slit width of 1.00 mm. is presented below. 163 The average molar absorbancy is given by c 6.6 6 6 EAisl(A)d(/\-/\O) “ 6A152(A)d(A'Ao) .. . o O 6.6 i , \ f SI(/\ NM '/\o) *j Sz(/\)d(/\ -/\o) -6.6 o (VII-3) 61 where 6A - molar absorbancy at wavelength A , up, for component i /\o - nominal wavelength, mp, and the slit mnctions S;l and 83 are given by 5100- A561)” a l (VII-ha) 52M) - - A5240 e 1 (VII-hb) .. Substitution of the values of Sl()\) and 8,3(A) given by equatims . (VII-ha) and (VII-lib) into equation (VII-3). and evaluation. of the denominator of the latter equation yields _ .6 o 6- £3 f éAidM‘ A0) * [ eAiLdégg/‘Dl ow) - A.) - -6.6 ~6.6 '1) 6'5 . VII-S) f eli‘i‘z'eg’idam-A.) ‘ ° _J The spectral data furnished by U. H. C. Shaw (130) were utilized in the evaluation of the three definite integrals of equation (VII-5). 161; 6 6 The integral} E A1 d( /\ - /\o) was evalnated with a planimeter from plots of molargbsorbancy vs. wavelength. The other two integrals of equation (VII-S) were evaluated by numerical integration, employing the trapezoidal rule; intervals of 10 A0 were employed in the integration. Equation (VII-5) has been derived on the basis of a slit width of 1.00 mm.3 slitwidths of 1.50 and 2.00 mm. were employed in the irradiation studies. The limits for the value of 2) - /\o are given by twice the product of the dispersion of the monochromator (66 A0 per mm.) and the slit width. Accordingly, equation (VII-5) is modified to incorporate the appropriate .value of the limits of A - /\0- Values of the nominal wavelengths and the limits of /\- /\0 were rounded off as follows: 253? A° to 251.0 i 100 i°, slit width - 1.50 no.3 280).; A0 to 2800 i 130 A0, slit width=2 .00 mm.; 2967 11° to 2970 i 100 A°, slit width=l.SO mm. The values of the average molar absorbancies calculated by this procedure are given in Table III, t0gether with the molar absorbancy at a wavelength corresponding to the "rounded off” nominal wavelength. . ‘ The fraction of radiation absorbed by a given component, A1, was computed for all experimental points by means of equation VII-2. utilizing average values for the molar absorbancies. Plots of A1 vs. time of irradiation were made and the value of the integral jaidt (over the limits corresponding to the irradiation interval. for which Ia was calculated) was determined by mmerical integration of the data obtained from the smooth curves drawn through the experimental points. TABLEXIX MOLAR ABSORBANCIES AT IRRADIATING WAVELENGTHS 165 Molar Absorbancies Components Average, 6- 6 251m A° 42537 A°l Ergosterol 5981 h831 Lumisterol h886 h811 Tachysterol 11570 llBhO Precalciferol 8770 8837 2800 11° (2801. A0) Ergosterol 10320 llh30 Lumisterol 8365 8873 Tachysterol 26830 29550 Precalciferol 5922 6029 2970 11° (2967 A°) Ergosterol hl88 h597 Lumisterol 3162 3280 Tachysterol 16800 172h0 Precalciferol 2058 l9h0 166 The trapezoidal rule was employed in the numerical integration process. These data are presented in Appendix III t0gether with the values of la. The data required to compute the value of the integral Jyt IaAidt from equation (VII-1) are made available by the procedure desgribed above. The calculated values of this integral are also presented in Appendix III. Since Ia was measured in quanta per minute, the calculated integrals were divided by Av0gadro's number and multiplied by 1000/ (volume of solution in ml. in sample cell) to give the reported integrals in units of moles of quanta absorbed by the component per liter of solution. In performing the computations described above, the concentration of calciferol was taken to be zero; the calculated concentration of calciferol.was generally less than the standard deviation. A value of zero was also employed for the concentration of lumisterol in all cases except in nrhexane at 280h and 2967 A0. The few small negative values that were obtained for the concentration of tachysterol were also con- sidered as zero in the calculations. B. Results of Kinetic Treatment Using the concentrationrtime data calculated in section VB and the irradiation data processed as described in section VIIA, the relation- ships predicted from the kinetic derivations have been checked. 1. Case of Equivalence of Optical and Derived Excited States The derivation based on the mechanism 167 E .11.}. Ex- .—...—..> P —————.—> Ta:- “_a_.-h T (VI-2h) P was found to yield the equations (E)° - (E) = ()Et ”f3 J (VI-39) (T) = %f [(P) +'i§] (VI-h2) (T) - his)" - (E) 4: IF). (VI-14h) In each case a linear dependence of the experimental quantity on the left hand side of the equation is predicted. The data used are presented in Table XI. Typical plots of each of the three equations are shown in Figure 17. A linear least squares procedure was applied to the data to obtain the values of 03, k5/k4, and 0?. The usual least squares procedure, which is based on the assumption that one variable is known exactly, was not employed, since both of the variables in the kinetic equations are subject to error. The procedure employed yielded a straight line for which the sum of the squares of the perpendicular distances from the experimental points to the line was minimized (35). Essentially, the data were fitted to the linear relation a l y--:E-'Sx (VII-6) where y and x are the variables and a and b are constants from which the slepe and intercept are calculated. The relationship presented by [(E)° - (EH or (T), 5 -1 moles liter x10 Figure 17 Typical Kinetic Plots, Case of Equivalent Optical and Derived Excited States 2537 i° 20% Mineral 011 Run III-18 168 2.8 2.6 — 0 - [(E)° - (3)] - ¢E"I’E lllTlllllll A- ('r) - ks/k‘IKP} c’i’PJ TE or [(P)+IP] - ‘~ .1 5 moles liter x 10 169 commandoo mas.m see.: wem.m mem.~ eaa.a 0m0.H 00m.m omnuo :::.: 00a.m em0.: mes.m maa.a gma.0 Nm0.m 0mmuo man.m m0m.~ :m0.m mea.m Hea.a «mm.0 00m.m onmuo MNN.N 0~0.N Haa.m 04:.H em~.H Ham.0 H00.e opato Nmm.H Na:.H 0m0.~ m~H.H mm0.a ema.0 0pm.: 0md.0 0mH.H 00H.H ~H0.H mem.o mam.0 ::H.0 m-.m 0e.0 msa.0 :mm.0 00H.H 0~0.0 H0e.0 aHH.0 are.m 00.0 as0.0 0am.0 40a.0 Hem.0 mm:.0 m00.0 04m.m 0s.0 3.3 03.0 «3.0 «3.0 zero :80 @000 8.0 a-uoama noses ouoa a H0H.p u onmv aH.HHH cam Hoaooaao mom 04 ammm 450:0 mam.n mem.m aHH.m wam.a H00.H mme.m 0Ha.0 emm.m Hem.2 mmm.m 2m~.m me~.H 00m.o som.m mom.o mma.: mm:.m ~H>.: mam.~ mam.a mm0.0 wmm.m mom.o Ha0.m 0mm.m Hee.m HmN.N 0am.e Nmm.0 0mm.m mn~.0 mme.m ~0H.N weH.m mam.a e0~.H mmm.0 emm.a me.0 nam.H Hma.a nmN.N aN:.H HH0.H NQH.0 ~a0.e . 0~H.0 0e4.H ~HN.H ama.a eeH.H 0He.0 NmH.0 a0e.: 0a.0 00H.H ama.0 0mm.a ma0.H Haa.0 mHH.0 mm0.m 00.0 0e0.0 H00.0 Hem.0 5H0.0 mmm.0 000.0 ems.m 04.0 0e:.0 mam.0 ems.0 ama.0 emm.0 me0.0 en0.m 0N.0 atop: nodes p.01” w 8H0 - on: 0H-HHH cam Honocaw,aaaonaoem o4 emmm #cnm- m .Fefia W. 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N. 0.5 E - E .5: 000 x 0.8000 808 80.0385 00.850 800 x 0- B00 .808 03 a 7.8.000 .802. 025000 8 .8983 - - . .00380é 03.858 Bu .8 300850808 088980 - .r 350.88 -0053 17h 00300008 000. m 00.0. m 80. 0 000. m 000. 0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.N 30.0 «00.0 000.0 000% 000.N 000.0 000.0 000.... 000.0 000.0 000.0 000.0 000.0 000.0 03.0 000.0 000.0 000.0 000.0 000.0 05.0 000.N 000.0 08.0 $0.0 000.: 00.0 000.0 000.0 000.0 08.0 000.0 000.0 000.: 00.0 «00.0 000.0 000.0 000.0 000.0 000.0 000.: 00.0 7.8000 808. 0.00 a 0.0:.W .. 08 00.00 5.0 000 00.8.50 00: 00 m0m~ .00. + E - 03 0.0. o b: 0.0 E .. 03 E E J1 E - .5: 000 0. 7.0300 809.. 000 x 0-08.00 809.. 400E300 .00 40.5300 000 x 0:00000 0000a 0000002000 0000:0x .Hopmpmomum 03.00208 EM 0..» 00000000202000 #:0000950 830.3080 I NH an. 17S 000.0 000.00 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 05.0 02.0 000.0 000.0 000.0 000.0 000.0 000. 0 000. 0 ~00. 0 000.0 000.0 000.0 000. 0 000. m 000. 0 000.0 000.0 000. 0 0mm. 02. 0 00m. 0 000.0 05.0 000.0 000.0 000.0 000.0 000.0 0000 000.0 000. ..- 0000 000. 0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 00.0 2.0. 0 000.0 02.. 0 000. 0 «8.0 00.0 000.0 «00.0 000.0 000.0 00.0.0 00.0 - H.300 $0000.00 ,0 000.0-.003 00.00-00 Sm 09.380... 00 00mm 0.0.0.0 000.00 000.0 000.0 000.0 000.0 000.0 000.00 000.0 000.0 000.0 000.0 000.0 000.0 000.0 000.0 08.0 000.0 000. 0 000.0 000. N 000. 0 08. 0 000.0 000.0 000.0 000.N 000.0 000.0 000.0 80.0 000.0 000.0 08.0 000.0 8.0 000.0 08.0 000.0 08.0 000.0 00-0 000.0 000.0 000.0 000.0 80.0 00.0 «00.0 000.0 000.0 08.0 000.0 00-0 000.0 000.0 000.0 08.0 08.0 00.0 0.0300 m0020 0-00 x 000.0 . 008 . 00-00 Se 05000.: 04 0000 0M m E - 03 E 0.00 .5: 000“ N 0.000.010 mmHos 5000.00.80 000.0500 00.0 N 0&8»: 000000 00.0 00 0.03.3” 00.008 finmzouah .00 400.00va - «Honmpmomhm 000.0058 90m 00 00509009000208 0.0808908 ll! Banfioo - H0 0004.0 176 Scarborough (35) to calculate the constant a was altered algebraicalxy to the following to facilitate the computations: 2 a. ’9' [1‘ (ii-:2] 23:; [23‘2” 23,2] _ ZnflZZX: Elxy' ‘_l_ x 2 2 _ 2 .8. 23y (23,). f2), [ (2 > +n<§:,x zyfl] e a Fn Zny (Ex - Hg), )J = 0 (VII-7) The constant b was calculated from the value of a from VII-7 and the relationship 2‘. a(2n.x n)4-1-«0— (VII-8) —')+b( The origin. 109., the point at zero time of irradiation was weighted as one experimental point in the calculations. During the course of these calculations it became evident that the least squares procedure described above yielded values of the quantum yields that were generally within.0.01 of the values Obtained from graphical plots. The values of the quantum yields for the case of equivalent excited states were all calculated by the above procedure, but subsequent calculations were made with the more simple usual least squares procedure. The results of the application of the kinetic equations are presented in Table III. 177 TABLE XXI THE RESULTS OF THE KINETIC TREATMENT, EQJIVALENT EXCITED STATES _ T Wavelength EEC 2537 A0 2801. A0 2967 A° Solvent ' 25 C. 4);; (DP 1%: $3 (pp £45 (1)3 ‘13}: T12: n-Hexane , ' 0.30).; .514 .15 .18 Lumisterol formed 20% Min. 05.1 . 0.561 .51 .17 .18 .33 .12 .12 .36 .10 .11 not Min. 011 1.192 -- -- -¢ 3 -- -- -- to .10 .11 i-Pr. Alcohol 2.068 .19 .18 .23 .27 .12 .11; .38 .10 .ll 20% Glycerol 7.135 .118 .19 .22 .25 .12 .12 .35 .11 .11 f The values of 433, (1)9, and k5/k4 are found to be dependent on both solvent and irradiating wavelength. A detailed interpretation of these effects will be presented in a later section. However; it is interesting to note at this point that the values of 83 are in approximate agreement with the quantum yield of calciferol formation as inferred from bioassay results. ' For example, a value of about 0.3 is obtained from the bioassay results of Steenbock and Hamans (16). The values of $3 (from the present study) are based on the conversion per excited ergosterol molecule; since the major product of the irradiation is precalciferol (which would be detected as calciferol in a bioassay), values of 1313 should be at least in rough agreement with the quantum yield of calciferol formation as derived from bioassay results . 2. Case of Non-Equivalent Optical and Derived Excited States The derivation based on the mechanism 178 E LL E*-——> L V'— i (VI-62) r £3; r*—> T was found to yield the equations (E)° - (E) - . $3 I 1;. J . (VI-58) 1' -= 4)” [’i;> 1 (VI-60) L .. tn [TE ] (VI-61) In each case a linear dependence of the experimental quantity on the left hand side of the equation upon the experimental quantity in square brackets on the right hand“ side of the equation is predicted. In compar- ing the experimental data with these equations, the irradiation data presented in Table I! and the ”I; values tabulated in Appendix III were used. Since the relationship (VI-58) is identical to that obtained in Case 1, it was necessary only to perform the additional calculations employing equations (VI-60) and (VI-61). The predicted linear plots were again obtained, cf. Figures 18-30. It is not surprising that a plot of (T) vs. I; will be linear as well as a plot of (T) vs. the quantity (P) 1- ’1}, since (P) and (T) both increase prOportionately. The usual least squares procedure was utilized to obtain values for ,8”: and ¢EZL3 the point at zero time of irradiation was again weighted as one experimental point. The results are presented in Table XIII . [(E)0 - (E)] or (T) moles liter‘l x 105 3.2 300 2.8 2.6 2.1; 2.2 2.0 1.8 1.6 ‘ 1.h 1.2 1.0 0.8 0.6 O.h 0.2 179 I Figure 18 Kinetic Plots, Case of Non-Equivalent Optical and Derived Excited States 2537 1° IsoprOpy1 Alcohol Run III-10 I I I I I If, I I I I I I o - [(E)° - (E)J - ¢E IE 0 ' (T) ' ¢Pffr _- --1 N N IE or Ip moles liter"l x 105 [(E)° - (E)] or (T) moles liter-1 x 105 3.0 2.8 206 2.14 2.2 2.0 1.8 1.6 1.h 1.2 1.0 0.8 0.6 0.11 0.2 180 Figure 19 Kinetic Plots, Case of Noanquivalent Optical and Derived Excited States a 2537 A9 20% Glycerol Run III-1h I I I I I I I I I I I o-Imf-(mJatfi: — n - (T) = if ¢PTP @_ .7 _I IIIllIIlIII IE or T} moles liter"1 x 105 [(E)o - (E)] or (T) moles liter'l x 105 Figure 20 Kinetic Plots, case of Non-Equivalent Optical and Derived Excited States Run III-22 n-Hexane 2537 1° 3.0 2.8... 2.6-— 2.1I... 2.2 - 2.0... +4 F’ e: +4 F4 c: to :7 c» (n O CO 006‘ O.h 0.2 -0 02 l T I I I o - ((3)0- (EIJ - (IE’fE 0"113 ‘ IPEE; I II I I ~ r-I IE or IP moles liter'l-x 105 I 181 [(E)° - (E)] or (T) moles liter'1 x 105 3.0 2.8 2.6 2.h 2.2 2.0 1.8 1.6 l.h 1.2 1.0 0.8 0.6 O.h 10.2 Figure 21 Kinetic Plots, Case of Non-Equivalent Optical and Derived Excited States 2537 1° 20% Mineral 011 Run III-18 182 I _I I I I l I I I I I _ O- [(E)° - (3)] .. ‘I’ETE _ __ 0" (T) = (bPT’i/P G —I __ o _. _. o _. I—— O —I _ G .— a __ o _I II _. Q _—I — n —-4 0 fl __ 0 -a ‘5 I.“ I I I I I I I I I I I ‘ 1 2 3 II 5 IE or ”fP moles liter-1 x 105 [(E)° - (12)] or (T) moles liter‘l x 105 183 Figure 22 Kinetic Plots, Case of Non-Equivalent Optical and Derived Excited States 280).; A0 ISOprOpyl Alcohol Run II-lh J I I .I I I I I T I I I I I I 3" "" O - [(3)0 - (E)] '3 $3135; 0' (T) " IJTTT’P 3-14— 2 .8... 2.6— 2m- 2.0— 1.8- loéI— 1.1;— 1.2.- 1.0_ 9 008'- OeéI— u 0.2+. n [(E)° - (3)] or (.T) melee“1iter'1.x 105 II.o 3.8 3.6 3J4 3.2 3.0 2.8 2.6 2.h 2.2 2.0 1.8 1.6 1.11 1.2 1.0 0.8 0.6 0.1; 0.2 Kinetic Plots, Case of Non-Equivalent Optical and Derived . Figure 23 Excited States 18h 280h A0 20% Glycerol Run II-9 I I T I I I I | T l I I I o-I(E)°-(E)I-¢ETE , o“ U-(T)'¢PT’I} " O .1 ..I O O _I _I G G _1 I I l I I I I 8 10 12 1h TEOI'TP moles 11ter'1 x 105 [(E)° ~- (13)] or (T) moles liter-1 x 105 Figure 2h Kinetic Plots, Case of Non-Equivalent Optical and 185 Derived Excited States 280h A0 n-Hexane Run II-18 he)”. I I I I I I I F I I I _ o - [(3)0 - (E)I = ¢EEF h.2——- 3, .__ CI" (T) '3 (bPTIP h.O-—- __. 3.8-—— ./ 3.6w_. ._. 3.hw—— C) "‘ 3.2«—- “—r 3.0-—— "‘ 2.8w—- '- 2.6m_. .__ 2.hr- C) "‘ 2.2(— o — 2.0_ 9 — l.8__ —— 1.6m_. -—- loIl— Q '— 1.2__ o I-— 1.0___ a __i O.8_—- __. 0.6.... O n ‘—'I O.h-— .__ a 0.2. cc) __ of... I I I I I I I I I I I O 2 h 6 8 10 5)] or (T) )° - <'~ T1 41'. [( moles liter”l x 105 . J II“ I (“Ivan 2K. .. _h—L‘) ..L \J ’1 Kinetic Plots, Case of Non-Equivalent Optical and Derived Excited States 280T 1° 20% Mineral 011 Run II-2h h-0 3.8 3.6 3.h 3.2 3.0 2.8 2.6 2.u 2.2 2.0 1.8 1.6 1.1 1.2 1.0 0.8 0.6 O.h 0.2I I I I I I I I I II I o-I°-I=¢E“I’E G D ’ IT) ‘ ¢PTET I‘II’E 0r FIIP moles liter-1 x 105 I(E)° - (3)] or (T) moles liter'l x 105 Figure 26 O Kinetic Plots, Case of Noanquivalent Optical and 2967 1° Derived Excited States Isopropyl Alcohol Run II-6l 3-I-I— 3.2-— 3,ou_. i 2.8—. 2.h._. 2.2-_- 2.0... 1.8—- 1.61—- 1.0... 0.8— 0.6._. O.hI—- 0.2 I I I I I I o - [(E)°- (En = IETE D“ (T) = (pr’i/P I I4 , 6 SEE 01‘ fl: moles liter"l x 105 I I I 187 [(E)°- (E)J or (T) moles liter“1 x 105 Figure 27 188 Kinetic Plots, Case of NonsEquivalent Optical and Derived Excited States 2967 A0 20% Glycerol Run II-6II I I I I ’ I I I I I 3.8- o - [(EIO- (EII .. IETE _ 3.6— ‘3‘ (T) “ ¢PTIP lI 3.1I— o .— 3.2— ~— 3.0.—— -4 2.8II—— O __ 2.6-— -— 20L].— _— 2.2__ _ O 2.0_ __ 1.8— _I 1.6— 0 — 1.h__ __ 1.2... __ 1.0— O — 0.8— o ..__I 0.6._. C) ' .4 0.1“. a — I 0.2 a _. {I O I I I I I I I I I 2 II 6 8 10 TE or "1’? 1 moles liter- x 10 I°— (EII, (T), or (L) -1 x 105 moles liter II.II h.2 II.0 3.8 3.6 3-I-I 3.2 2.8 2.6 2.h 2.2 2.0 1.8 1.6 l.h 1.2 1.0 0.8 0.6 O.h 0.2 Figure 28 Kinetic Plots, Case of Non-Equivalent Optical and Derived Excited Statessa, Run 11'53967 2967 A0 n“ Hexane I I ,I T I I I- o - [(E)°-(E)I - IE’i’E I.. I _ - o 4 I3 ‘ (T) ' ¢PTTP — ° ~ —'I A‘ (L) " I)ELIE V ' “A r— -—I o —I I— e r— 0 ~—- -fi 1. o _I I-—- —I I. _I 0 -fi 0 —- —T L— o. -— A u — n A A —I n n A A a _— ¢"l £3 a A P '1 I" ‘* AI I 1 I I I I I I 2 I4 6 8 10 it or i; moles liter‘l x 105 189 [(E)°-(E)] or (T) moles liter"1 x 105 3.8 3.6 3oII 3.2 3.0 2.8 2.6 2.h 2.2 2.0 1.8 1.0 0.8 0.6 O.h 0.2 190 Figure 29 Kinetic Plots, Case of N0n~Equivalent Optical and and Derived Excited States 2967 II° 2035 Mineral 0:11 Run II-=67 II I I I I I I II 0 w [(E)0 * (E)1 3 TE ‘1 U " (T) a ¢PTTP / _. I j —-I TE 01‘ If}; moles liter‘l x 1.05 I(E)°- (8)1 or (11) moles liter"1 3: 105 2.8 Figure 30 Kinetic Plots, Case of Non-Equivalent Optical and Derived Excited States 2967 1° 1401 Mineral 011 Run 11-70 I j I I I I I I I 3.6— ° " [(EIO‘ (3)] " Isis —‘ s-u— TIT-In?» a 302 3 .01 2.1; 2.2 2.0 0.6 . 0.1; 0.2 TE or’I’P moles liter” x 105 191 192 TABLE XXII \ RESULTS OF THE KINETIC TREATMENT, NON-EWIVAIMT EXCITED STATE~ Visc . ' . Wavelength 1 098 . 2527 11° 2801; 11° #2961 1° . Solvent 25 C. ¢PT 03 0P1! TE 0P1! IPEL n-Hexane 0.301; 0.51.; O .31 0 .38 0 .21; 0.111 0.19 0.06 20$ Min. 011.1 0.561 0.51 0.32 0.33 0.21 0.36 0.22 -- 140% Min . Oil 1 .192 ' . -- -- -- -- 0 .140 0 .21; ~- i-I’r. Alcohol 2.068 0.1;9 0.35 0.27 0.23 0.38 0.21; -- 20$ Glycerol 7.135 0.1;8 0.36 0.25 0.19 0.35 0.26 -- Application of equation (VI-61) to the data at 2801; A0 in n-hexane was not successful; lumisterol was not formed in sufficiently significant quantities. It is apparent that the values of ‘I’PT obtained by the above treatment differ appreciably from the values of the equivalent quantity, 0?, obtained for the case of the equivalent excited states. The significance of these differences will be discussed in detail in the next section. 193 VIII. INTERPRETATION OF KINETIC REULTS It is evident from the typical plots of Figure 17 that the kinetic expressions derived on the basis of the equivalence of Optical and derived excited states fit the kinetic data rather well. The values for 03 are in approximate agreement with the quantum yield of calciferol formation based on bioassay results. The quantities 0p and kB/k‘ appear to have values of reasonable magnitude, [and the values of the two quanti- ties are internally consistent. In general, the results yielded by the kinetic treatment based on equivalent optical and derived excited states appear to be capable of reasonable interpretation. Attempts to extend the first kinetic treatment--expression (VI~21I)-- to the case in which lumisterol was formed were unsuccessful. In addition, an important discrepancy existed between the values of III}; derived from the kinetic treatment and the result reported by Havinga's group for the value of the quantum yield for the process 1’ ——> T (33). They reported a value of 0.1; for the conversion of precalciferol to tachysterol; this value was; obtained by direct irradiation of precalciferol at 2537 A0 in ethanol. A value comparable to Havinga's result derived from the kinetic treatment of this study is the value 01"pr at 2537 11° in isoprOpyl alcohol; this value of (IF is about one-half of the reported quantum yield, cf. Table III. 0n the basis of the mechanism formlated by expression (VI-21;), a' value of 0.1) for (I? would mean that the build up of tachysterol should be almost as great as that of precalciferol. It is evident from a 1914 qualitative inspection of the concentration-time data, of. Figures l1;a-l to 1110-5, that precalciferol is present in mch larger quantities than tachysterol. Proceeding on the assumption that the value reported by Havinga's group is correct, and considering the resultant deduction with regard to tachysterol build up, one comes to the conclusion that pre- calciferol in its normal ground electronic state is a necessary inter- mediate for the formation of tachysterol by the irradiation of ergosterol. In effect , the data indicate that tachysterol is derived from the irradi- ation of precalciferol that is formed in the irradiation mixture. In order to resolve the discrepancy in quantum yields, the mechanism was modified to incorporate the inference that normal precalciferol is a necessary intermediate in the formation of tachysterol, of. expression (VI-62). The kinetic equations. derived from expression (VI-62) fit the data equally as well as the equations derived from mechanism (VI-211), as is evident from Figures 17-30. The value of 0.36 for (In at 2537 1° in isOprOpyl alcohol (Table XIII) is in good agreement with Havinga's value of 0.1; for the quantum yield of the process P -—> T. The quantum yield 03 is calculated from the same kinetic expression~-equations (VI-39, VI-58)--for both reaction mechanisms, and, as previously stated, the values of 03 are in accord with other reported data. In addition reaction scheme (VI-62) was capable of extension to yield a value for On; it should be noted that other reaction sequences, in which lumisterol was derived from precalciferol or tachysterol, were not consistent with the data. 195 In general, the kinetic relationships derived from the case termed non-equivalent optical and derived excited states satisfy the data of this investigation, and are in accord with data reported by other . investigators. The combined results of the two reaction'mechanisms“ in particular, the apparent requirement that normal precalciferol is a necessary intermediate in the formation of tachysterol--suggest that the optical excited states of the irradiation products are not identical to the reactive intermediates that are derived through internal rotational movements of the segments of the Optically excited ergosterol molecule. Several qualitative conclusions regarding solvent and wavelength dependence are apparent from the results of the kinetic treatment, cf. Table 11111. As previously discussed, the solvent dependence may be attributed in large measure to a viscosity effect while the wavelength dependence is distinct from an inner filter effect. The obvious and important conclusion regarding the formation of lumisterol only in a solvent of low viscosity has been discussed in Section V. The effects of viscosity on 03 and ¢PT are fairly consistent, but quite small. The values of 03 and ¢PT are considered to be reliable to i' 10%, estimating that the actinometric data are accurate to i 10% and the analytical (results are reliable to i 5%. In general, the differences among the values of 03 and 0m. in different solvents and at a given wave- length are only slightly greater than the estimated limits of reliability. However, the fairly consistent variance of 03 and ¢PT with viscosity suggests that the small viscosity effects are real. The quantum yield 03 196 decreases with increasing solvent viscosity in a consistent manner at 2537 and 2801; 1°. The results exhibit some irregularity at 2967 1°, but even at this wavelength, the results do establish the stated trend of variance of 133 with viscosity. The value of ¢PT varies directly as the solvent viscosity at each irradiating wavelength. A rather marked wavelength dependence is shown by both ()3 and 01.7. For a given solvent, 03 and ¢PT are appreciably larger at the short wave- length (2537 A0) than at the longer wavelengths (28014 and 2967 1°). There is some discrepancy in the wavelength dependence exhibited at 2801) A0, since the values of TE and 0m. are slightly larger (in most solvents) at 2801; A0 than at 2967 110. However, as a result of the experimental con- ditions employed, errors in the values at 2801.; A0 are considered to be somewhat greater than the results obtained at 2537 and 2967 A0. A larger slit width (2.00 mm.) was employed in irradiations at 2801; 1° than at 2537 and 2967 A0 (1.50 mm.). Consequently, the band width was greater and approximations introduced into the treatment of the actinometric data are of more limited validity. Examples of the approximations are the assunption of a triangular slit function and the utilization of average molar absorbancies over the band width. In addition, the larger slitwidth resulted in a stronger incident beam and the reaction proceeded more rapidly with the possible formation of over-irradiation products. The non-linearity of response of the photomltiplier tube was also greatest at 2801; A0 because of the relatively high incident intensity and lack of screening of the photomultiplier, (of. experimental section). 197 In any event, the wavelength effect on 03 and II)“- is quite marked and indicates that the energies of the quanta absorbed play an important role in the isomerization reaction. It was possible to obtain a value of 03L only at 2967 1°, and the concentration-time data (Tables IVIIa-IVIIc) indicate that lumisterol is formed in significant quantities only when the wavelength of irradiation is greater than about 2800 A0. The value of I’m. cannot be considered determined with any degree of precision; however, the appearance of significant amounts of lumisterol only in the least viscous solvent suggests that (In is strongly viscosity dependent and favored by low vis- cosity. The appearance of lumisterol only at the longer wavelengths suggests further that IJEL is wavelength dependent, but, because of the lack of precision in determination of lumisterol at low concentraticn, it is likely that lumisterol builds up to a low concentration at other wavelengths but is only clearly distinguishable from experimental error where the level of build-up is sufficiently high. The very low molar absorbancy of lumisterol relative to ergosterol and other components at 2967 ‘0 probably permits its build-up there to a detectable concentration under the most favorable conditions of low viscosity. It remains now to present a description of the photochemical iso- merization, using the concepts presented as a basis for the kinetic derivation, that is consistent with conclusions drawn above. As suggested in Section VI, a contributing type of reaction step may be pictured as a cross-over from the potential energy surface of an excited state of a precursor to a potential energy surface of some state of the given product. 198 Ergosterol and its irradiation products may be regarded as minima in the multi-dimensional potential energy hyper-surface Of the ground states of the system. The relative energies of the minima in the potential energy diagram nust, of course, be drawn arbitrarily, but it seems reasonable that the energies of lumisterol and ergosterol should be approximately equal, while that of precalciferol should be slightly higher, because Of the substitution of one fr-bond for one Osbond (even though the o=bond was weakened by steric repulsions), and because of the fact that steric repulsions do not permit conjugation of the added fl-bond of precalciferol with the other two ff-bonds. Tachysterol is probably the component of lowest energy, based on its extended trans configuration, which minimizes steric repulsions and permits conjugation Of the entire fI-network of three double bonds. Similar considerations apply to the Optical excited states and suggest that excited precalciferol, with the 05-010 double bond present in most of its contributing structures, but not conjugated with the excited ff-network, is higher in energy than excited ergosterol, which has contributing structures with the Cg-C10 single bond or with two conjugated double bonds (see Figure 16). Because of the complex nature of the reaction, it seems to be im- possible to represent the important transformations by means Of a single reaction coordinate. The transformations of ergosterol to precalciferol and lumisterol can, however, be described in terms of a single coordinate, which is essentially the angle of rotation about the bond 05-06. The subsequent transformation of precalciferol to tachysterol cannot be 199 pictured through a simple coordinate, since this step involves rotation about the bonds C5-Cg and 03-07. In Figure 31 an attempt is made to represent the energetic relation- ships. The solid curve in Figure 31a shows potential energ vs. rotation about the bond C5-Cg for ground state ergosterol and lumisterol as repre- sented by their valence bond structures shown in Figure 1; since the rotation is about a double bond and requires rupture of the 09-010 bond, this motion is strongly unfavorable for these structures. The solid curve in Figure 31b shows the corresponding potential energy relationship for precalciferol, as represented by its valence bond structure shown in Figure 1. Here a double minimm appears, with a barrier too low to permit isolation Of the two separate forms (perhaps 5-10 K..cal./mole),3 the two minima correSpond to the structures that would be Obtained directly by rupture of the 09-010 bond and slight rotation from ergosterol and lumisterol, respectively. The positions corresponding to ergosterol and lumisterol are marked on the diagram. One dashed curve in Figure 310 is an attempt to represent the potential energ of the species E* Obtained by Optical excitation Of ergosterol; its valence bond structure is assumed to be a‘composite of those shown in Figure 16. The other dashed curve in Figure 310 is a similar representation Of P*, the Optically excited state of precalciferol; its valence bond structure is assumed to, be a composite of corresponding ionic structures obtained from precalciferol, but with the 05-09 double bond preserved and the excitation involving only the conjugated electrons in the Opened ring B. Figure 31a. Potential Energy Curves, 200 E and L V E L I I ' I l J I E L Angle of Rotation about 05-03 Bond Figure 31b. Potential Energy Ourves, P V l I l I l I I I I I -—I:— i" 1 Angle of Rotation About Cs-Ce -- Figure 310. Potential fibergy Qirves-m “E, P. L, E and P \ \ .’ "I / I _1 E P A E P 7 P L Angle of Rotation’About 05-06 ' 201 Figure 31d. Potential Energy curves, r, T, P? and T* 202 Figure 310 is the composite energy diagram, including all the states shown in Figures 31a and 31b. Also shown is a vertical line correspond- ing to optical excitation of ergosterol and another correSponding to Optical excitation of precalciferol. It is apparent that excited ergosterol could cross over to give normal precalciferol (in a vibrationally excited level of the. ground electronic state). However, in a viscous medium the necessary rotational motion would be impeded (the rotational diffusion constant varies inversely with viscosity--Stokes-Einstein Law), and this would enhance the possibility Of collisional or fluorescent deactivation to the ground state of ergosterol. Thus (I13, the fraction Of 15* going to products, would be expected to vary roughly inversely with viscosity, as observed. It is possible that some of the excited ergosterol continues past the cross-over and is later deactivated to precalciferol or even to lumis- terol. The latter possibility requires considerable motion of bulky parts of the molecule against the viscous resistance of the solvent, so is feasible only in solvents of particularly low viscosity. The wavelength effect is not apparent from the diagram, since the excess energy of shorter wavelength may go into other vibrational modes. Since this excess vibrational energy does redistribute, before it is removed by collisions, some Of it may help with the motion required to form precalciferol and lumisterol. The increase of 03 at shorter wave- length bears this out. However, M was found significant only at the longest wavelength; it is felt that this is an artifice caused by (e) the impossibility of detecting with certainty low concentrations of lumisterol, 203 which made it unfeasible to include, in the mechanism, steps related to the subsequent fate of lumisterol, and (b) the aforementioned spectrum of lumisterol, which would permit its build-up much more strongly at the longest wavelength. Thus ¢EL prObabLy increases somewhat with decreasing wavelength, but the concentration of Lumisterol did not build up to detectable amounts in.the kinetic study because of its many times more rapid consumption at shorter wavelengths. From this diagram, it looks as though excitation of precalciferol should lead to ergosterol and lumisterol. This prdbably occurs to a small extent (Havinga.(3b) reported some ergosterol formed upon irradiation of precalciferol, with nearly quantitative formation of tachysterol), but return to precalciferol is relatively'more favorable here than was return to ergosterol after absorption of light by ergosterol. More important, an alternative reaction coordinate is available for excited precalciferol involving successive or simultaneous rotation about the 05-06 and 03—67 bonds to form tachysterol. The relationship between precalciferol and tachysterol is shown schematically in Figure 31d. Here, again, ground states are shown by solid curves and excited states by dashed curves. The figure shows how, for that fraction of the excited precalciferol which executes motion along this combinational coordinate, formation of tachysterol (fipr) is very favorable and favored by an increase of viscosity, Since deactivation over a large portion of the motion will lead prefer- entially to tachysterol rather than back to precalciferol. The wavelength dependence, again, can not be illustrated, but excess energy should make Excitation of the combined rotations relatively more favorable than the 20h simple rotation about the 05-06 bond, and should lead to increased quantum yield of tachysterol at shorter wavelengths, as Observed. There is, however, an alternative explanation of the results which must be given serious consideration. It has been clearly'demenstrated that there is a wavelength dependence apart from the inner filter effect , and also a solvent effect which may now definitely be said to be associated with viscosity. The mechanistic interpretation ascribes the wavelength dependence to the usefulness of excess energy per quantum in contributing to the isomerizations, and attributes the viscosity effect to a viscous barrier to the internal rotation necessary at the molecular level for the isomerizations. Both conCIusions are based upon the assumption of homOgeneity of the solution in the irradiation cell, which has been aided in these experiments by stirring and by the use of dilute solutions in thicker cells to give a diminished gradient of light intensity through the cell. If it be now assumed that the effect of viscosity is on bulk diffusion within the cell, and that there is a measurably greater probability of absorption of a quantum of light by'a molecule which has just been formed in an absorption act, the apportionment of the total light absorption among the absorbing species will be altered, but the spectrophotometrically determined concentrations of the individual species will.be unaffected. Starting with a uniform distribution of ergosterol in the cell, the initial absorption act will create some precalciferol and, perhaps, some lumisterol. These species as formed will be nonruniformly'distributed, each with a concentration gradient through the cell paralleling the incident intensity 205 gradient, with a preponderance in the front portion of the cell where the radiation intensity is greatest. This natural "orienting" influence of the incident intensity gradient will be in competition with the disorienting effects of diffusion and stirring, which will tend towards re-establishing a uniform concen- tration distribution. The effect of viscosity will be upon the disorient- ing effects, with diffusion coefficients varying inversely with bulk viscosity, and a higher viscosity favoring a laminar flow upon stirring, providing relatively little mixing. The resultant concentration gradients will reflect the outcome of the competition between the orienting and dis- orienting factors, and will clearly be the greater the more viscous the solvent medium--although with adequate stirring they may prove negligible throughout the viscosity range employed. If some concentration gradient remains, an apportionment of the absorbed light intensity at the next stage of the irradiation based on uniform concentrations throughout the cell will then ascribe too much absorption to ergosterol and not enough to precalciferol and lumisterol. As tachysterol.builds up through conversion of precalciferol, it will, to even a greater extent (because of both light intensity and precalciferol concentration gradients), be concentrated in the front portion of the cell. The calculated quantum yields according to equations (VI-58) and (VI-60) were given.by ¢E .. car’- (E) t fAEIadt O 206 and (T) t - f APIadt. o t t Here I AEIadt represents the light absorbed by ergosterol and APIadt represents the light absorbed by precalciferol, each during the time interval from t - O to t - t. But the calculated in AEIadt will be too large and the calculated 3: ATIadt will be too small, based on uniform concentration distribution. Hence the calculated value of ¢E will tend to be smaller than the correct value, and the calculated value of ¢PT will, tend to be larger than the correct value. The effect of viscosity will be toenhance the discrepancies, so that (PE will apparently tend to decrease and ¢PT will tend to increase with increasing viscosity; this prediction proves to be consistent with the experimental results. The appearance of significant amounts of lumisterol only at the longest wavelength and in the least viscous solvent is also consistent with this type of viscosity effect, since lumisterol, whether it be formed from ergosterol or precalciferol, will tend to be formed primarily in the most intense portion of the beam where it will be readily converted to products (probably precalciferol), unless it is removed to a less intense portion of the beam, as at lower viscosity, or unless its light absorption is relatively low, as at the longest wavelengths used. Fortunately the experimental data make it possible to choose between these two explanations. In the kinetic runs the absorbed light intensity varied between 3 and 15 x 101‘ quanta per minute in the irradiation cell. 207 The sample concentration in the 3 ml. irradiation cell ranged from S.h to 6.1 x 10‘5 moles/liter, which means there were about 1017molecules in.the irradiation cell. A given molecule would, on the average, be "hit“ with one quantum everywig-%g%%1§ min. or about 67 minutes or hOOO sec.- The probability of a given molecule absorbing a quantum of light in one second is-E%663 the prObability of a given molecule capturing two quanta in one second is (3%55)f ‘With stirring, the mixing time is of the order of one or two seconds, as observed by allowing a drop of dye to fall into the stirred solution. Even making allowance for the fact that the beam of light occupies only about 20$ of the volume of the solution in the cell, and allowing for the fact that the incident intensity in the front part of the cell is approximately double the value at the back, it seems necessary to rule out the possibility of reabsorption as a source of the observed viscosity dependence. A mechanistic interpretation thus appears justified. The interpretation in terms of a potential energy diagram is necessarily highly speculative at this state of our knowledge. However, it provides a framework for discussion of the mechanism of a reaction of this type, clearly involving electronically excited species, and it suggests the types of further information which we must obtain to gain additional insight into the behaviour of excited molecules and into the detailed mechanism of ergosterol irradiation. The speculative nature of some of the discussions must not be per- mitted to obscure certain more clearly defined conclusions from this study. First, it has been found possible to devise a purely" 208 spectrophotometric procedure giving reasonably accurate analysis of the ergosterol irradiation mixture. Second, there is clearly a wavelength dependence apart from inner filter effects. The wavelength dependence appears to indicate a usefulness of the excess energy per quantum in producing the isomerizations. Third, the solvent effect is primarily associated with viscosity; the effect almost certainly'can.be attributed to viscous resistance to rotational diffusion associated with certain internal rotations necessary to the isomerization. Fourth, the optical excited state of ergosterol must differ from that of precalciferol. Fifth, the position of lumisterol in the reaction sequence is most prob- ably as an alternative product to precalciferol resulting from excited ergosterol. 209 II. SUGGESTIONS FOR FURTHER WORK The present study, with its definite indications of viscosity and wavelength effects, points the way towards further related studies. The other components in the photochemical sequence--precalciferol, tachysterol, and lumisterol-~should be irradiated directly at several wavelengths and in several solvents. The irradiation of precalciferol in alcohol at 253? A? has been reported by Havinga's group, and their results have been very important in the development of the kinetic treat- ment of this thesis. In order to further establish the viscosity effect on the precalciferol irradiation step (on ¢PT) irradiation of precalciferol should be conducted as a function of solvent viscosity. It is possible that significant formationof ergosterol and lumisterol might be observed at lower viscosity and at longer wavelengths. In this investigation it was assumed that neither lumisterol nor tachysterol underwent further reaction in the irradiation mixture. The agreement of the data with the kinetic expressions indicates that mrther reaction of these components (including the reverse reactions to form their precursors) can occur only to a minor extent. However, both lumisterol and tachysterol were present in only small amounts and their irradiation products would not have been.perceptible. It is necessary to establish the fate of irradiated lumisterol and tachysterol for a more complete understanding of the reacticn. An inspection of the structures of ergosterol, lumisterol, and pre- calciferol suggests a question: are there two forms of precalciferol 210 differing in the relative orientation of the hydroxyl group on carbon-3 in the A ring? One of the suggested forms would be derived from ergosterol while the other would be formed from lumisterol. It has been assumed that the two forms are not separable. The irradiation of lumis- terol would help answer such a question. In order to more effectively utilize the available information on the ergosterol irradiation reaction, the energy relationships among the components of the irradiation sequence are required in.both the ground and excited states. Poseible studies that would contribute to this end are fluorescence and phosphorescence studies, very accurate determination of heats of combustion of the compounds, and a suggested study which may be termed "photothermochemistry." In the latter study a calorimetric measurement would be made of the fraction of absorbed radiant energy that is not utilized in.the photochemical reaction and is dissipated as heat energy. The calorimetric data would be combined with determinations of the total radiation absorbed and quantum yields to furnish information on the differences in energy among the components of the irradiation mixture. This more direct measurement of energr differences could, like heats of hydrogenation, circumvent the problem of small differences in large quantities which makes heat of combustion data impracticable here. In order to extend the usefulness of the computational analytical method, it is suggested that the matrix procedure be reformulated so that the stoichiometric relationship among the components is not utilized. The reformulation would involve the inversion of a S x 5 matrix rather than a h x h matrix. The resultant expression would enable the 211 calculation of the ergosterol concentration directly rather than by' difference, and the analytical method could be applied to any mixture which contained the components of the irradiation sequence along with spectroscopically inert materials. Still an alternative procedure would be a similar treatment of the four-component mixture of ergosterol, lumisterol, tachysterol, and precalciferol. Elimination of calciferol appears entirely justified where the analysis is to be applied to irradiation mixtures, since calciferol is formed only in the subsequent thermal rearrangement. A complete kinetic study of the thermal conversion of precalciferol to calciferol should be made, with study of the influence of medium to attempt to ascertain whether a hydrogen atom or proton is transferred. 212 X. SUMMARY A kinetic study has been made of the photochemical isomerization of ergosterol in several solvents-~isopr0pyl alcohol, 20% glycerol in iso- prOpyl alcohol, n—hexane, 20% mineral oil in nrhexane, and no; mineral oil in n-hexane--and employing three irradiating wavelengths (2537, 280h and 2967 11°)- In order to carry out this study, an analytical curve-fitting technique, the least squares matrix method, was applied to the ultraviolet absorption spectra of the mixture obtained upon irradiation of ergosterol. The method provided a rapid analysis of the complex mixture, and the components were determined within an average standard deviation of i h% in the weight percent of component. The analytical procedure was applied to the ultraviolet spectrum of the irradiation mixture, which was determined periodically during the irradiation; the concentration of each of the components was.obtained as a function of time of irradiation. The analytical procedure was verified by application to synthetic mixtures of known compo- sition? and in addition, the procedure was also applied to the spectral data of irradiated ergosterol solutions that were reported by Sharpe (37) in order to verify the applicability of the method to actual irradiation nuxtures. For the kinetic studies, a.novel recording photometric apparatus was develOped to continuously monitor the radiation absorbed by the solution undergoing irradiation. 213 A kinetic mechanism which could be expressed in general and specific forms was formulated, based upon stereochemical information, consider- ations of the excited states of the components of the irradiation mixture, and qualitative interpretation of the concentration-time data. The most general plausible mechanism led to relationships in which the concen- trations of the components were expressed as linear combinations of terms consisting of definite integrals representing the amounts of radiation absorbed by individual components during the given irradiation interval. The particular mechanism best capable of describing the experimental results was found to be l P -EX->’ P* ———>’T <—'—- where E, P, T, and L represent ergosterol, precalciferol, tachysterol, and lumisterol, respectively, and E* and P* represent optically accessible electronic excited states of ergosterol and precalciferol, respectively. This mechanism reduced the relationships to the simple linear expressions (VI-58,60,61) which could be compared with the experimental data (E)O'(E) ' ¢E ii (a) - 4)“ ’1', (VI-58,60,61) (L) " ¢EL In The kinetic treatment yielded values for quantum yields for the ”over-all. conversion of ergosterol ($3), the conversion of ergosterol to 21h lumisterol ((EL)’ and the conversion of precalciferol to tachysterol (¢PT). The kinetic runs were carried out in solvents with a range of viscosity, but fixed chemical nature, in a stirred reaction cell, so that any solvent effect may be ascribed to viscosity. The use of the integrated light absorption data in the kinetic treatment corrects for the inner filter effect, so that any Observed wavelength dependence must be ascribed to other factors. The kinetic analysis disclosed both a solvent and wavelength dependence (the latter beyond inner filter effects) on the individual reaction steps of the photochemical isomerization. The values Obtained are given in Table XXII. TABLE.IXII RESULTS OF THE KINETIC TREATMENT, NON-EQUIVALENT EXCITED STATES V' wavelength 180. o o o Cps. 2337 A__ 280i; A 2967 A Solvent 25°C. 03 @pT PE ¢PT TE @FT OEL n-Hexane 0 .301; 0 .514 0 .31 0 .38 0 .21; 0 .hl 0 .19 0.06 20$ Min. Oil 0.561 0.51 0.32 0.33 0.21 0.36 0.22 “- uoz Min. Oil 1.192 -- -- -- -- 0.10 0.2).; -- irPr. Alcohol 2.068 0.h9 0.35 0.27 0.23 0.38 0.2h -' 20% Glycerol 7.135 0.h8 0.36 0.25 0.19 0.35 0.26 -- The values of 0E are in qualitative agreement with the quantum;yield of calciferol formation as inferred from'bioassay results. In addition the value of ¢PT is in good agreement with the quantum yield for the conversion of precalciferol to tachysterol determined by Havinga and his associates (33)- 215 by the direct irradiation of precalciferol at 2537 A0 in ethanol. These results further substantiate the validity of the analytical scheme as applied to the actual irradiation mixtures. The quantum yield values obtained show individual variations with both wavelength and solvent. ¢E shows a definite trend of decreasing with increasing viscosity and with increasing wavelength. ¢PT also displays a trend towards lower values at longer wavelength, but shows a viscosity dependence in Opposite direction to that Observed for 0E. *EL could be determined only in the least viscous solvent and at the longest wavelength; the value of this quantum yield is believed to be strongly viscosity dependent, but the wavelength dependence is prObably an artifice associated with the low absorptivity of lumisterol at that wavelength. The data thus far accumulated on the ergosterol irradiation reaction are not yet adequate to permit a complete description of the process. However, the new quantum yield data as functions of viscosity and wave- length, coupled with the recent results of the Havinga group, suggest a.new framework for describing the behaviour of the system and point to certain information which would be particularly pertinent for extending our knowledge further. The photoinitiation of the reaction may be considered as proceeding through the Optically accessible singlet excited state of ergosterol. This excited state, which may be pictured as either ionic or diradical, almost surely has some major contributing structures with no bond between Cg and 310: and, accordingly, has an appreciably reduced barrier to 216 rupture of this bond and rotation about the cg-C, bond as compared with ground state ergosterol. The excited ergosterol molecule could undergo rearrangement to another structure or collisional or fluorescent deacti- vation to normal ergosterol. The motion required for formation of the prOposed precalciferol structure (see figure 1), constitutes an internal rotation, and would be governedby the viscosityhcontrolled rotaticnal diffusion constant, so that viscosity of the medium should influence the possible fate of the excited ergosterol molecule. A small fraction of the excited ergosterol may, particularly in media of low viscosity, undergo a more extensive rotation to form lumisterol. 1116 motions have been conveniently pictured in terms of a potential energy diagram. Precalciferol which has been formed from excited ergosterol is it- self capable of absorbing light and going-to an excited structure. The quantum yield data of Havinga on the conversion of precalciferol to tachysterol are incompatible with the possibility that the excited states of ergosterol and precalciferol are the same, and a consideration of the important contributing structures suggests the nature of the difference. The excited precalciferol has two principal modes Of motion accessible, one leading primarily back to precalciferol, the other to tachysterol. “Higher viscosity favors the path to tachysterol. In both photochemical steps ,‘ the excess energ available at shorter irradiating wavelengths is useful in promoting the isomerizations . Considerable further information is needed before our understanding of the mechanism is couplets. It is particularly desirable to study 217 irradiation of each of the intermediates with respect to wavelength and solvent effects. Any information leading to a clearer picture Of the relative energies Of states Of the isomers would also be very valuable. 218 LITERATURE CITED (1) Alder, K., and Schumacher, M. Fortschr. Chem. Org. Naturstoffe, 19. l (1953)- (2) Barton, D. H. R., and Kende, A. S. J. Chem. Soc., 688 (1958). (3) Bosart, L. w., and Snoddy, A. o. Ind. Eng. Chem., 39, 1377 (1928). (1.) Braude, E. A., and Wheeler, 0. H. J. Chem. Soc., 320 (1955). (5) Brockman, E., and Schodder, H. sex-.8, 1g, 73 (191.1). (6) Buchi, G., and Yang, N. c. J. Am. Chem. Soc., 12, 2318 (1957). (7) Calvert, J. G., and, Rechen, H. L. J. Am. Chem. Soc., .711: 2101 (1952). (8) Crombie, L. Quart. Revs., _6_', 101 (1952). (9) Crowfoot, D. E., and Dunitz, J. D. Nature, 18g, 608 (19118). (10) DaSler, W. Ph. D. Thesis, University Of Wisconsin, 1938. , (11) Dauben, W. G., Bell, I., Hutton, T. 11., Laws, 6. F., Rheiner, A. Jr., and Urscheler, H. ".J. Am.. Chem. Soc., 82, 11116 (1958). (12) Dwyer, P. S. Annals ‘Of Math. Stat., 15, 82 (191111). (13) Forbes, G. 3., and Heidt, L. ‘J. J. Am. Chem. Soc., 59,2363 (19311). (111) Frost, A. A., and Pearson, R. G. "Kinetics and Mechanism," John Wiley 6: Sons, Inc., New York,-l953. - (15) Grundmann, W. Z. Physiol. Chem” 222, 151 (1936). (16) Hamans, R. 31., and Steenbock, H. Ind. Eng. Chem. Anal. Ed., 8, (17) Harris, L., Kaminsky, J., and Simard, R. G. J. Am. Chem. Soc., 21, 1151. 1151: 0935)- ' - (18) Havinga, E., and Bots, J. P. L. Rec. trav. chim. Pays-Bas, I}, 393 (1951;). (19) Havinga, E., Koevoet, A. L., and Verloop, A. Ibid., 111, 1230 (1955). 2'19 (20) Havinga, E., Verloop, 1., and Hoevoet, A. 1.. £18., 15, 371 (1956). (2121(Iulgzr, H., Ewing, G. H., and Kriger, J. J. Am. (hem. Soc., _61, 609 (22) Inhoffen, H. H. Intertwine. 1.3, 396 (1956). (23) Inhoffen, H. H. Ber., _8_2, 2273 (1956). (21;) Inhoffen, H. H., Bruckner, H., Grundel, H., and minkert, G. Ber., _1, 11107, 11418 (19511)- (25) Inhggen, H. H., Bruckner, H., and Irmscher, K. Ibid., _8_§, 111211 ' 19 . . (26) Inhoffen, H. H., and Bruckner, I. Fortschr. Chem. Org. Haturstoffe, 11: 33 (19511)- (27) Koevoet, A. L., Verloop, A., and Havinga, 3. Bee. trav. chin. Pays-Baa, 11b 788 (1955)- (28) Lyness, w. 1., aninackenbush, r. w. Anal. 016111., g1, 1978 (1955). (29) War, r. J., Boborgh, J. H., Down, '13:. J., Kenning, x. J., and Hanewald, x. Rec. trav. chin. Pays-Bee, 16.: 733 (1957). (30) Murdock, D. 0., "Linear Algebra fer Undergraduates ,' John Wiley 8: Sons, Inc., New York, 1957, pp. 60-61. (31) Hield, c. H., mase1,'w.c., and zinerli, A. J. Biol. Chem, llé. 73 (19110). (32) Noyes, H. A. Jr., and Leighton, P. A. "The Photochemistry of Gases,“ Reinhold Publishing Corp., new York, 1911, p. 152. (33) Rappoldt, H. 2., Buisman, J. A. H., and Havinga, E. Rec. trav. chm' M'B‘a: 11: 327 (1958.). (31.) Rappoldt, H. P., Hesterhof, r. Hanewald, x. H., and Buisnan, J. A. x. _l_1_>__id., 11, 21.1 (19585. (35) Scarborough, J. 3. "Numerical Mathematical Analysis," The Johns Hopkins Press, Baltimore, 1950, ..pp. 1169-1472. - (36) Sebrell, w. H. Jr., and Harris, S. (editors), “The Vitamins," Vol. II, The Academic Press, Inc. ., New York, 195b,. (37) Sharpe, L. H. .Ph. D. Thesis, Michigan State University, 1957. 220 (38) Sheely, M. 1.. Ind. Eng. Chem., _2_h, 1060 (1932). (39) Shaw, U3 H. C., Jefferies, J} P., and Holt, T. E. Analyst, 82, 2, 3 (1957)! (ho) Shaw, H4'H. C. Private Communication, 1958. (bl) Szwarc, M. J. Chem. Phys., 2;, 20h (1955). (hZ) Velluz, L., Amiard, G., and Petit, A. Bull. soc. chim. France, 1115 (191.8); 16. 501 (19.19). (113) Velluz, L., and Amiard, G.’ Ibid., 205 (1955). (1.1.) Velluz, L., Amiard,'0., and Coffinet, B. Ibid., 13111-41955). (16) Velluz, L., Amiard, G., and Goffinet‘, B.. Oompt. rend., 2110, 2076, 2156, 2326 (1955). (h6) Verloop, AA, Koevoet, A. L., and Havinga, E. Rec. trav. chim. Pays-Bas,‘1g, 1125 (1955). ' (h?) VerlOOp, A., Koevoet, A. L., and Havinga, E. Ibid., 6, 689 (1957). (h8)'westerhof, P., and Buisman, J} A. K. Ibid., 75, 12h3 (1956). (1.9) westerhor, 1)., and Buisman, J. A. K. Ibid., 6, 679 (1957). (50) Van de Vliervoet, J. L. J., Westerhof, P., Buisman, J. A. H., and Havinga, E. Ibid., 75, 1179 (1956). (51) Yates, R. Ph. D. Thesis, Michigan State University, 1952. (52) Zechmeister, L. "Progress in ChromatOgraphy l938-19h7,” John'Hiley'& Sons, Inc., New YOrk, 1951, p. 27. . (53) Handbook of Chemistry and Physics, Chemical Rubber Company, Cleveland, Ohio, l9h7. ‘ APPENDICES APPENDIX I CALIBRATION OF PHOTOMETER Average Value Of Scale Reading - T i 221 Average Value Of Ti and Extrapolated Value of?!(1 are in Parentheses. W Irrad. ._ s Time .1 Scale Reading______ Percent q/a x 10 1 Min . Solvent Solution Average Conversion quanta/ in . 3 Run III-9 2537 A0 r Slit'Width 1.50 mm. Cone. of Actinometer Compound h.951 x 104 Mblar 0 + 0 (1.h7) 5.5 6.05 0.17 3.11 0.5h 1.h7 11 -5 .96 0 .111 3 .05 1.08 l .118 Run III-h 2537 A° Slit'Width 1.59 mm. Cone. of Actinometer Compound 3.261 x 10 5 Molar- 0 0 (l.h2) s 6.00 ' 1020 3 060 110814 .101-Ll 10 , S .95 l .19 3 .57 9 .57 1.140 15 « 6.05 1.26 3.66 1h.25 1.39 Run 111-8 2537 A° Slit Width 1.50 mm. Cone. Of Actinometer Compound 1.989 x 10‘5 Molar O 0 1.h7 5.5 6.60 2.98 h.79 8.26 l.h5 11.5 6.55 3.08 _h.82 16.62 1.h3 17 .5 6 .50 3 .16 11.83 2h .50 1 .hl Run III-2 2537 A° Slit‘Width 1.50 mm. Cone. of Actinometer Comm 1.980 x 10"5 Molar 0 (h.62) 0 (1.52) 5 6.26 2.86 b.56 7.31 1.50 10.5 6.19 2.95 b.57 15.00 1.50 16 6.20 3.08 11.611 21.96 1.118 22.5 6.20 3.21 h.70 29.85 1.h6 Run III-6 2537 1° Slit Width 1.50 mm. Conc. of Actinometer Compound,9.902 x 1.0"6 Molar 0 , (5.30) O (1.53) S 6.36 14-13 5.21: 9-55 1-50 10.5 6.33 h.20 5.32 18.90 1.h5 16 6.26 11.26 5.26 27.50 1.112 21.5 6.31. 11.1.1 5.38 35.52 1.1.0 n-._.l..l..__ -.1 222 AE'FEI‘IDT 1. I .- (1",r1t1'n1md a ..-.-.. .DI'L’I- . . 4- 1,. ..«3 ..o-- —- v- m‘.‘—- ' II’Tad c “15 Time 1 _ Scale Reading Percent q/c x 10 Min. Solvent Solution Average Conversion quanta/in.2 Run III~7 2537 A° Slit Width 1.50 mm. Cone. of Actinometer Compound 9.902 x 10'6 Molar 0 (5.32) (1.61) 5 6.11 1.26 5.31 9.61 1.57 10 6.31 1.26 5.28 18.05 1.50 15.5 6.27 1.33 5.30 26.11 1.17 21 6.27 1.15 5.36 31.38 1.11 Run Il~36 2801 1° Slit Width 2.00 mm. Cone. Of Actinometer Compound 1.951 x 10" Molar 0 (3.02) 0 (2.82) 5.5 5.52 0.50 3.01 0.88 2.77 10.5 5.55 0.18 3.02 1.61 2.71 15.75 5.55 0.18 3.02 2.11 2.67 Run 11~35 2801 A° Slit'Width 2.00 mm. Conc. 0f Actinometer Compound3.961;;10"5 MOlar 0 (1.13) 0 (1.06) 5.5 5.10 2.91 1.16 7.81 3.92 10.0 5.10 2.86 1.13 13.27 3.68 15.5 5.37 2.81 1.10 19.50 3.19 23.5 5.37 2.87 1.12 28.53 3.38 Run 11-12 2801 A° Slit'Width 2.00 mm. Cone. Of Actinometer Compound 9.902 x 10"6 Molar 0 (1.92) 0 (5.81) 6.0 5.30 1.53 1.92 11.90 5.67 12.0 5.26 1.51 1.90 28.65 5.62 18.0 5.29 1.60 1.91 10.87 5.16 Run II~16 2967 A° Slit Width 1.50 mm. Conc. 0f Actinometer Compound 1.951 x 10“ Molar 0 (3.05) 0 (3.63) 6 6.81 0.16 3.16 1.60 3.18 12.5 6.89 0.18 3.18 3.38 3.51 19.5 6.80 0.20 3.10 1.88 3.26 Continued APPENDIX I - Continued 223 much. ---y-- -—: Irrad. - Time ‘__ Scale figgging Percent q/a x 10’15 Min. Solvent Solution Average Conversion quanta/in.2 Run II-19 2967 A° Slit Width 1.50 m. Conc. Of Actinometer Cogomd 3.261 x 10"5 Molar 0 . (5.73 0 (1.35) 8 7 .03 1.1.72 5 .875 10.19 3 .83 16 7.01 h.hh 5.725 18.07 3.2h 21 6.95 1.25 5.600 25.78 2.96 Run II-71 2967A° Slit Width 1.50 mm. 2 Cone. of Actinometer Cogound 2.261 x 10"5 Molar 0 (6.17) 0 (1.27) 6 ,7ch8 5.15 6.32 7.78 3.90 11 7.87 8.98 6.20 13.61 3.59 17 7 .35 1.67 6.01 20 .11 3 .30 Run II—75 2967 A° Slit Width 1.50 mm. Cone. of Actinometer 00mpound 1.980 x 10'” Molar o ' (6.62) o (1.71) 5 7514 6.27 6.90 7-78 ho35 10.5 7.21 5.89 6.56 111.52 3.70 16 7.23 5.81 6.52 20.87 3.h0 21.5 7.26 5.77 6.52 7 27.03 .3.18 ABSORBANCY OF IRRADIATED ERGOSTEROL SOLUTIONS APPENDIX II AT ANALYTICAL'NAVELENGTHS 221 Time, . wavelength,’ Min. 252 256 260 261 . 268* 272 276 *280 281 288 292 296, 2537 A0 IsoprOpyl Alcohol Run III-10 0 .259 .319 .137 .180 .580 .681 .580 .681 .651 .393 .391 .359 20 .266 .326 .139 .179 .575 .671 .572 .661 .635 .391 .383 .351 10 .275 .331 .111 .182 .575 .667 .570 .658 .630 .389 .382 .316 60 .281 .339 .113 .183 .571 .658 .567 .619 .622 .390 .378 .311 90 .290 .316 .119 .188 .571 .661 .570 .616 .617 .393 .379 .310 120 .302 .357 .161 .198‘ .583 .659 .576 .651 .615 .395 .383 336 185 .317 .376 .177 .515 .598 .671 .596 .663 .629 .115 .101 .356 215 .335 .395 .192 .530 .616 .682 .615 .680 .637 .113 .120 .368 305 .350 .113 .509 .553 .636 .705 .612 .710 .660 .167 .117 .382 365 .365 .129 .521 .571 .661 .725 .670 .710 .680 .197 .176 607 110 .371 .111 .533 .585 .677 .739 .689 .758 .691 .521 .196 .122 2537.A° Isopropy1.Alcohol Run 111-2; 0 .255 .311 .128 677 .568 .681 .579 .668 .659 .101 .381 .363 20 .261 .316 .129 .173 .563 .661 .570 .611 .610 .391 .377 .952 10 .270 .326 .135 .180 .566 .669 .575 -65h .639 .398 -379 ~35? 60 .281 .335 .113 .186 .569 .666 .575 616 .637 .100 .379 .356‘ 90 .290 .317 .119 .192 .575 .669 .578 .650 .631 .102 .381 .352 120 .295 .352 .153 .195 .571 663 .578 615 .621 .103 .382 .350 180 .310 .369 .169 .508 .588 7.671 .591 .653 .635 .119 .396 .358 210 .325 .386 .186 .531 .609 .610 .619 .679 .656 .118 .119 .378 330 .313 .106 .500 .550 .630 .705 ,615 706 .669 .185 653 .100 120 .371 .136 .531 .583 .668 .739 .690 .755 .710— .526 695 .131 2537 A° n-Hexane Run III-22 0 .212 .263 .366 .393 .192 .561 .173 .578 .518 .311 .335 .280 20 .215 .267 .366 .390 .183 .551 .161 .563 695 .301 .320 .269 10 .219 .267 .360 .386 .170 .516 .157 .513 695 .298 .313 .262 60 .223 .272 .362 .389 .173 .538 .156 .511.190 .299 .310 .261 90 .230 .278 .367 .393 .176 .535 .151 .538 .177 .298 .312 .262 120 .235 .281 .370 .396 .175 .532 .156 .536 .180 .300 .309 .262 185 .219 .297 .380 .103 .183 531 .163 .531 .181 .310 .317 .265 210 .261 .310 .391 .116 .691 .561 .677 .566 .693 .331.329 279 330 .276 .326 .103 .131 .503 .550 .196 .558 .501 .351 .318 .289 120 .291 .316 .120 .155 .528 .570 .526 .589 .527 .388 377 315 Continued} APPENDIX II - Continued 225 Time, wavelength, 1° Min. 252 256 260 261 268 272 276 280 281 288 292 296 2537 1° 20; Mineral 011 Run 111+18 0 .212 .261 .362 .391 .179 .568 .171 .565 .539 .322 .321 .296 20 .212 .261 .357 .388 .167 .552 .163 .513 .520 .309 .311 .288 10 .220 .268 .362 .392 .169 .551 .162 .538 .521 .311 .312 .288 60 .221 .273 .361 .391 .169 .513 .159 .531 .508 .310 .308 .282 90 .236 .282 .370 .399 .173 .511 .163 .531 .511 .315 .309 .283 120 .212 .289 .372 .102 .176 .512 .161 .532 .505 .316 .310 .278 185 .261 .310 .389 .119 .187 .550 .179 .510 .510 .331 .326 .291 210 .273 .320 .398 .127 .198 .555 .189 .517 .506 .316 .338 .301 330 .281 .333 .107 .110 .507 .562 .508 .565 .535 .375 362 .320 101 .296 .317 .119 .156 .528 .575 .533 .588 .512 397 .385 .331 2801 A IserOpyl Alcohol Run 11411‘ 0 .252 .313 .131 .177 .583 .681 .571 .680 .611.393 .398 .352 11 .257 .316 .129 .173 .568 .662 .561 .651.611.385 .382 .315 29 .270 .330 .138 .176 .568 .655. .557 .636 .617 .381 .371 .338 19 .283 .312 .117 .180 .561 .613 .516 .622 .589 .369 .359 .320 58 .291 .352 .153 .188 .571 .610 .516 .618 .581 .376 .363 .322 88 .316 .371 .162 .199 .566 .633 .551 .607 .582 .383 .358 .321 118 .339 .391 .182 .518 .581 .651 .573 .618 .593 .102 .367 .339 213 .387 .111 .520 .558 .618 .661 .603 .638 .597 .131 .399 .317 273 .108 .170 .513 .587 .618 .681 .638 .666 .618 .171 .132 .371 2801 A 20% Glycerol Run 11:2 0 .217 .311 .129 .179 .576 .686 .579 .680 .657 .101 .396 .365 15 .251 .316 .130 .176 .560 .666 ..567 .610 .639 .100 .379 .365 30 .272 .330 .111 .180 .571 ..655 .555 .610 .601 .385 .376 .336 15 .281 .312 .111 .187 .565 .652 .557 .621 .606 .383 .369 .337 60 .291 .351 .150 .188 .562 .611 .551.610 .599 .389 .365 .328 90 .315 .375 .167 .501 .573 .611 560.616 .591 .389 .361 .333 120 .331 .391 .183 .515 .587 .638 .558 .619 .572 .381 .371 .316 150 .355 .113 .197 .531 «598 .617 .575 -621 .576 .101 .381 5330 210 .392 .152 .529 .573 .631 .671 .620 .618 .613 .158 .121 .368 305 .1201 .185 .561 .603 .671 .698 .655 .692 .627 .185 .156 .381 365 .136 .503 .578 .622 .688 .715 .682 .715 .658 .521 .181.110 Continued APPENDIX II - Contirmed 226 Wavelen h A Time, ' 0 run, 252 256 260 261 268 272 276 286 281 288 292 296* 2_8_q1__;° n-Hoxane Run II-18 0 .202 .258 .366 .395 .191 .570 .171 .577 .531 .320 .313 .293 15 .212 .261 .369 .395 .186 .560 .165 .565 .502 .306 .331 .282 30 .259 .305 .105 .128 .523 .600 .500 .593 .523 .322 .332 .273 15 .259 .307 .101 .121 .512 .567 .175 .562 .198 .313 .321 .253 60 .263 .311 .101 .126 .510 .567 .181 .553 .191 .308 .312 .260 90 .296 .311 .121 .117 .509 .561 .181 .517 .192 .317 .309 .250- 120 .313 .357 .133 .155 .523 .561 .190 .511 .188 .326 .311 .262 150 .323 .370 .113 .162 .526 .568 .191 .539 .188 .332 .321 .261 230 .368 .119 .189 .516 .570 .586 .539 .573 .509 .366 .352 .278 290 .383 9136 .197 .526 .588 .609 .567 .602 .527 .102 .377 .299 350 .396 .116 .506 .511 .602 .615 .586 .617 .538 .122 .397 .311 280 1° 20 Ifineral 011 Run 11-21 0 .208 .263 .368 .393 .189 .566 3.171 .571 .517 .311 .330 .273 15 .219 .271 .370 .391 .188 .553 .161 .559 .196 .309 .322 .266 30 .232 .280 .371 .397 .183 .516 .160 .518 .190 .303 .311.256 11 .239 .286 .376 .396 .172 .532 .152 .530 .179 .299 .306 .253 S9 .257 .303 .386 .109 .183 .536 .157 -529 .171 .302 .307 .251 89 .271 .311 .393 .111 .183 .530 .151 .511 .160 .301 .300 .212 119 .285 .329 .101 .121 .183 525.153 .508 .156 .306 .300 .211 189 .318 .363 .131 .150 .509 .511 181 .526 .162 .331 .319 .256 219 -330 -379 .113 .168 .520 519 «500 -536 .178 -357 .336 282 321 .311 .391 .155 .181 .512 .562 .536 .560 .191 .385 .362 .291 2967 1° Isopgopyl 1166161. Rug II-61 0 .257 .318 .136 .176 .585 .675 .578 .682 .628 .381 .393 .311 30 .267 .325 .131 .171 .570 .658 .561 .655 .602 .380 .375 .337 60 .283 .338 .138 .177 .567 .618 .555 .631 .605 .371 .366 .322 90 .297 .353 .150 .185 .572 .636 .519 .629 568 .358 .360 .299 120 .305 .358 .151 .181 .568 .625 .655 .609 .561 .361, .352 .302 195 .338 .391 .175 .501 .571 .622 .518 .601 .518 .367 .351 .293 285 .370 .121 .197 .525 .586 .625 .562 .600 .511 .381 .358 .301 375 .395 .116 .516 .511 .600 .630 .575 .605 .550 .100 .366 .301 2261 A0 291 Gycerol Em II-Q; 0 .257 .319 .136 .182 ‘.579 .682 .580 .682 .636 .388 .392 .312 30 .271 .332 .111 .178 .571 .661 .569 .657 .618 .386 .377 .331 60 .285 .312 .111 .185 .567 .655 .566 .610 .608 .385 .370 .331 90 .298 .353 .151 .187 .566 .615 .558 .622 .591 .379 .358 .326 120 .316 .370 .161 .199 .571 .612 .561 .621 .583 .380 .361 .313 200 .317 .100 .182 .516 .579 .639 .565 .611 .566 .382 .356 .310 290 .371 .125 .502 .535 .592 .610 .571 .610 .565 .399 .365 .313 380 .101 .151 .520 .555 .609 .616 .593 .617 .572 .118 .380 .322 APPENDIX II - Continued 227 Time, 'Wavelength A0 Min. 252 256 260 261 268 272 276 280 281 288 292 296 _g2615A0 n-Hexane Run II553 0 .230 .281 .381 .106 .501 .576 .186 .586 .531 .317 .338 .285 30 .231 .279 .372 .399 .182 .553 .165 .552 .509 .308 .317 .276 60 .213 .289 .378 .103 .180 .512 1160 .536 .190 .301 .309 .270 90 .255 .297 .380 .103 .175 .535 .153 .516 .187 .302 .300 .256 120 .263 .305 .381 .105 .171 .526 .118 .509 .178 .300 .291 .251 180 .281 .328 .101 .119 .182 .521 .153 .501 .160 .300 .291 .215 270 - .311 .351 .117 .138 .192 .526 .161 .500 .155 .310 .291 .211 330 .323 .365 .126 .119 .195 .526 .171 .501 .153 .319 .300 .213 375 .335 .380 .137 .159 .507 .530 .179 .509 .152 .326 .305 .253 2261_A° n-Hexane Run Iljéz 0 .217 .273 -372 .397 .192 -568 .177 .578 .530 -319 .335 .293 330 .323 .369 .132 .151 .507 .535 .176 .516 .159 .321 .305 .251 375 .337 .383 .110 .162 .513 .537 .182 .516 .161 .330 .310 .256 135 .319 .391 .152 .172 .522 .539 .191 .519 .156 .337 .311 .255 195 .360 .105 .159 .183 .529 .515 .501 .525 .162 .316 .321 .251 560 .371 .116 .166 .189 .535 .515 .506 .525 .161 .352 .325 .259 @QAO NZMMMIMI MnH67 0 .228 .276 .376 .106 .502 .578 .183 .578 .516 .325 .335 .286 30 .220 .269 .361 .392 .178 .519 .163 .519 .506 .305 .315 .272 60 .212, .288 .376 .103 .177 .513 .161 .533 .196 .301 .308 .267 90 .250 .296 .378 .102 .172 .536 .151 .518 .189 .301 .299 .260 120 .267 .308 .388 .111 .176 .532 .153 .515 .170 .299 .297 .251 180 .286 .327 .399 .120 .180 .523 .155 .501 .161 .303 .295 .217 285 .313 .357 .119 .139 .190 .520 .165 .502 .119 .315 .298 .252 360 .331 .373 .131 .153 .501 .528 .175 .506 .152 .327 .303 .251 2261 A9 10%.Mineral 011 Run 11:79 0 .212 .263 .359 .391 .177 .568 .173 .559 .511 .321 .326 .299 31 .221 .271 .361 .395 .166 .553 .166 .532 .529 .317 .313 .289 61 .237 .280 .365 .396 .160 .538 .156 .516 .509 .312 .303 .277 91 .219 ~296 .371 .103 .161 .531 .156 «512 .198 .309 .297 -271 121 .262 .306 .381 .106 .166 .531 .151 .509 .185 .308 .296 .269 211 .290 .332 .398 .123 .172 .523 .157 .195 .172 .315 .291 .262 301 .311 .355 .115 .110 .187 .526 .169 .199 .163 .328 .301 .268 391 .332 .376 .131 .156 .500 .532 .183 .509 .169 .312 .317 .270 APPENDIX III IRRADIATION REBUL’I‘S--ACTINOMETRIC DATA (Note: Units of ft IaAidt- moles of quanta per liter of solution.) 0 228 _. -14 t t Iaxm , v v Interval, Quanta ‘f‘ AEdt \f\ APdt Interval,‘jo IaAEdt ‘1; IaApdt Min. Per Min. t t Min. .x 105 x 105 2537 1° Isoprogyl Alcohol Run 111-10 0-20 1.32 18.96 .80 0-20 .153 .019 20-10 1.26 17.29 2.28 0-10 .861 .073 10-60 1 .22 16.06 3 .11 0-60 1.236 .153 60-90 1.20 22.11 6.39 0-90 1.757 .302 90-120 1.11 20.83 7.35 0-120 2.231 .170 120-150 1.23 19.10 8.20 150-185 1.33 21.00 10.18 0-185 3.192 .913 185-215 1.12 16.78 9.52 215-215 1 .16 15 .76 9 .86 0-215 3 .991 1.390 215-275 1.51 11.83 10.19 275-305 1.58 13.91 10.51 0-305 1.717 1.912 305-335 1.82 13.05 10.76 _, 335-365 1.89 12.19 10.88 0-365 5-395 2.193 365-395 5 ~05 11.35 10999 395-110 5-01 5.11 5.51 0-110 5.863 2.955 2537,A° 2oz Glycerol Run 111-11 0-20 3.87 18.77 0.77 0-20 .102 .016 20-10 3.78 17.29, 1.97 0-10 .761 .058 10-60 3 .78 16.35 3 .12 0-60 1.106 .123 60-90 3.96 23.09 6.10 0-90 1.612 .257 90-120 3.73 21.52 7.30 0-120 2.056 .107 120-150 1.01 20.03 8.13 150-180 1.00 18.55 8.81 0-180 2.911 .783 180-210 1.08 17.10 9.33 1 210-210 1.11 15.68 10.01 0-210 3.651 1.222 210-270 1.30 11.56 10.51 270-300 1-31 13 .79 10-71 300-330 1.12 13.16 10.80 0-330 1.651 1.995 330-360 1.51 12.68 10.80 360-390 1 .65 12 .23 10 .80 390-120. 1.78 11.71 10.80 0-120 5.598 2.830 Continued 229 APPENDIX III - Continued "1' 10'“ t f' a X .9 Interval, Quanta dbt' AEdt \fm' APdt Interval, ‘é‘IaAEDT o IaAPdt Min. Per Min. 1:. 1'. Min. 2: 10‘5 x 105 25371° n-Hexane RungllI-ZZ 0-20 3.58 19.10 .58 0-20 .381 .012 20-10 3.51 18.20 1.71 0-10 .711 .016 10-60 3.56 17.07 2.88 0-60 1.077 .102 60-90 3.60 23.71 6.10 0-90 1.550 .221 90-120 3.51 21.90 7.50 0-120 1.976 .370 120-150 3.33 20.32 8.18 150-185 3.38 21.83 10.91 0-185 2.758 .730 185-215 3.16 17.18 10.26 215-210 3.53 13.33 9.12 0-210 3.318 1.105 210-270 3.70 11.91 11.39 270-300 3.75 13.89 11.89 300-330 3.83 12.92 12.31 0-330 1.216 1.816 330-360 1.07 12.00 12.71 360-390 1.17 11.08 13.06 390-120 1.26 10.11 13.29 0.120 1.980 2.717 2537 1° 20% Mineral 011 Run 111-18 0-20 3.55 19.08 1.01 0-20 .375 .020 20-10 3.56 17.51 2.12 0-10 .720 .068 10-60 3.60 16.37 3.35 0-60 1.016 .131 60-90 3.71 22.86 5.09 0-90 1.516 .239 90-120 3.69 21.19 6.11 0-120 1.919 .361 120-150 3.70 19.61 7.02 150-185 3.77 21.00 11.29 0-185 2.789 .713 185-215 1.02 16.18 10.72 215-210 3.98 12.80 9.55 0-210 3.138 1.192 210-270 1.10 11.33 11.93 270-300 1.09 13.21 12.30 300-330 1.21 12.18 12.67 0-330 1.316 2.036 330-360 1.36 11.13 12.97 360-390 1.52 10.18 13.23 390-101 1.51 1.10 6.23 0-101 1.979 2.835 Continued 230 APPENDIX III - Continued 14 t - — t Ia X 10 , - Interval, Quanta ft. AEdt ft! APdt Interval, ‘4. Ia‘A‘Edt ‘4: IaAPdt Min. Per Min. 1'. 1’. Min. 1: 105 x 105 2801_A° Isogropyl Alcohol Run II-11 0-11 11.12 13.68 .22 0-11 1.092 .018 11-29 13.79 13.98 .71 0-29 2.159 .071 29-19 13.18 17.56 1.76 0-19 3.169 .205 19-58 13.52 7.51 1.08 0-58 1.031 .286 58-88 13.18 23.35 1.55 0-88 5.731 .618 88-118 13.33 21.01 5.19 0-118 7.286 1.023 118-118 13.16 19.09 6.12 118-178 13.25 17.26 6.75 178-213 13.09 17.91 8.59 0-213 11.273 2.596 213-213 13.37 13.59 7.81 213-273 13.17 12.07 8.01 0-273 13-l59 3.757 273-293 11-09 7.31 5.38 293-318 13.99 8.17 6.72 0—318 11.381 1.702 2801 A0 291 Glycerol RunI132 0-15 13.99 11.52 .38 0-15 1.121 .029 15-30 13.38 13.67 .98 0.30 2.136 .102 30-15 13.23 12.98 1.12 0-15 3.087 .206 15—60 12.89 12.37 1.80 0-60 3.969 .331 60-90 12.93 23.10 1.61 0-90 5.622 .666 90-120 12 . 58 21.16 5 .87 0-120 7 .096 1.075 120-150 12.77 19.33 6.80 0-150 8.162 1.556 150-180 12 .86 17 .11 7 .31 180-210 12.91 15.16 6.13 210-210 12.98 13.55 7.69 0-210 11.781 3.089 210-270 13.09 11.96 8.16 270-305 13.05 12.71 9.75 0-305 13.568 1.381 305-335 13 .11 10 .33 8 .57 335-365 13.27 10.09 8.71 0.365 15.060 5.617 Continued 231 APPENDIX III - Continued _. -14 t t Ia X 10 , Interval, Quanta f“ AEdt ft' Apdt Interval, ‘C IarAEdt Jr: 18‘9“ Run. Per Min. t t Min. 1:105 2:105 28017A° n-Hexane Run II-18 0-15 10.61 11.69 .15 0-15 .862 .009 15-30 8.65 11.07 .18 0-30 1.536 .032 30-15 10.97 13.15 .86 0-15 2.353 .081 15-60 10.21 12.81 1.27 0-60 3.078 .156 60-90 10.21 23.90 3.79 0-90 1.129 .370 90-120 10.25 21.51 5.30 0-120 5.619 .670 120-150 10.66 19.22 6.50 0-150 6.783 1.051 150-180 10.55 17.01 7.11 180-210 10.16 11.90 7.58 210-230 10.82 8.76 5.28 0-230 9.163 2.226 230-260 10.96 11.39 8.23 260-290 10.88 9.1 8.51 0-290 10.122 3.239 290-320 11.09 "7.65 8.81 320-350 10.82 6.22 9.06 0-350 11.261 1.321 2801_1° 20% Mineral 011 Run 11-21 0-15 11.11 11.19 .33 0-15 .915 .021 15-30 11.31 13.55 .96 0-30 1.763 .081 30-11 10.92 11.91 1.12 0-11 2.183 .167 11-59 11.17 12.05 2.02 0-59 3.228 .292 59-89 11.07 22.13 5.23 0-89 1.581 .612 89-119 10.90 19.75 6.16 0-119 5.775 1.002 119-151 11.05 20.19 8.69 151-189 10.81 18.13 9.38 0-189 8.116 2.096 189-219 11.31 13.71 8.37 219-219 11.16 12.19 8.62 0-219 9.751 3.168 219-281 11.09 12.25 10.32 281-321 11.03 12.11 0-321 11.195 1.512 11.31 Continued 232 APPENDIX III - Continued w——'v ——~ .. -14 t t Ia x 10 , Interval, Quanta ft' 53211: ft. APdt Interval, f0 IaAEdt Jo. IRA?“ Kin. Per Pun. t * ‘ t ' Min. 1: 10‘5 x 105 2261 ‘0 Isoprogzl Alcohol Run II-61 0-30 6 .32 29 .31 .71 0-30 1.025 .026 30-60 6.16 27 .86 l .80 0-60 1.975 .087 60-90 6.17 26.10 2 .56 0-90 2 .876 .175 90-120 6.10 21.98 3 .31 0-120 3 .720 .286 120-150 6 .13 23 .17 3 .98 ' 150-195 6.53 32 .19 7 .19 0-195 5 .718 . .688 1957225 6.73 19 56 5 .53 225-255 6.87 18 .13 5 .91 255-285 7 .17 16.76 6.26 0-285 7 .801 1.368 285-315 7-11 15-15 6-53 315-315 7.65 11.720 6.79 .315-375 7 .72 13 ~02 7 .92 0 .375 9 .595 2 .221 2261 5° 20: Glycerol Run II-Q, 0-30 6 .06 28 .52 .80 0-30 .956 .027 30-60 6.12 26.23 1.97 0-60 1.815 .091 60-90 6.35 21.56 2 .81 0-90 2 .708 .192 90-120 6.37 .23 .16 3 .51 0-120 3 .521 .316 120-150 6.38 21.85 1.10 159-180 6.51 20.60 1. 180-200 6.78 13 .05 3 .31 0-200 5.528 .752 zoo-230 6 .87 18 .52 5 .32 230-260 6.88 17 .31 5 .65 260-290 7 .16 16.13 6.00 0-390 7 .530 1.107 290-320 7 .19 11 .91 6 .31 320-350 7 .72 I3 .72 6.60 350-380 12 .58 6.77 0—380 9 .281 2 .216 7 .85 _ Contitmed APPENDIX III - Continued 233 .. -14 t t Ia X 10 , Interval, Quanta J‘t'AEdt f“ APdt Interval, J; IaAEdt ‘6 IaArdt Nfin. Per Min. t t Min. x 105 x 105 29671§° n-Hexane Runs 11-53,,11-67 0-30 5.77 28.89 ..71 0-30 .922 .023 30-60 5.67 26.96 1.80 0-60 1.768 .079 60-90 5.58 25.30 2.70 0—90 2.550 .162 90-120 5.62 23.77 3.15 0-120 3.289 .270 120-150 5.58 22.32 3.97 150-180 5.57 20.91 1.11 0-180 1.623 .528 180-210 5.63 19.17 1.81 210—210 5.61 17.96 5.19 210-270 5.86 16.17 5.57 0-270 6.321 1.021 270-300 5.90 15.06 5.91 300-330 6.13 13.86 6.19 0-330 7.286 1.121 330-350 6-37 8-67 1.21 350-375 6.16 10.21 5.39 0-375 7.957 1.766 375-105 6.77 11.31 6.58 105-135 6.93 10.28 6.71 0-135 8.776 2.270 135-165 7.20 9.25 6.82 165-195 7.35 8.27 6.88 0-195 9.181 2.822 195-525 7.52 7.12 6.93 525-560 7.61 .7.88 8.11 0—560 10.123 3.151 2967A° 2oz Mineral 011 Run 11-57 0—30 5.60 29.62 .55 0-30 .918 .017 30—60 5.70 28.28 1.57 0-60 1.810 .067 60—90 5.78 26.61 2.60 0—90 2.662 3.150 90-120 5.68 21.99 3.56 0-120 3.118 .262 120-150 5-97 23.10 1-37 150-180 6.06 21.81 5.01 0-180 1.952 .575 180-210 6.22 20.26 5.53 210—210 6.12 18.86 5.91 210~285 6.37 25.85 9.58 0-285 7.200 1.301 285-315 6.88 15.68 6.79 315-360 6.85 21.18 10.61 0-360 8.600 1.966 360-390 7.22 12.57 7.31 390-120 7.27 11.31 7.17 0-120 9.557 2.560 Continued 231 APPENDIX III - Continued _v_ __,_ 8.103 .. -14 A t t Ia x 10 , 1 . Interval, Quanta ft '11,301; ft, Ardt Interval, ‘8 IaAEdt ‘8 IaAPdt Min. Per Min. t ‘ t ' Min. 1: 105 x 105 2967 1° 10mneral 011 Run 11-70 ,1 , _, 0-31 5.73 29.78 .79 0-31 .911 .025 31-61 5 .83 26.82 2 .09 0-61 1.810 .092 61-91 5 .52 ' 25 .08 2 .90 0-91 2 .576 .181 91-121 5 .66 23 .11 3 .60 0-121 3 .310 .291 121-151 5.89 21.85 1.25 151r181 5.91 20.20 1.88 181-211 6 .06 18 .59 5 .50 0-211 5 .310 .777 211-211 6.32 17 .02 6.06 211-271 6.17 15.58 6.16 271-301 6.70 11 .21 6.71 0-30]. 6 .990 1.170 301-331 7 .12 12 .92 6.93 331-361 -~ 7 .25 11.75 7 .06 .. 361-391 7 .19 lo .86 7 .20 0-391 2 .313