LEQL‘ET SCQWERMG Cir SQPQEYMERS 1. EFFECT OF DiLUTifiN DLéEili‘éG CG?OL"£’MER§ZA"§E§?€ ON CHAIN COMFGSITiON AND MGLECKELML WEIGHT Thesis for the Degree of 57?: S. fiifiéiEGAM STATE URi“~!ERSiTY HELEN MARE KUMISCH 1970 l: HERE'S-5:3 A WWW“ “45:15:? '5; ml " H “ “W G I‘MWWML; 7465 , " LIGHT SCATTERING OF COPOLYMERS I. EFFECT OF DILUTION DURING COPOLYMERIZATION ON CHAIN COMPOSITION AND MOLECULAR WEIGHT By Helen Marie Klimisch A THESIS submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE 1970 ABSTRACT LIGHT SCATTERING OF COPOLYMERS I. EFFECT OF DILUTION DURING COPOLYMERIZATION 0N CHAIN COMPOSITION AND MOLECULAR WEIGHT by Helen M. Klimisch Differential refractometry measurements were made on two homopolymers, polyvinylidene chloride and poly- isobutylene. A procedure is demonstrated which allows one to determine the specific refractive increment, dn/dc, for a homopolymer in a particular solvent in which the polymer may not be soluble. Light scattering and differential refractometry measurements were made on two copolymers of vinylidene chloride and isobutvlene. The datauere'treated accord- ing to the procedure first described by Stockmayer etuggf and expanded by Bushuk and Benoit‘. The molecular para- meters derived from this treatment were weight-average molecular weight and cOmposition distribution. The composition distribution during copolymerization were used to determine the effect of dilution on the resulting copolymers. Copolymers I and II were prepared in tetrahydro- furan solutions of 2g_and 8.5M concentrations respectively. From the differential refractometry measurements, the weight fraction of each monomer was calculated. These results indicate no difference in weight fraction of vinylidene chloride and isobutylene between the two Helen Marie Klimisch copolymers. The weight fraction as calculated from dn/dc measurements was 0.81 vinylidene chloride as compared to 0.87 vinylidene chloride from NMR analysis. The light scattering results also indicate that the two copolymers have approximately the same weight-average molecular weight. The molecular composition parameters, however, do indicate a difference of approximately 18% in the compositional distribution. ACKNOWLEDGMENTS The author is indebted to Professor J. B. Kinsinger for the helpful guidance and assistance offered during the course of this investigation. She also wishes to express thanks to the Dow Corn- ing Corporation for their financial assistance and for their permission to use the light scattering and differen- tial refractometry instruments. Finally, the author is grateful to Mrs. Ardath Chubb for typing the final draft of this manuscript. TABLE OF CONTENTS Page MODUCTIONOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.0.. l MORYOOOOOOOOOOOOOOO00.0.0.0...00000000000000. mSTRIMNTSANDMATERIAIS...OOOOOOOOOOOOOOOOOOO Light Scattering Photometer............... Differential Refractometer................ POlyIner swpleSOOOOOOOOOOOOOOOOOOOOOCOOOOO SOlventSOOOOOOOOCOOOO0.0...0.0.0.0.0000... mochREOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO... l2 l—‘KOKOKO KO F Light ScatteringOOOOOOOOOOOOO0.0.0.0000... 12 Differential Refractometry................ l5 RESULTSANDDISCUSSION.0.00.00.00.00.0...COO... 21 Differential Refractometry................ 21 Light Scattering Measurements............. 28 Molecular Parameters...................... 32 BELIOGRAPI-IYOOOOO00.0.00...OOOOOOOOOOOOOOOOOOO. 242 APPENDIX....................................... 43 LIST OF FIGURES Figure Page 1. Refractive Increment Data for POlyiSObutyleneOOOOO00.0.0000.0.000.000. l7 2. Refractive Increment Data for Poly- vinylidene Chloride..................... l8 3. Refractive Increment Data for Copolymer I. 19 h. Refractive Increment Data for COpOlmer II............................ 20 5. Specific Refractive Index Increment_v§, Refractive Index of Solvent for Polyvinylidene Chloride and Polyisobuty- lene.................................... 24 6. Specific Refractive Index Increment gs. Refractive Index of Solvent for Copolymers I and II..................... 26 7. Zimm Plot for Copolymer II in Cyclohexanone........................... 29 8. Zimm Plot for Copolymer I in 0-DiChlorObenzeneo0000000000000000000000 30 9. Alternative Method of Plotting Light Scattering Data — Copolymer I in Amy]. AcetateOOOOOOOOOOOOOOOOOOOOOOOOOOOO 31 10. Apparent Molecular Weight of Copolymer I VSO (VA f VB)/V° 000000000000000000000 35 ll. Apparent Molecular Weight of Copolymer II VSO (vA ” VB)/v° 00000000000000000000 36 12. NMR Spectra of Copolymer I................ M5 13. NMR Spectra of Copolymer II............... 46 LIST OF TABLES TABLE Page I. Refractive Index Values of Solvents Used in This Study..................... 21 II. Refractive Index Increments of Poly— vinylidene Chloride and POlyiSObutyleneOOOOOOO0.000000000000000 22 III. Refractive Index Increments of Copolymers I and II.................... 23 IV. Light Scattering Results for Copolymers Imd II.OOOOOOOOOOOOOOO0.0.0.0000.00.. 32 V3 Molecular Parameters for Copolymers I'md II.OOOOOOOOOOOOOOOOOO0.0.0.00...O 33 VI. Summary of Derived Data for COpOlyTnerSIaIld IIOOOOOOOOOOOOOOOOOOOO 37 LIST OF APPENDIX Page I. NMR Analysis of Vinylidene Chloride- Isobutylene Copolymers................... “A INTRODUCTION Light scattering has become one of the standard methods for the determination of molecular weights of polymers. Debye1 demonstrated the utility of this technique by proving that the amount of light scattered by solutions of high polymers is related to the mass of the solute molecules. It must be emphasized that the polymer molecules must vary only in molecular weight and not in chemical composition to apply this technique with any success. As early as 1952, it was noted2 that the light scattering molecular weight of a butadiene-styrene copolymer varied with the refractive index of the solvent. It was suggested that this behavior could be due to variations in composition between the polymer chains. The complications arising from this problem, i.e., heterogeneities in the composition of the polymer chains, were first discussed by Stockmayer et al3 by considering the light scattered from a copolymer sample containing .units A and B. They derived an equation which indicated how the intensity of this scattered light varies with the composition distribution of the copolymer sample. One fundamental assumption made was that the specific refractive index increment of a copolymer in a solvent varies linearly with the composition of the copolymer. The equation of Stockmayer et al3 allows one to obtain not only the weight-average molecular weight, but 2 also a measure of the chemical heterogeneity of a co- polymer by evaluating light scattering data separately in three solvent media. The validity of this equation has been investigated experimentally by Bushuk and Benoit4 Krause5 and Leng and Benoits. These authors have shown the equation to be correct within experimental error. Bushuk and Benoit have also indicated how the parameters of weight—average molecular weight and composition distribution can be used in the interpretation of co— .polymerization kinetics. Kinsinger et a1?"8 have studied the microstructure of isobutylene-vinylidene chloride copolymers by NMR spectroscopy. They have shown that this system is very amenable to NMR analysis and allows one to postulate possible mechanisms for the copolymerization. It was suggested that a light scattering study on the copolymers of isobutylene and vinylidene chloride might also lend some insight into the mechanism of the copolymerization. It was the intent of the author, therefore, to investi- .gate the effect of dilution on the resulting copolymers L of isobutylene and vinylidene chloride. It was hoped that this study would provide insight into the sensitivity of this technique as a means of analyzing changes in molecular weight and chain composition heterogeneity. To this end, two copolymers were made at different dilutions but some monomer feed—ratio were analyzed in four solvents. Samples of the two homopolymers were 3 analyzed by differential refractometry to allow the parameters of molecular weight and composition to be calculated. THEORY In a homopolymer all the elements scatter in the same manner and the only difference within the sample is due to molecular weight heterogeneity. In a copolymer there may be two or more types of scattering elements depending on the number of monomer types that make up the copolymer. These scattering elements are affected by the molecules of different molecular weight and different chemical composition. The theoretical treat~ ment given here follows that given by Bushuk and Benoit‘. It is assumed that the refractivity of a copolymer is a simple sum of the refractivities of the two component homopolymers and independent of molecular weight. Stockmayer et a13 pointed out that this should not introduce a very large error. The light scattering in- vestigations of copolymers by Bushuk and Benoit‘ and Krause5 agree with the light scattering theory and thus Justify this assumption. Bushuk and Benoit also showed that the mole fraction of each mer, as determined from measurements of specific refractive increments, is within 2% of that obtained through chemical analysis. Kinsinger et al9 have also investigated the colligative nature of the specific refractive increments over a wide range of mer composition. They have shown this technique to be useful and nearly as precise as chemical analysis for carbon. The specific refractive index increment of the copolymer can be calculated from 4 vo= XVA + (l - X) VB (1) where v'is the specific refractive index increment, (dn/dc), of the copolymer; VA and \{Bare the (dn/dc) values for the two homopolymers A and B3 and X'is the weight fraction of component A with concentration in gms/cc. According to the classical theory on light scatter- ing, the excess scattering due to homogeneous solute L particles of mass M, concentration.cz and having v for the specific refractive index increment can be put in the form R a K'v2 cM, (2) where K' = (2 112 mayo“ N), in which no is the refrac- tive index of solvent, A is the wavelength of the incident light in vacuum and N is Avogadro's number. For a solution of a copolymer which may show polydispersity of chain composition in addition to poly- dispersity of molecular weight,equation (2) can.be put in the form R = K' ZViZ Ci Mi (3) where Ci is the concentration of molecules of mass M1 and composition Xi° The intensity of the scattered light that is measured in a copolymer is given by R = K'voz c Map (4) o where V0 is the average refractive index increment and Map is the apparent molecular weight obtained from the data. After equating the intensities given by equations (3) and (A), the apparent molecular weight is given by Map = (l/Voz) Evie Y1 Mi (5) where Yi is defined as the relative concentration of molecules of composition Xi' For a copolymer with heterogeneous composition, equation (5) can be expanded by substituting for Vi the value given by equation (1). The new equation for the apparent molecular weight becomes T ., Map :: (VA VB/Voz )N‘IW + LVA (VA -\)B)/V02] A. MA + LVB(VB -.A)/Vo J ( “ X ) MB ( ) where Mw is the weight—average molecular weight of the copolymer, MA and MB are the weight-average molecular weights of the parts of the copolymer formed of monomer A and B respectively and X is the average weight fraction of component A. From measurements in three solvents it is possible to solve for the three parameters MA, MB and M“ from which the compositional heterogeneity of the copolymer can be determined. Bushuk and Benoita also recast equation (5) using 6Xi 2" Xi " X0 (7) 7 where 5x1 is the deviation in composition of molecules of type i from the average composition, X0. Equation (1) for the specific refractive index increment becomes Vi = v0 + 6 Xi (VA - VB) (8) and the equation for the apparent molecular weight be- comes F F 13 mp=m+2Pum-vme +Quu—vmeu (9) The two new parameters P and Q are equal to ZYiMiéxi and ZYiMiSXiz respectively and are a measure of the degree of heterogeneity of composition. The values of the parameters of equation (9) can be calculated by either of two methods. One method is to use the data from the measuiements in three solvert; to solve a set of simultaneous equations. The second method is to plot Map against (VA - VB)/Vo. The points of this plot should describe a parabola from which the values of M”, P and Q can be calculated. The theoretical limits on P and Q are -XoI'--I(., S P S. (l — X0) MW, e .<. a £14le - x0 (1 — 3(0)] The parameter Q/Mw for a specific copolymer may be defined as a quantitative measure of the polydispersity of chain composition. Therefore, the ratio of the value of Q/Mw [I — Xo(l - X0)j seems to to the maximum possible value, J, 8 be a convenient index of the polydispersity in chain composition which can be used as an additional parameter for characterizing c0polymers. INSTRUMENTS AND MATERIALS Light Scattering Photometer A SOFICA PGD (Mechrolab Model 701)1° light scattering instrument was used for characterization. Optical align- ment and calibration of the instrumentweue accomplished by the scattering of a pure solvent (benzene). Measure- ments were made using the green mercury line (5460A) at 35 i O.5°C. Differential Refractometer All measurements of the specific refractive index increment, (dn/dc), were made with a Brice-Phoenix Differential Refractometerll. The instrument was cali- brated for the green mercury line (5460 A) and a tempera- ture of 35 f 0.05°C with five sucrose solutions. Polymer Samples The polyvinylidene chloride used was supplied by Dr. J. B. Kinsinger of Michigan State University. The polyisobutylene was purchased from Polysciences, Inc. of Rydal, Pennsylvania. The two copolymer samples used in this study were prepared by W. C. Page under the direction of Dr. J. B. Kinsinger of Michigan State University. Both samples were solution polymerized using a tetrahydrofuran solvent medium with a one to one mole ratio of vinylidene chloride and isobutylene. The initiator was azo—bis-isobutyroni— trile at a concentration of 0.1g per 50 cc reaction 9 10 mixture. Ultraviolet light was used to promote the decomposition of the azo compound. C0polymer I was prepared by adding equimolar amounts of isobutylene and vinylidene chloride to a glass bomb. Enough tetrahydrofuran with the initiator dissolved in it was added to the bomb to give a total molarity of 2. After filling, the bomb was freeze-thawed to remove dissolved oxygen and sealed. The bomb was placed in a 30°C thermostat and subjected to uv irradiation. After 4.6% conversion the sample was quenched in a dry ice methanol slush, precipitated from methanol and collected. Copolymer II was prepared by a similar procedure as copolymer I except that the total molarity was 8.5 with a conversion of 2%. Solvents All of the solvents used were reagent grade and distilled prior to use. After two distillations, the 1- bromonaphthalene remained slightly yellow; however, it did not absorb any light at the wavelength used. The solvents used for polyvinylidene chloride were N, N—dimethylacetamide, cyclohexanone and a 3:1 mixture of cyclohexanone : l—bromonaphthalehe. The solvents used for polyisobutylene were 1, l, 1— triehloroethane, chlorobenzene, amyl acetate and o—dichlor- obenzene. The solvents used for the two copolymers were amyl acetate, cyclohexanone, chlorobenzene and o—dichlorobenzene. ll The refractive indicies of the solvents were deter- mined at 35 f 0.05°C on an Abbe Refractometer. These values, which were at the sodium D line, were converted to the green mercury line using dispersion tables. The densities of the solvents at 35 j 0.05°C were either measured or available in the literature. PROCEDURE The experimental procedure discussed below was greatly influenced by the very small quantity of copoly— mer I available. This small quantity required the author to recover the polymer after each run. Light Scattering For each copolymer-solvent system, a stock solution was prepared by weighing polymer and solvent into an acid- washed bottle. The concentration was calculated in g/lOO cc using the density of the solvent. Because of the low concentrations used in this work, the density of the copolymer was assumed to have a negligible effect on the concentration. Several attempts were made to clarify the solvents and stock solutions by pressure filtration through a sintered glass ultra-fine filter. Probably because of the rather viscous nature of most of the solvents, this procedure did not remove enough of the dust. Success was finally achieved using a pressure filter and a double filtration through three thicknesses of Metricel Filter Type Alpha 8 with pore size of 0.20 micron. A quantity of solvent sufficient for all of the light scattering measurements in a particular solvent was filtered into a carefully cleaned burette. The solvent was again filtered to clarify it sufficiently for the photometer. This freshly filtered solvent was used to dilute the stock solution to four more concentrations. 12 13 The stock solution was also filtered through a triple thickness of the membrane filters. The second filtration was made directly into weighed light scatter— ing cells. Each cell was again weighed to determine the amount of stock solution added. A weighed amount of filtered solvent was added to four of the cells to give a total of five concentrations on which the light scat- tering measurements were made. The concentrations were again calculated from the known density of the solvent. For all of the copolymer I — solvent systems, except cyclohexanone, a slightly different procedure was necessary. The quantity of copolymer I available for study was too small to prepare enough stock solution for five separate concentrations. For these runs, the second filtration of the stock solution was made into three weighed light scattering cells. The cells were again weighed and diluted as before to give a total of five concentrations, two of the solutions were again diluted by adding a weighed amount of solvent. This dilution was made only after the scattering data were collected on each solution. The concentrations of the solutions were calculated from the known weights of stock solution and solvent added. A The scattering datauere collected by placing the cell containing the pure filtered solvent into the con— stant temperature bath of the SOFICA. The cell was allowed to come to temperature equilibrium for ten 14 minutes. Measurements were made at angles of 37.5° to 142.5° to the incident with duplicate readings at each angle to check the accuracy. The scattering data for each concentrationimne collected in the same manner. The parameters, Ke/R and Sin2 6/2 + kc, were cal- culated by a computer. The data was treated according to the extrapolation method of Zimml8 for the Rayleigh ratio of benzene (16.3 x 10"6 for 5461 A at 25°C). Depolarization of the scattered radiation was assumed to be negligible. The relation Kc/R = mSin2 6/2 + 2Bc + (Kc/R)C e O 0 relates the parameters obtained from the scattering data, i.e. weight average molecular weight, second virial coefficient, z-average radius of gyration, and the ex- perimental parameters (solution concentration, Rayleigh ratio, and optical constants for the polymer solvent system). The usual procedure consists of plotting the parameter (Kc/R) versus Sin2 6/2 + kc. A grid-like plot (Zimm diagram) is obtained. The second virial coefficient is obtained from the slope of the zero angle line defined by extrapolation of the data points of constant concentration to zero angle. The radius of gyration is obtained from the initial slope of the zero concentration line defined by extrapolation of data at constant angle to zero concentration. Molecu~ 1ar weights are given by the reciprocal of the ordinate, (Kc/R)8 , determined by the previous extrapolations I! ll 0 O 15 of the zero angle and zero concentration lines. Another method was also used to determine the second virial coefficients and molecular weights. This method consists of plotting the parameter (Kc/R) versus Sing 0/2 and extrapolating the constant concentration points to zero angle. The values of (Kc/R)e = 0 thus determined were plotted versus c (solution concentration). The extrapolation of the zero angle points to zero concentra- tion yields the reciprocal of the molecular weight. The slope of this extrapolation yields the second virial coefficient. Differential Refractometry The differential refractometry measurements on the two copolymers were made on the solutions prepared for light scattering measurements. After the scattering datavere collected on each solution, the solution was poured into a small vial. The solution side of the re- fractometry cell was rinsed thoroughly with the solution, filled and allowed to reach temperature equilibrium for ‘ten minutes. Solvent was kept in the other half of the divided cell. Measurements were made by taking at least three readings for each of two positions of the cell. These readings, d1 and d2, were subtracted to give a d for the solution from which the reading for pure solvent had to be subtracted to give a Ad. This value can have either a positive or negative sign depending on whether the polymer has a lower or higher refractive index than 16 the solvent. From the relation KAd = An, An can be calculated using the calibration constant of the instru- ment for a wavelength of 5460 A and temperature of 35 f 0.05°C. The relation determined for this instrument is An = 0.967Ad. This value of An was plotted versus solu- tion concentration in g/100cc. The slope of this plot gives the specific refractive index increment, dn/dc, for a particular polymer-solvent system at a given temperature and wavelength. The differential refractometry measurements for each of the homopolymers, polyvinylidene chloride and poly— isobutylene, were made using a similar procedure to that used with the copolymers. Here, four individual solutions for each polymer-solvent system were prepared. Measure- ments were taken and plots of An versus c were made, from which the specific refractive index increment, dn/dc, was calculated. Figures 1 through 4 are the plots of An versus c for .the two homopolymers and two copolymers. Figure 1 shows the data for polyisobutylene in amyl acetate, 1, 1, l- trichloroethane, chlorobenzene and o-dichlorobenzene. Figure 2 gives the data for polyvinylidene chloride in N, N-dimethylacetamide, cyclohexanone and a 3:1 mixture of cyclohexanone: l—bromonaphthalene. Figures 3 and 4 give the data for copolymers I and II respectively in amyl acetate, cyclohexanone, chlorobenzene and o-dichloro— benzene. an -6 -4 AMYL ACETATE LIJ- TRICHLOROETHANE _. ' / CHLOROBENZENE o- DICHLOROBENZENE l ‘ l J I l O '3 ‘6 IOOC ‘9 LZ L5 Figure I. Refractive Increment Data for Polyiso'butyl’ene at 54603 and 35°C an IO _. N,N’D|METHYLACETAMIDE CYCLOHEXANONE 31| MIXTURE ._... o CYCLOHEXANONE 3 erROMONAPHTHALENE l l I I .3 .6 .9 l2 l00 c FlgureZ. Refractive Increment Data for Polyvinylidene Chloride 015460A and 35°C L5 An re l2 s O 4 AMYL ACETATE o 6. O 4 O 2 CYCLOHEXANONE o 5 4 / 3 2 I CHLOROBENZENE o I I I I I .3 .s .9 I2 :5 I000 4 O 3 2 . o-DICHLOROBENZENE 0 I I I I o 4 .8 I2 I.6 2.0 IOOc Flame 3. Refractive Increment Data for Copolymer I at 54603 and 35°C An 20 AMYL ACETATE 2 — CYCLOHEXANONE I -— CHLOROBENZENE o- DICHLOROBENZENE — — .3 .6 .9 l.2 I00 c Figure 4. Refractive Increment Data for Copolymer II at 5460A and 35°C I.5 RESULTS AND DISCUSSION Differential Refractometry Differential refractometry measurements were made on the two homopolymers and the two copolymers at a wavelength of 5460 A and a temperature of 35 f 0.05°C. Table I gives the refractive indicies of the solvents used in this study. (The list contains both measured values at 35°C with the sodium D line and those calcu- lated for 35°C at 5460 i. TABLE I Refractive Index Values of Solvents Used in This Study Solvent no - 35°C na — 35°C 5460 A Amyl Acetate 1.3952 1.3969 1, l, l-Trichloroethane 1.4282 1.4303 N, N, ~Dimethyacetamide 1.4308 1.4333 Cyclohexanone 1.4439 1.4461 3:1 Mixture of Cyclohexanone: l-Bromonaphthalene 1.4952 1.4987 Chlorobenzene 1.5159 1.5202 o—Dichlorobenzene 1.5446 1.5490 a. Calculated from dispersion tables Table II lists the specific refractive index increments for the two homopolymers in the various solvents. Table III lists the specific refractive index increments for the two copolymers in the four solvents used in the light scattering study. 21 22 msoshaomoaon you as .w> oe\ce mo Poam Eon“ eecaahopom .s mmo.o- awo.o- mmo.o ecoseoeosoanoaeuo Hmo.o- :mo.o- smo.o . aeoseeeosoaeo mmo.o mamasspemscansmrH "accessosoacao mo endpxflz Hum mmo.o mmo.o emo.o oeoessoeoaoao soa.o measseeoeaeeosaeuz.z aeo.o oseeeoOAoHeoase-a .H .H oaa.o moa.o mma.o evapoo< Hhfig “.msnpxmv m> A.msezv m> A.asnpxmvs<> “.msozv ¢> mama as snomwmaom oeanoano esooaaasaaaHoa peasaom mcmH%QSQOmw%Hom was meflnoaso mcoufiahgfibhaom we mpumaonocH KmUCH c>Hposs9mm E. 5BR 23 TABLE III Refractive Index Increments of Copolymers I and II Copolymera I VCopolymer II Solvent (hes ) (E? trao;)»(fle. .) (Ext?a8.) Amyl Acetate 0.111 0.115 0.114 0.115 Cyclohexanone 0.078 0.082 0.076 0.083 Chlorobenzene 0.031 0.033 0.035 0.035 o-Diehlorobenzene 0.015 0.014 0.017 0.017 a. Determined from plot of dn/dc vs no for ca- _polymers The two copolymers and homopolymers were not soluble in the same solvents, so an extrapolation tech— nique was used to determine the specific refractive index increments, dn/dc, for the four polymers in the same four solvents. The technique used was to measure the specific refractive index increments for the homo- polymers in at least three solvents with a broad range of refractive indicies. The dn/dc of the homopolymer for each solvent was plotted against the refractive index of that solvent at 35°C and a wavelength of 5460 A. Figure 5 is such a plot of dn/dc versus n for poly- vinylidene chloride and polyisobutylene. It was from this plot that the values of the specific refractive index increments were determined for those solvents in which the two homopolymers were not soluble. These values are listed in Table II. A least squares analysis was done on the homopolymer data to 24 3: {Exam e0 32: On... comm es flower. 6 2233338 e5 an.— Nm._ Om; m¢._ 0: o: it. , mEcoEo 0323::an .3 m>=oo¢mm m> .oe\c_e £595.05 .82: 9.80:2”. 2:0on . m 830C ml: O¢._ mm; L _ _ A _ sneeze 88:23.8 . _ _ 3233359. _ _ _ 36.3230 Ix 6:56:3me 0 use 0 4 80 NO. mo. m.. give the curves shown in Figure 5. The equations of the lines ‘ are VA = -O.547 no + 0.888 (11) for polyvinylidene chloride and vB = ~1.14 no + 1.71 (12) for polyisobutylene. Figure 6 is a plot of dn/dc versus n for the two copolymers. The scale is displaced slightly for Co- polymer I because of the small differences in the dn/dc values. A least squares analysis was also done on the data for Copolymers I and II which yields the curves as shown. The equations of the lines are v1 = -o.67o nO + 1.06 (13) for Copolymer I and . v2 = —o.623 no +-o.985 (1H) for Copolymer II. The compositions of the copolymers were calculated using equation (1) and the equations for the homopolymers and copolymers relating the dn/dc to the refractive index of the solvent. The weight fraction of vinylidene chloride can be calculated from equation (I) by V0 b VB (15) VA - VB X: Instead of using the dn/dc values as calculated from the equations, the equations for the data expressed as V = k no + c were used. After substituting these values for dn/dc into equation (I), the weight fraction is 26 Qomm uco 400.90 E Hm ecu H 23.5800 .3 .o: .2823. *0 x22: 3.80:3. m> .mn\cu $5533. .82.. o>tootmm 2:0QO .0 832m 0 c 8.. wm; mm... on; m¢._ we; in. N¢._ o¢._ mm; . IL all BEoEtmaxmlo I] no.1 00.] H .oEanoo H 353300 J 0 wall 0 .I ma] L 2.] .oEQEtoqul o J m_.fi.l _0. no. NO. m... on Eu 27 defined as x no(kc - kB) + (CC - CB) (if) = 0 no (RA - RB) + (CA -' CB) Using the equations as determined from the data for the homopolymers and copolymers, the compositions of the Copolymers I and II are the same within experimental error and are calculated to be 81% vinylidene chloride and 19% isobutylene. The accuracy of the data can also be analyzed using equation (16) defining the weight fraction, X. The com— position of a copolymer must be independent of the refractive index of the solvent in which a series of measurements may be made. This fact allows one to set dX/dn = 0. Equation (17) gives this derivative of the weight fraction, X, with respect to the refractive index, n, k - 1 ) C - C ) - k - k ) C - C ) ( C B ( A B ( A B ( C B = o (17) [new 91:3) + (cl - 013)]? —- The numerator therefore must be equal to zero for the equality to hold, (kc - kB)(CA — CB) = (kA - kB)(CC - CB) (18) Using the k‘s and c's as calculated from the dn/dc data and substituting these values into equation (18) gives .an agreement of better than 1% for both Copolymers I and II. The composition of the copolymers can also be de- termined by NMR analysis. From this analysis, the weight 28 fraction of vinylidene chloride was determined to be 87%, which is in reasonable agreement with the value of 81% determined from differential refractometry. The NMR data and spectra for the two copolymers can be found in the Appendix. Light Scattering Measurements Light scattering measurements were made on the co- polymers in four solvents: amyl acetate, cyclohexanone, Chlorobenzene and o-dichlorobenzene. Figures 7, 8 and 9 are representative Zimm plots of the light scattering data. Figures 7 and 8 are plots of Kc/R versus Sin28/2 + C and illustrate the usual method of displaying the data. Figure 9 illustrates an alternative method for determining the molecular weight. It is a double plot of Kc/R versus Sin28/2 and then a plot of (Kc/R) a = 0 versus c. Figure 7 is a plot of the data for Copolymer II in cyclohexanone. The data points are in good agreement for the scattering angles from 75° to 142.5°. The data for the lower angles of 37.5° to 60° showed a very pronounced downward curvature and are not on the plot. The reason for the curvature is not completely understood. Figure 8 is a Zimm plot for Copolymer I in o-dichloro— benzene. For this case the data points define a sinusoi- dal curvature, however, the extrapolation is quite straightforward. Figure 9 is the double plot for Copolymer I in amyl acetate. Here again some scatter is evident at the lower 29 ‘ 00mm ecu 72336 2.29.. 8.30.22 38234 .0. 2:9... 0. . \e. NIX 35 O. N. .v. m. m. 36 $23.0 ”2.5 .chEtwaxm .3. cozoacm E0: 33.3.00 200 .5333. 8:... .HH 55:22.00 .8 VXWth .n> ma_<\.¢ZV 23.25 6.3202 «Stung .: 050.... O . \ sir O. N_. a; m. 9. 37 which also indicates a broader composition distribution. A plot such as this can also be used to determine the values of P and Q. For P, the slope of the curve at (vA—vB)/“vo = O is equal to 2P. A qualitative examina— tion of the plots indicate a negative value of P is re- quired which has been shown to be the case. Another aspect of copolymers is illustrated by Figures 10 and ll. These plots demonstrate the dependence of molecular weight on the refractive index of the solvent. The de- gree of heterogeneity of the copolymer is the cause for this dependence and even allows one to measure an appar— ent molecular weight that is lower than the true weight average molecular weight. As indicated in the theoretical section, it is possible to determine the weight—average molecular weights of the two fractions comprising part A and B of the copolymer. Table VI lists the values obtained for the two copolymers used in this study. TABLE VI Summary of Derived Data for Copolymers I and II Copolymer MAa°X 10"4 MBbx 107* MW X 10'4P/Mw Q/Mw Q/Qmaxg I 0.74 21.3 5.61 -0.62 0.44 0.54 II 1.17 17.4 5.27 —0.53 0.37 0.44 a. A—Polyvinylidene Chloride b. B—Polyisobutylene A approach of Leng and BenoitG which uses the following The values for M_ and MB listed were calculated using an equations Q Xo(l - Xo)(2-1A + MB - MW). (19) Table VI is a summary of the derived data for Co— polymers I and II. The table includes all of the molecu— lar parameters determined in this study. The last column of Table VI gives the ratio Q/Qmax: where O is the upper limit on Q. 0 “max vmax 1s calculated -~ Q from the relation :1 - Xo(l - X0); which for both co— polymers is approximately O.82. This ratio can be used as a measure of the heterogeneity of chain composition as compared to the maximum value of unity. To summarize the results of this study, it should be noted trat the techniques of differential refrActn- metry and light scattering are very useful for analyzing c0polymers. The extrapolation technique used to deter- mine the specific refractive increments of the homopoly— mers has been shown to be an effective one. The only limitation on this technique is the refractive index difference between the two homopolymers. As the differ- ence between the refractive indicies of the homepolymcrs decreases, the accuracy of the compositions calculated from the data also decreases. The technique of plotting dn/dc vs no and using the equations of the lines as determined from a least squares analysis does allow one to minimize the experimental error. The compositions of the copolymers have been calculated from the differential Lu W refractometry data. Copolymer I, which was orepareo in a 2M solution, consists of 81% vinylidene chloride and 19% isobutylene. Copolymer II, which was prepared in an 8.5M solution, also consists of 81% vinylidene chloride and 19% isobutylene. ' Theorya predicts that the apparent molecular weight of a c0polymer, as measured by light scattering, should be dependent on the refractive index of the solvent used in the measurement. This refractive index dependence is readily apparent from equations (6) and (9) which define the relationship between apparent molecular weight, refractive index increment, weight fraction, true molecu- lar weight and composition functions. Table IV summarizes the light scattering results and indicates a wide variation in apparent molecular weight with solvent. The extreme cases are for Copolymer I in cyclohexanone, Map = 1.62 x 104, and o-Dichlorobenzene, Map = 83.9 x 10? The molecular parameters, P and Q, as calculated for the two copolymers indicate a difference of approxi- mately 18% in the compositional distribution parameters. Table V lists the normalized values for P and Q with Copolymer I having a broader compositional distribution than Cepolymer II. However, both copolymers are quite broad and have a larger quantity of isobutylene in the higher molecular weight molecules, as indicated from the 40 negative values of P. The breadth of the composition distributions is also indicated from the ratio of Q/Qmax which are 0.54 and 0.44 for Copolymers I and II respectively. The maximum value for this ratio is unity which indicates the heterogeneous nature of the copolymers. Theory also allows one to calculate the weight-average molecular weights of the two fractions comprising part A and B of the copolymer. For cepolymers of homogeneous composition, the sum of the molecular weights of the components is equal to the true weight— average molecular weight. As the data in Table VI indicates, the sum of the components does not equal the true molecular weight. The predominating fraction is isobutylene and also points to a heterogeneous com- position. Again, Copolymer I has a somewhat broader distribution than Copolymer II. The theory of copolymerization predicts that high conversion copolymers will in general be of heterogeneous chain composition. However, these are low conversion copolymers. Copolymers I and II have conversions of 4.6% and 2.0% respectively. All of the differential refractometry and light scattering results indicate copolymers with heterogeneous compositions. Copolymer I, with the highest percentage conversion, does appe r approximately 18% broader in composition than Copolymer II. The explanation for the heterogenc01s nature of 41 these cepolymers must lie in the kinetics of the co— polymerization of isobutylene and vinylidene chloride. Perhaps some type of equilibrium exists which influences the composition of the chains during copolymerization. In conclusion, the findings of this work indicate how the differences in two copolymers prepared as a function of dilution can be analyzed by light scattering. However, much more work could be done to determine the exact sensitivity of this technique in measuring dif- ferences in composition distribution. 10. ll. 12. 130 BIBLIOGRAPHY Debye, P., J. Phys. a Colloid Chem. 21, 18 (1947). Tremblay, B., Rinfret, M. and Rivest, R., J. Chem. Phys._§9, 523 (1952). Stockmayer, w. H., Moore, L. D., Jr., Fixman, J. and Epstein, B. N., J. Polymer Science, 16, 517 " -‘ —-— (1995). Bushuk, W. and Benoit, H., Can. J. Chem.,_§§, 1616 (1958). Krause, S., J. Phys. Chem., 62, 1618 (1961). Long, M. and Benoit, H., J. Polymer Science, Q1, 263 (1962). Kinsinger, J. B., Fischer, T. and Wilson, C. W. III, J. Polymer Science B, 4L 379 (1966). Kinsinger, J. B., Fischer, T. and Wilson, C. W. III,. J. Polymer Science B, 2, 285 (1967). Kinsinger, J. B., Bartlett, J. S., and Rauscher, w. H., J. Applied Polymer Science,_§, 529 (1962) Whippler, C. and Scheibling, G., J. Phys. Chimie_§l (4) 201 (1954) Brice, B. A. and Halwer, J., J. Opt. Soc. AM. 41, 1033 (1951). Zimm, B. H., J. Chem. Phys._;§ (12) 1093 (1948). Carr, C. I., Jr. and Zimm, B. H., J. Chem. Phys. .Ig, 1616 (1950). .42 APPENDIX 43 APPENDIX I NMR Analysis of Vinylidene Chloride-Isobutylene Copolymers ,. . '78 Kinsinger et al) have illustrated the utility of NMR in studying the microstructure of vinylidene chloride-isobutylene copolymers. The NMR spectra were taken with a Varian HR—lOO NMR spectrometer with TMS as an internal standard. The spectra were taken at ambient temperatures in bromobenzene as solvent at approximately 8 wt. % copolymer. The spectra are shown in Figures 12 and 13. Kinsinger et alv have given the formulas to be used in calculating the mole fractions of the monomer units from the spectra. The mole fraction of pairs is {an 2 X 11.“. X+§X+Z~ 8 4 2r _ Y 11313 -12: - .38! /(x + 5Y/8 + Z/4) where X, Y and Z are the areas under the spectra as designated in Figures 12 and 13. The mole fraction of monomer units is fA == fAA + fAB and fB = fBB + fBA The experimental data as calculated from these formulas are 3 AA 42 be Figure l2. NMR Spectra of Copolymer I Figure I3. NMR Speciro of C0p0|ymerlI 46 Copolymer M8%evgifction fAA fAB fBB I 0.80 0.64 0.16 0.03 II 0.81 0.64 0.17 0.02 The mole fraction of vinylidene chloride, M can be A 1 converted to weight fraction, XA’ with the following equation X A I‘vfl‘l B MA = xA mwB + x B BE‘IA where MWB is the monomer molecular weight of isobutylene and MUA is the monomer molecular weight of vinylidene chloride. Using this formula, the weight fraction of vinylidene chloride in Copolymers I and II is 87%. HICHIGRN STRTE UNIV. LIBRARIES III "I ll illlll IIIHIIIIIIIU 9 1 6 65 312 30 09 74