DILUTE SOLUTION PROPERTl-EE OF A STRICTLY ALTERNATING COPOLYMER Thesis for ”19 Degree of ph. D. MECHIGAN STATE UNIVERSITY Joseph H. McCoy 1963 \ .' hg- __L.:'iJ.-;._‘{:‘. H" L L - I my LIBRARY NMC‘r'EGlfl STA’ °° ' “V ‘. RV! b Michi an State :1 EAST LANSING, MICHIGAN a g ,1 University 9' " . ,. 9A ‘. . a. an ‘4. . .. ..‘ v. ABSTRACT DILUTE SOLUTION PROPERTIES OF A STRICTLY ALTERNATING COPOLYMER by Joseph H. McCoy A completely alternating copolymer of isobutylene and methyl a- cyanoacrylate was characterized principally by light scattering and viscosity measurements. Some of the physical properties of the c0poly- mer were compared to those of the two parent homopolymers through ex- isting theories. The bulk copolymer was separated into 27 fractions from a dilute benzene solution by the fractional precipitation method. Elemental analysis of 18 of the fractions representing about 91% of the recovered sample indicated that within experimental error the theoretical 50:50 mole percent composition maintained throughout all molecular weights. Phase studies furnished the critical data necessary to determine the theta temperature of the c0polymer in 2—ethoxy ethanol and of the methyl a-cyanoacrylate homopolymer in cyclopentanone. The theta tem- peratures are 86.6 i 1.20 and 85.0 i 3.2°C, respectively, for the two systems. Intrinsic viscosities were determined for all c0polymer fractions in nitromethane, for 16 fractions in acetonitrile, and for h fractions at the theta temperature in 2-ethoxy ethanol. Intrinsic viscosity-- molecular weight relationships were established in all three solvents on the basis of light—scattering molecular weights of seven fractions. and the unfractionated c0polymer in nitromethane. The resulting relationships are: Joseph H. McCoy in nitromethane, [77] = 3.89 x 10-4 <;M >b0-585 in acetonitrile, [72] b.7 x 10'4 <‘M >h9.56 in 2—ethoxy ethanol [7219 5.99 x 10'4 < M >h0.504 Similar measurements on three fractions of poly-(methyl d—cyanoacrylate) in nitromethane resulted in the tentative Mark-Houwink expression: [77] = b.17 x 10-5 <:M >fi°°75. End-to—end dimensions of the copolymer in nitromethane were calculated from the angular distribution of scat- tered light using both the Debye dissymmetry and Zimm methods. Unper— turbed end—to-end dimensions were also determined from viscosity measure- ments in the theta solvent. Assuming the universal parameterifi to have the commonly accepted value 2.1(i 0.2) x 1021, the unperturbed dimensions were calculated to be only 1.95 times those for free rotation about the bonds. Using the preferred experimental value, ¢'= 1.2(i 0.2) x 1021, the corresponding ratio of the dimensions is 2.33. The actual dimensions of the copolymer based on the measurements of the dissymmetry of the highest molecular weight fractions in nitromethane are about 3.3 times the freely rotating chain dimensions, indicating an expansion of the chain above that which would be expected on the basis of the unperturbed dimensions and the low value of the exponent a in the Mark—Houwink equation. This extra expansion probably results from repulsions of the alternating units of widely differing polarity. DILUTE SOLUTION PROPERTIES OF.A STRICTLY ALTERNATING COPOLYMER By Joseph H. McCoy A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1963 n- ACKNOWLEDGMENTS The author wishes to express his sincere appreciation to Dr. Jack B. Kinsinger for his assistance, encouragement, patience and understand- ing throughout the course of this investigation, and for his many help- ful suggestions and criticisms which made possible the preparation of this thesis. It would be impossible to mention all the colleagues, friends and loved-ones whose counsel, faith and encouragement have aided the author immeasurably during his tenure at Michigan State University. To all of them the author is grateful. Special thanks are given to Michigan State University for providing Graduate Teaching Assistantships, to The Research Corporation and to the Petroleum Research Fund of the American Chemical Society for addi- tional financial assistance. ii TABLE OF CONTENTS Page I. INTRODUCTION -. . . . . . ... ....... ... . . ... ... ... 1 II. THEORY 5 A Solubility . . . . . . . . . . . . . . . . . . . S B Fractionation . . . . . . . . . . . . . . . . . . 8 C. Phase Equilibria . . . 11 D. Relation of Viscosity to Size of Polymer in ' ” Solution . . . . . . . . . . . . . . . . . . 18 E Light Scattering . . . . . . . . . . . 20 F Osmotic Second Virial Coefficient . . . . . . . . 2h III. EXPERIMENTAL .. . . . . . . . . . . . . . . . . . . . . . 26 A. Polymer Samples . . . . . . . . . . . 26 l. Poly-(methyl a-cyanoacrylate) . . . . . . . . 26 2. Copolymer . . . . . . . . . . . . . 27 B. Solvents . . . . . . . . . . . . . . . . . . . . 27 l. Nitromethane . . . . . . . . . . . . . . . . 27 2. 2-ethoxy ethanol . . . . . . . . . . . . . . 27 3. Cyclopentanone . . . . . . . . . . . . . . . 27 c. Solubility . . . . . . . . . . . . . . . . . . . 28 D. Fractionation . . . . . . . . . . . . . . . . . . 28 l. Copolymer . . . . . . . . . . . 29 2. Poly-(methyl a-cyanoacrylate) . . . . . . . . 30 E. Determination of Phase Separation . . . . . . . . 31 1. Density . . . . . . . . ... ........ .1. . . 33 a. Solvents . . . . . . . . . . . . . . . 33 b. Polymers . . . . . . . . . . . . . . . 3h F. Viscosities . . . . . . . . . . . . . . . . 36 1. Solution Preparation . . . . . . . . . . 37 2. Measurement at theta Temperature . . . . . . 39 6. Light Scattering . . . . . . . . . . . . . . NO 1. Instrumental and Operation . . . . . . . . . ho 2. Calibration . . . . . . . . . . . . . DO a. Working Standard . . . . . . . . . . . .hl b. Standard Polystyrene’ . . . . . . . . . L2 c. Results of Calibration . . . . . . . . h2 3. Light Scattering Measurements . . . . . . . . h3 a. Solvent . . . . . . . . . . . . . . . . Lb b. Solutions . . . . . . . . . . . . . as H. Specific Refractive Index Increment . . . . . . . h8 1. Interferometer . . . . . . . . . . . . . . . h9 2. Differential Refractometer . . . . . . . . . N9 a. Cells . . . . . . . 51 b. Calibration of Differential Refractometer53 (1) Sucrose . . . . . . . . . . S3 (2) Alkali chlorides . . . . . . . . 55 iii TABLE or CONTENTS (Cont.) Page IV. RESULTS AND DISCUSSION . . . . . . . . . . . . . . . . S7 A. Solubilities . . . . . . . . . . . . . . . . . 57 B. Fractionation . . . . . . . . . 61 1. Analysis of Fractionation Data . . . . . . 65 C. Phase Data .. . . . . . . . . . . 67 D. Polymer Dimensions and Molecular Weight . . . . 73 1. Zimm Method . . . . . . . . . . . . . . . . 73 2. Dissymmetry . . . . . . . . . 7h 3. Extrapolation of Light Scattering Data . . 7h E. Osmotic Second Virial Coefficient . . . . . . . 88 F. Viscosities . . . . . . . . . . . . . . . . . . 89 1. Copolymer . . . 89 2. Degradation of Poly-(methyl a- cyanoacrylate) 99 V. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . . . . . 117 REFERENCES.......................120 APPENDICES . . . . . . . . . . . . . . . . . . . . . . 125 iv LIST OF TABLES Table Page I. Flow Times of Solvents in Two Viscometers . . . . . . 36 II. Solubility Behavior of Methyl a-cyanoacrylate/iso- butylene Alternating Copolymer . . . . . . . . . 57 III. Solubility Behavior of POly4(methyl a-cyanoacrylate). 58 IV. Solubility Behavior Of Polyisobutylene . . . . . . . 59 V. Data from Copolymer Fractionation I and Results of Elemental Analysis . . . . . . . . . . . . . . . . . 62 VI. Data from Copolymer Fractionation II and Results of Elemental Analysis . . . . . . . . . . . . . . . . . 63 VII. Critical Data for TwO Polymers in their Theta Solvents . . . . . . . . . . . . . . . . . . . . . 71 VIII. Thermodynamic Parameters from Phase Equilibria . . . 72 IX. Results from Dissymmetry Measurements on Copolymer in Nitromethane (250) . . . . . . . . . . . . . . . . 85 X. Results from Zimm Plots of Copolymer Experimental Light Scattering Data in Nitromethane . . . . . . . . 86 XI. Corrected Light Scattering and Viscosity Results in Nitromethane . . . . . . . . . . . . . . . . . . . 87 XII. Viscosity Results for Poly-(methyl a—cyanoacrylate/ isobutylene) from Fractionation Run I . . . . . . . 97 XIII. Viscosity Results for Poly-(methyl a-cyanoacrylate/ isobutylene) from Fractionation Run II . . . . . . . 98 XIV. Viscosity Results for Poly—(methyl a-cyanoacrylate) Fractions in Nitromethane . . . . . . . . . . . . 101 XV. The Expansion Factor and Its Dependence on the Molecular Weight of Copolymer Fractions in Nitromethane 107 XVI. Unperturbed Dimensions of Poly-(methyl a-cyanoacrylate/ isobutylene) in 2- -ethoxy ethanol . . . . . . 108 XVII. Comparison of Molecular Displacement Lengths for Two Copolymers and Their Parent Homopolymers . . . . . . 109 XVIII. Interaction Par/meterx and K-Values Obtained from a Plot of [77}? 3/M1/ 3 Versus Iii/[7)] for Poly-(methyl a-cyanoacrylate/isobutylene) in Good and Ideal Solvents 112 Figure 10. 11. 12. 13. 1h. 15. LIST OF‘FIGURES Typical phase diagram Densities Of the theta solvents as a function of temperature . . . . . . . . . . . . . . . . . ... . . . Integral and differential distribution curves for methyl a-cyanoacrylate/1sobutylene copolymer fractions . . . . Binary phase diagrams for methyl a- -cyanoacrylate/ISOa butylene c0polymer in 2- -ethoxy ethanol . . . . Binary phase diagrams for methyl a-cyanoacrylate homo- polymer in cyclopentanone. . . ... ... . ..... . .,. Reciprocal critical temperatures versus the molecular size function for three MCyA homo olymer fractions in cyclopentanone and for four MCyA B copolymer fractions in 2- -ethoxy ethanol . . . . . . . . . . . . Zimm plot for MCyA/IB copolymer Fraction 12 in nitromethane . . . . . . . . . . . . . . . . . . . Zimm plot for MCyA/IB copolymer Fraction 20b in nitromethane . . . . . . . . . . . Zimm plot for MCyA/IB unfractionated copolymer in nitromethane . . . . . . . . . . . . Zimm plot for MCyA/IB copolymer Fraction h in nitromethane . . . . . . Zimm plot for MCyA/IB copolymer Fraction 3 in nitromethane . . . . . . . . . . . . . . . . . . . . . Zimm plot for MCyA/IB copolymer Fraction 203-B in nitromethane . . . . . . . . . . . . . Zimm plot for MCyA/IB copolymer Fraction l-X in nitromethane . . . . . . . . . . . . . . Zimm plot for MCyA/IB c0polymer Fraction 202 in nitromethane . . . . . . . . . . . . . . Viscosities in acetonitrile of MCyA/IB copolymer fractions from Run I . . . . . . vi Page 16 35M 66 68 69 7O 75 76 77 78 79 80 81 82 91 Figure 16. 17. 18. 19. 20. 21. 22. LIST OF FIGURES (Cont.) Page Viscosities in nitromethane of MCyA/IB copolymer fractions from Run I . . . . . . . . . . . . . . 92 Viscosities in nitromethane of MCyA/IB copolymer fractions from Run II . . . . . . . . . 93 Viscosities in 2- -ethoxy ethanol of MCyA/IB copolymer fractions from Run II . . . . . . . . 95 Viscosities in nitromethane Of MCyA homopolymer fraCt10n5.1. o o o o o o o o o o o o o o o o o o o o a o 103 Mark-Houwink plots for MCyA/IB copolymer in nitromethane, acetonitrile, 2-ethoxy ethanol; and for MCyA homopolymer in nitromethane. Also shown is the log-log relation between the osmotic second virial coefficient A2 and the weight-average molecular weight of the copolymer in nitromethane . . . . . . . . . . . . . . . . . . . . . . 10h Relation between [7712/é/M1/3 and M/'[77] for MCyA/IB copolymer in a good and in an ideal solvent . . . . 111 Root-mean-square end-tO-end dimensions of the copolymer . as a function of the square root of the molecular weight . . . . . . . . . . . . . . . . . . . . . . . . . 11h vii INTRODUCTION Following the initial report by Tremblay, Rinfret and Rivest (1) that the intensity Of light scattered by a c0polymer in dilute solution depends not only on the molecular weight of the solute but also on the compositional variations of the various scattering elements, an increas- ing interest became centered on the dilute solution properties of co- polymers. Light scattering studies, in particular, have received most of the attention of various investigators, both from the experimental (2,h-7) and theoretical (2-6) points of view. The most formidable prob- lem in the study of copolymers to date has been their compositional heterogeneity. Stockmayer and co-workers (2) derived an equation which related the intensity of scattering to the degree of nonuniformity in composition of c0polymers. The complication arises here from the fact that the intensity of light Scattered by a solute is proportional to the difference in refractive indices of solvent and solute; thus a solute such as a c0polymer having two differing refractive species gives rise to dissimilar intensities from different points within the same molecule. If the two Species composing the copolymer happen to have the same re- fractive indexnlmfichistfighly unlikely, then regardless Of their composi- tional distribution the resulting scattering will be the same as if the copolymer were a simple hcmOpOlymer. Essentially the same behavior re- sults if the copolymer is reasonably homogeneous, such as when the aver- age sequence lengths Of the constituents are very small compared with the wave length of light used for illumination. When the average sequence . C. .r» v s 2 length reaches the limiting value of one unit, a completely alternating copolymer results which is a special class of copolymer having optical prOperties Similar to those of an ordinary homopolymer. In the present work the fractionation of such a copolymer and the characterization Of some of its properties by dilute solution measure- ments are reported. The alternating copolymer, which could also be called a polymer of repeating unit ~AB-, where A represents the methyl a-cyanoacrylate (MCyA) groups and B represents isobutylene (ID), has the structural unit: Based on steric considerations, the structural formula has a head-tO-tail configuration Of the successive monomers, although polar effects Obviously influence the manner of placement. NO conclusive evidence for head-to- head addition is known. Other systems have been known to produce high degrees of alternation in copolymers, notably the polysulfones (8), vinylidene cyanide/vinyl acetate copolymers (9), and c0polymers of ethylene and butene-2 (10). The latter two systems have compositions reported over a wide range of values, but the polysulfones and some co- polymers of vinylidene cyanide (9) have strictly alternating units. Thus the effect of the polarity of a monomer cannot be underestimated in its influence on the alternating tendency in copolymerization. The .1 .x. _~ .... .» similarity of methyl a-cyanoacrylate to vinylidene cyanide, H2C=C(CN)2, is readily apparent and it, too, would be expected to have a tendency to alternate in c0polymers. Most of the dilute solution properties of copolymers reported to the present time have been on statistical (2,h,6) and block (h,6,7) co- polymers Of styrene and methyl methacrylate. NO light scattering—— viscosity results have been reported on the alternating copolymers prepared by Natta or from vinylidene cyanide/vinyl acetate. The only report of dilute solution properties of an alternating copolymer is the recent work of Ivin, Ende and Meyerhoff (11) on hexene—l polysulfone in ideal (theta) solvents. However, the properties of the polysulfones cannot be compared to the individual parent homopolymers since sulfur dioxide does not homOpolymerize. In the present work the MCyA/IB alter- nating copolymer of random coil configuration was studied in both a good and a theta solvent. The studies included measurement of the size of the coils by light scattering and comparison of these dimensions through existing theories to the solution viscosity. An attempt was made to compare the solution prOperties of the copolymer to those of the two parent homOpolymers, but degradation of the poly-(methyl a-cyanoacrylate) at higher temperatures and in some solvents prevented a quantitative comparison. The solution prOperties studied in this work fall under two general classifications: Thermodynamic and hydrodynamic. In the former are in- cluded such areas as solubility, phase equilibria, and weight-average molecular weights and osmotic second virial coefficients as determined by light scattering. The principal hydrodynamic property is the viscos- ity and its relation to the size of the polymer molecule in solution. Solubilities aided in selecting solvents for fractionation and for the subsequent studies; phase studies provided critical data which en- abled a comparison of experiment to theory Of dilute solution properties. o I (‘\' THEORY Solubility Any theoretical considerations of the solubility Of a polymer in a solvent must necessarily consider the free energy of mixing of the two phases. By a statistical mechanical treatment, both Flory (l2) and Huggins (13) independently derived analytical expressions for the free energy of mixing based on a lattice model of the liquid. This model considered both solvent molecules and polymer segments as occupying equivalent Sites in the lattice. The formation of a solution is con- sidered to occur in two steps: disorientation of the polymer molecules and mixing of the disoriented polymers with solvent. The latter contri- bution is by far the more significant, but separate entropy contributions are calculated for the two processes. The first may be represented by the approximation (for large x): (l/an) ASdis = k ln[(z-l)/e] (1.1) where x is a molecular size parameter equal to the ratio of the molar - volumes Of polymer and solvent, n2 is the number of polymer molecules;lr and z is the lattice coordination number. The entrOpy of mixing in the second step is given as: ASm = —k (nllnvl + nzlnvz) (1.2) where v1 and v2 are the molecular volumes of solvent and solute, re- spectively, and k is the Baltzmann constant. Hildebrand (1h) has derived an alternate method of calculating the entropy of mixing based upon the free volumes available to each type of molecule. The free volume, which represents the difference between the actual volume occupied by the constituents in a solution and the minimum volume each would occupy in a tightly packed state, is considered to be always the same fraction of the total volume. Although this implication Of incompressible molecules with rigid dimensions is somewhat unrealis- tic, the concept is free of the assumptions connected with the lattice model and has proved useful in the limit by giving the same result. Normally the two separate approaches give slightly different values Of the entropy of mixing, but since ASm is always positive, it is the heat of mixing term which is more important in determining thesfign of the free energy of mixing. Two substances will mix whenever AFm is negative. The heat of mixing results from replacement Of solvent-solvent and polymer—polymer contacts by solvent—polymer contacts. The magnitude of this contribution to the free energy depends upon the degree of inter- action Of the unlike species in solution. The product of the energy change Aw12 associated with the formation Of each solventLpolymer contact pair and the number of such pairs occurring in solution gives the heat of mixing, thus AHITI = Awlzplz (103) Considering the total number of polymer chain segments and the num- ber of solvent molecules forming pair contacts, the average value of the number of such contacts is calculable according to the theory so that the heat of mixing expression becomes: CI t. q.‘ AHm kaanrvz (1.11) X, zAw 1 2x l/kT where.ka is a dimensionless quantity characterizing the interaction energy per solvent molecule divided by kT. Combining the expressions for AFm = AHm - TASm leads to the result: ’ AFfi = kT(nllnv1 + nzlnvz +.X&n1v2) (1.5) for a two—component system. This equation finds utility in the section on phase equilibria. Since there are two different polymer Species present in a binary copolymer instead of one which the above theory considers, the expression for the interaction energy must be amended to include the additional interactions. Stockmayer, et 31. represented4)q for a binary copolymer as: X1 = $11 X111 * Spa X113 ' gap. We XAB(1°6) where Q and QB are mole fractions of A and B in the copolymer, XlA and jKTB are the interaction energies for the homopolymers A and B with pure solvent, and ;(AB is a parameter expressing A-B interactions. It is questionable if equation (1.6) would apply to a copolymer in which the sequence lengths are short (e.g.,alternating copolymer) because the solvent would have difficulty in distinguishing just two kinds of co- polymer segments. For an alternating copolymer having large repulsive A-B interactions, J TC complete miscibility occurs in all prOportions.* Lowering the temperature pro- duces a phase separation as soon as the condition [52(AFm)/bX22] = 0 occurs. The critical temperature TC, can be experimentally determined from the maximum in the phase diagram. While the above theory is general for any two—component liquid system, it also applies to polymer-solvent systems. In this case it is necessary to employ volume fractions instead of mole fractions (volume fractions are more appropriate when the molar volumes of the two molecular Species are quite different ). The volume fraction, v2, refers to the volume element and not to the solution as a whole. From general solution theory of polymers the relative partial molar free energy AF (or chemical potential per mole) can be obtained from the condition (aAF/an1)n2,T,P° When equation (1.5) is treated in this manner on a molar basis the expression becomes: H1 ' LL10 = RT[ln(l‘V2) + (l ‘ %)V2 4' X1V22] (2'6) where u, R, T and v2 have their usual significance;:K; is the thermo- dynamic interaction parameter; and x is the molecular size function equal to the ratio of the molar volumes of polymer and solvent, < M >'V/V1, where < M >lis the average molecular weight (which for a heterogeneous polymer is the number-average), V is the specific volume of the polymer, and V1 is the molar volume of the solvent. * Recent evidence has been reported concerning the existence in polymer solutions of a lower consolute temperature, above which phase separa- tion occurs (11,31). 15 Applying the critical conditions for phase separation to equation (2.6) gives the first and second derivatives of the chemical potential with respect to volume fraction equal to zero as follows: 1 1 W.” .. (l - i) — 2X1V2 = o (2.7) I O TIE—VET: - 2X1 (2.8) Simultaneous solution of these two equations for the critical values ><1c and v2c gives p... “Z 1...; VZC g (1+XI; 2) —172 (2.9) ug ch = (1+X1/2)2/2x 1/2 + 717; (2.10) X where the approximations refer to large values of x. Thus the critical concentration for phase separation Occurs at very small values Of the volume fraction of polymer. This results in an exceedingly unsymmetrical phase diagram which is characteristic of polymers. Equation (2.9) expresses the location Of the critical composition in mathematical terms, but in order to get a clearer idea of the reasons for this dissymmetry in the location of the binodial, one must consider the osmotic forces in existence. Whenever phase separation occurs in a pOlymer solution the more concentrated phase is somewhat erronerously called the "precipitated" state. In this condition the polymer molecules find their Own environment more satisfying than that of the solvent, but 16 the greater volume of the more dilute phase induces the polymer molecules to disperse in it. Being much greater in number, however, the solvent molecules are much more effective in equilizing their number per unit volume and hence both phases are dilute. For this reason the term "pre- cipitated phase" is misleading and one should speak in terms of the more concentrated and more dilute phase, while realizing that both are dilute. O A 1 l I L A a # 2 b o 8 10 12 1h 102v2 Figure 1. Typical binodial for a polymer-solvent system showing both experimental (solid) and theoretical (dashed) curves. Phase studies as related to the dilute solution properties Of poly- mers are most useful for the purpose of providing a means of determining from experimental measurements the temperature at which a polymer of infinite molecular weight will become soluble in a given solvent. 'This temperature, called the Flory or "theta" temperature, 6, has a more use- ful purpose in that in the dilute solution theory of polymers it represents 3v .1 17 the temperature at which the excess chemical potential vanishes and the solution thus behaves ideally (i.e., van't Hoff's law is obeyed for a given poor solvent —— polymer system). Theoretically a polymer molecule assumes random—flight behavior. Thus a solvent which is "poor" solu- bility-wise for a given polymer can be an ideal solvent, thermodynamically speaking. The theta temperature is therefore analogous to the Boyle point of a real gas, at which condition the gas behaves ideally with no change in the pressure-volume product for a changing pressure over a limited range. The interaction parameter )(l, which expresses the first neighbor interaction free energy (divided by kT) between solvent and polymer molecules, is actually a combination of the heat and entropy of dilution parameters (32) represented by‘Kl and Ipfi, respectively, and defined as: Thus )(1 is related to the heat and entrOpy parameters through the excess chemical potential expression (pl - u1°)B RTCKI - H/1)v22 (2.12) Then )(1 which reduces to the value 1/2 at the ideal conditions similarly to (1/2 Mil) - 1,], (2.13) equation (2.10) for the hypothetical case of a polymer of infinite .molecular weight at 9. The theta temperature is defined as: e =K1T/ 1,}, (2.111) 18 which, when substituted into equation (2.13), gives x =1/2-VI1-9) (215) 1 1 T - combining equations (2.10) and (2.15) gives a linear relationship be- tween critical temperatures TC and the molecular size function x from which it is possible to evaluate the theta temperature and entrOpy of dilution parameter from experimental critical temperatures. Thus: 8 l WANT) =17. . .1— (2.16) c )( 2 2x which rearranges to: 1 l l 1 1 = + ( +—) (2.17) Tc O gITIEITZI 2x - Relation of Viscosity to Size of Polymer in Solution The enhancement Of the viscosity of a solvent by a dissolved polymer molecule is quantitatively expressed by the intrinsic viscosity,‘defined as: In] 2 g (771. - 1)/c = C3 (lung/c (3.1) c where 77r is the relative viscosity and c is the concentration of solute in g./IOO ml. Of solution. The intrinsic viscosity is customarily deter- mined from the Huggins equation (33): (Hr - 1)/c [77] + k'inlzc (3.2) (In Tip/c [77] - Min 12c (3.3) In the Fox-Flory theory (3b) the intrinsic viscosity is given as: [77] = Ls/M (3.11) J . :4 ..v ..n 19 so that it depends upon two parameters; 9 a complex function which 2 should be universally constant for all systems, and the ratio of the volume encompassed by the molecule in solution to its molecular weight. At the theta temperature, where a polymer can asSume dimensions that are governed only by the nature of the polymer (i.e. skeletal structure and steric effects), the ratio of these so-called "unperturbed" dimen- sions to the molecular weight is constant. Non-ideal solvents which interact with the polymer cause the chain to eXpand, resulting in a larger volume of the molecule. Equation (3.h) has therefore been rep- resented by: [n] = KMl/Z 03’ (3.5) where K is a constant related.tc>@ and the "unperturbed" dimensions, and the factor a represents the degree of expansion of the polymer as a result of the presence of a non-ideal solvent. On the basis of its inception into the theory, the factor a has the value unity in a theta solvent at T = O. From measurements of the viscosity in good and ideal solvents the eXpanSion factor may be calculated. This gives a direct relationship between the dimensions as determined by light scattering and the "unperturbed" dimensions. Thus L = aLo, where L represents the root—mean-square distance separating the ends of the polymer chain (Lo may also be determined directly by light scattering at the theta temper— ature). The expansion factor a has also been related to the thermodynamic interaction parameter )(1 in another theory by Flory (28c). The expres- sion is: y 2O \ /2 2CM(1/2 - X1)Ml/2 = 2cMnj,(l — o/T)IVI1 a5 - a3 (3.6) 2cM [(9/2n).(m/10233/2 (I'r/Nvi) / where Ipi, the entropy parameter, and the other symbols have been defined previously. Values of CK, Obtained by this theory are approximately one- half as large as those obtained by a more rigorous theory due to Zimm, Stockmayer, and Fixman (35). Light Scattering Lord Rayleigh, who was the first to correctly explain the phenom- enon of light scattering (36), expressed the intensity of light as observed at a distance r from a scattering center as: ierz 8:141! azno‘1t R = = .. (1 + c0329) (h.l) 9 IO 4 l0 where Re is the reduced intensity (Often called the Rayleigh ratio); ie is the intensity of light Scattered at an angle 6; IQ is the unpolarized incident intensity;]/ is the number Of isotropic scattering particles :per unit volume having polarizability a; and n0 is the refractive index at wave length Ao- Following Debye's application of the Rayleigh theory of scattering 'to the measurement Of scattering from polymer solutions (37), the tur- lDidity, which is the reduction of the incident intensity of light per Lunit of scattering volume, has been commonly employed: thus, ier2 2n 428 I sin one 0 (1611/3) Re/(l + cosZO) T (L2) T 9" I r I. ‘lq .4. Hula. Iv r. .r. . .~‘ ”I ..14 v. . . ... .. ... rm .1 ..A I I‘\ no a u. a e e .C s . F\~ av Q as! u ~ nsu A .. . .. a .<‘ .1. . A s r. C a ._‘ ae .~< h e . . a \ ..- 21 The Rayleigh scattering from gases and liquids arises from their non-homogeneous molecular structure. Making a solvent even more inhomo— geneous by adding a solute increases scattering. From this initial work by Rayleigh and Debye, knowledge of the number, size, and structure of solute particles can be drawn from observations on the angular dis— tribution of the scattered light. Considering the non-ideality of the system, the expression for the concentration dependence of the scattering can be given in virial form as: Kc 2fl2noz(dn/dc)2 c 1 ...IT. = o — = FI- + 2A2C 4' 3BC2 + 000(LL03) 9° N7‘04 R90 or alternatively, Hc _ l T " M + ZAZC (Li-)4) by neglecting higher virial terms, where the concentration is in g/cc., and M is the weight-average molecular weight. The optical constant H = (16n/3)K.depends only upon the wavelength of radiation, the refractive index, no, of the solvent at wave length No, and the Specific refractive increment at 10, (dn/dc). Equations (h.3) and h.h) apply only to solute particles which are small compared to the wave length of the incident radiation (<‘N’X/2O). For particles much larger than this, interference occurs in the scattered radiation, resulting in an unsymmetrical angu- lar scattering pattern. In this case equation (h.h) is multiplied by a factor P(O) (37) which corrects the Observed scattering to the value it would have in the absence of the interference. Tables of this func- tion have been tabulated for various particIe sizes and shapes (38,39). 22 Equation (h.h) then assumes the form % = f- =—l—- + 2A2c (mu) One of the major problems in light scattering has been that of re- lating the scattering intensity to the dimensions of a randomly coiling, linear chain molecule in solution. Owing to its continuous change in configuration as a result of rotation about the bonds, the dimension ob— tained is a time-average dimension. Zimm (hO) approached the problem by recognizing that the scattering, which is a function of both angle and concentration for large polymer molecules, could be plotted simultaneously as a function of O and c. The limiting value of P-1(O) is expressed as: Lim p"1(e) = 1 + £6.11": (R' )2 sin2 3- + (14.5) c=O 3X2 9 where (R'g)2 is the radius of gyration of the polymer molecule. For a random coil configuration (R'g)2 = L2/6, where L2 is the mean-square end- tO—end distance of the chain. Substituting equation (h.5) into (h.h7) gives 1 1 8n2 L. KC . e dig—'R=MPIBT=M(1+WLZSIHZE+'°') “"8 e . Thus the limiting lepe of the zero angle line in a plot of Kp/Re against Sin2 % t kc (where k is an arbitrary constant chosen to suitably spread out the data) yields the osmotic second virial coefficient A2; the ratio of the limiting slope Of the zero concentration line to the intercept gives the mean-square end-to-end dimension; and. the reciprocal of the intercept represents the weight-average molecular weight, <:M >w. 5/. a ~o ~“" va-‘ .‘1 a... r E, .- /. ... E . . a a .. a a v 1 r I . .4 3 a w . a a 23 However, the dimensions of the molecule Obtained in this manner are "z-average" dimensions, and some knowledge of the molecular weight dis- persity of the sample is required before the weight—average dimensions can be calculated from the expression: < L2 >w = < L2 >z (h + l)/(h + 2) (LI-7) where h is the parameter in the distribution formula used by Zimm (hOa). A molecular weight measurement by another method, for example, osmotic pressure, which yields a number-average molecular weight, and comparison of the two gives immediate information on the heterogeneity of a sample. An equation similar to (h.7) could then be written <:M >n = <:M >w h/h+1. An absolutely monodisperse polymer has a ratio <.M >v/k M >n = l and h = 00. In the case of a heterogeneous polymer having the "most prob- able distribution", h = l and the full ratio of averages becomes : : ::3:2:1(28d). z w n In measuring the light Scattered by dilute solutions of c0polymers, the preceeding equations will apply only if the distribution of the two monomer components is uniform throughout the copolymer and their sequence lengths are very short compared with the wavelength of light. In co- polymers where a considerable disparity in composition may occur the equation for Rayleigh Scattering has been expressed by Stockmayer and co-workers and Benoit (2,h) as: = t 2 ' Re K Elli ci Mi (b.8) where 7],, c. 1, Mi are the specific refractive index increment, weight concentration and the molecular weight, respectively, Of scattering .or :» a r /— 2h component i. For such systems the actual measured quantity is R6 = 10272 c Mapp (11.9) where an apparent molecular weight is obtained from an average value of the specific refractive increment, EA The specific refractive increment is assumed to depend linearly on composition, and the recent work of Kinsinger, gt 31. (bl) has given support to this assumption. Their study of the colligative nature of this increment showed that it is possible to calculate the average composition of a copolymer based on the measure- ment Of the dn/dc of the whole c0polymer and the individual parent homo- polymers A and B in the same solvent. Hence (dn/dc) i7 =x 2/A + (1 -xA)vB (11.10) copolymer= A where XA = cA/XCA + CE) is the weight fraction of Species A having weight concentration cA in the copolymer. The weight fractions may then be used to determine the mole fractions. Osmotic Second Virial Coefficient Since the osmotic second virial coefficient, A2, appears in the virial eXpansion Of the equation Of state for Rayleigh scattering from a solution (h.3), it is a measure of the deviation of the solution from ideality and may be related to factors causing these deviations. Essentially A2 is a measure of the tendency Of the solvent to inter- act with the segments of the polymer chain in preference to the existence of polymer-polymer and solvent-solvent contacts. The smaller A2, the lower the tendency for interaction and the poorer the solvent until at .A2 = O the chain assumes its random flight behavior, having dimensions 25 governed only by the Skeletal effects of the chain to the complete ex-. clusion of any Osmotic effects. Large values of A2 mean that the poly- mer segments tend to avoid one another as a result of their van der Waal's "excluded volume" and prefer to interact with the solvent mole- cules. The former condition (A2 = 0) results in a polymer having a tightly coiled configuration, whereas the latter case would represent a more expanded structure. Zimm (h2) was the first to predict a dependence Of A2 on the molec- ular weight. With A2 also depending on the dimensions of the molecule, the interrelation Of A2 and [77] was suggested. Newman, _e_t 31. (113) have related both A2 and [TH to the excluded volume effect, which generally introduces non-Gaussian character in chain configurations. This is in agreement with the widely accepted view presented by Flory and Fox (ht) that the molecular weight dependence of EU] is more closely related to the excluded volume effect than to the draining effect. According to theories and results reported to date, A2 values de- crease slightly with increasing molecular weights of the polymer. Flory's theory expresses the dependence in the form A2 = cME, where c and 6 are constants, the latter having values ranging usually from -O.1 to -O.3. EXPERIMENTAL Polymer Samples l. Poly:(methy1 a-cyanoacrylate).— MCyA monomer was obtained from the Rohm and Haas Company, Philadelphia, Pennsylvania. The monomer was inhibited against autopolymerization and was stored in an air-tight polyethylene bottle at 00 until ready for use. A typical polymerization was carried out as follows: to a large test tube was pipetted 25 ml. of the chilled monomer. Dry, oil-pumped nitrogen was bubbled through the monomer for several minutes to sweep out any dissolved air. One or two drops of a boron fluoride etherate solution (cationic catalyst) was added to inhibit possible anionic polymerization. About 50 mg. of a, a'—azobis-isobuter-nitri1e (AIBN), a free radical initiator, was added. (The observation that MCyA mono— mer can be readily polymerized by free radical methods has been reported by Canale and co-workers (h5)). After the catalyst was mixed into the contents of the tube, it was then lowered into a water bath and illum- inated at close range by the ultraviolet radiation from a mercury— vapor lamp for 18-2h hours. After this period of time, the polymeric material had assumed a hardened, contracted form with numerous voids visible within the tranSparent mass. The block of material was easily removed from the tube by warming it in an oven. Further mild warming completed the polymerization or volatilized any remaining monnmer. This heating was accompanied by a slight yellow discoloration of the polymer. 26 . .. «\— n P. c. / . I. 9. o 2 r g .«E a; ... . . ~. .u r . .. a . a ... .. . .. . .. ._ ... . . T. v a . . «at :m p/. . l . 4 a . a ... .. t .r. .v a a . . .... .s. a «\a . . o . i Q t. \ “J- .l\ I‘ I . ~v — \ 27 This polymer was designated as JM to distinguish it from a sample labeled RKG obtained from the Rohm and Haas Company. 2. Copolymer.- The methyl a-cyanoacrylate/isobutylene copolymer (MCyA/IE), furnished by the Rohm and Haas Company, was a fluffy, white, non-tacky powder. NO details of the polymerization conditions were given. Solvents The solvents for the phase equilibria, Viscosities, and light scattering measurements were purified before use. 1. Nitromethane.- Different batches of C.P. grade nitromethane (Commercial Solvents) were dried initially over calcium chloride and finally over calcium hydride. Middle cuts were taken in the distilla- tions through a 26-inch column packed with glass helices. The purified solvent was stored in an automatic buret in the low humidity instrument room. Physical constants were: b.p., 99-100o at 737 to 7h6 mm. Hg; n50 = 1.3813 i 0.0001. 2. 2aEthoxy ethanol (Cellosolve).- A fresh research-grade sample 'was used as received from Union Carbide Chemicals Company without further purification; nfi°= l.hO73. 3. Cyclopentanone.- Twenty-five milliliters of a previously dis- tilled sample was redistilled through a short Vigreux column. Later distillation Of a fresh sample after drying over calcium chloride gave the following constants: b.p., 127—128o (7H2 mm.); n5°= l.h363; d20/4 = 0.92181 (literature Values (97) - b.p., 130.6 (760 mm.); 28 n50 = 1.1366; dag/L1 = 0.9118). Solubility Solubility tests were performed on both the MCyA/TB copolymer amdpoly- (methyl a-cyanoacrylate). TO ca. 20-25 mg. of polymer sample contained in a small test tube was added 1/2 ml. of the solvent under considera- tion. Tube and contents were then heated to an elevated temperature range (usually 75-800) for a period up to one hour. If no detectable solubility occurred the liquid was designated a non-solvent for the polymer being tested. If partial or complete solubility occurred, the solution was then cooled below room temperature for further observa- tion. Classification of the organic liquids as solvents or non-solvents was more or less arbitrary (Tables 11 and III). Fractionation Solubility behavior of the copolymer indicated that benzene (8 = 9.16) was a suitable solvent for the fractionation medium and petroleum ether (8 = 6.9) satisfied the requisites for a non-solvent. Using this solvent-precipitant pair, two complete fractionations were made by step- wise addition of the ether to a progressively more dilute solution of the copolymer. Twenty—one fractions were separated in the first at- tempt which was carried out over a period of several months in a 30-1. water bath at 30.0 i 0.50. The initial solution volume was 2 l. Eighteen of these first fractions were analyzed for carbon, hydrogen and nitrogen content. Information obtained from this initial fraction- ation enabled a second, more precise, fractionation to be performed, thereby producing a larger number of fractions which were smaller in - A. S .-" 29 size and presumably more homogeneous in molecular weight. The homopolymer was fractionated in a manner similar to the co- polymer. A weighed quantity of the polymer was dissolved in suffic- ient acetonitrile to produce a 1% solution. Preliminary tests indicated that ethanol was preferable to water, acetone, or dioxane as a precipi- tant. Copolymer (Run I). To 2 liters of benzene contained in a 5-1. round bottom flask was added 20.06 g. of the copolymer. The contents were warmed slightly to insure complete solution. The petroleum ether was added dropwise from a graduated separatory funnel to the stirred solution which was maintained at a temperature about 2-3 degrees above the final equilibrium temperature of 30 i 0.50. As soon as a slight turbidity developed which persisted, addition of the non-solvent was stopped and the mixture was warmed until the turbidity disappeared, indicating the existence of a single phase once again. According to Huggins (h6), the addition of non-solvent to solution in this manner produces local var- iations in the composition of the solvent mixture and hence in molecular weight distribution between the phases. Warming the mixture until a homogeneous single phase results, and then permitting Slow cooling with stirring until thermal equilibrium is attained gives more uniform phase separation. Fractions were separated from solution in this manner, with about 2b hrs. being required for the precipitated phase to settle. The supernatant phase was forced by air pressure through a siphon tube into a similar flask where the procedure was repeated for the next fraction. 30 The fraction was dissolved in warm benzene, filtered through a coarse fritted filter, then poured slowly into a large excess of stir- red petroleum ether. The copolymer separated as a white, fluffy precip- itate. The fraction was again dissolved in benzene and the process repeated. The final precipitate was collected in a tared, fritted- glass filter, washed with petroleum ether, and dried to constant weight in a vacuum oven at 55-600. Results appear in Table V. (Run II).- For the second fractionation only one-half the amounts of materials were used as in the first run. For this fractionation a constant temperature bath with a capacity of over 50 gals. was regulated at 30.0 i 0.0050. Evidently, improved temperature regulation along with the benefit of improved manipulative techniques and data acquired in the first run led to vastly improved sharpness in the fractions. Dry nitrogen pressure was used to force the supernatant solution from the flask. Fractions were doubly precipitated from benzene solutions as in I, collected on tared filter crucibles, washed with petroleum ether, and dried in a vacuum oven at 75-800. Several fractions (205- 208) were inadvertently dried at 1000, producing a hard, button-like cake. Since this form of the samples hindered their ease of solution, they were freeze—dried from benzene solutions to render them in a light, expanded form more suitable for use. Complete results are shown in Table VI . ‘Poly:(methyl a-cyanoacrylate) To a 1% solution Of the homopolymer in acetonitrile was added ca. 1/10 an equivalent volume of ethanol which produced an appreciable turbidity. Warming the mixture while stirring permitted most of the 31 separated phase to solubilize. The solution was returned to its 200 en- vironment and sufficient time allowed for phase separation to once again occur. After siphoning Off the supernatant, the first fraction was taken up in acetonitrile and precipitated into excess ethanol. The dispersion required heating on a steam bath to produce a coagulated, filterable fraction which was redissolved a second time in acetonitrile and finally precipitated into water before drying and weighing. Succeeding fractions were reprecipitated into water from aceto— nitrile solutions, with the exception of Fraction JM—2 which was re- precipitated into acetone from a nitromethane solution. This fraction was too large (1.7 g.) and was refractionated into five sub-fractions, each being finally precipitated from acetonitrile solution by either water (2a, 2b) or ethanol (2c, 2d, 2e). Vacuum oven temperatures of less than 1000 were employed for drying of these sub-fractions. Remaining fractions were dried below 1000 with the exception of JM-3, which was dried at 105°. A careful study showed that temperatures in excess Of 1011—108O cause considerable degradation of the MCyA homopolymer samples. Determination of Phase Separation Precipitation temperatures, T were determined by the visual 3 method of Shultz and Flory (A7) for four fractions of the MCyA/IE coe‘ polymer in 2-ethoxy ethanol and three fractions of poly—(methyl a- cyanoacrylate) in cyclopentanone. The molecular weights of copolymer fractions 203—B, 205, 208 and 212 were determined by log <:M >w = (log [ n ] + 3.lilO)/O.585 to have the values 296,000; 126,000; 63,500; and 36,700 respectively. Molecular weights of the homopolymer Q\» 32 fractions 2-B, 2-C and 3 were determined from the tentative molecular weight-viscosity relationship log <:M'>fi g (10g [7? ] + h.380)/O.76 to be 283,000; 195,000; and lh0,000 respectively. All solutions were prepared by weighing polymer and solvent into h-inch test tubes. Dilutions were made in Sign by weighing the solvent from a hypodermic syringe. The tubes were stoppered with corks having a small V-notch cut to admit a wire stirrer. Details of the Oil bath have already been described by Wessling (h8). After initially approximating the precipitation temperature by rapid cooling (ca. lo/min.), a slower cooling rate of l/L to l/BO/min. begin- ning a degree or so above the precipitation temperature was used. T values were quite sharp, usually within 0.10 (see Appendix A), reproduc- ible, and independent of cooling rate. However, in trying to determine precipitation temperatures by warming, a higher temperature as well as a higher range of phase separation was encountered. Shultz and Flory (A7) point out that reversibility of the phase separation occurs only upon slow heating begun with a few tenths of a degree below Tp. Since measurements were being made simultaneously on two or three solutions of different Tp, accurate measurements upon warming were impossible. The uncertainty of Tp represents the complete range from the onset of the initial turbidity to the appearance of complete opacity as judged by the disappearance of the sight of a graduated scale, con- sisting of parallel black lines l/l6-inch wide and l/h-inch apart ruled on a white background. The precipitation temperatures determined in this manner represent a condition of intermediate turbidity, which for the narrow ranges encountered would correspond to the maximum rate 33 of change in the turbidity-versus-time curve. The sizes of the geometri- cal symbols in the phase diagrams correspond to the range in Tp, the un- certainties in the volume fraction being about the same or slightly less than that in Tp' The wider range at higher dilutions may have re- sulted in part from the larger volumes of solution which resulted. In the homopolymer—cyclopentanone system, the points for all frac- tions except 2B represent the results of more than one run. In the copolymer-ether system, only the curve for Fraction 208 represents data from a single run. The good agreement within all the other fractions verifies the reproducibility of the precipitation temperatures. Phase diagrams were constructed by plotting the experimentally observed precipitation temperatures against the volume fractions of 37w; w1/(31 "' V w,2 V is the Specific volume of the polymer, Q, is the density of the sol- polymer in the solutions as calculated from v2 = , where vent, and w is the weight in grams of each component indicated. The following section gives the details on the density determination on both solvents and polymers. Density (a) Solvents.- Densities of the theta solvents (2-ethoxyethanol and cyclopentanone) were measured in a Gay-Lussac pycnometer at four different temperatures over the range 20-800. The 10 ml. pycnometer had been calibrated previously using both water and mercury at 21 and 0°, respectively. The values agreed within six parts in 105. The usual precautions were taken to exclude moisture, Oil, etc. from the pycnometer by carefully wiping Off all excess fluid, cooling 3b to room temperature in a desiccator, and handling with Chamois finger cots. All weights were measured on a Mettler H-l5 semi—micro automatic balance. Least squares lines drawn through the experimental points (Figure 2) had the following equations: 2-ethoxy ethanol, Qt 0.9523 — 9.06 x lO-?t(OC) (5.1) cyclOpentanone, Qt 0.9672 - 9.55 x 10-4t(°C) (5.2) The experimental data for 2-ethoxy ethanol (Cellosolve) was linear, but slight curvature existed in the data for cyclopentanone (Shown by dotted line). This deviation from linearity, though small, indicates the need for higher order terms in the density-temperature equation. Neglecting an additional term introduces less than 1% error, however. Part of the curvature may also be attributable to experimental error, mainly due to evaporation of the solvent while equilibrating to room temperature and during weighing, thereby giving values too low. No correction was made for the volume expansion of the pycnometer over the temperature range used. Fortunately this error compensates to some extent that due to solvent evaporation. (b) Polymer .- The value of the density of poly-(methyl @- cyanoacrylate) used was the one reported by Canale and co-workers (b5). Specific volumes were determined from the reciprocals of the density equations with the exception of the copolymer. No uniform, solid bulk material was available for density measurements; therefore, the specific volume of McyA/IB was calculated as follows: The specific volume was assumed to be a colligative prOperty of the two constituents in a man- ner Similar to the glass transition temperature, Tg (h9,50). Since T9 for the copolymer is the mean of the individual values for the . 35 Figure 2. Densities Of the theta solvents as a function of temperature. E] - cyclopentanone 80» Q - 2-ethoxye thano 1 60. T(°C) to- 30' v.88 .89 .90 .91 .92 .93 .91 .95 density (g/ml) ... 36' homopolymers (51) and, furthermore, since T9 for different amorphous polymers is a state Of constant free volume (52), it is valid to as- sume a linear relationship of the specific volumes of the homopolymers. These Specific volumes are: V, 0.7625 + 2.73 x 10'4t (00) (5.3) VB 1.077 + 6.8 x 10‘4t (0c) + %§‘* (5.8) which give for the copolymer: The = 0.920 + 1.77 x 10‘4t (00) + %% (5.5) (A represents methyl a-cyanoacrylate homOpolymer and B the polyisobutylene.) The last term in equation (5.5) is negligible for molecular weights in excess of ca. 32,000. Viscosity Modified Cannon-Ubbelohde (suspended-level) viscometers were used in measuring flow rates of all solvents and solutions. Table I gives the flow times (sec.) for the solvents at various temperatures in the two different viscometers used. Table I. Flow Times of Solvents in Two Viscometers T v Solvent Temp.(°C) Viscometer efflux time (sec.) Khlh/5O A88/50 Acetonitrile 30 112.5 99 Nitromethane 30.2 139.3 121.8a 2-ethoxy ethanol 86.5 202.7 a. 30.00 The semi-micro dilution-type viscometer (Khlh/50) which requires only 1 - 1 1/2 ml. of liquid was employed for all runs except for those *Reference 53. 37/ in acetonitrile. Flow times were always in excess of 98 seconds. A Meylan stopwatch graduated in 0.1 second was used to measure the flow times, three to six of which were recorded until at least three values agreed within 0.1 second. In some instances agreement was within 0.05 second for three consecutive runs. An average of these values was taken. Kinetic energy corrections were determined for the semi-micro viscometers and were found to be negligible. They were not negligible, however, for the acetonitrile solutions in the macro-size viscometer, A-88/50. Shear corrections were considered unnecessary for the low intrinsic Viscosities obtained. All Viscosities measured in nitromethane for both the copolymer and the MCyA homopolymer were made at 30.20 in a 30 1. water bath regu- lated at i 0.0l°. The viscometer was clamped into position by two buret clamps and aligned vertically by sighting at right angles along a plumb line on the window of the water bath. The Pyrex tank was insulated with asbestos except for the windows, and covered on top to minimize evaporation and heat loss. Solution Preparation Solutions were prepared by weighing the dried polymer into either 5- or 25 ml. glass-stoppered volumetric flasks, warming gently or per- mitting overnight contact with the solvent until the sample completely dissolved, shaking vigorously, then diluting to the mark after allowing sufficient time for the solution to cool to 20°. This dilution process took place in the instrument (Infrared) room kept at a constant tempera- ture of 20 i 1°. Note was always made of the temperature registered by 38 a thermometer kept adjacent to the solvent storage buret. Purification and storage of solvents were described previously (p. 27). Dilutions to the mark were made only when the temperature was within one-half degree of 20°. Concentrations at 30.20 were calculated from the solvent densities. Since the solutions nearly always contained less than 1% polymer (weight per unit volume), the density of the solution was taken to be equal to the solvent density. The density values are: for acetonitrile (Mb), Qt = 0.8035 - 1.055 x 10'3t, where t is in de- grees Centigrade; for nitromethane, 630.2 = 1.12h, calculated from the density values of 1.13816 and 1.12h39 at 20 and 30°, respectively, and the temperature coefficient of density, (d Q/dt) = 1.377 x 10‘3 (5k). For fractions on which light scattering measurements were made, the same solutions were used for viscosity measurements. This has the extra advantage of giving a more accurate correlation between viscosity and molecular weight, especially if the polymer is subject to degradation. Since at least three solutions of conveniently Spaced concentrations were prepared for each light scattering run and normally two dilutions of the most concentrated one were made, this furnished five solutions for rela- tive viscosity determination. Three of these were free Of any possible systematic error to which the successive dilution method is susceptible. .All solutions were filtered before they were introduced into the vis- cometer. Those on which light scattering measurements were made needed no additional filtration, since they had been filtered through ultrafine porosity glass frits until completely dust-free. A coarse grade fritted filter sufficed for all other solutions. Where dilutions were made in the viscometer, solvent was added directly from a hypodermic syringe 39 weighed before and after the addition. Whenever possible, concentrations were chosen such that solution flow times remained between 120 - 190% of those of the solvent. Measurement at the Theta Temperature The relatively high theta temperature (359.8°K) for the copolymer in 2-ethoxyethanol required an alteration in the usual method of deter— mining viSCOSities. In this system solutions undergo phase separation at temperatures a few degrees below the theta temperature (see Figure 5). The following procedure was therefore adopted for determining Viscosities at the theta temperature: The clean viscometer and a coarse grade fritted glass funnel were heated in a drying oven at ca. 100°. A small sample preparation tube containing weighed portions of solvent and copolymer, and a Nichrome wire for stirring was stoppered and placed in the exhaust port on top of an oven, with the top half-inch of the tube protruding from the oven. When the polymer appeared to be in solu— tion, the stirring wire was removed and the tube immediately restoppered and placed inside the oven. The fritted filter was wrapped with insu— lating cloth, removed from the oven, and placed into the exhaust port on top of the oven, with the tip extending down into the opening of the viscometer which remained upright inside the oven. The polymer solution was immediately removed from the oven and filtered into the viscometer. Slight nitrogen pressure aided the filtration. In this manner solutions were obtained free of foreign matter with only a slight loss of solvent by volatilization. Lbually a rinse with weighed portion of warm solvent was necessary to remove traces of polymer remaining in the sample tube and the filter. Concentrations were still sufficiently high to permit to three dilutions to be made. For these the solvent was added from a weighed hypodermic syringe directly to the viscometer in a silicone Oil bath regulated at 86.5 i 0.10. Concentrations were calculated from the volumes of solvent as determined by means of the density relationship for 2-eth0xy ethanol, equation (5.1). Light Scattering Instrumental and Operation All light scattering measurements were performed with a Brice- Phoenix* Light Scattering Photometer of the 1000 Series located in a low humidity, constant temperature (20 i 1°) instrument room. Details of the instrument are given in the Brice-Phoenix manual. The mercury lamp was always allowed to warm up at least a half hour and usually an hour or more to insure stability of illumination before attempting any measurements. Tfiwapowersupply for the photo- multiplier tube was switched on about 5 — 10 min. after the lamp was actuated. After the warm-up period the dark current was checked, gal- vanometer zeroed if necessary, and then the instrument was ready for measurements. Calibration Two different calitxration methods have been employed to check on the operation and performance of the light scattering instrument. One method is a calibration at 0°, the other at 90°. Most methods of calibration consist of measuring the amount of light scattered by a known pure liquid or other substance. Benzene, *Pboenix Precision Instrument 00., 3803—05 N. Fifth St., Phil. NO, Pa. Lil as an example of the former, has most frequently been employed as a re- sult of the intensive amount of study on the absolute scattering of this liquid (55,56); and a solution of a widely distributed standard poly— styrene sample has been measured and used as a secondary standard, even though Duty and Steiner stated that "... an accurate absolute calibra- tion cannot be based upon the Scattering of any liquid nor upon the scattering of a substance of known molecular weight" (38). Still another method which is Often employed, mainly by followers of the original Brice method, involves a "working standard" Substitution for a properly compensated opal glass, the diffuse transmittance of which has been corrected to a perfect diffusor (57). In this work the Opal glass method was used periodically to cali- brate the instrument, and then frequent checks were made by using fresh solutions of the standard polystyrene. The procedures, in brief, are as follows: WorkinggStandard.- This consists of a small opal glass plate dark— ened on one Side to reduce the intensity of the primary light beam when measuring intensities at or near 0° angle. Galvanometer ratios are measured from intensities of light detected at 0° when the light passes first through the working standard with the cell table empty, then through the standard opal glass placed on the cell table after removing the working standard from the beam (neutral filters adjust the intensity of the beam in order to avoid damage to the photomultiplier tube). After interrelating the two "standards", the working standard is then semi- permanently mounted on the turntable arm for all measurements of intensity at 0°. Recently the accuracy and validity of this method of calibration was reported by Tomimatsu and Palmer (58) after a careful study. Standard Polystyrene.— A dust-free 0.5% solution of this standard in toluene has been reported (38,59,60) as having an excess turbidity* at 90° of (3.30 to 3.53) x 10'3 cm"1 at N358 A. An average value of 3.51 x 10‘3 cm‘1 has customarily been employed, although the lower limit was adopted by the National Bureau of Standards in 195h. Recently, Kratohvil and co-workers (61) in a comprehensive review of themethods of calibration of light scattering instruments have stated that a more reliable value lies at the lower edge of the reported range of values. The turbidity value as reported is not the true total turbidity of the standard sample but that of an imaginary sample which scatters the same amount of light at 90° and yet scatters symmetrically around 90°. For the green line (5h6l A), which was used exclusively in this . work, Kratohvil et 31. (61) reported a preferred value in the range (1.25 — 1.30) x 10-3 cm'1 for the excess turbidity of the polystyrene standard. Carr and Zimm (56b) have standardized this polymer in other sol- vents and at other wavelengths as well. Results of Calibration.- A value of 73 1.31 x 10‘3 cm"1 at 0 5h6l A was obtained using the Wittnauer (cylindrical) scattering cell. For blue light a slightly high value of 'T==3.6l x 10’3 cm"1 (cor- rected for fluorescence) was determined for a 0.5% solution in dried, distilled toluene. * i.e., solution turbidity minus solvent turbidity. b3 Since the working standard was in place during the measurements, the good agreement of the excess turbidity values with the reported values indicates that an error Of less than 2% is incurred by using the Opal g lass standard . Light Scattering Measurements Light scattering measurements were performed on seven fractions of the c0polymer in addition to the unfractionated sample. The fractions were selected from those which were isolated in each of the two frac- tionations, with preference given to the higher molecular weight samples, yet trying to keep a reasonable Spread in the molecular weights. Nitromethane, the “good" solvent used for the measurements, was found to fluoresce appreciably when irradiated with blue light, but not measurably with green light. Therefore all measurements were carried out using the unpolarized 5h6l A line of mercury. The initial solution of each fraction was checked for fluorescence by interposing a red ad- sorbing filter between the scattering solution and the detector. If no fluorescence was present, measurements were continued as described below. If some doubt existed concerning the presence of fluorescence, the most concentrated solution was tested. If an appreciable amount of fluor- escence was then present, the solutions were rejected. Fraction 206 was rejected for this reason. The cause of the fluorescence was believed to be due to the presence of some decomposed solvent or other impurity which imparted a slight discoloration to this fraction. Dry, distilled solvent and solutions were clarified by pressure filtration through ultrafine sintered glass filters. Normally a pressure MI of 6 - 8 lbs./in.2 was sufficient to filter even the most concentrated solution. The Wittnauer cell was rinsed with several portions of the filtered solvent (solution) until completely dust-free as observed by means of a mirror held near the emergent beam. The minimum volume neces- sary for making measurements was ca. 23 ml. In the dilution method, solvent was filtered directly into the most concentrated solution upon completion of light scattering measurements on the latter. Before diluting the solution a second time, 5 ml. aliquots (duplicates where the solution volume permitted) were with- drawn at 20° with a pipet for dry weight determinations. Gentle heating to constant weight in a vacuum oven reduced the aliquots to dry polymer. Results on duplicates agreed withh11%. A portion of each solution was also set aside for dn/dc and viscosity measurements. In addition to the above precautions on the clarity of the solu- tion, the external surface of the cell was checked for the presence of dust particles, smudges, etc. by grazing white light along the surface of the cell. If not optically clear, the surface was most effectively cleaned by wiping with an acetone-soaked tissue followed by brushing with an anti-static brush. . Scattering measurements were made in the following way: Solvent.- A full-scale galvanometer deflection was obtained at 0° with all neutral filters in the beam, then with all filters removed, measurements made at h5°, 50°, at 10° intervals up to 130°, and finally at 135°. After running through this series of angles, the shutter was closed so that the dark current could be zeroed, if necessary. Then intensities at the above series of angles were measured in the reverse 15 order, ending at 0°. Again the shutter was closed to check the dark current. The whole procedure was repeated in the above manner, giving a total of four galvanometer readings at each of the 12 angles measured. For each of the four columns of measurements the ratio 08/00 was calcu- lated for each non-zero scattering angle, where G9 is the galvanometer reading at angle 9, and 60 that for 0°. This method was preferable to » taking ratios of the average of the four values obtained for each angle, even though it entailed considerably more calculations. The average of the ratios was then multiplied by the product of the filter combinations used, which was always (f1 x f2 x f3 x f4) for solvent. The relative scattering intensities always showed good reproduci- bility and reasonably good symmetry about 90°, neglecting small devia- tions due to the characteristics of the cell. The latter, of course, always cancelled when solvent scattering ratios were subtracted from solution scattering ratios to obtain the excess scattering due to solute. Solutions.— Scattering ratios for solutions were obtained in es— sentially the same manner as above. A minor difference involved the initial adjustment of the photomultiplier sensitivity so that a nearly full-scale deflection of the galvanometer Spot could be achieved at both 90° (without filters) and at 0° (with filters). For the initial series of angular measurements the shutter was closed after each angle measure- ment was made, permitting the galvanometer to "zero" before continuing with the next reading. various filters were used in order to keep the galvanometer deflection in the range 70 - 100 mm (full scale = 100 mm). Occasionally, however, it was necessary to record deflections as low as ca. 1/2 of full scale. Once the filter combination was known for each .1 uxv — .-. _ «a, v - A “ .x. ;\ 16 angle, the whole series could be run through in short time without closing the shutter. Minor differences in ratios of the extreme angles in adjacent columns, caused by a slow but steady decrease in photo- multiplier response with exposure time, averaged out over the four meas- urements. This method had the advantage of rapidity of measurement, and still gave values within experimental error of values obtained by the method of Opening and closing the shutter for each angle. Early measurements with the cylindrical cell produced anomalous intensity readings in the range 70-800. Extraneous reflections were suspected and eventually found to be emanating from the side of the nar~ row slit on the cell table. The trouble was eliminated by placing a light shield on the edge of the cell table and by painting the back side of the cell with a flat, black, spray paint. Most of the solutions show- ed peculiar scattering behavior at angles of L5, 50 and 135°. The lower turbidities measured at these angles, particularly the low angles, probably resulted from the occurrence of secondary scattering, since a check on the angular characteristics of the cell with a dilute, aqueous fluorescein solution (0.1 mg/l.) gave no indication of abnormal optical qualities in the cell. In no case did the amount of scattering from the most dilute solution of a given series have a value less than three times that of the solvent. A detailed treatment of the data from a typical solution is shown in Appendix C. In principle the data should be corrected for depolarization of the scattered light induced by the anisotropically polarized molecules. While usually appreciable with small molecules, though not always ap— plied even in these cases because of Spurious and oft—misinterpreted axu b7 results (62), this correction is considered to be negligible for high polymers and to amount to no more than 1% for molecular weights > 10,000 (63). The scattering dissymetry ratio was less than 1.2 in virtually every solution; therefore the Fresnel correction for the back reflection of light at the glass/air interface was not applied (6h). It should be mentioned that attempts to measure Rayleigh ratios of the copolymer in acetonitrile solutions were unsuccessful due to the inability to obtain clear solutions. Repeated filtrations through an ultra-fine filter failed to eliminate the presence of bright specks in the solutions. It is believed that microspheres or clusters of un- dissolved polymer were reSponsible for the bright specks, as similar results were obtained for poly-(methyl a-cyanoacrylate) in nitromethane before it was discovered that heating the solutions on a steam bath during the early stages of the solution process virtually eliminated the specks. Prior to the heating procedure, neither ultrafiltration nor centrifugation for one hour at 32,500 x gravity succeeded in eliminating _the specks. The necessity of heating the solutions before they could be clarified gives some indication of the solvent power of the partic— ular solvents mentioned toward these polymers. Light scattering measurements were completed on several fractions of the poly-(methyl a-cyanoacrylate) in nitromethane, before and after the above heating procedure was adopted. The final results were in some doubt due to the apparent instability of the polymer. Results of three fractions were compared with some previous data of Dr. J. B. Kinsinger to obtain a tentative Mark-Houwink relationship. 2. h8 Specific Refractive Index Increment In order to determine reliable values of the molecular weights of polymers by light scattering it is necessary to accurately measure the specific refractive increment, dn/dc, since this quantity appears as a squared term in the optical constant in Debye's equation (b.h). It is desirable for the dn/dc to be as large as possible, because the amount of light which is scattered by a polymer in solution is also proportional to the square of this value. For this reason several solvents with as large a difference in refractive index as possible from that of the polymer were investigated before choosing one for light scat- tering measurements. In this respect the sign of dn/dc may be positive or negative depending on whether the refractive index of the polymer is higher or lower than that of the solvent. However, the sign is unim- portant to the results for the reason mentioned above. The usual range of values encountered for dn/dc is 0.08 to 0.2 dl/g., though occasionally values below this range must be employed. Since solutions are usually at a concentration of ca.l% or less, this means that one is dealing with differences in the third decimal place of the refractive index and requires a measurement capable of detecting changes of the order of S x 10‘6 unit, which is far greater than can be obtained with instruments designed to measure absolute refractive indices. Consequently, instruments which measure differences between the refrac- tive index of solvent and solution are necessary. Several types of instruments based on different principles are currently used for such measurements and two of these have been employed in this laboratory. b9 One is an interferometer of the Rayleigh type (65,66) as modified by Carl Zeiss (Jena) and the other is a differential refractometer of the Brice-Halwer type (67). The former is more sensitive and hence re- quires greater skill in alignment and Operation in addition to more stringent temperature control. Interferometer The interferometer, in principle, is an instrument which divides a collimated beam of light from a single source into two parallel beams by means of two adjacent slits. After traveling through the fluid under consideration, the beams are recombined and produce a vertical set of interference fringes. Any difference in the optical path of one of these beams causes a lateral shift in the set of fringes. This shift is observed in a telescope and its magnitude is found in the num- ber of fringes displaced from the original position by comparison with a stationary set of reference fringes. It is due to the fiduciary sys- tem being a similar set of fringes and not a cross hair that the method surpasses all others in accuracy. Differential Refractometer The principle of the differential refractometer is based upon the deviation of a narrow beam of light upon passing through a divided cell. The slit image is projected into a telescope where it is followed manu- ally on a scale by means of a filar and micrometer (67) or may be de- tected photoelectrically as in the type of instrument designed by Schulz (68). 50 When carefully calibrated the Brice—Halwer instrument (67) is capable of having a sensitivity of 5 x 10‘6 refractive index unit. This sensitivity is achieved by mounting the cell on a turntable capable of rotating 180°, thereby doubling the deviation produced by the beam passing through the partitioned cell. Although this instrument does not have the theoretical accuracy of the interferometer, it is nevertheless preferred because of its simplicity of Operation and for the reproduci- bility of the results. The principal components of the differential refractometer consist of a monochromatic light source, slit, cell, projection lens, and tele- scope having a micrometer eyepiece. A medium-pressure mercury vapor lamp (AH-h) Provides the radiation. The 5b6l A line is isolated by a green gelatin Kodak filter whose transmission was checked on a Beckman DK—2 Recording Spectrophotometer and found to have a sharp cut-off on either side of the SD60 A region. The square cell has a single parti- tion set at an angle of approximately 69° to the two faces normal to the path of the light beam. It may be calibrated either by geometry or by reference to standard solutions, with the latter being preferred. References most frequently employed are sucrose or sodium and potassium chlorides. Extensive tables of refractive index data for these compounds may be found in the literature (cf. Refs. 69 and 76). All three refer- ence solutions were used for calibration in the present study, with the most consistent results provided by the chlorides. The cell and cell holder (including thermostated jacket), projec- tion lens, and telescope with micrometer were purchased from the Phoenix Precisi<3n Instrument Co. and, along with the other components, were .51 mounted on a heavy-duty Gaertner Optical bench having a millimeter scale along nearly its entire length. This enabled exact location of each component on the bench to be specified. The instrument was cali- brated for two different sets of positions of the components. Results are given in Appendix B. By selecting two settings of the optical bench components, a wider applicability of the instrument was assured due to the extent of deviation of the slit image for a solution of given refractive index. Whenever encountering solutions having very small Specific refractive increments, the setting giving the larger deviation can be selected. Similarly, if concentrated solutions of salts, sugars, or other small molecules are used, the setting which gives the smaller deviation would be selected. Otherwise, the deflection of the beam of light may fall outside the limits of the scale. With most polymer solutions, however, the deviations are not very pronounced and the main criterion for choos- ing a setting of the components is that which requires a minimum amount of refocusing Of the telescope to sharpen up the slit image after the cell has been rotated through 180°. The position finally selected for making dn/dc measurements was the one having this feature. w For ordinary liquids having relatively low vapor pressures the cell having the removable cover plate may be used with confidence. In the case of more volatile liquids, however, a means to prevent mixing of solvent and solution must be assured. With such liquids solvent creep readily occurs up the edges of the cell by capillary action, and unless an.mpenetrable barrier separates solvent and solution, 52 dilution of the solution will occur. This problem was encountered using both acetonitrile and nitromethane in the cell with the removable cover plate. Contact between the cover glass and cell rim produced immediate "wetting" around the entire rim, thereby furnishing direct contact be— tween solvent and solution, and causing dilution of the latter. Various cells have been devised to eliminate this problem, with most of them having either a mercury seal (70) or a permanent top. One of the latter type with all-fused joints was purchased from the Phoenix Prescision Instrument Company. The cell has a quarter—inch thick permanently fused top having a tapered hole Opening into each compartment which can be stoppered with small penny-head ground glass stoppers. The capacity of the cells is ca. b ml. (2 ml. per compartment), with l l/L - 1 1/2 ml. being sufficient for performing measurements. While the calibration constants are principally dependent upon the relative positions of the various Optical components, particularly that of the cell and projection lens with respect to the telescope, it was found that the lateral placement of the cell within the cell block also had a small affect on the deviation of the light beam. For this reason the cell, once calibrated, was not and should not be removed from the cell block unless absolutely necessary. Teflon* square sheets served as convenient spacers for positioning the cell in the block. In addi- tion, the slick surface of the Teflon facilitated insertion and removal of the cell from the block when removal was necessary. * Tradename for DuPont's polytetrafluoroethylene. ‘53 Optimum alignment of the cell exists when a minimum deviation occurs in readings taken for 180° rotation of the cell with solvent in both com- partments. Ideally, proper alignment would be indicated only when the slit image is undeviated by the 180° rotation. However, Brice and Speiser (71) found that some liquids inherently produce a small devia- tion, while others do not. All solvent used in this work gave a small deviation. It is important to know whether the refractive index of the polymer is higher or lower than that of the solvent in which it is dissolved. A simple trial will suffice to indicate which side of the cell should be chosen for the solution, but care must be taken to note the direction of the lever arm used to rotate the cell block so that consistency may be maintained in the placement of solvent and solution. Otherwise, in- stead of the deviation of the slit image being in the same direction as that of the solvent alone for a given cell position, the deviation will be reversed and the solvent reading will have to be added to instead of subtracted from the reading for solution versus solvent. Calibration of Differential Refractometer (l) Sucrose.- All calibration measurements were made at 20 i 10 using both the blue (h358 A) and green (5h6l 3) lines of mercury. The data of Brice and Halwer (67) as well as the National Bureau of Stan— dards data (69) on sucrose are given only for the sodium—D line (5890 A) and they exhibit nearly a 1% variation over a five-fold concentration range. More recent data by Maron and Lou (72) for both the blue and green lines of mercury are given for 25°. By using Morris' and Gosting's Sh value (73) for the temperature coefficient of the Specific refractive index increment, b(dn/dc)/bT = - 1.51; x 10'4, a limiting value Of (dn/dc)5461 = 0.1hb6 was calculated for 20°. The corresponding value at 0358101 is 0.1147. In calibrating their differential refractometer with sucrose, Carpenter and Krigbaum (60) assumed that (dn/dc)4358 = 0.1h5 at 30°, which is reasonable since increasing temperature and wavelength have Opposing effects on the change in refractive index. However, in meas- uring the dn/dc of the standard Cornell Polystyrene sample, the latter authors obtained a value of (dn/dc)4358 = 0.118 for a 0.5% solution in toluene, which is high when compared with the average value of 0.111 i 0.001 reported by the International Union of Pure and Applied Chem- istry (7h). If this value is accepted as the correct value, then the value reported by Carpenter and Krigbaum is about 5% too high. Their assumption of 0.1b5 for the dn/dc of sucrose, however, would not account for this large a difference. It should also be noted that the concentration-dependent part of the refractive index expression as expanded by Stigter (75) shows that the data of Maron and Lou (72) changes for both wavelengths about 6% in the concentration range under study. This represents a change which is nearly proportional to the sucrose concentration. In our calibration, the value for dn/dc of sucrose equal to 0.1h35 (green line) was measured on the absolute Rayleigtheiss interferometer at 20° and assumed to be correct. Subsequent calibrations of the Brice- TyPe differential refractometer also produced "high" readings on the Cornell Polystyrene which prompted further calibration with the alkali chloride solutions. 55 The sucrose used for the calibration was a fresh sample from Nutritional Biochemicals CO. which was dried at 110° for one hour be- fore weighing. Concentrations of the solutions were checked by measur- ing their densities in a calibrated pycnometer at 21°. (2) Alkali Chlorides.- The calibration of the refractometer was rechecked at 5h61 A using the data of Kruis (76) for potassium and sodium chlorides as tabulated by Stamm (77). Perlman and Longsworth (78) re- ported the concentration dependence of the refractive index of potas- sium chloride as An/c = 0.01lh65 - 0.00100 cl/é. Whereas the temperature coefficient of the specific refractive index increment is larger for potassium chloride than for sucrose, it only amounts to about 0.2%/°C. rise in temperature (67). Fisher Reagent~grade potassium chloride was dried at 110° for several hours and cooled over magnesium perchlorate in a desiccator before weighing samples. Four solutions covering a broad range in con- centration and having values very near to those of Kruis (76) in order to minimize any errors in interpolation on the graph of concentration versus refractive index were prepared using conductivity water. Con- centrations are expressed on the basis of g. of the salt per Kg. water. Calibration with these solutions gave excellent agreement for two sets of component positions on the optical bench. These results are also shown in Appendix B. Later calibration of the closed-top cell at the preferred settings of the components using both potassium chloride and some sodium chloride solutions (courtesy of Curtis C. Wilkins) gave a calibration constant 56' o at 51.61 A of o.81.1 x 10'5 for k = An/Ad, where Ad is the difference in the deviations produced before and after rotation of the cell corrected for the deviations produced by the solvent. Thus, (dn/dc) = 51:3 = 0'8“: 1°15 [(d2 - d1) - (d2° — 010)] (6.1) where the subscripts refer to the position of the lever on the cell table and the superscripts refer to pure solvent. As a check on the calibration value for the refractometer two dif- ferent Cornell Polystyrene solutions were measured over a period of several months. The average value Obtained from the measurements was (dn/dc)5451 = 0.112 t 0.008, Showing very good agreement with the I.U.P.A.C. value (7b). RESULTS AND DISCUSSION '”Solubilities"'k Tables II and III give a list of the 35 solvents investigated for the copolymer and a Similar number studied with poly-(methyl a—qyanoacry- late) as well as the conditions under which the designation "solvent" or "non-solvent" was applied. Also listed for comparison are some $01- vents, including theta solvents, for polyisobutylene (Table IV) taken from the literature. Where known, the value of the solubility parameter, 6= (C.E.D.)1/2, and its source are listed for each solvent and non- solvent. Several good solvents were found for each of the polymers, but very few of these were feasible for light scattering measurements be- cause they either had a high volatility or an unsuitable refractive index. Theta solvents were found for both the copolymer and poly-(methyl a-cyanoacrylate), although the theta temperatures were both considerably above room temperature (86.6°C for the copolymer, 85.0°C for the homo- I power). . It is interesting to compare the solubility parameters of the polymers as palculated by Small's method (16) with those of the solvents and non-solvents as taken from other sources (79,80). For polyiso— butylene with a calculated 5= 7.7 (cal./cc.)1/2, several goOd solvents are known in this neighborhood (Table IV), With a value of 5= 9.1. (cal./cc.)1/°, the copolymer has one good solvent, chloroform, listed at the same value and two others nearby at 9.3 and 9.5 delta units; on the contrary, 2-ethylhexanol at 8= 9.5 (cal./cc.)1/2 is a now-solvent. 57 58 Table II. Solubility behavior of Methyl a-cyanoacrylate/isobutylene alternating Copolymer So lve nt 5 Ref . Non-so lve nt* 5 Ref . benzene 9.16 81 petroleum ether ca.6.75-7.25 79,81 h—methylcyclohexanone 9.3 80 n-heptane 7.h3 81 chloroform 9.b0 81 methyl amylacetate 8.0 80 chlorobenzene 9.53 79 cyclohexane 8.2 81 Cellosolvea 9.9 80 chlorocyclohexane - - methyl Cellosolve 10.8 80 methyl—isobutylketone 8.h 8O ethyl cyanoacetate 11.0 81 carbontetrachloride 8.62 81 cyclohexanol 11.b 8O diisobutylketone - - acetonitrile 11.9 81 methyl propyl ketone 8.7-8.9 80,81 dimethylformamide 12.12 79 butyl Cellosolve 8.9 81 nitromethane 12.69 79 toluene 8.91 81 dimethylsulfoxide 13.00 11 methyl ethyl ketone 9.1h39.22 79,81 phenyl acetonitrile - '- 2-ethy1hexanol 9.5 80 phenetole - - l-heptanol 9.65 81 methyl phenyl ketone - - l-hexanol 9.97 81 cyclopentanone 10.b2 79 diethyl Carbitolb - — (MCyA/IE copolymer 9.b calc'd.) methanol 1h.5 79 isobutylchloride - - cyclohexyl methyl acetate- - *Refers to those liquids which do not dissolve the copolymer below 75°. aSoluble above ca. 600 (O solvent). bPolymer swells Slightly at 25°. 59 Table III. Solubility behavior of Poly-(methyl a-cyanoacnylate) Solvent 5 Ref. Non—solvent” 5 - Ref. cyclopentanonea 10.b2 79 Common aromatics ' 8.9-9.2 81 propionitrileb 10.8 79 chlorinated solvents8.6-9.8 79,81 ethyl cyanoacetate 11.0 81 ethyl trifluoroacetate - - nitroethaneC 11.1h 79 acetone 9.71 16 benzonitrile 11.17 79 cyclohexanone 9.72 79 acetonitrileC 11.9 81 dioxane 9.73 16 dimethylformamide 12.12 79 n-butyronitrile - — nitromethane 12.69 79 iso-butyronitrile _ ._ phenyl acetonitrile - - 1-nitropropane 10.38 79 2-nitropropane - ._ 2-ethylbutanol 10.5 80 (McyA homopolymer 11.5 calc'd)methy1 Cellosolve 10.8 80 dimethylphthalate 10.71 79 2-pentanol - - n-butanol 11.25311.h8 79,81 cyclohexanol ll.b 80 n—propanol 11.9;12.l 79,81 *Refers to those liquids which do not dissolve the polymer after heating 1 hr. at 80°. aDissolves the polymer above ca. 60° (0 solvent). bDissolves the polymer above ca. 65°. CSlight turbidity develops upon cooling to ca. ~30°. 60 Table IV. Solubility behavior of Polyisobutylene Solvents 5 0(°C) Ref. n-heptane 7.h3 3b diisobutylketone 7.8 3h hexadecane 7.99 3h cyclohexane 8.2 82 carbontetrachloride 8.62 3h ethyl benzene 8.79 -2h 3h toluene 8.91 —13 1 3h benzene 9.16 2h 82 2,2,3-trimethylbutane 3b diisobutylene 3h ethyl n—heptanoate 3h 83 phenetole 9b 3b anisole 11h 3b (polyisobutylene 7.75 - calc'd.) .61 Poly-(methyl a-cyanoacrylate) has a delta value Of 11.5 (cal./cc.)1/2, yet the two closest values to this belong to non—solvents, n—butanol and cyclohexanol. Acetonitri 1e and benzonitrile at 3 = 11.9 and 11.17 (cal./bc.)1/é, respectively, have the closest delta values among the solvents for this hOmOpolymer. Also worthy of note in this respect is the double grouping of 501— vents for the copolymer, as one would expect. The group having delta values between 10.8 and 12.7 (cal./cc.)1/2 give ample evidence of the influence which the polar cyanoacrylate unit has on the solubility of the copolymer. This is just one manifestation of the unusual properties possessed by this copolymer. The polar nature of the methyl a-cyanoacry- late unit thus accounts for the deviation from Small's theory of the mutual solubility of polymer and solvent having near values of the co- hesive energy density. Fractionation TWO complete fractionations of the copolymer from dilute benzene solutions were carried out in order to produce the relatively homo- geneous samples necessary for characterization measurements. The first was largely used to check on the effectiveness of the precipitation method used and to provide samples for elemental analysis. Lack of a sufficiently uniform temperature throughout the fractionation and pos— sible failure to achieve equilibrium in the phase separation apparently led to the inconsistent molecular weight distribution found for the fractions. However, knowledge obtained from this initial fractionation made possible a second, more accurate, fractionation producing sharper 62 fractions. A total of 27 fractions were obtained in the second fraction- ation, with nearly the theoretical uniform decrease in molecular weights being achieved, and a total weight recovery of 91 %. The elemental analysis on each fraction obtained in Run I along with the analysis of the unfractionated bulk c0polymer clearly_show (Table V) that the composition is uniform, within experimental error, throughout all the fractions. The experimental data agree well with the theoretical composition for a strictly alternating c0polymer (50 mole % of each monomer). It is therefore highly likely that only a negligible amount of random c0polymerization could have occurred in a reaction.whichpro- duced such a uniformity in composition over the 50— to 60-fold range in molecular weights in the bulk sample. For the same reason there is little possibility for the existence of an appreciable amount of block copolymer or of parent homopolymer species; otherwise their presence would have been indicated in the elemental analysis. The same conclusion might also have been predicted from the solubility behavior of the homo— polymers (Tables III and IV). It is easily seen that benzene does not solubilize methyl a-cyanoacrylate homopolymer and it is only a theta solvent for polyisobutylene (h3). In addition to the exceptionally large number of fractions isolated, the most notable aspect of the data from Run II is the large Size of fraction 203 (Table VI). A comparatively large volume of precipitant was necessary to produce an appreciable turbidity in the initial separ— ation of this fraction, although the amount of turbidity appeared to be no more than for the other fractions. The fact that it accounted for over h1% of the total sample weight indicates that the initial precipitation temperature may have been higher than for the other 63 Table V. Data from Copolymer Fractionation I and Results of Elemental Analysis Volume Fraction Precipitant wi %C %H %N (ml.) (9.) Whole Polymer 20.06 63.80 7.90 8.5b 1 150 1.617 63.39i0.01 7.5hi0.l 8.9hi0.12 l—X 29 O.hh2 6b.b7 7.72 8.26 2 to 1.80 6h.57i0.17 7.82:0.02 8.6i0.06 3 35 1.70 68.52 7.67 8.33 h 10 1.355 6h.b2 7.72 8.72 5 15 0.60 61.21 7.69 8.38 6 13 0.208 (insufficient sample for analysis) 7 20 0.708 63.88 7.78 8.77 8 20 1.329 6h.09 7.83 9.22 9 l7 nu 0.85 6b.10 7.78 8.83 10 15 0.951 6b.l6 7.7h 8.39 11 12 0.655 6b.h7 7.6h 8.52 12 19 0.87b 6h.20 7.81 8.22 13 15 0.573 6h.00 7.75 8.22 lb 15 0.7lb 6b.02 7.73 8.2b 15 16 0.352 6b.05 7.82 9.89 16 2h 0.205 6b.l5 7.82 8.06 17 26 0.528 6h.36 7.83 7.88 18 27 0.555 61.10 7.81 8.20 19 35 0.53b -- -- ~- 20 excess 1.b02 -- -- -- Theoretical MCyA/IE 6b.65 7.8h 8.38 Composition MCyA 5h.05 b.5b 12.61 IB 85.63 lb.37 -- *Analysis performed by Micro-Tech Laboratories, Skokie, Ill. 61 Table VI. [hta from Copolymer Fractionation II. Volume Fraction Precipitant w, §jwi 10‘5< M >. "i[7?]i (ml.) (9.) 201 90 0.1700 6.3762 2.06 0.0862 202 25 0.6968 9.0951 7.12 0.718 203* 53 3.8571 _- (See below) _- 201 21 0.6087 1.9635 1.38 0.239 205 18 0.1550 1.3518 1.26 0.171 206 20 0.7200 3.6071 0.701 0.192 207 17 0.1900 2.3807 0.618 0.0168 208 30 0.5061 2.8871 0.635 0.127 209 26 0.3328 2.1907 0.523 0.0716 210 18 0.1159 1.7651 0.105 ' 0.0282 211 28 0.2019 1.6192 0.371 0.0377 212 32 0.2372 1.1113 0.367 0.0133 213 16 0.2238 1.1771 0.279 0.0317 211 12 0.1915 0.9533 0.217 0.0257 215 11 0.1119 0.7618 0.209 0.0186 216 16 0.1387 0.6199 0.162 0.0157 217 51 0.0991 0.1812 0.160 0.0111 218 76 0.1065 0.3818 0.150 0.0115 219 78 0.0782 0.2753 0.112 0.0071 220 88 0.0152 0.1971 0.091 0.0037 221-2 250 0.1519 0.1519 0.013 0.0076 *203—A 12 0.0911 8.3983 1.25 0.0695 203-B 9 0.5682 8.3072 1.15 0.130 203-0 5 0.0702 7.7390. 3.38 0.0169 203-0 7 0.3591 7.6688 3.21 0.233 203.3 10 0.9371 7.3097 2.96 0.579 203-F ' 21 1.0188 6.2026 1.79 0.169 203-0 10 0.2203 5.1838 1.12 0.0886 203-H 36 0.2927 3.8998 0.789 0.0831 203-J 95 0.0982 1.8579 0.131 0.0186 From equation (7.2), Wop? ]o= 11.09. Total of column 6 is 3.92. 65 fractions. Refractionation of 203 yielded 9 subfractions at a total re- covery of 91.7%. As would be expected from refractionation of so large a fraction (3.86 g.), the two lowest subfractions (203—H and -J) gave a slight overlap in [77] with the succeeding fractions from the main solu- tion. The initial fraction from any precipitation fractionation would be expected to be the most heterogeneous of the group and may therefore fall out Of line. Part of the reason for the seemingly low value of the molecular weight of 201 probably resulted from adding an excess of pre- cipitant to the 1% initial solution, requiring addition of 200 ml. of benzene to lessen the turbidity and prevent the premature separation of some lower molecular weight species. Apparently the additional sol— vent helped to some extent in this respect. Analysis of Fractionation Data The conventional method first given by Schulz and Dinglinger (81) was used in analyzing the fractionation results. In Table VI are shown the weights and weight-average molecular weights of the fractions, most of which were‘determined from the intrinsic Viscosities and the empir- ical relationship, (8.2). The integral weight distribution was obtained by plotting the cumulative weights Of the fractions I(M) expressed as the fraction of the total weight of polymer recovered versus the weight- average molecular weight <.M >w (Figure 3). The cumulative weight fraction is given by l a 1 27 I‘M) =W f1 dwi -Wo— Z Ni (7.1) i=1 where W0 is the weight of the initial heterogeneous polymer being 66 6-2 x z .3303 2808: o a - m m a. m. .N w o o «.0 a . «.0 m I .- M, . MQJAU r . N.O .m W F a o l ..u C R r o m 6.6 _ . a o o t m; 0 ._ m m.o . 4.0 l a t mm .04 m6 7. 6:30.08.“ 359.0900 ocoahfifiom{OOmHzpomocmxoua H1309: pom mot/.30 comusflupmwp Hmwpcouowmmu 0cm kumoucH .m 0.33m Mass Fraction of Molecular Weight M, dF(M) 67 fractionated (10.0 g. in the present case), wi is the weight of the 132» fraction, and E3”; is the combined weight of all fractions having aver-» age molecular weight up to and including (<.M >w)i° The differential distribution curve was determined by a graphical integration of the integral distribution curve. Slopes of the integral curve were determined on a large plot for increased accuracy. This gave a reasonable approximation to the location, breadth, and height of the maximum in the differential curve. The possibility of degradation was checked by the formula: Z W, m. = 11.177 1. (7.2) I 1 where wf and [77]i are the weight fraction and intrinsic viscosity, 1 respectively, of fraction i, and.[77]O is the intrinsic viscosity of the unfractionated copolymer. Degradation was found to be negligible, if not entirely absent. Phase Data Phase separation temperatures, Tfi, were determined on four frac- tions of the c0polymer at a total of 10 concentrations in 2-ethoxy ethanol, and on three fractions of the methyl a-cyanoacrylate homo- polymer at 27 concentrations in cyclopentanone. Smooth curves were drawn through the points in plots of Tp against volume fraction,‘U'2. The resulting phase diagrams are shown in Figures 1 and 5. Critical data from these curves are shown in Table VII. Reciprocals of the critical temperatures in °K as determined from the maxima of the binodials are plotted in Figure 6 against the molecular Size function x 68 . Hocmfio hNonposw 5 00830000 003.3338“\Opmahpomocmhond finance OH 2590me 0.0.ch ..Cmcmm .4 0030mm N , >~0H 0.0 0.0 0.4 o.m 0 - 1 — 4 u d fl d om . mm D D D D DD 1 ow . mo mew -.\ .. 2. m8 1 J . ma. 0 mumON III < L cane 69 70* T (0C) 66- 61' 621 n 1 l I l L n 0 ' 1.6 3.2 1.8 6.1 102v 2 Figure 5,_IMB.inary phase diagrams for methyl a-cyanoacrylate homopolymer in 70 Figure 6. Reciprocal critical temperatures versus the molecular size function for three MCyA homo olymer fractions in cyclopentanone and for four MCyA B copolymer fractions in 2-ethoxy ethanol 3.00 2-95 103 W) 2.90 2.85 2.80 P — O l 2 3 b [x'l/z + (2x)‘1] 10?- 71 Table VII. Critical data for two Polymers in their Theta Solvents Fraction TC(°K) [x-J‘/2 +(2x)-11102 <.M >fi,x 105 x A. Poly-(methyl a-cyanoacrylate/isobutylene) in 2-ethoxy ethanol 203-E 350.1 3.21 3110 1.812 205 311.3 1.38 1330 2.783 208 338.5 0.695 666 3.955 212 331.7 0.101 385 5.23 B. Poly-(methyl a-cyanoacrylate) in cyclOpentanone JM-ZB JM-2C JM-3 311.7 311.1 338.6 2.83 1.95 1.10 2356 1626 1170 2.081 2.518 2.967 72 according to equation (2.17). The intercepts with the y-axis give the reciprocal of the theta temperature and the ratio of the intercept to the lepe of the lines furnish the values of the entrOpy of dilution parameter, 9U,. These values are then used in conjunction with equa- tions (2.11) and (2.11) to calculate the excess entropy and heat of dilution. The results in terms of volume fraction are Shown in Table VIII. Table VIII. Thermodynamic Parameters from Phase Equilibria Studies 0 AH ‘62 5 v22 Polymer Solvent (°K) {fa cal.mole-'1 calimolendeg:1 MCyA/TB 2-ethoxy + copoly‘mer ethanol 35908—102 0.628 11118 1.25 MCyA cyclo- + homopolymer pentanone 358°2T3‘2 0.510 363 1-01 The values of the entropy of dilution parameter iffl are similar for both.polymer-solvent systems. The slightly smaller heat of dilution for dyclopentanone indicates that it is a better "thermal" solvent for the homopolymer than is its companion solvent for the c0polymer. However, no sharp distinction can be made as a result of the greater uncertainty in the extrapolation of the homopolymer data. Although the values of 9”, determined in this manner are from solutions having very low volume fractions of polymer, the fact that each solution was near phase separa- tion requires a distinction between such solutions and dilute solutions as employed for light scattering measurements. The results, however, are useful in describing the miscibility of the solvent-polymer liquid 73 system and indicate moderate endothermal heats of dilution and small positive deviations from normal entropies of dilution. The determination Of the theta temperature in the above manner is quite accurate, and with the present polymer-solvent systems would un— doubtedly be superior to the light scattering method at a series of tem- peratures which includes the theta temperature (where the slope of Kc/RO versus c is zero). Polymer Dimensions and Molecular Weights The averaged dimensions of the copolymer molecules in dilute solu- tions were determined from the angular distribution of scattered light in two ways: (a) from Zimm plots and (b) from Debye's dissymmetry method. Molecular weights were determined from (a) alone. Zimm Method Reciprocal reduced intensities Kc/Re were plotted against sin2(0/2) + kc according to the composite equations (1.1') and (1.6). The limit- ing slope/intercept ratio at zero concentration was equated to the quantity (8n2/912)L2, where 1. is the wave length of the radiation in the medium (Io/h), and L2 is the mean-square end-tO-end distance of the polymer coils. Dimensions determined in this manner are "z"-average dimensions, and must be converted to the usual weight-average quantities by means of equation (1.7). Values of the parameter h were carefully estimated by analysis of the fractionation results, Since no absolute measurements were made which give a number-0r a "z"-average molecular weight for comparison with the weight average. However, Since all samples except the whole polymer were fractionated and, furthermore, 71 since most well-fractionated samples have a molecular weight dispersity (i.e., <:M >w/kiM >n value) in the range 1.05—1.20,(28g»,the values chosen for h are quite reasonable. 0n similarly fractionated copolymers others have utilized values of h in the range 1 to 10 (2), the latter corresponding to more efficiently fractionated cuts. Dissymmetry Method Because the uncertainty of the results of the Zimm method increases with decreasing molecular weights, the dissymmetry method iS usually preferred below MI\Il x 105, not only for the reason mentioned but also for its Simplicity. A prime assumption required in this method which is not required in the Zimm method is that of choosing a particular model or shape to fit the polymer in question (random coil, rod, Sphere, etc.). From the dissymmetry Z = 1450/11350, which is merely the ratio of the light intensity scattered at two angles symmetrical about 90°, plots of 1/(2-1) against concentration extrapolated to infinite dilu- tion yield a value of the intrinsic dissymmetry, [2]. Published tables (38, 39) then are used to obtain the characteristic dimension in terms of L/X. Extrapolation of Light Scattering Data From the intensity distribution of scattered light, Zimm plots were constructed for seven fractions and the unfractionated copolymer (Figures 7-11). Straight lines were first drawn through the points of constant concentration and extrapolated to zero angle (denoted by hexa- gons); then straight lines were drawn through the best average, by sight, of the location of the points at constant angle and extrapolated .ocmdpoEoufic 5 NH compomnm 88.30000 mH\.oz now beam EEMN .2 0.53m 89 1. 00 can O.N 02H 04. {a N4 0:6 0.0 0.0 4.0 m0 0 u - 1 OH 00H X m NH 3 0:20.088»? 5 m coHpOmnnH 0053008 m<<~€£ now 030 EEHN .HH 0.53m 009 + N\0 Nch 0.H .H.H NH 0.H 0.0 0.0 4.0 m0 0 00H NMw OH NH 80 000000083? 5 mumom coHpomnm 00050000 mH\<\noz mom ..HOHQ EEHN .NH 086$ 82 + 800 ~ch 0.1 04 a: m; 04 0.0 0.0 0.0 0.0 0 - . I a .2 0. OH x 0M 81 0003008000? E xiH coHpomnm n0E~AHOQOO mH\<>oE now poHQ EEHN o00H + 0\0 Ncam N.H 0.H. 0.0 0.0 4.0. N0 1 I .mH mesmaa .000000800 0H: ca . NON coHpOmnm 005540000 0 m 02 + Q0 Noam Q06: .80 boa 5:0 w.0 .4H 0uzmHm u 83 to zero concentration (denoted by circles). Next, straight lines through these two sets of extrapolated figures were drawn to a common intercept son the ordinate (except where curvature resulted at the higher angles, in which case the limiting slope was represented by a dotted straight line). All the data were fairly well represented by a linear extrapola- tion, except for Fraction 1. Apparently abnormally high turbidity in the solution of highest concentration caused it to deviate from the rest. The extrapolation therefore ignored this solution. The reciprocal of the intercept on the ordinate gave the weight-average molecular weight, <.M >0“ The second osmotic virial coefficient, A2, was obtained for each sample from the Slope of the zero angle line. The z-average end- tO—end dimensions were determined from the slope/intercept ratios of the zero concentrations lines° Through the use of Debye's method molecular weights and particle dimensions may be Obtained from measurements at only four angles: 0, 15, 90, and 135° in the semi-octagonal dissymmetry cell. In the present work the smaller, cylindrical cell (C-lOl) was used for all measure- ments and a more complete scattering envelope was measured between 15 and 135°. The results Showed considerable variation in the 15 and 135° scattering, probably due either to secondary scattering or to changes in the optical clarity of the cell window (dust, smudge, etc.) from one solution to another which were not balanced by the solvent sub- traction. All possible precautions were taken to see that the latter was not the reason. By plotting the complete scattering pattern accord- ing to the Zimm method (where measurements below 15° are desirable), these variations from the averaged behavior are easily shown by the best straight line through all the data. Dissymmetries were therefore deter- mined from Z = (KC/R135o)/(Kc/R450) by reading values directly from 81 the location on the straight line corresponding to these angles instead of taking ratios of the raw data which sometimes differed by as much as 1.1%. Perhaps these variations may not have been as pronounced if the dissymmetry cell had been used, but volumes of solutions employed pro- .hibited its use. Therefore, prior to making dissymmetry calculations with data obtained in the Wittnauer (cylindrical) cell, the complete angular scattering envelope should be plotted in the Zimm manner to as- certain if the 15°/l35° intensities are reasonable. Even when employing the above technique the Z-values did not always vary systematically with concentration. For most fractions a reasonable straight line could be drawn through the eXperimental 2 values and ex— trapolated to infinite dilution to obtain [2]. If the variation was just the reverse of the normal, as in Fraction 12, or completely random, as in Fraction 201, an average Z'was taken and used in place of [Z]. This only occurred with the two fractions of lowest molecular weight where experimental uncertainty was greatest. With these intrinsic values the more complete tables of dissymmetries by Beane and Booth (39) were used for all the fractions, assuming that they are mono-disperse random coils. For the unfractionated whole polymer the tables of Doty and Steiner (38) for polydisperse coils were employed. The results of the light scattering data treated according to both the Debye and Zimm methods are given in Tables IX and X. The Zimm re- sults corrected for heterogeneity are compared with the Debye results in Table XI. For the parameter h in equation (1.7), a value of 1 was used for the lower fractions from the first fractionation, a value of 5 for Fraction 12, and a value of 10 (corresponding to much more effici- ent fractionation) for the three fractions from the second fractionation. 85 Table IX. Results from Dissymmetry Measurements on Copolymer in.Nitro— methane (25°). Coné. : ‘ Fraction (g/al.) "-.Z :.145/3135 1/(2-1) [21 L173“ 1% 12 0.122 1.090 . 11.11 12 0.562 1.097 } 1.099 10.31 (1.071) 0.125 191 12 0.712 1.111 :.008 9.00 :.005 :20 201 0.106 1.101 9.62 _ 201 0.755 1.081 1.095 12.31 (1.116 0.123 186 * 201 0.915 1.092 :.008 10.86 :.025) :.005 :20 201 1.152 1.103 9.71 Unfract'd 0.396 1.153 6.51 _ Unfract'd 0.626 1.132 1.139 7.58 ‘1.151 0.128 507 Unfract'd 1.065 1.133 :.009 7.52 +:.018 :.009 :36 1 0.337 1.208 1.81 1 0.762 1.115 1.165 6.90 -1;278 0.208 822 ’ 1 1.030 1.113 :.028 6.99 :.025 : 013 :51 3 0.386 1.135 7.11 3 0.632 1.116 1.119 8.62 1.192 0.171 686 3 0.809 1.101 :.008 9.90 :.025 :.013 :51 3 1.009 1.125 8.00 203-B 0.103 1.110 9.09 203-B 0.528 1.102 9.80 203-B 0.680 1.103 .098 9.71 1.136 578 203-B 0.818 1.088 -.008 11.36 :.010 :20 203-9 1.020 1.089 11.23 1-x 0.376 1.176 5.68 1-x 0.192 1.191 .181 5.21 1.211 772 1-x 0.678 1.176 .007 5.68 :.009 :20 202 0.373 1.188 5.33 202 0.531 1.191 1.163 5.15 1.299 . 881 202 0.665 1.111 :.028 6.91 :.013 :.007 :28 202 0.802 1.125 8.00 *Dimensions as a fraction of X/h = %£§§§.R. 86 Table X. Results from Zimm Plots of Copolymer experimental light scat- tering data in nitromethane. ‘52. X 9?? IO A A c ‘8. ° 8 "* E’ti a 15 ¢ 2 8A0) >< ~38 2\ l0 4-) 5.4% 3 S... 194 HA ARI-I 3 30 A 8.3 >< 3 x02): 2 p ‘4 (IN 2: 0C N . V V ,4 a: 12 10.28 0.973 0.189 (2.93) 33.60 . 91.1 201 7.27 1.375 0.183 3.67 32.61 128. Unfract'd 5.316 1.88 0.256 3.73 15.52 156. 1 1.614 2.15 0.188 1.11 ‘ 86.77 186. 3 3.56 2.81 0.313 3.51 55.65 153. 203-B 2.107 1.15 0.385 3.65 68.15 200. 1-x 1.625 6.15 0.355 3.17 63.12 236. 202 1.104 7.12 0.536 3.16 95.30 239, Average (an/dc)5461 = 0.0922 ml/g.used in calculation of x. 87 Corrected Light Scattering and Viscosity Results in Nitro- Table XI. methane L”, (3) (< M 5177]) W 0 x 10'?-1 FraCtiO“ h Zimm Dissym. x 10‘4 Zimm Dissym. 12 5 529 197:20 3.015 0.205 0.218 201 10 511 531:51 5.101 0.335 0.355 Unfract'd 1 551 581:20 8.16 0.507 0.125 1 1 828 822:51 10.97 0.193 0.198 3 1 667 686:51 18.15 0.611 0.562 203-B 10 789 578:20 31.12 0.61 1.63 l-X 1 711 772i20 55.66 1.55 1.21 202 10 931 881:28 73.31 0.909 1.07 88 Molecular weights (Table X) of the fractions were plotted against the intrinsic Viscosities in nitromethane and acetonitrile on a log-log plot. The slopes and intercepts were determined by least squares, giv— ing the Mark—Houwink equations, (8.2) and (8.3). In a similar manner the Viscosities of four fractions (Table XIII) in 2-ethoxy ethanol at the theta temperature were plotted against their molecular weights as determined by equation (8.2). All three relations are shown in Figure 20. Also shown by a dashed line for comparison are the tentative results for three poly-(methyl a-cyanoacrylate) fractions in nitromethane. (In cal- culating molecular weights of the latter, a (8373?) value of 0.0973, an average of 25 measurements, was used). Osmotic Second Virial Coefficient From the slopes of the zero concentration lines on the Zimm plots, values of the osmotic second virial coefficient, A2, were obtained. The usual decrease in A2 with increasing molecular weight is readily appar- ent from the results (Table X), which are fairly well fitted by A2 oc M-O'069 according to the least-squares method (with the fraction of lowest molecular weight omitted because of uncertainty in the extrapola- tion). The magnitude of the exponent is significant in that it roughly parallels the index of solvent power toward the polymer in question. In this respect the inference of low solvent power of nitromethane towards the copolymer is supported by the low value of 0.585 for the exponent a in the familiar Mark-Houwink equation. This eXponent, theoretically, can range from 0.5 to 0.8 for randomly coiled linear polymers obeying a Gaussian distribution (28), whereas the exponent 6 for the A2 de- pendence normally ranges from -0.1 to -0.3. 89 Although the values of A2 have a surprisingly low dependence on molecular weight, the absolute values are quite similar to values found for other acrylate-containing copolymers in a nitroparaffin solvent (2). However, they are five-to-six times larger than values obtained for non- polar 00polymers in a non-polar solvent (100). This is apparentLy in- dicative of greater solvent interaction in the present case and also suggests considerable repulsion between the dissimilar segments.* The osmotic coefficients are not as sensitive anindex to the di- mensions of the polymer chain as the intrinsic viscosity. This fact can easily be seen from the trend in the values of the ratio A2< M >h/TT7]. Small variations from the trend result from experimental error in the determination of A2. However, the definite trend cannot be dismissed as eXperimental error, and possibly may indicate deviations from Gaussian behavior. Empirically, of course, the trend is merely a re- “00069 and flection of the approximate dependence of A2 and [U ] on M M°°555 respectively. Trends have been observed by others in homopoly- mers (62), although not to the extent found here. Viscosities Copolymer Relative Viscosities were determined on the whole copolymer and all 27 fractions from Fractionation II in nitromethane at 30.20, and for four *Repulsive interactions have frequentLy been noted in dilute solu- tions of mixed pairs of polymers which are chemically "unlike" (96,98). The same effect, which was observed in an ca. 50/50 mole % styrene methyl methacrylate block c0p01ymers (2,89), has been attributed to re— pulsive interactions between chemicalLy different sections of each poLy- mer molecule. 90 of these fractions in 2-ethoxy ethanol at the theta temperature. In addition, Viscosities were determined on the whole copolymer and six fractions from Fractionation I in acetonitrile at 300 and for four of 3 these fractions in nitromethane at 30.20. The data were treated accord- ing to Huggins' equations (3.2) and (3.3) and representative results are plotted in Figures 15 - 18. The results of the extrapolations are col- lected in Tables XII and XIII. Viscosities in acetonitrile were esti- mated for the remaining fractions from Fractionation I by a single solu— tion measurement and the relation: 17 ] = (x - Y)/1' + Y; where x is the value of (77r - l)/c Y is the value of (in 77r)/c, and k' is as- : sumed to be the average value, 0.375 (28h). Intrinsic Viscosities determined in the above manner (excluding the single solution determinations) and the Huggins constants k' and k" are quite consistent. The latter especially give good agreement with the theoretical k' + k" = 0.5 value. The nearly uniform decrease in intrinsic viscosity with fraction number (Run II), ignoring the always heterogeneous initial fraction, attests to the effectiveness of the fractionation scheme employed. By employing the familiar Mark-Houwink relationship: [77] = K' <:M >8 (8.1) where both K' and a are constant over a considerable molecular weight range for a given temperature and solvent-solute pair, and <'M > is the weight-average molecular weight,* the following relations were *Strictly speaking, the equation is established from weight-average molecular weights on sharp fractions. Thereafter the equation may be applied to samples of any heterogenity, giving viscosity-average molecu- lar weights. For fractions having narrow distribution the difference between the two averages is negligible. Even for broad distributions the ratio <.M >V/2.M >w is closer to unity than is the ratio v/n' (See, e.g., ref. 85). Figure 15. 91 Viscosities in acetonitrile of MCyA/1B copolymer fractions from Run I. 2 I V ' 3 .51 t 171:1 _ ' c 1 (Open) v 1n 7r h C 0 (36118-145 - O - o .39 - U .33 ” 8 K 12 ~27 7 M . . 0 0.1 0.8 1 2 1.6 2.0 C(g/lOO m1) . 92 Figure 16. Viscosities in nitromethane of MCyA/IE copolymer fractions from Run I 1.12 1.01 .96 .88 77r-l c (0 en) 1 p .80 ’ n77r 0 (solid) .72 ~ 3 .61 ' .56 - 1 F IL .18 ' I“If“" .10 - m '32 i-:="” q'____A'L, O O 2 O 1 0.6 O 8 l O l 2 93 Figure 17. Viscosities in nitromethane of MCyA/1B copolymer fractions from Run II. 1.36 l" 202 1.28 - 1.20 _ 1.12 " 1.01 t 771*1 203-13. c 'v (Open) V in 77. C (solid) .88 " .80 - . 203-C , 0 A 203-E .56 - 4 ' ‘ ‘ 0 0.2 0.1 0.6 0.8 1.0 1.2 C(g/100 ml.) ‘nr'l C (open) 1n 9. c (sblid) -91 Figure 17(contL‘Viscosities in nitromethane of MCyA/TB c0p01ymer fractions from Run II. .18' .10 .367 .32 201 203-1‘ ‘ 0 . , Unfractionated 201 205 6 0.2 0.1 0:6 C(g/IOO ml.) 0.8 1.0 1.2 95 Figure 18. Viscosities in 2-ethoxy ethanol of MCyA/1B copolymer fractions from Run II. '51,, 0.1 0.8 1,2 1.6 203-E ‘L .16' .12— E C (Open) 11177r _ c (solid) .31 .16 .12 I I ‘l .08 _L I l 1 l 0 0.8 1.6 2.1 3.2 1.0 C(g/lOO m1.) 96 Figure 18.(cont.). Viscosities in 2-ethoxy ethanol of MCyA/IE copolymer fractions from Run II. .10‘ .36’ _ O .32: ' 205 77171 c t 1. (Open) hiqr 3 C . (36118) ’ ' .21 _. .20 b 208 .16 ‘_ W 0 0.1 0.8 1.2 1.6 2.0 C(g/EOO m1.) 97 Table XII. Viscosity results for poly-(methyl a—cyanoacrylate/isobutylene) from Fractionation Run I. Fraction [77]d1/g k' k" k' + k" A. In Acetonitrile at 30° 1—X n40.67 2 0 655 0.291 0.189 0.180 3 .501 .378 .192 .570 1 .131 .798 .082 .880 Whole .378 .358 .111 .502 8 .321 .208 .225 .133 12 .282 .382 .122 .501 B. In Nitromethane at 30.2° l-X 0.905 0.266 0.092 0.358 3 .616 .295 .138 .133 1 .510 .392 .122 .511 12 .313 .198 N O N .198 98 Table XIII. Viscosity results for poly-(methyl a-cyanoacrylate/iso— butylene) from Fractionation Run II. Fraction [7)] k' k" k' + k" A. In 2-ethoxy ethanol at 86.50 (theta) 203—E 0.310 1.126 -0.361 0.765 201 .230 1.371 - .567 .807 208 .158 0.915 - .333 .612 212 .120 .382 + .139 .521 B. In Nitromethane at 30.2° 202 1.03 .393 - .122 .515 203-A 0.763 .366 - .110 .506 203—B .757 .122 - .103 .525 203-c .67 .303 - .181 .181 203-0 .65 .318 - .150 .198 203—E .62 .375 .130 .505 201 .507 .350 — .151 .501 Whole .15 .383 - .132 .515 203-F .161 .371 - .111 .512 203-0 .102 .312 — .181 .193 201 .393 .519 ~ .002 .521 205 .375 .339 - .151 .193 203-H .285 .171 - .053 .527 206 .266 .621 + .071 .552 208 .251 .533 - .012 .515 207 .217 .677 + .139 .538 209 .221 .110 - .088 .188 210 .193 .987 + .103 .581 211 .181 .107 - .091 .198 212 .182 .353 - .150 .503 213 .155 .867 + .298 .569 211 ( 131) (.077) ( .238) (- 161) 215 .131 .218 - .291 .509 216 .118 .150 — .055 .505 217 .112 .711 + .131 .577 218 .1095 .053 - .573 .626 219 .091 .536 n4 (3 .536 99 established for the copolymer: in nitromethane, [77] = 3.89 x 10-4 < M >fi0°585 (8.2) in acetonitrile, [77] = 1.7 x 10‘4 < M >w°°56 (8.3) in 2-ethoxy ethanol [7718 = 5.99 x 10.4 <.M >w°°5°4 (8.1) Equations (8.3) and (8.1) have been established on the basis of intrinsic Viscosities run on fractions of which the molecular weights were deter— mined either directly from light scattering in nitromethane solutions, or from the empirical equation (8.2) established from light scattering results. Relative Viscosities were also determined for several fractions and two whole polymers of poly-(methyl a—cyanoacrylate) in nitromethane. Results were not as consistent as for the copolymer owing to sample degradation. Degradation of4901y—(methyl a-cyanoacrylate) During the viscosity measurements of two unfractionated methyl 0- cyanoacrylate homopolymer samples having different sources (JM and RKG), continued inability to achieve consistency prevailed. Numerous runs each produced different results with very little certainty of the true or most probable value of the intrinsic viscosity. When heating became suspect as the probable cause of the random results, a controlled heat- ing period was applied to the samples with the following results: the intrinsic viscosity was reduced about one-half (0.65 to 0.313 dl/g.) for sample JM after the dry polymer had been subjected to 110° for 10 hours; likewise, the same decrease (0.178 to 0.211 dl/g.) in viscosity occurred in sample RKG after heating at 101° in excess of 18 hours before solutions 100 were prepared in nitromethane. This is conclusive evidence of the effect of heat on the stability of the molecular chains and points out the care that should be exercised in the drying of all poly-(methyl a— cyanoacrylate) samples. In addition to heat applied directly to the polymers as in the above situation, heating solutions of the homopolymer in acetonitrile on a steam bath also apparently causes degradation. During the repre- cipitations of the polymer fractions from nitromethane and acetonitrile, heating was necessary to coagulate the dispersion. Brown discoloration accompanied the heating and apparently led to degradation of the polymer. This degradation,whether it occurred in the reprecipitation or drying of the fractions, apparently was the reason for the anomaly in the order of molecular weights of some fractions (e.g., JM-3 and JM-2c). A higher oven temperature (105°) was used for drying of Fraction JM-3. The surprising discovery that all the recovered fractions had lower intrinsic viscosities and, therefore, lower molecular weights than the initial unfractionated homopolymer was overt evidence of degradation during the fractionation and/or drying procedure. The tentative Mark—Houwink equation obtained from light scattering measurements on three poly-(methylarcyanoacrylate) fractions (see Table XIV) is: [77] = 1.17 x 10‘5 < M >w0-76 (8.5) This equation was determined from three points corresponding to fractionated sample; it gives excellent agreement with the expression reported by Kinsinger in reference 15, obtained on higher molecular weight, unfractionated samples. 101 Table XIV. Viscosity Results for Poly-(methyl a-cyanoacrylate) fractions in Nitromethane Fraction [771,81/1. <.M >wx 1075 k' k" k' + k" T = 30.20 JM(whole) 0.65 3.31 0.193 0.059 0.552 JM-2b .582 2.83 .391 .13 .521 JM-2d .508 2.10 .136 .097 .513 RKG(whole) .175 2.19 .192 .019 .511 JM—2c .137 1.95 .315 .157 .502 JM-5 .115 1.75” .318 .119 .197 JM—3 .35 1.11* .631 .091 .72 .189 - 037 .152 RKG-l .318 1.23* .198 .275 .173 *<:M > determined by light scattering. Remaining molecular weights were calculated from empirical equation (8.5)° 102 The value of a = 0.56 in acetonitrile compared with a = 0.585 in nitromethane indicates that the latter is a better solvent for the co- polymer, and that the former is close to being a theta solvent. How- ever, no indication of a phase separation was in evidence when a dilute solution of the copolymer in acetonitrile was cooled well below 0°. In the theta solvent for the copolymer the deviation of Huggins' constants k' and k" and their sum (Table XIII) from the usual values is not too surprising. Similar unusual behavior has been noticed for poly—(methyl methacrylate) in an ideal solvent where samples having a molecular weight above 560,000 gave k' values ranging from 1.00 to l.62(86). The normal trend is observed in the slopes (Figure 18) as expressed by Huggins' equation (1.2). If any significance can be attached to the apparent decrease in the (k' + k") sum with molecular weight, it may possibly represent some residual interaction which diminishes with de- creasing number of segments. This would refute the basic premise of the theory, however, and some other explanation should be sought. Equation (8.1) gives excellent agreement with the theoretical relation: [7716 = 1011/2 (8.6) which is a special form of the more general relation due to Flory and Fox (11) as: 2 < Lo > [7]] =9 (T)3/Z Nil/2 (13 (8.7) where L0 is the unperturbed root-mean—square end-to-end distance* of the * The double average notation employed here is necessary in the strictest sense of the word for the following reasons: (cont. pg. 105) 103 Figure 19. Viscosities in nitromethane of MCyA homOpolymer fractions. JM .801 O O -75 . O JM-2B .70 - 77171 0 (Open) .651 . JM—2D o/ lnin} 0 (solid) .60 . R30 55 ' .50 - .15 ' 0 0.2 0.1 0.6 0.8 1.0 1.2 1.1 c(g/lOO ml.) 101 ~< mod m.m: 3 9m .2 3 2m 3 9.1 q u q _ a . - O‘HI . 1 w.o- - - 6.6- at; mg I J.OI I NOOI 335 82005003: I D Hocmnpo xKonpoum 1 o oawanCOpoom 1 < ocmcmeoupH: 1 0 no .mcmcoweoufic 5 00530000 05 Mo 2303 033305 ommugmupcmaoa 05 tam ~< 0:33.308 HMS? 9808 03058 on» coozpon CompmHoH moflumoH on» mw . czocm 02¢ .ocmcomsoufi: cw nogfloaoEon <50: no.“ ocm 3955.0 honocpoum .. .mHflHuHCOpoom «magausoupwc cu" .HuaEQOQOU mH\<.AOE how. muoHQ xcwkjomthmz ..ON mhsmwm 105 randomly coiled polymer chain; Q is a universal constant (which.Eebye prefers to call a parameter) having a commonly accepted value of 2.1 (i0.2) x 1021 (28e); and a is the intramolecular expansion factor. This factor assumes the value 1 in a theta solvent at T = 0 where there is no net interaction between polymer and solvent; thus, theoretically, the chain assumes random flight behavior. The intrinsic viscosities obtained at the theta temperature, when combined with those determined on the same fractions in nitromethane furnished a direct measure of the expansion of the chain in a good sol- vent through the Fox-Flory relation (31): a3 = 17211771; (8.8) Light scattering data on high molecular weight fractions in the theta solvent are preferable for the computation of a from equation (8.7), especially since recent theories (87,88) and experimental results (89,90) have established that the exponent of a in equation (8.8) is closer to 2.5 than to 3. To establish the prOper value of the exponent, reliable values of the radii of gyration of well-fractionated, high molecular weight samples would be needed in addition to their viscos— ities. However, since the newer theory still has the ratio [77 1/[7719 as a function only of a for most cases of interest, the use of equation (8.8) should not seriously affect the calculation of a for the present C6138 . *(cont. from pg. 102) 1. Since one is dealing with a randomLy coiled chai7,which is con- tinuously in motion, the capital letter L (equal to (F2)1 2 in Flory's notation) represents the time-average of all configurations of the molecule. 2. Even in a well-fractionated sample some heterogeneity is invar— iably present; thus the angular brackets indicate an average over these species (See Ref. 13). Hereafter the brackets will be omitted with the understanding that the species are assumed to be homogeneous. 106 Since increasing temperature has a small affect on the unperturbed chain dimensions through the lowering of the barrier to rotation about the individual bonds, the validity of a direct comparison of the intrin— sic viscosities by means of equation (8.8) might be questioned as a re- sult of the difference of ca. 56° between the temperatures employed for the intrinsic viscosities in the two solvents. The validity of the com- parison may be justified, however, if one assumes that nitromethane is a good solvent for the copolymer. It has been shown that the intrinsic viscosity is independent of temperature over a wide range (Au75°) for polyisobutylene in good solvents (31) and presumably holds for other systems as well. The fact still remains that nitromethane cannot be unambiguously designated as a good solvent on the basis of the value of‘a in the Mark—Houwink equation; therefore, the values of a determined in the above manner should be taken with some reserve. Regardless of the questionable nature of a valid comparison of the intrinsic viscosities in the above case, the method is still useful in providing a good estimate of the chain expansion and its dependence on molecular weight. From equation (8.8) the expansion factor was cal- culated for four copolymer fractions, each increasing in molecular weight by a factor of two over its predecessor. From this eight-fold spread in molecular weight an increase with molecular weight was found for a and for (a5 - as)/M1/%, which is a rearrangement of equation (3.6). Theoretically, the eXpression (a5 - as)/.M1/2 should be independent of molecular weight, but this is rarely found experimentally. The results for the c0polymer are given in Table XV. 107 Table XV. The Expansion Factor and its dependence on the Molecular Weight of Copolymer Fractions in Nitromethane. Fraction M x 10-5 as = [771/17716 a [(05-03)/M1/21 x 103 212 0.367 1.52 1.15 2.556 208 0.635 1.58 1.167 2.301 205 1.26 1.63 1.176 1.716 203-E 2.96 1.82 1.22 1.617 Determining a values in the above manner gave directly a measure of the expansion of the chain as a result of interaction with the sol- vent and by intramolecular interactions with distantly related segments of the same copolymer molecule. The unperturbed dimensions of a chain are related through the constant K to the intrinsic viscosity. Thus by combining equations (8.6) and(8.7) and relating them to the experi- mentally determined relationship between [77]e and M°’5 expressed in equation (8.1), K for the copolymer was found to be: K = o (LS/T11)?“2 = 5.99 x 10‘4 (8.9) By accepting the "universal constancy" of 6, the eXperimentally determined value of K for the copolymer was used to calculate the un- perturbed displacement length (Lg/M)1/2 'which is characteristic of each 3 type of polymer having an invariant structure.* This quantity isolates the'effects of hindrances to rotation about the bonds as well as the act- ual bond angles and distances, but depends upon the weight of each monomer unit. By 1nvar1ant structure 15 meant a polymer of f1xed comp051t1on (specified in case of a copolymer). 108 Table XVI shows the results from four copolymer fractions. The un- perturbed diSplacement lengths were calculated from equation (8.7), as- suming a = l at 0, and using both the "normal" and experimental values of b, 2.1 and 1.3 x 1021, respectively. Results are given.with L in terms of Angstroms instead of centimeters. The value of (L(2,/1"I)1/2 cal- culated from equation (8.9) indicates an unperturbed root-mean—square end—to-end dimension of 6581 for a chain of molecular weight 1 x 105. This is in agreement with the individual values calculated assuming the usual value of b. The last column gives a more reliable average value of the unperturbed dimensions which was calculated from the experimentally determined value of b. The actual dimensions of the copolymer in a good solvent are related to the unperturbed dimensions by L = 0 L0- Table XVI. Unperturbed dimensions of Poly-(methyl a-cyanoacrylate/iso— butylene) in 2-ethoxy ethanol. Fraction, ([7:106E1/2) (Lg/M)3/2 (Lg/M)1/2 cheo. QeXp. 5theo. Qexp. 212 6.26 0.298:.057 0.182:.076 0.668:.013 0.781: 01 208 6.27 .298,:.057 .182:.076 .669:.013 .785:.o1 205 6.18 .309:.059 .198:.079 .676:.011 .792:.012 203—s 6.25 .2975:.057 .180:.076 .668:.013 .783:.01 The values of the molecular displacement length as determined from K and ¢1for the alternating copolymer and literature results of the same quantity for a statistical c0polymer of 50:50 mole % composition plus results on the parent .homopolymers are listed in Table XVII. Also 109 Table XVII. Comparison of Molecular Displacement Lengthéifor two C0polymers and their Parent HomopoLymers. Polymer 0 Temp. K x 104 (Lg/M)1/2 (LE/Mf/2 (La/Lz)l/é R f C0polymer °C x 1011 x 1011 0 f e ' (calc'd (calc'd from K) from: 0=109.5o 1=1.51 A ) PMCyA 85 292 this work P(MCyA/IB) 86.5 5.99 658 c 337 1.95 this work (786) (2.33) FIB 21 10.6 760 112 1.80 92 PMMA 30 6.5 680 310 2.20 13 P(MMA/S) 25 906 305 2.97 93 50:50mole% PS 25 711 302 2.35 93 PS ca 25 8.3 735 302 2.11 91 PS 70 7.5 710 302 2.35 91 aValues were calculated assuming1b = 2.1 x 1021. bPMCyA -- poly-(methyl a-cyanoacrylate) PIB -- polyisobutylene PMMA -- poly-(methyl methacrylate) PS -- polystyrene. CValue calculated from experimental value of §1= 1.3 x 1021' 110 shown for comparison with the experimental values of the unperturbed dis- placement lengths are the values calculated assuming free rotation about the bonds. The freely rotating chain displacement lengths (Liz/MH/2 were cal- culated from the expression given by Flory (91) for tetrahedrally bonded chains: 1/2 (L?) = n.lz(1 + cos 6)/(l - cos 0) (8.10) where.1 is the length of each bond, 0 is the angle between successive bonds in the polymer chain, and n is the number of such bonds (equal to twice the degree of polymerization). For the alternating copolymer of methyl a—cyanoacrylate and isobutylene the number of bonds is given by: n = m/11.75 (8.11) where 11.75 is the average weight per chain bond and M is the molecular weight of the chain. The normal tetrahedral angle of lO9.5° and carbon- carbon distance of 1.51 A'were assumed. It is also of interest to apply another relation of Flory and Fox(11) to compare the value of K as defined in equation (8.8) and determined experimentally. According to this theory a plot of [7) ]2/3/M1/3 against M/[77] should have a slope equal to 20MK5/°(l/2 -‘)(1) and an intercept at vanishing M/[77] of K2/9,‘where CM is a constant related to the un- perturbed chain characteristics (defined in equation (3.6)), and :X3 is the usual interaction parameter. Utilizing the viscosities in both the good and ideal solvents, a reasonably straight line is fitted to the results from each group of solutions (Figure 20). The value of K obtained 111 Figure 21. Relation between [7712/ 3/111/ 3 and WW] for MCyA/113 copolymer in a good and in an ideal solvent .1 .2 3 1 s, . 7. 10‘5 111/[77] 1.15” 1.10“ 1.05- 1.00- 102[7)]2/3 iMl/B 97577 GE) - e G '6 l .71 ‘ L . n n 1 O 2 1 6 8 10 12 112 from the theta temperature measurements is within experimental error of that obtained from the Mark-Houwink plot, as expected [compare results in Table XVI to equation (8.1)]. The disparity in the two intercepts is not understood, for the theory predicts K to be independent of solvent. Part of the cause of the discrepancy is the temperature differential, which has the same affect as discussed in the section on the expansion factor.a. It is a fact that values of K decrease with increasing temper- ature (28f). Actually, Ke = Kins, so that in a theta solvent with temperatures above (a > 1) or below (a < l) 0 the equation is still valid. But for different solvents, including a theta solvent at the same temperature, different K values have been found experimentally (95); thus there seems to be an unresolved weakness in the theory. Obviously more experimental results are needed, especially in pure theta solvents instead of critical consolute mixtures which probably lead to specific solvent effects not realized. Table XVIII. Interaction parameter 9<1 and K values obtained from a plot of [77]2 3/M1/3 versus M/[77] for poly-(methyl a.- cyanoacrylate/isobutylene) in good and ideal solvents. Solvent Temp. (°C) K.x 104 (1/2 - :ka) Nitromethane 30.2 8.59 .0029 2-ethoxy ethanol 86.5 6.05 0 Unperturbed dimensions L0 of the c0polymer as determined at the theta temperature in 2-ethoxy ethanol from the Fox-Flory (31) relation, 103 = [77]eM/a>, assuming it: = 2.1 x 1021, are 1.95 times the values calculated assuming free rotation about the bonds. In nitromethane at 113 30°, perturbed dimensions are 2.10 times as large. From light scatter- ing measurements in nitromethane at the same temperature, equation (1.5) gives for the copolymer root—mean-square end-to—end dimensions which are ca. 3.3 times the values for free rotation. Figure 22 shows the relative effect of the two solvents on the chain dimensions as determined from viscosities and, for comparison, from light scattering in nitromethane alone. The latter dimensions are larger than predicted on the basis of the viscosities, assuming that the system obeys Fox-Flory's theoretical relation, including the accepted value of the universal parameter 9 = 2.1 (i 0.2) x 1021. Calculations show that the value of1¢ is closer to 1.3 (i 0.2) x 1021 when using the light scattering dimensions of the three fractions of higheSt molecular weight, (ca. 1 - 7 x 105). Lower molecular weights yield even lowerifi values; but the experimental uncertainty is greater in this range, probably being no better than 5% for molecular weights and 15% for end- to-end dimensions. The true value of ¢>could be even larger if the heterogeneity of the samples is much larger than was assumed. Newman, at 31. (13), in analyzing the effect of molecular weight heterogeneity on calculated values of 0, found that even for a relatively sharp dis- tribution (< M >w/< M >n = 1.15) the true value of 4) may be 20% higher than the value obtained before correction for the heterogeneity. Since reasonable heterogeneity values were used and the fact that even a 50% increase in most cases would not have given the "accepted" value of 2.1 x 1021 forlb, the results are believed to be representative of the true situation, at least for the higher molecular weights. mhwgm 8% 115 This is in line with results obtained by Kotera, gt al.(99) on iso- tactic polypropylene, where values of Q’ranged from 0.7 to 2.5 x 1031 and didn't reach the accepted value until a molecular weight of well over one million was measured. The low results, however, are surprising in view of the fact that the theoretical value of §’in theta solvents has been reported (100) as 2.81 x 1021. But, again, the high value should be applicable only to a normal homopolymer system. Ivin and collaborators (ll) found1¢ to have an average value of 1.8(i0.2) x 1021 for hexene-l polysulfone alternating c0polymer in n-hexyl chloride at the theta temperature. From dilute solution studies of a fluorinated copolymer in an inert, though good, solvent, Morneau and co-workers (101) calculated a value of ¢1which is six times smaller than the "accepted" value. From these results and the present ones, it would appear that copolymers are con- siderably more expanded in solution than theory predicts for "regular" polymers. This is only partly due to the nature of the solvent inter- action; it is mostly a result of the repulsion of the dissimilar com- ponents of the chain. If the extra repulsions present in a binary copolymer did not exist, it would be possible to predict the molecular extension parameter of a c0polymer from information obtained on the homopolymers in their unperturbed state (2). Stockmayer and coaworkers thus expressed the relationship as: (Loz/M) = gag/11>, + deoz/M)B (9.2) where wA and wB are weight fractions of the species A and B present in the copolymer. Equation (9.2) was predicted to be valid for block 116 copolymer, but questionable when applied to statistical copolymers hav- ing short sequence lengths and greater repulsions Operative between the dissimilar segments. It is strange, therefore, that Stockmayer and co- workers found at least semi-quantitative agreement between equation (9.2) and results from an "azeotropic" copolymer of styrene and methyl meth- acrylate (16 weight % of the latter), even though measurements were not made at the theta temperature. This fact alone may possibly be the reason that the good agreement was obtained. Recent measurements (93) on a block copolymer having nearly equal molar compositions of the same two constituents as above gave results far above those predicted by equation (9.2). Obviously this equation has only limited utility and cannot apply to copolymers having appreciable repulsions. It would un- doubtedly not apply to the present alternating c0polymer. SUMMARY A copolymer of isobutylene and methyl a-cyanoacrylate in which these components alternate along the chain was characterized by solubility, phase equilibria, viscosity and light-scattering measurements. (The copolymer exhibited unusual solubility characteristics as a result of its unique composition and was readily soluble in such widely differing solvents as benzene and acetonitrile. Thus a double range of solvents on the cohesive energy density scale exists. Using benzene as the fractionation medium, the bulk copolymer was carefully fractionated from dilute solution to provide more homogeneous (in molecular weight distribution) samples for characterization and for comparison with properties of the parent homopolymers. Molecular weights of several fractions were determined from the amount of monochromatic light scattered by dilute nitromethane solutions. Solution viscosity measurements in acetonitrile, 2-ethoxyethanol and nitromethane enabled the following Mark—Houwink relations to be established: in nitromethane, [T7] 3,89 x 10-4 < M;>w0.585 I! in acetonitrile, [77] 1,7 x 10‘4 < M >wo.ses in 2-ethoxy ethanol [77]e 5,99 x 10'4 <:M >w0°504 The latter equation gives excellent agreement with the theoretical de- pendence of intrinsic viscosity on molecular weight in theta solvents, [77] ,\,M1/2. 0 The theta temperature, which is the temperature at which there are no net interactions in a given theta solvent/polymer system, was found 117 118 to be 86.6 i l.2°C for the copolymer in 2-ethoxy ethanol and 85.0 i l.2°C for poly-(methyl-a-cyanoacrylate) in cyclopentanone as determined by phase separation measurements on the fractions. The Mark-Houwink relation established for poly—(methyl-a-cyanoacry— late) in nitromethane, [77] = 1.17 x 10-5 <.M >w°'75, can only be con- sidered a tentative one since degradation of the samples occurred to some extent during fractionation and subsequent treatment. Even so, the equation gives unusually good agreement with one obtained by Kinsinger (15) on unfractionated, higher molecular weight samples. In this work the molecular weights were not sufficiently high and therefore measurements were not sufficiently accurate to calculate end-to-end di- mensions for the homopolymer; thus no test could be made on the equation given by Stockmayer, at El. (2), (LS/M)“, = A0311), + wBué/mB using the measurements on the copolymer and the methyl a-cyanoacrylate homopolymer along with available literature data for polyisobutylene. Theoretically the equation allows one to predict the unperturbed molec- ular extension of a copolymer of known, fixed composition from measure- ments on the parent homopolymers. The actual end—to-end dimensions of the copolymer as calculated by the dissymmetry method from light scattering measurements in nitromethane indicate that the c0polymer chain is extended to a greater degree than would be expected on the basis of viscosity measurements. The dimensions are 3.3 times the values calculated assuming free rotation about the bonds. The universal parameter §1has a preferred average value of 1.3(iO.2) x 1021 instead of the more commonly accepted value of 119 2.1(i0.2) x 1021. The smaller value is justified on the basis of the larger dimensions which are encountered for a given viscosity. (It should be pointed out that low values of D are not uncommon for copolymers and have even been found for sterOSpecific homopolymers.) The extra expan- sion in the copolymer chain is believed to result from repulsive inter- actions of the two dissimilar components of the chain -- the highly polar cyanoacrylate group and the non-polar isobutylene. It is con- cluded that this type of behavior should, in general, hold for all addi- tion—type copolymers having a high degree of alternation of components which differ appreciably in polarity. -\] 10. 11. 12. 13. 11. 15. 16. 17. 18. 19. 20. 21. O\\J"l£"w REFERENCES R. Tremblay, M. Rinfret and R. Rivest, J. Chem. Phys. 29, 523(1952). . H. Stockmayer, L. D. Moore, Jr., M. Fixman and B. N. Epstein, . Polymer Sci. 16, 517(1955). Liz H. Benoit and C. Wippler, J. chim. Phys. 51, 521(1960). W. Bushuk and H. Benoit, Canad. J. Chem. 36, 1616(1958). H. Benoit and M. Leng, Ind. Plas. Mod. 2, 12(1960). M. Leng and H. Benoit, J. chim. Phys. 58, 180(1961). S. Krause, J. Phys. Chem. 65, 1618(1961). R. E. Cook, F. S. Dainton and K. J. Ivin, J. Polymer Sci. 26, 351 (1957). _— H. 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W. R. Krigbaum, L. Mandlekern and P. J. Flory, J. Polymer Sci. 2, 381(1952)- ' S. N. Chinai and R. I. Samuels, J. Polymer Sci. 52, h63(1956). W. H. Stockmayer and H. E. Stanley, J. Chem. Phys. 16, 153(1950). N. A. Lange, Handbook of Chemistry, Sixth Ed., Handbook Publishers, Inc., Sandusky, Ohio, 19h6, p. 517. G. Allen, G. Gee and J. P. Nicholson, Polymer l, 56(1960). A. Kotera, K. Takamizawa, T. Kamata and H. Kawaguchi, Reports on Progress in Polymer Physics in Japan, 6, 131(1961). G. J. Meyerhoff, J. Polymer Sci. 65, 269(1960). G. A. Morneau, P. I. Roth and A. R. Shultz, J. Polymer Sci. 55, 609(1961). K. A. Stacey, Light Scattering in Physical Chemistry, Butterworths Scientific, London, 1956, p. 60. International Critical Tables 1, McGraw-Hill, New York, 1930, p. 3h. APPENDICES 1. Phase [Eta for Poly-(methyl a-cyanoacrylate/isobutylene) in 2-ethoxy ethanol. 2. Phase Data for Poly-(methyl a-cyanoacrylate) in cyclopentanone. 1. Results of Calibration of Removable—top Differential Refractometer Cell at two Settings Using Potassium Chloride Solutions. 2. Results of Calibration of Sealed—top Differential Refractometer Cell Using Alkali Chloride Solutions. Calculation of Reduced Intensity 1. Raw Light-Scattering Data from Fraction 202 in Nitromethane. 2. Detailed Calculation of Light-Scattering Data from Fraction 202. 125 APPENDIX A 1. Phase data for poly-(methyl a-cyanoacrylate/isobutylene) in 2-ethoxyethanol. Fraction v2 TE(°C) Fraction v2 Tp(°C) 203-E .0893 76.87 i 0.22 208 .0581 65.25 i 0.15 " .0889 76.95 i 0.05 " .0375 68.9 i 0.3 " .0882 76.80 i 0.05 " .0255 63.8 i 0.5 " .0363 76.05 i 0.05 " .0208 62.6 i 0.3 " .0357 76.75 i 0.05 " .0188 61.95 i .25 " .0306 76.65 i 0.05 " .0153 61.0 i 0.2 " .0293 75.98 i 0.03 " .0128 59.8 i 0.2 " .0253 76.25 i 0.05 212 .0888 59.3 i 0.10 " .0237 75.80 i 0.05 " .0650 58.5 i 0.10 " .0200 75.60 i 0.10 “ .0625 58.75 i 0.15 " .0195 75.88 i 0.03 " .0608 58.6 i 0.10 " .0167 75.35 i 0.05 " .0503 57.95 i 0.20 " .0187 75.05 i 0.05 " .0868 57.65 i 0.15 205 .0887 70.9 i 0.1 " .0369 57.55 i 0.35 " .0366 71.1 t 0.3 " .0307 55.80 i 0.10 " .0337 70.8 i 0.3 " .0278 56.05 i 0.30 n .0297 70.75 i 0.25 N .0223 58.9 t 0.3 " .0223 70.2 i 0.8 " .0136 51.7 i 0.3 " .0218 70.3 i 0.3 " .0188 69.9 i 0.8 " .0178 69.9 i 0.5 " .0138 68.9 i 0.9 126 2. Phase data for poly-(methyl 127 a—cyanoacrylate) in cyclopentanone Fraction v2 2p(°C) Fraction v2 Tp(°C) 2b .0502 69.55 i 0.15 3 .0828 68.10 i 0.05 " .0358 70.85 i 0.10 " .0388 68.63 i 0.025 " .0292 70.90 i 0.10 " .0279 65.00 i 0.05 " .0216 71.82 i 0.08 " .0219 65.22 i 0.08 " .0168 71.55 i 0.05 " .0129 65.22 i 0.05 " .0186 71.35 i 0.05 " .0138 65.30 i 0.10 " .0113 70.95 i 0.10 " .0099 65.87 i 0.13 " .0095 70.70 i 0.10 " .0059 63.65 i 0.55 " .0086 61.8 i 2.0 2c .0596 68.82 i 0.08 " .0838 65.85 i 0.05 " .0323 66.75 i 0.05 " .0285 67.35 i 0.10 " .0190 67.68 i 0.08 " .0150 67.78 i 0.08 " .0109 67.88 i 0.17 " .0073 67.85 i 0.25 " .0055 66.80 i 0.50 " .0083 63.3 t 3.5 APPENDEX B 1. Results of calibration of removable-top differential refractometer cell at two settings using potassium chloride solutions Conc. 3 Ad 7 k x 105 * (g/kg H20) AHXIO 1 2 1 2 T = 2000 6.3270 0.883 106.2 90.2 0.798 0.935 x = 58618 22.7388 2.981 373.2 320.9 0.7988 0.9291 Settings 39.2880 5.120 639.2 588.0 0.8010 0.9383 #1 and #2 Av. 0.798 0.933 :0.003 :0.005 2. Results of calibration of sealed-top differential refractometer cell using alkali chloride solutions. Salt Come. 3 ' 5 7 KCl 6.3270 0.883 100.8 0.880 T = 20°C 0 NaCl 1.9895 0.381 81.6 0.820 x = 5861A NaCl 2.7073 0.876 56.3 0.885 Setting #1 NaCl 3.375 0.5925 69.8 0.858 NaCl 8.888 0.855 100.8 0.888 AVg. 0.881 i0.009 *Position of components on optical bench (cm.). Setting Scope lens cell slit lamp 1 zero to end 25.8 60.0 76.9 118.0 2 zero to end 21.0 66.0 86.0 118.0 128 APPENDIX C CALCULATION OF REDUCED INTENSITY From the galvanometer ratios (see Light Scattering, Experimental), the steps necessary to arrive at final turbidity, or reduced intensity, values are detailed below. After the average galvanometer ratios are multiplied by the appro- priate product of filter factors F, the excess ratio is obtained by sub; tracting the solvent ratio from the solution ratio: [F (68076700) F(GGO7GOO) = F 1.. NC (I) a) a) ‘9 £3 '8 LL. Lt. _ 85 ..768 ‘,058 0.710 0.8718 0.3387 .1188 6.77 0.988 .186 50 .661 .087 .618 .5823 .333 .1182 6.805 0.981 .179 60 .515 .039 .876 .6928 .3298 .1171 6.869 1.052 .250 70 .823 .038 .389 .8816 .3274 .1162 6.922 1.131 .321 80 .369 .031 .338 .9563 .3232 .1187 7.013 1.215 .813 90 .388 .029 .319 1.0000 .319 .1132 7.106 1.302 .500 100 .357 .030 .327 .9563 .3127 .1110 7.286 1.389 .587 110 .397 .032 .365 .8816 .3072 .1091 7.3715 1.873 .671 120 .875 .038 .837 .6928 .3026 .1075 7.882 1.552 .750 130 .601 .087 .553 .5823 .2999 .1065 7.553 1.623 .821 135 .688 .055 .629 .8718 .2965 .1052 7.686 1.650 .858 Intercept (c = 0, G = 0) = 1.804 x 10‘6 Slope (C = 0) = 0.750 x 10-6 <.M ’8’: 712,000 Slope (e = 0) = 6.92 x 10'6 z = 145/1135 = 1.125 WISIAJ Llonnnl