— -._ —“I-‘—"w—‘-V “_.. . V LQWER CRITICAL SOLUTEQN TEMPERATURES F655 PGLYD {METHYLS‘E LO KANE Thesis for Hm Deqpoo of M. 5. WCHESM SHE'E UHWERSETY George Ear! Verge! 1966 14% {a M W“; 1&1qu gm (lfll m w mum! M ll ‘ LIBRARY Michigan Stan University War } U31” 3 a tic-q, 3 02500? LOWER CRITICAL SOLUTION fEthhAEURES FOR EOUYDImETHYLSILLXARE By George Earl Vogel A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of ABbIHACT LOWER CRITICAL SoLUfICh LEiIERArUhES bCR rtLYDlanHlLSILOXAhE by George E. Vogel Lower critical solution temperatures, TCL’ were determined for five well characterized fractions of poly~ dimethylsiloxane in n—pentane, n—butane, propane, neopentane, tetramethylsilane, dimethyl ether, and methyl chloride. Linear relationships were found for l/l‘CL vs l/xfi, where x is the polymer size function. These relationships show that the L.C.S.T. data can be treated in a manner similar to upper critical solution temperature data, as given in the Flory-Huggins treatment, even though the L.C.S.I. phenomena are not predicted by this theory. Entropy of dilution parameters, ”/1, and 9L temperatures were calculated for each solvent. It was found that the e temperatures correlated reasonably well with the solvent L critical temperatures. It was also found that linear relationships exist for TCL vs l/x”. This is in accordance with a more recent theoretical treatment of Patterson, Delmas, and Somcynskys. More and different types of data are needed before any distinctions between the two treat- ments can be made. The effect of pressure on the L.C.b.r. data is dis- cussed. Pressure corrections could alter considerably the quantitative nature of the data; however, the qualitative nature would remain essentially unchanged. ACKhOWLFDGmlhfS The author is indebted to Professor J. B. Kinsinger for the helpful guidance and assistance offered during the course of this investigation. He also wishes to express his thanks to the Dow Corning Corporation for their financial assistance, and also to Robert Buch and Helen Klimisch of the Dow Corning Corporation for preparing, fractionating, and determining the molecular weights of the iolymer samples used in this study. Finally, the author is eSpecially grateful to his wife, Judy, whose encouragement, Ivatience, and assiStance in preparing the manuscript were invaluable toward the completion of this proJeCt. TABLE OF COhTENTS IRERODUCTICN . . . . . . . . . . . . . . . . THE'CRY O O O O O O O O O O O O O O O O O 0 O EXP-£31131. l\.D.AL o o o o o o o o o o o o EQllipment o o o o o o o o o o o o o o o Polymer Samples . . . . . . . . . . . . SOlVEIltS O O O O O O O O O O 0 O O O O 0 Preparation of Tubes . . . . . . . Determination of Lower Critical Solution Temperatures o o o o o o o o o o 0 Measurement of Specific Volume of Solvent RESULTS [211“.1) DILCUSSIOL o o o o o o o o o o 0 Phase Diagrams . . . . . . . . . . . . . Molecular Weight Dependence of Lower Critical Solution Temperatures . . Solvent Dependence of Lower Critical Solution Temperatures . Pressure Dependence of Lower Critical Solution Temperatures . BIBLIOGRAPHY AfrEhDICES LIST OF FIGURES System exhibiting a U.C.SJT. . . . . . System exhibiting a L.C.L.T. . . . . . System exhibiting both U.C.S.T. and INC.S.T. with U.C.S.T. ) L.C.e.r. . System exhibiting both U.C.:.r. and LoCobolfio Yu’fiith UoCoSoL|o < 1.100.501... . Variation of chemical posential with composition . . . . . . . . . . . . Dependence of X on T . . . . . . . . Phase diagrams for PDnb fractions in Il-pentane . . . . . o o o o o o o 0 Phase diagrams for PDLS fractions in n-bth arle . O O O O O 0 O O O O O 0 Phase diagrams for :DLS fractions in propane O O O O O O O O O O O O O 0 Phase diaarams for PDhS fractions in neopentane . . . . . . . . . . . . . Phase diagrams for PDmS fractions in tetramethylsilane . . . . . . . , , Phase diagrams for ans fraCtions in dimethyl ether . . . . . . . . . . 14. Plot of 1/r vs. 1/x“ for runs in n-pentan and n-butane , , , , , , , Plot of 1mgL vs. 1/x/2 for anS in propane and neOpentane . . . . . . Plot of l/T L vs. l/xfl for IDLE in tetrametgylsilane and dimethyl ether 1‘. Plot of r vs. l/xfl for PDms in pentang . . . . . . . . . . . . . . eL temperature as a funCtion of solvent size , . . . . . . . . . . . temperature vs. solvent critical temperature . . . . . . . . . . . . 9L \O Figure P.) H m m LIST OF F GURLS (CCLTIhULD) chromatogram chromatogram chromatogiam chromatOgram for for for for n-pentane . . . . Il-buCaIle o o o o neOpentane . . . tetramethylsilane chromatogram for dimethyl ether . Chromatogram for methyl chlo;ide . TABLE I. II. III. IV. VI. LIST CF TABLES Page Molecular Weight Data for Polydimethyl- siloxane . . . . . . . . . . . . . . . . 18 Purity of Solvents . . . . . . . . . . . . . 19 Specific Volume for Solvents and Polydimethylsiloxane . . . . . . . . . . 50 Lower Critical Solution Temperatures and Molecular Weight Data for Poly— dimethylsiloxane Fractions in Various Solvents . . . . . . . . . . . . 51 Entropy of Dilution Parameter and 9L Data for Polydimethylsiloxane in Various Solvents . . . . . . . . . . . 57 Correlation of a data with Solvent TC . . . 44 L II. III. IV. VI. VII. VIII. LISE OF AIPIRDICES Phase separation PDmS fraCtions Phase separation PDmS fractions Phase separation PDLS fracoions Phase separation PDLS fractions Phase seyaration rDmS fractions Phase separation PDmS fractions Phase separation PDLS fractions Gas chromatograms of solvents . . temperatures for in n-pentane . . temperatures for in n-butane . . temperatures for in EI‘OPEiIie o o o temperatures for in neopentane . . temperatures for in tetramethylsilane temperatures for in dimethyl ether . temperatures for in methyl chloride Page 51 55 54 55 ,--x' v.' (I' ILTRCDUCLlCn Although it now appears that the exiStence of lower critical solution temperatures (L.C.S.r.) may be universal in polymer—solvent systems, this phenomenon was first observed in pure hydrocarbon mixtures only in very recent years. A great deal of attention is being direCted toward this subject because of the thermodynamic implications of the L.C.S.T.'s, and the classical conventional polymer solution theories will require some drastic revisions to provide a theoretical framework for the ihenomena. Freeman and Rowlinsonl firsc observed the L.C.S.T. phenomena for hydrocarbon solutions of hydrocarbon polymers. Nearly all the systems they inveseigated exhibited L.C.S.T.'s, all of which were between the normal boiling ioint and the gas—liquid critical Loint of the pure solvent. The existence of L.C.S.T.'s in solutions of certain pairs of polar liquids and even in aqueous solutions of certain polymers had been recognized for some time, but never had they been observed in comple.ely nonpolar systems. In the O ‘ former, the observed L.C.S.r.'s were attributed to an entropy increase upon breaking hydrogen bonds between solvent and solute. However in the latter case (the completely nonpolar systems), the L.C.E.T.'s obviously result from forces of an entirely different nature. The authors of this initial .report attributed this phenomenon to the decreasing config— ltrational energy and increasing molar volume of the solvent 1 2 which result in the solvent becoming thermodynamically poorer at higher temperatures. In conjunction with the above work, Rowlinson and Freeman2 reported their findings of a study of the misci- bility of a series of pure hydrocarbons containing between 24 and 57 carbon atoms with ethane and propane. No liquid- liquid phase separations were observed in the propane sys— tems up to the critical endpoint of the solutions. However, L.C.S.T.'s ranging from 5.70 to 27.700 were observed for all the ethane solutions. These findings are an indication of the importance of the molecular size and energy of inter— action differences between the solvent and solute. Davenport and Rowlinson5 have subsequently studied the miscibility of liquid methane with a large number of hydro- carbons having from four to eight carbon atoms. Some hydrocarbons containing five carbon atoms and nearly all those containing more than five carbon atoms were incompletely miscible with methane, with many of the systems exhibiting L.C.S.T.'s. In general the miscibility decreased with increasing numbers of carbon atoms in the solute. However, other factors were also found to affect the miscibility: branched isomers were more miscible than straight chain isomers, olefins were less miscible than paraffins, diolefins and acetylenes were less miscible than olefins, cyclics were less miscible than non-cyclics, and aromatic compounds were found to be very insoluble. The authors suggest that a L.C.S.T. occurs whenever the solute is a molecularl dense y 3 liquid of strong intermolecular forces and the solvent a liquid of low molecular density and weak intermolecular forces. A solvent that is approaching its gas—liquid critical ioint fulfills this last condition well. Baker and co-workers4 have studied the phase equilib— ria of solutions of polyisobutene of various molecular weights in n-pentane, and also measured the thermodynamic properties of these solutions. They found that polymer solutions which are approaching a L.C.S.r. are incompatible with the Flory-Huggins equation since they exhibit negative heats and entrOpies of dilution. These, indeed, are ther- modynamic requirements of any binary solution whose misci- bility is decreasing with increasing temperature, i.e., approaching a L.C.S.T. This also implies that the Flory free energy of interaction parameter, X , should be increasing with temperature near a L.C.S.T. The authors show that this is indeed the case for the system n—pentane- polyisobutene. Since, in the lower temperature regions where the Flory-Huggins equation is valid, £¥§ is negative, X passes through a minimum at some temperature. Using solubility parameter theory and the molecular theory of polymer solutions developed by Prigogine and co- 5 workers, Delmas, Patterson, and Somcynsky have developed an expression for the free energy of interaction parameter, X : Rx = A(rl/T) + B(T/rl) (1) where rl is the number of segments in the solvent molecule, 4 and A and B are constants depending on the solvent-polymer pair. The authors measured calcrimetrically the heats of mixing for polyisobutylene (unfractionated) in the n-alkane solvents. Using values for A and B calculated from these data and from other published data, they used equation (1) to predict the L.C.S.2. for these syStems. Their predicted values are in fair agreement with those found experimentally by Freeman and Rowlinsonl. Kinsinger and Ballard6’7, as a result of a study of the phase equilibria in solutions of well characcerized fractions of polyoctene-l-in n-pemtane, have shown quanti- tatively the dependence of the L.C.S.r. on the molecular weight of the solute. A linear relationship was observed when l/TCL was plotted against l/xfi, where x is the polymer size function defined in the Flory—Huggins theory as: x = vap/Vl. (2) Here, vp is the Specific volume of the polymer at the precipitation temperature, Mp is the weight-average molec- ular weight of the polymer, and V1 is the molar volume of the solvent at TCL' In this respect, the L.C.S.f. 1he- nomena correSpond to the familiar upper critical solution temperatures (U.C.S.T.) where such plots are common, and are used to calculate the entropy of dilution parameter, ”/1, and the Flory temperature, a. The authors, therefore, re-designate this Flory temperature as SH, and define a corresponding temperature, a which is obtained from plots L9 of the above type, for systems exhibiting a L.C.S.r., by 5 extrapolating to infinite molecular weight (l/xé-—> O). TetreaultE determined the L.C.b.f.'s for characterized fractions of a number of poly-cz-olefins in n-pentane and n-butane. He likewise observed a linear relationship between l/I‘C and l/Mfl. The author also reports, for the first time, L.C.E.f.'s of a three component system (two solvents and one polymer). The L.C.S.£. behavior in this system is quite similar to that in binary systems. The dependence of a L.C.b.T. on pressure has been demonstrated recently by Allen and Bakera. They investi- gated the L.C.p.f. of the polyisobutene-isopentane syStem as a function of pressure up to 4t0 p.s.i., and found the fairly large pressure coefficients, ch/dP, of c.46 and 0.40 deg. atm.-l for two different fractions of polyiso- butene. hrlich and co-workerslc’ll’lg, on the other hand, have observed that at very high pressures (hundreds of atmospheres) some systems exhibit negative pressure coef- ficients. They have in fact determined critical solution pressures for polyethylene in hydrocarbon solvents. How- ever, these are of an entirely different nature than the L.C.S.:.'s under discussion. Since the temperatures required were well above the solvent critical temperatures, their work involved gas-liquid instead of liquid—liquid equilibria. Virtually all the L.C.S.f. investigations made to date have involved polymers with carbon-carbon or carbon— oxygen chains and hydrocarbon solvents. The lone exception 6 to this is a brief mention by Freeman and Romlilsonl of a silicone, eironeously reported as polydimethylsiloxane, exhibiting a L.C.S.T. of —100 with ethane. It was the intent of the author, therefoxe, to investigate thoroughly the L.C.S.T. phenomena for a polymer system other than the above mentioned organic types, in hopes that the results of such a study would be of some value to those attempting to interpret these phenomena on a theoretical basis. The polymer system thus chosen was that of polydimethylsiloxane in carefully prepared and well characterized fractions. THEORY When two unlike liquids are mixed, many ty;es of behavior can occur, depending on the nature of the pair. The liquids may be completely miscible at all temperatures and concentrations, they may exhibit complete miscibility over only limited temperature and concentration ran es, or they may be incompletely miscible for all temperatures over certain concentration ranges. Those syStems exhibiting incomplete miscibility ere characterized by having either an upper critical solution temperature (U.C.S.T.), above uhich the two components are miscible in all proportions, or a lower critical solution temperature (L.C.S.f.), below which the two components are miscible in all proportions, or both. Exanples of each of these general situations are illustrated as phase diagrams in Figures 1 through 4. The stability of a binary liquid system can be char— acterized through the chetical potential, iii’ of each component. For a binary systet whose components are in equilibrium, it can be shown from first principles of thermodynamics13 that "a-fl = M < C, (5) 3n2 anl where Di is the number of moles of component i. Using the Gibbs—Duhem relation, it can be further shown that 51111 = Xl Bill and 3E2 ___ X2 M2 (4) 3112 11 3x2 anl n 3x1 ' one phase '13 336.517." ’ one phase X2 "—'> X2 —’ Figure 1. System Figure 2. System exhibiting exhibiting a U.C.S.T. a L.C.S:f. T.Ju£lh.Ts-.. ..... one phase 6 phases Figure 5. System exhibit— Figure 4. System exhibit- ing both U. C.S.f. ing both U.C.S l & L. C. s with & L. C. S. T: with CTI U.C.S.I‘.>L.C.S.‘l‘. .U..CS. .T,P. Therefore, the condition for stability is 32? -""—"'2' > 0, (8) 8x2 and at the critical point 32F ——R = O. (9) 8x24 C The shape of the coexistence curve for a two component system, i.e., whether the system exhibits a lower or an upper critical solution temperature, depends upon the mean molar enthalpy of the mixture in the following wayglaa age At a L.C.S.T., "“Z )> o (10) 23x2 C 3%: and at a U.C.S.T., —-——2 <: o. (11) 3x2 C These conditions require that the heat of mixing, A‘HM’ is decreasing with temperature for systems near their L.C.S.T. and increasing with temperature for systems near a U.C.S.r. The above conditions can also be expressed in terms of the molar entrOpy of the system by considering the relation F = fi - Te. (12) From equation (9) it follows that 11 age a‘s -——* = T --w (15) C c 3x2 0 3x2 0. The curvature of the molar entropy is therefore the same as that for the molar enthalpy, and from equations (10), (11), and (15), we have the additional critical conditions: 32s ') > . -. 3;;gg C O for a L.C.S.f. (14) aza and -———2 25x2 C o for a U.C.S.T. (15) The pressure dependence of solution critical temperatures can be expressed as follows}—jb dT a‘v 59s ..2 = ____2 ____§ (16) d? 5x2 0 3x2 0. From equations (14), (15), and (16), we can see that for a L.C.S.T., dTC 32V ——- has the same sign as -———7 (l7) dP 3x24 C and for a U.C.S.T., dT C 32V ——— has the opposite sign to ————2 (18) dP BX' C. 2 The effect of pressure on the critical temperature is thus determined by the curvature of the mean molar volume, i.e., whether the volume of mixing is positive or negative at the critical point. Until recently, the solution theory used almost 12 exclusively for high molecular weight polymers has been the conventional Flory—Huggins liquid lattice theorqu. Although this theory treats the phenomena of U.C.S.f.'s adequately, it does not explain many features of L.C.b.f.'s. The entropy and enthalpy of mixing expressions derived from the liquid lattice model require that the solvent-polymer interactions continually decrease as the temperature increases, and this would be manifested in a correSponding decrease in the value of the free energy parameter, X . With this restriction imposed, it is not possible to fulfill the critical requirements (10) and (14) for a L.C.S.B. from this model. It has become evident, therefore, that a more rigorous theoretical treatment for polymer solutions is needed. One quantitative treatnent of this Lroblem was proposed 5 by Delmas, Patterson, and Somcynsky who used an approxi- mation of the quasicrystalline lattice or cell model of . . 15 h . - - , - in Frigogine . From conSiderations of the intersegment potential energies they develop the following expression for the heat of mixing, AHN: AHM = A - BCT/r )2 (19) (no. base moles polymer) v1 1 where rl is the number of segments in the solvent molecule, and A and B are constants characteristic of a given solvent- polymer pair, and are defined as: A = sz = zeiloZR/B (20) l5 and B = 10.5(kd/ze12)N. (21) :3 Here, 2 is the lattice coordination number, eij represents the minimum potential energy between segments i and j with subscripts l and 2 referring to the solvent and solute respectively, k is the Boltzman constant, K is Avogadro's number, and 6 is given by 622/611 - l. The authors subse- quently develop an expression for the Flory free energy of interaction parameter, x , which is given by RX = A(rl/T) + B(T/rl). (22) For a given solvent system, rl is constant, and for purely hydrocarbon systems, r1 = (n+1)/2, where n is the number of carbon atoms in the solvent. The above equation is a quadratic in T and two roots are obtained for every value of x ; that is, X passes through a minimum. The temperature, T0, at which this minimum in X: occurs is given by T OR) = (A/B)r12. (25) Therefore, either increasing or decreasing the temperature from T0 will result in an increase in X and hence the sol- vent quality becomes poorer. At some critical value of X , the polymer will precipitate from solution, and the roots of T at this point should correspond to the U.C.b.T. and the L.C.S.T. This behavior is illustrated in Figure 6. For a polymer of infinite molecular weight, the critical value, X c’ is 1/2, and the U.C.b.f. and the L.C.b.r. and 9 become 9 respectively. For polymers of finite U L 14 Figure 6. Dependence of x on T. b-—-----"-- b---—---—— UOCOSOTO EAL -LQCOLQ;I‘O T —————4> molecular weight, X10 is somewhat larger than 1/2, and is given by p % r 1 X0 = l/L. + l/X + l/CX. ((4) Solving equation (22) for TC/rl, we obtain 2 “/5 Rx : [(Rx C) 42:13] Tc/rl = C 25 . (CR) Depending on the constants A and B, various particular cases may be distinguished. If A=O (the liquids differ only in their chain lengths), one of the roots of T (the U.C.S.f.) is zero, and the other (the L.C.5.T.) is given by Tc/rl = R/EBa (26) assuming that 3X0 = 1/2 (molecular weight of polymer is infinite). If 4AB(%R)2, there are no real roots and hence no critical temperatures; the polymer and solvent are not soluble in all prOportions at any ‘temmerature, there being only swelling of the polymer to a nmrximum value at T0. The authors compare the results of tflie above treatment with experimental results obtained by . l . .. Faceeman and Rowlinson With a conSiuerable amount of success, arui Tetreault8 and Ballard7 found fair agreement with echerimental data on hydrocarbons. However the merits of tliis treatment with its many assumptions have yet to be ariequately demonStrated. Flory, Orwoll, and Vrij16 have recently developed a chnfiguration partition function for liquids and liquid Imtxtures of a homologous series. In this treatment they use: as a model a linear sequence of segments, each of Whjxih has a hard Sphere type repulsive potential and an intnermolecular energy which depends only on the volume 0f"the segments. This treatment results in a reduced egluation of state which is parametric in character. The reqnnired parameters can be evaluated from volume, thermal exlnansion, and compressibility data. The authors derive exDressions for the various thermodynamic functions in£filuding an expression for the chemical potential, Lt]:~;ilO/RT, as a function of the characteristic parameters of. each of the components in a binary system. Application Of"the conditions for critical miscibility, as given in equationfla), to this expression for chemical potential results finally in the following equation: * * 2 ~ I * r a; A Bxlcl(l--T:L /Too ) / (1-4vlT/fl )+2xl 1312/Tvl = l (27) where x1 is the number of segments in the solvent, c1 and * T are characteristic parameters of the solvent, Too is a * l ckuaracteristic temperature of a homolog of infinite chain lfiength, $3 is the reduced volume of the solvent, and fil2 is; a constant derived from the parameters of each of the ccnrponents. By inspection of equation (27) me find that it kmas a quadratic form, and therefore gives two roots for T, mflnich are the U.C.E.T. and the L.C.S.T. reSpectively. Algthough this treatment gives good to excellent agreement unith.experimental results for a number of the thermodynamic thnctions, the calculated and experimentally found values fox? the L.C.S.T. are in only moderate agreement. So it 8I5,ears then that further refinement of the above approach Wilfll be required before the L.C.b.r. phenomena can be Prexiicted accurately from a strictly theoretical standpoint. EXFIRImEhTAL Equipment All the lower critical solution temperature determin- aations were made using a variable temperature stirred bath (nontaining Dow Corning 550 Fluid. The rate of heating of tflne bath was controlled by varying the voltage on a blade tyqoe heater with a Variac. The polymer solutions were contained in small sealed almpules made of three mm. bore Pyrex capillary glass tubing. 'Tlie tubes were suspended in the bath with a small wire tnasket which held up to four tubes at onetime. Accurate teamperatures were insured by using mercury thermometers tflnat had been calibrated against a certified National Ifixreau of Standards thermometer. P_Olymer Samples All of the samples of polydimethylsiloxane used in tths study were prepared and carefully fractionated at the Ifmsearch.1aboratories of Dow Corning Corporation. After PITrparing the polymer by conventional techniques, a solvent fI‘actionation was carried out by dissolving the polymer in tOluene, and then adding acetonitrile, a non—solvent, to Callse precipitation of the successive fraCtions. The sol- ‘VeIIt was removed from the fractions by stripping at 10000, 0-:L mm. Hg pressure for eight hours. The molecular weight of‘ each fraction was determined also at Dow Corning Corp- OI‘Eition using light-scattering techniques. Five of these 17 18 fractions were selected for use in this study. The weight- average molecular weights of these five fractions are listed in Table I. Number-average molecular weights were also determined for two of these fractions by intrinsic . . _ x . , , _ . l7 ,, Viscos1ty measurements uSing the Barry equation . These are also listed in Table I. The close agreement between the number and weight average molecular weights indicates that the fractions are fairly monodiSperse. TABLE I. Molecular Weight Data for Polydimethylsiloxane Fractions - . ”.5 .. -5 Fraction kw x lo mn x 10 C 800]. "’ D 4.78 4.25 F 1.17 .866 Solvents Technical grade normal pentane was twice distilled on a 50" spinning band column, retaining only a center cut in each distillation. The pentane thus purified had a constant boiling point of 36.000. Research grade normal propane, and.pure grade normal butane and neopentane were purchased I:firom.Phillips Petroleum Company. Purities of 99.64 mol. 19 per cent and 99 mol. per cent are claimed by the supplier for the research grade and the pure grade respectively. Dimethyl ether, having a stated purity of 99.0 mol. per cent, was purchased from the Fatheson Company, and the tetramethylsilane was n.m.r. standard grade purchased from the Stauffer Chemical Company. The methyl chloride used in this study was a commercial grade obtained from the Dow Chemical Company. The purity of these solvents was determined or verified by passing a sample of each through an F and M Model 50C gas chromatograph. A two foot column packed with polydimethylsiloxane gum on Chronosorb P was used. Figures 1) through 24 in Appendix VIII show the chromatograms thus obtained, and the purity data are summarized in Table II. TABLE II. Purity of Solvents Solvent Per Cent Purity Calcul— ated from Chromatogram n-Pentane 99.2 n—Butane jj.C Propane 99.9 Neopentane >79.9 Tetramethylsilane >yq.7 Dimethyl Ether >7aO9 methyl Chloride >jj.9 Preparation of Tubes The tubes containing gentane solutions were made up in the following manner. Solutiens of known concentration of each of the five fractions of polymer were made up in small vials. Successive dilutions of each of these solutions were used to obtain other solutitns of known concentrations. Samples of each solution were added to the tubes with a hypodermic syringe. The tubes were then attached one at a time to a vacuum line. After freezing the solutions with liquid nitrogen, the tubes were Opened to the vacuum system to remove the permanent gases, and then sealed with a flame. All of the other tubes contained solutions with either gaseous or very low boiling solvents and were prepared in the following way: Varying amounts of pentane solutions of each of the fractions were added to previously tared tubes with a hypodermic syringe. The pentane was removed by heating the tubes in a vacuum oven at 5500, after which the tubes were re-weighed to determine the amount of polymer in each. The tubes were then attached one at a time to a vacuum line where they were evacuated, and the solvent distilled into the tubes. After cooling the tubes with liquid nitrogen, they were sealed off with a flame. The ‘tubes were again re—weighed to determine the amount of ssolvent added to each. The polymer was soluble in all the Esolvents at room temperature and solution was effected by ESimply shaking the tubes. 21 Determination of Critical Solution Temperatures With the tubes containing the polymer solutions im- mersed in the bath, the temperature was raised at a rate of about one degree per minute until the polymer just began to precipitate. Knowing the approximate precipitation temperature, the temperature of the bath was lowered a few degrees, and the tubes were shaken again to insure solution homogeniety. The temperature of the bath was then raised very slowly (at a rate of about 0.2 degree per minute) until the precipitation temperature, Tp, of each of the solutions was reached. This temperature was taken as the point where a very sudden increase in solution cloudiness occurred. Shortly before this temperature was reached (a few tenths of a degree below Tp) the solutions developed a very slight haziness which gradually increased until Tp was reached. he endpoint is very sharp and so easily recognized that Tp could be reproduced to within one tenth of a degree. Immediately or very shortly after Tp was reached, the heavier phase began to settle out. This phase separation occurs quite rapidly because of the low density of the solvent at these temperatures. .flmasurement of Specific Volume of Solvent at Temperatures _§@rresponding to the L.C.S.T. Samples of each of the pure solvents were introduced :into tared 5 mm. I. D. glass capillary tubes similar to ishose used above. The tubes were then cooled with liquid Ilitrogen, evacuated, sealed off, and re-weighed to determine 22 the weight of solvent in each. These tubes had been previ- ously calibrated for volume by introducing weighed incre- ments of mercury into the tubes, and noting the change in liquid column height with a cathetometer. Using the density of mercury at ambient temperature, the volume as a function of liquid column height was determined. The tubes con- taining the pure solvents were immersed one at a time in the bath, which was then brought to the desired temperature. Using a cathetometer, the liquid column height was measured, the corresponding volume determined from the calibration graph, and the specific volume computed from the weight of solvent in the tube. These tubes had been filled fairly full so the error due to solvent in the gas phase was minimized. RESULDS AED DISCUSSICR Phase Diagrams Lower critical solution temperatures for solutions of five fractions of polydimethylsiloxane (:DhS) in various solvents were determined. The precipitation temperatures, Tp, were determined as a function of concentration for each polymer fraction. The L.C.S.T.'s were taken as the minima in the resulting phase diagrams, plotting Tp against the concentration in weight fraction. These phase diagrams are shown in Figures 7 through 12. Because of higher than normal pressures, which resulted in rupture of nearly all of the tubes containing the methyl chloride solutions, insufficient data was obtained to construct phase diagrams for this system. Volume fraction is also shown on the phase diagrams across the upper abscissa, since it is the conventional concentration unit in the treatment of U.C.S.T. data. Volume fractions were calculated from the specific volumes of the solvent and of the polymer at the temperatures cor- responding to the approximate L.C.S.T. with the assumption that the excess volume of mixing is negligible. The specific volumes of the solvents were determined experimentally and the specific volume of the polymer was calculated from data in the literaturela. The values obtained for these specific volumes are listed in Table III. The molar volumes of the solvents are also included since they will be used to calcu- late the size function, x, of the polymer fractions (see equation 2). [\3 \N 24 Figure 7. Phase diagrags fOr mes fractiOns in n‘Pentane Y I ' ‘ 0C]. .C‘E 0C5 .CIL VI. C 187‘ I 186 . 18: 184 (CC) 1851 1814 Y .02 .94 \ du- ,(d ’,C C/ Figure 8. fhase diagrams for EDLS fractions in n-butane V I U ' .L1 .02 .c3 .o4 v, C 140$ E 139.- 158w D C $57 A Op B ( c) A 156* W D 155+ 154* .02 .64 ' .te ' .5. ' .10 W» HM». Ia. 26 Figure 9. Phase diagrams for PLLS fractions in prOpane I I U I .01 .02 .05 .04 V2 79 .. 74. V 4r- .10 {l’ .;O f“ 27 Figure 1C. Phase diagrams for PLmS fractions in neopentane 147« l46< 1454- 144 « (00) 143. 1411 T I I 001 .C2 .C3 .C-‘4 1h l6l< 160‘ 157- 156- 155' A j Figure 11. 2a ihase diagrams for IDMS fractions in tetramethylsilane U V I .01 T ' .02 .03 Jr- 0C4 .CE' .06 29 Figure 12. Phase diagrams for PDmS fractions in dimethyl ether I I I T I .01 .02 .05 .04 .05 v, 115“ ‘4_/_—O/ E 114« D 113" C 1120 Tp A (00) 111" 110+ ' .o'2 - .C4 ' .023 Y .00 .10: WA TABLE III. Specific Volume for Solvents and Polydimethylsiloxane * Sp. Vol. Molar Vol. Sp. Vol.** Temp. Solvent Solvent Solvent PDhS (Oc) (cc./g.) (cc./mol.) (cc./g.) 75.9 Propane 2.48 109.1 1.076 110.1 Dimethyl Ether 2.15 98.0 1.116 129.5 Methyl Chloride 1.58 79.8 1.140 154.6 Butane 2.50 146.2 1.146 140.7 Neopentane 2.55 167.8 1.154 154.6 Tetramethylsilane 2.29 201.5 1.171 181.6 Pentane 2.42 174.2 1.207 *These temperatures correspond to the 6 temperature of the polymer solutions in the respective sdlvents (see page 57)- :kt , . . These are spec1fic volumes of PDmS at T = 9 In most respects the phase diagrams are quite similar in character to those found for hydrocarbon polymer systems . V 4,6,7,9 . - . . by preVious authors: The general shape is the same, the L.C.S.T.'s occur in roughly the same concentration range, and the increase of L.0.S.T. with decreasing molecular weight is a similar characteristic. There does appear to be, hov- ever, a dependence of the critical volume fraction on molec- ular weight. Although this dependence ranges from very slight in some solvents (propane, butane) to fairly pro- 7 )l nounced in others(pentane, tetramethylsilane), it is never- theless present in all cases. This type of behavior would be anticipated if the L.0.S.D. assumed the same character as the familiar U.0.S.T., in which case the critical volume 14a 1 . fraction is given by VA = 1/x‘ . This behavior is 20 notably absent from previously reported L.0.S.T. data, however. In Table IV are listed the L.C.S.L.'s, and the molecular weights for each of the polymer fractions in the various solvents. TABLE IV. L.0.s.f. and molecular Weight Data for Polydimethylsiloxane FraCtions in Various Solvents. Polymer . ~ *6 ‘ o Solvent Fraction Lol. wt.(X10 ) L.C.S.T.( K) n—Pentane A 2.48 455.5 " B 1.96 455.8 " C .801 456.4 " D .478 456.9 n E .117 459.1 n-Butane A 2.48 408.6 " B 1.96 408.9 " C .801 409.4 " D .478 409.8 " E .117 412.2 52 TABLE IV. Continued Polymer , Solvent Fraction hol. wt.(X100) L.c.e.1.(0K) Propane A 2.48 548.0 " B 1.96 548 2 " C .801 548.9 " D .478 549.4 " E .117 551.8 Neopentane A 2.48 414.9 " C .801 415.7 " D .478 416.5 " E .117 419.1 Tetramethylsilane A 2.48 428.8 " C .801 429.8 " D .478 450.4 " E .117 455.2 Dimethyl Ether A 2.48 584.0 " C .otl 584.8 " D .478 585.5 " E .117 587.2 Methyl Chloride A 2.48 405.4 I! m H H \‘l 4: C“ \1 \3 55 As is the case with organic polymers, the L.0.S.T. phase diagrams for polydimethylsiloxane are quite broad; much broader than the correSponding U.C.S.T. phase diagrams. The exact significance of this is not known; however, this broadness suggests that the solubility parameter x is much less concentration dependent in the L.C.S.T. region than in the lower temperature U.C.S.T. region. Molecular Weight Dependence of L.C.S.T. The molecular weight dependence of the familiar U.C.S.T. (for sufficiently large molecular weights) is expressed in the Flory—Huggins treatment as followsl4b: %— = El, [1 + (Hypo/#9)] (14) C where ‘V1 is the entrogy of dilution parameter, and x is the polymer size function previously defined (equation 2). If the assumption is made that the L.0.S.T.'s exhibit a molec— ular weight dependence of this sane character, then a plot of 1/TCL vs. 1/xfi should give a Straight line. Plots of this type were made for each of the solvents used, and are shown in Figures 15 through 15. It is to be noted that all of these plots are, indeed, remarkably linear. Previous 6’7’8 also have found such linear relationships with authors other polymer-solvent systems. So it appears from these findings that, at least within the range of experimental results reported, the L.C.S.D. and the U.C.E.f. data can be similarly treated in this one respect. '1 Therefore, as is done in the case of U.C.S.1. data, Figure 15. Plot of l/T \N n n—pentane agd n-butane 1‘2 . __\_‘_ . . vs. l/x’ for runs in 2.180w 2.170‘ 3.4404 2.420‘ V (I n—pentane n—butane in.“ I1 l 5. ring:- 1.0 1/x”(x ltd) l l t . Figure 14. 55 Elot of l/TC vs. l/xfl for anS propane and Eeopentane in 2.870' 2.860 2.850 \\ if 2.400” Propane C) ReOpentane 2.0 1/x%(x 102) \N Figure 15. Plot of l/T ,. 30 vs. 1/Xfl for PLhS in tetra— methylsilangLand dimethyl ether 1000 TCL (0K4? 2.6101 2.600 2.580 tetrameth;lsilane dinethyl ether 1.0 % .2 l/X (X 10 ) 5.0 57 the above graphs were used to calculate the entrOpy of dilution parametery g“) and.the critical miscibility temperature for lolymer of infinite molecular weight, 8L. These values are easily obtained from the slope and intercept of the graphs. The values of‘lfll and e thus conputed are L listed in Table V. TABLE V. Entropy of Dilution Parameter and 6 Data for PLnS in Various Solvents L Igtepcept eL Solvent Slope ( K X1000) V€_ (OK) Pentane -.CLC617 2.1994 —5.56 454.7 Butane -.OOO778 2.4520 -5.15 407.8 PTOpane -.001525 2.8814 -2.18 547.1 Neopentane —.CCOB51 2.4170 -2.64 415.7 Tetramethylsilane -.CCO798 2.5565 -2.55 427.6 Dimethyl Ether -.0C0975 2.6990 —2.65 585.5 Methyl Chloride (-.00154) (2.4660) (—1.66) (402.5) Values in parentheses only approximate. There are a number of things to be noted about the calculated values of the entrOpy of dilution para eter: They are all negative in sign which requires that the excess entropies of mixing for these solutions at their lower critical temperature are also negative. Baker and co— 3 4 ‘I ' .L. ' 1 ' worxers have snown this to be true in tne system polyiso— 58 butene-n—pentane. Although the calculated values of 9yl are relatively constant with changing solvent, there is a definite trend for the absolute value of 9V1 to increase as the solvent size increases. Finally, they are all of relatively large magnitude which indicates that excess entropy contributions are quite important in determining solution properties near its L.C.S.E. In the treatment of upper critical solution temperature data, the determination of the Flory temperature, a is of U9 significance since it represents a temperature where there are no net thermodynamic interactions in solutions of polymers of infinite molecular weight. It has been sug— 6’8 that the temperature 9L determined from L.C.S.T. data also represents a temperature where gested similarly thermodynamic departures from ideality vanish. It is pointed out, however, that in the latter case, the balance of thermodynamic forces assumes a different character; namely, that favorable solvent—polymer interactions just balance the solvent-solvent interactions which cause the solvent to expand as it nears its critical temperature. In considering the treatment of L.C.S.T.'s given by 5 Delmas, Patterson, and Somcynsky , which results in equation (25'), if either A = O, or the product 4AB << (RX0)2’ then the equation can be re-mritten as r1301:. = 1‘13 Xc/B- (28) Since from equation (24) it is seen that X c is proportional 5 9 to l/x%, the above equation indicates that a plot of TC vs. l/x1/é should give a Straight line (still assuming either of the above mentioned conditions). One plot of this type, for ghe pentane-PDhS system, is shown in Figure 16, and it can be seen that the data does indeed give a Straight line. The data from the Other solvent systems give similar linear relationships. In the above treatment, the first condition (that A = C) L_‘” seems hardly justifiable in the present case since it has I: .1 been shown“ that this condition is true when the polymer ‘3‘4 and solvent differ only in chain length. Polydimethylsiloxane . in a hydrocarbon type solvent obviously does not fall into this category. This means that if the Delmas-Patterson- Somcynsky treatment is valid for this system, then the second condition, 4AB‘<<(RJ(C)E, must hold, at least within the range of the eXperimental results. Unfortunately, the independent evaluation of the constants A and B is not possible at the present time, due to lack of sufficient thermodynamic data on the PDLS system. Likewise, the value of rl is also unknown for the PDhS system. From the experimental results obtained then, no distinction can be made between the theory of Delmas, Patterson and Somcynsky and treatment which is analogous to the Flory-Huggins theory. The probable reason for this is that the range of eXperinental data is not sufficiently broad to allow this distinction. If the L.C.S.r.'s were studied over a much broader polymer molecular weight range, 40 1,. Figure 16. TCL vs. l/xfl for PLhS in pentane 460, 457 . CL (OK) 456 “ u e 1/x”(x 10‘) 41 and therefore a broader teLperature range; perhaps some distinction ceuld be made. It is not possible to attempt any correlations of the experimental results obtained with Flory's most recent 16 . .. - . in wnich he derives theoretical treatment of this problem equation (27) from a configuration partition function, because the data required to calculate the necessary para— meters for the PDnS were not experimentally obtained and 4 p...- are not in the literature. Solvent Dependence of L.C.S.f. .VM-Aflon .‘w 2 f. 4". I T ' 'L’._7 A variety of solvents were used in this investigation in order to study the effect of changes in solvent character on the position of the L.C.S.T. The choice of solvents was limited, however, by two factors: The polymer had to be completely miscible in the solvent at some temperature, and also, to avoid thermal rearrangement of siloxane bonds in the polymer, solvents in which the lower critical temper- atures were not over ca. 2LCOC had to be chosen. For the PDLS system, it is observed that in any given solvent, the 9L temperature is considerably higher than those found for pure organic polymersl’4’7’8’9 This is interpreted to be mainly a reflection of the relative magnitudes of the heats of mixing for rDmS and organic polymers in these solvents at room temperature. Newlinglg, for example, has found large values of iAHfi for PDhS compared to those of most organic polymers, and this would account for the greater miscibility (higher 9L) observed in the PDiS system. As Allen and Baker? have pointed out, the position of a L.C.S.T. depends both on the cherical nature of the two components, and on the relative molecular sizes of the solvent and solute. If we examine, therefore, solvents of a similar chemical nature, such as the homogolous series of n—alkanes, then the dependence of the L.C.S.r. should be strictly one of molecular size. In Figure 17, the 9L temperatures of PDhS in prOpane, n—butane, and n-pentane are plotted against the molar volumes of the solvents at the corresponding 9 tenperatures. It is found that the L dependence is indeed linear. It is of interest to note that the L.C.S.2. of -10C reported by Freeman and Rowlinsonl for a silicone polymer in ethane also falls nearly on this line. Their polymer, however, was not a true PBhS but a dimethyl-phenylmethyl siloxane copolymer. If, on the other hand, we examine solvents of the same molecular size, the L.C.E.E.'s should be in some ray dependent on the chemical nature of the solvent. This can be illustrated by examining the solvents propane, dimethyl ether, and methyl chloride, which are roughly comparable in size (see Table III). If the chemical nature of these solvents is expressed in terms of their dipole moments, they fall in the order propane < dimethyl ether ( methyl chloride. 1 It is noted that the e temperatures also fall in tnis sane L order. \n O O 450 4C0 500 Figure 17. 0 L temperatures as a function of solvent size A n-pentane n-tutane propane * ethane * Data of Freeman and Rowlinson 60 Nolar Volume Of Solvent (cc./mcl.) 44 The effects of both the molecular size of a solvent and its chemical nature, as reflected in the magnitude of the intermolecular forces, are manifested in the gas-liquid critical temperature of the solvent. An atterpt was there- fore made, to correlate the e temperatures with the sol- L vent critical temperatures, TC. Table VI shows both the ratio GL/TC and TC-e It can be noted that all the e L' L temperatures are quite near the correspondinb gas—liquid critical temperatures, and that the ratio eL/TC is relatively constant. On the other hand, one can still note trends in the values of rC—e i.e., in the n—alkanes L; the observed order is n-pentane < n-butane ( propane, and similarly for the solvents of comparable size, the trend in TC-GL is methyl chloride < dimethgl ether ( propane. TABLE VI. Correlation of a Data with Solvent TC. L Solvent TCCOK) GLCOK) “EL TC-GLCOK) c Pentane 476.4 454.7 .967 15.7 Butane 426.2 407.8 .957 18.4 Propane 568.8 547.1 .941 21.7 Neopentane 453.8 415.7 .954 20.1 Tetramethylsilane 458.2 427.6 .955 30.6 Nethyl Ether 406.5 555.5 .¢58 17.0 methyl Chloride 416.5 (402.5) (.366) (14.0) Values in Parentheses only approximate. 45 In Figure 18, e is plotted against T0 for each of the L solvents. A reasonable relationship is observed, with the pure hydrocarbon solvents falling on a straight line. Similar relationships were found by Tetreault8 for hydrocarbon polymer systems. Even the more polar solvents dimethyl ether and methyl chloride are not too far removed from the line. However, tetramethylsilane, which is chemically similar to PDmS, lies considerably off the line, and exhibits a proportionately lower degree of miscibility with PDhS. The effect of branching in the solvent can be observed by examining the data for n-pentane and neopentane. It is seen that the branched isomer, neopentane, exhibits a lower degree of miscibility with ears than the normal isomer. This is in contrast to the findings of Davenport and 5 Rowlinson who found in pure hydrocarbon systems that branching in the solute caused reater miscibility. 'c). \J Pressure Dependence of L.C.E.T. The marked dependence of L.C.S.T.'s on pressure has been adequately demonstrated by Allen and Bakerg, and should not be ignored in any discussion on the subject. They found pressure coefficients, dTCfi of 0.46 and 0.40 deg. atm."l for two different fractigis of polyisobutene in isopentane. This type of behavior would be anticipated since the appear— ance of a L.C.S.D. requires that the molar volume of the solvent should increase rapidly with temperature; this would be suppressed by increasing the pressure. The sign 470 440 420 (OK) 410 400 590 370 Figure 18. eL 46 temperature vs. n-pentane C) tetramethylsilane neOpentane n—butane C) methyl chlorine O dimethyl ether propane A L l 560 360 420 440 460 solvent critical temperature 4'7 of the above pressure coefficients is also in agreement with that predicted thermodynamically. From equation (17) it can be seen that the pressure coefficient will be positive if the system exhibits a negative volume of mixing, i.e., A BFV is positive. It has been shown4 that polymer-solvent syggems near their L.C.S.f. do indeed exhibit negative volumes of mixing. Existing polymer solution theories do not take into ccount this pressure effect, and this is probably a reason that the correlation of experimentally determined L.C.S.2. data with values predicted from the various theories has not been wholly successful to date. In the present work, the vapor pressures of the solu— tions at their restective L.C.S.f.'s are moderately high (ca. 2C-50 atm); there is therefore likely to be a consid- erable pressure effect reflected in the data obtained. The vapor pressures of the different solutions are of roughly the same order of magnitude, so any pressure correction required would be comparable in all solvents. The trends noted in the 6 data are therefore at least qualitatively L valid. This pressure effect is reflected in a more subtle way in the values of the entrOpy of dilution parameter, 911’ For any one polymer—solvent system, there are small vapor pressure differences between solutions of the various molecular weight fractions (due to TCL differences). In the pentane system, for example, the vapor pressure dif— ference between solutions of fractions A and E is r~1.4 atm. 48 Assuming a pressure coefficient of 0.4 deg. atm.—l, an error of n90.60 in TCL would result. This would cause a 20 per cent error in the value of 911' Even so, the values of V11 obtained are at least qualitatively, if not quanti— tatively accurate. Perha s the best way to treat this problem would be to measure the L.C.S.T.'s at a number of pressures, and extrapolate back to some standard pressure such as 1 atm. or zero pressure. This would require, however, going to even higher pressures, and more s0phisticated equipment. We are near the maximum pressure limit of the existing equipment, and indeed have surpassed this limit in the case of the methyl chloride solutions. The alternative to this would be to have available a theoretical treatment which adequately takes into account the pressure of the system- l—J O m 0 \N o 14. 15. 16. 17. 18. 19. BIBLICiRArHY P. I. Freeman and J. S. Rowlinson, Polymer, l, 20(1960). J. S. Rowlinson and P. I. Freeman, J. Pure Appl. Chem,, 2. 529 (1961). A. J. Davenport and J. S. Rowlinson, Trans. Faraday C. H. Baker, N. B. Broth, G. Gee, J. S. Rowlinson, D. Stubley, and R. E. Yeadon, Polymer, 5, 215 (1962). G. Delmas, D. Patterson, and T. Sorcynggg, J. Polymer Sci., 57, 79 (1962). J. B. Kinsinger and L. E. Ballard, Polymer Letters, g 879-882 (1964). L. E. Ballard, "Dilute Solution Properties of Poly- octene-l", Ph.D. Thesis, Fichigen State University, 1965. R. J. Tetreault, "Lower Critical Solution Temperatures for Poly—«I—Olefins", h. S. Thesis, kicnigan State University, 1965. G. Allen and C. H. Baker, Pol mer, 6, 181 (1965). P. Ehrlich and E. B. Graham, J. Poly. Sci., 45, 246 (1960). P. Ehrlich and J. J. Kurpen, ibid., A1, 5217 (1965). I. Ehrlich, ibid., A5, 151 (1965). I. Prigogine and R. Defay, "Chemical Thermodynamics", London: Longmans Green and Co., 1954, p. 240. a) p. 286, b) p. 288. P. J. Flory, "Principles of Polymer Chemistry", Cornell University Press, lj55, chapters 12 and 15. a) p. 544, b) t. 545. I. Prigogine, N. Trappeniers, and V. hathot, Discussions Faraday Soc., i2, 95 (1955). P. J. Flory, R. A. Orwoll, and A. Vrij, J. Am. Chem. Soc., 86, 5507 (1964). A. J. Barry, J. Appl. Physics, 12, 1020 (1946). R. Simha and A. J. Havlik, ibid., as, 197 (1964). M. J. Newling, Trans. Faraday Soc., 46, 615 (195C). 49 APPElxDICES 50 AIPTLDIX I Phase separation temperatures for PDmS fractions in n-pentane Wt. Fraction Polymer TP(OC) Fraction A 0.005 182.5 0.010 182.4 0.020 182.5 0.050 182.4 0.040 182.5 0.060 182.8 0.100 184.5 Fraction B 0.005 182.8 0.010 182.7 0.020 182.6 0.050 182.7 0.040 182.8 0.060 185.0 0.100 184.6 Fraction C 0.005 185.5 0.010 185.5 0.020 185.2 0.050 185.5 0.040 185.4 0.060 185.6 0.100 185:6 Fraction D 0.005 184.0 0.010 185-8 0.020 185-7 0.050 185-8 0.040 183-7 0.060 185-9 0.100 186.4 Fraction E o.ce5 186-5 0.010 186.5 0.020 186.0 0.050 186.0 0.040 185-9 0.060 186°C 0.100 187-4 51 APPENDIX II Phase separation temperatures for PDmS fractions in n—butane Kg. Polymer Kg. Solution Wt. Fraction T (00) Polymer p Fraction 0.7 112.0 0.006 155.6 1.6 91.8 0.017 155.5 2.9 109.5 0.027 155.4 4.5 156.4 0.052 155.4 6.0 157.2 0.044 155.5 8.4 155.9 0.065 155.8 15;? 200.7 0.068 155.8 Fraction 0.4 115.0 0.004 155.9 1.5 152.2 0.010 155.8 2.4 127.2 0.019 155.7 5.9 156.1 0.029 155.8 5.2 142.5 0.057 155.8 8.2 126.8 0.065 156.1 15.9 151.7 0.092 156.5 Fraction 0.8 100.1 0.008 156.5 1.5 141.2 0.011 156.4 2.5 120.5 0.021 156.2 4.4 118.5 0.057 156.2 8.4 104.9 0.080 157.0 14.2 112.8 0.126 157.6 Fraction 0.6 106.5 0.006 156.8 1.5 122.2 0.012 156.7 2.7 120.5 0.022 156.6 4.5 96.4 0.045 156.9 5.4 142.4 0.058 156.6 8.6 124.9 0.069 157.0 15.2 182.8 0.072 157.0 Fraction 1.4 155.9 0.010 159.4 2.8 150.1 0.022 159.0 5.9 119.9 0.052 159.0 5.4 129.1 0.042 159.1 8.5 155.5 0.054 159.2 15.2 152.5 0.100 140.1 Phase separation temperatures for PDhS fractions in prOpane Kg. Polymer Kg. Solution Wt. Fraction T (00) Polymer p Fraction A 0.9 156.2 0.007 75.0 2.0 107.5 0.019 74.9 5.6 127.4 0.028 74.8 4.5 117.7 0.058 74.9 6.2 126.5 0.049 74.9 9.2 124.8 0.074 75.1 14.5 160.9 0.089, 75.2 Fraction 0.8 121.4 0.007 75.2 1.6 122.2 0.015 75.1 4.5 129.5 0.055 75.0 8.5 125.0 0.066 75.2 15.8 161.6 0.085 75.5 Fraction 1.0 119.4 0.008 75.9 1.7 142.0 0.012 75.8 5.0 152.0 0.025 75.7 4.0 111.6 0.056 75.7 6.2 126.8 0.049 75.7 8.8 151.6 0.067 75.8 12.8 125.7 0.102 76.0 Fraction 5.0 157.2 0.022 76.2 4.5 129.2 0.055 76.1 6.0 155.4 0.045 76.2 12.8 140.6 0.091 76.5 Fraction 0.8 102.1 0.008 78.8 2.9 124.6 0.025 78.6 5.7 127.0 0.045 78.6 8.4 126.2 0.067 78.7 55 APPELDIX IV Phase separation temperatures for PDmS fractions in neopentane Mg. Polymer Lg. Solution ht. Fraction T (00) Polymer p Fraction A 1.0 122.5 0.008 141.9 1.8 126.7 0.014 141.8 2.4 116.2 0.021 141.8 5.8 124.5 0.051 141.8 6.4 140.8 0.046 141.9 10.2 161.2 0.065 142.1 Fraction 1T2 116.4 0.010 142.7 1.9 125.4 0.015 142.6 5.5 117.4 0.028 142.5 4.9 121.8 0.040 142.6 6.1 150.2 0.047 142.6 10.5 126.1 0.075 145.0 Fraction 1.0 115.7 0.009 145.5 1.7 126.1 0.015 145.2 2.6 119.2 0.022 145.1 4.0 127.0 0.052 145.1 6.0 115.8 0.052 145.5 10.2 159.0 0.072 145.7 Fraction 0.9 108.5 0.008 146.5 2.0 106.9 0.019 146.0 2.8 115.1 0.024 146.0 4.1 124.6 0.052 145.9 5.7 116.0 0.049 146.0 8.6 185.8 0.047 146.1 15.4 141.6 0.095 146.9 54 AEI’EL‘HDIX V Phase separation temperatures for runs fractions in tetramethylsilane kg. Polymer Mg. Solution Wt. Fraction T (00) Polymer p Fraction A 0.5 122.1 0.005 155.9 1.4 127.8 0.011 155.7 2.7 142.7 0.019 155.6 4.2 140.8 0.050 155.6 6.0 181.8 0.055 155.7 8.5 158.8 0.060 156.0 15.0 158.9 jfif 0.094 156.5 Fraction C 0.8 155.8 0.006 156.9 1.8 158.5 0.015 156.7 2.8 122.2 0.025 156.6 4.4 122.5 0.036 156.6 5.5 151.7 0.042 156.6 8.7 128.1 0.068 156.9 15.0 142.5 0.091 157.9 Fraction_Q;_ 0.9 122.5 0.007 157.5 1.1 155.0 0.008 157.4 2.2 154.0 0.016 157.2 4.2 152.8 0.052 157.5 4.6 126.4 0.056 157.5 8.5 146.6 0.057 157.4 10.0 151;4 5__ 0.076 158.0 Fraction E 1.5 145.5 0.009 160.8 1.1 145.7 0.008 161.0 2.6 158.1 0.019 160.2 4.6 154.4 0.054 160.0 6.0 128.1 0.047 160.2 8.5 156.9 0.061 160.5 15.5 151.9 0.102 161.9 55 ABEEhDIX VI Phase separation temperatures for PDmS fractions in dimethyl ether Mg. Polymer Mt. Solution we. Fraction T (00) Polymer p Fraction A 1.2 205.2 0.006 111.4 2.1 189.0 0.011 111.2 5.6 180.6 0.020 110.8 4.7 174.9 0.027 110.8 6.0 161.2 0.057 110.9 10.1 155.9 0.066 111.5 Fraction 0 0.7 171.7 0.004 112.0 1.6 177.9 0.009 111.7 5.4 156.9 0.025 111.6 4.4 140.1 0.051 111.7 5.2 160.9 0.052 111.8 8.1 174.4 0.047 111.9 .1500 H902 ___L C‘OO76 112.03 FractionAD 1.0 176.5 0.006 112.9 1.4 57.7 0.009 112.7 5.1 129.5 0.024 112.2 4.5 164.6 0.026 112.5 6.0 156.9 0.044 112.6 8.8 146.8 0.060 112.9 15.8 119:4 _, 0.115 114.8 Fraction E 0.5 159.6 0.005 114.7 1.4 174.8 0.008 114.4 5.7 198.9 0.019 114.5 7.1 196.2 0.056 114.0 12.2 175.7 0.070 114.1 .56 APPEEDIX VII Phase separation temperatures for PDhS fractions in methyl chloride Mg. Polymer Mg. Solution Wt. Fraction T (00) Polymer p Fraction A 2.2 212.2 0.010 150.2 Fraction E 216.1 0.059 154.4 281.9 0.046 154.7 OR) Due to greater than normal pressures, nearly all the tubes containing methyl chloride solutions ruptured during the run, so appreciable data could not be obtained for this system. 5’7 APPELDIX VIII Gas Chromatograms of Solvents 58 Figure 19. Gas chromatOgram for n—pentane 59 Figure 20. Gas chromatogram for n-butane 60 Figure 21. Gas chromatogram for neopentane 61 Figure 22. Gas chromatogram for tetramethylsilane . Gas chromatogram for dimethyl ether m \N Figure 65 Figure 24. Gas chromatogram for methyl chloride MICHIGAN STQTE UNIV. LIBRQRIES 31293101787681