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Roth, M. (1990). Solubility Parameter of PDMS as a Function of Temperature and Chain Leigth. J. Pol. Sci. Part B, Pol. Phys. 28 (3).pdf

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Solubility Parameter of Poly(dimethy1 Siloxane) a8 a Function of Temperature and Chain Length INTRODUCTION Gas chromatography is often used to study the thermodynamics of polymer solutions in the limit of infinite dilution of the low-molecular-weight component.'.' We recently reported some thermodynamic characteristics of solutions of five hydrocarbons in eight samples of poly( dimethyl siloxane) ( P D M S ) of different mean chain
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  Solubility Parameter of Poly dimethy1 Siloxane) a a Function of Temperature and Chain Length INTRODUCTION Gas chromatography is often used to study the thermodynamics of polymer solutions in the limit of infinite dilution of the low-molecular-weight component.'.' We recently reported some thermodynamic characteristics of solutions of five hydrocarbons in eight samples of poly( dimethyl siloxane) (PDMS) of different mean chain length^ ^ In this note, smoothed values of the activity coefficients from the previous study are manipulated to yield the solubility parameter of PDMS. Effects of temperature and mean chain length on the solubility parameter are discussed. THEORY The infinite-dilution limit of the Flory-Huggins interaction parameter, X , is related to the mass fraction-based activity coefficient Qp of the solute (1) at infinite dilution in the polymer (2) by' where VYL s the molar volume of the pure liquid solute, A zn is the number-average molar mass of the polymer, and u1 and u2 are the specific volumes of the solute and polymer, respectively. Provided that dispersion interactions only are operative between the solute and the polymer, the Flory- Huggins interaction parameter may be expressed by an approximate relation5 where R is the molar gas constant, T is the thermodynamic temperature, l and 62 are the solubility parameters of the solute and the polymer, respectively, and is a dimensionless parameter related to the entropy of mixing. Rearranging eq. (2 , one obtains6 Equation 3) ontains both 6 and as unknowns, therefore, separate values for the two parameters cannot be obtained from eq. (3) without introducing an additional independent assumption? Early theoretical arguments5 suggest that P should be in the range of 0.1 to 0.2 and that it should be independent of 6 . This means that the term RTB/VyL may amount to only a few percent of 6 for a plausible value of 6 . and that RT@/VyL hould be even less significant when compared with 2~46 . Accordingly, if values of X are available for several different solutes at a given temperature, the polymer solubility parameter 6 is usually estimated from the slope of a straight line obtained by plotting the left-hand side of eq. (3) against 6 . In principle, the square of the slope-based value of 6 may be compared with the intercept of the line to check the relative magnitudes of 6: and the mean value of RTj3/VyL for the solutes employed. In order to estimate the values of at several different temperatures, the values of Xa and for the respective solutes at the respective temper- atures have to be known. The solubility parameter of a solute is defined by where AU is the cohesive energy of the solute. At temperatures well below the critical temperature of the solute, the volumetric behavior of the saturated vapor of the solute conforms to the virial Journal of Polymer Science: Part B: Polymer Physics, Vol. 28, 2715-2719 (1990) 1990 John Wiley Sons, Inc. CCC 0887-6266/90/01302715-05 04.00  2716 J. POLYM SCI : PHYS ED : VOL 28 (1990) equation of state truncated after the second term. The cohesive energy of the solute is then given by where AHuI s the enthalpy of vaporization of the solute, Py is the vapor pressure of the pure solute at saturation, and Ell is the second virial coefficient of the solute. The pure component parameters appearing in eq. 5) may be obtained from suitable generalized correlations. The molar volume V~L an be calculated using the Campbell-Thodos equation.' The quantities Bll and dBll/dT may be derived from the Hayden-O'Connell correlation? The vapor pressures of the solutes may be calculated from the Antoine equation, In Py = A B/ + C) (6) For a number of compounds, the constants A B, nd C of eq. (6) have been compiled by Reid et al? If the temperature dependence of the vapor pressure is described by eq. 6), he enthalpy of vaporization of the solute may be calculated from where VyG s the molar volume of the saturated vapor of the solute, Eqs. (4)-(8) provide a tool to calculate the solubility parameter of the solute as a function of temperature. In a previous rep~rt,~ he temperature dependence of the infinite dilution Raoult law activity coefficient of the solute in the polymer was expressed by In yl = cln T+ d/T+ e (9) The constants c, d, and e were obtained by regression analysis of the experimental data. In the limit of infinite dilution of the solute, the Raoult law and the mass fraction-based activity Coefficients are related by where MI is the molar mass of the solute. From eqs. (9) and 10). the activity coefficient may be calculated for any temperature within the range of the experimental data (see below). The resultant value of In fly is then used in eq. ( 1 to obtain the interaction parameter at the respective temperature. The specific volume of the solute can be calculated from the molar volume (see above) and the molar mass. The temperature dependences of the specific volumes of the PDMS samples may be taken from the low-pressure results of Lichtenthaler et a1.I' EXPERIMENTAL The experimental procedures have been described elsewhere? The hydrocarbon solutes employed were C5 to CB n-alkanes and cyclohexane. The samples of PDMS were commercial gas chro- matographic stationary phases obtained from various suppliers. The number-average and mass- average molar maas of the PDMS samples are listed in Table I. These values were determined by size exclusion chromatography. For all the solute-polymer pairs, the activity coefficients were derived from the specific retention volumes measured at temperatures within 30 to 95°C in about 5OC increments.  NOTES 2717 TABLE I Number-Average and Mass-Average Molar Mases of PDMS Samples Sample no. 2,410 3,480 3,480 4,820 15,100 20,700 208,000 218,000 18,000 8,810 16,600 28,800 28,700 95,300 580,000 480,000 RESULTS AND DISCUSSION Employing the procedure described in the Theory section, the solubility parameters of the eight samples of PDMS were calculated at temperatures of 30, 40, 50.60, 70.80, and 90°C. The values of 62 derived from the slopes of the respective linear fits according to eq. (3) 6, = slope/2) are listed in Table 11, and a typical plot is shown in Figure 1. At the 95% confidence level, the regression analysis yields Student's test-based uncertainty limits of up to 2% and up to 4% for the slope and the intercept, respectively. A comparison of the slope with the intercept (see Theory section) shows that, in all the samples of PDMS at all temperatures, the average values of RTO/VYL or the five solutes are positive and less than 5% of the respective slope-based values of 6:. However, the precision of the regression analysis is not sufficient to yield reliable absolute data on the average values of RT@/VYL. n all the samples of PDMS, the values of A decrease systematically as the temperature increases. The most significant source of uncertainty in the resultant solubility parameters is the lack of a univocal way to derive separate values for a and B from eq. (3) (see Theory section). The dominant source of experimental error in the determination of XW s the uncertainty in the amount of polymer in the column packing?* - The uncertainty in the calculated solubility parameters of the solutes generally increases with increasing vapor pressures of the solutes. Together with an adverse effect of a broad distribution of chain length of the PDMS samples used in this study, the above sources of error effectively obscure the dependence of the resultant solubility parameters on the number-average molar mass of PDMS. It can be seen from Table I1 that, at a constant temperature, the solubility parameters do not vary with the chain length, at least within the range of A?zn covered in this study. Therefore, the solubility parameters of the PDMS samples Nos. 1-8 in Table I1 may be averaged to yield the mean values, . The temperature TABLE I1 Solubility Parameters of PDMS Samples [( J/C~~)~'~] Temperature ( C) Sample no. 30 40 50 60 70 80 90 14.9 14.9 14.9 14.9 14.9 14.9 15.0 14.9 14.6 14.7 14.7 14.7 14.7 14.7 14.7 14.7 14.4 14.4 14.4 14.4 14.4 14.4 14.4 14.4 14.1 14.2 14.2 14.2 14.2 14.2 14.2 14.2 13.9 13.9 13.9 13.9 13.9 13.9 13.9 13.9 13.6 13.6 13.6 13.6 13.6 13.6 13.7 13.6 13.3 13.4 13.4 13.3 13.4 13.4 13.4 13.3  2718 J. POLYM. SCI.: PHYS. ED.: VOL. 28 (1990) 2bO - z 0 >- 220 c m I r m- 200 100 5 1 16 Fig. 1 Plot to determine solubility parameter of PDMS sample no. 8 t 6OoC. n-pentane. 2 n-hexane, 3 n-heptane, 4 n-octane, 5 cyclohexane. dependence of the average solubility parameter for PDMS within 30 o 95OC may be fitted by an empirical linear function 2 = 15.7 0.026t (11) where t is the temperature ( C), and the units of 8 are (J/cm3)'/'. At 25OC. eq. (11) ields a value of 8 = 15.1 (J/cm3)'l2. This result is within the range of 14.9 o 15.6 J/cm3) ' quoted in the literat~re,'~ nd compares favorably with the values of 15.0 and 15.1 (J/cm3) ', derived in the same way from the interaction parameters measured by static vapor sorptionI6 and by gas chromatography,17 respectively. I am indebted to a referee for bringing Ref 6 to my attention. References 1. J. R. Conder and C. L. Young, Physicochemical Measurement by Gas Chromatography, 2. J. S. Aspler, Theory and applications of inverse CC. in Pyrolysis and GC in Polymer Analysis, 3. M. Roth and J. NovHk, Macromolecules. 19. 364 1986). 4. D Patterson, Y. B. Tewari, H. P. Schreiber, and J. E. Guillet, Macromolecules, 4, 356 Wiley, Chichester (UK), 979, . 190. S. A. Liebman and E. J. Levy (Eds.), Marcel Dekker, New York, 1985, p. 399-523. ( 1971 .

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