The Second Virial Coefficient of Monodisperse Polystyrene in Cyclohexane below the Theta Point

Abstract

ABSTRACT:A light scattering study was made on monodisperse polystyrene + cyclohexane solutions in the range of molecular weight from 10000 to 500000 and that of temperature from 34.5°C (8) down to a value about I oc above the cloud point. The second virial coefficient A2 was found to depend essentially on temperature only, at least in the range of molecular weight examined. This result is not in conformity with any current two-parameter theories for A2 of polymer solutions.KEY As will be noted later, Wolf and Adam's finding does not conform to the prediction of the two-parameter regime in regard to molecular weight dependence. However, it seems too early to accept this as definitive, and more experiments must be undertaken before a general conclusion, if any, may be established on A 2 of polymer solutions below e.In the course of our recent experimental evaluation of the Flory-Huggins interaction parameter, we had an opportunity of carrying out light scattering measurements to estimate A 2 on six monodisperse polystyrene samples in cyclohexane below 8. 8 These samples ranged in molecular weight from 10 x 10 3 to 500 x I 0\ and the measurement on each was effected down to a temperature as close to the cloud point as possible. The finding is presented in this paper. EXPERIMENTAL Polystyrene SamplesWe started with five standard polystyrene samples Fl, F2, F4, F20, F40 supplied by Toyo Soda Co., and one laboratory-made sample F7 (anionically polymerized by Mr. H. Watanabe of our department). These samples were subjected to precipitation and/or column fractionation to sharpen further their already sufficiently narrow molecular weight distributions. The main fractions of the respective series of fractions were chosen as the test samples. By GPC measurements, their ratios of weight-average to number-average molecular weights were found to be smaller than 1.03. Hence, in the present data analysis, any of the samples was treated as completely monodisperse in molecular weight.The molecular weight M determined by light scattering in benzene at 25°C was 10000, 21500, 43600, 181000, 498000, for the samples F1, F2, F4, combined with small angle laser light scattering gave an M of 74000 for the sample F7. Preparation of SolutionsEach polystyrene sample was dissolved in benzene and repeatedly filtered through a Millipore membrane until no light scattered by dust particles could be observed in the laser beam passing through the solution. The filtered solution was then freezedried in a vessel covered with a Millipore film. A proper amount of the dry polymer was weighed into a cylindrical light scattering cell and again thoroughly dried. The solvent cyclohexane was distilled and immediately poured into the cell in a dry bag filled with nitrogen. The cell was then sealed with a ground glass stopper. The solution was left standing overnight at a temperature between 30 and 40°C with occasional shaking. Complete dissolution of the polymer was confirmed by observing transparency of the solution, and also by the absence of unusual inten...

Flory Enthalpy Parameter at Infinite Dilution of Polymer Solutions Determined by Various Methods

“…Here Xo is the concentration independent coefficient and Xo c is the critical Xo· Xo c is related to Tc, 1/1 0 , and 0 through the relation (22) Here v is the specific volume of polymer and note that 1/1 0 estimated by eq 22 corresponds to the finite molecular weight. 0 is determined as the temperature at which A 2 becomes zero.…”

“…Ko values thus determined by Miyaki and Fujita scatter fairly largely, probably due to experimental difficulty of LS measurements of solutions of polymers with M w 10 7 • Ko= 0.22 at 308 K was obtained for M w = oo from line c in the figure, constructed by the least-squares method. Tong et al 22 determined A 2 of five monodisperse PS samples in the temperature range from 307.7 K to about 1 K above the cloud point and they found A 2 for monodisperse PS in CH below 0 to be independent of M, within the ranges of T and M studied. Since unfortunately the A 2 values were not described in their paper, we estimated (oA 2 /oT) 9 from the initial slope of the plot of -A 2 vs. T-1 (Figure 4 of ref 22 10 MiyakiFujita, 20 • 21 and Tong et al 22 The Ko value at infinite molecular weight for each study is shown in the table.…”

Repulsive and Attractive Interactions between Polystyrene Chains in a Poor Solvent

“…On the other hand, ð@Å=@cÞ=RT for the fraction F1-2 with M w ¼ 10500 takes a minimum around " c c % 0:1 g/cm 3 at 15 C. Similar concentration dependencies of ð@Å=@cÞ=RT for cyclohexane solutions of polystyrene with M w % 10 4 near the temperature have already been reported previously. 14,15 From data points at low " c c, we have determined M w and A 2 for each fraction, using eq 5. The results are listed in Table I.…”

“…Therefore, we can more critically test the perturbation theory by comparing it with the poor solvent system. So far, the osmotic compressibility of cyclohexane solutions of polystyrene was investigated over wide ranges of the concentration by several workers [11][12][13][14][15] However, most of them used rather high molecular weight polystyrene samples, and may not be suitable for the purpose of the present study. On the other hand, the second virial coefficient A 2 of oligo-and polystyrenes in cyclohexane over a wide molecular weight range was measured by Yamakawa et al 16,17 We have utilized their A 2 data to determine the interaction parameters d and " of polystyrene in cyclohexane, as explained below.…”

Osmotic compressibility in dilute polystyrene-cyclohexane and polystyrene-methylcyclohexane solutions: Correlation of polystyrene virial coefficients with solvent quality

“…The least squares parameters for the correlation lines are reported in Table III . The least squares parameters of the correlation lines are reported in Table III. CORRELATION OF OSMOTIC VIRIAL COEFFICIENTS WITH SOLVENT QUALITY by the observations of Tong et al 29 and Perzynski et al 30 for PS/CH and Takano et al 52 for polyisoprene/dioxane solutions. That work showed that the A 2 decays smoothly with T in the poor solvent region (T Ͻ ).…”