Polystyrene second virial coefficient

Krigbaumf measured the second virial coefficient of polystyrene in cyclohexane at several different temperatures. The observed values of B as well as some pertinent volumes at those temperatures are listed below ... 

These manipulations may appear to add little except for needless complication to an interpretation of the second virial coefficient for random coils. Recall, however, that Equation (81) allows the variation of solvent goodness caused by temperature changes to be described quantitatively. Thus the interaction parameter x is used to describe how B changes when a polymer is dissolved in different solvents. By contrast, 9 is used to describe the variation in B when a given polymer-solvent system is examined at different temperatures. This has been done for the polystyrene-cyclohexane system at three different temperatures the results are discussed in Example 3.4. 

EXAMPLE 3.4 Theta Temperature of A Polymer Solution from Second Virial Coefficient Data. Values of the second virial coefficient along with some pertinent volumes are tabulated below for the polystyrene-cyclohexane system at three temperatures. 

Table 12. Second virial coefficient At of polystyrene in toluene at 25° C...

Calculate the for solutions in chlorobenzene of polystyrenes with molar weights of 2 x 105,5 x 105 and 106 g/mol the intrinsic viscosity, the critical concentration, the swelling factor, the hydrodynamic swollen volume, the second virial coefficient and the Flory-Huggins interaction parameter. 

Universal plot of second virial coefficient for linear polystyrenes in decalin (filled circles have Mw = 4400000 gmor open circles have Mw= 1 560 000 gmol filled squares have Mw = 1050000 gmol open squares have Mw - 622 000g mol , filled triangles have Mw = 186 000 g moU , open triangles have = 125 000 g moF and filled inverted triangles... 

Problem 3.6 The osmotic pressure data for polystyrene of molecular weight 1.6x10 yielded, according to Eq. (3.72), the following values for the second virial coefficient (a) 2.88x10 mol cm in dichloroethane and (b) —0.37x10 mol cm in cyclohexane, both at 22°C. Determine x for the polymer-solvent systems. Which is a better solvent ... 

The thermodynamic affinity of a solvent to a polymer changes with temperature, and this predetermines the type of critical solution temperature. If the positive values of the second virial coefficient A2 and the negative values of AGmix decrease as temperature drops, it may be predicted that the system will separate into two phases on cooling, i.e., UCST is observed (e.g., solution of polystyrene in cyclohexane). If the positive values of A2 and the negative values of AGmix decrease as temperature rises, the system will separate on heating, i.e., it possesses LCST (e.g., solution of polyisobutylene in pentane). 

Problem 4.18 For the polystyrene sample in Problem 4.17 calculate (a) the second virial coefficient, (b) the root mean square end-to-end distance, and (c) the root-mean-square radius of gyration. 

The theoretical parameters which we need are the area S of the equivalent Brownian chain, and the parameter z. For polystyrene, the area S is given as a function of mass by eqn (15.2.12). On the other hand, z will be determined, either from swelling (the best method) or from the second virial coefficient. Let us emphasize, however, that this correspondence is only a very good approximation. 

Let us examine the experimental results. Daoud et al.,20 and thereafter Wiltzius, Haller, Cannell, and Schaeffer2 made systematic measurements of as a function of p for semi-dilute solutions of polystyrene (neutron and X-ray scattering). Figure 15.27 shows the results of Wiltzius et al. The quotients JRg,z are brought on the vertical axis, where RG z is the radius of gyration in the limit p -> 0. The overlap ratios are brought on the horizontal axis. These ratios are determined by the measurement of the second virial coefficient [see (15.4.3)]... 

Make a Zimm plot using the data and determine the weight-average molecular weight of the polymer. Determine also the second virial coefficient F2 and the radius of gyration of the polymer in solution. (For toluene, ii = 1.4976 and for polystyrene-toluene solutions dhldc = 0.112 cm /g.)... 

Light-scattering measurranents of three polystyrene standards were carried out using the Zetasizer Nano S by Malvern Instruments (Zetasizer Nano application note, MRK577-01), which measures the intensity of the light scattered at 173°. Kd values as a function of polymer concentration in toluene solution are reported below. From these, detomine M and the second virial coefficient Aj. 

From these data determine the second virial coefficient and the theta temperature of poly(a-methyl styrene) in cyclohexane, knowing that K = K hl AhlAcf, where K = 18.17 mol cm , the refractive index increment (d /dc) is 0.199 ml gr, and the temperature dependence of the refractive index is expressed by = -0.0005327 x T (°C) + 1.446. Static light-scattering measurements were carried out by Zimm (1948b) on polystyrene in butanone at 340 K at two concentrations. 

Values of the second virial coefficient derived from osmotic pressure measurements (Krigbaum, 1954) for a polystyrene fraction of molecular... 

MOS Moses, C.L. and van Hook, W.A., Pressure dependence of the second virial coefficient of dilute polystyrene solutions, J. Polym. Sci. Polym. Phys., 41, 3070,2003. 

Second Virial Coefficient below the 0 Temperature Though not specially mentioned, the discussion up to this point has been limited to the polymer in solvents in which A2 is non-negative, so that /3 and 2 are zero or positive in the binaiy cluster approximation. Available data on A2 for polymer solutions below 0 are still scant and fragmentary. This is mainly due to the technical difficulties explained in Section 2.3 of Chapter 4. Recently, Tong et al. [84] undertook fairly systematic measurements of A2 on polystyrene in cyclohexane, and Takano et al. [85] did similar work on poly(isoprene) in... 

Thus, in these poor solvents, the second virial coefficient A2(r) for ring polystyrene was positive at the 9 temperature 6(1) for linear polystyrene, where... 

Roovers and Toporowski [59] found that A it) for polystyrene in cyclohexane has a definite positive value at B 1). This was a veiy important finding, because it demonstrated thcit repulsion arises between a pair of unperturbed macrorings. Casassa [68] calculated A2(t) to first order in 2. In terms of the reduced second virial coefficient h defined in Section 2.2 of Chapter 2 his result is expressed as... 

Polystyrene square radii of gyration and second virial coefficient for cyclic and linear chains. Macrocyclic fractions with 11,500 < /W < 181 000 [223, 224]... 

Two separate experiments on a blend of polystyrene and poly(2,6-dimethyl-1,4-phenylene oxide) show that the two polymers are compatible. Bromination of the poly(phenytene oxide) causes a decrease in the second virial coefficient, A 2, which would lead to a phase separation if the degree of bromination was sufficiently high. 

Theta solvents have been established for poly(A -vinylcarbazole) in single solvents and for polystyrene in single and binary mixtures of 1-chlorodecane-3-methyl cyclohexanol. This has allowed Bazuaye and Huglin to determine the unperturbed dimensions as a function of solvent and temperature for polystyrene, from which it was observed that these were always higher in mixed solvent systems compared with the single theta solvent, and that preferential adsorption was not responsible. Friedrich and Prochazka carried this one step further and examined polystyrene in toluene-MEK—2-methylpropan-l-ol mixtures, i.e., two solvents and one precipitant. They showed that the composition at which the second virial coefficient was zero and at which [ /] attained the values comparable to a theta solvent, were not identical, but in this case preferential adsorption was used as an explanation. 

Figure 2,24. Second virial coefficient A2 for polystyrene in cyclohexane at different temperatures near the theta temperature. (From Ref. 16.)...

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