Poly second virial coefficients

A graphical method, proposed by Zimm (thus tenned the Zinnn plot), can be used to perfomi this double extrapolation to detemiine the molecular weight, the radius of gyration and the second virial coefficient. An example of a Zinnn plot is shown in figure Bl.9.6 where the light scattering data from a solution of poly... 

Fig Second virial coefficients as a function of Molecular weight for a solution of poly (methyl methacrylate) in acetone. 

As pointed out in Chapter III, Section 1 some specific diluent effects, or even remnants of the excluded volume effect on chain dimensions, may be present in swollen networks. Flory and Hoeve (88, 89) have stated never to have found such effects, but especially Rijke s experiments on highly swollen poly(methyl methacrylates) do point in this direction. Fig. 15 shows the relation between q0 in a series of diluents (Rijke assumed A = 1) and the second virial coefficient of the uncrosslinked polymer in those solvents. Apparently a relation, which could be interpreted as pointing to an excluded volume effect in q0, exists. A criticism which could be raised against Rijke s work lies in the fact that he determined % in a separate osmotic experiment on the polymer solutions. This introduces an uncertainty because % in the network may be different. More fundamentally incorrect is the use of the Flory-Huggins free enthalpy expression because it implies constant segment density in the swollen network. We have seen that this means that the reference dimensions excluded volume effect. 

Fig. 15. The relation between q0 and the second virial coefficient Ae for a number of poly(methyl methacrylate) networks in various diluents (acetone, toluene, benzene and chloroform). The first number in the code refers to the concentration of methyl methacrylate in the solution before polymerization, the second to the tenfold percentage of divinylbenzene added (by volume of methyl methacrylate) [Rijke...

Table 1.2 Reduced osmotic pressures (tt/c)c=o, number average molecular weights Mn and osmotic second virial coefficient A2 for poly(pentachlorophenyl methacrylate) fractions in toluene at 25°C and benzene at 40°C (tt in cm of benzene or toluene) (c in g dl-1). (From ref. [44])...

In polymer science, the ideal form of the thermodynamic equations is preserved and the nonideality of polymer solutions is incorporated in the virial coefficients. At low concentrations, the effects of the cl terms in any of the equations will be very small, and the data are expected to be linear with intercepts which yield values of and slopes which arc measures of the second virial coefficient of the polymer solution. Theories of poly mer solutions can be judged by their success in predicting nonideality. This means predictions of second virial coefficients in practice, because this is the coefficient that can be measured most accurately. Note in this connection that the intercept of a straight line can usually be determined with more accuracy than the slope. Thus many experiments which are accurate enough for reasonable average molecular weights do not yield reliable virial coefficients. Many more data points and much more care is needed if the experiment is intended to produce a reliable slope and consequent measure of the second virial coefficient. 

Figure 7.10 The effect of poly-isobutylene (PIB) concentration on the zero-shear viscosity of the suspensions described in Fig. 7-9. The lines were calculated assuming / r,o(0) = K exp(—atTniin/A er), with values of the second virial coefficient A2 of 6 X 10 8 X 10 and 10 ". (From Buscall et al. 1993, with permission from the Journal of Rheology.)...

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. 

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... 

Figure 6. Second virial coefficient as a function of salt concentration for 1)poly(4VMP/pSS),...

Fig. 5.4. Reduced viscosity /j ed function of the concentration c for sodium poly(styrene sulfonate) (PSSNa) of different molar masses in aqueous solution.The second virial coefficient of the viscosimetry, is equivalent to the slope of the curves and is given for each molar mass. The Huggins constant Ky is constant and independent of the molar mass. Data from [35,91]...

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. 

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