Fractionation of polymers

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

From appropriate ratios of these sequence lengths, what conclusions can be drawn concerning terminal versus penultimate control of addition The following are experimental tacticity fractions of polymers prepared from different monomers and with various catalysts. On the basis of Fig. 7.9, decide whether these preparations are adequately described (remember to make some allowance for experimental error) by a single parameter p or whether some other type of statistical description is required ... 

A plot of these values is shown in Fig. 8.1. Note the increase in the entropy of mixing over the ideal value with increasing n value. Also note that the maximum occurs at decreasing mole fractions of polymer with increasing degree of polymerization. 

Next we consider the fraction of n-mer in a specific phase. The volume of n-mer in each of the phases is given by pVp and q q > therefore the fraction of polymer in the two phases is... 

The polyamides are soluble in high strength sulfuric acid or in mixtures of hexamethylphosphoramide, /V, /V- dim ethyl acetam i de and LiCl. In the latter, compHcated relationships exist between solvent composition and the temperature at which the Hquid crystal phase forms. The polyamide solutions show an abmpt decrease in viscosity which is characteristic of mesophase formation when a critical volume fraction of polymer ( ) is exceeded. The viscosity may decrease, however, in the Hquid crystal phase if the molecular ordering allows the rod-shaped entities to gHde past one another more easily despite the higher concentration. The Hquid crystal phase is optically anisotropic and the texture is nematic. The nematic texture can be transformed to a chiral nematic texture by adding chiral species as a dopant or incorporating a chiral unit in the main chain as a copolymer (30). 

Miscible Blends. Sometimes a miscible blend results when two polymers are combined. A miscible blend has only one amorphous phase because the polymers are soluble in each other. There may also be one or more crystal phases. Simple theory (26) has supported the empirical relation for the permeabihty of a miscible blend. Equation 18 expresses this relation where is the permeabihty of the miscible blend and ( ) and are the volume fractions of polymer 1 and 2. 

Larger injection volumes, e.g., 2% of the total column volume, are sometimes advantageous in the preparative fractionation of polymers (33). More samples can be injected using larger injection volumes with a slight decrease in resolution. When the same amount of sample is injected with a smaller injection volume and a higher sample concentration, the resolution decreases more significantly. 

The fraction of polymer confined in the interphase layers was estimated using the empirical formula [60, 61] ... 

Most values of / have been measured at zero or low conversions. During polymerization the viscosity of the medium increases and the concentration of monomer decreases dramatically as conversion increases (i.e. as the volume fraction of polymer increases). The value of / is anticipated to drop accordingly. 32, u 9j % For example, with S polymerization in 50% (v/v) toluene at 70 °C initialed by 0.1 M AIBN the instantaneous" / w as determined to vary from 76% at low conversion to <20% at 90-95% conversion (Figure 3.3).32 The assumption that the rate of initiation (kAf) is invariant with conversion (common to most pre 1990s and many recent kinetic studies of radical polymerization) cannot be supported. 

Second, Schneider s article reviews recent work (notably by Rowlinson, Kohn and co-workers) on phase relations in binary liquid systems where one of the components is much more volatile than the other (D1, D2, E3, M8, R9). Such systems may have lower critical solution temperatures for these systems, an increase in temperature (and, indirectly, pressure) causes precipitation of the heavy component, thereby providing a possible separation technique, e.g., for the fractionation of polymers. 

Feed ratio of OC2H5 TEOS groups to OH chain ends. b Volume fraction of polymer present at swelling equilibrium in benzene at room temperature. c Elongation at initial upturn in modulus. d Ultimate strength as represented by the nominal stress at rupture. Energy required for rupture... 

Weight fraction of polymer of length j Monomer conversion... 

PRINT "THE WEIGHT FRACTION OF POLYMER IN THE MIXTURE - " WA 2010 PRINT... 

W Gog M) d log M = weight fraction of polymer with log(molecular weight)... 

If the units of primary molecules of uniform length are subjected to cross-linking at random, the weight fraction of polymer molecules comprised of z primary molecules is ... 

For the purpose of testing the validity of what we have called the deformation factor, it is convenient to plot rl a — l/a ) vs. a if rubbers swollen permanently (not merely for purposes of equilibration) are included, the quantity roV2 /(a — l/a ) is to be preferred, where To is the tension referred to the cross section when unswollen and unstretched, and V2 is the volume fraction of polymer in the swollen mixture (see Appendix B, Eq. B-5). According to theory, both of these quantities should be independent of the deformation, and the latter should be independent of the degree of swelling as well. On the basis... 

Fig. 111.—Experimental values of the interaction parameter %i plotted against the volume fraction of polymer. Data for polydi-methylsiloxane M =3850) in benzene, A (New-ingi6). polystyrene in methyl ethyl ketone, (Bawn et aV ) and polystyrene in toluene, O (Bawn et alP) are based on vapor pressure measurements. Those for rubber in benzene, T (Gee and Orr ) were obtained using vapor pressure measurements at higher concentrations and isothermal distillation equilibration with solutions of known activities in the dilute range.

The critical concentration at which phase separation first appears on passage to the two-phase region is thus predicted to occur at a very small volume fraction of polymer for a polymer having a molecular weight of a million (a 10 ), for example, y2c=0.01. Substituting Eq. (4) in either of the equations (3), we obtain... 

Fractionation by GPC was sessed by changing injected concentrations and by GPC analysis of polymer before and after fractionation. Efficiency of fractionation of polymer from monomer did not appear to be a source of error. In fact, an advantage of this method over others is that the separation of monomer from the polymer can be clearly monitored and controlled,... 

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