Random copolymers, fractionation systems

As has been described in Chapter 4, random copolymers of styrene (St) and 2-(acrylamido)-2-methylpropanesulfonic acid (AMPS) form a micelle-like microphase structure in aqueous solution [29]. The intramolecular hydrophobic aggregation of the St residues occurs when the St content in the copolymer is higher than ca. 50 mol%. When a small mole fraction of the phenanthrene (Phen) residues is covalently incorporated into such an amphiphilic polyelectrolyte, the Phen residues are hydrophobically encapsulated in the aggregate of the St residues. This kind of polymer system (poly(A/St/Phen), 29) can be prepared by free radical ter-polymerization of AMPS, St, and a small mole fraction of 9-vinylphenanthrene [119]. 

First, retention does not yield Dj directly, but rather the Soret coefficient, which is the ratio of to the ordinary diffusion coefficient (T>). Because compositional information is contained in alone, an independent measure of D must be available. Second, a general model for the dependence of on composition has not been established therefore, the dependence must be determined empirically for each polymer-solvent system. Fortunately, Dj is independent of molecular weight, and for certain copolymers, the dependence of Dj on chemical composition has been established. With random copolymers, for example, Dj is a weighted average of the Dj values for the corresponding homopolymers, where the weighting factors are the mole fractions of each component in the copolymers [9]. As a result, the composition of random copolymers can be determined by combining thermal FFF with any technique that measures D. 

Advances in our understanding of thermodiffusion in polymer solutions have led to the application of ther-mal FFF to copolymers. With random copolymers, for example, the dependence of on chemical composition is now predictable [6], so that compositional information can be obtained from retention measurements. With block copolymers, thermal FFF can still be used to separate components according to molecular weight, branching, and composition, but independent measurements on the separated fractions must be made in order to get quantitative information, except when special solvents are used. Special solvents yield a predictable dependence of Dj on composition even for block copolymers [6]. Different solvents are special for different copolymer systems. 

Replacing the volume fractions above with weight fractions, one obtains the so-called Wood Equation, which is often used for random copolymer systems (Wood 1958). 

However, traditional chemical thermodynamics is based on mole fractions of discrete components. Thus, when it is applied to polydisperse systems it has been usual to spht the continuous distribution function into an arbitrary number of pseudo-components. In many cases dealing, for example, with a solution of a polydisperse homopolymer in a solvent (the pseudobinary mixture), only two pseudo-components were chosen (reproducing number and mass averages of molar mass of the polymer) which, indeed, are able to describe some main features of the liquid-liquid equilibrium in the polydisperse mixture [1-3]. In systems with random copolymers the mass average of the chemical distribution is usually chosen as an additional parameter for the description of the pseudo-components. However, the pseudo-component method is a crude and arbitrary procedure for polydisperse systems. 

In blends of random copolymers, or in blends of a polymer with random copolymer, the presence of repulsive forces among segments (other than specific interactions discussed before) may lead to miscibility (Wang et al. 2006). The effect of ethylene-styrene cmitent on the miscibility and cocrystallization was studied extensively by Chen (2001). They showed that the miscibility of the system depends only oti the comonomer content with composition expressed as weight fraction. Based on the experimental observations, they constructed a miscibility map for binary blends (Fig. 10.34). 

For cases involving a random copolymer or a miscible blend of two amorphous rubbery polymers, the behavior is generally a volume fraction weighted average of the permeabilities of the two homopolymers. On the other hand, the transport properties of immiscible blend systems depend significantly on the relative permeabilities and the morphology of the immiscible blend. 

Fig. 8. Depression of spinodal temperature T with increasing volume fraction (pj of the added copolymer AB, calculated for the system homopolymer A, homopolymer B, and random copolymer AB with Vj = Vj, Vj = lOVj, fj = fj = 0.5. The volume fraction of homopolymer A in the initial binary mixture is indicated (From Rigby, Lin, and Roe )...

For another type of rod-coil copolymers [132] the authors varied the fraction of the rod segment and analyzed the photoluminescence in this system. The random rod-coil system is built from the rigid segment poly( i-phenylenebenzoZiMthiazole) and the flexible poly(benzo f thiazoledecamethylene) (see Figure 34(b)). 

Stejskal J, Kratochvil P (1978) Fractionation of a model random copolymer in various solvent systems. Macromolecules 11 1097-1103... 

On cooling a typical copolymer melt, one observes, after the customary supercooling, crystallization of pure A. The melt must thus increase to some degree in concentration B as predicted by the liquidus line of Fig. 4.23. But in copolymer systems, one neither reaches the liquidus concentration, nor observes the eutectic point. The system freezes to a metastable state before the eutectic temperature is reached. Usually only one component crystallizes in random copolymers. All of the component B and a large fraction of A remain in the amorphous portion of the semicrystalline sample. For a more extensive discussion of the irreversible melting of homopolymers and copolymers see Ref. 57, Chapters IX and X. 

Figure 13 illustrates the comparison between the experimental xsans(F) data for a pair of systems that are labeled by Graessley et al. [28] as H38/D25 and H25/D38 and the BLCT xsansCF) as calculated from Eq. 37 for the set of caa. sbej ab> and y specified above. The notation H38/D25, for example, denotes the isotopic blend of hydrogenated (H) and deuterated (D) polybutadiene random copolymers, and the numbers indicate the fractions of 1,2 units in each of the blend components. The experimental points [28] are designated in Fig. 13 by circles and triangles, whereas the fines represent the theoretical fits. Figure 13 demonstrates that the theory reproduces the overall values of the X parameters within the experimental error bars of 1.5 x 10 [28]. 

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