Polydisperse systems copolymers

Continuous thermodynamics provides a simple way for the thermodynamic treatment of polydisperse systems. Such systems consist of a very large number of similar species whose composition is described not by the mole fractions of the individual components but by continuous distribution functions. For copolymers, multivariate distribution functions have to be used for describing the dependence of thermodynamic behavior on molar mass, chemical composition, sequence length, branching, etc. 

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 order to obtain the specific form of T(q), we now apply the random phase approximation (RPA) [22-26] to our system. The RPA provides a classical treatment of concentration fluctuations for incompressible mixtures of very large molecular weight molecules. It assumes a self-consistent potential uniformly acting on all species of monomers to ensure the incompressibility condition. The details of the RPA method, as applied to our polydisperse block copolymer blend, are given in Appendix 5.B. The result leads to... 

The application of SCFT to polydisperse diblock copolymer systems is of recent date and, because of computational considerations, so far mainly restricted to diblock copolymers with polydispersity for only one of the blocks. A characteristic... 

A prime example of these features can be found in the synthesis of styrene/ (meth)acrylate random copolymers. By controlling the initiator/total monomer ratio, the molecular weight can be accurately controlled for both styrene/methyl methacrylate and styrene/butyl acrylate random copolymers. As can be seen in Figure 2.3 the polydispersity for both systems is essentially 1.10-1.25 over comonomer ratios ranging from 1/9 to 9/1. 

The synthesis of graft copolymers can be achieved either by "grafting from or by grafting onto processes.— The former method seems more versatile, but it does not allow an adequate structure control, and it often yields rather polydisperse samples. On the contrary "grafting onto" methods allow a precise control of the size and of the nunber of grafts, but it is only applicable to a limited number of systems. 

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