Polydisperse systems homopolymers

For a polydisperse system of homopolymers, one finds in the same manner as outlined for the static scattering66,70 72)... 

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. 

Here hence denotes the position of monomer with label i (i= 1,..., N) in the feth chain molecule (fe = 1,..., N ). For simplicity, we have specialized here to a monodisp>erse system of linear homopolymers hut the generalization to polydisperse systems or to heteropolymers or to branched architecture is straightforward, as well as to multicomponent systems (including solvent molecule coordinates, for instance). Typically, the volume in which the S3 tem is considered is a cubic LxLxL box (in d = 3 dimensions, or a square LxL box in d = 2 dimensions), and one chooses periodic boundary conditions to avoid surface effects but if the latter are of interest, the corresponding change of boundary conditions is straightforward. All of what has been said so far applies to lattice models as well as to models in the continuum. 

Block co-polymers have been synthesised in [C4Ciim][PF6] by ATRP of butylacrylate and acrylate monomer.[62] The outcome of the reaction depends significantly on the order of substrate addition. If, for example, methyl acrylate was added to a two-phase system of poly-butylacrylate and ionic liquid, the resulting copolymer has a narrow polydispersity and is essentially free of homopolymer. A markedly higher amount of homopolymer was formed when butyl acrylate was added to a solution of poly-methyl acrylate and the degree depended on the stage of the MA polymerisation. Below 70% conversion, copolymer without homopolymer was formed, while above 90% conversion, practically no co-polymer was produced. 

The advantages to be expected from such a method are important. In fact, we shall see that this approach is very flexible. It enables us to treat, without special difficulties, monodis perse systems as well as systems with a given polydispersion, linear polymers and branched polymers, homopolymers and copolymers. Thus, a large investigation domain is covered by this method. 

These materials represent the first observation of the SmC (zig-zag) and SmO (arrow head) structure in rod-coil diblock copolymers [41] in contrast to the homopolymer of poly( -hexyl isocyanate) which only form a nematic mesophase (both lyotropic [65] and thermotropic [66]). This confirms the idea by Halperin [60, 69] that rod-coil systems are a microscopic model for smectic liquid crystals in general. Although the SHIC rod-coil system has a relatively broad polydispersity, a smectic mesophase over a size scale of as much as 10 xm has been observed (Fig. 4B). This indicates that microphase separation plays a very important role in determining the self-assembly of the liquid crystalline process of these blocks. The existence of only a nematic phase in the rod homopolymer system is probably due to its broad polydispersity in contrast to the fact that a smectic meso-... 

Several experimental studies on the effects of the F Z) / on diblock copolymer self-assembly have appeared in the literature. Bendejaq et al. synthesized severalpoly(sty-rene)-fc-poly(acrylic acid) copolymers with broad molecular weight distributions and found that these systems produced well-ordered structures [22]. Blends of a homopolymer hA and a diblock copolymer A-B can also be considered as a pure copolymer system with large polydispersity. These systems were extensively studied, for more details on this topic the reader is referred to my diploma thesis [23]. 

These results indicate that spinodal decomposition can be induced by flow even in a homopolymer system, which results in an oriented nematic phase with long chains and an isotropic liquid with short chains. Though the above argument is based on a bimodal system, the same principle has also been applied to the polydisperse case [67]. However, this approach still does not take flow-induced conformational ordering into account, which may couple to the anisotropic interactions. 

Fundamentals of continuous thermodynamics as applied to homopolymers characterized by univariate distribution functions have been reviewed extensively [28, 29]. Hence, this chapter will provide the fundamentals in their most general form by considering systems composed of any number of polydisperse ensembles described by multivariate distribution functions and any number of solvents and by referring to the papers [28, 29],... 

This review reports the state-of-art in the development and applications of continuous thermodynamics to copolymer systems characterized by multivariate distribution functions. Continuous thermodynamics permits the thermodynamic treatment of systems containing polydisperse homopolymers, polydisperse copolymers and other continuous mixtures by direct use of the continuous distribution functions as can be obtained experimentally. Thus, the total framework of chemical thermodynamics is converted to a new basis, the continuous one, and the crude method of pseudo-component splitting is avoided. 

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