Non-uniform polymer

There are many varieties of density functional theories depending on the choice of ideal systems and approximations for the excess free energy functional. In the study of non-uniform polymers, density functional theories have been more popular than integral equations for a variety of reasons. A survey of various theories can be found in the proceedings of a symposium on chemical applications of density functional methods [102]. This section reviews the basic concepts and tools in these theoretical methods including techniques for numerical implementation. 

Although the exact nature of the B-D transition is not well understood, Wu (8) has shown that Tgp is related to the ability of plastics to be deep-drawn. Since the implications of such behavior to coatings are obvious, we desired to learn if non-uniform polymers offered any advantage in this respect. 

The effect of non-uniform polymer composition is shown in Figure 11 for the case of a 50/50-methyl methacrylate/ethyl acrylate copolymer made by a linear power feed process in which the near tank initially contained only ethyl acrylate and the far tank only methyl methacrylate. Compared with its uniform counterpart, the non-uniform polymer had a T D approximately 25° lower and a respectable... 

At a constant concentration of living polymers, the pseudo-first order rate constants for each monomer addition remain the same whether the polymers are or are not uniform. However, their rate of dissociation into a specified monomer is smaller in the system discussed here than in that involving the appropriate uniform polymers. While each uniform polymer may dissociate into its monomer, only a fraction of non-uniform polymers, i.e. those possessing the appropriate ending, is capable of degrading into that monomer. Therefore, the stationary concentrations of the respective monomers are given by their true equilibrium concentrations multiplied by the mole fractions of those with the required ending, viz. 

Actual solid surfaces are always rough at some level and are also generally chemically non-uniform (amorphous vs. crystalline portions of a polymer surface. 

In [332] it was noted that the strength of samples cut out at different locations of an article made from filled thermoplastics by pressure molding may differ widely — which is due to the non uniform orientation of the polymer at different locations of the mold. The very high strength parameters of composites with PMF in molded specimens are obviously also due to orientation effects, while for standard mixed samples of similar composition (that is, a matrix which, apart from the filler, contains some superhigh molecular polyethylene imitating the PMF coats) the... 

Since feed streams are not added after the start of a batch reaction one need only be concerned with proper initial addition and blending procedures. Streams flowing into a CSTR, however, are being introduced into a polymer latex. If added improperly, these streams can fail to be mixed completely and they can cause flocculation. Streams should be introduced where they are mixed rapidly and the ionic concentration should be as low as possible. Introduction of such streams as initiator solutions at high concentrations or in the wrong location can cause local flocculation and/or non-uniform reaction. 

Owing to the chain orientation distribution the fracture mechanism of oriented polymer fibres is different from that of isotropic fibres. The presence of this distribution leads to a non-uniform distribution of the strain energy between the domains. The strain energy is defined by... 

Polymer materials are frequently used under stress loadings and these may be concentrated at certain parts of the structure. Thermal stresses may be induced by non-uniform heating or by differential expansion coefficients the latter may be an important factor in the degradation of fibre-reinforced composites in the radiation environment of space. 

Background on Spin Casting. As early as 1958, Emslie, et al. (A) proposed a theoretical treatment of spin casting for nonvolatile Newtonian fluids. This theory predicted that films formed on a flat rotating disc would have radial thickness uniformity. They predicted that the final film thickness would depend on spin speed (w) and viscosity (ij) as well as other variables such as liquid density and initial film thickness. The dependence of thickness on u> and ij was also recognized by many of the other authors reviewed in this paper, and their proposed relationships are compared in Table I. Acrivos, et al. (5) extended the Emslie treatment to the general case of non-Newtonian fluids, a category into which most polymers fall. Acrivos predicted that non-Newtonian fluids would yield films with non-uniform radial thickness. 

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