Compositional inhomogeneity

Such a distinction in composition inhomogeneity of the copolymers may have caused the variation in transparency which was observed experimentally by Sloco-mbe [36]. He examined forty-four three-component systems and established several empirical rules enabling the interpretation of experimental data on the transparency of high-conversion terpolymers. These empirical rules were explained later [37] in terms of the theory of dynamic systems whose methods have been successfully employed for qualitative analysis of the solutions of the set of dynamic... 

It is easy to notice a certain formal resemblance between this expression and the expression (11) for the composition inhomogeneity of the products of high-conversion copolymerization describable by the ideal model. In both expressions angular brackets denote the operation of averaging the bracketed quantity... 

When considering the composition inhomogeneity of Markovian copolymers, the finiteness of the chemical size of macromolecules cannot be ignored, because fractional composition distribution W(/ f) in the limit / -> oo turns out to be equal to the Dirac delta function 5(f - X). For macromolecules of finite size f2> 1 the function W(/ f) is the Gaussian distribution whose center and dispersion (Eq. 2) are described by relationships (Eq. 8) and the following one... 

The center and dispersion (Eq. 2) of the Gaussian distribution describing the composition inhomogeneity of a random copolymer comprising macromolecules whose length is 12> 1 have the very simple appearance... 

One of the prime objectives of the statistical chemistry of these polymers is establishing the dependence of their composition inhomogeneity on a macromolecule length l and on the reaction system parameters. A quantitative measure of this inhomogeneity is the dispersion (Eq. 2) of the composition distribution... 

For the copolymerization products obtained under the conversion less than 10 percent exhibit the composition inhomogeneity substantially exceeding that described by the traditional theory of free-radical copolymerization. 

The above phenomenon is due to the pronounced polydispersity of these products in their chemical size l described by the Flory exponential distribution. Because the composition of each macromolecule of the sample under investigation is unambiguously related to its degree of polymerization l, the Flory distribution for l in a polymer sample is responsible for its significant composition inhomogeneity. 

Compositional inhomogeneities in InGaN are often underlined see for example [4], Immiscibility of InN in a nitride alloy is very strong and InN microscopic inclusions as well as metallic In are found in the specimens grown currently. Although no studies of ensuing transport properties were made, analogies with other precipitated semiconductor materials point to possible influences on both mobility and carrier concentration. 

In contrast to the above mentioned models, the similar statistical description of the products of the complex-radical copolymerization occurring through the scheme (2.5) has been carried out quite recently [37, 49, 55-60]. Within the framework of this Seiner-Litt model, both copolymer composition [37,49, 55-58] and fractions of the different triads and blocks of the monomer units in the macromolecules were calculated [57]. The probability approaches which were applied in these works, are regarded as being of limited applicability in contrast to the general statistical method [49, 59, 60], By means of the latter method, the sequence distribution and composition inhomogeneity of the copolymer were completely described [49, 60] and also thorough calculations of its microstructure with the account for the tactidty were carried out [59, 60]. 

All the statistical characteristics of copolymer chain structure and composition inhomogeneity, (including the ones reported in the above papers) can be easily calculated by means of the Markov chain formalism for any of kinetic models presented in Sect. 2. Then it does not seem advisable for the solution of such problems to apply the Monte-Carlo method with which the simulation of the copolymer chain growth was carried out [83-93]. 

In Refs. [173-176] it was suggested to use the weight composition distributions instead of the molar ones and the results of their numerical calculation for some systems were reported The authors of Ref. [177] carried out a thorough theoretical study of the composition distribution and derived an equation for it without the Skeist formula. They, as the authors of Ref. [178], proposed to use dispersion of the distribution (5.3) as a quantitative measure of the degree of the composition inhomogeneity of the binary copolymers and calculated its value for some systems. Elsewhere [179-185] for this purpose there were used other parameters of the composition distribution. In particular the discussion of the different theoretical aspects of the binary copolymerization is reported in a number of reviews by Soviet authors [186-189], By means of numerical calculations there were analyzed [190-192] the limits of the validity of the traditional assumption which allows to ignore the instantaneous component of composition distribution of the copolymers produced at high conversions. 

Since the stable SPs are usually located at the apexes of the m-simplex x = 5is, it is important to know which products are formed in such SP vicinity. It is determined by the number v of the reactivity ratios rri exceeding 0.5 [202], When v = 0, at p - 1 in the composition distribution arises a mode, the maximum of which corresponds to the homopolymer Ms. When 1 v (m — 2), it was found that the product of the copolymerization at its final stage is random (v + 1)-component copolymer of monomer Ms with those v monomers Mj whore parameters rsi > 0.5. At last, in the care v = m — 1 when all rsi > 0.5, a new mode of composition distribution does not arise at p - 1 and at high conversion the formation of the random copolymer containing all m types of monomer units occurs. In the latter case the stable SP under consideration, referred to as regular, does not really contribute to the composition inhomogeneity of the copolymer. 

Some interesting results have been obtained by Russian scientists [320, 321] who studied the influence of composition inhomogeneity on some service properties and supermolecular structures of copolymers. Two samples of copolymers of butyl acrylate with methacrylic acid were synthesized which had a similar average... 

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