Random distribution, Flory model

Solution of long-chain molecules When two liquids mix to form a mixture, the entropy change is similar to that of the volume expansion, as long as the solute molecules have the same size as the solvent molecules and are randomly distributed. But when the solute forms long-chain molecules, the correct method of calculating the entropy was given by Flory. First consider a lattice model where the solvent and the solute molecules have the same volume. Let i and 2 be the number of solvent and... 

The Flory distribution is a random distribution useful in several modes of polymerization. This distribution results from addition polymerization reactions when the only significant processes that interrupt macromolecular growth are either or both of chain transfer (to any species but the polymer) or termination by disproportionation. Likewise, this molecular weight distribution describes linear condensation polymerization when equal reactivity is assumed for all ends only when the reaction involves an equilibrium between polymerization and depolymerization. The model describes the distribution with one parameter which is the number average molecular weight. The distribution equation is ... 

Equation 3.6, together with Equation 3.4, describes a random distribution of molecular sizes this distribution is also known as the Flory-Schulz distribution or the most probable distribution [5]. Recently, Wutz and Kricheldorf [6] proposed a model describing the frequency distribution (/ ) and formulated the weight distribution (w,) of linear chains in step-growth polymerizations considering the cyclation reaction, which is one of the most important side reactions in step-growth polymerization. 

The unit distribution was estimated by IR and melting-point methods. IR data for the 4-methylpentene-l unite are based on the relative intensity of the 997 cm band in the copolymer spectra (Fig. 10) and show that these copolymers have a significant tendency to blodc formation ( i f2 3—5). This conclusion was supported by melting-point measurements 114,167). The copolymer melting points are evidently lower than those for homopolymer mixtures, thus demonstrating that a real copolymerization takes place (167), but they have an upward deviation from the theoretical curve calculated for the random copolymer model by means of the Flory equation (Section III.E) with d ff = 4710 kal/ mol (171). 

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