Flory parameter, repulsion between chains

One question that these simulations can address is the relation between different estimates of the incompatibility between polymer species, i.e. How can one identify the mutual repulsion between polymer species parameterized by the product of the Flory-Huggins parameter and chain length, xfV, for a specific microscopic polymer model [65,78] ... 

Depending on the Flory parameter x, there is a particular special temperature T = 6 at X = 1/2, which corresponds to an exact cancellation between steric repulsion and van der Waals attraction between monomers, and thus the chains are nearly ideal. This temperature is known as the collapse temperature or theta temperature [15]. Equation (15.10) for the free energy of mixing is an expression that finds wide use in physical chemistry. A quantitative understanding of hydrophobie eollapse is required to understand the initial stage of protein folding, as proteins are often a finite chain consisting of a 50-300 amino acid residue linear chain, which in many aspects resembles a heteropolymer. 

When the concentration of the free polymer is set equal to zero, the situation corresponds to pure steric stabilization. The free energy of interaction due to the interpenetration of the adsorbed polymer chains has a range of 26, where 6 is the thickness of the adsorbed layer. This free energy is proportional to the quantity (0.5 - x), where x is the Flory interaction parameter for the polymer-solvent system. Thus, a repulsive potential is expected between two particles when x < 0.5 and this repulsion is absent when x = 0.5. For this reason, it was suggested [25] that instabilities in sterically stabilized dispersions occur for x > 0.5, hence for theta or worse-than-theta conditions. However, the correlation with the theta point only holds when the molecular weight of the added polymer is sufficiently high... 

It is clear from Equation (12.10) that when the Flory-Hugging interaction parameter, y, is less than 0.5 - that is, the chains are in good solvent conditions - then will be positive and the interaction repulsive, and wiU increase very rapidly with decreasing h, when the latter is lower than 25. This explains the strong repulsion obtained between water droplets surrounded by PHS chains. The latter are highly soluble in the hydrocarbon medium, and any attempt to overlap the chains results in very strong repulsion as a result of the above-mentioned unfavourable mixing. 

In a poor solvent, one parameter is no longer sufficient and now the three-body terms must be taken into account, not only implicitly but also explicitly. The second basic parameter required to study chains in the vicinity of TF is the repulsive three-body interaction c. The comparison made in Chapter 14 between the Flory-Huggins theory and the continuous model suggests calculating c by the formula... 

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