Real Chain in Good Solvent

The value of v was first calculated by Flory. The fundamental assumption is to consider an homogeneous monomer concentration within the volume of the coil. In a space of dimension d, the internal concentration is given by 

The repulsive interaction is proportional to the number of contacts between monomer units, and since we consider a pair interaction the energy per unit volume is proportional to c2. The total repulsive energy for a given ccmformation is 

Minimizing versus R the entropy (equation 2-4) and repulsive contribution (equation 2-7), Flory obtains (1) 

Chain with local stiffiiess Kratky-Porod model. 

In a real polymer the positions between neighboring monomer units are sttongly correlated. A simple model proposed by Kratky and Pored (4) describes the properties of a chain with local rigidity. The constraint applied to the monomer units, with a monomer unit length equal to a, is 

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Real chains in good solvents have the same universal features as self-avoiding walks on a lattice. These features are described by two "critical" exponents y and v. The first is related to chain entropy, the second to chain size a real chain has a size that is much larger than that of an ideal chain (Nv instead of N1/2, where v 3/5 in good solvents) in good solvents the conformation of the chain is "swollen". 

The Real Chains in Good Solvents Intermediate Range... 

We now turn to a discussion of real chains in good solvents, when external constraints are applied. The basic situations are listed in Section 1.1. in connection with ideal chains. We shall see that all exponents ate modified strongly by excluded volume effects, and that nwst of them can... 

If we consider a real chain in good solvent, we must use within the Kirkwood approximation, but the spring constant is also changed. Eq. (VI.44) tells us that K T/Rp. Then we get... 

The End-To-End Vector Distribution for a Real Chain in Good Solvent Scaling Laws... 

In good solvents, the mean force is of the repulsive type when the two polymer segments come to a close distance and the excluded volume is positive this tends to swell the polymer coil which deviates from the ideal chain behavior described previously by Eq. (1). Once the excluded volume effect is introduced into the model of a real polymer chain, an exact calculation becomes impossible and various schemes of simplification have been proposed. The excluded volume effect, first discussed by Kuhn [25], was calculated by Flory [24] and further refined by many different authors over the years [27]. The rigorous treatment, however, was only recently achieved, with the application of renormalization group theory. The renormalization group techniques have been developed to solve many-body problems in physics and chemistry. De Gennes was the first to point out that the same approach could be used to calculate the MW dependence of global properties... 

The conformations of a real chain in an athermal or good solvent are determined by the balance of the effective repulsion energy between... 

Kuhn monomers with Kuhn length h. Recall that the unperturbed size of the real chain confined to the air-water interface in good solvent is hA [Eq. (3.54)],... 

The Real Chain in a Good Solvent - Floiy s Approximation.37... 

THE REAL CHAIN IN A GOOD SOLVENT - FLORY S APPROXIMATION... 

Formally, this transition is very similar to the worming transition. Flory s approach to a real chain in a good solvent is the base of discnssion (see paragraph 3.6). Flory considered in his seminal paper the balance between attraction among the monomers, wanting to collapse the polymer chain into itself, and the entropy of the chain, wanting to expand the chain. Flory s approach revealed the end-to-end distance of the swollen chain in a good solvent... 

In the formula above is the distance between two beads of the chain, 1 is the lattice spacing, and is a negative constant. With = 0 the model reduces to the model of a real chain in a good solvent, where mutual attractions of the chain segments could be ignored. Energy of the entire chain is a sum of the binary contributions XEy. 

The real situation is perhaps in between the above two case, i.e. the polymer chains may undergo some interpenetration and some compression. Providing the dangling chains (A chains) are in good solvent (i.e. strongly solvated by the solvent molecules), this local increase in segment density wiU result in strong repulsion as a result of two main effects. 

The conformation of a real chain in a good solvent is determined by two effects the effective repulsion energy between segments that tends to swell the coil and the entropy loss due to such a deformation. In equilibrium, the sum of both is minimal leading to an increased radius of the coil of... 

The free energy of stretching a real linear chain in a good solvent has a stronger dependence on size R than the quadratic dependence of the ideal chain ... 

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