Real Chains in a Good Solvent

In an ideal solvent, the interaction between subunits is equal to the interaction of a subunit with the solvent. In a real solvent, the actual radius of gyration can be larger or smaller. In a good solvent, a repulsive force acts between the monomers. The polymer swells and Rg increases. In a bad solvent, the monomers attract each other, the polymer shrinks, and Rg decreases. Often a bad solvent becomes a good solvent if the temperature is increased. The temperature, at which the polymer behaves ideally, is called the theta temperature, Tq. The ideal solvent is called a theta solvent. 

To take the interaction between polymer segments into account, Flory [1320] introduced the excluded volume parameter v in units of m. In good solvents (T To), the polymer segments repel each other and v is positive. For many calculations, we simply approximate v= The excluded volume decreases with decreasing solvent quality to v = 0 for solvents. It decreases even further and becomes negative for poor solvents (T T ), where the segments attract each other. 

1) Paul John Flory, 1910-1985, American physicochemist, Nobel Prize, 1974. 

The excluded volume changes with the quality of the solvent. A good approximation for many linear polymers in organic solvents is [1318] 

The factor of 2 accounts for the fact that otherwise each pair of interacting segments would be counted twice. 

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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 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 ... 

In these dilute solutions, the effect of solvency is most clearly seen, with a poor solvent (x = 0.5) giving the highest adsorbed amounts. In a good solvent (X = 0), 0 is much smaller (see the dashed lines in Figure 16.3) and it levels off for long chains to attain an adsorption plateau which is essentially independent of the molecular weight. It should be noted that in most real situations the x value is somewhere between 0 and 0.5 (probably nearer the latter value). 

The real situation perhaps lies between the above two cases, i.e. the polymer chains may undergo some interpenetration and some compression. Provided the dangling chains (the A chains in A-B, A-B-A block or BA graft copolymers) are in a good solvent, this local increase in segment density in the interaction zone will... 

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

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... 

The second important solvent property is solvent quality with respect to the macromolecule. Depending on solvent quality, polymers adopt different conformations. In a theta solvent, interactions between monomers are canceled by interactions with the solvent, and the polymer thus behaves as an ideal chain with zero excluded volume. In good and athermal solvents, the polymer behaves as a real chain with positive excluded volume, that is, it adopts a more loosely packed coil conformation. In poor solvents, the excluded volume is negative and the chain is more compact than an ideal chain. Obviously, these differences in conformation may influence the mobility of spin labels and of spin probes interacting with the chain. Both solvent quality and viscosity depend on temperature. For example, many solvent-polymer pairs have a theta temperature at which ideal-chain behavior is adopted. 

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... 

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