The excluded volume of a flexible polymer depends on its radius of gyration, which is sensitive to the polymer-solvent interaction. In a good solvent, solvent molecules are preferably accessible to a polymer, which extends the chain segment and increases the excluded volume. On the contrary, V e is small in a poor solvent, which enhances interactions between different parts of the polymer.
Pure and Applied Chemistry
Many polymer solution theories have been developed for the excluded volume of flexible polymers. It is important that the excluded volume be directly related to the second virial coefficient of polymer solutions, so this is an apt criterion for the ideality of the solutions.
The excluded volume effect is more significant for nucleic acids at lower salt concentration, where the stiffness or persistence length of the chain segment is influenced by polyelectrolyte effects. The excluded volume effect is also the primary basis for the ability of water-soluble polymers, such as polyethylene glycol, to precipitate proteins. Preferential Hydration is partly due to steric exclusion, in that a larger cosolvent is more effectively excluded from protein surface than water Fig.
This situation is a very difficult mathematical and physical problem and of great importance to polymer science. Not surprising, many scientist have investigated the self-avoidance problem by means of analytical methods, such as perturbation theory or self-consistent-field theory.
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So far, there is no exact treatment of self-avoidance for long chain molecules. Thus, considerable work has been devoted to numerical methods such as exact enumeration, Monte Carlo or algebraic methods recursion formula methods. A good overview of these methods has been given by Binder.
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A good starting point is a simple linear chain. This problem was first addressed by Flory 3.
Excluded Volume (Molecular Biology)
We have chosen a slightly different approach since his formula somewhat overestimates the swelling of a polymer chain. Let us further assume that the majority of the segments can be found in a spherical volume with a radius equal to R and that the solvent molecules are randomly distributed in this volume R 3. These assumption are difficult to justify and one might argue that they lead to erroneous expressions. However, as Masao Doi 4 and others have shown, the relations that can be derived from these assumptions describe, at least qualitatively, the approximate behavior of a self-avoiding polymer chain.
as Explained by the Renormalization Group
The good agreement with experimental findings might be the compensation of errors. Therefore, the probability distribution W R of the end-to-end distance of a real chain is proportional to the product of the above described two factors: 5.
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Excluded Volume (Molecular Biology)
Get permission to re-use this article. Create citation alert. Journal RSS feed. Sign up for new issue notifications. When the local intrinsic stiffness of a polymer chain varies over a wide range, one can observe both a crossover from rigid-rod—like behavior to almost Gaussian random coils and a further crossover towards self-avoiding walks in good solvents.