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In the book of Edwards The Theory of Polymer Dynamics, at page 24 it is given that

2.5 Excluded volume effect

In the models of polymers considered in the previous sections, the interaction among the polymer segments is limited to within a few neighbours along the chain. In reality, however, segments distant along the chain do interact if they come close to each other in space. An obvious interaction is the steric effect: since the segment has finite volume, other segments cannot come into its own region. This interaction swells the polymer; the coil size of a chain with such an interaction is larger than that of the ideal chain which has no such interaction. Even when there are attractive forces, as long as the repulsive force dominates, the polymer will swell. This effect is called the excluded volume effect.

(the emphasis is mine)

I'm having trouble understanding what the authors mean by "[...] since the segment has finite volume, other segments cannot come into its own region". Can someone explain it in a more explicitly manner?

Our
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2 Answers2

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It means that you and I cannot occupy the same space. I have a finite volume, and you cannot occupy it at the same time as me.

mike stone
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The first and simplest model is to approximate the shape of the polymer chain as a three-dimensional random walk. But the random walk can cross its earlier path, occupying the same points in space multiple times.

With a molecule, this is clearly not the case. We must modify the model to a self-avoiding random walk. In this model locations occupied by other segments of the molecule are excluded from the space of possible positions for the Nth segment. That's all this is saying.

Depending on the steric shape of the molecule (i.e. extended side groups or not) and the magnitude of additional intramolecular interactions, we may have different amounts of excluded, inaccesible volume around the chain. Depending on the polymer and solvent, the resulting shape of the molecule differs from that given by the simplest, self-intersecting random walk model to varying extent.

jklebes
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