Chain dimensions long-range steric interaction

The dimensions of a linear flexible molecule in solution can be readily calculated using an extension of the random walk concept first introduced to describe the movement of gas molecules. The influence of chain connections, bond lengths, bond angles and short- and long-range steric interactions can all be introduced into the calculation. The random walk problem readily lends itself to computer-based numerical methods and it is possible to generate pictorial representations which reflect the chemical constitution of the backbone polymer and the interactions of the polymer with itself and the solvent. 

In the bulk state each polymer molecule is surrounded by other polymer molecules of the same type. Expansion of a given chain to relieve long-range intramolecular steric interactions only serves to create an equal number of intermolecular steric interactions with neighboring chains. These opposing volume exclusion effects exactly counteract each other and so in a bulk amorphous polymer the polymer molecules adopt their unperturbed dimensions (i.e., a = 1). 

The latter quantity a represents the effect of long-range interactions which can be described as an osmotic swelling of the chain by the solvent-polymer interactions, while the imperturbed dimension (r ) q represents the effeet of short-range interactions such as bond angle restrictions and steric hindrances to internal rotation. The steric hindrances are also influenced by the torques exerted on the chain by solvent molecules, but the effect is rather small in many cases (11). 

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