Theory of Twisted Stiff Chains. I

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Abstract
The Kratky-Porod wormlike chain is extended to a stiff chain model with three characteristic lengths by taking the continuous limit of a chain composed of hindered-rotating bonds with fluctuating bond angles. The limiting results are classified into four cases depending upon whether these three characteristic lengths possess their imaginary parts and whether they are degenerated or not. The persistence vector and chain dimension of this continuous limit model indicate that the model is statistically equivalent to a superposition of three Kratky-Porod chains with different persistence lengths and chain directions, when the three lengths are all real and different. When two of the lengths are conjugate complex, the model shows the rotation of the direction of a component Kratky-Porod chain owing to the twisting freedom of the model, and when the lengths are degenerated, interaction effects of component Kratky-Porod chains appear.

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