Abstract
The partial differential equation that yields the free energy and conformational properties of a long wormlike polymer in confinement is discussed and analyzed. In the strong confinement limit, the confinement free energy and polymer extension display the Odijk power laws; numerical solutions of the differential equations are obtained and analyzed to produce these power-law coefficients for tubes with square and circular cross sections; the result verifies recent determination of the coefficients, one of them by the same method and the others by the Monte Carlo simulation method. In the weak confinement limit, the free energy displays the typical De Gennes power law, which was obtained by examining the Gaussian polymer model; numerical solutions are obtained here for the free energy and segmental orientational properties in the crossover region from strong- to weak-confinement limits, for a long wormlike polymer confined in a tube with a circular cross section.
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