Yang Yingzi, Burkhardt Theodore W, Gompper Gerhard
Institut für Festkörperforschung, Forschungszentrum Jülich, D-52425 Jülich, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Jul;76(1 Pt 1):011804. doi: 10.1103/PhysRevE.76.011804. Epub 2007 Jul 19.
We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D<<P<<L the free energy of confinement DeltaF and the length of the channel R parallel occupied by the polymer are given by Odijk's relations DeltaF/R parallel=A(o)kB(TP)-1/3 D(-2/3) and R parallel =L[1-alpha(o)(D/P)2/3], where A(o) and alpha(o) are dimensionless amplitudes. Using a simulation algorithm inspired by the pruned enriched Rosenbluth method, which yields results for very long polymers, we determine A(o) and alpha(o) and the analogous amplitudes for a channel with a rectangular cross section. For a semiflexible polymer confined to the surface of a cylinder, the corresponding amplitudes are derived with an exact analytic approach. The results are relevant for interpreting experiments on biopolymers in microchannels or microfluidic devices.
我们考虑一种长的半柔性聚合物，其持久长度为(P)，轮廓长度为(L)，在直径为(D)的狭窄圆柱形通道中波动。在(D\ll P\ll L)的情况下，聚合物的受限自由能(\Delta F)和平行于通道的聚合物占据长度(R_{\parallel})由奥迪克关系给出：(\Delta F/R_{\parallel}=A_0k_BT P^{-1/3}D^{-2/3})和(R_{\parallel}=L[1 - \alpha_0(D/P)^{2/3}])，其中(A_0)和(\alpha_0)是无量纲振幅。使用受修剪富集罗森布鲁斯方法启发的模拟算法（该算法可得出非常长聚合物的结果），我们确定了(A_0)和(\alpha_0)以及具有矩形横截面通道的类似振幅。对于限制在圆柱表面的半柔性聚合物，通过精确的解析方法得出了相应的振幅。这些结果对于解释微通道或微流控设备中生物聚合物的实验具有重要意义。
