周期性通道中的熵粒子输运
Entropic particle transport in periodic channels
摘要：
布朗运动的动力学具有广泛的应用，从设计的微通道中的传输扩展到其在分子马达和布朗马达中诱导传输的突出作用。在这里，布朗输运的研究在微尺寸，二维周期性通道，表现出周期性变化的截面。此外，颗粒受到沿纵向通道轴线方向作用的外力。对于一个固定的通道几何形状，二维问题的动力学的特征在于由一个单一的无量纲参数，这是成比例的施加的力和颗粒环境的温度的比率。在这种结构中，熵效应可能起主导作用。在某些条件下，二维动力学可以近似为粒子在纵向方向上的有效一维运动。朗之万方程描述这一减少，一维过程是类型的菲克-雅各布斯方程。它包含一个熵势确定的消除通道方向的变化的延伸，和一个修正的扩散常数，引入了一个空间相关的扩散。这个修正项的不同形式以前已经提出过，我们在这里比较了一个特定的模型类别。我们通过分析估计以及与全二维随机动力学数值结果的比较来分析菲克-雅各布斯方程的有效性机制。对于非线性迁移率，我们发现一个温度依赖性，这是相反的，已知的粒子运输周期性电位。讨论了熵效应对非线性迁移率和有效扩散常数的影响。
英文摘要：
The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two dimensional periodic channels, exhibiting periodically varying cross sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two dimensional dynamics can be approximated by an effective one dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant.
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