Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
Electrophoresis. 2011 Feb;32(5):506-17. doi: 10.1002/elps.201000259.
We present a theoretical model for describing the electric field-driven migration and dispersion of short anisotropic molecules in nanofluidic filter arrays. The model uses macrotransport theory to derive exact integral-form expressions for the effective mobility and diffusivity of Brownian particles moving in an effective one-dimensional energy landscape. The latter is obtained by modeling the anisotropic molecules as point-sized Brownian particles with their orientational degrees of freedom accounted for by an entropy penalty term, and using a systematic projection procedure for reducing the system dimensionality to the device axial dimension. Our analytical results provide guidance for the design and optimization of nanofluidic separation systems without the need for complex numerical simulations. Comparison with numerical solution of the macrotransport equations in the actual, effectively two-dimensional, geometry shows that the one-dimensional model faithfully describes the field- and size-dependences of mobility and diffusivity, with maximum difference on the order of 10% under the experimentally relevant electric fields.
我们提出了一个理论模型，用于描述短各向异性分子在纳米流过滤阵列中电场驱动的迁移和分散。该模型使用宏观输运理论，推导出布朗粒子在有效一维能量景观中运动的有效迁移率和扩散率的精确积分形式表达式。后者通过将各向异性分子建模为具有取向自由度的点大小布朗粒子，并通过熵罚项来表示，以及使用系统的投影过程将系统维度降低到器件轴向维度来获得。我们的分析结果为纳米流分离系统的设计和优化提供了指导，而无需进行复杂的数值模拟。与实际的、有效二维几何形状的宏观输运方程的数值解进行比较表明，一维模型忠实地描述了迁移率和扩散率的场和尺寸依赖性，在实验相关电场下最大差异约为 10%。
