ICREA and Dept Chemical Engineering, Polytechnic University of Catalonia, Barcelona, Spain.
Adv Colloid Interface Sci. 2011 Oct 14;168(1-2):278-91. doi: 10.1016/j.cis.2011.03.009. Epub 2011 Apr 1.
The principle of local thermodynamic equilibrium is systematically employed for obtaining various transport properties of long straight nano-channels. The concept of virtual solution is used to describe situations of non-negligible overlap of diffuse parts of electric double layers (EDLs) in nano-channels. Generic expressions for a variety of transport properties of long straight nano-channels are obtained in terms of quasi-equilibrium distribution coefficients of ions and functionals of quasi-equilibrium distribution of electrostatic potential. Further, the Poisson-Boltzmann approach is used to specify these expressions for long straight slit-like nano-channels. In the approximation of non-overlapped diffuse parts of double electric layers in nano-channels, simple analytical expressions are obtained for the apparent electrophoretic mobilities of (trace) analytes of arbitrary charge as well as for the salt reflection coefficient (osmotic pressure), salt diffusion permeability and electro-viscosity (electrokinetic energy conversion). The approximate solutions are compared with the results of rigorous solution of non-linearized Poisson-Boltzmann equation, and the accuracy of approximation is shown to be typically excellent when the nano-channel half-height exceeds ca.3 Debye screening lengths. Due to non-negligible electrostatic adsorption of ions by nano-channels, the apparent electrophoretic mobilities of counter-ionic analytes in nano-channels are smaller than in micro-channels whereas those of co-ionic analytes are larger. This dependence on the charge is useful for the separation of analytes of close electrophoretic mobilities. The osmotic pressure is shown to be positive, negative or pass through maxima as a function of applied salt-concentration difference within a fairly narrow range of ratios of nano-channel height to the Debye screening length. The diffusion permeability of charged nano-channels to single salts is demonstrated (for the first time) to be typically larger than that of neutral nano-channels of the same dimensions due to electrical facilitation of salt diffusion.
系统地应用局部热力学平衡原理来获得长直纳米通道的各种输运性质。采用虚拟溶液的概念来描述电双层（EDL）扩散部分在纳米通道中不可忽略重叠的情况。根据离子的准平衡分布系数和静电势的准平衡分布泛函，得到了长直纳米通道各种输运性质的通用表达式。此外，使用泊松-玻尔兹曼方法来指定这些长直狭缝状纳米通道的表达式。在纳米通道中双电层扩散部分不重叠的近似下，得到了任意电荷（痕量）分析物的表观电泳迁移率以及盐反射系数（渗透压）、盐扩散渗透率和电粘滞系数（电动能量转换）的简单解析表达式。将近似解与非线性泊松-玻尔兹曼方程的严格解进行了比较，结果表明，当纳米通道半高超过约 3 个德拜屏蔽长度时，近似的准确性通常非常好。由于离子在纳米通道中存在不可忽略的静电吸附，纳米通道中反离子分析物的表观电泳迁移率比微通道中的小，而共离子分析物的则较大。这种对电荷的依赖性可用于分离具有相近电泳迁移率的分析物。渗透压表现为正、负或在相当小的应用盐浓度差范围内通过最大值，这与纳米通道高度与德拜屏蔽长度的比值有关。证明了带电荷的纳米通道对单盐的扩散渗透率通常大于相同尺寸的中性纳米通道，这是由于盐扩散的电促进作用。
