SCHULTZ S G, SOLOMON A K
J Gen Physiol. 1961 Jul;44(6):1189-99. doi: 10.1085/jgp.44.6.1189.
The effective hydrodynamic radii of small uncharged molecules in dilute aqueous solution were determined using Einstein's classical theory of viscosity. The radii thus obtained are those of a hypothetical sphere whose hydrodynamic behavior is the same as that of the solute molecule plus that water of hydration which is too firmly bound to partake in the viscous shearing process. The results obtained compare favorably with radii determined from molecular models constructed in accordance with atomic dimensions compiled by Pauling. Although the application of the Einstein theory to molecules whose size is comparable to that of water represents a considerable extrapolation, the results suggest that this deviation from the assumptions of the theory, in the case of the molecules studied, is of second order importance. Employing the viscometric radii, we have formulated an empirical correction of the Stokes-Einstein diffusion equation. This correction is similar in form to those previously proposed by Cunningham (22) and Millikan (21) and is of particular significance when the solute molecule is comparable in size to the discontinuities of the surrounding medium. The molecular radii of a number of small organic molecules obtained by means of the corrected Stokes-Einstein equation do not differ significantly from the radii obtained from molecular models of these compounds.
利用爱因斯坦经典粘度理论测定了稀水溶液中不带电小分子的有效流体动力学半径。由此得到的半径是一个假想球体的半径，该球体的流体动力学行为与溶质分子以及那些结合过于紧密而无法参与粘性剪切过程的水化水的行为相同。所得结果与根据鲍林汇编的原子尺寸构建的分子模型所确定的半径相当吻合。尽管将爱因斯坦理论应用于尺寸与水相当的分子代表了一种相当大的外推，但结果表明，在所研究的分子情况下，这种与理论假设的偏差具有二阶重要性。利用粘度半径，我们对斯托克斯 - 爱因斯坦扩散方程进行了经验修正。这种修正的形式与坎宁安（22）和米利肯（21）先前提出的修正相似，并且当溶质分子的尺寸与周围介质的不连续性相当时具有特别重要的意义。通过修正后的斯托克斯 - 爱因斯坦方程得到的一些小有机分子的分子半径与从这些化合物的分子模型得到的半径没有显著差异。
