Ferri JK, Stebe KJ
Johns Hopkins University, Department of Chemical Engineering, Baltimore, MD 21218, USA.
Adv Colloid Interface Sci. 2000 Feb 1;85(1):61-97. doi: 10.1016/s0001-8686(99)00027-5.
Consider the example of surfactant adsorbing from an infinite solution to a freshly formed planar interface. There is an implicit length scale in this problem, the adsorption depth h, which is the depth depleted to supply the interface with the absorbed surfactant. From a mass balance, h can be shown to be the ratio of the equilibrium surface concentration gamma eq to the bulk concentration C infinity. The characteristic time scale for diffusion to the interface is tau D = h2/D, where D is the diffusivity of the surfactant in solution. The significance of this time scale is demonstrated by numerically integrating the equations governing diffusion-controlled adsorption to a planar interface. The surface tension equilibrates within 1-10 times tau D regardless of bulk concentration, even for surfactants with strong interactions. Dynamic surface tension data obtained by pendant bubble method are rescaled using tau D to scale time. For high enough bulk concentrations, the re-normalized surface tension evolutions nearly superpose, demonstrating that tau D is indeed the relevant time scale for this process. Surface tension evolutions for a variety of surfactants are compared. Those with the smallest values for tau D equilibrate fastest. Since diffusion coefficients vary only weakly for surfactants of similar size, the differences in the equilibration times for various surfactant solutions can be attributed to their differing adsorption depths. These depth are determined by the equilibrium adsorption isotherms, allowing tau D to be calculated a priori from equilibrium surface tension data, and surfactant solutions to be sorted in terms of which will reduce the surface tension more rapidly. Finally, trends predicted by tau D to gauge what surfactant properties are required for rapid surface tension reduction are discussed. These trends are shown to be in agreement with guiding principles that have been suggested from prior structure-property studies.
考虑表面活性剂从无限溶液吸附到新形成的平面界面的例子。这个问题中存在一个隐含的长度尺度，即吸附深度h，它是为向界面提供吸附的表面活性剂而耗尽的深度。从质量平衡来看，h可表示为平衡表面浓度γeq与本体浓度C∞的比值。扩散到界面的特征时间尺度为τD = h²/D，其中D是表面活性剂在溶液中的扩散系数。通过对控制扩散控制吸附到平面界面的方程进行数值积分，证明了这个时间尺度的重要性。无论本体浓度如何，表面张力在1 - 10倍的τD内达到平衡，即使对于具有强相互作用的表面活性剂也是如此。用悬滴法获得的动态表面张力数据使用τD来缩放时间。对于足够高的本体浓度，重新归一化的表面张力演变几乎重叠，表明τD确实是这个过程的相关时间尺度。比较了各种表面活性剂的表面张力演变。τD值最小的那些表面活性剂达到平衡最快。由于对于类似大小的表面活性剂，扩散系数变化很小，各种表面活性剂溶液平衡时间的差异可归因于它们不同的吸附深度。这些深度由平衡吸附等温线决定，从而可以根据平衡表面张力数据先验计算τD，并根据哪种表面活性剂溶液能更快降低表面张力对其进行排序。最后，讨论了由τD预测的趋势，以衡量快速降低表面张力需要何种表面活性剂性质。这些趋势与先前结构 - 性质研究提出的指导原则一致。
