Dynamic surface excess

Figure 8.5 Dynamic surface excess of C TAB surfactants in the OFC without added electrolyte ( ) m = 14, (A) m = 16, (0) m = 18. Arrows mark the erne s of the three surfactants. Dotted line indicates the equilibrium surface excess for CigTAB [15]. Data have been amalgamated and re-plotted from references 9 and 12.

Figure 8.6 correlates the coefficients of ellipticity measured on the OFC to the surface excess values determined by NR or, for C12TAB, by tensiometry. >12 The significance of the near-linear response is that this calibrated elfipsometric measurement can be used to determine dynamic surface excess values for this family of surfactants. Ellipsometry has signif-... 

Figure 8.6 Relationship between dynamic ellipticity and dynamic surface excess for CigTAB ( ), CigTAB (o) and C14TAB ( ) and for equilibrium ellipticity and equilibrium surface excess for C12TAB ( ). Reprinted with permission from [12], (2003) American Chemical Society.

It was noted in connection with Eq. III-56 that molecular dynamics calculations can be made for a liquid mixture of rare gas-like atoms to obtain surface tension versus composition. The same calculation also gives the variation of density for each species across the interface [88], as illustrated in Fig. Ill-13b. The density profiles allow a calculation, of course, of the surface excess quantities. 

A second equation is needed to determine the surface tension as a function of axial position. We adopt the quasistatic assumption that a is a unique equilibrium function of the surface excess concentration, T, even during dynamic events (17). A surface species continuity balance dictates how T varies along the interface. Upon neglect of surface diffusion and for h <1, the steady state form of this balance is... 

Equation (46), one form of the Gibbs equation, is an important result because it supplies the connection between the surface excess of solute and the surface tension of an interface. For systems in which y can be determined, this measurement provides a method for evaluating the surface excess. It might be noted that the finite time required to establish equilibrium adsorption is why dynamic methods (e.g., drop detachment) are not favored for the determination of 7 for solutions. At solid interfaces, 7 is not directly measurable however, if the amount of adsorbed material can be determined, this may be related to the reduction of surface free energy through Equation (46). To understand and apply this equation, therefore, it is imperative that the significance of r2 be appreciated. 

With respect to the dynamical properties of the hydrated electron in cluster systems, the first principle dynamics using ab initio molecular dynamics and so on have been extensively applied. [135, 180, 371, 408, 446] They revealed information about the structure and relative stabilities of the isomer clusters. Nonadiabatic dynamics of a solvated electron in various photochemical processes has also been studied experimentally. [62, 123, 294, 329] Rossky and co-workers [327, 468] also studied the relaxation dynamics of excess electrons using quantum molecular dynamics simulation techniques. Here the nonadiabatic interactions were taken into account basically within the scheme of surface hopping technique. [444]... 

One way to circumvent the problem raised above is to measure the dynamic surface tension, instead of the equilibrium surface tension (described so far). The dynamic surface tension is the surface tension measured at short times after a surface has been formed and hence it is a non-equilibrium property. If an imaginary cut is made through a liquid and the molecules are not allowed to relax into an equilibrium state, the surface tension at the cut section will be the arithmetic average of the surface tensions of the present components. After equilibrium is reached, however, the most surface-active species, the one with the lowest surface tension, will be found in excess at the liquid/air surface. This relaxation of the surface tension, from an arithmetic mean to an equilibrium surface tension, is called the dynamic surface tension. If the surface tension is measured at short times after a surface has been formed, it reflects the surfactant bulk concentration, without the preferential adsorption of the more surface-active species which are present in small amounts. Hence, dynamic surface tension measurements are preferred for determining... 

Back in 1983, the concept of mixed solvent layer [16] resulted from the determination of water surface excess concentrations at different interfaces by interfacial tension measurements that showed that, in the case of the H2O-DCE interface, and unlike the liquid water-vapor or the water-heptane interfaces, the water excess concentration was less than a monolayer as expected for aqueous 1 1 electrolyte. The molecular dynamics results of Wick and Dang seem therefore to corroborate this early concept of interfacial structure in the presence of electrolytes in the aqueous phase. 

In summary, molecular dynamics has confirmed what was expected from surface excess concentration measurements—that the more miscible the solvents, the rougher the interface, the lower the interfacial tension. It has also confirmed that lipophilic ions are specifically adsorbed on the organic side of the interface. In addition, it has introduced the concept of water protrusions or water fingers in the organic phase. It has clearly shown that the presence of ionic species enhances the formation of protrusions. In the case of solvents with a hydrocarbon chain such as hexanol, heptanone, or nitrophenyloctyle-ther, molecular dynamics has demonstrated the layering of the first organic solvent molecules. 

Most spraying processes work under dynamic conditions and improvement of their efficiency requires the use of surfactants that lower the liquid surface tension yLv under these dynamic conditions. The interfaces involved (e.g. droplets formed in a spray or impacting on a surface) are freshly formed and have only a small effective age of some seconds or even less than a millisecond. The most frequently used parameter to characterize the dynamic properties of liquid adsorption layers is the dynamic surface tension (that is a time dependent quantity). Techniques should be available to measure yLv as a function of time (ranging firom a fraction of a millisecond to minutes and hours or days). To optimize the use of surfactants, polymers and mixtures of them specific knowledge of their dynamic adsorption behavior rather than equilibrium properties is of great interest [28]. It is, therefore, necessary to describe the dynamics of surfeictant adsorption at a fundamental level. The first physically sound model for adsorption kinetics was derived by Ward and Tordai [29]. It is based on the assumption that the time dependence of surface or interfacial tension, which is directly proportional to the surface excess F (moles m ), is caused by diffusion and transport of surfeictant molecules to the interface. This is referred to as the diffusion controlled adsorption kinetics model . This diffusion controlled model assumes transport by diffusion of the surface active molecules to be the rate controlled step. The so called kinetic controlled model is based on the transfer mechanism of molecules from solution to the adsorbed state and vice versa [28]. 

Measurements of the surface excess by ellipsometry (Figure 8.3b) show very similar trends to the surface tension data. As explained later, the higher the value of the ellipticity , the lower the surface excess. The greatest difference between dynamic and static ellipticities (and hence adsorbed amounts) occurs at lower concentration than for the surface tension. This difference reflects the fact that dy/dF increases with increasing F At higher coverages, a small difference in srudace excess results in a larger difference in surface tension. 

The influence of surfactants and plant species on the retention of spray solution has been examined by de Ruiter and Uffing. They reported a linear relationship between retention and the logarithm of surfactant concentrations. It would appear that there is a need to add a surfactant concentration far in excess of the critical micelle concentration (CMC) and that the diffusion of surfactant from the bulk to the surface of the flattening drop is a retention-determining factor. The dynamic surface tension is regarded as a useful parameter determining surfactant type and concentration with respect to efficient surface retention. 

Spall is the process of internal failure or rupture of condensed media through a mechanism of cavitation due to stresses in excess of the tensile strength of the material. Usually, a dynamic failure is implied where transient states of tensile stress within the body are brought about by the interaction of stress waves. Free surfaces are assumed to be well removed from the material point of interest and play no role in the spall process. 

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