Surfactant monolayer model

At the level of approximation of the pseudo-phase model, the surfactant tails are viewed as an independent pseudo-phase in which an uniform effective concentration of solute is assumed. In the surfactant monolayer model, the water/oil interface is supposed to be covered by a monolayer of surfactant molecules into which the solute can be adsorbed. In this latter case, the mole fraction of solute at the interface is defined by the interfacial composition k (37), with the assumption that no water and no oil is adsorbed in the surfactant film, given as follows ... 

Figure 9.9. Schematic representation of the different localization states of a hydrophobic solute in a microemulsion. The solute could be solubilized in the oil microdomain or at the interface. The interfacial surfactant area is noted as a and the curvature radius as R. This schematic represents the case of a nonionic surfactant where the hydration of the polar head is temperature (r)-dependant. With the pseudo-phase model, the solute concentration is considered over the volume occupied by the tails of the surfactant, whereas in the surfactant monolayer model, the binding of the solute into the surfactant monolayer is considered...

Studies of the order within surfactant monolayers have been reported for many decades. Multilayer assemblies have been studied by electron as well as infrared absorption. Motivated by an older model proposed for the orientation of molecules (Langmuir, 1933 Epstein, 1950), and by recent theoretical calculations, these two potential models for tilt disorder in the monolayer have been examined. Both models arise because the monolayer structure tries to compensate for the difference between the equilibrium head-head and chain-chain distances that each piece of the molecule would want to attain if it were independent. In one model, the magnitude of the tilt is fixed, but the tilt direction wanders slowly through the lattice. In the second... 

A generalized nonideal mixed monolayer model based on the pseudo-phase separation approach is presented. This extends the model developed earlier for mixed micelles (J. Phys. Chem. 1983 87, 1984) to the treatment of nonideal surfactant mixtures at interfaces. The approach explicity takes surface pressures and molecular areas into account and results in a nonideal analog of Butler s equation applicable to micellar solutions. Measured values of the surface tension of nonideal mixed micellar solutions are also reported and compared with those predicted by the model. 

The purpose of this paper will be to develop a generalized treatment extending the earlier mixed micelle model (I4) to nonideal mixed surfactant monolayers in micellar systems. In this work, a thermodynamic model for nonionic surfactant mixtures is developed which can also be applied empirically to mixtures containing ionic surfactants. The form of the model is designed to allow for future generalization to multiple components, other interfaces and the treatment of contact angles. The use of the pseudo-phase separation approach and regular solution approximation are dictated by the requirement that the model be sufficiently tractable to be applied in realistic situations of interest. 

The pseudo-phase separation approach has been successfully applied in developing a generalized nonideal multicomponent mixed micelle model (see I4) and it is Interesting to consider whether this same approach can be used to develop a generalized treatment for adsorbed nonideal mixed surfactant monolayers. The preferred form for suoh a model is that it be suitable (at least in principle) for treating multiple components and be extendable to other interfaoes and properties of interest suoh as oontaot angles. Earlier models (5, 18, 27) based on the pseudo-phase separation approach and... 

Results for the various binary mixed surfactant systems are shown in figures 1-7. Here, experimental results for the surface tension at the cmc (points) for the mixtures are compared with calculated results from the nonideal mixed monolayer model (solid line) and results for the ideal model (dashed line). Calculations of the surface tension are based on equation 17 with unit activity coefficients for the ideal case and activity coefficients determined using the net interaction 3 (from the mixed micelle model) and (equations 12 and 13) in the nonideal case. In these calculations the area per mole at the surface for each pure component, tOj, is obtained directly from the slope of the linear region in experimental surface tension data below the cmc (via equation 5) and the maximum surface pressure, from the linear best fit of... 

Adopting this viewpoint, the net interaction parameter for surface mixing in the present model may be seen as a useful way to account for changes in the surface free energy in nonideal mixed surfactant monolayers. Here, the parameter must not only account for the effects due to counterions, but for changes in molar surface... 

The reason for the success of such a simple model is that the dominating force in determining the surfactant composition on the surface originates from the free energy gain of replacing hydrocarbon-water contacts with hydrocarbon-hydrocarbon and water-water contacts when a surfactant molecule is adsorbed into the surfactant monolayer. 

Both the adsorption velocity and the adsorbed amount in equilibrium rise with increasing concentration. The adsorption isotherm (adsorbed amount as a function of the concentration) shows a plateau in the vicinity of ceff. That was interpreted basing on a two-step model [27] as formation of a surfactant monolayer. From the adsorbed amount of about 1.2 0.3 pmol/m2 at ceff an area per molecule of 1.3 0.3 nm2 was calculated which is typical for a loose monolayer of the used type of surfactant. 

Beyond the simple thin surfactant monolayer, the reflectivity can be interpreted in terms of the internal structure of the layer, and can be used to determine thicker layers and more complex surface structures, and this can be done in two different ways. The first of these uses the optical matrix method [18, 19] developed for thin optical films, and relies on a model of the surface structure being described by a series or stack of thin layers. This assumes that in optical terms, an application of Maxwell s equations and the relationship between the electric vectors in successive layer leads to a characteristic matrix per layer, such that... 

Therefore, the effect of the monolayer is brought down to additional resistance of the equivalent by thickness aqueous layer h. It was shown that the permeability of the adsorption layer depends on surface tension (packing density) and size of the diffusing gas molecules [482], For many surfactants h is within the range of 7 to 12 nm. This means that the permeability of thick films is determined by the rate of molecular diffusion, while for black films (h 10 nm) Eq. (3.147) is valid and their permeability is determined by the properties of the surfactant monolayers. Electrolytes do not affect significantly the permeability of monolayers. It was considered that gas diffusion through the monolayer occurred as a result of creation of microscopic vacancies between the surfactant molecules. This model was called model of energy barrier. However, later this model proved unsatisfactory. [483]... 

One of the primary compounds that the cell membrane is composed of is DMPC, because of its surface activity caused by a hydrophobic zwitterion. A hydrodynamic model of the DMPC membrane can evaluate the intrinsic viscosity (r]i) of the surfactant monolayer, eliminating the contribution of the viscosity of dodecane and aqueous phases. The T]i values listed in Table 10.1 are about 2-4 times higher than the apparent i. The maximum t]i value, 0.75 Pa s, is comparable to that of a common viscous liquid such as glycerin (0.945 Pa s). This study demonstrated that a single molecule probing method could successfully measure the hydrodynamic properties of the interface. 

Holland, R, Nonideal mixed monolayer model, in Phenomena in Mixed Surfactant Systems, Scamehorn, J.F., Ed., ACS Symposinm Series 311, American Chemical Society, Washington, D.C., 1986, chap. 8. 

This surface phnle change can be studied by statistical mechanics/ It is affected by changes in ionic strength and surface cherge density. An aanlogous approach can be employed to study the formation of condensed surfactant monolayers on air-water interfaces. This provides a mechanism for the establishment of a surface charge density at this interface in the coulombk model. 

Figure 8.5 Two-dimensional cut through a bicontinuous microemulsion comprising water (white) and oil (black) separated by a surfactant monolayer. The same picture can also represent the inside and outside of the so-called L3 sponge phase where a surfactant bilayer separates inner and outer regions of a single solvent. Note that the domains have a well-defined iength scaie. The detaiis of the model used to generate this representation are discussed in Ref. 28.

The surface light scattering method has been used to show that the low interfaciai tensions in the Winsor I and II systems (O/W microemulsion in equilibrium with excess oil and W/O microemulsion in equilibrium with excess water, respectively) are due to the large surface pressure of the surfactant monolayer coating the interface, which almost balances the bare oil/water interfaciai tension [36,37]. Schulman and Montagne [38] proposed early that the low interfaciai tensions in microemulsion systems should be associated with these large surface pressures tt, i.e., 7 = 70 - tc 0. In other models, the origin of the low interfaciai tensions was attributed to the vicinity of critical points [39,40]. 

The most lucid way of conceptually and quantitatively understanding the rich structural variation and structural transitions of microemulsions is to use the framework of the flexible surface model (35). The basic assumption in this model is to describe a surfactant monolayer or bilayer as a mathematical surface dividing space into two or more separate regions. With each configuration of the surface one associates a curvature (free) energy G. obtained as a surface integration of a local curvature free-energy density... 

The stability of foams and emulsions depends critically on whether formation of a stable Newton black film or a hole leading to coalescence is favored. Kabalnov and Wen-nerstrom (4) addressed this question by developing a temperature-induced hole nuclea-tion model applicable to emulsions. They point on that the coalescene energy barrier is strongly affected by flic spontaneous monolayer curvature. The aufliors consider a flat emulsion film, covered by a saturated surfactant monolayer, in thermodynamic equi-... 

A number of molecular dynamics (MD) simulations of surfactant monolayers have been published during the last decade. In these studies, the water surface was often modelled as a flat, amorphous plane. Due to severe computer power restrictions, there have been only a few attempts in which the surface was modelled in all atomic details. Monolayers of trimethylammonium chloride at the air/water interface and the properties of tetradecyltrimethylammonium bromide monolayers have been simulated. In addition to these computer experiments, the structures of phenol, p-n-pentylphenol and A,V -diethyl-p-nitroaniline adsorbed on water have been investigated by MD simulations. Recently, molecular dynamics simulations of sodium dodecyl sulfate at the water/vapour and the water/CCU interfaces in regimes of small surface concentrations have been performed (4). 

Bonfillon, A. and Langevin, D., Electrostatic model for the viscoelasticity of ionic surfactant monolayers, Langmuir, 10, 2965, 1994. 

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