Dilatational surface elasticity

A final substitution of Eq. (5.271) into relation (5.267) and taking into account Eq. (5.266) we find the dynamic dilational surface elasticity of micellar solutions... 

Three techniques may be applied for measurement of the dilational surface elasticity and viscosity (25). The first method applies surface waves to the interface (with frequency co). The dilational elasticity, e, is given by the expression... 

The dynamic surface tension of a monolayer may be defined as the response of a film in an initial state of static quasi-equilibrium to a sudden change in surface area. If the area of the film-covered interface is altered at a rapid rate, the monolayer may not readjust to its original conformation quickly enough to maintain the quasi-equilibrium surface pressure. It is for this reason that properly reported II/A isotherms for most monolayers are repeated at several compression/expansion rates. The reasons for this lag in equilibration time are complex combinations of shear and dilational viscosities, elasticity, and isothermal compressibility (Manheimer and Schechter, 1970 Margoni, 1871 Lucassen-Reynders et al., 1974). Furthermore, consideration of dynamic surface tension in insoluble monolayers assumes that the monolayer is indeed insoluble and stable throughout the perturbation if not, a myriad of contributions from monolayer collapse to monomer dissolution may complicate the situation further. Although theoretical models of dynamic surface tension effects have been presented, there have been very few attempts at experimental investigation of these time-dependent phenomena in spread monolayer films. 

Figure 20. (a) The (dimensionless) lateral compressibility (dilatational modulus, elastic area expansion modulus) (left ordinate) and the dimensionless area per molecule (right ordinate) as a function of the tail length (t) of the PC lipids in equilibrium bilayer membranes. The conversion to real compressibilities and areas per molecule is discussed in the text, (b) The (dimensionless) surface tension and the (dimensionless) lateral compressibility as a function of the relative expansion for the C PC lipid... 

At equilibrium, the surface elasticity, or surface dilational elasticity, EG, is defined [15,25] by ... 

Lucassen-Reynders, E.H. Surface Elasticity and Viscoaity in Compression/Dilation in Anionic Surfactants Physical Chemistry of Surfactant Action, Lucassen-Reynders, E.H. (Ed.), Dekker New York, 1981, pp.173-216. 

Another indirect method for the estimation of Gibbs elasticity modulus is based on the determination of the surface dilatation modulus E in experiments in which the surfaces of the surfactant solutions undergo small amplitude deformations of oscillatory nature [100-102], It is shown [100, see also Chapter 7] that the concentration dependence of a Gibbs elasticity modulus at constant film thickness should be nearly the same as the concentration dependence of (twice) the surface elastic modulus E when film thickness and frequency are related by... 

E.H. Lucassen-Reynders, Surface Elasticity and Viscosity in Compression/ Dilation, in Anionic Surfactants Physical Chemistry and Surfactant Action E.H. Lucassen-Reynders, Ed., Marcel Dekker (1981). (Review of dllatlonal rheology mode, emphasis on Gibbs monolayers includes discussion on 2D equations of state.)... 

In respect of the classical mechanics, E is an "ideal" coefficient, like the elasticity modulus in Hooke s model. Most of the practical compressions/dilatation experiments carried out with adsorption layers are comparable to the screening of elastic properties in material science. In analogy to the coefficients of the 3D-elasticity theory, we have to consider complex coefficients in surface rheology. The surface elasticity coefficient written as a complex modulus therefore has the form... 

Using the classical equation of Boussinesq (1913) for the surface dilational viscosity, a relationship between surface tension change, surface elasticity and surface dilatation viscosity is obtained. 

Lucassen-Reynders, E.H., "Surface Elasticity and Viscosity in Compression/Dilatation", in Surfactant Science Series, Vol. 11, (1981)173 Lucassen-Reynders, E.H., Marcel Dekker, Surface Science Series, 11(1986)1 Lucassen-Reynders, E.H., J. Colloid Interface Sci., 117(1987)589 Lucassen-Reynders, E.H., Colloids Surfaces, 25(1987)231 Ludviksson, E.N. and Lightfoot, J., AlChE J., 14(1968)674 Lunkenheimer, K. and Kretzschmar, G., Z. Phys. Chem. (Leipzig), 256(1975)593 MacLeod, C.A. and Radke, C.J., J. Colloid Interface Sci., (1993)... 

The Marangoni elasticity can be determined experimentally from dynamic surface tension measurements that involve known surface area changes. One such technique is the maximum bubble-pressure method (MBPM), which has been used to determine elasticities in this manner (24, 26). In the MBPM, the rates of bubble formation at submerged capillaries are varied. This amounts to changing A/A because approximately equal bubble areas are produced at the maximum bubble pressure condition at all rates. Although such measurements include some contribution from surface dilational viscosity (23, 27), the result will be referred to simply as surface elasticity in this work. 

The main relations between the complex dynamic surface elasticity and the kinetic characteristics of micellisation are presented below [103, 133, 134]. Let a small surface element of the area S be subjected to a small periodic surface dilation 5 S... 

This relation describes not only periodic deformations of a liquid surface. Using methods of integral transformations it is possible to show that the dynamic surface elasticity is a fundamental surface property and its value determines the system response to a small arbitrary surface dilation [161]. With this method it is also possible to determine the dynamic elasticity of liquid-liquid interfaces where the surfactant is soluble in both adjacent phases [133]. Moreover, similar transformations lead to an expression for the dynamic surface elasticity for the case when the mechanism of the slow step of micellisation is determined by scheme (5.185) or for frequencies corresponding to the fast step of micellisation [133,134]. However, as stated above, it is the slow process which mainly influences the adsorption kinetics from micellar solutions. 

With respect to the rheological parameters fliey come to the conclusion that surface elasticity effects are superior to surface viscosity effects. This, however, apphes to pure surfactant layers and may be different for pure protein or mixed surfactant/protein adsorption layers. It has been stressed also by Langevin (26), in her review on foams and emulsions, fliat studies on the dynamics of adsorption and dilational rheology studies for mixed systems, in particular surfactant-polymer systems, are desirable in order to understand these most common stabilizing systems. 

If the interface exhibits viscoelastic properties, as it often appears when surfactant is adsorbed, the surface tension becomes frequency dependent (7), Y = Y + i(A)N, where N is a surface viscosity associated to the vertical motion of the interface, different from shear (L) and dilatational (M) surface viscosities. These two viscosities are associated with frequency dependent shear S and dilatational K elastic moduli and hence,... 

The first involves a study by Malysa et al. [5] of the surface elasticity and dynamic stability of wet foams for a homologous series n-alcohols (C4-Cxo). On ascending the series, the authors found that foam stability passed through a maximum with the Cg-Cg alcohols. This effect was found to be unrelated to the Marangoni dilational modulus. However, the authors also determined a parameter they called the effective elasticity which depended on the kinetics of adsorption. They foimd that at short time scales (0.05-0.10 s), the effective elasticity correlated well with foam stability, reaching a maximum value with the C7 alcohol. 

Film Elasticity. The differential change in surface tension with relative change in area. Also termed surface elasticity, dilational elasticity, areal elasticity, compressional modulus, surface dilational modulus, or modulus of surface elasticity. For fluid films the surface tension of one surface is used. The Gibbs film (surface) elasticity is the equilibrium value. If the surface tension is dynamic (time-dependent) in character then, for nonequilibrium values, the term Marangoni film (surface) elasticity is used. The compressibility of a film is the inverse of the film elasticity. 

DOrc monolayers, due to the unsaturation, i.e. kinks of the alkyl chains, are in the liquid expanded phase, which is a fluid phase at all film pressures FI [3,13,15]. At 21 °C and T1 >25 mN m DPPC monolayers are in the solid analogous phase [3,13,16], which is highly incompressible and condensed [13,16]. Shah and Schulman [13] show that the effect of cholesterol on either saturated or unsaturated phospholipids is strikingly different. Cholesterol increases the surface elasticity, the dilational and the shear viscosity of unsaturated phospholipid monolayers [3,13,14,17]. In saturated monolayers cholesterol disturbs the order between phospholipid molecules fluidifying the solid monolayer [13,14,18] and lowering its shear viscosity [18]. Pure cholesterol monolayers are liquid [13] and have very low surface shear viscosities which are hardly detectable [18]. 

In a previous study [3] we found that the surface elasticity and the surface dilational viscosity are higher for DPrc/cholesterol than for DOPC/cholesterol monolayers... 

Table 1 The surface elasticity and the surface dilational viscosity of DPPC-cholesterol and DOPC-cholesterol monolayers as determined in [3]...

Shearer and Akers [5], Callaghan et al. [114] supposed that the mechanism involves elimination of surface tension gradients (see Section 4.4.3) as indicated by elimination of surface elasticity. These authors studied the effect of PDMSs on the surface elasticity of crude oil. PDMSs are used as antifoams to assist gas-oil separation during crude oil production and are apparently effective at the remarkably low concentration of 1 part per million (which presumably still exceeds the solubility limit). Callaghan et al. [114] find that PDMS diminishes the frequency-dependent dynamic dilational (elastic) modulus e = doAo (0/d In A(t) relative to that found for the uncontaminated oil. Here Oao(0 is the time-dependent air-crude oil surface tension, and A(t) is the area of a constrained element of air-crude oil surface subject to time-dependent dilation. The effect is more marked the higher the molecular weight (or viscosity) of the PDMS. This correlates with an enhanced antifoam effectiveness found with increase in molecular weight. 

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