Surface dilatational modulus elasticity

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... 

The surface rheological properties of the /3-lg/Tween 20 system at the macroscopic a/w interface were examined by a third method, namely surface dilation [40]. Sample data obtained are presented in Figure 24. The surface dilational modulus, (E) of a liquid is the ratio between the small change in surface tension (Ay) and the small change in surface area (AlnA). The surface dilational modulus is a complex quantity. The real part of the modulus is the storage modulus, e (often referred to as the surface dilational elasticity, Ed). The imaginary part is the loss modulus, e , which is related to the product of the surface dilational viscosity and the radial frequency ( jdu). 

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... 

The film elasticity was derived from tt-A isotherms as E = — A (d7r/dA). The surface dilatational modulus (E) of films with its elastic and viscous components (Ed and Ev) and loss angle tangent (tan 8) were obtained by sinusoidal periodic compressions and expansions. 

Elastic component of the surface dilatational modulus as a function of surface pressure for E4M, E50LV and E4M at a frequency of 20 mHz. 20°C, pH 7 and 1 = 0.05M. iTa indicates pressure corresponding to the transition from Structure I to Structure II. 

For the first measurements we followed the evolution of y(t) during the adsorption process. After having reached equilibrium, the complex surface dilatational modulus e is obtained from the response of the surface to a sinusoidal dilatation/compression deformation. As usual, the real part corresponds to the elastic properties and the imaginary part to the dissipative properties ... 

The viscoelasticity is a complex number determined by the dilatational elasticity and viscosity [19, 94, 95]. The viscoelasticity modulus (or surface dilatational modulus) incorporates a real and imaginary constituent, elasticity and viscosity, respectively. 

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. 

In the case where E is used to describe purely the elasticity, then E can be termed the film elasticity of compression modulus . In the general case where the surface behaviour has both an elastic and viscous component, then E can be termed the surface dilational modulus . Basically, E is the measure of the ability of a film to adjust its surface tension in an instant of stress and should be relatively large for the film to remain stable. By combining equation (2.2) with the Gibbs adsorption isotherm equation, it can be shown that E is proportional to (dy/dc), where c is the concentration of the surfactant in the thin film. 

Lucassen-Reynders EH, Cagna A, Lucassen J (2001) Gibbs elasticity, surface dilational modulus and diffusional relaxation in nonionic surfactant monolayers. Colloid Surf A 186(l-2) 63-72... 

The surface dilational modulus is then split into the elastic ( ) and viscous E") components. If the surface is purely elastic, then the phase lag (0) will be zero if it is viscous, then 0 = 90. In practice, the behavior is usually intermediate between the two extremes, and the two components can be calculated as follows ... 

Gibbs adsorption isotherm is valid in thermodynamic equilibrium. In equilibrium, the surface tension should not depend on the total surface area if new surface is produced, surfactant from the bulk diffuses to the surface and the same surface tension is estabhshed as before. If, however, the system is not given enough time to equilibrate, the local surface tension changes with an expansion or shrinkage of the geometric surface area A This is characterized with the surface elasticity E, also called surface dilatational modulus [684]. The surface elasticity is defined as... 

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

Figure 24. A comparison of the data obtained from a range of surface rheological measurements of samples of /3-lg as a function of Tween 20 concentration. ( ), The surface diffusion coefficient of FITC-jS-lg (0.2 mg/ml) at the interfaces of a/w thin films (X), the surface shear viscosity of /3-lg (0.01 mg/ml) at the o/w interface after 5 hours adsorption ( ), the surface dilational elasticity and (o) the dilational loss modulus of /3-lg (0.2 mg/ml).

Experiments with the /3-lg/Tween 20 system were performed at a macroscopic a/w interface at a /3-lg concentration of 0.2 mg/ml [40]. The data obtained relate to the properties of the interface 20 minutes after formation. Up to R = 1, the storage modulus (dilational elasticity) was large and relatively constant, whereas the loss modulus (dilational viscosity) increased with increasing R. As R was increased to higher values there was a marked decrease in the storage modulus (dilational elasticity) and a gradual increase in the loss modulus (dilational viscosity). In summary, the data show the presence of a transition in surface dilational behavior in this system at a solution composition of approximately R = 1. At this point, there is a transformation in the adsorbed layer properties from elastic to viscous. 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

If it concerns a monolayer of an amphiphile that is insoluble in the bordering phases, the modulus is purely elastic (although at strong compression, i.e., large AA/A, the surface layer may collapse), and SD is constant in time and independent of the dilatation rate. If the surfactant is soluble, exchange of surfactant between interface and bulk occurs, and Esr> will be time dependent. This means that also an apparent surface dilatational viscosity can be measured ... 

Benjamins et al (24) studied the effects of aging on the elasticity of (i-casein and K-casein films. The dilatational modulus of K-casein was larger than that of -casein and increased by a factor of three with film age, whereas the dilatational modulus of -casein films changed little with time ( ). K-casein unfolds less at the air/water interface since it has less random structure than Q-casein. This can also be interpreted in terms of K-casein having less direct contact with the film surface at any given protein concentration (25). Significant protein-protein interactions i.e. steric/electrostatic repulsion, are believed to occur between segments of polypeptide chains which extend both above and below the plane of the air/water interface in surface protein films (16,26)... 

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