Complex dilatational modulus

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 5 Real (open symbols) and imaginary (filled symbols) parts of the complex dilational modulus of an adsorbed layer at equilibrium. The circles, diamonds and triangles correspond to the MeC concentration of 3 x 10 4, 0.1 and 16 gfl, respectively...

The main factors, which determine the foam formation ability and physical stability of the foams in mixed Lys-MR solutions, are surface activity and complex dilatation modulus. With increase of MR concentration in certain range a surface activity and complex dilatation modulus of interfacial layers increased and phase angle decreased. It means that viscoelasticity of interfacial layers became higher. In these conditions the foam volume and mutiplicity as well as stability of foams were growing. This effect may be used for creation of mixed protein-MR system foam type for pharmaceutical applications with improved physical stability and wide range of antibacterial actions. 

The surface tension variation in Eq. (12) can be expressed with the help of the complex dilatational modulus e(icb) [9-11]... 

The regimes of transient and established oscillations are observed for pure liquids as well as for surfactant solutions. For surfactant solutions the characteristic frequencies and the attenuation in the system depend on the relaxation processes in the adsorption layer and the system behaviour becomes more complicated. Many surfactants are characterised by a diffusion mechanism of the surface relaxation, and the complex dilatational modulus is given by [11]... 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

The complex interfacial dilational modulus ( ) is a key fundamental property governing foam and emulsion stability. It is defined as the interfacial tension increment (da) per unit fractional interfacial area change (dA/A) i.e.,... 

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). 

Introducing the modulus (= absolute value in complex number language) of the surface dilational modulus K° as... 

The results revealed a significant effect of surface-active and nonsurface active polysaccharides on the properties of adsorbed protein films at the air-water interface. To explain the observed effects on the dynamics of adsorption, the rates of diffusion and rearrangement and the surface dilatational modulus were taken into accoimt (i) the competitive adsorption, (ii) the complexation, and (iii) the existence of a limited thermodynamic compatibility between protein and polysaccharide at the air-water interface and in the aqueous bulk phase. 

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. 

In the frequency sweep test, a repeated sinusoidal shear loading is applied at 10 frequencies and at a given temperature while a varying axial load is applied to prevent dilation of the specimen. The loads and deformations are used to calculate the complex shear modulus, G, and phase angle, 5, of the specimen at each frequency. 

Many technologies and natural phenomena involve processes of fast expansion or compression of fluid interfaces covered with surfactant adsorption layers. The dynamic system properties depend on the mechanisms and rate of equilibrium restoration after a deformation. At small magnitudes of deformation the mechanical relaxation of an interface can be described by the complex dilational viscoelastic modulus [1,2]. For sinusoidal deformations it is deflned as the ratio of complex amplitudes of interfacial tension variation and the relative surface area variation f (I ty) = dy /din A being a function of frequency. This modulus may include... 

We have reported [66] a limited study of spread polymethyl methacrylates and polyethylene oxide. Figure 12.19 shows the variation in surface tension, shear viscosity and dilational modulus obtained from SQELS data as a function of surface concentration. The viscoelastic moduli both show maximum values at finite values of the surface concentration. As the capillary waves generate oscillatory stress and strain, these are related via the complex dynamic modulus of the surface... 

In the situation described above, the dynamic experiment was cturied out in dilation the resulting complex modulus was divided into a real ( elastic ) and an imaginary ( viscous ) part. As a counterpart, the experiment can also be carried out in shear, resulting in a complex surface shear viscosity G°, consisting of a real (viscous) part, the surface shear viscosity G° and the surface shear loss viscosity, G"" identical to the elasticity. This inversion of method is formally identical to measuring complex dielectric permittivities instead of complex conductivities, discussed in sec. I1.4.8a. In that case, flg. 3.26 is modified in that panel (b) describes G°, panel (c) G " and jianel (d) the sum, with - tan 0 = G" /G. ... 

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... 

For an air/liquid system a measure of the surface-tension variation resulting from the imposed periodic area variation in the Langmuir trough is performed. If both dilational viscous = (f) and dilational elastic j = e (f) data are needed, and if a Langmuir-type trough is used, then one barrier can be oscillated and another barrier can be used to adjust the extent of the interfacial area. The calculation of the complex modulus, , requires complete scans at different frequencies. 

The aim of this chapter is to investigate the effects of MR on the air/ water interfacial properties (interfacial dilatational complex modulus and interfacial pressure) of lysozyme comparing with effect on its foam formation ability (volume, multiplicity, stability of foams). 

This is a measurement of the resistance that an interface shows to the creation of new regions with higher surface tensions (higher surface area). In a more general case, the response of the interface would have also a viscous response due to relaxation phenomena at the interface. In the case of a sinusoidal perturbation to the interfacial area of frequency v (v = 2nco) and small amplitude, the response of the interface is a complex magnitude the dilatational elastic modulus. 

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