Dilational loss modulus

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).

Keywords Monolayers Surface light scattering Capillary waves Dispersion equation Dilational elastic modulus Dilational loss modulus Scaling exponent... 

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). 

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. 

A torsion pendulum apparatus was used to get information about the shear rheological properties of the surfactants at the interface. This sensitive instrument was not capable of detecting significant elastic or viscous properties except for Lecithine. The analysis provided data that indicated a low viscous resistance for Lecithine with an interfacial shear loss modulus of about 0.03 mN/m. Hence, we can conclude, that no network-like superstructures were formed, and that the large dilatational elastic response was mainly caused by Gibbs- and Marangoni-effects. 

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. ... 

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. 

The two basic types of mechanical deformation, from a physical and molecular standpoint, are shear and dilatation. The experimental methods described in the preceding three chapters yield information primarily about shear only in extension measurements on hard solids does a perceptible volume change influence the results. By combining shear and extension measurements, the bulk properties can be calculated by difference, as for example in creep by equation 55 of Chapter 1, but the subtraction is unfavorable for achieving a precise result. Alternatively, bulk properties can be measured directly, or they can be obtained by combining data on shear and bulk longitudinal def ormations (corresponding to the modulus M discussed in Chapter 1), where the subtraction does not involve such a loss of precision. Methods for such measurements will now be described. They have been reviewed in more detail by Marvin and McKinney. ... 

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