Dilatational elastic modulus

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

A second more detailed type of investigation is the determination of the dilational elastic modulus at a given frequency during the adsorption process. This allows us to determine the variation of e with the surface pressure. 

We have also measured y(t) and e(t) during polymer adsorption for a given concentration. In Figure 6, the e-n curve, the equation state of the layer during the adsorption process, is presented. At low surface pressure, one observes a linear increase of the dilational elastic modulus with the surface pressure n. From the slope of the linear part of the e-n curve, a value of 0.66 was found for the excluded volume critical exponent. The same value has been measured elsewhere with another technique.12 This result indicates that, unlike the excluded volume chain behaviour in the bulk, the air water interface is not a good solvent for MeC. At intermediate surface pressures, the modulus levels off and then increases again until the equilibrium surface pressure is reached. 

MeC adsorbs at the air water interface leading to a decrease in the surface tension. An equilibrium state is only reached at very long times, due to the high molecular mass of methylcellulose. The layer which is present at the interface at equilibrium is almost purely elastic with a large dilational elastic modulus. The value of the excluded volume critical exponent extracted from the E-n curve indicates that the air-water interface is not a good solvent for the polymer. 

The curves have a typical shape with a maximum at a certain concentration which corresponds to a surface concentration of about 50% of the maximum surface coverage. The maximum is caused by the competitive effect of two phenomena increase of the dilational elasticity modulus Eq with concentration and increase of the exchange of matter with increasing concentration, diminishing the effective elasticity. 

Fig. 6.13 Dilational elasticity modulus of n-dodecyl dimethyl phosphine oxide determined for oscillating bubble experiments ( ), and calculated from the adsorption isotherm ( ) according to Wantke etal.(1993)...

Dilational elasticity modulus of Triton X-lOO solutions at the water/dodecane interface determined from longitudinal wave damping according to Bonfillon Langevin (1993)... 

Fig. 6.17 Dilational elasticity modulus determined from longitudinal wave damping experiments,BSA(B), lysozyme(D) according to Graham Phillips (19S0a)...

While the tilt is a measure of the dilational elasticity, the thickness is proportional to the exchange of matter rate, sometimes named dilational viscosity. The ellipse thickness corresponds to the phase shift between the generated area oscillation and the surface tension response. With increasing frequencies the thickness decreases while the tilt angle increases up to a final value of representing the dilational elasticity modulus So. 

This is the dilational elastic modulus or the interfacial tension gradient which is in phase with the area change. 

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. 

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. 

The dilatational elastic modulus contains important structural information about adsorbed interfacial layers (Benjamins et al., 2006 Maldonado-Valderrama et al., 2005a). Moreover, the elastic... 

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