Modulus of dilatation

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). 

When a craze occurs around a rubber droplet the droplet is stressed not only in a direction parallel to the applied stress but also in the plane of the craze perpendicular to the applied stress (see Figure 3.9). Such a triaxial stress leading to dilation of the particle would be resisted by the high bulk modulus of the rubber, which would thus become load bearing. The fracture initiation stress of a polyblend should not therefore be substantially different from that of a glass. 

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).

Poisson s61 ratio a is the change in length per unit length, usually the contraction in one direction due to the dilatation in the perpendicular direction (for isotropic elastic bodies, —1.0 < a < + 0.5). Young s62 modulus Y, also called the linear modulus of elasticity, is the 3x3 tensor of the stress P divided by the strain s ... 

Figure 17.9 Variation of the storage relaxation modulus E, with temperature measured during a heating experiment. Ep represents the actual value of the storage relaxation modulus in absence of dilatational forces which reduce the longitudinal tension.

Figure 3.48. Dilational modulus of bovine serum albumin and ovalbumin monolayers. (Courtesy of J. Benjamins).

What value of a corresponds to the double reptation model In Section 9.3, we have presented theoretical arguments and experimental data supporting the value a =4/3 in -solvents (and melts with ideal chain statistics). What is the expression of the stress relaxation modulus of tube dilation models corresponding to a = 4/3 ... 

In Figure 14.3c a normalization in a single master curve of E vs. tt data reflects the interfacial behavior of emulsifier adsorbed films for different emulsifier concentrations, at different adsorption times, and under different processing conditions (Nino and Patino, 2002 Nino et al., 2003). The plot suggests that interactions between adsorbed emulsifier molecules (residues) increase with tt. In fact, at lower tt values the slope of the -tt plot was close to 1, which corresponds to the behavior of an ideal gas with low emulsifier interactions. However, at higher tt values the slope changes, which implies an important nonideal behavior with higher molecular interactions as the amount of emulsifier at the interface increases. These data indicate that the interfacial activity and the surface dilatational modulus of emulsifier films are mainly a result of the amount of adsorbed emulsifier. 

It is generally agreed that thermally induced vibrations of atoms in solids play a major role in melting [2.144]. The simple vibrational model of Linde-mann predicts a lattice instability when the root-mean-square amplitude of the thermal vibrations reaches a certain fraction / of the next neighbor distances. However, the Lindemann constant/varies considerably for different substances because lattice anharmonicity and soft modes are not considered, thus limiting the predictive power of such a law. Furthermore, Born proposed the collapse of the crystal lattice to occur when one of the effective elastic shear moduli vanishes [2.138], Experimentally, it is found instead that the shear modulus as a function of dilatation is not reduced to zero at Tm and would vanish at temperatures far above Tm for a wide range of different substances [2.145]... 

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...

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)... 

Figure 7. Dilatational modulus of C12AOS, C14AOS, and CJ6AOS solutions at 3.16 x lCr2 M + 1 % NaCl concentration as a function of the bubbling frequency. (Reproduced from reference 22 Copyright 1986 American Chemical Society.)...

Flow resistance of foams is much higher than that of the liquid or gas phases alone. This characteristic is utilized for foam-based mobility control in enhanced oil recovery (41—46). The gas mobility in porous medium and the dilatational modulus of a-olefin sulfonates are plotted in Figure 12 (22). The displacement efficiency of the foam in the porous medium is higher if the blocking efficiency of the foam is higher. In the systems... 

In the case of dilatant cracks we have the two equations for the Young modulus = 2(1 -I- v)G and the Poisson coefficient ... 

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)... 

Unit weight/ Modulus of Compression Poisson s Cohesion/ Dilatancy Internal friction... 

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