Elastic modulus of gels

The methods for measuring the elastic modulus of gels are reviewed in Ref. 

The effect of oxidative irradiation on mechanical properties on the foams of E-plastomers has been investigated. In this study, stress relaxation and dynamic rheological experiments are used to probe the effects of oxidative irradiation on the stmcture and final properties of these polymeric foams. Experiments conducted on irradiated E-plastomer (octene comonomer) foams of two different densities reveal significantly different behavior. Gamma irradiation of the lighter foam causes stmctural degradation due to chain scission reactions. This is manifested in faster stress-relaxation rates and lower values of elastic modulus and gel fraction in the irradiated samples. The incorporation of O2 into the polymer backbone, verified by IR analysis, conftrms the hypothesis of... 

Polarization in the point dipole model occurs not at the surface of the particle but within it. If dipoles form in particles, an interaction between dipoles occurs more or less even if they are in a solid-like matrix [48], The interaction becomes strong as the dipoles come close to each other. When the particles contact each other along the applied electric field, the interaction reaches a maximum. A balance between the particle interaction and the elastic modulus of the solid matrix is important for the ER effect to transpire. If the elastic modulus of the solid-like matrix is larger than the sum of the interactions of the particles, the ER effect may not be observed macroscopically. Therefore, the matrix should be a soft material such as gels or elastomers to produce the ER effect. 

From the experimental results, the ER effect in polymer gels is explained as follows (Fig. 8). When an electric field is applied, the particles electrically bind together and cannot slip past each other. Larger shear forces are needed in the presence of an electric field. Thus, the electric field apparently enhances the elastic modulus of the composite gel. The difference in ER effects between an oil and a gel is that the polarized particles necessarily cannot move between the electrodes to produce the ER effect in a gel. In order for the ER effect to occur, it is important to form migration paths before application of an electric field. 

The elastic modulus of laminated composite plate in which an ER silicone gel of carbonaceous particles is sandwiched between two PVC sheets also changed under the influence of an electric field. It was found that an electric field of 1.17 kV/mm caused a gain in the elastic modulus of the gel of 13% [57]. 

Such control over the mechanical strength of the supramolecular gel network is of particular interest for applications in cell culture, particularly in stem cell research because the elastic modulus of cell substrates has been found to dictate the differentiation pathways chosen by mesenchymal stem cells [57]. 

Three common methods of measuring crosslinking (swelling, elastic modulus, and gel point measurements) have recently been critically appraised by Dole (14). A fourth method using a plot of sol + sol against the reciprocal dose has also been used extensively. However, Lyons (23) has pointed out that this relation, even for polyethylenes of closely random distribution, does not have the rectilinear form required by the statistical theory of crosslinking. Flory (19) pointed out many years ago that the extensibility of a crosslinked elastomer should vary as the square root of the distance between crosslinks. More recently Case (4, 5) has calculated that the extensibility of an elastomer is given by ... 

Here pg and p f are the mass densities of the gel and the solvent, respectively, K is a bulk modulus, c0 is the speed of sound, and i s is the solvent shear viscosity. The solvent bulk viscosity has been neglected. The terms proportional to / arise from an elastic coupling in the free energy between the density deviation of gel and that of solvent The p in Eq. (6.1) coincides with the shear modulus of gels treated so far. We neglect the frequency-dependence of the elastic moduli. It can be important in dynamic light scattering, however, as will be discussed in the next section. 

The results obtained by the present mechanical measurements are also consistent with the previous experimental results of the dynamic light scattering studies of the collective diffusion coefficient of gels and the rheological studies of the shear modulus of gels. The studies published by different researchers indicate that the concentration dependence of the collective diffusion constant of the polymer networks of gel and that of the elastic modulus are well represented by the following power law relationships [2, 3, 5]... 

The reduced modulus Gr is defined as the ratio of the elastic modulus of the gel at a given degree of swelling Qv = l/v 2 to that one of the same gel after its preparation. Gr is given for a network of Gaussian chains by (Flory 1953)... 

The properties of the curdlan gel have been shown to be intermediate between those of the elastic gelatin gel and the brittle agar gel. The relationship between the breaking strength and the elastic modulus of agar, curdlan, and gelatin is shown in Figure 9. 

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