Modulus of gel

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

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]... 

G = shear modulus of gel f = friction factor between network and solvent. 

Oakenfull, D. G., Parker, N. S., and Tanner, R. I. 1989, Method for determining absolute shear modulus of gels from compression tests. J. Texture Stud. 19 407-417. 

Polymer gels are diluted polymer networks. The diluent can be other polymer chains or solvent. The modulus of gels decreases on dilution, in ways that depend on the details of the polymer-solvent interaction. When immersed in an excess of an appropriate solvent, polymer networks can often swell considerably. The swelling is driven by the favorable free energy... 

Dynamic oscillatory methods may also be employed to provide information concerning both the structure and modulus of gel systems. This information may then be usefully employed in the development of formulations that will offer optimal clinical and nonclinical (e.g., stability) performance. Examples of these aspects are provided in the following subsection. 

Figure 9. Values of shear modulus of gels of wood cellulose microcrystals Log-log plot. Line drawn to fit dataf has slope of 3.6 (11)...

Stress relaxaticm experiments at romn temperature showed almost irubber elastic behaviour (Fig. 145), at least up to 200 min the slopes, d(logo)/ d(logt), vary from —0.01 to —0.03. The compression modulus of the gds is constant up to the temperature of the monotectic transition. Above that temperature gels with c < Cm become liquid-like, whilst the compre on modulus of gels with c> Cm gradually decreases this decrease is faster if the concentration is lower. In the case of gels in 1-phenyldodecane this dependence is less clear. 

Clark and Ross-Murphy [1,487] calculated the concentration dependence of the equilibrium shear modulus of gels by making use of Hermans treatment [488], in which the a ociation of primary chains is described by a monomer-dimer equilibrium. The crosslinks ate treated as dimer interactions and, hence, their functionality is 4. From that consideration they were aUe to calculate the equilibrium shear modulus as a function of the reduced concentration, Le. c/Po, where c is the minimal concentration needed for network formation. 

The osmotic response of swollen polymeric networks was studied on the basis of the scaling theory by Horkay et al. [17-19,22,23,133]. They measured both the swelling pressure, CO, and the shear modulus of gels, G, at different stages of dilution. The swelling pressure vs. polymer volume fraction data were analyzed according to the equation [22]... 

Figure 4.7 Modulus of gels of gellan gum in the presence of varying concentrations of calcium (squares), sodium (triangles) and potassium (circles) ions (adapted from Ref. 21 ).

Figures 6-4 and 6-5 present the change of Vickers hardness and Young s modulus of Gel No. 2 in Table 6-5 respectively, with heating temperature (Adachi and Sakka, 1990). It is seen that above 900°C both Vickers hardness and Young s modulus rapidly increase. These rapid increases correspond to the rapid increase of bulk density, as shown in Figure 6-2. The hardness increases from 4 to 780 kg/mm for the value of fused silica glass. Young s...

Figure 6-5. Change of Young s modulus of Gel No. 2 in Table 6-5 as a fnction of heating...

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