Correlation between elastic modulus values

Figure 6. Correlation between elastic modulus values obtained in compression mode (x-axis) and retracing mode (y- axis).

To determine the crosslinking density from the equilibrium elastic modulus, Eq. (3.5) or some of its modifications are used. For example, this analysis has been performed for the PA Am-based hydrogels, both neutral [18] and polyelectrolyte [19,22,42,120,121]. For gels obtained by free-radical copolymerization, the network densities determined experimentally have been correlated with values calculated from the initial concentration of crosslinker. Figure 1 shows that the experimental molecular weight between crosslinks considerably exceeds the expected value in a wide range of monomer and crosslinker concentrations. These results as well as other data [19, 22, 42] point to various imperfections of the PAAm network structure. 

Wilkes and Emerson (97) studied the time-dependent behavior of a polyester polyurethane (MDI-BD based 40% hard segment) which was heated to 160°C for 5 min, then rapidly quenched to room temperature. To monitor changes in phase separation, SAXS intensity values (at a fixed angle) were recorded as a function of time. Furthermore, the elastic modulus and soft-segment Tg were followed with time. The results, shown in Figure 14, reveal an approximately exponential decay toward equilibrium with a good correlation between properties (Tg and modulus) and structure (inferred by SAXS intensities). 

In conclusion, it can be said that the theory can well describe the development of the gel structure. The correlation between the equilibrium modulus and sol fraction is very good so that the sol fraction can alternatively be used for determination of the concentration of EANC s if an accurate and precise determination of conversion meets with difficulties. It is to be recalled here that the Gaussian rubber elasticity theory does not apply to highly crosslinked networks of usual stoidiiometric systems. When a good theory is available, the calculated value of taking possibly into account the topological limit of the reaction will be ne ed. 

For more concentrated suspensions, other parameters should be taken into consideration, such as the bulk (elastic) modulus. Clearly, the stress exerted by the particles depends not only on the particle size but on the density difference between the partide and the medium. Many suspension concentrates have particles with radii up to 10 pm and a density difference of more than 1 g cm . However, the stress exerted by such partides will seldom exceed 10 Pa and most polymer solutions will reach their limiting viscosity value at higher stresses than this. Thus, in most cases the correlation between setfling velocity and zero shear viscosity is justified, at least for relatively dilute systems. For more concentrated suspensions, an elastic network is produced in the system which encompasses the suspension particles as well as the polymer chains. Here, settling of individual partides may be prevented. However, in this case the elastic network may collapse under its own weight and some liquid be squeezed out from between the partides. This is manifested in a dear liquid layer at the top of the suspension, a phenomenon usually... 

Scanning force microscopy (SFM) was used for probing micromechanical properties of polymeric materials. Classic models of elastic contacts, Sneddon s, Hertzian, and JKR, were tested for polyisoprene rubbers, polyurethanes, polystyrene, and polyvinylchloride. Applicability of commercial cantilevers is analyzed and presented as a convenient plot for quick evaluation of optimal spring constants. We demonstrate that both Sneddon s and Hertzian elastic models gave consistent and reliable results, which are close to JKR solution. For all polymeric materials studied, correlation is observed between absolute values of elastic moduli determined by SFM and measured for bulk materials. For rubber, we obtained similar elastic modulus from tensile and compression SFM measurements. 

The bulk modulus of elasticity Eg is used since the thin test sample is well-supported laterally, thus approaching the condition of hydrostatic compression. An apparent problem arises here in that this modulus is not one of the controlled test parameters, and further, its effective value at the extremely high strain rates (as much as 400,000 /sec) is unknown. However, since the result sought is the statistical probability of reaction based on the experimental incidence rate for the material, whichreflects the effect of the modulus, whatever it may be, it turns out not to be a problem because the relative controllable test parameters alone are sufficient to determine the statistical correlation between laboratory results and field application as shown later in this paper. 

The relation adduced in Figure 5.15 between the probability of the formation of frame bonds T and the spectral dimension d assumes a certain correlation d and the mechanical properties of epoxy polymers, particularly the elasticity modulus. In Figure 6.5 the dependence of the elasticity modulus E at compression on the value d is adduced, which confirms this supposition. According to the data of Figure 6.5 the greatest value of E for the studied epoxy polymers can be estimated, which is equal to 5 GPa at the maximum value d = 1.73 [31]. 

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