Correlation between elastic moduli from values

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. 

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. 

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... 

The microhardness technique is used when the specimen size is small or when a spatial map of the mechanical properties of the material within the micron range is required. Forces of 0.05-2 N are usually applied, yielding indentation depths in the micron range. While microhardness determined from the residual indentation is associated with the permanent plastic deformation induced in the material (see section on Basic Aspects of Indentation), microindentation testing can also provide information about the elastic properties. Indeed, the hardness to Young s modulus ratio HIE has been shown to be directly proportional to the relative depth recovery of the impression in ceramics and metals (2). Moreover, a correlation between the impression dimensions of a rhombus-based pyramidal indentation and the HIE ratio has been found for a wide variety of isotropic poljuneric materials (3). In oriented polymers, the extent of elastic recovery of the imprint along the fiber axis has been correlated to Young s modulus values (4). 

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