Correlation between elastic moduli from

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. 

The correlation between z2/d4 and the elastic modulus, c44, for various AB compounds with a NaCI structure. Data from J. J. Gilman, Progress in Ceramic Science 1 (1961) 146-94. 

Figure 13.6 Examples of correlation between responses from different scales when the interfacial modifier is changed Left, tensile strength at break point (up) and relative crystalline variation for the polypropylene matrix (down) versus the grafting level in the interfacial modifier right, elastic moduli (tensile/DMA) ratio (up) and components of the complex modulus from DMA tests (down) versus the grafting level in the interfacial modifier. (From References 32 and 55 with permission of John Wiley Sons, Inc. and Elsevier, respectively.)...

It has been shown that the elastic recovery in drawn HDPE can be a sensitive measure for the efficiency of draw (11,12). The correlations between this property and morphology (14) and tensile modulus (11) have been discussed. Thus, we measured thermally induced elastic recovery for each sample portion separated from the characteristic deformation components in the low and the high MW HDPE extruded at 90 and 110°C to EDR 12 and 25. When a drawn specimen was immersed and freely floated in a silicon oil bath kept at 160 C, the elastic shrinkage quickly occurred and completed within a few seconds. The shrinkage was evaluated in terms of % recovery (R) and molecular draw ratio (MDR) defined previously (11,12). 

The deformation ability of networks strongly swollen with benzene and those slightly swollen in cyclohexane was unexpectedly found to be the same. What is surprising here is the absence of any correlation between the volume increase of model networks on swelling and their deformation under compression or elongation [130], as it would have to foUow from the classic theory of rubber elasticity. This theory does not predict any difference between the extensional modulus and the shear modulus that controls the swelling. Nevertheless, the experimental ratio of Ce(CH)/ Ce(BZ) = 6 is twice as large as the ratio of E(CH)/E(BZ) = 3 (irrespective ofp) [123]. 

Fig. 19. Correlation between the critical strain for crazing, and the product of the cohesive energy density (CED), the difference between the test temperature and the glass-transition temperature AT, and the elastic modulus E. Reprinted from Ref. 129, with permission from Elsevier.

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... 

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