We address three problems that limit the use of the atomic force microscope when measuring elastic moduli of soft materials at microscopic scales. The first concerns the use of sharp cantilever tips, which typically induce local strains that far exceed the linear material regime. We show that this problem can be alleviated by using microspheres as probes, and we establish the criteria for their use. The second relates to the common use of the Hertz contact mechanics model, which leads to significant errors when applied to thin samples. We develop novel, simple to use corrections to apply for such cases. Samples that are either bonded or not bonded to a rigid substrate are considered. The third problem concerns the difficulty in establishing when contact occurs on a soft material. We obtain error estimates for the elastic modulus resulting from such uncertainty and discuss the sensitivity of the estimation methods to error in contact point. The theoretical and experimental results are compared to macroscopic measurements on poly(vinyl-alcohol) gels.

The swelling behavior of fully neutralized sodium polyacrylate gels was investigated in aqueous solutions of alkali metal (LiCl, NaCl, KCl, CsCl) and alkaline earth metal salts (CaCl2, SrCl2, BaCl2). The total salt concentration and the ratio of monovalent to divalent cations were varied in the biologically significant range. It is found that the concentrations of both monovalent and divalent cations vary continuously and smoothly in the gel despite the abrupt change in the gel volume. The individual elastic, mixing, and ionic contributions to the free energy of the gel were separately determined as a function of the degree of network swelling to elucidate the thermodynamics of swelling. Shear modulus measurements performed at different Ca2+ concentrations suggest that Ca2+ does not form stable cross-links between the polymer chains. At low and moderate swelling ratios the concentration dependence of the shear modulus follows a power law behavior, G variation of phi n, with n = 0.34 +/- 0.03. At high swelling degrees, however, the shear modulus increases with increasing swelling. The value of the Flory-Huggins interaction parameter, chi, determined from osmotic swelling pressure and shear modulus measurements, strongly depends on the ionic composition of the equilibrium solution and increases with increasing Ca2+ concentration.

No abstract