Scaling analysis on elasticity of agarose gel near the sol–gel transition temperature

Abstract

The elastic shear modulus G′ of gel and the correlation length ξ were, respectively, described by G′∝ϵ t (1) ξ∝ϵ −ν (2) where ϵ is the deviation from sol–gel transition point ( ϵ=| P− Pc| in percolation; P: percolation probability, Pc: percolation threshold), t is the critical exponent of the elastic shear modulus and ν is the critical exponent of the correlation length. We experimentally evaluated not only the elastic modulus of a sol–gel transition system but also the correlation length, since the critical exponent t is related to spatial dimension and the critical exponent of correlation length, depending on the characteristics of elasticity. We could determine the correlation length of agarose gel by the dynamic light scattering method. The temperature dependence of the elasticity of agarose gel was evaluated by the ellipticity as the percolation parameters. The correlation length also diverged when the ellipticity approached the sol–gel transition point. The logarithm of the correlation length was a linear function of the logarithm of the deviation in ellipticity from the sol–gel transition point. The critical exponent of the elastic modulus was described by the scaling law ( t=1+ ν( d−2); d: spatial dimension), which De Gennes drew on the basis of the scalar elasticity neglecting the bending deformation for a network chain. This suggests that agarose fibers are stiff enough to show the scalar elasticity.