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Phase behaviors of agarose gel
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33. The references of the experimental studies on the critical elasticity of the gel are listed in the references 13,17.
34. In references 13,17, the exponents are determined in the dilute regions of agarose solutions, c.a., below 0.25 g/100 ml. The spinodal decomposition of the solution does not influence the value of these exponents because the spinodal temperature of the system in these concentration region becomes much lower than the room temperature as shown in Figure 1.
35. Phase Transitions, Cargese 1980, Nato Advanced Study Institute Series, Series B: Physics, Vol 72 (Eds., M. Levy, J. C. Le Guillou, and J. Zinn-Justin) (Plenum Press, 1982).
36. R. Houwink, Elasticity, Plasticity and Structure of Matter (Cambridge University Press, 1937), p. 70. See also the 3rd edition of the book of the same title that is edited by R. Houwink and H. K. de Decker, (Cambridge University Press 1971), p. 186.
37. T. Nakagawa, Rheology (in Japanese) (Iwanami, 1978).
38.In above references 36,37, the elastic modulus of the porous material that consists of the aggregated structure of the cells of thin wall is calculated as a function of the ratio L0/L where L0 is the typical size of the cell and L the thickness of the wall. The elastic modulus of the whole system, γ, is written as follows. Here, γ0 is the elastic modulus of the bulk material that consists the wall. If the typical size of the system is L0/L = 10, the elastic modulus of the whole system becomes 2.5 × 10−2 of the elastic modulus of the wall material itself. Of course, the elastic modulus of the whole system is also influenced strongly whether the structure of the cell is open or close.
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We present evidence for the existence of phase separation in the gel state of agarose having the mixture of water and methanol as the gel solvent. Firstly, the sol-gel transition line and the cloud point line are determined independently as a function of the concentration of agarose as well as the concentration of methanol in the mixed solvent by the quasi-equilibrium cooling of the solutions. Then the spinodal line is determined by quenching the solutions below the sol-gel transition line. We find that the spinodal line appears below the cloud point line and both lines are entirely buried below the sol-gel transition line in the aqueous agarose system. The concentration fluctuations are, therefore, frozen into the polymer network of agarose gel that promotes the opacity of the resultant gel. The structure of agarose gel is observed by the confocal laser scanning microscope (CLSM) imaging technique that reveals that the density fluctuations are grown up to micrometer scale in space. The phase separation boundary is found to shift to the higher temperature region than the sol-gel transition line when the concentration of methanol in the mixed solvent is increased. The results indicate that the position of the phase separation boundary in relative to the sol-gel transition line varies with the quality of solvent. These results are in agreement with the theory of the sol-gel transition in which both the divergence of the connectivity and the thermodynamic instability are taken into account.
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