Mathematical Characterization of Thermo-reversible Phase Transitions of Agarose Gels

The thermal phase transition temperatures of high (HMP) and low melting point (LMP) agarose gels were investigated by using UV–vis spectroscopy techniques. Transmitted light intensities from the gel samples with different agarose concentrations were monitored during the heating (gel-sol) and cooling (sol–gel) processes. It was observed that the transition temperatures, Tm, defined as the location of the maximum of the first derivative of the sigmoidal transition paths obtained from the UV–vis technique, slightly increased by increasing the agarose concentration in both the HMP and LMP samples. Here, we express the phase transitions of the agar-water system, as a representative of reversible physical gels, in terms of a modified Susceptible-Infected-Susceptible epidemic model whose solutions are the well-known 5-point sigmoidal curves. The gel point is hard to determine experimentally and various computational techniques are used for its characterization. Based on previous work, we locate the gel point, T0, of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating), T0 is greater than Tm, i.e. later in time, and the difference between T0 and Tm is reduced as the agarose content increases. For the sol-gel transition (cooling), T0 is again greater than Tm, but it is earlier in time for all agarose contents and moves forward in time and gets closer to Tm as the agarose content increases.