Mathematical Characterization of Thermo-reversible Phase Transitions of Agarose Gels
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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 T-m 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 T-0 of sol-gel and gel-sol transitions in terms of the horizontal shift in the sigmoidal transition curve. For the gel-sol transition (heating) T-0 is greater than T-m i.e. later in time and the difference between T-0 and T-m is reduced as the agarose content increases. For the sol-gel transition (cooling) T-0 is again greater than T-m but it is earlier in time for all agarose contents and moves forward in time and gets closer to T-m as the agarose content increases.