Mechanism and quantitative study of specific heat change during glass transition of amorphous polystyrene and Pd<sub>40</sub>Ni<sub>10</sub>Cu<sub>30</sub>P<sub>20</sub>

Abstract

<sec>The nature of glass transition is one of the most interesting problems in modern condensed matter physics. There is a theory that shows that when the particle's diffusion motion probability <i>P</i> is less than <inline-formula><tex-math id="M2">\begin{document}$ {{\rm{e}}^{ - 2{{\rm{e}}^3}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200331_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200331_M2.png"/></alternatives></inline-formula>, the proportion of particles whose diffusion motion is frozen is not less than 1 + 2e<sup>3</sup>/ln<i>P</i>. Based on the modulus temperature formula of this theory and the experimental modulus-temperature curve of polystyrene in the literature, the free volume expansion coefficient of polystyrene is determined to be in a range of 0.00045－0.00052. </sec><sec>In this paper, we first quantitatively study the specific heat temperature relationship in the glass transition of polystyrene. Based on this theory, the specific heat-temperature formula in the glass transition region is derived. The material in the glass transition region is a mixture of rubber and glass, and this two-component (rubber and glass) system’s total specific heat is the product of the specific heat of the rubber and the percentage of rubber in the two-component system plus the product of the specific heat of the glass and the percentage of glass in the two-component system. Let <i>b</i> be the number of atoms in the main chain of the segment, then the proportion of rubber will be the <i>b</i>-th power of free volume fraction. This specific heat-temperature formula with polystyrene is tested. By substituting the obtained free volume expansion coefficient of the polystyrene into the specific heat-temperature formula, the resulting formula can accurately and quantitatively describe the specific heat-temperature relationship in the glass transition of polystyrene without fitting any parameters. </sec><sec>In this paper, we also study the change of motion in the glass transition of polystyrene. According to the analysis, the glass transition process of polystyrene is a process in which the diffusion movement of the main chain atoms is activated or frozen, which is consistent with the conclusions of relevant research on amorphous alloys. When the main chain atom is used as the molar unit of measurement, the specific heat change in the glass transition of polystyrene is 1.61<i>R</i> (<i>R</i> is the gas constant), which is consistent with the law, i.e. “the specific heat change in the glass transition of the amorphous alloy is about 1.5<i>R</i>”. These consistent conclusions predict that the glass transitions of amorphous alloys and glass transitions of polystyrene have the same essence. Based on this idea, the specific heat temperature formulas of the amorphous alloy Pd<sub>40</sub>Ni<sub>10</sub>Cu<sub>30</sub>P<sub>20</sub> and polystyrene are verified and prove to be consistent.</sec>