## 4 Theoretical
\begin{split} E=E_{g}\Big{[}1-\Big{(}\frac{1}{C_{2}}-\frac{1}{T_{g}} \Big{)}\big{(}T-T_{g}\big{)}+\frac{1}{C_{2}}\Big{(}\frac{1}{C_{2}}-\frac{1}{T_{ g}}\Big{)}\big{(}T-T_{g}\big{)}^{2}\Big{]}\\ =E_{g}\Big{\{}1-\Big{(}\frac{1}{C_{2}}-\frac{1}{T_{g}}\Big{)}\big{(}T-T_{ g}\Big{)}\Big{(}1-\frac{1}{C_{2}}\Big{)}\big{(}T-T_{g}\big{)}\Big{\}}\end{split}  \tag{22}\]  
The following assumption holds: in a given series, it is possible to limit ourselves to only the linear term if it is much larger than the next one. This is possible if the following condition is met:  
\[\big{(}T-T_{g}\big{)}<<C_{2} \tag{23}\]  
Thus, based on three known quantities (\(C_{l}\), \(C_{2}\), and \(T_{g}\)), and using Equations (12), (18), and (22), it is possible to calculate the dependence of the activation energy of viscous flow on the temperature in the temperature range (2). Table 2 contains the coefficients \(D_{1}\) and \(D_{2}\) for the chalcogenide glasses analyzed, which are compared with the characteristics of the activation energy \(E(T)\) versus \((T-T_{g})\) plots obtained directly from the experimentally known temperature dependence of viscosity [20; 21; 22; 23; 24; 25]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**\(\mathbf{\mathsf{M}}\)**} & \multirow{3}{*}{**Composition, mol.\%**} & \multicolumn{6}{c}{**Calculated Using (17) and (21)**} & \multicolumn{6}{c}{**Polynomial of 2 nd Degree**} & \multicolumn{6}{c}{**Polynomial of 3 rd Degree**} \\ \cline{3-11}  & & & \(D_{1}\) & \(D_{2}\) & \(D_{1}\) & \(D_{2}\) & \(\mathbf{R^{2}}\) & \(D_{1}\) & \(D_{2}\) & \(\mathbf{R^{2}}\) \\ \cline{2-11}  & **Sb** & **Ge** & **Se** & & & & & & & & \\ \hline
1. & 5 & 10 & 85 & 0.135 & 0.0007 & 0.446 & 0.0013 & 0.995 & 0.261 & 0.0030 & 0.998 \\
2. & 10 & 10 & 80 & 0.280 & 0.0023 & 0.372 & 0.0050 & 0.998 & 0.293 & 0.0019 & 0.995 \\
3. & 5 & 15 & 80 & 0.225 & 0.0016 & 0.361 & 0.0010 & 0.998 & 0.316 & 0.0052 & 0.995 \\
4. & 15 & 10 & 75 & 0.256 & 0.0020 & 0.554 & 0.0022 & 0.995 & 0.399 & 0.0012 & 0.999 \\
5. & 10 & 15 & 75 & 0.141 & 0.0006 & 0.310 & 0.0018 & 0.998 & 0.213 & 0.0024 & 0.999 \\
6. & 20 & 10 & 70 & 0.394 & 0.0045 & 0.529 & 0.0021 & 0.998 & 0.524 & 0.0003 & 0.999 \\
7. & 15 & 15 & 70 & 0.313 & 0.0027 & 0.447 & 0.0013 & 0.995 & 0.324 & 0.0017 & 0.999 \\
8. & 10 & 20 & 70 & 0.409 & 0.0048 & 0.326 & 0.0070 & 0.998 & 0.291 & 0.0001 & 0.993 \\
9. & 20 & 15 & 65 & 0.575 & 0.0087 & 0.482 & 0.0014 & 0.991 & 0.358 & 0.0031 & 0.997 \\ \hline \multicolumn{11}{c}{} & \multicolumn{2}{c}{Ge} & \multicolumn{2}{c}{Se} & \multicolumn{6}{c}{Se} & \multicolumn{6}{c}{Se} & \multicolumn{6}{c}{Se} \\ \hline
1. & 8 & 92 & 0.380 & 0.0046 & 0.514 & 0.0001 & 0.988 & 0.779 & 0.0063 & 0.998 \\
2. & 10 & 90 & 0.496 & 0.0004 & 0.547 & 0.0015 & 0.998 & 0.651 & 0.0029 & 0.999 \\
3. & 15 & 85 & 0.135 & 0.0006 & 0.342 The parameters of the function \(E(T)\) versus \((T-T_{g})\) expressed as a polynomial of the second degree were calculated using the Microsoft Excel spreadsheet software, with results shown in Figures 5-7, where the dots indicate the dependence of the activation energy on the temperature difference, obtained according to Formula (1) using experimental data from [20; 21; 22; 23; 24; 25]. In a sufficiently large temperature range, however, the contribution of the third-degree term in the Taylor series may increase, which affects the estimate of the effective value of \(D_{2}\). In this regard, in the calculations of the required energy, a polynomial was used to the appropriate extent. Nevertheless, taking into account the application of this assumption, the data obtained turned out to conform well with the experiment. Thus, we conclude that the temperature dependence of the activation energy in a wide temperature range for chalcogenide glasses Ge-Se, As-Se, P-Se, As-Se-Tl-Se, and As-Se  
Figure 5: Results of processing the temperature dependence of the activation energy of viscous flow for As-Se molten glass. The content of As is 3 mol.%, Se—97 mol.%. Points and experimental data taken from [20], curve polynomials.