# Evaluation of Changes in Structure of Modified Cement Composite Using Fractal Analysis
## 3 Results and Discussion
\begin{table}
\begin{tabular}{l c c c c} \hline \hline  & **Microstructure** & **AA** & **AB** & **BA** & **BB** \\ \hline  & **Status Function** & **Deterministic** & **Deterministic** & **Deterministic** & **Deterministic** \\ \hline H & 13.07 & 10.22 & 10.3 & 10.33 \\ \hline H\({}_{\rm max}\) & 18.92 & 14.8 & 14.91 & 14.95 \\ \hline H\({}^{*}\) & 10.43 & 8.49 & 10.22 & 8.52 \\ \hline S = H\({}^{*}\)/H\({}_{\rm max}\) & 0.55 & 0.57 & 0.69 & 0.57 \\ \hline \(\Delta\)H = H\({}_{\rm max}-\) H\({}^{*}\) & 8.49 & 6.31 & 4.69 & 6.43 \\ \hline R = 1 \(-\) S & 0.45 & 0.43 & 0.31 & 0.43 \\ \hline Transmitted information & 0.42 & 0.3 & 0.5 & 0.3 \\ \hline New information & 0.58 & 0.7 & 0.5 & 0.7 \\ \(\rm H_{new}/H^{*}\) & 2.64 & 1.73 & 0.08 & 1.81 \\ \hline \(\rm D_{leguli}\) & 0.89209 & 0.87534 & 0.8753 & 0.8805 \\ \hline D\({}_{\rm Inon-equil}\) & 0.83098 & 0.83175 & 0.83473 & 0.83609 \\ \hline K = exp(H) & \(4.7\times 10^{5}\) & \(2.7\times 10^{4}\) & \(2.94\times 10^{4}\) & \(3.1\times 10^{4}\) \\ \hline K\({}^{*}\) = exp(H\({}^{*}\)) & \(3.4\times 10^{4}\) & \(0.5\times 10^{4}\) & \(2.7\times 10^{4}\) & \(0.5\times 10^{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Entropy parameters of the control additive-free sample. Figure 3: Results of the multifractal analysis of the electron microscopic image of control sample structure: the effect of the \(d\) scale on the information entropy of \(D1\) and \(\Delta D\). The deterministic function of the information system of the image of the control sample microstructures has the relative randomness S = 0.55 \(-\) 0.69 and the relative organization R = 0.31 \(-\) 0.45. One can note the value of 70% of the renewal of active elements of the microstructure in the spectrum of levels of the dynamic state of microstructures of the AB and BB cells. The entropy of the equilibrium levels of the AB and BB cells is D1 eq = 0.87534 and D1 eq = 0.8805, respectively. For the BA cell (Table 1), the update is 50%, and the structural entropies of the static and dynamic states are close in magnitude. The invariant variety is observed in the change \(\Delta\)D (Figure 3) in the form of increasing the resonant maxima in a wide range of changes in the scale of \(d\). The relative organization of the functional state of the information system of the BA microstructure is R = 0.31. The structural entropy of the static state exceeds the entropy of the dynamic state in the information system of the AA microstructure, so the information capacity of \(K=exp(H)=4.7\times 10^{5}\) is higher than the capacity of \(K^{*}=exp(H^{*})=3.4\times 10^{4}\). The high potential of choice (information capacity) of the static state forms a gradient force of influence on the dynamic state, probably providing the increase of the relative organization of R = 0.45 of the microstructure of the AA cell. A single information maximum is observed in the near-order change of \(\Delta\)D in the scale change interval of \(d\). It can be assumed that the development of the crystal intergrowth is provided due to the high potential of choice (information capacity) of the static state of the information system. This confirms the nonequilibrium of states due to the presence of gradient-phase components in the microstructure of the control sample. The results for determining the entropy parameters of structure of the control additive-free sample are presented in Table 1, where H is the general structural information entropy, \(H_{max}\) is the maximum information, \(H^{*}\) is the configuration entropy, \(R\) is the value of relative organization of the system, \(D1 equil\) is the value of the information dimension, \(K\) is the information capacity, and \(\Delta D\) is the measure of randomness. The results of the multifractal analysis of the electron microscopic image of the microstructure of the modified sample are shown in Figure 4. The entropy parameters of the static and dynamic stability of microstructure are given in Table 2.  
Figure 4: \(Cont\).