# Evaluation of Changes in Structure of Modified Cement Composite Using Fractal Analysis
## 3 Results and Discussion
The functional state of the microstructure of the modified sample is determined by the deterministic and stochastic functions of the information system. Parameters of the deterministic function:  
(1) Equilibrium level: \(D_{1 max}\) = 0.851-0.97; orderliness \(K_{\rm s}\) = 5.2 \(-\) 31.6 \(\times\) 10\({}^{-3}\); scale of structure elements \(d\) = 10-29 pixels; relative orderliness \(R\) = 0.931-0.94. (2) Non-equilibrium level: \(D_{1 min}\) = 0.798-0.842; orderliness \(K_{\rm s}\) = 7.4 \(-\) 45 \(\times\) 10\({}^{-3}\); scale of structure elements \(d\) = 49-50 pixels; relative orderliness \(R\) = 0.37-0.67. Parameters of the stochastic function:  
(1) Equilibrium level: \(D_{1 max}\) = 0.8909; orderliness \(K_{\rm s}\) = 16.37 \(\times\) 10\({}^{-3}\); scale of structure elements \(d\) = 13 pixels; relative orderliness \(R\) = 0.91. (2) Non-equilibrium level: \(D_{1 min}\) = 0.8253; orderliness \(K_{\rm s}\) = 29 \(\times\) 10\({}^{-3}\); scale of structure elements \(d\) = 50 pixels; relative orderliness \(R\) = \(-\)0.08. Figure 4: Results of the multifractal analysis of electron microscopic image of the modified sample microstructure: the effect of the \(d\) scale on the information entropy of \(D1\) and \(\Delta D\). \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multicolumn{1}{c}{**Microstructure**} & **AA** & **AB** & **BA** & **BB** \\ \hline \multicolumn{1}{c}{**Status Function**} & **Stochastic** & **Deterministic** & **Deterministic** & **Deterministic** \\ \hline H & 6.89 & 9.53 & 8.537 & 10.11 \\ \hline H\({}_{\rm max}\) & 9.97 & 13.8 & 12.36 & 14.64 \\ \hline H\({}^{*}\) & 10.73 & 8.72 & 4.11 & 7.74 \\ \hline S = H\({}^{*}\)/H\({}_{\rm max}\) & 1.08 & 0.63 & 0.33 & 0.53 \\ \hline \(\Delta\)H = H\({}_{\rm max}-\) H\({}^{*}\) & \(-\)0.757 & 5.08 & 8.25 & 6.9 \\ \hline R = 1 \(-\) S & \(-\)0.08 & 0.37 & 0.67 & 0.47 \\ \hline Transmitted information & \(\rm H_{old}/H^{*}\) & 0.39 & 0.1 & 0 & 0.21 \\ \hline New & & & & \\ Information H\({}_{\rm new}/H^{*}\) & 0.61 & 0.9 & 1.0 & 0.79 \\ \hline H \(-\) H\({}^{*}\) & \(-\)3.34 & 0.83 & 4.43 & 2.37 \\ \hline D\({}_{\rm lequil}\) & 0.89085 & 0.907 & 0.8502 & 0.85076 \\ \hline D\({}_{\rm non-equil}\) & 0.82523 & 0.8416 & 0.7976 & 0.80827 \\ \hline K = exp(H) & \(9.82\times 10^{2}\) & \(1.4\times 10^{4}\) & \(5.1\times 10^{3}\) & \(2.4\times 10^{4}\) \\ \hline K\({}^{*}\) = exp(H\({}^{*}\)) & \(2.1\times 10^{4}\) & \(6.1\times 10^{3}\) & 60 & \(2.3\times 10^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Entropy parameters of the modified sample microstructure. The analysis of the spectrum of information-entropy levels of the dynamic state of the information system of the microstructures of control and modified samples (Figures 5 and 6) shows an increase of the information entropy of \(D_{1i}\) and a decrease of the orderliness of \(K_{S}\) levels with a scale change (the increase of the cell size of \(d\)). It should be noted that the modification of cement composite increases the thermodynamic fluctuations of chemical and phase compositions, affectsthe parameters of \(K_{s}\) orderliness and the entropy of D\({}_{1}\) in the information system of microstructure, and leads to disorder both of the scale invariance and the monotony of dependencies. The break points of the dependencies correspond to non-equilibrium phase transitions. The modification is accompanied by the increase of the orderliness of \(K_{s}\)\(\times\)\(10^{-3}\) and the decrease of the information entropy in spectrum of dynamic deterministic state of the composition, with the additive due to the processes of dynamic self-organization in the course of information transformations. The processes of thermodynamic self-organization are observed as non-equilibrium phase transitions in the form of violations of scale invariance in Figures 5 and 6 at the \(d\) scale up to 45 pixels. Based on the fractal analysis of the images, it can be concluded that soot particles act as centers with a high energy potential during the modification of cement composite.