**3.1 Determining the filler activity by the positive root of the parabola equation, which describes the dependence of the pitch composite strength on the filler content**

The dependence of the pitch composites of the semicoke's strength on the mass ratio of the pitch and filler is investigated. As a rule, an extreme dependence of the strength on the degree of filling was observed, characterized by the presence of a concentration maximum.

A second-order equation is a reasonable approximation. For all the equations, we calculate the discriminant and determine the roots.

**Table 3** shows the equations of the second-order curves describing the dependence of the strength of the semicoke from the pitch composites on the composition


**Table 3.**

*Strength of pitch composites depending on the filler.*

of all the excipients that were tested, the roots of these equations *x1* and *x2*, and the determination coefficients (*R*<sup>2</sup> ) of the interaction y = f(x).

We do not consider the negative values of the roots x1 because they do not match the condition of the problem.

The physical meaning of the roots x2 of the parabola equation is some hypothetical ratio of filler binding, in which the strength of the pitch composite falls to zero. The x2 indicator can be used as an indicator of the activity of the filler. The higher the value of x2, the greater the filler activity.

There is some physical meaning of the roots x2 of the parabola equation. The x2 indicator can be used as a measure of the activity of the filler or of the sintering ability of the pitch. The higher the value of x2, the greater the activity of the filler is. That is, the more active the filler, the more its quantity will be agglomerating. By x2, it is possible to rank the binders for the sintering ability to the fillers. The activity of the filler is the amount of the inverse sintering power of the pitch [21]. In accordance with this indicator, fillers are located (in descending order) in a row:

$$\text{Anthracite} \text{---SC - T---PC---SC -glass---sand}$$
