The Limiting Characteristics of Polycondensation Process

Devalues, obtained for PAr and PUAr poly condensation process, showed, that the indicated processes were realized by aggre tion cluster-cluster mechanism [49], i.e., by small macromolecular coils joining in larger ones [23], Thus, polycondensation process is a fractal object with dimension D. reaction. Such reaction can be presented schematically in a form of devil s staircase [80], Its horizontal parts correspond to temporal intervals, in which reaction is not realized. In this case polycondensation process is described with irsing fractal time t, which belongs to Kantor s set points [81], If polycondensation process is considered in Euclidean space, then time belongs to a real number set. 

The mathematical calculus of fractional differentiation and integration is used for the description of evolutionary processes with fractal time [81 ]. As it has been shown in paper [82], in this case the fractional exponent v coincides with fractal dimension of Kantor s set and indicates fraction of system states, maintaining during all evolution time t. Let us remind, that Kantor s set is considered in onedimensional Euchdean space (d = 1) and therefore its fractal dimension dj l in virtue of fractal definition [52]. For fractal objects in Euclidean spaces with Mgher dimensions (d l) dj,fractional part should be accepted as v or [83]  

Let us consider the physical sense and definition of fractional exponent Vg. value in the given context. As it is known [84, 85], polycondensation process ceases in gelation point, for which the fractal dimension dj of a forming stmcture is equal to 2.50. This means, that fractal (macromolecular coil) fraction, not included in evolution (poly condensation) process, at gelation point reaches its maximum value V =1.0. From the said above it follows, that in the considered case at v =1.0 d=D = 

fraction of macromolecular coil p, subjecting to evolution (chemical reaction in polycondensation process) can be defined as follows [76] Eq. (46)  

FIG LIRE 20 The relation between hmiting conversion degree and fractional exponent 

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