ABSTRACT
Figure 7.1. The dependencies of scissions number s per one macromolecule on a thermooxidative degradation duration tag at Tag=513 K for PC films, obtained from solutions in methylene chloride (1), chloroform (2), 1.4-dioxane (3) and tetrahydrofuran (4) [6]. Table 7.1Fractal dimension A/of a macromolecular coil for PC samples, ob-_______________tained from different solvents [7]_______________Solvent AfMethylene chloride 2.45Chloroform 2.54Tetrahydrofuran 2.691.4-dioxane 2.74
Earlier it was shown, that the macromolecular coil fraction p</, disintegrated in a degradation process, depends on A/ and is determined by the equation (6.3). Therefore, the real value of a reactive sites number Nbuik in a macromolecular coil bulk can be written as follows [3]:
(7.2) where Nm is reactive sites number per macromolecule at the condition of their complete accessibility. It is obvious, that the value Nm is defined by a polymer chemical constitution.The relation of parameters Nbuik and Nsurf is controlled by a fractal object bulk Vfr and the surface Sfn which is equal to [12]:
(7.3)
where R is a fractal object radius, in our case equal to a gyration radius Rg of a macromolecular coil.In its turn, the value Rg for the considered polymers can be determined according to the following equations: for PAASO in chloroform [7]: (7.4)
(7.5) and for PC in chloroform [13]:
where M w and Mr[ are average weight and average viscosity molecular weights, respectively. In the equations (7.4) and (7.5) the values Rg are obtained in nm.The combination of the equations (7.1)-(7.5) allows to receive structural criterion of an oxidation kinetic curves transition from an autodecelerated (sigmoid) mode to an autoaccelerated one [3-7]: (7.6)
where N rf is critical value of A/ at the indicated transition d is the dimen sion of Euclidean space, in which the fractal is considered and Rg is also given in nm.Let’s mark two important features of the equation (7.6). At first, in this equation the parameter Nm is absent, i.e., the value N rf does not depend on
a polymer chemical constitution. Secondly, the increase Rg results to A" raising. This is completely agreed with the assumption, having served the basis for derivation of the equation (7.6): the value Ntuik increases proportionally to cube Rg, whereas Nsurf - quadrate Rg, i.e., the increase Rg leads to the raising the ratio Vfr/Sfr.Let’s consider boundary conditions for the equation (7.6). For Ar 0, i.e., for the doted zero-dimensional object, Rg=0 and the criterion (7.6) is correct for such object. For A/=3 Rg-»<x> or, as well as it was necessary to expect, for the Euclidean object the measurement scale is of no importance [6],Calculated according to the equation (7.6) with the relationships (7.4) and (7.5) using the values A" are equal to 2.76 for PC and 2.78 for PAASO, that is excellently corresponded to the mentioned above experimental values Af for this transition [3].Let’s consider the effect of a macromolecular coil structure on the autoacceleration mode of a thermooxidative degradation. As it was shown in paper [13], the product which is responsible for an autoaccelerated mode of a kinetic curves, can be the aldehydic groups forming from the methylic groups (which are present in PAASO and PC) according to the scheme(6.15). In its turn, an aldehydic groups oxidation, proceeding according to the scheme (6.16), results to active free radicals R» and low-molecular radicals H 02* formation. The latter are mobile radicals, that allow to consider them as random walks and use for their description the reaction of type (4.32) [14, 15]. The standard classical reaction of the order one-half is described by the relationship [16]:
where p is random walks density.For the microscopically heterogeneous (fractal) mediums the relationship (7.7) is modified as follows [16]:
and the integration of this relationship for reaction rate can be written this way (with the calculation of quadratic dependence of N(h or s on t [1])
(7.7)
(7.8)
[7]: (7.9)
where pRWq is the initial density of random walks, h is the heterogeneity exponent in the relationship (1.68) (0</Kl). Besides, the exponent in the relationship (7.9) can be defined according to the equation (1.69) as effec tive spectral dimension ds of medium, in which reaction is proceeding [6].
