Microgels fractal dimensions

FIGURE 66 The dependence of reaction rate constant on microgels fractal dimension... 

FIGURE 11 The dependence of microgels fractal dimension on curing reaction duration t for the system EPS-4/DDM. The condition D(.= const for the system 2DPP + HCE/DDM was shown by a shaded line. 

FIG U RE 20 The dependences of microgels fractal dimension Dj (1) and reactive medium initial viscosity q (2) on the parameter A value for the system 2DPP+HCE/DDM. 

FIGURE 21 The dependence of parameter on microgels fractal dimension Dj. for the... 

FIGURE 29 The comparison of experimental (1) and theoretical (2) dependences of the first gelation point time on microgels fractal dimension Df in logarithmic coordinates for the system 2DPP+HCE/DDM. 

FIGURE 41 The dependence of limiting conversion degree Q,. of curing reaction on microgels fractal dimension for the system 2DPP+HCE/DDM. 

In the insert the dependence p on D is shown, from which p decrease at microgel fractal dimension growth follows. This assumes Levy flights probability decrease at the system viscosity increase. Hence, the ability to control active time gives the possibility of reaction conrse operation. 

Figure 10.15 A correlation between viscosity of reaction medium rig and fractal dimension of microgels D for system 2DPP + HCE/DDM.

The combination of Equations (10.13) and (10.14) allows the estimation of the value The comparison of experimental and theoretical dependencies of the gelation time for its first point of appearance from the fractal dimension of microgels D for system 2DPP + HCE/DDM is given in Figure 10.16. 

Figure 10.19 Dependence of the fractal dimension of microgels, D, on the reaction time, t, for system EPS-l/DDM. The broken line shows the condition D = constant for...

This chapter considers the reasons for a variation of microgel structure characterised by its fractal dimension, D, formed in the cure of epoxy resin systems. Quantitatively, change of D during the increase of reaction time is well described within the framework of mechanism of aggregation cluster - cluster. The fractal space, in which the reaction curing proceeds, is formed by a structure of the greatest cluster in system. 

The curing temperature of system EPS-l/DDM was 393 K. Values of fractal dimension D of microgels varied within the limits of 1.61-2.38 [1]. 

It follows from the Equation (13.1) that in the case of absence of microgel distribution on their fractal dimensions, i.e., in the case Dj=D2=...=Dj, the large cluster differs from smaller ones which form it, only by sizes and Equation (13.1) D= Dj=D2=...=D . Equation (13.1) shows that the distribution of the values of Dj, i.e., small microgels (analogues of macromolecular coils for linear polymers) should have different dimensions of D, i.e., Dj D2 D3 t...5tD . Theoretically we can estimate the possible variation of D(t) in the following way. If we assume that at the moment of time (q) the distribution of D of microgels is equal to according to the Equation (13.1) it is possible to calculate Dj=D under... 

Let us note in conclusion the strong dependence of k on the microgels structure, characterized by the fractal dimension Z) (Fig. 66). As it follows... 

Let us consider further the Eq. (27) of Chapter 1 application for the system 2DPP+HCE/DDM curing kinetics description. In Fig. 18 the dependences 0, in double logarithmic coordinates corresponding to the Eq. (27) of Chapter 1, were adduced. As one can see, they ate linear, that allows to determine from their slope the value of fractal dimension of microgels, forming in curing process. As the... 

TABLE 2 The comparison of experimental microgels for system 2DPP+HCE/DDM. and theoretical fractal dimension of... 

Thus, the stated above results have demonstrated that both scaling Eq. (86) of Chapter 1 and fractal Eq. (27) of Chapter 1 (or Eq. (61) of Chapter 2) describe well to an equal extent haloid-containing epoxy polymer 2DPP+HCE/DDM curing reaction kinetics at different curing temperatures. In virtue of this circumstance there exists intercoimection between parameters included into the indicated equations. The fractal Eq. (61) of Chapter 2 introduces in the kinetics problem consideration reaction products structure (in the given case structure of microgels and condensed state after gel formation point), characterized by its fractal dimension D, that makes this conception physically more informative [34]. 

Therefore, the stated above results have confirmed again that D, values distribution is the main reason of microgels stracture variation, characterized by its fractal dimension Dp Dp change at reaction duration growth is well described quantitatively within the frameworks of aggregation mechanism cluster-cluster. Fractal space, in which curing reaction proceeds, is formed by the stracture of the largest cluster in system [55],... 

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