The Activation Energy of Viscous Flow

A similar thing takes place when we consider flow curves obtained at different temperatures. As seen from Fig. 7, if we take a region of low shear rates, then due to the absence of the temperature dependence Y, the apparent activation energy vanishes. At sufficiently high shear rates, when a polymer dispersion medium flows, the activation energy becomes equal to the activation energy of the viscous flow of a polymer melt and the presence of the filler in this ratio is of little importance. 

Activation energies of the viscous flow, dielectric relaxation process and orientational process in an electric field... 

An equation similar in form to Mooney s equation was derived by Kunnen [44], who proceeded from the additivity of the reciprocal values of the activation energy of the viscous flow for binary solutions, emulsions and dispersions ... 

PE-g-IA ones. Here, blends with PE concentrations below 25 wt% are characterized by extremely low apparent activation energy of the viscous flow. For (75PP/25PE)-g-lA systems, the activation energy can even be negative. 

On the basis of presented data we can conclude that the activation energies of the viscous flow are higher than the activation energies of the monomolecular chain termination found via kinetic curves of the postpolymerization. It once more confirms the assumption we made when we deduced the kinetic equation, according to which the monomolecular chain termination rate is controlled by the rate of its propagation. Thus, monomolecular chain termination cannot be considered as passive active radical freezing . 

The temperature dependence of viscosity of the solvents used does not exhibit Arrhenius behavior even in the temperature ranges studied. This follows from Fig. 11, which clearly shows nonlinearity of the plots in log q versus l/T coordinates. Consequently, the activation energy of the viscous flow of the solvent, cannot be... 

Telegina et al. 72> showed that the activation energy for the viscous flow of a polyester oligomer filled with glass microspheres is 46.9 kJ/mol, while that of an epoxy oligomer is 78.3 kJ/mol. They also established the important fact that the addition of microspheres to an oligomer composition does not change the temperature viscosity coefficient. This means that the viscosity of a mixture with microspheres can be controlled, if the temperature dependence of the viscosity of the binder is known. 

To simplify the situation and exclude the temperature dependence of viscosity, a relative variation of the parameter is considered, where tio is the initial value of the viscosity of the reactive system. This assumption is valid, if the activation energy of a viscous flow is constant during gelation, since in a general case E must vary with conversion [49],... 

The apparent activation energies, E, derived from the plot of T against 1/7 are different above and below Ty, and are in fair agreement with the activation energies of macroscopic viscous flow (cf. in. 1.4). 

Rheology. Both PB and PMP melts exhibit strong non-Newtonian behavior thek apparent melt viscosity decreases with an increase in shear stress (27,28). Melt viscosities of both resins depend on temperature (24,27). The activation energy for PB viscous flow is 46 kj /mol (11 kcal/mol) (39), and for PMP, 77 kJ/mol (18.4 kcal/mol) (28). Equipment used for PP processing is usually suitable for PB and PMP processing as well however, adjustments in the processing conditions must be made to account for the differences in melt temperatures and rheology. 

In order to go further into the experimental check we constructed Arrhenius plots of the fluorescence quantum yield of BMPC in a few solvents (methanol, ethanol, propanol, hexanol and methylene chloride), all of which showed good linearity. The activation energies and A/kp ratios, calculated from the slopes and intercepts of those plots, are collected in Table 1. The smooth increase of both parameters in the alcohol series is mainly associated with the increase of solvent viscosity. On the other hand, decrease of the solvent dielectric constant from 32.7 (methanol) to 8.9 (dichloromethane) causes a small but significant increase of the activation energy also, this increase is probably somewhat compensated by the decrease of the viscous-flow... 

In both the cases, the activation energy of the infiltration process (Fig. 1) is practically the same ( 40 kJ/mol) and close to that of the cobalt viscous flow (37.3 kJ/mol) [8], i.e. the observed variations in kinetics of the infiltration are caused by the difference between viscosities of cobalt and its alloys. According to [8] y= Aq exp(Ea/RT), where y is the kinematic viscosity, Aq is the constant, Ea is the activation energy of viscous flow, R is the universal gas constant, T is the absolute temperature. Correlating this formula with Eq. (2) and considering that q = py, where p is the density of the liquid, we have for k ... 

A generalized kinetic model of cure is developed from the aspect of relaxation phenomena. The model not only can predict modulus and viscosity during the cure cycle under isothermal and non-isothermal cure conditions, but also takes into account filler effects on cure behavior. The increase of carbon black filler loading tends to accelerate the cure reaction and also broadens the relaxation spectrum. The presence of filler reduces the activation energy of viscous flow, but has little effect on the activation energy of the cure reaction. 

Additive content increase in the compositions results in a regular increase in the value of Bt and the values of the viscous flow activation energy at 20 °C (see Table 3). 

The most important effect of plasticization is the lowering of the Tg of the polymer, which was discussed in Section 6.D. Another effect of plasticization is that the activation energy for viscous flow of the solution at T>1.2-Tg is usually smaller than the activation energy of the pure polymer since ET)p Er S for most polymer-solvent combinations. Our preliminary calculations show that Equation 12.21 may often be preferable to Equation 12.19 for describing the behavior of Er SS, at least for Op l. This issue must, however, be considered in greater detail in order to reach more definitive conclusions. In particular, ET SS must be examined as a function of Op in the limit of Op—>1. Furthermore, the dependence of the behavior of ET SS as a function of Op on the strength of the interactions between the polymer and the solvent needs to be considered. 

Table 7.6. Activation energies of the monomolecular chain termination ( a ) and viscous flow E )for dimethacrylates...

The respective values of Ep and Ep p calculated from Fig.5 are about 4.8 Kcal/mole and 2.3 l cal/mole respectively the low activation energy of the isothermal process being indicative of a viscous flow mechanism while.the relatively higher value of Ep j is comparable with those generally found in diffusive processes (17-19). The concept of apparent activation energies for transport in a temperature gradient arises from the different dissolution enthalpies of the permeant on opposite partition sides. From the definition of enthalpy it follows that... 

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