First order reaction viscosity dependence

The thermal decompositions of dicyclohexylidene diperoxide and tricyclohexyli-dene triperoxide are first-order reactions, which show rate increases in more polar solvents and are also dependent upon the viscosity of the solvent. However, product yields are not markedly influenced by the solvent, although yields of macrocyclic hydrocarbons from decomposition of tricyclohexylidene triperoxide did increase with temperature. Mechanisms for these reactions have been suggested. 

As an example of applying our simulator to model a specific effect in a polymer flood, we consider chemical degradation of polymer and its dependence on temperature. Many laboratory studies have appeared in the literature on the bulk phase stability of EOR polymers (eg 19-21). Although the process appears to be quite complex, the ultimate result is that a desirable property (eg viscosity) is eroded with time. If we assume a simple first order reaction for the polymer degradation term, R, then we may define the polymer half-life at a given temperature as ... 

We can also turn the question around. In chemical kinetics, we need a model to fit the data. This model can be simple, as in first-order reactions where the decay is exponential, or more complicated depending on a complex mechanism. If we do not have a model, our data are just that, data. We could try to fit to a variety of functions, but as there is an infinite number of different functions, that is a pointless exercise. As we have seen in the classical part of this chapter, even for a simple reaction a variety of models are possible, based on dissipative classical dynamics, and we can use these models to try to understand our data. This often involves varying the external parameters, temperature, pH, viscosity, and polarizabihty, but our model should tell us what to expect for such variations for instance, how the rate constant for a reaction depends on those parameters. If our models are quantum mechanical in nature, it is mandatory that we also provide a mechanism for decay, and show how the decay constant or constants depend on external parameters. 

Figure 4.4 Dependence of the logarithm of rate of contraction, . (proportional to the rate of polymerization) on time showing zero-order kinetics in Interval n, and first-order kinetics initially in Interval III. The termination reaction is diffusion controlled increasing viscosity in Intoval HI reduces ki increasing the rate. Ultimately the propagation reaction becomes diffusion controlled also and the rate decreases again. (Reproduced by permission of Verlag Chemie [66].)...

It can be noted that the first-order corrections for the reaction rate coefficients depend on the same functions and G ij which define the additional diagonal elements of the pressure tensor connected to the bulk viscosity and relaxation pressure. 

The breakdown of the structure is similar to a series of consecutive first-order chemical reactions where formation is meant by behavior that is time-dependent, whereas the breakdown occurs when the viscosity of the fluid acts as a Newtonian mixture that is independent of both the shear rate and the duration of shear (Figure 3-14). 

Heat treatment of the S-type fluoride in a fluorine atmosphere Based on the results above mentioned, Fujimoto et al. developed a new fluorination procedure in order to prepare the perfluorinated pitch, and obtained two types of other fluorinated pitches [23,24], The new process is by the heat treatment at 200-400°C of S-type of fluorinated pitch prepared at relatively low temperature in a fluorine atmosphere. They firstly fluorinated the mesophase pitch at 70°C for 10 h (first step for the preparation of S-type fluorinated pitch) and then heated up to a selected temperature between 200°C and 400°C, and maintained this temperature for 12 h (second step for the heat-treatment of fluorinated pitch). Thus, they obtained two kinds of fluorocarbons, a transparent resin (R-type) and a liquid (L-type). L-type is a viscous fluid containing some volatile materials and the viscosity gradually becomes higher when it is kept for a few weeks in an air atmosphere even at ambient temperature. They reported that the R-type was obtained in the nickel boat in the heating zone and L-type at the bottom of the vertical reaction vessel which was cooled down by the water. Therefore, it is likely that the liquid fluorocarbon is formed by the vaporization of some component contained in the S-type fluoride or decomposition reaction during the heat treatment of the S-type fluoride. The yields of these compounds depends on the heat treatment temperature. In Fig. 3, the yields of the R-type and L-type fluorocarbons are plotted as a function of the heat treatment temperature of the S-type fluoride. The yield of the former decreases with increase of the heat treatment temperature and finally, at 400 C, it can not be obtained at all. On the other hand, the yield of the latter increases with increase of temperature and it is selectively obtained at 400°C. 

Attempts are also known to relate the type of time dependence of viscosity in the curing process to the kinetics of the reaction. Thus, upon curing of diglycidyl ester of Bisphenol A by triethanolamine, the viscosity curve Tj (t) was approximated by two linear segments [40]. The appearance of an inflection point is explained by the authors on the basis of the formation of a meshing network an the linearity of the tj (t) dependence in the first party by the fact that a curing reaction is of a zeroth order. 

Investigation of kinetic orders of considered polymerization reactions by monomer showed that with the increase of initial AG and MAG concentrations the initial polymerization rate was increased sharply and non-linearly and reaction was characterized by exceeding the first variable order by monomer (Figures 2 and 3). As it is obvious from Figures 2 and 3 the dependence of intrinsic viscosity of resulted PAG and PMAG polymers is symbatic to the change of polymerization rate for both polymerization systems. 

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