Cure reaction expression

The kinetics of the cure reaction, expressed in terms of either the heat evolved or the torque modulus obtained by the MDR and RPA... 

Kinetic models determine the minimum time required to cure the resin (i.e., guarantee sufficient physical and mechanical properties). They also determine the heat of reaction of the resin for use by heat transfer models and the degree of crosslinking for use in viscosity submodels. The exothermic cure reaction for the transformation of the epoxy resin to the cured matrix polymer can be expressed as ... 

Although the simple rate expressions, Eqs. (2-6) and (2-9), may serve as first approximations they are inadequate for the complete description of the kinetics of many epoxy resin curing reactions. Complex parallel or sequential reactions requiring more than one rate constant may be involved. For example these reactions are often auto-catalytic in nature and the rate may become diffusion-controlled as the viscosity of the system increases. If processes of differing heat of reaction are involved, then the deconvolution of the DSC data is difficult and may require information from other analytical techniques. Some approaches to the interpretation of data using more complex kinetic models are discussed in Chapter 4. 

Kinetic Model for Curing Reaction and Comparison Between Predicted and Measured Degree of Cure. We modeled the epoxy curing reaction for all H/R studied, using the n-th order rate equation (1.1) substituting for the rate constant k in (1.1) the expression from the Arrhenius equation in (3.4.1)... 

Since epoxy homopolymerization may be neglected in the absence of catalysts (T), the major cure reactions can be assumed to be the reactions between epoxide and amine groups as expressed in Scheme I. 

The model satisfactorily described the cure behavior for the entire range as experimentally monitored by FTIR, DSC, and torsional braid analysis (TBA). This model satisfactorily explained the cure behavior of both catalyzed and uncatalyzed systems over a wide range of temperature and throughout the curing process. The authors proposing the kinetic model considered the reaction to be triggered by the adventitious water and phenol impurities (whose reactions with the cyanate ester is considered as an equilibrium reaction). Catalysis by the added metal ions, which stabilizes the imino carbonate intermediates by complex-ing, is also considered. The model has considered all possible reaction paths and intermediates as detailed in Sect. 4 and depicted in Scheme 14. Considering the various reactions, expressions could be obtained for the individual apparent empirical rate constants of the second order auto catalytic model in terms of the actual rate constants and equilibrium constants. 

The overall rate of cure is expressed in terms of heat evolved from this reaction ... 

It should be said that the state of cure at time t is expressed in this paper by the heat evolved at time t from the cure reaction as a fraction of the total heat evolved. 

The cure reaction is obviously highly complex, and expressing such a system of reactions in a simple first-order reaction with an activation energy results from a strong assumption. As the problem is vast, only two studies are considered the one concerned with the sulfur vulcanization process, and the other more specifically based on the explanation of the scorch delay kinetics. 

There are various ways to determine the parameters of the kinetics of the cure reaction. The parameters to consider are the cure enthalpy, which is the heat evolved from the overall cnre reaction the order of the reaction which is concerned with the concentration of active agent remaining free during the reaction at time t and the two parameters that allow defining of the effect of the temperature on the rate of the reaction, that is, the energy of activation and a constant that depends only on the compound, by following the Arrhenius expression. Thus, by considering aU these parameters, the cure of rubbers is considered a simple reaction. 

We have to understand that if the heat flux defined by Equation 3.5 at the rubber sensor is of interest, because it provides the intensity and shape of the cure exotherm, the other taking place in the air, expressed by Equation 3.6, is characterized by the loss in heat for the cure reaction. From a first approach, based on a logical consideration, this loss in heat affects essentially the values of the enthalpy of cure which is reduced somewhat. The shape of the exotherm, which gives rise to the kinetics of the reaction, should not be affected as in Equation 3.6, the loss in heat is proportional to the difference in temperatures, in the same way as for the gradient of temperature shown in Equation 3.5. The loss in heat could follow kinetics similar to that observed on the sensor of the calorimeter. 

The result is expressed in terms of the state of cure-time history obtained at various values of the temperature of the reservoir T. The curves drawn in Figure 5.1 show the increase in the state of cure of the rubber with time, as they are calculated under isothermal condition by using the kinetic parameters of the cure reaction collected in Table 5.1. 

As it follows from the adduced in Fig. 16 plots, the dependences [In (100-Q)] (t) proved to be linear, i.e., corresponding to the Eq. (86) of Chapter 1. This means that the system 2DPP + HCE/DDM curing reaction at all used T can be considered as classical reaction of the first order, proceeding in medium with small density fluctuations [17], The plots linearity allows to determine the coefficient A value in the Eq. (86) of Chapter 1 from their slope. It is easy to see from the data of Fig. 16 that T inerease results to A growth. Therefore in Fig. 17, the dependence of Aj 2 on T for the studied system is adduced which is approximated well enough by linear correlation and it can be expressed analytically as follows [34] ... 

Shrinkage—The volume reduction occurring during adhesive curing, sometimes expressed as a percentage volume or linear shrinkage size reduction of adhesive layer due to solvent loss or catalytic reaction. 

The curing reactions of UPRs based on glycolyzed PET and maleic anhydride were studied by differential scanning calorimetry and various kinetic parameters were obtained from dynamic data using the Kissinger expression [59]. It was demonstrated that the polymerization heat, associated with styrene and polyester double bonds, can be calculated by extrapolating the heat of reaction obtained from different styrene contents. 

Basically, there are two forms of kinetic expressions (or models) describing the cure reactions of thermosets empirical and mechanistic models. An empirical model assumes an overall reaction order and is fit to experimental data to determine numerical values of the parameters appearing in the model. Such empirical models cannot provide information on the mechanism(s) of reaction kinetics. Different research groups. 

Using Eq. (14.13), we can now predict the viscosity of unsaturated polyester during cure once information on a during cure is available to us. In order to use Eq. (14.13) to describe the variation of r/ during cure of unsaturated polyester, one must have an expression describing the kinetics of the cure reactions. Below, we present experimental methods that can be used to determine an expression for cure kinetics. 

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