Resin cure kinetic model

The mechanism for cross-linking of thermosetting resins is very complex because of the relative interaction between the chemical kinetics and the changing of the physical properties [49], and it is still not perfectly understood. The literature is ubiquitous with respect to studies of cure kinetic models for these resins. Two distinct approaches are used phenomenological (macroscopic level) [2,5,50-72] and mechanistic (microscopic level) [3,73-85]. The former is related to an overall reaction (only one reaction representing the whole process), the latter to a kinetic mechanism for each elementary reaction occurring during the process. 

The mechanistic models are more representative of the resin curing kinetics because they are based on stoichiometric balances of reactants involved in the elementary reactions. As a consequence, they are much more complex than the phenomenological models, but they can better represent the kinetics of cure. The physical and mechanical behaviors of the cured resins are determined by the chemical reactions that occur dining cure. The understanding of the mechanism and kinetics of cure is one of the most important steps in evaluating the... 

Cure kinetics and chemorheological models are key for characterizing and modelling RTM processes. For example, Lobo (1992) utilized the following kinetic and chemorheological models for a vinyl ester RTM resin. The kinetic model is given by... 

Hedreul et al. (1998) examined a model of the cure kinetics of a thermally and microwave-cured rubber-modified epoxy-resin formulation. The phenomenological cure kinetic model used was... 

As discussed in this chapter, a VARTM prcx ess is affected by many fundamental factors such as resin viscosity, fiber preform compaction, fiber preform permeability, resin cure kinetics and temperature control. Flow modeling and curing process modehng can help one to avoid these potential problems during the resin infusion and the curing cycle. 

Journal of Applied Polymer Science 77, No.7, 15thAug.2000,p.l419-31 CURE MODELING AND MONITORING OF EPOXY/AMINE RESIN SYSTEMS. 1. CURE KINETICS MODELING... 

An investigation using differential scanning calorimetry was carried out under both isothermal and dynamic curing conditions to determine the cure kinetics of four epoxy/ amine resins. Various cure kinetic models were used to compare them with the results of the DSC results. Good fits were found, in good agreement with the experimental results for the resin systems. 22 refs. 

Because of all these minor components (e.g., catalysts and inhibitors, added to major ones) the cure of vinyl ester resins is very complex, involving many competitive reactions. There are some new variables to account for, such as the inhibitor and initiator concentrations and induction time. Several papers [81,96,200,201] use the mechanistic approach, claiming that the phenomenological models do not explicitly include these facts, resulting in a new parameter characterization after each change in resin formulation [96]. Despite these arguments, the phenomenological approach is the most widely used and is based on an autocatalytic model which has been successfully applied to epoxy resins. Many authors [30,34,74,199,202,203] proposed the Equation 2.30 to describe the cure kinetic of unsaturated polyesters ... 

Several researchers have modeled the cure kinetics of thermosetting resins in the past, including an unsaturated polyester resin [8], epoxies [9-11], and bismaleimide [5], As an example, a graphite/BMI material, IM6/3100, was modeled in [5] using... 

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. 

In general the amine-epoxy resin curing reactions show complex kinetics typified by an initial acceleration due to autocatalysis, while the later post-gelation stages may exhibit retardation as the mechanism becomes diffusion-controlled. However some workers 72 80) have found that over a limited range of conversion the kinetic data may be described by the simple models of Eq. (2-6) or (2-9). 

Wei, J., DeMuse, M. and Hawley, M.C., Kinetics modelling and time-temperature-transformation diagram of microwave and thermal cure of epoxy-resins, Polym. Eng. Sci., 1995, 35, 461. 

The model that best represents the curing kinetics of thermosetting resins such as epoxy and unsaturated polyester, and as reflected in a TTT-diagram, is a diffusion modified Kamal-Sourour reaction model [9, 14, 13]. To model autocatalytic cure kinetics, the model can be applied as... 

Fig. 30a. Conductivity data of Acitelli for the 57 °C cure of a low molecular weight DGEBA resin with m-phenylene diamine. (Reprinted from Ref. 60) with the permission of the publisher Butterworth Scientific, Ltd.), b) Simulation of the data of Figure 30a using a chemical kinetic model to determine Tg versus time and a WLF Equation to determine the conductivity. (Reprinted from Ref. 35) with permission of the Massachusetts Institute of Technology)...

The starting point for the use of scanning DSC for chemorheology of systems such as cure of an epoxy resin is the kinetic model which links the variables of temperamre and reactant concentration to the rate of reaction. This is chosen to be a simple Arrhenius relation governed by the pre-exponential factor, A, and the activation energy, E, ... 

Three-dimensional analyses of heat transfer and cure in pultrusion of epoxy-resin composites have been examined by Chachad et al. (1995, 1996) and Liu et al. (2000). Carlone et al. (2006) review finite-difference and finite-element process models used for predicting heat transfer and cure in pultrusion. In this work they recommend the following empirical nth-order cure model for predicting cure kinetics of epoxy-resin composites, which is then coupled to the system s energy balance to predict thermal properties and cure conversion ... 

Abadie et al. (2002) showed that the following auto-catalytic kinetic model was useful for modelling the UV cure of epoxy-resin systems ... 

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