Cure reactions diffusion control

Observed monomer concentrations are presented by Figure 2 as a function of cure time and temperature (see Equation 20). At high monomer conversions, the data appear to approach an asymptote. As the extent of network development within the resin advances, the rate of reaction diminishes. Molecular diffusion of macromolecules, initially, and of monomeric molecules, ultimately, becomes severely restricted, resulting in diffusion-controlled reactions (20). The material ultimately becomes a glass. Monomer concentration dynamics are no longer exponential decays. The rate constants become time dependent. For the cure at 60°C, monomer concentration can be described by an exponential function. 

The reaction of curing the epoxy-amine system occurring in the diffusion-controlled mode has little or no effect on the topological structure of the polymer 74> and on its properties in the rubbery state. However, the diffusion control has an effect on the properties of glassy polymers 76 78). 

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 it is apparent that these reactions are very complex and precise kinetics cannot be predicted with confidence for given compositions and conditions. The early stages of cure may show auto catalytic features while the onset of gelation can introduce a degree of diffusion-control of the kinetics. Orders of reaction between 0 and 4 have been reported, and the apparent order may change during the reaction. 

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). 

We shall see that throughout the literature there has been an implicit assumption of thermally activated processes, both for cure kinetics and for the intrinsic dipolar and ionic mobilities. However, it is well known that reaction kinetics become diffusion controlled at the later stages of cure, which leads to deviations from simple rate... 

Figure 1 shows kinetic curves of the DGER-mPhDA (P = 1) cure reaction at different T.ure. From these curves, the existence of the conversion at which the reaction stops due to diffusion control, adlf, can be seen. The measurement of the total reaction heat Q at different Tcure and its comparison with the estimated value based on the specific heat of epoxy ring opening give the values of adif for any T 16). 

Curing of epoxy resins is a typical example where overall diffusion control can become operative. During curing, the glass transition temperature of the system increases and may reach or exceed the reaction temperature. This phenomenon is dealt with in several reviews of this volume, particularly in those by J. K. Gillham and E. F. Oleinik. 

Neither model is entirely satisfactory in fitting the experimental data. The complexity of epoxy curing reactions contributes to the discrepancies. Many different mechanisms have been proposed The diffusion controlled nature of the... 

Phase separation or partial segregation occurring during curing may be an important factor determining the time dependence of rheokinetic parameter. It may be caused first of all by thermodynamic incompatibility or by diffusion controlled fluctuations for some types of reactions. Then, microgel can be formed before the bulk of the system is transformed into a macrogel. 

RTV-2 adhesives are solidified with a curing agent like all two-component adhesives. This reaction is not diffusion-controlled, so that the adhesives are suitable for bonding (and sealing) large adhesion gaps. There are two different reaction types for initiation of crosslinking condensation reaction and addition reaction. The end products differ in their chemical structures. 

The rate coefficients for the secondary-amine reactions were found to be only 17% of those for the primary-amine reaction, thus explaining the residual secondary amine found at the end of cure. This equation was found to explain the development of the main crosslinking site, namely the tertiary-amine site formed on the DDS, corresponding to network interconnection. However, overlaid with the rate equation for chemical conversion that implies that all reagents are accessible to one another is the effect of the development of the network so that the reactions become diffusion-controlled. This is of interest since this means that the rate coefficients now reflect the chemorheology of the system, not just the chemistry. Thus, if and represent the rate coefficients for diffusion and chemical control, the measured rate coefficient, k, will be given by (Cole et ai, 1991)... 

Figures 6 and 7 show the transformation between mass transfer cind kinetic control during the nitration of benzene and toluene for differing initial concentrations of nitric acid. Where the plots of log(Aw - At) cure linear, chemical kinetics are rate controlling, curved plots indicate the diffusion controlled and a treuisition region. If the initial concentration of nitric acid is low enough, the entire reaction is kinetically controlled.

These data show that EPl does not leave the glassy state when RTC samples are post-cured at 40°C for 1 h (PC40), either in the bulk or in the layers. Therefore, PC40 proceeds under diffusion control and is only little accelerated. As for RTC, the gross reaction rate slows down due to the decreasing mobility and only some additional oxirane conversion is obtained, but not full consumption (Pig. 30.3). Hence, the glass transition rises to only = 66.6 0.3 °C in the bulk... 

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