Photopolymerization rate equation

Moreover, it should be noticed that polymerization rates were determined from the maximum slope of the kinetic curves, namely at degrees of conversion between 20 and 40%. At that time, the large increase in viscosity of the photoresist may already have reduced the chain mobility, thus favoring radical isolation and first-order termination. It is therefore very likely that the intensity exponent of the photopolymerization rate equation will be less than 0.85 in the early stages and that it increases with conversion to reach almost unity in the solid network. Such a kinetic behavior was indeed observed for the photopolymerization of neat hexanedioldiacrylate (31). 

Using the condition yo= Co 1 for the layer 0,0+cbr accurate determination of the endless thin layer differential and integral characteristics of the process coincide. Therefore, the photopolymerization rate may be described by the initial equation (5.75), in which Vj= yscolo cxpi-ysIoO and is a function of time. 

Figure 5.25. Experimental dependencies (symbols) and dependencies calculated using equation (5.86) (lines) of maximal photopolymerization rate for DEGDA on thickness of layer at different concentrations of photoinitiator cq 0.08 (1), 0.06 (2), 0.03 (3), 0.02 mol/1 (4) o=40.6 W/m / =2xl0 m.

For most practical photopolymerizations there is appreciable attenuation of light intensity with penetration and the dependence of polymerization rate on monomer, photoinitiator, and light intensity is more complex (see Eqs. 3-54 and 3-55 for exact definitions). Equation 3-54 is especially useful for analyzing the practical aspects of a photopolymerization. When polymerizing any specific thickness of reaction system it is important to know Rp at various depths (e.g., front, middle, and rear surfaces) than to know only the total Rp for that system thickness. If the thickness is too large, the polymerization rate in the rear (deeper) layers will be too low, and those layers will be only partially polymerized—the result would be detrimental because the product s properties (especially the physical properties) would be... 

The rate of polymerization is assumed to be equal to the ordinate of the DSC trace, dQJdt [51]. At each time t, the concentration of the remaining monomer is proportional to (Q - Q), with Q corresponding to the total heat released when the photopolymerization is completed (% = 100%). Equation 10.8 can then be written as follows ... 

Both the conversion degree and the rate of polymerization exhibit in all cases a linear dependence on the light intensity (Fig. 3). The quantum yield (< >p) of the photopolymerization reflects the effectivity of the reaction and corresponds to the number of polymerizable functional groups per absorbed photons. From the polymerization rate the following equation results ... 

Cho and Hong (2005) used photodifferential scanning calorimetry to investigate the photocuring kinetics of UV-initiated cationic photopolymerization of 1,4-cyclohexane dimethanol divinyl ether (CHVE) monomer with and without a photosensitizer, 2,4-diethylthioxanthone (DETX) in the presence of a diaryliodonium-salt photoinitiator. Two kinetic parameters, the rate constant (k) and the order of the initiation reaction (m), were determined for the CHVE system using an auto-catalytic kinetics model as shown in the following equation ... 

The photopolymerization steps can thus be divided into two main parts the photochemical event that leads to the first monomer radical, the classical chemical propagation and termination processes of the reaction. The rate of a radical polymerization is defined by Equation 10.5, where kp and kt are the propagation and termination rate constants and 7abs the amount of light absorbed. 

Above equation is based on an analysis that indieates eharge transfer and exciplex formation of acrylonitrile with earbazole forms as the intermediate. Gao et al., carried out kinetie studies of photopolymerization of methyl methacrylate by using piperazine sulfur dioxide eharge-transfer eomplex as a photoinitiator. The polymerization rate (Rp) is dependent on the molar ratio of piperazine to sulfur dioxide, and the eomplex with a eomposition of piperazine to sulfur dioxide in a molar ration of 1 2 is the most effeetive. By using the complex as die photoinitiator, flie polymerization kinetics was expressed as,... 

According to the experimental data Pa Vi, and using equation (5.81) it follows that A >> 1. This leads to the expre.ssion for the maximum rate of the photopolymerization lVo=(d/Vdf)o, which corresponds to the point of the inflection of the kinetic curve... 

The analysis of equation (5.86) on maximum normalized rate of photopolymerization which in terms of the accepted value dP/ l-P)dt =-d/n(l-F)/d/ establishes the relationship between the ordinate F and rate W =(dF/d/), which corresponds to the point of inflection of the kinetic curve of the shape ln(l-P)=f /) and the maximum polymerization rate (-d(ln(l-F))/df)ma,... 

Third, taking into account that the thickness of layer I of the photopolymerization composition and its optical density ecal are small in our experiments, let us assume, that the obtained kinetic models will be approximately adequate in the variant of the photoinitiated polymerization in the case when we do not use the differential rate of the photoinitiator decomposition according to equation (6.51), but an average one upon the layer. Under the definition of average values in equation (6.51), we obtain... 

Effect of Temperature and Photoinitiator Anion. The polymerization temperature has a significant effect on both the rate of polymerization and the final limiting conversion. For example. Figure 9 contains a series of plots of reaction rate as a function of time for photopolymerization of an epoxide monomer. This figure illustrates that as the temperature is increased, the peak reaction rate increases and the reaction time decreases. The increase in reaction rate with increasing temperature ultimately arises from the effect of temperature on the propagation rate constant (which increases with increasing temperature as described by the Arrhenius equation for the rate constants). The rate of photoinitiation is... 

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