Conversion at vitrification

Poncet et al. (1999) monitored frequency-dependent dielectric measurements to examine the phase-separation process in poly(2,6-dimethyl-1,4-phenylene ether) (PPE) in a DGEBA-MCDEA resin. Dielectric measurements measured the build up in Tg both in the PPE-rich continuous phase and in the epoxy-rich occluded phases for 30-60-wt.% PPE mixtures. In the 30% PPE mixmre, the rate of reaction of the thermoset phase is equivalent to that of the neat system due to two opposing effects, namely a slower reaction rate due to dilution and a low level of conversion at vitrification due to the presence of high-Tg PPE. In the 60-wt.% mixture the dilution effect of the PPE has a large effect of decreasing the reaction rate. The continuous thermoplastic-rich phase vitrifies first, followed by the thermoset occluded phase. The final morphology (size of occluded particles and composition of continuous phase) is affected by kinetics, diffusion and viscosity during phase separation. 

In an experimental exploration [120], all approaches show the expected decrease in vitrification time with increasing frequency (LMDSC results shown in Figure 2.25). However, even with the extended frequency range (ca. 2 decades for LMDSC) the simultaneously measured heat flow is not accurate enough to correlate a specific frequency with the reaction kinetics of the different epoxy thermosetting systems. Indeed, there is a considerable experimental error (see scatter in Figure 2.25) and the variation of the vitrification time and the conversion at vitrification associated with 2 decades in frequency is only about 15 min and 6%, respectively. The latter is below the accuracy of the (partial) reaction enthalpy determination (LMDSC). 

In the course of the previous sections, several striking differences between the two epoxy systems were noted concerning the conversion at vitrification, the diffusion-controlled region in non-isothermal experiments, the critical heating rates, etc. These differences can be related to the chemical structure of the monomers, which influence the reactivity and the growing network structure. 

To evaluate, in more detail, the effect of the chemical structure of the reactants upon isothermal curing, the rate of conversion at vitrification (dx/dt)DF o.5 can be compared to the average rate before vitrification, (dx/dt), which equals XDF o.5ltDF o.5- It is necessary to work with ratios or relative rates r (Table 2.1) because the amine-epoxy system is much more reactive than the anhydride-epoxy system. For the latter system, the ratio r of (dx/df)Dir o.5 to (dx/df) is lower than 1 5 over the temperature range considered, which is much smaller than the lowest ratio of 1 2.4 for the epoxy-amine system. The ratio r also decreases with increasing cure temperature. 

The variations of this ratio correlate to the differences in final isothermal cure state. Since the rate of conversion at vitrification is non-zero, conversion and Eg further increase in the (partially) glassy state with a rate dependent on the relative rate at vitrification. A relatively lower (dx/d/) )f .o.5 or ratio r results in a smaller increase in conversion and Eg after vitrification. For example, Eg at the end of the isothermal cure at 70°C for the epoxy-anhydride system amoxmts to 85°C, whereas a value of 103°C is determined for the amine system under similar isothermal cure conditions. 

As the heating rate is increased, vitrification peak 2 shifts to a higher temperature until it merges with devitrification peak 3. This upward shift with increased heating rate is the result of the interaction of reaction rate, reaction time, and the degree of conversion at vitrification. 

Photopolymerization of 7 at 25 °C resulted in approximately 80% conversion of double bonds and a Tg of 70 °C. Apparently, the Tg of the material increased as crosslinking proceeded, but the reaction stopped at only partial conversion when vitrification occurred. The result was a Tg only 20-40 °C higher than the sample temperature. In addition, trapped free radicals were detected in crosslinked films of 7 by electron spin resonance (ESR) (28). 

Two main transitions may take place during the formation of a polymer network gelation, a critical transition defined by the conversion at which the mass-average molar mass becomes infinite (Chapter 3) glass transition, or vitrification, characterized by the conversion at which the polymer begins to exhibit the typical properties of a glass. 

The situation is completely different for the glass transition. The possibility of producing cooperative movements of fragments of the thermosetting polymer must increase with temperature. So, the conversion at which vitrification takes place increases with the cure temperature. 

Depending on the shape of temperature vs conversion trajectories, vitrification may take place at particular locations in the part. If this happens, the constitutive equations describing the kinetics must include the diffusional resistance that characterizes the sharp decrease in the polymerization rate when entering the vitrification region. In particular, vitrification can occur at the wall if Tw < TgltCl. In the examples that illustrate this section, it will be assumed that vitrification does not take place, but in the following section the influence of vitrification on the cure in a heated mold will be discussed. 

Fig. 23. Critical conversions at different Tcure (DGER-mPDA, P = 1). °av — start of vitrification (rise of dynamic Young modulus, Fig. 24)...

Whereas the calculation of the time to gelation is relatively simple, the calculation of the time to vitrification (tyu) is not so elementary. The critical point is to obtain a relationship between T, and the extent of conversion at T, (Pvu)- Once the conversion at Tg is known, then the time to vitrification can be calculated from the kinetics of the reaction. Two approaches have been examined one calculates tyu based on a relationship between T, and Pyj, in conjunction with experimental values of Pvit the other approach formulates the Tg vs. pyj, relationship from equations in the literature relating Tg to molecular weight and molecular weight to extent of reaction... 

In the above model, data for the extent of reacticm at vitrification are needed. These data were obtained using infrared spectroscopy. The extent of conversion of the epoxy group was monitored as a function of time at a series of temperatures. A corresponding set of TBA experiments was performed, and the time to vitrification data were... 

Figure 3.33 shows the effect of conversion of epoxy (i.e. increasing viscosity) on the wavelength of the maximum emission for excitation at 475 nm and the ratio of emission intensity at 588 and 564nm. There is a sharp increase in emission intensity but no spectral shift at the conversion corresponding to the Tg at the cure temperature, indicating that the probe is sensitive to both conversion and vitrification. 

In contrast to the shift of the sulfur monomer/polymer floor temperature to higher temperatures, recent work from our laboratory shows that nanoconfinement shifts equilibrium in free radical methyl methacrylate (MMA) polymerization towards monomer [93]. Results are shown in Fig. 11.9 again for MMA polymerized by 0.5 wt% AIBN, where the equilibrium conversion is plotted versus temperature. Conversions at low reaction temperatures are less than 100 % due to the effect of vitrification (i.e., the reaction cannot reach equilibrium because the reaction mixture turns to a glass and the reaction stops prior to 100 % conversion being reached). As the reaction temperature approaches and rises above the glass transition of the neat polymer (Tg p 110 °C), vitrification effects disappear and the conversion reaches the maximum value of 1.0. At higher temperatures, conversion again decreases. 

Network formation by photopolymerization has been studied for tetraethyleneglycol diacrylate (TEGDA) using isothermal calorimetry (DSC), isothermal shrinkage measurement and dynamic mechanical thermal analysis (DMTA). Due to vitrification the polymerization does not go to completion at room temperature. The ultimate conversion as measured by DSC seems to depend on light intensity. This can be explained by the observed delay of shrinkage with respect to conversion. 

In this contribution we present results obtained with tetra-ethyleneglycol diacrylate (TEGDA). This compound was chosen since its polymer shows an easily discernible maximum in the mechanical losses as represented by tan 5 or loss modulus E" versus temperature when it is prepared as a thin film on a metallic substrate. When photopolymerized at room temperature it forms a densely crosslinked, glassy polymer, just as required in several applications. Isothermal vitrification implies that the ultimate conversion of the reactive double bonds is restricted by the diffusion-limited character of the polymerization in the final stage of the reaction. Therefore, the ultimate conversion depends strongly on the temperature of the reaction and so does the glass transition. 

Figure 4.13 shows three possible adiabatic trajectories in the CTT diagram. For the trajectory with the lowest ATad(< Tgoo — T0), the straight line is intercepted by the vitrification curve. But when the system vitrifies, the reaction practically ceases, and there is no more possibility of getting out from the glassy state because the only source of temperature increase is the chemical reaction therefore, full conversion cannot be attained, and a postcure step at T > Tgoo is necessary to complete the polymerization. 

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