Conversion at gelation

If the Pw of the primary chains remains constant throughout the reaction, the condition for gelation reads again q0 = ljPw or expressed as the critical conversion at gelation cce... 

The conversion at gelation is generally assumed to follow from Flory s theory... 

Flory [1] has outlined a general method for determining the extent of the reaetion at whieh sueh a network beeomes possible, and has derived a simple general equation (Eq. [1]) connecting the critical conversion at gelation ( c) with the wei t-average functionality ( ,) of the initial system for the ease of polycondensation reaetions. 

On the other hand, Simpson et al. [29] investigated the structure of DAP prepolymer in detail, demonstrating that cyclization is an important phenomenon in DAP polymerization and should have a major bearing on gelation theory. It was suggested that the existence of extensive formation of cyclic structures may be partially responsible for the poor correlation between the Stockmayer equation and actual degree of conversion at gelation. 

Gordon [30] has pointed out that even Simpson s treatment considerably underestimates the importance of the effect and has extended the network theory to include a formal allowance for cyclization. He predicted that the conversion at gelation for a polymerizing monomer which undergoes cyclization is given by... 

As seen in Figure 2.26, the Tg — x data obtained from the residual cure (MT)DSC experiments are well described by the optimised Tg— x relationship [Eq. (27)] of the diffusion-controlled cure model (Tg is the solid line and Tga is the dashed line). The departure of the experimental data from the continuous dashed line is due to the effect of increasing crosslinking beyond the gel point. The conversion at gelation correlates well with the value of 25% measured with dynamic rheometry (using the criterion G = G ). 

Theoretical calculations to predict the conversions at which gelation of polyfunctional monomers occur are reviewed in reference 40. The gelations of DAP, DAIP, and diallyl terephthalate (DATP) near 25% conversion are Httle affected by conditions and are much higher than predicted. 

None of the Cr(III) products from Equations 6 or 7 are effective crosslinkers since a chromic aqua ion must be hydrolyzed first to form olated Cr to become reactive. Colloidal and solid chromium hydroxides react very slowly with ligands. In many gelation studies, this critical condition was not controlled. Therefore, both slow gelation times and low Cr(VI) Cr(III) conversion at high chromate and reductant concentrations were reported (9,10). 

Figure 3.10 shows the evolution of the fraction of branching units, and crosslinks with conversion. Before gelation there are no crosslinks in the system. At full conversion their concentration is equal to that of branching units, because every initial A3 molecule has become a crosslink of the polymer network. 

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. 

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... 

First, we tried to determine the gel point precisely. Figure 1 shows the graph for determination of the gel point in the bulk polymerization of DAP as a typical example [33]. The gel point was estimated as the conversion at the time when the gel starts to be formed. The gel point was determined as 22.3%, being somewhat lower than the 25% stated by Simpson [31]. This author estimated the gel point from the extrapolation of the conversion-time curve obtained in the early stage of polymerization to the time at which the fluidity of the reaction mixture was lost by gelation. 

Invariably in all experimental studies where the loss of fluidity has been taken as marking the gel point, the conversion at the observed gel point has been found to be higher than that (calculated) at the theoretical gel point. This is explained by the model proposed by Bobalek et al [20] for the gelation process, as shown in Fig. 5.9. According to this model, at the theoretical gel point, a number of macroscopic three-dimensional networks (gel particles) form and undergo phase separation. The gel particles so formed remain suspended in the medium and increase in number as reaction continues. At the experimentally observed gel point, the concentration of gel particles... 

Can the system be reacted to complete conversion without gelation If not, what is the extent of conversion of the acid functionality at the gel point calculated from (a) the Carothers equation and from the statistical approaches of (b) Flory-Stockmayer and (c) Macosko-Miller ... 

Problem 7.21 Calculate the conversion at which gelation should be observed in styrene containing 0.14 mol% p-divinylbenzene (DVB) and 0.04 mol/L benzoyl peroxide initiator at 60°C. Assume for this calculation that the vinyl groups in both styrene and DVB are equally active and that chain termination occurs solely by coupling. [Data at 60°C kj, = 2.4 x 10 s f = 0.4 fcp/fcj for styrene = 4.54x10 L mor s". ]... 

Since the OH is the limiting reactant, its conversion at the gel point (Carothers) = 0.88. So complete conversion of OH without gelation is not possible. 

---