Tromsdorff effect.

With growing viscosity, the diffusion rate of propagating macromolecules decreases, the probability of their effective collision is diminished, and thus also the rate of bimolecular termination. As the rate of initiation is not appreciably affected by increasing viscosity, in a certain phase some radical polymerizations pass from a stationary to a non-stationary state in which the number of radicals increases. The polymerization is appreciably accelerated. This situation is called the gel effect or the Norrish-Tromsdorff effect [55]. As the change in the rate of termination contributes considerably to the gel effect, it will be discussed in detail in Chap. 6, Sect. 1.3. 

Norrish and Smith [29] and later Tromsdorff et al. [30] described a polymerization of methyl methacrylate, the rate of which increased from a certain conversion. The number of monomers of similar behaviour was extended by methyl acrylate [31 ], butyl acrylate [32] and other acrylates [33] and methacrylates [34], and vinyl acetate. The effect was explained by the reduction of the termination rate caused by hindered macroradical mobil-ity in viscous medium it was called the gel effect, or the Norrish-Tromsdorff effect. The gel effect is clearly manifested in radical polymerizations of weakly transferring monomers in bulk. It is significant also in the presence of a good solvent. The gel effect is suppressed by the presence of poor solvents++ and by... 

Diffusion control of termination is presently beyond any doubt. Various authors differ, however, in their opinion concerning the type of diffusion and the quantitative contribution of diffusion in the collection of processes manifested as the gel effect. Attempts to explain the Norrish-Tromsdorff effect on a molecular level are still of empirical character [8, 12, 36-38],... 

All the described procedures can reproduce surprisingly well the autoac-celerating course of the rate and the degrees of polymerization for the products of radical polymerizations in bulk or in concentrated solutions. From the point of view of the technological control of these systems it is a success. On the other hand, this very agreement hinders our approach to a real understanding of the basis of the Norrish-Tromsdorff effect because it is difficult to abandon incorrect ideas that have, nevertheless, been successful. 

Autoacceleration is also known as the gel effect or as the Tromsdorff effect or NorrishSmith effect after pioneering workers in this field. 

At the levels of divinyl monomer used in the formation of imprinted polymers the gel point is typically reached after a few minutes and at low conversion of monomer, usually below 5% [18,19]. In a study using 25% EDMA and AIBN as initiator at 70°C, high conversions were reached rapidly with over 90% conversion after just 20 min. (Fig. 2.5A) [19]. At this point, however, the viscosity is so high that the propagation becomes diffusion controlled and the rate of initiation decreases at the expense of initiator radical recombination. The Tromsdorff effect also sets in [1]. This is related to a slower termination by recombination, leading to an increase in the concentration of free radicals. By plotting the conversion X versus time, the variation of the product kp[M ] with time can be calculated (Fig. 2.5B) ... 

The explanation for this effect (known variously as the gel effect, Tromsdorff effect or auto-acceleration effect) is that the chain termination reaction slows down during conversion and, as can be seen by reference to equations (2.5) and (2.6), a decrease in the termination rate constant leads to an increase in both overall rate and molecular weight. The reason for the drop in termination rate is that as the reaction mixture becomes more viscous the radical ends of the polymer chains find increased difficulty in diffusing towards each other, leading to the important mutual termination reaction. Small monomer molecules on the other hand find little difficulty in diffusion at moderate conversion so that propagation reactions are relatively little affected, until the material becomes semi-soUd, when the propagation rate constant also decreases. It is of interest to note that the gel effect may be induced by the addition of already formed poly(methyl methacrylate) or even another polymer such as cellulose tripropionate because such additions increase the viscosity of the system. 

In view of Eq. (6.26) for ideal polymerization kinetics one would normally expect the reaction rate to fall with time, since the monomer and initiator concentrations decrease with conversion. However, the exact opposite behavior is observed in many polymerizations where the rate of polymerization increases with time. A typical example of this phenomenon is shown in Fig. 6.10 for the polymerization of methyl methacrylate in benzene solution at 50°C [49], At monomer concentrations less than about 40 wt% in this case, the rate (slope of conversion vs. time) is approximately as anticipated from the ideal kinetic scheme described in this chapter, that is, the rate decreases gradually as the reaction proceeds and the concentrations of monomer and initiator are depleted. An acceleration is observed, however, at higher monomer concentrations and the curve for the pure monomer shows a dramatic autoacceleration in the polymerization rate. Such behavior is referred to as the gel effect. (The term gel used here is different than the usage in Chapter 5 as it refers only to the sharp increase in viscosity and not to the formation of a cross-linked polymer.) The autoaccelerative gel effect is also known as the Tromsdorff effect or Norrish-Smith effect after pioneering workers in this field. It should be noted that the gel effect is observed under isothermal conditions. It should thus not be confused with the acceleration that would be observed if a polymerization reaction were carried out under nonisotherraal conditions such that the reaction temperature increased with conversion due to exothermicity of the reaction. 

Polymerizations as part of liquid-phase organic reactions are also influenced by mass and heat transfer and residence time distribuhon [37, 48]. This was first shown with largely heat-releasing radical polymerizations such as for butyl acrylate (evident already at dilute concentration) [49]. Here, a clear influence of microreactor operation on the polydispersity index was determined. Issues of mass transfer and residence time distribution in particular come into play when the soluhon becomes much more viscous during the reachon. Polymerizahons change viscosities by orders of magnitude when carried out at high concentration or even in the bulk. The heat released is then even more of an issue, since tremendous hot spots may arise locally and lead to thermal runaway, known in polymer science as the Norrish-Tromsdorff effect. 

Time required for 80% conversion is certainly unrealistic. However, it should be noted that Equation 10.2 holds only for the initial few percentage points of polymerization. At high conversions substantial deviations occur — recall the Tromsdorff effect. 

Kinetics of Photopolymerization. For each of these monomers, the polymerization rate is relatively low at low monomer concentration (less than 1 Wt%). This is because dilution reduces initiator efficiency and prevents auto-acceleration (Tromsdorff effect), which is typical of bulk photopolymerizations. The polymerization rate increases with increasing monomer concentration (IS), Similar observation was made by following the double bond conversion of the diacrylate (IS). The maximum polymerization rate and the conversion at maximum rate increase with increasing monomer concentration, suggesting that, at low monomer concentration, the mobility in the mixtures is high and decrease of rate at later stages results from a depletion of monomers and a decrease in the mobility of the polymer-rich phase as crosslink density increases (5). The polymerization rate is also dependent upon the architecture of the monomer. In dilute solution, differences in mobility are less, and factors such as the electronic structure of the monomers is important. 

There may be an autoacceleration in the rate of polymerisation as the result of a Tromsdorff effect near the end of the polymerisation. 

Another aspect of the problem with free-radical cases is the phenomenon known as autoacceleration, or the Tromsdorff effect (see Fig. 6-7). This occurs because the reaction is controlled by the rate of diffusion of the reactants, which lowers the termination rate. 

Fig. 6-7 The Tromsdorff effect (autoacceleration) for polymethyl methacrylate polymerization [15].

For polymerization in the liquid state, the reaction kinetics is even more complicated due to the heat and the increase in viscosity associated with the reaction, the so-caUed Tromsdorff effects [47]. The reaction accelerates itself as the polymerization proceeds as a result of a positive feedback loop generated by the increase in heat as well as in viscosity and the diffusion-controlled termination of the polymerization process [48, 49]. An example is illustrated in Figure 6.5 for a mixture of a polystyrene doubly labeled with anthracene and fluorescein (PSAF) dissolved in MMA monomer [50]. A PSAF/MMA (5/95) mixture containing 2wt% of Lucirin TPO as a photoinitiator and 6 wt% of ethylene glycol dimethacrylate (EGDMA) as a... 

In the case of polymerization-induced phase separation, due to the positive feedback arising from the Tromsdorff effects, it was found that the phase separation induced by polymerization also becomes autocatalytic. The phase separation proceeds with a maximum rate in the vicinity of the irradiation time at which the rate of polymerization reaches its maximum. As a consequence, a local strain field is generated and develops as the reaction continues. For small-molecule systems, this reaction-induced strain quickly relaxes and its effects on the subsequent reaction and phase separation are not significant. For polymeric systems, this reaction-induced strain is not negligible and therefore affects the concentration fluctuations as a long-range interaction. 

The preceding conveys the approach to be used in the kinetic modeling of free radical polymerization encountered e.g., with styrene, vinylacetate, methylmetacrylate. For practical applications the reaction scheme should be completed with further elementary steps Uke chain transfer between the macroradicals and the monomer and the solvent. These add terms to the RHS of the continuity equations (1.6.2-3 to 1.6.2-5), but the development followed here is not affected. Also, diffusion control of propagation and termination (Tromsdorff effect) may have to be accounted for [Gerrens, 1976]. The kinetic modeling of the various types and techniques of polymerization and the application to the reactor modeling and process development were reviewed by Kiparissides [1996] and Villa [2007]. 

Many factors that can influence the kinetics of the template polymerization can lead to effects similar to the template effect. The increase of the reaction rate is known as the Tromsdorff effect or gel effect. The polymerization classified as the template process often proceeds in a nonhomoge-neous system, for instance, with precipitation of the complex formed. Some authors explain the template effecf by a... 

As simple as this seems, some serious difficulties can be encountered, particularly in free-radical bulk polymerizations. One of them is illustrated in Figure 12.1 [1], which indicates the course of polymerization for methyl methacrylate by either bulk polymerization or solution polymerization using various concentrations of benzene, an inert solvent. The reactions were carefully maintained at constant temperature. At low polymer concentrations, the conversion versus, time curves are described by Equation 9.19. As polymer concentrations increase, however, a distinct acceleration of the rate of polymerization is observed which does not conform to the classical kinetic scheme. This phenomenon is known variously as autoacceleration, the gel effect, or the Tromsdorff effect. 

Much as any industrial chemical plant must consider numerous factors beyond the chemistry of a reaction, industrial polymerization processes require adequate control of temperature (especially to remove large exothermic heats of reaction), provide mixing, and involve appropriate separation techniques. Bulk polymerizations offer pure polymers in a reaction vessel, allowing the greatest possible yield per reactor volume. However, disadvantages such as vitrihcation, the Tromsdorff effect, and extraction of unreacted monomer have led to other polymerization methods, including solution, suspension, and emulsion polymerization. 

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