Termination rate constant, molecular

Development of a relationship which gives the decrease in the termination rate constant as a function of temperature and polymer molecular weight and concentration. 

In order to estimate the dependence of the termination rate constant on conversion, molecular weight and temperature, the following is assumed k- becomes diffusion controlled when the diffusion coefficient for a polymer radical Dp becomes less than or equal to a critical diffusion coefficient D ... 

Constrained by the assumption that propagation rates are independent of solution viscosity, termination rate constants have been correlated with media viscosity, cxamulative molar concentration of macroradicals, and molecular size (11,12,13). 

The termination rate constants and molecular weights for the different copolymerization models have also been studied for purposes of discriminating between different copolymerization models [Buback and Kowollik, 1999 Landry et al., 1999]. 

Assuming monomer termination as the main termination reaction, L6hr et al. (64) estimated the termination rate constant from the molecular weight distribution of the polymers. No direct evidence for the termination mechanism assumed was given, however. 

This decrease in termination rate constant, which will be referred to as gel-effect, always causes a significant increase in rate of polymerization and can also shift the molecular weight distribution to higher molecular weights, but the magnitude of the shift depends upon which reactions control molecular weight development. By increase in polymerization rate we mean the increase over the rate which would have been observed had gel-effect been absent. 

Mn = number average molecular weight rp = polymerization rate rt = chain transfer rate kt = termination rate constant ... 

Termination reactions occur between two relatively large radicals, and termination rates arc limited by the rates at which the radical ends can encounter each other. As a result, kt is a decreasing function of the dimensions of the reacting radical. The segmental diffusion coefficient and the termination rate constant increase as the polymer concentration increases from zero. This initial increase is more pronounced when the molecular weight of the polymer is high and/or when the polymerization is carried out in a medium which is a good solvent for the polymer. For similar reasons, k t is inversely proportional to the viscosity of reaction medium. A model has been proposed that accounts for these variations in k, in low-conversion radical polymerizations [15,16]. 

We assume here that the concentrations of monomer and initiator remain sensibly constant during the polymerization, and that any dependence of termination rate constants on macroradical size and concentration or autoacceleration effects can be neglected. Tliis means that the molecular weight distributions to be derived can be expected to apply to low-conversion polymers. Commercial macromolecules, whose polymerizations are often finished at high conversions, may have distributions that differ from those calculated here. Section 6.14.2 discusses the size distributions of such polymers. 

One of the most striking features of CCT is the exceptionally fast rate at which it takes place. The molecular weight of a polymer can be reduced from tens of thousands to several hundred utilizing concentrations of cobalt catalyst as low as 100—300 ppm or 10 3 mol/L. The efficiency of catalysis can be measured as the ratio between the chain-transfer coefficients of the catalyzed reaction versus the noncatalyzed reaction. The chain-transfer constant to monomer, Cm, in MMA polymerization is believed to be approximately 2 x 10 5.29 The chain-transfer constant to catalyst, Cc, is as high as 103 for porphyrins and 104 for cobaloximes. Hence, improved efficiency of the catalyzed relative to the uncatalyzed reaction, CJCu, is 104/10 5 or 109. This value for the catalyst efficiency is comparable to many enzymatically catalyzed reactions whose efficiencies are in the range of 109—1011.18 The rate of hydrogen atom transfer for cobaloximes, the most active class of CCT catalysts to date, is so high that it is considered to be controlled by diffusion.5-30 32 Indeed, kc in this case is comparable to the termination rate constant.33... 

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. 

For a steady-state situation, what is important is the rate at which radicals are being formed, Rj . It is this which, when compared to the rate of substrate removal or (molecular) product formation, will allow one to decide whether the overall reaction is largely free-radical or ionic in nature. The steady-state concentration, in itself has little meaning unless it can be related to the rate of radical formation. Fortunately, it is generally possible to do this, since the rate of radical formation is given by the steady-state concentration divided by the radical lifetime, r. Radical lifetimes either can be experimentally measured in the system or, in many cases, can be obtained from literature data of termination rate constants. The relationship between the rate of radical formation and the steady-state radical concentration depends on whether the radical decays by first- or second-order kinetics. 

Typical termination rate constants are in the range of 10 -10 L/mol-s or orders of magnitude greater than propagation rate constants. The much greater value of kt (whether ktc or ktd) compared to kp does not, however, prevent high molecular weight polymer formation because the concentration of radical species is very small (low value of kd) and because the polymerization rate is dependent on only the one-half power of kt (see p. 443). 

Furthermore, the authors pointed out that they obtained in the emulsion polymerization of styrene (monomer to water ratio 1 2) with an inisurf concentration of 5.4 X 10 mol/1 water in the presence of an alkylated poly (oxyethyl-ene) emulsifier (alkyl chain length C16 -18 and 20 oxyethylene units 4% by weight related to water) the same overall rate of polymerization as with water-soluble initiators in the concentration range 10 to 10 mol/1 water. The polymer produced in the presence of inisurf has a molecular weight of some of 10 g/mol mainly due to the lowered termination rate constant. 

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