Termination rate constant, variation

More recent work has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates.5" 161,1152 There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section 7.4.1) and the various diffusion control models (Section 7.4.2) have seen new life and have been adapted by substituting the terminal model propagation rate constants (ApXv) with implicit penultimate model propagation rate constants (kpKY -Section 7.3.1.2.2). 

Since the entire emulsion polymerization takes place under diffusion controlled conditions, the variation in the termination rate constant may be conveniently expressed as a ratio of the values appropriate at different times during the reaction. 

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]. 

Schulz et al.12,13 estimated the elementary rate constants for methyl methacrylate in solvents whose viscosities varied by a factor of 170, indicating that the termination rate constants were inversely proportional to the viscosity of the solvents. The variation of propagation rate constants was much less than that of termination rate constants. They have also obtained similar results in the free radical polymerization of benzyl methacrylate. 

More recent wmrk has shown that the observed variation in propagation rate constants with composition is not sufficient to define the polymerization rates."" There remains some dependence of the termination rate constant on the composition of the propagating chain. Thus, the chemical control (Section... 

One of the problems of radical polymerization is high-termination-rate constants by combination ( ) or by disproportionation ( ). In view of this, polymer chains of controlled chain length cannot be formed and this technique is ill-suited for precise control of molecular structure (e.g., in star, comb, dendri-mers, etc.) required for newer apphcations like microelectronics. The major breakthrough occurred when nonterminatmg initiators (which are also stable radicals) were used. Because of its nonterminating nature, this is sometimes called living radical polymerization and the first initiator that was utilized for this purpose was TEMPO (2,2,6,6-tetramethylpiperidinyl-l-oxo) [36,37]. A variation of this is atom-transfer radical polymerization (ATRP) in which, say for styrene, a mixture of 1 mol% of 1-phenyl ether chloride (R—X) and 1 mol% CuCl with two equivalents of bipyridine (bpy) is used for initiation of polymerization. Upon heating at 130°C in a sealed tube, bpy forms a complex with CuCl (bpy/CuCl),... 

Each simulation, done in real time at a computer terminal, takes but a moment to complete. It is thus quite practical to vary in turn each of the starting conditions and rate constants for different time ranges. This procedure allows the investigator to assess how important the variation of one parameter is in determining the concentration of each species. (This is a sensitivity analysis.)... 

Thus, the terminal model for copolymerization gives us expressions for copolymer composition (Eqs. 6-12 and 6-15), propagation rate constant (Eq. 6-71), and polymerization rate (Eq. 6-70). The terminal model is tested by noting how well the various equations describe the experimental variation of F, kp, and Rp with comonomer feed composition. 

In view of this, one may ask whether in certain cases, the determination of the initiation rate (and as a consequence, of the rate constants of propagation and of termination) by the method used by Cooper and Melville was not in fact disturbed by this phenomenon of selfinhibition. In point of fact, this method is based on the investigation of the variation of the rate of oxidation as a function of time in the presence of an inhibitor (hydroquinoiie) added at the start. If, then, the reaction is self-inhibited, the experiment gives nothing but the total variation of its rate resulting from the competition between the consumption of the inhibitor added at the start and the appearance of an autoinhibitor during the course of the oxidation process. 

For long chain lengths, many molecules of hydroperoxide are formed per free radical initiating the reaction before termination occurs and hence variations of over-all rate constant K essentially reflects changes in the rate of propagation, i.e. in eq. (8)... 

What then are the kinetic corrollaries of such regular variations in the termination constant occurring in conjunction with the propagation of drain length Assuming that the interaction rate constant for macroradicals whose degree of polymerization... 

The calculation procedures [the 0 method, Kb method, and constant composition method] developed in Chap. 2 for conventional distillation columns are applied to complex distillation columns in Sec. 3-1. For solving problems involving systems of columns interconnected by recycle streams, a variation of the theta method, called the capital 0 method of convergence is presented in Secs. 3-2 and 3-3. For the case where the terminal flow rates are specified, the capital 0 method is used to pick a set of corrected component-flow rates which satisfy the component-material balances enclosing each column and the specified values of the terminal rates simultaneously. For the case where other specifications are made in lieu of the terminal rates, sets of corrected terminal rates which satisfy the material and energy balances enclosing each column as well as the equilibrium relationships of the terminal streams are found by use of the capital 0 method of convergence as described in Chap. 7. 

---