Rate constants propagation

Largest polymer chain length in polymer distribution Smallest polymer chain length in seed distribution and reactor effluent Initiation rate constant Propagation rate constant... 

These equations identify the dominant source and loss processes for HO and H02 when NMHC reactions are unimportant. Imprecisions inherent in the laboratory measured rate coefficients used in atmospheric mechanisms (for instance, the rate constants in Equation E6) can, themselves, add considerable uncertainty to computed concentrations of atmospheric constituents. A Monte-Carlo technique was used to propagate rate coefficient uncertainties to calculated concentrations (179,180). For hydroxyl radical, uncertainties in published rate constants propagate to modelled [HO ] uncertainties that range from 25% under low-latitude marine conditions to 72% under urban mid-latitude conditions. A large part of this uncertainty is due to the uncertainty (la=40%) in the photolysis rate of 0(3) to form O D, /j. 

Fourier transform infrared spectroscopy glycidyl methacrylate group transfer polymerization 2-hydroxyethyl methacrylate hydrophobic-lipophilic-balance hydroxypropylcellulose 2-hydroxypropyl methacrylate initiator concentration decomposition rate constant propagation rate constant termination rate constant... 

Table 6.4 Rate Constants at 60 C and Activation Energies for Some Propagation Reactions...

Inhibitors are characterized by inhibition constants which are defined as the ratio of the rate constant for transfer to inhibitor to the propagation constant for the monomer in analogy with Eq. (6.87) for chain transfer constants. For styrene at 50°C the inhibition constant of p-benzoquinone is 518, and that for O2 is 1.5 X 10. The Polymer Handbook (Ref. 3) is an excellent source for these and most other rate constants discussed in this chapter. 

Ionic polymers may exist as undissociated, unsolvated ion pairs undissociated ion pairs solvated to some extent solvated ions dissociated to some extent or some combination of these. The propagation rate constant kp and the dissociation equilibrium constant K of the lithium salt of anionic... 

In writing Eqs. (7.1)-(7.4) we make the customary assumption that the kinetic constants are independent of the size of the radical and we indicate the concentration of all radicals, whatever their chain length, ending with the Mj repeat unit by the notation [Mj ], This formalism therefore assumes that only the nature of the radical chain end influences the rate constant for propagation. We refer to this as the terminal control mechanism. If we wished to consider the effect of the next-to-last repeat unit in the radical, each of these reactions and the associated rate laws would be replaced by two alternatives. Thus reaction (7. A) becomes... 

Although there are a total of four different rate constants for propagation, Eq. (7.12) shows that the relationship between the relative amounts of the two monomers incorporated into the polymer and the composition of the monomer feedstock involves only two ratios of different pairs of these constants. Accordingly, we simplify the notation by defining... 

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

For the reaction of radical i with monomer j, Price and Alfrey assume that the cross-propagation rate constant can be written as... 

What is significant about these reactions is that only two possibilities exist addition with the same configuration (D -> DD or L LL) or addition with th< opposite configuration (D DL or L LD). We shall designate these isotactic (subscript i) or syndiotactic (subscript s) additions, respectively, and shal define the rate constants for the two steps kj and k. Therefore the rates o isotactic and syndiotactic propagation become... 

Under these conditions, a component with a low rate constant for propagation for peroxy radicals may be cooxidized at a higher relative rate because a larger fraction of the propagation steps is carried out by the more reactive (less selective) alkoxy and hydroxy radicals produced in reaction 4. 

Efficiency of Intermediate Formation. The variation of the efficiency of a primary intermediate with conversion of the feed hydrocarbon can be calculated (22). Ratios of the propagation rate constants ( 2 / i) reactor type (batch or plug-flow vs back-mixed) are important parameters. 

Kinetics. Details of the kinetics of polymerization of THF have been reviewed (6,148). There are five main conclusions. (/) Macroions are the principal propagating species in all systems. (2) With stable complex anions, such as PF , SbF , and AsF , the polymerization is living under normal polymerization conditions. When initia tion is fast, kinetics of polymerizations in bulk can be closely approximated by equation 2, where/ is the specific rate constant of propagation /is time [I q is the initiator concentration at t = 0 and [M q, [M and [M are the monomer concentrations at t = 0, at equiHbrium, and at time /, respectively. 

The thiol ( -dodecyl mercaptan) used ia this recipe played a prominent role ia the quaUty control of the product. Such thiols are known as chain-transfer agents and help control the molecular weight of the SBR by means of the foUowiag reaction where M = monomer, eg, butadiene or styrene R(M) = growing free-radical chain k = propagation-rate constant = transfer-rate constant and k = initiation-rate constant. 

Thus the thiol 0 2 25511 is capable of terminating a growiug chain and also initiating a new chain. If the initiation-rate constant, k is not much slower than the propagation-rate constant, the net result is the growth of a new chain without any effect on the overall polymerization rate (retardation). That represents a tme chain transfer, ie, no effect on the rate but a substantial decrease iu molecular weight (12). 

A parameter such as a rate constant is usually obtained as a consequence of various arithmetic manipulations, and in order to estimate the uncertainly (error) in the parameter we must know how this error is related to the uncertainties in the quantities that contribute to the parameter. For example, Eq. (2-33) for a pseudo-first-order reaction defines k, which can be determined by a semilogarithmic plot according to Eq. (2-6). By a method to be described later in this section the uncertainty in itobs (expressed as its variance associated with cb. Thus, we need to know how the errors in fcobs and cb are propagated into the rate constant k. 

In this equation, Mp is the monomer concentration within forming particles, pa is the adsorption rate of oligomeric radicals by the forming particles, Vp is the volume fraction of forming particles within the system, and kp and k, are the rate constants of propagation and termination, respectively. 

Photoinitiation is an excellent method for studying the pre- and posteffects of free radical polymerization, and from the ratio of the specific rate constant (kx) in non-steady-state conditions, together with steady-state kinetics, the absolute values of propagation (kp) and termination (k,) rate constants for radical polymerization can be obtained. 

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