Chain-transfer constant

Various methods can be employed, based on the Mayo equation, to determine the values of the chain transfer constants. The following sections review some of these methods. 

A special case of Eq. (6.148) is of interest. Consider polymerization in the absence of a solvent or added chain transfer agent, so that [S] = 0. For steady-state polymerization, Eq. (6.25) can be used to express in terms of i p as 

Since Eq. (6.152) is quadratic in Rp, the plot of 1/DP vs. Rp is curved, the extent of which varies with the initiator. However, the initial portion of the plot, corresponding to small Rp values, is linear. By extrapolation of this linear part to i p = 0 yields Cm as the intercept. Moreover, the slope of the linear portion is given by 2zkt / k [m] from which the mode of termination or kp/kt may be determined, provided the other is known. For AIBN initiator C is negligibly small as a result Eq. (6.152) is practically linear in Rp even at higher values of Rp. 

Problem 6.25 The following data of rate of polymerization and degree of polymerization at low conversion were obtained in bulk polymerization of monomer M (initial concentration 8.3 mol/L) using different concentrations of thermal initiator I at 60°C  

The plot of 1/DP vs. Rp (Fig. 6.6) is seen to be linear at low (i.e., the first 3 points) according to Eq. (6.154). Therefore the values of the intercept and slope are determined from a least-squares calculation using the first 3 data points, yielding = Intercept = 6.03x10 and u 

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The magnitude of the individual terms in the summation depends on both th( specific chain transfer constants and the concentrations of the reactants undei consideration. The former are characteristics of the system and hence quantitie over which we have little control the latter can often be adjusted to study particular effect. For example, chain transfer constants are generally obtainec under conditions of low conversion to polymer where the concentration o polymer is low enough to ignore the transfer to polymer. We shall return belov to the case of high conversions where this is not true. 

If an experimental system is investigated in which only one molecule ii significantly involved in transfer, then the chain transfer constant to tha... 

This suggests that polymerizations should be conducted at different ratios of [SX]/[M] and the molecular weight measured for each. Equation (6.89) shows that a plot of l/E j. versus [SX]/[M] should be a straight line of slope sx Figure 6.8 shows this type of plot for the polymerization of styrene at 100°C in the presence of four different solvents. The fact that all show a common intercept as required by Eq. (6.89) shows that the rate of initiation is unaffected by the nature of the solvent. The following example examines chain transfer constants evaluated in this situation. 

Estimate the chain transfer constants for styrene to isopropylbenzene, ethylbenzene, toluene, and benzene from the data presented in Fig. 6.8. Comment... 

Fairly extensive tables of chain transfer constants have been assembled on the basis of investigations of this sort. For example, the values of acryla-... 

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. 

Evaluate the chain transfer constant (assuming that no other transfer... 

Table 1. Polymerization and Chain-Transfer Constants for Various Monomers ...

Table 2. Chain-Transfer Constants for Polymerization of Acrylamide in Water...

Table 10. Chain-Transfer Constants to Common Solvents for Poly(ethyl acrylate) ...

The molecular weight of a polymer can be controlled through the use of a chain-transfer agent, as well as by initiator concentration and type, monomer concentration, and solvent type and temperature. Chlorinated aUphatic compounds and thiols are particularly effective chain-transfer agents used for regulating the molecular weight of acryUc polymers (94). Chain-transfer constants (C at 60°C) for some typical agents for poly(methyl acrylate) are as follows (87) ... 

Chain transfer is an important consideration in solution polymerizations. Chain transfer to solvent may reduce the rate of polymerization as well as the molecular weight of the polymer. Other chain-transfer reactions may iatroduce dye sites, branching, chromophoric groups, and stmctural defects which reduce thermal stabiUty. Many of the solvents used for acrylonitrile polymerization are very active in chain transfer. DMAC and DME have chain-transfer constants of 4.95-5.1 x lO " and 2.7-2.8 x lO " respectively, very high when compared to a value of only 0.05 x lO " for acrylonitrile itself DMSO (0.1-0.8 X lO " ) and aqueous zinc chloride (0.006 x lO " ), in contrast, have relatively low transfer constants hence, the relative desirabiUty of these two solvents over the former. DME, however, is used by several acryhc fiber producers as a solvent for solution polymerization. 

Chain transfer to solvent is an important factor in controlling the molecular weight of polymers prepared by this method. The chain-transfer constants for poly(methyl methacrylate) in various common solvents (C) and for various chain-transfer agents are Hsted in Table 10. 

Table 4. Chain-Transfer Constants in Free-Radical Styrene Polymerization...

Solution Polymerization. Solution polymerization of vinyl acetate is carried out mainly as an intermediate step to the manufacture of poly(vinyl alcohol). A small amount of solution-polymerized vinyl acetate is prepared for the merchant market. When solution polymerization is carried out, the solvent acts as a chain-transfer agent, and depending on its transfer constant, has an effect on the molecular weight of the product. The rate of polymerization is also affected by the solvent but not in the same way as the degree of polymerization. The reactivity of the solvent-derived radical plays an important part. Chain-transfer constants for solvents in vinyl acetate polymerizations have been tabulated (13). Continuous solution polymers of poly(vinyl acetate) in tubular reactors have been prepared at high yield and throughput (73,74). 

Chain transfer to monomer is the main reaction controlling molecular weight and molecular weight distribution. The chain-transfer constant to monomer, C, is the ratio of the rate coefficient for transfer to monomer to that of chain propagation. This constant has a value of 6.25 x lO " at 30°C and 2.38 x 10 at 70°C and a general expression of 5.78 30°C, chain transfer to monomer happens once in every 1600 monomer... 

Liquid trichloroethylene has been polymerized by irradiation with Co y-rays or 20-keV x-rays (9). Trichloroethylene has a chain-transfer constant of <1 when copolymerized with vinyl chloride (10) and is used extensively to control the molecular weight of poly(vinyl chloride) polymer. 

Solution Polymerization. This method is not commercially important, although it is convenient and practical, because it provides viscous cements that are difficult to handle. Also, the choice of the solvent is a key parameter due to the high solvent chain-transfer constants for acrylates. 

Cumene hydroperoxide [95], benzoyl peroxide, or tert-h iiy peroxide [96]. can be used as accelerators with alkylboron initiators. The chain transfer constant for MMA to tributylborane has been estimated to be 0.647, which is comparable to tripropylamine [97]. 

It is clear that many procedures used to evaluate chain transfer constants can also be used to evaluate the kinetics of inhibition. The following sections will show that the mechanism for inhibition is often more complex than suggested by Scheme 5.11. 

Chain transfer is kinetically equivalent to copolymerization. The Q-e and Patterns of Reactivity schemes used to predict reactivity ratios in copolymerization (Section 7.3.4) can also be used to predict reactivities (chain transfer constants) in chain transfer and the same limitations apply. Tabulations of the appropriate parameters can be found in the Polymer Handbook 3 ... 

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