" ln X n ln Ap in .NET

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EX n has a value of about 60 kJ mol 1 for thermal initiator decomposition, and X n decreases rapidly with increasing temperature. EXn is about the same for a purely thermal, self-initiated polymerization (Fig. 3-16). For a pure photochemical polymerization EXn is positive by approximately 20 kJ mol 1 , since Ed is zero and X n increases moderately with temperature. For a redox polymerization, EXn is close to zero, since Ed is 40 60 kJ mol 1 , and there is almost no effect of temperature on polymer molecular weight. For all other cases, X n decreases with temperature. When chain transfer occurs in the polymerization, X n is given by an appropriate form of Eq. 3-108. The temperature dependence of X n can be quite complex depending on the relative importance of the various terms in Eq. 3-108. For the case where chain transfer to compound S is controlling (Eq. 3-119), one obtains
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ln  ! M 1 1 kp Ap Ep Etr;S ln ln S X n X n 0 RT ktr;S Atr;S 3-172
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The quantity Ep Etr;S is now EXn and can be obtained from a plot of either of the two forms of the left side of Eq. 3-172 versus 1=T. Etr;S usually exceeds Ep by 20 65 kJ mol 1 , with the more active transfer agents having lower values. The term (Ep Etr;S ) is usually 20 to 65 kJ mol 1 (Table 3-14) and the molecular weight decreases with
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TABLE 3-14 Activation Parameters for Chain Transfer in Styrene Polymerization (60 C)a Transfer Agent Cyclohexane Benzene Toluene Ethylbenzene Isopropylbenzene t-Butylbenzene n-Butyl chloride n-Butyl bromide n-Butyl iodide Carbon tetrachloride
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Ep Etr;S 56.1 62.0 42.3 23.0 23.0 57.4 58.6 46.1 29.3 20.9
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log (Atr;S =Ap ) 3.1 3.9 1.7 0.55 0.47 3.8 4 2 1 1
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Data from Gregg and Mayo [1948, 1953a,b].
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increasing temperature. The frequency factors for transfer reactions are usually greater than those for propagations, and the low transfer constant of a particular transfer agent is a consequence only of the high activation energy. 3-9b 3-9b-1 Thermodynamics of Polymerization Signi cance of DG, DH, and DS
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The thermodynamic characteristics ( G, H, S) of polymerization are important to an understanding of the effect of monomer structure on polymerization [Ivin, 2000]. Further, knowledge of H allows one to maintain the desired Rp and X n by appropriate thermal control of the process. The G, H, and S for a polymerization are the differences in free energy, enthalpy, and entropy, respectively, between 1 mol of monomer and 1 mol of repeating units in the polymer product. The thermodynamic properties of a polymerization relate only to the propagation step, since polymerization consists of single acts of initiation and termination and a large number of propagation steps. Chain polymerizations of alkenes are exothermic (negative H) and exoentropic (negative S). The exothermic nature of polymerization arises because the process involves the exothermic conversion of p-bonds in monomer molecules into s-bonds in the polymer. The negative S for polymerization arises from the decreased degrees of freedom (randomness) for the polymer relative to the monomer. Thus, polymerization is favorable from the enthalpy viewpoint but unfavorable from the entropy viewpoint. Table 3-15 shows the wide range of
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TABLE 3-15 Enthalpy and Entropy of Polymerization at 25 Ca;b Monomer Ethylene Propene 1-Butene Isobutylene 1,3-Butadiene Isoprene Styrene a-Methylstyrene Vinyl chloride Vinylidene chloride Tetra uoroethylene Acrylic acid Acrylonitrile Maleic anhydride Vinyl acetate Methyl acrylate Methyl methacrylate
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H 93 84 83.5 48 73 75 73 35 72 73 163 67 76.5 59 88 78 56
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S 155 116 113 121 89 101 104 110 89 112 109 110 117
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Data from Brandrup and Immergut [1989]; Sawada [1976]. H refers to the conversion of liquid monomer to amorphous or (slightly) crystalline polymer. S refers to the conversion of monomer (at a concentration of 1 M) to amorphous or slightly crystalline polymer. The subscripts lc are often used with H and S to show the initial and nal states (that is, Hlc and Slc ). The units of H are kJ mol 1 of polymerized monomer; the units of S are J K 1 mol 1 . c Data are for conversion of gaseous monomer to crystalline polymer.
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