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where Z is the inhibitor or retarder. Z acts either by adding to the propagating radical to form Mn Z or by chain transfer of hydrogen or other radical to yield Z and polymer. The kinetics are simpli ed if one assumes that Z and Mn Z do not reinitiate polymerization and also that they terminate without regeneration of Z. The steady-state assumption for the radical concentration leads to

Ixl > e/2. -e/2 < x < e/2.

d M Ri 2kt M 2 kz Z M 0 dt 3-135

(E2)

3-136

2 3 4



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Equation 3-136 has been used to correlate rate data in inhibited polymerizations. A consideration of Eq. 3-136 shows that Rp is inversely proportional to the ratio kz =kp of the rate constants for inhibition and propagation. This ratio is often referred to as the inhibition constant z:

Figure F.1 A plot of the rectangular barrier (F.2).

z kz kp 3-137

We can use the intuitive relation lime-+o Ye(x) = o(x) to deduce a very popular representation of the delta function in physics. Consider the Fourier transform of Ye(x),





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It is further seen that Rp depends on Ri to a power between one-half and unity depending on the relative magnitudes of the rst two terms in Eq. 3-136. Two limiting cases of Eq. 3-136 exist. When the second term is negligible compared to the rst, the polymerization is not retarded, and Eq. 3-136 simpli es to Eq. 3-25. For the case where retardation is strong (kz =kp ) 1), normal bimolecular termination is negligible. Under these conditions the rst term in Eq. 3-136 is negligible and one has

:F [Ye(x)] (k)

Equation 3-138 shows the rate of inhibited polymerization to be dependent on the rst power of the initiation rate. Further, Rp is inversely dependent on the inhibitor concentration. The induction period observed for inhibited polymerization is directly proportional to the inhibitor concentration. The inhibitor concentration will decrease with time and [Z] at any time is given by

e, 2

Z Z 0 Ri t y 3-139

-e/2

where Z 0 is the initial concentration of Z, t is time, and y is the number of radicals terminated per inhibitor molecule. Combination of Eqs. 3-137, 3-138b, and 3-139 yields

= ek sm "'2 .

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in a ratio of about 2 : 1.) Crosslinked polystyrene ful lls many of the requirements of a support it is an inexpensive, readily available polymer with good mechanical, chemical, and thermal stability. Very importantly, polystyrene can be functionalized by many routes, such as chloromethylation, lithiation, carboxylation, acylation, and sulfonation. The chloromethyl and lithio derivatives are the most useful. The two complement each other by reacting with nucleophilic and electrophilic reagents, respectively, to yield a wide range of functionalized polystyrenes. For example, ammonium, carboxylate, aldehyde, thiol, cyanide, and diphenyl phosphine groups can be introduced by reacting chloromethylated polystyrene (Sec. 9-6) with an amine, RCOOK, NaHCO3 , RSK, KCN, and LiPf2, respectively. Lithiated polystyrene can be obtained by direct lithiation of polystyrene with n-butyllithium in the presence of tetramethylethylenediamine (or indirectly by reaction of brominated polystyrene with n-butyllithium):

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(ek)

9-66

The lithio derivative of polystyrene offers a route to polystyrenes containing OH, COOH, B(OH)2 , RSnCl2 , and Pf2 groups by reaction with ethylene oxide, CO2 , B(OR)3 , MgBr2 followed by RSnCl3 , and f2 PCl, respectively The usual polystyrene support contains 1 2% DVB, as this yields a mechanically strong support that is microporous; that is, it is highly swollen by solvents for polystyrene Swelling is accompanied with a signi cant expansion in volume Much higher degrees of crosslinking, up to and sometimes exceeding 20% DVB, yield rigid polymers that are macroporous or macroreticular They are produced by carrying out the copolymerization of styrene DVB in the presence of signi cant amounts of diluent This keeps the polymer in an expanded form during preparation and results in the macroporous structure.

(E3)

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