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One involves short-stopping a polymerizing system by adding a highly ef cient terminating agent All propagating centers are quickly terminated with incorporation into the polymer of an end group derived from the terminating agent The end groups in the polymer are analyzed after separation of the polymer from the other components of the reaction system This method is limited by the general dif culty of end-group analysis since the concentration of end groups can be quite low and by the need to assume that the terminating agent terminates all propagating centers 2-Bromothiophene has been used to short-stop styrene polymerization with the bromine content of the polymer being analyzed by neutron activation [Higashimura et al, 1971] Termination of isobutylene polymerization by 2,6-di-t-butylphenol invovles aromatic alkylation in the para position of the phenol by the propagating carbocations.



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a 2 - 2abcos2() + b2 ,

Analysis of the 2,6di-t-butylphenol end groups is accomplished by UV spectroscopy [Russell and Vail, 1976] The second method for determining the propagating species concentration involves direct UV visible spectroscopic analysis of the propagating species during polymerization The high extinction coef cients of some aromatic carbocation propagating species coupled with the availability of highly accurate spectrophotometers has resulted in extensive use of this method Measurement of the UV absorbance of the polymerizing system as a function of time allows one to determine ki , Ri , the concentration of propagating species, and kp The UV method has also been used to study very fast polymerizations.

(4.102)





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In stopped- ow, rapid-scan spectroscopy, separate monomer and initiator solutions are rapidly forced through a mixing chamber (where instantaneous mixing occurs) and then into a capillary tube located in a spectrophotometer, ow is stopped and the progress of reaction followed by measuring the change in absorbance with time [Chance, 1974; Givehchi et al, 2000; Sawamoto and Higashimura, 1979; Szwarc, 1968] More recent advances in experimental techniques offer potential for improvements in our knowledge of the concentrations of propagating species and the values of propagation rate constants Conductivity and spectroscopic methods have improved because of modern instrumentation, allowing a more reliable measurement of the propagating center concentration A new method referred to as the diffusion clock method offers an alternate approach to obtain propagation rate constants.

((~a2)

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This involves polymerization in the presence of an highly active terminating agent, such as allyltrimethylsilane, speci cally known to have a rate constant for reaction with carbocations at the diffusion-controlled reaction limit (k % 3 109 L mol 1 s 1 ) The ratio of the rate constant for propagation to that for termination is obtained from measurements of the amounts of monomer and terminating agent consumed This ratio multiplied by the diffusion-controlled reaction rate constant k yields the propagation rate constant The carbocation propagation rate constant for isobutylene is reported as 6 108 L mol 1 s 1 and 3 10 108 L mol 1 s 1 by two different laboratories using the diffusion clock method, values that are in good agreement with the values obtained by other methods (Table 5-3) [Roth and Mayr, 1996; Schlaad et al, 2000]..

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+ b2 ,

5-2e-2

(4.103)

Most reported values of kp and other rate constants and kinetic parameters are questionable for several resons. First, as discussed above, there is ambiguity about the concentration of propagating species. Second, the calculations of various rate constants and kinetic parameters are often based on inadequately substantiated reaction kinetics and mechanisms [Kennedy and Marechal, 1982; Plesch, 1971, 1990]. Even if the propagating species concentration is accurately known, the use of Eq. 5-31 without veri cation can lead to incorrect results. This occurs when the kinetics of cationic chain polymerization deviate from Eq. 5-31 and the scheme described in Sec. 5-2d-1 under certain reaction conditions (Sec. 5-2f). Third, there is the large question of how to interpret any obtained rate constants in view of the known multiplicity of propagating carbocation propagating species. The kinetic expressions in Sec. 5-2d are written in terms of only one type of propagating species usually shown as the ion pair. This is incorrect, since both ion pairs and free ions are simultaneously present in most polymerization systems, usually in equilibrium with each other (Sec. 5-1). Thus the correct expression for the rate of any step (initiation, propagation, termination, transfer) in the polymerization should include separate terms for the respective contributions of the two types of propagating species. As an example, the propagation rate should be written as

5-48

= a 2 + 2abcos2()

where [YM ] and [YM (IZ) ] are the concentrations of free ions and ion pairs, respectively, and kp and kp are the corresponding propagation rate constants. Most reported kp values are only apparent or pseudo or global rate constants, kapp , obtained from the polymerization rate p using the expression

1 a = - cosh r, 2

5-49

(4.104) (4.105)

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