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Bulk or mass polymerizations is the simplest process for step polymerizations, since it involves only the reactants and whatever catalyst, if any, which is required [Menikheim, 1988] There is a minimum of potentialities for contamination, and product separation is simple Bulk polymerization is particularly well suited for step polymerization because high-molecular-weight polymer is not produced until the very last stages of reaction This means that the viscosity is relatively low throughout most of the course of the polymerization and mixing of the reaction mixture is not overly dif cult Thermal control is also relatively easy, since the typicaly reaction has both a modest activation energy Ea and enthalpy of polymerization H Although some step polymerizations have moderately high activation energies, for example, 1004 kJ mol 1 for the polymerization of sebacic acid and hexamethylene diamine (Table 2-8), the H is still only modestly exothermic.



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(2.133)

The exact opposite is the case for chain polymerizations, which are generally highly exothermic with high activation energies and where the viscosity increases much more rapidly Thermal control and mixing present much greater problems in chain polymerizations Bulk polymerization is widely used for step polymerizations Many polymerizations, however, are carried out in solution with a solvent present to solubilize the reactants, or to allow higher reaction temperatures to be employed, or as a convenience in moderating the reaction and acting as a carrier 2-8b Different Reactant Systems.

= 11"2

For many step polymerizations there are different combinations of reactants that can be employed to produce the same type of polymer (Table 1-1). Thus the polymerization of a hydroxy acid yields a polymer very similar to (but not the same as) that obtained by reacting a diol and diacid:

J' d k {le l J'

2-119





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d 3 k N2 '"' {Po;,s + e2k 2 qo;,s, 1 ~ 2 2 }

2-120

0;,8

On the other hand, it is apparent that there are different reactant systems that can yield the exact same polymer. Thus the use of the diacid chloride or anhydride instead of the diacid in Eq. 2-120 would give exactly the same polymer product. The organic chemical aspects of the synthesis of various different polymers by different step polymerization processes have been discussed [Elias, 1984; Lenz, 1967; Morgan, 1965]. Whether one particular reaction or another is employed to produce a speci c polymer depends on several factors. These include the availability, ease of puri cation, and properties (both chemical and physical) of the different reactants and whether one or another reaction is more devoid of destructive side reactions.

(2.134)

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The ability to obtain high-molecular-weight polymer from a reaction depends on whether the equilibrium is favorable. If the equilibrium is unfavorable as it is in many instances, success depends on the ease with which the polymerization can be driven close to completion. The need for and the ease of obtaining and maintaining stoichiometry in a polymerization is an important consideration. The various requirements for producing a high polymer may be resolved in quite different ways for different polymers. One must completely understand each type of polymerization reaction so as to appropriately meet the stringent requirements for the synthesis of high-molecular-weight polymer. Various step polymerizations are described below and serve to illustrate how the characteristics of a polymerization reaction are controlled so as to obtain high polymer. 2-8c Interfacial Polymerization

The canonical variables qR,s and PR,s are independent of qI,s and PI,s, Their Poisson brackets are given by30 (2.135) and (2.136) Now, notice that if we define the complex canonical position and momentum variables by [108] (2.137) these complex canonical conjugate variables will have the following simple Poisson brackets: (2.138) and (2.139) As we go to the quantum regime, the commutators of the qo,s and Po,s will be given by the value of their Poisson brackets multiplied by in (canonical quantization). Then the complex canonical position and momentum operators will have the following commutators: (2.140) and (2.141) We can define the creation and annihilation operators just as in Section 2.4.1 but now using non-Hermitian canonical position and momentum operators rather than Hermitian ones. The reader can easily verify using (2.140) and (2.141) that defining the annihilation operator by (2.142) we have the expected commutation relations between creation and annihilation operators: (2.143) and (2.144)

Many of the polymers that are produced by the usual high-temperature reactions could be produced at lower temperatures by using the faster Schotten Baumann reactions of acid chlorides. Thus polyesters and polyamides could be produced by replacing the diacid or dieser reactant by the corresponding diacyl chloride

2-121

300therwise. the equations of motion (2.131) will not be derivable from the Hamiltonian (2.132).

2-122

From (2.130), (2.137), (2.134), and (2.142), we find that in terms of the quantized reciprocal-space field components, as(k) is given by (2.145) Inverting (2.145), using (2.125)-(2.127), and then substituting in (2.124), we find the following expressions for the quantized free-space radiation fields 31 :

2-8c-1

(2.146)

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