Cross associate

However, the mechanisms by which the initiation and propagation reactions occur are far more complex. Dimeric association of polystyryllithium is reported by Morton, al. ( ) and it is generally accepted that the reactions are first order with respect to monomer concentration. Unfortunately, the existence of associated complexes of initiator and polystyryllithium as well as possible cross association between the two species have negated the determination of the exact polymerization mechanisms (, 10, 11, 12, 13). It is this high degree of complexity which necessitates the use of empirical rate equations. One such empirical rate expression for the auto-catalytic initiation reaction for the anionic polymerization of styrene in benzene solvent as reported by Tanlak (14) is given by ... 

The substances H S, C02 and (C Hj-UO (diethyl ether) were treated as slightly active as there afen ndications that with these compounds cross-association occurs in liquid water. In the case of diethyl ether this conclusion is supported by the considerably higher mutual solubility for the H-O- -HgJgO system compared with water-alkane systems as shown Tn Table 5. To keep the number of parameters low, the following procedure was adopted in accounting for cross-association ... 

Further work is needed to be able to predict the properties of the cross-dimers and thus reduce the number of adjustable parameters in cases where cross-association must be considered. More complex associated species may have to be postulated to improve the results. 

Polymerization in aliphatic hydrocarbons is considerably slower than in aromatic hydrocarbons because of decreased dissociation of initiator and propagating ion-pair aggregates. The course of reaction in aliphatic hydrocarbons is complex compared to that in aromatic solvents. Initiation is very slow at the start of reaction hut proceeds with autoacceleration as cross- or mixed association of initiator and propagating ion pairs replaces self-association of initiator. Cross-association is weaker and results in an increased concentration of monomeric initiator. This effect may also explain the higher-order dependence of Rj on initiator (typically between and 1-order) in aliphatic solvents, especially for r- and f-butyllithium. Rp is still -order in initiator independent of solvent. 

Another complication introduced by the associative properties of organolithium solutions in non-polar solvents is the fact that the alkyllithium initiators are themselves associated and can be expected to "cross associate" with the active polymer chain ends. Thus some of our studies (26) on the effect of added ethyl lithium on the viscosity o -polyisoprenyl lithium solutions in n-hexane support the following association equilibrium... 

The reaction sequences described above are simplified, since "living" chain end self-association and cross-association may further complicate the reaction. 

Page 64, line 30 cross-association was not considered should be cross-association did not have to be considered. ... 

The presence of cross-associated species needs to be considered in the interpretation of copolymerization kinetics. It has been found 269) that the reaction of poly(butadie-nyl)lithium with p-divinylbenzene in benzene solution proceeds at a rate which increases markedly with time. Such a result implies that the poly(butadienyl)lithium aggregate is less reactive than the mixed aggregate formed between the butadienyl-and vinylbenzyllithium active centers. Interestingly, no accelerations with increasing reaction time were found with poly(butadienyl)lithium and m-divinylbenzene nor with poly(isoprenyl)lithium and either the m- or p-divinylbenzenes. This general behavior was subsequently verified 270) by a series of size exclusion chromatography measurements on polydiene stars (linked via divinylbenzene) as a function of conversion. 

The reactions of poly(styryl)lithium in benzene with an excess of diphenyl-ethylene 272) and bis[4-(l-phenylethenyl)phenyl]ether158) also were found to proceed by a first order process. However, the reactions of poly(styryl)lithium with the double diphenylethylenes l,4-bis(l-phenylethenyl)benzene and 4,4 bis(l-phenyl-ethenyl)l,l biphenyl gave l58) non-linear first order plots with the gradients decreasing with time. This curvature was attributed to departure from a geometric mean relationship between the three dimerization equilibrium constants (Ka, Kb and Kab). The respective concentrations of the various unassociated, self-associated and cross-associated aggregates involved in the systems described by Equations (49) to (51) are dependent upon the relative concentrations of the two active centers and the respective rate constants which govern the association-dissociation events. 

Lithium Alkyls. Organolithium compounds have been widely used as initiators, being readily available and experimentally very convenient. Their aggregated form in hydrocarbon solvents is readily broken down by addition of donor molecules, and initiation becomes fast and efficient. The presence of common impurities such as alkoxides can have a strong influence, almost certainly through cross-association, and may increase the rate of initiation in some solvents while depressing it in others. ... 

The cross-association between active polymer molecules and alkyllithium molecules forming mixed aggregates is demonstrated and their possible roles in affecting propagation rates and cross-propagation rates are suggested. 

Cross-associations of polymer-lithium and n-butyllithium, (RLi)6 resulted in reductions of solution viscosity. It is believed that R2D2Li4, R3DL14 and RSLi2 are the major products where D is the polydienyl and S the polystyryl moiety. 

As a second example, let us consider the case of N molecules or groups (1) that self-associate and N2 molecules or groups (2) that cross-associate only with groups (1) (Figure 2.2). 

As already mentioned, the starting point is the combination of one of the thermodynamic frameworks of Appendix 2.A with the above hydrogen bonding formalism. For simplicity of presentation we use the LF framework and we confine ourselves to the case of one self-associated (e.g., OH=OH) and one cross-associated (e.g., 0H=0(ether)) hydrogen bonding interaction. 

Case 2 Molecules or groups that self-associate and cross-associate but there is cooperativity in self-association 1-1... 

Let us have again Ni and N2 molecules (groups) between which there are A n self-association and Ni2 cross-association bonds (1 = -0-H, 2 = B). However, now, the bond for dimer formation is weaker than any subsequent bond of the multimer complex. 

Case 3 Same as case 2 but, now, there is cooperativity in both self-association and cross-association... 

Various modifications of the SAFT equation of state have been already proposed over the last several years. These have been presented in recent reviews.It is worth mentioning that in all these SAFT modifications different attractive terms are proposed, i.e., different terms for the of Equation 16.78. The chain and association terms remain unchanged. SAFT is available in existing process simulators by Aspen Tech and Simulation Sciences, and it is nsed by several indnstries (examples of applications have been reported by Exxon Research and Engineering Company and Shell Oil Company). However, in these simulators, only the nonassociating contributions are incorporated. The SAET eqnation of state has been extensively applied to nonpolymeric systems as well, including mixtures of hydrocarbons, water, alcohols, and phenols. A few applications to cross-associating systems, e.g., alcohol-water, have been also reported. 

The initiation and propagation mechanism of the anionic polymerization of styrene using NBL has been the subject of considerable investi tion and has been found to be very complex [71]. This is due to the associated complexes of the initiator and polystyryllithium as well as cross association between the two species. The simultaneous initiation and propagation that occurs in CSTR processes adds further complications. Try berg and Anthony [72] simplified this problem by initiating the polymerization in a separate reactor. They con-added the low molecular weight polystyryllithium solution to a CSTR polymerization reactor. 

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