Cyclic oligomers formation thermodynamics

Irrespective of the reaction mechanism, the polymerization of lactams leads to an equilibrium between monomer, cyclic oligomers and polymer. Tobolsky and Eisenberg [9] showed that the thermodynamic parameters are independent of the reaction mechanism, so that the polymerizability may be rationalized in terms of the ease of formation of the cyclic monomer, or, its opening into a linear chain unit. The simple relation between the equilibrium monomer concentration [L]e, temperature, and standard heat and entropy of polymerization. 

The kinetics and thermodynamics of this process show close similarities to the polymerization of D4 initiated by CF3SO3H [3,4]. Both processes involve simultaneous formation of cyclic oligomers and polymer and lead to equilibrium, with similar proportions of cyclic-to-linear fractions [3-5], They also show similar thermodynamic parameters and a similar effect of water addition on the initial rate of polymerization. The specific feature of the polymerization of >2 is that cyclic oligomers 03 and D4 are formed simultaneously with the polymer fraction, but they equilibrate with monomer much faster than the polymer fraction. This behavior is best understood assuming formation of the tertiary oxonium ion intermediate, which isomerizes by ring expansion-ring contraction [3]. These kinetic features of the polymerization of make this monomer an interesting model for deeper studies on the cyclic trisilyloxonium ion question. 

Various authors, who studied the mechanism of cationic ring-opening polymerization, observed the formation of some specific cyclic oligomers there were, however, no attempts to rationalize observed distribution on theoretical grounds, i.e. the preferential formation of certain oligomers or the apparent absence of cyclic oligomers in some systems. Several reviews have been published on macrocyclization but usually they concentrate either on the thermodynamic 5) or synthetic aspects 4). Indeed, both these approaches, thermodynamic and synthetic , were developed simultaneously but have not correlated with each other. In the most papers concerned with synthesis the Jacobson-Stockmayer theory was not even quoted. 

The small contribution of macrocyclization in the polymerization of THF is due to two effects The formation of smaller cyclic oligomers like dimer and trimer is thermodynamically unfavorable (in contrast to the formation of e.g. 1,4-dioxane in the polymerization of ethylene oxide) because 10- and 15-membered cyclic ethers are strained. It is also kinetically hampered since the rate of chain transfer to polymer which leads to ring formation is low due to the lower basicity of the polymer units than that of THF. 

The ring-opening polymerization of D4 is controlled by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cyclization equilibrium constants of dimethylsiloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equilibrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equilibrium constant of the formation of each cyclic is approximatdy equal to the equilibrium concentration of this cyclic, Kn [(SiRjO) J. Thus the total concentration of cyclic oligomers in the equihbrium is independent of the initial monomer concentration. As a consequence, the amount of linear polymer decreases until the critical dilution point is reached, at which point only cyclic products are formed. 

FAB analysis, together with the application of Eq. 7.1, has been also performed in order to detect the distribution of cyclic oligomers formed in the polycondensation of isophthalaldehyde with ethylenediamine. The FAB-MS spectrum of the crude polymer (Figure 7.8) shows only peaks due to cyclic Schiff bases from dimer up to heptamer. This indicates that the reaction proceeds essentially without the concomitant formation of linear oligomers. The relative abundance of the macrocycles formed decreases in proportion to a factor close to n , consistent with a thermodynamic equilibrium. ... 

Among the oligomers, the cyclic trimer has been postulated to be uniquely stable [53, 54], This could be due to either a mechanism favouring the formation of trimer (kinetic control) or to the trimer having a lower energy than other oligomers (thermodynamic control), thus decreasing its rate of further reaction. 

In a recent thermodynamic and spectroscopic study Redington66 -68) evaluated AH and AS for the formation of cyclic and open-chain oligomers of hydrogen fluoride. His best fit to vapor density, heat capacity, excess entropy, excess enthalpy, and infra red absorption data shows a monotonous increase in AH per hydrogen bond with increasing number of HF molecules both for open-chain and cyclic clusters, using the relation... 

Scheme 7.3), a useful intermediate on the way to cryptophane synthesis. The facile formation of the cyclic trimer (as opposed to polymers and higher oligomers) is an interesting aspect of this chemistry, and it is not known whether this is a result of thermodynamic equilibration (possibly driven by insolubility of the product), or the result of a kinetic template effect. 

As to the thermodynamically controlled formation of acyclic polymeric assemblies in solution, there are only a few examples in the literature. The main problems are due to a) competition with cyclization processes b) low association constants c) low solubility of the oligomers. In fact the first reported polymeric assembly in solution made of zinc 5-(4-pyridyl)-10,15,20-triphenylporphyrin (ZnPyTPP) units [47], actually consists, as successively demonstrated, of a cyclic tetramer (Sect. 3.3). The linear polymer, however, was unambiguously detected in the solid state by X-ray analysis of a ZnPyTPP single crystal [47]. This is one of the first examples in the literature of met-alloporphyrins, illustrating the fact that the stability of an assembly may be strongly dependent on the aggregation state. 

Although the mechanism of the base-induced formation of calixarenes has been studied in some detail, the reaction pathways remain uncertain. The most intuitively reasonable proposal is that the immediate precursor of any particular calixarene, regardless of size, is the linear oligomer carrying the requisite number of aryl residues. Another proposal, however, postulates that calix[8]arenes, for example, arise from intermolecularly hydrogen-bonded dimers (hemicalixarenes) formed from a pair of crescent-shaped, intramolecularly hydrogen-bonded linear tetramers. Calix[4]arenes, formed under considerably more strenuous conditions, have been postulated to be the result not of direct cyclization of the linear tetramer but of reversion of the calix[8]arene. The cyclic octamer is viewed as the product of kinetic control, and the cyclic tetramer is viewed as the product of thermodynamic control. The particular efficacy of KOH and RbOH for the formation of calix[6]arenes suggests that the hexamer is the product of template control. 

---