Jacobson-Stockmayer theory

The ring-opening polymerization of is controUed by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cycHzation equihbrium constants of dimethyl siloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equihbrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equihbrium constant of the formation of each cycHc is approximately equal to the equihbrium concentration of this cycHc, [(SiR O) Thus the total... 

Jacobson-Stockmayer theory (L2.). Usually transfer and termination reactions in polymerization have energies of activation higher than propagation. Thus, we attempted coupling reactions at temperatures lower than usually applied. In order to assure the access of dichlorosilane to the surface of the sodium, the dispersion was continuously regenerated by ultrasonication. 

Fig. 21 Macrocyclisation equilibrium constants for polydimethylsiloxane. Experimental data are shown as dashed curves as follows I, Brown and Slusarczuk II, Hartung and Camiolo III, Carmichael and Wigner. The solid curve is calculated from Jacobson Stockmayer theory. (Reproduced with permission from Flory, 1969)...

Fig. 24 Plot of symmetry-corrected 0A5° (e.u.) against number of single bonds for macrocyclisation equilibria of formals [30], calculated from data reported by Yamashita et al. (1980). The curve was calculated from Jacobson-Stockmayer theory. For the meaning of the arrows see text...

J-acid, 9 402, 403 Jackets, heat-transfer, 16 111—718 Jacobsen s ligand, 20 305 Jacobson-Stockmayer theory, in siloxane polymer manufacture, 22 558 Jacquinot advantage, 14 228 J-aggregation, 9 508 Jahn-Teller distortion, 22 203 Jahn—Teller effect, 6 611 Jai Tire process, 21 476 Jameson cell, 16 653 Jamming phase diagram, 12 18 Jams... 

The molar cyclization equilibrium constants, Kx, of PDMS are measured. Using the Jacobson and Stockmayer equilibrium theory of macrocyclization, the dimensions of PDMS chains with 40-80 chemical bonds in the bulk polymer at 383 K are deduced. Dilution effects in the PDMS systems are contrasted with predictions of the Jacobson-Stockmayer theory, and the experimental molar cyclization equilibrium constants of the smallest siloxane rings are discussed in terms of the statistical properties of the corresponding oligomeric chains using tire RIS model of PDMS of Flory, Crescemi, and Mark [S 116]. 

Cyclic oligomers with x - 2-9 are found to be present in poly(1,3-dioxolane) samples prepared by monomer-polymer-equilibrations using boron trifluoride diethyl etherate as catalyst. The molecular cyclization equilibrium constants 7fx are measured and the values are in agreement with those calculated by the Jacobson-Stockmayer theory, using an RIS model to describe the statistical conformations of the corresponding chains and assuming that the chains obey Gaussian statistics. 

A theoretical model to determine the probability of loop formation, based on an elaborated form of the Jacobson-Stockmayer theory of cyclization equilibria, is developed and used on RNA chains of homogeneous puckering and lengths up to 2 residues. 

The ratio of back- and end-biting reactions depends on the reaction conditions, and may differ considerably in polymerizations of various monomers. In cationic polymerization, methyloxirane produces mainly a mixture of cyclic tetramers [335] and chloromethyloxirane yields both dimers and tetramers [336]. Under similar conditions, 1,3-dioxolane or 1,3-dioxepane yield a number of cyclic derivatives [337], the distribution of cyclics being in agreement with the Jacobson-Stockmayer theory [338],... 

Indeed, it was shown mat cyclic oligomers are always formed in the cationic polymerization of cyclic acetals and their distribution agrees well with the thermodynamic distribution calculated on the basis of Jacobson-Stockmayer theory (with exception of small rings with n = 2-4) [89]. 

These and related phenomena can be explained in terms of the thermodynamic theory of macrocyclics distribution, formulated by Jacobson and Stockmayer9) and its kinetic extension 10). The Jacobson-Stockmayer theory, relating the distribution of cyclic oligomers to the conformational probability of ring closure, does not take into account kinetic limitations and has mostly been used as a convenient tool for studying the conformation of macromolecules in solution s). A number of papers appeared in which distribution of cyclic oligomers was studied with this aim and which ignored mechanistic and kinetic aspects of the cyclization processes. 

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. 

This apparent duality has led to certain misunderstanding and confusion and for the reader less acquainted with this field the relation between theoretical distribution predicted by Jacobson-Stockmayer theory and the distributions observed in real systems (frequently different from those predicted by the theory) could be not clear. Thus, in this section we describe the theories and then explain major experimental results in terms of the thermodynamics and kinetics of cyclization. 

The Jacobson-Stockmayer theory is based on several assumptions and describes only systems in true thermodynamic equilibrium. Some systems fulfill these assumptions. In most real systems, however, either some of these assumptions do not apply or the state of thermodynamic equilibrium cannot practically be reached. For such systems the distribution of cyclic oligomers cannot be described exclusively by the theory based on the idealized thermodynamic approach and the influence of kinetic factors has to be taken into account. 

Application of the Jacobson-Stockmayer Theory to Cationic Ring-opening Polymerizations... 

In the systems conforming to the Jacobson-Stockmayer theory (e.g. 1,3-dioxolane-BF3) each cyclic oligomer has its own equilibrium concentration. Thus, after attaining the equilibrium, the concentration of each cyclic oligomer should be equal to this equilibrium concentration which depends neither on the initial monomer concentration nor on temperature. 

Equal reactivity of the reaction sites is a prerequisite to obtain the distribution of macrocycles predicted by the Jacobson-Stockmayer theory. This condition is usually fulfilled for reaction sites located along the chain as the macromolecule is constructed of the same repeating units. There is, however, at least one reaction site which is structurally different, i.e. the end-group ... 

In such a system concentration of each oligomer should pass through a maximum (provided that cyclization is fast enough to compete with chain growth) and then decreases approaching the equilibrium concentration predicted by the Jacobson-Stockmayer theory 10). On the other hand, when random back-biting is the only... 

As shown in Sect. 3.2.1, the rate of cyclic oligomer formation (expressed by the probability of attaining the corresponding conformation) is proportional to n 3/2. Thus, for systems conforming to the Jacobson-Stockmayer theory, the distribution... 

In the majority of systems studied the influence of the conformational preferences is so important that the distribution of cyclic oligomers can no longer be described in terms of the Jacobson-Stockmayer theory which neglects these factors. 

In Fig. 20, experimental molar cyclization equilibrium constants Kx for sodium metaphosphates (NaPC>3)x in molten sodium phosphate at 1000 K are compared with theoretical values (2 76). The latter were calculated by the Jacobson-Stockmayer theory (21) assuming that chains of all lengths obey Gaussian statistics and using... 

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