Equilibrium oligomer concentration

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. 

If the equilibrium concentrations of the individual oligomers are taken together, the equilibrium concentration of the cyclic fraction is obtained. On the basis of the 

In the equilibrated system the polymer concentration is [M]0 — [M]e. Thus, if this value is lower than [M]cril practically all polymer should exist in the form of cyclic macromolecules. This was pointed out by Jacobson and Stockmayer in their original paper g and discussed in detail by Enikolopyan et al. as early as 1967 15), but has not received enough attention. 

Apparently, this largely forgotten phenomenon was, at least partially, responsible for the long-lasting controversy concerning the proportion of the cyclic fraction in cyclic acetal polymers 16 . 

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  

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Thus, for each individual macrocycle a certain thermodynamic equilibrium concentration exists having the same physical meaning as the equilibrium monomer concentration. Increasing the ring size n, the equilibrium oligomer concentration decreases according to Eq. (3-2). 

The theory requires that cyclization proceeds with zero enthalpy change (all rings are strainless), i.e., cyclization is exclusively entropy driven and equilibrium is attained by maximization of the entropy. Thus, the equilibrium oligomer concentration, contrary to the equilibrium monomer concentration, does not depend on temperature. 

The equilibrium oligomer concentration [M]e is related to the entropy of formation AS° by... 

In the polymerization of tetrahydrofuran (THF) initiated with HO-SO2CF3 in CD3NO2 solvent at 35° C (molar ratio [THF]/[CD3N02]/ [CF3SO3H] = 20.8/24.6/1), the equilibrium monomer concentration (i.e., the ultimate conversion of monomer to polymer) is reached in 2 hr. At this stage of polymerization, concentration of cyclic oligomers is still very low [90]. 

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. 

If pure polymer is treated with trifluoromethane sulphonic acid under the same conditions, eventually exactly the same final state (referring to type and amount of monomer, oligomer and polymer) is reached (see Fig.8). Hence it is surely a matter of a thermodynamic equilibrium polymerization. Within a range of initial monomer concentration between 0,2 to 0,5 Mol/1 the equilibrium monomer concentration is constant and amounts at 0°C to (0,0146 - 0,0016) Mol/1. The equilibrium concentration of the dimer at 0°C is (0,0236 -0,0013) Mol/1. The temperature dependence of these concentrations was studied for the polymerization in methylene chloride between -25°C and +3.0°C with trifluoromethane sulphonic acid as catalyst.A Dainton-plot of the results is shown in Fig.9. We calculated from the slope and the intercept Hss (-1,9 0,2) kcal/Mol = (-7,95 0,8)kJ/Mol and A SO = (+1,5 i 0,5) cal/Mol K = (+6,24 2,1) J/Mol K. The small and positive entropy is noticeable. 

This polymerization has attracted much attention because it is very fast compared to the hydrolytic polymerization of fi-caprolactam, which takes several hours, whereas the anionic polymerization is complete within minutes, even below the melting point of the polymer. However, no large-scale process is known [190, 191]. The anionic polymerization of caprolactam is described in melt in extruders [192, 193], in direct polymerization to fibers [194] and in casting and RIM processes [195]. The latter processes, particularly, are performed below the melting temperature, so the equilibrium monomer (and oligomer) concentration is much lower (1-3%) compared to the hydrolytic polymerization (10-12%), where a monomer extraction step is necessary. 

Here, Kj are the equilibrium binding constants and q are the oligomer concentrations. The selectivity of polymers was found to be very great even if the difference in complexation free energies is very small, in good agreement with experiment. 

Depending on the final polymerization conditions, an equilibrium concentration of monomers (ca 8%) and short-chain oligomers (ca 2%) remains (72). Prior to fiber spinning, most of the residual monomer is removed. In the conventional process, the molten polymer is extmded as a strand, solidified, cut into chip, washed to remove residual monomer, and dried. In some newer continuous processes, the excess monomer is removed from the molten polymer by vacuum stripping. 

Monomer-oligomer equilibria. [Ni(Me-sal)2], mentioned above as a typical planar complex, is a much studied compound. In pyridine it is converted to the octahedral bispyridine adduct (/zsoo = 3.1 BM), while in chloroform or benzene the value of is intermediate but increases with concentration. This is ascribed to an equilibrium between the diamagnetic monomer and a paramagnetic dimer, which must involve a coordination number of the nickel of at least 5 a similar explanation is acceptable also for the paramagnetism of the solid when heated above 180°C. The trimerization of Ni(acac)2 to attain octahedral coordination has already been referred to but it may also be noted that it is reported to be monomeric and planar in dilute chloroform solutions. 

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