Monomer-polymer equilibria

When a sufficiently high concentration of polymer is formed at equilibrium, monomer-polymer interactions have to be taken into account. 

Lack of termination in a polymerization process has another important consequence. Propagation is represented by the reaction Pn+M -> Pn+1 and the principle of microscopic reversibility demands that the reverse reaction should also proceed, i.e., Pn+1 -> Pn+M. Since there is no termination, the system must eventually attain an equilibrium state in which the equilibrium concentration of the monomer is given by the equation Pn- -M Pn+1 Hence the equilibrium constant, and all other thermodynamic functions characterizing the system monomer-polymer, are determined by simple measurements of the equilibrium concentration of monomer at various temperatures. 

Cationic polymerization of cyclic acetals generally involves equilibrium between monomer and polymer. The equilibrium nature of the cationic polymerization of 2 was ascertained by depolymerization experiments Methylene chloride solutions of the polymer ([P]0 = 1.76 and 1.71 base-mol/1) containing a catalytic amount of boron trifluoride etherate were allowed to stand for several days at 0 °C to give 2 which was in equilibrium with its polymer. The equilibrium concentrations ([M]e = 0.47 and 0.46 mol/1) were in excellent agreement with that found in the polymerization experiments under the same conditions. The thermodynamic parameters for the polymerization of 1 were evaluated from the temperature dependence of the equilibrium monomer concentrations between -20 and 30 °C. 

The critical concentration, that is, the monomer <=> polymer equilibrium dissociation constant for polymerization of ADP-actin, is 25-fold that for polymerization of ATP-actin. However, in both cases the filament is made of F-ADP subunits, and the rate constant for association of ADP-actin to filament ends is only 2.5-fold lower than the rate constant for association of ATP-actin. In the absence of free ATP, the... 

The ring expansion mechanism is of course only a special case of the well-known mechanism by which dioxolan reacts with non-cyclic formals e.g., (I) and CH2-(OMe)2 give (MeOCH2OCH2-)2 in this way. It also accounts in a simple manner for the cleanness of the monomer-polymer equilibrium and for the high yields of cyclic dimer (without any detectable linear fragments) which are obtainable from 1,3-dioxane and 1,3-dioxepan [8]. 

Because the onset of monomer-polymer equilibrium can occur before the filaments achieve their own equilibrium concentration behavior, these filaments will undergo polymer length redistribution. This is a slow process in vitro that in many respects resembles crystallization (See Ostwald Ripening). 

Monomer Ring size Monomer polymer states Enthalpy of polymerization, AHp (kJ/mol) Entropy of polymerization, ASp (J/mol K) Monomer concentration at equilibrium, [M]eq (mol4-) Ceiling temperature, (°K)... 

The equilibrium position for the monomer-polymer equilibrium in Eq. 3-174 will be dependent on the temperature with increased temperature, resulting in a shift to the left, since the forward reaction is exothermic. The reaction isotherm... 

Busfield, W. K., Heats and Entropies of Polymerization, Ceiling Temperatures, Equilibrium Monomer Concentrations, and Polymerizability of Heterocyclic Compounds, pp. 295-334 in Chap. II in Polymer Handbook, 2nd ed., J. Brandrup and E. H. Immergut, eds., Wiley-Interscience, New York, 1989. 

Monomer-polymer equilibrium, in more general sense,... 

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. 

Theoretical Model for Determining Monomer-Polymer Reaction Stoichiometry from Equilibrium Gel Partition... 

Polymerization leads to a contraction in the volume of the system so that the equilibrium of a monomer-polymer system shifts in the direction of the reaction as the hydrostatic pressure increases. This was demonstrated by Weale (40) in his studies of a-methylstyrene polymerization under high pressure. The ceiling temperature increased from 61° C at 1 atm to 170° C at 6480 atm. 

It was once thought that the Tc of THF was very low, in fact near room temperature (23). However, in recent years, as catalyst systems have been improved and more intensive studies have been carried out, the presumed Tc has risen first to 60—70° (18,24) and finally to 85 2° C (25, 26, 27). The lower values were probably the result of working with systems where a true monomer-polymer equilibrium was not obtained. Possibly also, careful enough techniques were not used in the isolation of the lower molecular weight polymers obtained near the ceiling temperature. Precipitation in water cannot always be used because low molecular weight PTHF s are partially soluble in water. 

These polymerizations depend upon the ability to oxidize the monomer to a radical cation, whose further reactions lead to polymer. Since the oxidation potentials of the polymers are lower than those of the corresponding monomer, the polymer is simultaneously oxidized into a conducting state so that it is non-passivating. Some of the more important electrochemically-synthesised structures are discussed in more detail below and Chandler and Pletcher U4) have reviewed the electrochemical synthesis of conducting polymers. Detailed discussion in terms of thermodynamic parameters is impossible because the polymerizations are irreversible, so that E0 is undefined for the monomer-polymer equilibrium. 

The molecular weight of the polyoxacyclobutane through any one polymerization may rise to a maximum and then decrease (19) but in similar experiments with ethylene oxide the observed maximum was no greater than the experimental error of the weight measurements. This point is of considerable interest and deserves more attention than it has received, for it raises once again the question of monomer-polymer equilibrium and suggests that such an equilibrium may be obscured in the epoxides by the non-equilibrium depolymerization to dioxane. It could also mean however that oxonium ion formation is much slower with oxacyclobutane than with epoxides so that depolymerization becomes important only towards the end of the reaction. 

In a conventional polymerization, termination is the irreversible step which prevents the attainment of an equilibrium between polymer and its monomer. Hence, if a sufficiently large amount of initiator is available, all the monomer will be converted eventually into polymer. This is in principle impossible in a polymerization involving living" polymers. 

After having reached the equilibrium ratio polymer/monomer the intrinsic viscosity shows its maximum value, depending on the temperature, concentration and sort of catalyst (29, 49, 94). By prolonged heating the intrinsic viscosity decreases and after a very sharp decrease during the first stage the viscosity approaches a certain limiting value which depends on the m temperature and on the sort and concentration of j- 7 catalyst (fig. 2). This decrease is a result of... 

The equilibrium ratio polymer/monomer is the same in the base catalysed polymerization as in the hydrolytic process (43, 94) and so is the equilibrium content of cyclic oligomers in both processes (43). Using the extremely fast basic polymerization it was made possible to follow the equilibrium in the range of very low temperatures, where it was hardly possible before. It was found that in polymers which were prepared below their melting point, the monomer content is essentially lower than would be expected from the extrapolation of the temperature depend-ence of the equilibrium monomer content obtained at higher temperatures (94) (fig. 5). This indicates that the crystaline fraction of the polymer does not participate in the equilibrium. It is possible to establish the concentration of the amorphous part independently, e. g. 

The fast establishement of the monomer-polymer equilibrium in the presence of basic catalysts makes it possible to arrange depolymerization... 

The ROMP of cycloheptene can lead mainly to dimer or to high polymer depending on the conditions. The equilibrium monomer concentration is temperature-dependent271. 

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