Critical monomer concentration

In the polymerization of St initiated with type II MAI composed of polyvinylpyrrolidone (PVP), block efficiency was kept to 80% when feed concentration was above 3 mol/L, but it drastically decreased below 3 mol/ L (Fig. 2) [36,37]. AIBN, the typical low-molecular weight azo initiator, shows a drastic decrease in its initiation efficiency below a critical feed monomer concentration, i.e., 0.5 mol/L. In the case of MAI, it seems that a similar decrease in initiation efficiency occurs at much higher critical monomer concentration due to immobility of macroinitiating radicals. 

Any carbenium ions which are not paired have both their complexation sites occupied by the most polar or polarisable species available, which can be the solvent or the monomer, according to their relative polarities, polarisabilities, and concentrations for paired cations, the picture applies to their other, still vacant, site. Such a situation will generally prevail in nonpolar solvents because in these the concentration of paired cations is dominant. In a polar solvent, both sites at an unpaired cation can be occupied by solvent, or one by solvent and one by monomer, or both by monomer. In the radiation polymerisations, one sees clearly that as the monomer concentration is reduced from bulk monomer, the kinetics change and they eventually become first order in monomer, whatever the solvent the critical monomer concentration at which this happens depends on the polarity of the solvent [12]. 

Figure 3.2 compares the level of cyclics on a molar, wt%, or yield basis as a function of reaction concentration. Note that as the reaction concentration dropped, the yield increased to near 100 %, as predicted from theory. However, the amount of cyclic PBT on a molar or wt% in solution basis remained constant at the critical monomer concentration, which is about 0.050 M, regardless of the concentration of polymer in solution. In fact, if one calculates the amount of cyclic present in an equilibrated melt (1-2 %), it is also about 0.05 M cyclic. The same amount of cyclic was generated via the ring-chain equilibration process, regardless of the reaction concentration only the amount of polymer which remains as a by-product... 

Here, the ratio k-lk+ defines the critical monomer concentration [M], the point below which no polymerization can occur. Integration of -d[M]df = k+ [Mo] - [M ] yields the expression ... 

It should be remarked that dilution of the monomer decreases the entropy of polymerization and, hence, even if its value were positive for pure monomer it eventually becomes negative at a sufficiently high dilution. Therefore, for any system showing the phenomenon of floor temperature, polymerization becomes impossible at any temperature below a certain critical monomer concentration. 

The most significant kinetic analysis is that of Dainton and coworkers (46—49). Under conditions where termination by metal ions was not important, Rv varied as [M]2 at low monomer concentrations and as [M] at high concentrations. The critical monomer concentration for transition from one region to another varied with the rate of initiation, first decreasing and then increasing as the rate of initiation increased. Data in the literature giving exponents of [M] of either one and two are apparently reconciled in this way. 

When nucleation is highly unfavorable (i.e., a l) the polymer system exhibits a biphasic behavior depending on the total monomer concentration A0. In this case there is a sharp phase transition between the all-monomer state for A0 < 1 /K, where l/K is the critical monomer concentration. When A0 exceeds 1 /K the free monomer concentration stays fixed at [A eq = l/K. This type of nonsmooth behavior at x = lforcr = 1 is called a transcritical bifurcation in non-linear dynamics [191]. It is also widely known as phase transition in physics. Figure 10.5 shows that for a less than unity, the transition is smooth. Hence we see that the... 

In contrast, recent kinetic investigation of the polymerization of spacerless G2 dendron-substi-tuted styrene and methylmethacrylate, respectively, in solution lead to the unexpected conclusion that above a certain critical monomer concentration a strong increase in the rate of the free radical polymerization is observed [21]. The results can be explained by self-organization of the growing polymer chain to a spherical or columnar superstructure in solution, depending on the degree of polymerization (DP, Fig. 2). The rate constants and low initiator efficiency lead one to conclude that the self-assembled... 

It was predicted that, in the limit of an infinite value of there is a critical monomer concentration erne = nEM below which the solution is virtually solely composed of the self-assembled macrocycle and above which the concentration of the latter remains constant, with the excess monomer then producing only non-cyclic species. 

Amphiphilic molecules such as lipids have an extremely low solubility in water and tend to self-associate and form lyotropic liquid crystals [1] if their monomer concentration in aqueous surroundings exceeds a critical value (the critical monomer concentration, (CMC), [2]). This self-organization is due to the hydrophobic effect [2], It leads to the formation of micro- and mesoscopic structures, among them micellar, hexagonal, lamellar and cubic phases [3] and the respective transitions between them. ... 

However, if formation of linear polymer is not possible, and the initial concentration of monomer is above the critical monomer concentration, then the ratio p = [M]/Jfi becomes higher than 1. Otherwise the sum on the right-hand side of eqn [18] would be, at the most, equal to the critical cyclic concentration (cf. eqn [8]), and the eqn [18] would not hold. 

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