Cyclization constant

In studies of the polymerization kinetics of triaUyl citrate [6299-73-6] the cyclization constant was found to be intermediate between that of diaUyl succinate and DAP (86). Copolymerization reactivity ratios with vinyl monomers have been reported (87). At 60°C with benzoyl peroxide as initiator, triaUyl citrate retards polymerization of styrene, acrylonitrile, vinyl choloride, and vinyl acetate. Properties of polyfunctional aUyl esters are given in Table 7 some of these esters have sharp odors and cause skin irritation. 

The cyclization constant (7, which may be evaluated from the observed ratio of the two products at a given concentration c, affords a measure of the tendency for a given bifunctional compound to cyclize. A plot of log C vs. the ring size n for the lactonization of w-hydroxy acids... 

Fig. 6.—Log of the cyclization constant C for the lactoniza-tion of co-hydroxy acids vs. ring size. The point for n = 5 represents a minimum value. (Data from Stoll and Rouv. )...

In resting muscle, creatine phosphate forms due to the high level of ATP. If there is a risk of a severe drop in the ATP level during contraction, the level can be maintained for a short time by synthesis of ATP from creatine phosphate and ADP. In a nonenzymatic reaction [6], small amounts of creatine and creatine phosphate cyclize constantly to form creatinine, which can no longer be phosphorylated and is therefore excreted with the urine (see p. 324). 

The end-to-end distribution of short polymer molecules (represented by a RIS model that includes long-range interactions through a hard-sphere potential is calculated by means of a Monte-Carlo method. The model predictions are contrasted with experimental data of the equilibrium cyclization constants. 

A Monte-Carlo study is conducted of the formation of benzo-crown ethers from an acyclic precursor. The major features of the computed cyclization constants are in harmony with trends observed in kinetic constants reported. 

Theoretical and experimental studies have also been carried out on sodium phosphate.48 Theoretical values for molar cyclization constants for the oligomeric molecules were calculated using the rotational isomeric state model. Specifically, calculations... 

The data obtained in these equilibrium studies have been treated quantitatively by Carmichael and Heffel (53) and by Brown and Slusarczuk (33), who evaluated the equilibrium data in terms of cyclization constants. The latter are identical with ring-chain constants of the type of Eq. (29) where the concentrations are expressed in mole fractions of building units. Table XI... 

We have investigated the free-radical polymerization of a variety of diallyl dicarboxylates extensively, especially DAP, DAI, and DAT, in terms of allyl polymerization, cyclopolymerization, and gelation [38]. The cyclopolymerization resulted in cyclization constants Kc of 7.5, 1.6, and 0.6 mol/L at 60 °C for DAP, DAI, and DAT, respectively. In this coimection, it should be noted that in the polymerizations of DAP, DAI, and DAT, two different modes of intramolecular cyclization should be considered. The cyclization reaction of DAP... 

Fig. IS. Experimental molar cyclization constants Kx (in mol dm ) for cyclics (CO C6H4 CO O CHj CHj 0) t with X = 2-9 in the melt at 543 K (delated o) are plotted as log against logx. They are compared with theoretical values calculated by the Jacobson and Stockmayer theory assummg that the corresponding open chain molecules obey (Jausrian statistics (these ralues are denoted )...

Figure 3. Arrhenius plot of cyclization constant Kc for the cyclopolymerization of...

Several theoretical treatments of cyclocopolymerization have been reported previously (8-11). These relate the compositions of cyclocopolymers to monomer feed concentrations and appropriate rate constant ratios. To our knowledge, procedures for calculating sequence distributions for either cyclocopolymers or for copolymers derived from them have not been developed previously. In this paper we show that procedures for calculating sequence distributions of terpolymers can be used for this purpose. Most previous studies on styrene-methacrylic anhydride copolymerizations (10,12,13) have shown that a high proportion of the methacrylic anhydride units are cyclized in these polymers. Cyclization constants were determined from monomer feed concentrations and the content of uncyclized methacrylic anhydride units in the copolymers. These studies invoked simplifying assumptions that enabled the conventional copolymer equation to be used in determinations of monomer reactivity ratios for this copolymerization system. 

Due to the difficulty of working with styrene-methacrylic anhydride copolymers, we have elected to determine reactivity ratios and cyclization constants from the compositions and structures of styrene-MMA copolymers derived from these copolymers. As is discussed in the experimental section it is possible to measure the styrene contents and the proportions of methoxy proton resonance occurring in three different areas (designated A, B and C) from the 1H-NMR spectra of S/MMA copolymers. The proportions of methoxy proton resonance observed in the A (F ), B (Fjj) and C (Fc) areas obey the following relationships in conventional styrene-MMA copolymers (6 7). 

Reactivity Ratios and Cyclization Constants Estimated for Styrene-Methacrylic Anhydride Copolymerization... 

These equations are similar to those assumed for the reactivity ratio determination. In contrast to what has been observed for conventional styrene-MMA copolymers, however, these equations indicate that a substantial proportion of the (SMM+MMS)-type resonance appears to occur in the C-area. The proportion of methoxy resonance observed in the C-area, in fact, exceeds P(SMS) by a substantial amount for many of the copolymers. This can be due to the assumption of an inadequate model for the copolymerization reaction, to the use of incorrect reactivity ratios and cyclization constants for the calculations or to an inadequate understanding of the methoxy proton resonance patterns of S/MMA copolymers. It is possible that intramolecular reactions between propagating radicals and uncyclized methacrylic anhydride units present on propagating chains result in the formation of macrocycles. Failure to account for the formation of macrocycles would result in overestimation of rc and rc and in underestimation of the proportions of MMA units in SMS triads in the derived S./MMA copolymers. This might account for the results obtained. An alternate possibility is that a high proportion (>50%) of the M-M placements in the copolymers studied in this work can be expected to have meso placements (], J2), whereas only a small proportion of such placements ( 20%) are meso in conventional S/MMA copolymers. Studies with molecular models (20) have indicated that the methoxy protons on MMA units centered in structures such as the following can experience appreciable shielding by next nearest styrene units. 

On the effect of the modification of the benzene rings in St-C3-St on the cyclopolymerization, we have still not had much information. It will be interesting to polymerize monomers substituted at benzene rings symmetrically or unsymmetrically by some groups. At the present moment, we have only one example, the polymerization of VN-Cj-VN, which has more bulky groups but wider TT-systems than St-Cj-St (22). Although more detailed works are still needed to compare the data of the cyclopolymerization of VN-C3-VN with those of St-C3 St, the monomer seems to be cyclo-polymerized equally readily to St-C3-St The rc values, the cyclization constant defined by Aso and his associates (41), for the cyclopolymerizations of St-C3-St and VN-C3-VN were 0.15 mol/... 

INTRODUCTION The molar cyclization constants from ring-chtiin equilibration reactions of poly(phenylmethylsiloxane) (PPMS) in both the bulk state and in solution were investigated in detail by Beevers and Semiyen. Based upon these studies Clarson and Semiyen have described scaling up such reactions to successfully isolate cyclic poly(phenylmethylsiloxanes), that is,... 

Other weU-behaved ring-chain systems (DLs) based on the transesterifi-cation reaction were studied over the years in the field of polymer chemistry. For instance, Semlyen and coworkers investigated DLs of cyclic and linear polyethyleneterephthalates, polydecamethyleneadipates, polytrimethylene-succinates, polydecamethyleneftiniarates and polydecamethylenema-leates. ° In all cases, a large number of molar cyclization constants (EM values) were obtained for the macrocycles involved. 

It has been known empirically for a long time that intramolecular reactions are usually faster than intermolecular reactions. In 1934, Stoll proposed that the cyclization constant (Q defined in Eq. (1) could be used to quantify this phenomenon. In the same year, Kuhn suggested that a theoretical parameter Ceff could be used to predict the rate constant for an intramolecular reaction from the rate constant hnter for an intermolecular reaction using the same relationship. ... 

The general equation for determination of the equilibrium cyclization constants for the composed cyclics is in fact the one shown previously in Section 4.04.2 (eqn [24]), because the equilibrium in polymerizations of such monomers is the same as in copolymerization of corresponding simpler monomers (e.g., 1,3,5-trioxepane polymerization versus 1 1 copolymerization of 1,3-dioxolane and formaldehyde). 

Figure 1 Cyclization constants K (mol dm" ) for cyclosiloxanes (Me2SiO) in a ring-chain equilibrate in toluene (black line) compared to theoretical values calculated according to eqn [9] (blue line). Adapted from Flory, P. Semiyen, J. A. I Am. Chem. Soc. 1966,88,3209, with kind permission of Springer Science and Business Media and ACS, respectively.

---