Cyclization equilibrium constants

According to the Jacobson-Stockmayer theory4 4, the molar cyclization equilibrium constant is defined by... 

Molar Cyclization Equilibrium Constant (Kx) and the Rate Constant of Propagation (kp x) and Depropagation (kj x) for Cyclic x-mer at 0eC with LiO-t-Bu (4.5xl0-3M)... 

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]. 

Calcd. quantities 0 / x/2 = 3.3 Molar cyclization equilibrium constants, Kx... 

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. 

More quantitative chemical evidence for random coil configuration comes from cyclization equilibria in chain molecules (49). According to the random coil model there must be a very definite relationship among the concentrations of x-mer rings in an equilibrated system, since the cyclization equilibrium constant Kx should depend on configurational entropy and therefore on equilibrium chain and ring dimensions. Values of /Af deduced from experimental values on Kx for polydimethylsiloxane, both in bulk and in concentrated solution, agree very well with unperturbed dimensions deduced from dilute solution measurements(49). 

For convenience, the cyclic populations of ring-chain equilibrates are expressed in terms of the molar cyclization equilibrium constants Kx for the individual x-meric ring molecules M, thus... 

C. Theoretical Expression for Molar Cyclization Equilibrium Constants... 

In their classic paper published in 1950, Jacobson and Stockmayer (21) presented a theory giving a precise expression for the concentrations of macrocyclics Af, in ring-chain equilibrates. The molar cyclization equilibrium constants Kx were given by... 

Fig. 4. Molar cyclization equilibrium constants for cyclics ((CH3)2SiO)jc at 383 K for a bulk equii-ihrate (o) are compared with a solution equilibtate ( ) and with values calculated (x) as described in the...

Fig. 6. Experimental molar cyclization equilibrium constants for cyclics (R(CH3>SiO) K in undiluted equilibrates at 273 K (R = H) and 383 K (R =...

Experimental molar cyclization equilibrium constants for cydics in the undiluted equilibrate (containing 81% linear polymer) and the solution equilibrate (containing 14% linear polymer) are plotted as tog versus tog x in Fig. 11. The values are... 

Fig. 11. Experimental molar cyclization equilibrium constants Kx (in mol dm ) in undiluted (o) and solution ( ) equilibrates of poly( 1,3-dioxolane) at 333 K compared with values calculated (x) by the J obson and Stockmiqrer theory...

Experimental molar cyclization equilibrium constants for cyclics in the PDA n%lt and the P1 melt at 423 K are own dotted as log gainst Ic x in Fig. 12 and 13. They are compared with theoretical values calculated by the Jacobson and Stockmayer ex esrion Eq. (6) with - 2jc- Values of < / >q required by this expression were comfHited by the exact mathematical methods of Flory and Jemi-gan 37,30) using the rotational isomeric state models for the polyesters set up by Flory and Williams 27,128). Agreement between experiment and theory is excel-... 

By contrast, the corresponding values for the large cyclics decrease along the same series. The total weight fraction (experimental) of cyclics in these bulk equilibrates are listed in Table 4. The effect of dilution with cyclohexanone in the syntheses of these same polymers is illustrated in Figure 3. In all cases, a critical dilution point was reached as predicted but it was reached at a lower diluent volume than the theoretical value. Molar cyclization equilibrium constants for undiluted poly(methylphenyl)siloxane were later measured (19) and found to be similar to those previously obtained in the case of poly(ethylmethyl)siloxanes. 

In addition to the above thermodynamic conditions for ring formation, the kinetics of the reactions must be considered. Thus, for a reaction to take place the two ends of the polymer chain must be in the correct conformation for sufficient time for the new bond to form. The kinetic factor for cyclization is proportional to Rg, so the net effect of the thermodynamic and kinetic factors is that rings are not favoured between n = 8 and k = 11. Suter (1989) has considered the theoretical approaches of Jacobsen and Stockmayer and compared theoretical and experimental values for macrocyclization equilibrium constants. This has also been performed for Monte Carlo as well as rotational-isomeric-state calculations for the statistical conformations of cyclic esters (decamethylene fiimarates and maleates) and agreement with experimental molar cyclization equilibrium constants found (Heath et al, 2000). 

Fig. 3.1. Experimental molar cyclization equilibrium constant (K, = [MJmol -l-1) in bulk ( ) and solution (O) polymerization of 1,3-dioxolane compared with values (x) calculated by the Jacob-...

The ring-opening polymerization of D4 is controlled by entropy, because thermodynamically all bonds in the monomer and polymer are approximately the same (21). The molar cyclization equilibrium constants of dimethylsiloxane rings have been predicted by the Jacobson-Stockmayer theory (85). The ring—chain equilibrium for siloxane polymers has been studied in detail and is the subject of several reviews (82,83,86—89). The equilibrium constant of the formation of each cyclic is approximatdy equal to the equilibrium concentration of this cyclic, Kn [(SiRjO) J. Thus the total concentration of cyclic oligomers in the equihbrium is independent of the initial monomer concentration. As a consequence, the amount of linear polymer decreases until the critical dilution point is reached, at which point only cyclic products are formed. 

Extensions of the measurements of the molar cyclization equilibrium constants for dimethylsiloxane cyclics into the macrocyclic range, first studied by Brown and Slusarczuk (18), have been made by Wright (16,20) using g.p.c. as the main analyt-... 

Fig. 5. Molar cyclization equilibrium constants for cycHcs ((O SiO) in an undiluted equilibrate at 383 K (o) are compared with values in diglyme at 333 K (a), in toluene at 383 K ( ) and with calculated values (-----) (see text). Kx values are in mol dm-3...

Fig. 8. Experimental molar cyclization equilibrium constants Kx for (H(CH3)SiO)x at 273 K (denoted by and ) and for (CH3CH2(CH3)SiO)x at 383 K (denoted by o and ). Kx values in undiluted equilibrates are denoted by and o, and those measured in toluene solution close to the critical dilution points are denoted by and . Units of Kx are mol dm-3...

In a recent study (120), measurements were made of the molar cyclization equilibrium constants Kx for cyclics (0(CH2)i00C0(CH2)4C0)x with x = 1—5 in an undiluted equilibrate of poly(decamethylene adipate) (PDA) at 423 K, and for cyclics (0(CH2)30C0(CH2 )2 CO)x with x = 1-7 in an undiluted equilibrate of poly(trimethylene succinate) (PTS) at the same temperature. The polymers were prepared from dimethyl adipate and decamethylene glycol and from dimethyl succinate and 1,3-propane diol using tetraisopropyltitanate and equilibrated at the required temperature in four-necked glass reaction kettles. Cyclics were extracted from the polymeric equilibrates and analysed by g.p.c. by methods described in Ref. (120). Individual cyclics were also prepared from the polyesters by the general pyrolytic method of Carothers and these were used for identification and calibration purposes. 

Fig, 12. Experimental molar cyclization equilibrium constants Kx (in mol dm-3) for cyclics (O(CH2)10OCO(CH2)4CO)x in the PDA melt at 423 K (o) are plotted as log Kx against log n, where n represents the number of skeletal bonds in the ring. They are compared with theoretical values calculated by the Jacobson and Stockmayer theory ( )... 

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... 

Characteristic ratio (r ) jnf Derived from molar cyclization equilibrium constants Bulk state at 383 K Toluene at 383 K Derived from GPC toluene at 292 K 10.7 10.4 8.8 (1.5) (2.6)... 

Characteristic ratio — Derived from molar cyclization equilibrium constants in 50% toluene solution at 383 K 7.8 (2)... 

Large cyclic ether-esters from oxyethyleneglycol succinate, prepared by dilute solution transesterification, were also characterized by FAB-MS. " As for the PDT cyclic oligomer, the molar cyclization equilibrium constant was found in agreement with the Jacobson-Stockmayer theory. 

Table 1.5 summarizes the studies on cyclics of poly(di-methyl siloxane) and derivatives, and Table 1.6, those of other polymers. In these tables, refers to the molar cyclization equilibrium constant and RIS, to the rotational isomeric state scheme to analyze chain conformations. 

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