Cyclization Equilibrium Constants Research Articles

Lipase-Catalyzed Polyester Synthesis in Organic Medium. Study of Ring−Chain Equilibrium

Enzyme-catalyzed synthesis of aliphatic, unsaturated, and semiaromatic polyesters from diesters and diols was carried out in toluene at different temperatures in the presence of supported lipases from Candida antarctica. Whatever the monomer structure, rings were formed concurrently with linear chains except when dimethyl fumarate was used. The yield of cyclics depends on several parameters such as the monomer structure and the initial concentration of the reactive functions and strongly influences the average molar masses of unfractionated samples. Qualitatively, this is a general feature of the ring−chain equilibrium. Once the existence of this equilibrium was shown, the molar cyclization equilibrium constants (K) for aliphatic, unsaturated, and semiaromatic polyesters were determined, and it would appear that the molar distribution of the ringed species obeys the Jacobson−Stockmayer equation (ln K = ln B − 5/2 ln n, where B and n represent a constant and the number of monomer units of each type in the ...

Enzyme‐catalyzed polyester synthesis in organic medium: Ring‐chain equilibrium

AbstractEnzyme‐catalyzed synthesis of aliphatic, unsaturated and semi‐aromatic polyesters from methyl diesters and diols was carried out in toluene at 60°C in the presence of supported lipases. Whatever the monomer structure, rings were formed concurrently to linear chains excepted when dimethyl fumarate was used. The yield of rings depends on several parameters such as the monomer structure and the initial concentration of the reactive functions and strongly influences the average molar masses of the unfractionated samples. For aliphatic, unsaturated and semi‐aromatic polyesters, the molar cyclization equilibrium constants (K) were determined and it would appear that the molar distribution of the ringed species obeys Jacobson‐Stockmayer equation: LnK = LnB − 5/2 Lnn, where B and n represent a constant and the number of monomer units of each type in the ring, respectively.

Cyclic polyesters: 5. Cyclics prepared by poly(decamethylene terephthalate) ring-chain reactions

Cyclic oligomers of poly(decamethylene terephthalate) (PDT) were prepared successfully and cleanly from a ring-chain equilibrium reaction in dilute solution of chlorobenzene. A variety of catalysts were investigated for this purpose. The reactions were monitored up to equilibrium and the molar cyclization equilibrium constants K x deduced. Satisfactory yields of cyclics [O(CH 2) 10OCO C 6H 4CO] x were obtained, together with a higher molar mass linear polymer. Mass spectroscopic investigation showed that no monomeric ring was formed in the PDT reaction. The individual cyclics with x = 2–14 corresponding to 36–252 skeletal bonds were completely resolved using PL-gel mixed-E gel permeation chromatographic columns. The lower mass cyclics ( x = 2–5) were cleanly extracted and then characterized. The yield of cyclics in ring-chain equilibrates corresponding to a solvent/polymer dilution ratio of 30 1 , 60 1 and 100 1 were ca 11%, ca 30% and ca 50%, respectively. The K x values for PDT cyclics were used to compare the statistical conformations of the corresponding PDT chains in chlorobenzene with an aliphatic polyester, poly(decamethylene adipate), which was studied previously.

Cyclic polyesters: 4. Cyclics prepared by poly(decamethylene adipate) ring-chain reactions

Ring-chain equilibration reactions of poly(decamethylene adipate) (PDA) were carried out in the presence of large amounts of diluent. Good yields of cyclics [CO(CH 2) 4COO(CH 2) 10O] x were obtained virtually free of linear species. The individual cyclics with 18–198 skeletal bonds were completely resolved using PL-gel mixed-E gel permeation chromatographic columns and their molar cyclization equilibrium constants were compared with the corresponding theoretical values predicted by the Jacobson-Stockmayer theory as well as those obtained previously for undiluted PDA ring-chain equilibrates.

Effect of Terminal Bond on Configurational Statistics of Poly(dimethylsiloxane)

A modified FCM (Flory, Crescenzi, and Mark) model is developed to study the configurational statistics of poly(dimethylsiloxane) (PDMS) chain. In the model, the theoretical molar cyclization equilibrium constants Kx for small dimethylsiloxane ring are in agreement with the experimental data, and the theoretical characteristic ratio Cn=〈R2〉/nl2 and its temperature coefficient for long ring are close to the experimental results.

Configurational statistics of poly(dimethylsiloxane). 2. A new rotational isomeric state approach

A new RIS treatment, compatible with the molecular mechanics and dynamics considerations of a preceding paper, is introduced. The model yields satisfactory agreement with experiments on the mean-square unperturbed end-to-end separations, the mean-square dipole moment and its temperature dependence, and the molar cyclization equilibrium constants for dimethylsiloxane oligomers. It cannot account for the positive temperature coefficient of the unperturbed chain dimensions

Studies of cyclic and linear poly(dimethyl siloxanes): 3. Neutron scattering measurements of the dimensions of ring and chain polymers

The dimensions of both cyclic and linear poly(dimethyl siloxanes) in dilute solution in benzene- d 6 have been measured by small-angle neutron scattering. The mean-square radii of gyration of the linear polymers are consistent with values predicted from published data, including experimental molar cyclization equilibrium constants. The average dimensions of the cyclic poly(dimethyl siloxanes) in fractions containing z-average numbers of bonds n ̄ z in the range 130 < n ̄ z < 550 , were found to be considerably smaller than those of the corresponding linear polymers. The neutron scattering results give a value for the ratio of the z-average radii of gyration for linear and ring poly(dimethyl siloxanes) (containing the same number of monomer units) 〈s 2〉 z,l <s 2〉 z,r = 1.9 ± 0.2 . This ratio may be compared with the value of 2.0 predicted theoretically for ‘flexible’ high molecular weight linear and cyclic polymers, unperturbed by excluded volume effects.

Introductory lecture: levels of order in amorphous polymers

Early theoretical predictions that amorphous and liquid polymers should be devoid of significant order down to dimensions commensurate with the diameter of the chain are supported by an extensive body of evidence from X-ray scattering at small and at wide angles, neutron scattering at small and at intermediate angles, recent electron microscopic investigations, analysis of rubber elasticity including, especially, its dependence on temperature and dilution, and cyclization equilibrium constants. If the nodular domains previously observed in electron micrographs are dismissed as artifacts, as studies documented in this Discussion indicate, then depolarized Rayleigh scattering (DRS) offers the only substantial evidence for a detectable degree of order in liquids consisting of long-chain molecules. This evidence is examined in detail. The analysis presented leads to the conclusion that the enhancement of the DRS of higher n-alkanes by factors of 2–2.5 over the values that would be observed for uncorrelated molecules is attributable to: (i) steric constraints on relative orientations of neighbouring chains which restrict them to orientations generated by rotation about one axis only, this axis being normal to their plane of contact, and (ii) a small preference in the alignment of neighbouring chains. These correlations do not imply order in the sense in which this term customarily is used. Rather, they complement the distance correlations manifested in the radial distribution functions deduced from wide-angle X-ray scattering; like them, they are of very short range.

Equilibrium ring concentrations and the statistical conformations of polymer chains: 14. Calculation of the concentrations of medium sized cyclics in poly(dimethyl siloxane) equilibrates

Theoretical molar cyclization equilibrium constants K x for dimethyl siloxane cyclics [(CH 3) 2SiO] x in undiluted poly(dimethyl siloxane) equilibrates are calculated for values of x in the range 7 < x < 13. The Jacobson and Stockmayer theory is used for the calculations and K x values are computed by finding the statistically weighted fraction of the 3 2 x−3 conformations [defined by the Flory, Crescenzi and Mark (FCM) rotational isomeric state model of poly(dimethyl siloxane)] that have terminal atoms in close proximity for ring formation. The FCM model gives theoretical K x values in good agreement with experiment for x = 8, 9, 10 but yields a K 11 value that is nine times greater than that found experimentally. This result is discussed in terms of the molecular structure of dimethyl siloxane chains. The effect on the calculated K x values of modifying the FCM model by assigning a smaller value to the SiOSi bond angle is explored.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 13. Cyclics in two aliphatic polyesters

Methods have been developed for measuring the molar cyclization equilibrium constants K x for cyclics [O(CH 2) 10OCO(CH 2) 4CO] x with x=1–5 in an undiluted ring-chain equilibrate of poly(decamethylene adipate) (PDA) at 423K, and for cyclics [O(CH 2) 3OCO(CH 2) 2CO] x with x=1–7 in an undiluted equilibrate of poly(trimethylene succinate) (PTS) at the same temperature. The experimental K x values are compared with theoretical values calculated by the Jacobson and Stockmayer theory. The latter were obtained by assuming that chains in the undiluted melts adopt random-coil conformations obeying Gaussian statistics and have average dimensions predicted by the rotational isomeric state model of Flory and Williams. The agreement between experiment and theory is excellent for the cyclic oligomers containing 54, 72 and 90 skeletal bonds in the PDA equilibrate. By contrast, the experimental K x values for cyclic oligomers of comparable size in the PTS equilibrate are approximately half the calculated values. These differences suggest that the statistical conformations of oligomeric aliphatic polyester chains depend on the relative numbers of methylene groups and ester linkages that they contain.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 12. Cyclics in molten and solid nylon-6

The molar cyclization equilibrium constants K x for cyclics [NH(CH 2) 5CO] x with x = 1−6 were measured for an undiluted melt equilibrate of nylon-6 at 525K using gel permeation chromatography as the principal analytical technique. They were compared with the corresponding theoretical values calculated by the Jacobson and Stockmayer theory using the rotational isomeric state model of Flory and Williams to describe the statistical conformations of the corresponding open chain molecules. Ring-chain equilibration reactions were carried out on samples of nylon-6 at a temperature 46K below the melting point of the polymer. Polymers were prepared at 459K over periods of more than 30 days by (i) heating nylon-6 containing 11.5% w/w cyclic oligomers, (ii) heating nylon-6 containing no cyclic oligomers, (iii) polymerizing ϵ-caprolactam alone. These polymers were all found to contain ∼2% w/w cyclics [NH(CH 2) 5CO] with x = 1−6. However, although the concentrations of the larger cyclic oligomers were identical within experimental error in the samples prepared by (i) and (ii), they were strikingly different from those in the sample prepared by (iii). These differences in cyclic concentrations are discussed in terms of the structures of the solid polymers at the equilibration temperature.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 11. Cyclics in poly(ethylene terephthalate)

Methods have been developed for extracting cyclic oligomers from poly(ethylene terephthalate) samples and for analysing the extracts by gel permeation chromatography. These methods have been used to measure the molar cyclization equilibrium constants K x for cyclics (CO.C 6H 4.CO.O.CH 2.CH 2.O) t with x=3–9 in the undiluted polymer at 543K and in solution in 1-methyl naphthalene at 523K. The close agreement between the measured K x values over the range x=3–9 shows that oligomeric ethylene terephthalate chains adopt similar conformations in the two environments (which contain 95% w/w and 6% w/w linear polymer respectively). K x values were calculated by the Jacobson and Stockmayer theory by assuming that the corresponding open chain molecules obey Gaussian statistics and describing their statistical conformations by Williams and Flory's rotational isomeric state model. These theoretical values were found to be lower than the experimental values by factors of at least two over the whole range of cyclics x=3–9. Poor agreement between experiment and theory was also obtained when K 3 and K 4 values were calculated by computing the end-to-end distances of acyclic trimeric and tetrameric ethylene terephthalate chains in all discrete conformations defined by the Williams and Flory model. It is suggested that these discrepancies might result, at least in part, from substantial correlations between the positions and directions of the termini of oligomeric ethylene terephthalate chains. Observed decreases in the concentrations of cyclics in commercial poly(ethylene terephthalate) samples resulting from heating the samples in the solid state are discussed briefly.

Cyclization equilibrium constants and the conformations of polydimethylsiloxane chains

AbstractExperimental molar cyclization equilibrium constants for dimethylsiloxane cyclics having from 8 to ca 400 skeletal bonds are presented. The results for an undiluted equilibrate, an equilibrate in toluene solution, and an equilibrate in diglyme solution are compared. The increases in the equilibrium concentrations of cyclic oligomers, previously found to be large in good solvents (e.g., toluene) are found to be small in the poor solvent (diglyme). For macrocyclics, the cyclization equilibrium constants in the undiluted equilibrate and in diglyme (theta conditions) are found to be in good agreement with calculations which were carried out by assuming that chains are unperturbed and by using the rotational isomeric state model of Flory, Cresenzi, and Mark for polydimethylsiloxane. However, with chain polymer in dilute solution in a good solvent (toluene), the macrocyclization equilibrium constants are found to be lower than in the other two equilibrates. This result confirms the work of other authors who suggested that in this case the chains were expanded by excluded‐volume effects.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 10. Cyclics in a polymeric paraffin-siloxane

Cyclic oligomers [(CH 3) 2Si(CH 2) 4(CH 3) 2SiO] x with x=2−10 were found to be present in poly(2,2,7,7-tetramethyl-1-oxa-2,7-disilacycloheptane) samples prepared by monomerpolymer equilibrations using concentrated sulphuric acid as catalyst. The molar cyclization equilibrium constants, K x , for cyclics [(CH 3) 2Si(CH 2) 4(CH 3) 2SiO] x with x=1−6 were measured for undiluted equilibrates at 298, 333, 383 and 423K. Apart from K 1 for the monomer, the K x values were found to be independent of the temperature of equilibration. Experimental molar cyclization equilibrium constants K x for the cyclics with x⩾3 were close to theoretical values calculated by the Jacobson-Stockmayer theory, using a rotational isomeric state model to describe the statistical conformations of chains in the undiluted equilibrates and assuming that the chains obey Gaussian statistics.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 9. Sodium metaphosphates in Graham's salt

The molar cyclization equilibrium constants K x for oligomeric metaphosphates (NaPO 3) x in high molecular weight sodium phosphate melts at 1000K are calculated using a rotational isomeric state model to describe the statistical conformations of the corresponding open chain molecules. The model is based on a previously published analysis of the molecular structure of the polyphosphate chain. Each skeletal bond is assigned to one of three rotational states in trans ( ø=0°) and gauche ( ø=±120°) positions, and the interdependence of adjacent pairs of bond rotational states is taken into account by assuming that only Coulombic interactions between charged non-bonded atoms of the chain separated by eight or fewer chemical bonds need to be considered. The probabilities that polyphosphate chains (OPO 2) x (with x=3−10) will intramolecularly cyclize are calculated by computing the statistically weighted fraction of the 3 2 x−3 conformations defined by the rotational isomeric state model that have their termini in close proximity for ring formation. Molar cyclization equilibrium constants calculated by this direct computational method are compared with experimental values deduced from data of Thilo and Schülke, as well as with values calculated assuming that the polyphosphate chains obey Gaussian statistics.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 8. Calculation of small ring concentrations in polydihydrogensiloxane and polydimethylsiloxane equilibrates

Theoretical molar cyclization equilibrium constants K x for small, unstrained cyclics [H 2SiO] x ( x=4−8) and [(CH 3) 2SiO] x ( x=4−9) in undiluted polydihydrogensiloxane and polydimethylsiloxane equilibrates are calculated using the Jacobson and Stockmayer theory, without assuming that the corresponding chain molecules obey Gaussian statistics. The statistical conformations of dihydrogensiloxane chains are described by a simple rotational isomeric state model with skeletal bonds assigned to trans ( ø=0°) and gauche ( ø= ±120°) states with equal probability; and the statistical conformations of dimethylsiloxane chains are described by Flory, Crescenzi and Mark's (FCM) rotational isomeric state model. Dihydrogensiloxane and dimethylsiloxane chains in undiluted equilibrates are assumed to be unperturbed by excluded volume effects, and the probabilities of intramolecular cyclization are calculated by simply computing the statistically weighted fractions of the total number of conformations defined by the rotational isomeric state models that have terminal atoms in juxtaposition for ring closure. The calculated K x values for cyclic dihydrogensiloxanes are compared with the published experimental K x values for the homologous cyclic hydrogenmethylsiloxanes and dimethylsiloxanes. The FCM rotational isomeric state model of polydimethylsiloxane gives theoretical molar cyclization equilibrium constants for the cyclics [(CH 3) 2SiO] 8 and [(CH 3) 2SiO] 9 in excellent agreement with the experimental values. However, it is shown that before the FCM model can be used to calculate the molar cyclization equilibrium constants for smaller dimethylsiloxane rings, it must be modified so that it takes into account the mutual interdependence of sequencies of bond rotational states.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 7. Cyclics in poly(1,3-dioxolane)

Cyclic oligomers [CH 2OCH 2CH 2O] x with x = 2–9 were found to be present in poly(1,3-dioxolane) samples prepared by monomer-polymer equilibrations using boron trifluoride diethyl etherate as catalyst. The molar cyclization equilibrium constants K x for cyclics [CH 2OCH 2CH 2O] x with x = 1–8 were measured for an undiluted and a solution equilibrate at 333K. The K x values for the cyclics with x ⩾5 were in agreement with those calculated by the Jacobson-Stockmayer theory, using a rotational isomeric state model to describe the statistical conformations of the corresponding chains and assuming that the chains obey Gaussian statistics.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 5. Stereoisomeric cyclics in poly (phenylmethylsiloxane) equilibrates

The molar cyclization equilibrium constants K x for cyclic phenylmethylsiloxanes, [C 6H 5(CH 3)SiO] x ( x = 3–50), have been measured in the undiluted polymer at different temperatures and in solution in toluene. The K x values for [C 6H 5(CH 3)SiO] x in the bulk polymer at 383 K are the same, within experimental error, as those found previously for the corresponding cyclics [CH 3CH 2(CH 3)SiO] x and it is concluded that phenyl and ethyl groups have similar influences on the statistical conformations of siloxane chains. The weight fraction of cyclics in a high molecular weight undiluted phenylmethylsiloxane equilibrate at 383 K is 0.30 and this weight fraction increases to 0.90 when equilibration is carried out in the presence of 47% by volume of toluene. The K x values for the cyclic tetramer and pentamer in the latter equilibrate are nearly twice as large as their values in the former, whereas the K x values for the large cyclic phenylmethylsiloxanes are the same in both. The configurational isomers of the cyclic trimer, tetramer and pentamer were separated completely by gas-liquid chromatography. They were found to be present in the equilibrates in proportions close to those expected from the random cyclization of an atactic polymer. The configurational isomers of [C 6H 5(CH 3)SiO] 3 and the isomer of [C 6H 5(CH 3)SiO] 4 with all its phenyl groups in cis positions were the only stereoisomers that were found to be strained relative to the open siloxane chains.

Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 3. Substituent effects in polysiloxane systems

The molar cyclization equilibrium constants K x for cyclics [R(CH 3)SiO] x, where R = H ( x = 4–15), R = CH 3CH 2 ( x = 4–20), R = CH 3CH 2CH 2 ( x = 4–8) and R = CF 3CH 2CH 2 ( x = 4−20), have been measured in some undiluted and solution equilibrates with an accuracy of ±10%. K 4 and K 5 increase along the series R = H < CH 3CH 2 < CH 3CH 2CH 2 < CF 3CH 2CH 2, whereas the K x values for large cyclics ( x > 10) decrease with increasing size of the substituent group R. The limiting proportionality between K x and x −5 2 predicted for macrocyclics by the Jacobson and Stockmayer theory is found for values of x > ca 12 when R = H and for x > ca 15 when R = CH 3CH 2 but only for values of x > ca 25 when R = CF 3CH 2CH 2. The weight fractions of cyclics in high molecular weight poly(hydrogenmethylsiloxane), poly(ethylmethylsiloxane) and poly(3,3,3-trifluoropropylmethylsiloxane) equilibrates increase with solvent dilution up to critical points corresponding to complete conversion of siloxane to ring molecules. The amounts of solvent required to attain these critical dilution points are ca 10% by volume of cyclohexanone at 383 K when R = CF 3CH 2CH 2, ca 60% by volume of toluene at 383 K when R = CH 3CH 2 and ca 80% by volume of toluene at 273 K when R = H. As in the poly(dimethylsiloxane) system, K x values for the low molecular weight cyclics in poly(hydrogenmethylsiloxane) and poly(ethylmethylsiloxane) equilibrates increase with solvent dilution, whereas those for larger cyclics remain constant.

Equilibrium ring concentrations and the statistical conformations of polymer chains I—Oligomeric dimethylsiloxanes

The molar cyclization equilibrium constants Kx of dimethylsiloxanes [(CH3)2SiO]x have been measured in the bulk polymer to within ±5 per cent at 110°C (x=4–40) and 145°C (x=4–30). Values at 110°C are compared with those of Brown and Slusarczuk for an equilibrate containing 0.22 g. ml−1 siloxane in toluene, and it is concluded that K4–K10 increase markedly with solvent dilution whereas K11–K40 remain constant. Using the Jacobson and Stockmayer equilibrium theory of macrocyclization, the dimensions of dimethylsiloxane chains with 40–80 chemical bonds in the bulk polymer at 110°C are deduced. They are found to be similar to those in Brown and Slusarczuk's equilibrate and in two θ-solvents of different cohesive energy density. Dilution effects in dimethylsiloxane 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 Flory, Crescenzi and Mark's rotational isomeric state model of poly(dimethylsiloxane).