Copolymer Composition Equation Research Articles

Study of target spacing of thermo-sensitive carrier on the activity recovery of immobilized penicillin G acylase.

The immobilized penicillin G acylase (PGA) is an important industrial catalyst, the activity recovery rate of it directly affects enterprise efficiency. How to improve the enzyme activity recovery rate has been a research focus in this field. Based on the above problems, this work further improved the activity recovery rate by adjusting the target spacing for the first time. Glycidyl methacrylate (GMA) was used as the immobilized target and methyl methacrylate (MMA) as the copolymer monomer. According to the copolymer composition equation of P(MMA-co-GMA), the thermo-sensitive copolymers, PDEA-b-PHEMA-b-P(MMA-co-GMA) with different target spacings, were synthesized rapidly and efficiently via reversible addition-fragmentation chain transfer (RAFT) polymerization method. The error range between the theoretical and actual values of MMA and GMA in the copolymers carrier was (0-4)%, which demonstrated that the reliability of using composition equation to accurately and quickly synthesize copolymers with specific spacing. Studies on the thermo-sensitive showed that the low critical solution temperature (LCST) of the copolymer carrier decreased with the increase of hydrophobic monomer. Most importantly, the activity recovery rate increased with the increase of target spacing, and when the molar ratio of MMA to GMA in the copolymer was 8.75:1, the recovery of activity of immobilized PGA could be up to 63.50%, which was 21.70% higher than that of pure GMA. This work provided an important idea for improving the activity of immobilized PGA.

Synthesis and characterization of hydrolytically degradable poly(N-vinylcaprolactam) copolymers with in-chain ester groups

Poly(N-vinylcaprolactam) (PNVCL) is attracting increasing interest as a polymer for biomedical application. However, it is not biodegradable, which is an important drawback for such applications. The present paper describes the synthesis and characterization of novel thermosensitive PNVCL copolymers able to hydrolytically degrade, which were prepared by the RAFT/MADIX copolymerization of NVCL and 5,6-benzo-2-methylene-1,3-dioxepane (BMDO). The RAFT/MADIX polymerization process displayed a moderate degree of control under the experimental conditions employed as proven by GPC measurements. The formation of the NVCL-BMDO copolymers was demonstrated by 1H NMR analyses which showed the presence of the in-chain ester groups resulted from the ring-opening polymerization of BMDO. The BMDO content of the copolymers was much lower than in the feed, indicating a higher reactivity of NVCL, which was confirmed through the estimation of the monomer reactivity ratios by applying the non-linear least squares method to fit the experimental results to the Lowry-Meyer integrated form of the Mayo-Lewis copolymer composition equation. The glass transition temperature of the copolymers diminished with the BMDO unit concentration within the chain. The phase transition temperature of the copolymers in 0.5-wt% aqueous solution decreased with the BMDO content as proven by transmittance measurements, in agreement with the increasing hydrophobic character. The degradability of the copolymers was demonstrated by the hydrolysis of the in-chain ester groups in 1-N KOH solution. The degraded polymer displayed a higher phase transition temperature than the original polymer, as expected. The results described within this paper may find applications for the synthesis of new biomaterials.

Reactivity Ratio Estimation from Cumulative Copolymer Composition Data

AbstractThe goal is to present an alternative technique for reactivity ratio estimation in copolymerization. Typically, reactivity ratios are estimated using the instantaneous copolymer composition equation, based on low conversion copolymer composition data. However, using experimental data from the full copolymerization trajectory would, in principle, be more advantageous, and shy away from commonly used restrictive assumptions. Estimation using cumulative copolymerization data and models eliminates the difficulties associated with stopping reactions at low conversion, while one gains to study the full polymerization trajectory. The error‐in‐variables‐model (EVM) method is used for parameter estimation. Two cumulative model forms, the analytical integration of the differential composition equation and the one resulting from the direct numerical integration of this equation, are employed. Using these two types of models improves the reactivity ratio estimation and, in particular, the latter model form is a more reliable and direct method of estimating reactivity ratios. magnified image

Theoretical Analysis of the Copolymer Composition Equation in Chain Shuttling Copolymerization

Theoretical Analysis of the Copolymer Composition Equation in Chain Shuttling Copolymerization

Estimating Reactivity Ratios From Triad Fraction Data

AbstractReactivity ratio estimation is a non‐linear estimation problem. Typically, reactivity ratios are estimated using the instantaneous copolymer composition equation, otherwise known as the Mayo‐Lewis model, based on low conversion (<5%) copolymer composition data. However, there are other instantaneous models, which can be used to estimate reactivity ratios, such as the instantaneous triad fraction equations. The aim of this paper is to determine the potential improvement in reactivity ratio estimates when triad fraction data is used in place of and in combination with copolymer composition data. The interest in using triad fraction data in parameter estimation, stems from the fact that there are a greater number of responses measured (six triad fractions) compared to composition leading to data with theoretically more information content. In principle this should lead to reactivity ratio estimates having less uncertainty. In this study, the parameter estimates are obtained by employing the error in variables model (EVM), assuming a multiplicative error structure. Several case studies involving published literature data for different copolymer systems are presented. As the case studies demonstrate in general more precise estimates can be obtained from triad fraction data. Combining the triad fraction with composition data leads to little additional improvement. However, discrepancies arise between reactivity ratios estimated from composition data compared with those obtained from triad fraction data depending upon the copolymer system. Those copolymer systems exhibiting more heterogeneity due to phase separation during polymerization may be showing more discrepancy.

Determination of monomer reactivity ratios usingin situ FTIR spectroscopy for maleic anhydride/norbornene-free-radical copolymerization

Monomer reactivity ratios for maleic anhydride (MAH) and norbornene (Nb) free-radical copolymerizations were estimated by using a linear graphical method, which is based upon the terminal model developed by Mayo and Lewis. Reactions were performed by using optimized reaction conditions that were previously determined. MAH/Nb copolymerizations (3 mol % AIBN initiator, 60% solids in THF, 65°C, 24 h). Copolymerization data were collected via in situ FTIR to low degrees of conversion (∼ 10%) for copolymerizations of MAH and Nb. The following five different MAH/Nb comonomer feed molar ratios were analyzed: 40/60, 45/55, 50/50, 55/45, and 60/40. Conversion data that were measured with in situ FTIR were employed in the rearranged copolymer composition equation to estimate MAH and Nb reactivity ratios. Both of the reactivity ratios were determined to be near 0 (rMAH = 0.02, rNb = 0.01), which was indicative of an alternating copolymerization mechanism. The highest observed rate constant for copolymerization was obtained at an equal molar concentration of monomers. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3240–3246, 2004

The use of Solver in Excel to solve copolymer composition equation in terminal and penultimate models of copolymerization

The standard Solver in Excel 97 was applied in order to solve the copolymer composition equation in terminal and penultimate models of copolymerization. An unquestionable advantage of this software is easy access standardbecause Solver is a part of Microsoft Office package. The radical copolymerization of styrene with acrylonitrile in bulk was chosen to prove the usefulness of the calculation procedure of Solver. These monomers system displays a significant penultimate effect. For comparison the classical methods such as curve-fitting, Mayo-Lewis, Fineman-Ross, Kelen-TudOs and Ezrielev-Brokhina-Roskin for the terminal model were also applied. The solutions obtained by Solver for penultimate model were compared with those obtained earlier by non-linear least squares minimizing method and Nelder-Mead simplex method. It was found that the precision of Solver is comparable with those obtained by above methods. The influences of started values, precision and convergence on the values of minimized function and so on the values of set of reactivity ratios have been also studied.

Radical copolymerization of citraconic acid with styrene in dioxane solution

Styrene and citraconic acid (CA) were copolymerized in the dioxane solution ranging mole fraction of CA in feed from 0.1 to 0.9 at 70 °C. The terminal and penultimate models were used to fit the copolymer composition equation. Curve fitting, Mayo–Lewis, Joshi–Joshi, Fineman–Ross, Ezrielev–Brokhina–Roskin, Kellen–Tüdős methods were used to solve the copolymer equation in terminal model. Besides these methods Solver in Excel 97 was used to solve copolymer equation in terminal and penultimate models of copolymerization. Experimental mole fractions of CA and those predicted from both models are agreed within the precision of the method used for the copolymer analysis, so the copolymer composition does not permit a definite choice of the adequate copolymerization model.

Bulk and solution copolymerization of methyl methacrylate and vinyl acetate

AbstractA series of batch, bulk and solution (in toluene) copolymerizations of methyl methacrylate and vinyl acetate was performed under various reaction conditions to high monomer conversions. In addition, low conversion bulk experiments were performed to estimate monomer reactivity ratios using the error in variables model method, based on terminal model (Mayo–Lewis) kinetics. A combination of the low and high conversion data with data from a previous study yielded reactivity ratio (r) estimates of 27.465 and 0.0102 for rMMA and rVAc, respectively, using the integrated copolymer composition (Meyer–Lowry) equation. In the high conversion experiments the effects of various factors on the reaction rate, cumulative copolymer composition, number‐ and weight‐average molecular weights, and molecular weight distribution were studied. The factors included the monomer feed composition, initiator concentration, temperature, solvent concentration, and the addition of n‐dodecyl mercaptan chain transfer agent. These factors were examined in light of the wide difference in the monomer reactivity ratios. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 82: 1238–1255, 2001

High-temperature solution polymerization of butyl acrylate/methyl methacrylate: Reactivity ratio estimation

Solution copolymerizations of butyl acrylate/methyl methacrylate in toluene were performed over an expanded temperature range (60–140°C) compared to more typical ranges that do not exceed 80°C. From a large amount of data collected independently at two laboratories, reactivity ratios were estimated at five different temperatures. The reactivity ratios were estimated from low conversion copolymer composition data using both the error-in-variables model method and a nonlinear parameter estimation based on the integrated copolymer composition equation. Using all of the available data, temperature-dependent expressions were developed for the reactivity ratios and compared to previously published bulk copolymerization values. No significant differences appeared to exist between the bulk and solution polymerization reactivity ratios. Furthermore, the copolymer composition data conformed to the Mayo-Lewis kinetic model over the entire temperature range. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 602–609, 2000

Effects of temperature on cure kinetics and mechanical properties of vinyl-ester resins

The relationships among cure temperature, chemical kinetics, microstructure, and mechanical performance have been investigated for vinyl–ester resins. Fourier transform infrared spectroscopy was used to follow the reactions of vinyl–ester and styrene during isothermal curing of Dow Derakane 411-C-50 at 30 and 90°C. Reactivity ratios of vinyl–ester and styrene vinyl groups were evaluated using the copolymer composition equation. The results indicate that the ratio of vinyl–ester to styrene double bonds incorporated into the network is greater for 30 than for 90°C cure. Mechanical properties were obtained for systems subjected to isothermal cures at 30 and 90°C and postcured above ultimate Tg. The results show that the initial cure temperature significantly affects the mechanical behavior of vinyl–ester resin systems. In particular, values of strength and fracture toughness for postcured samples initially cured isothermally at 30°C are significantly higher than those obtained for samples cured isothermally at 90°C. Examination of fracture surfaces using atomic force microscopy revealed the existence of a nodular microstructure possessing characteristic nodule dimensions that are affected by the temperature of cure. Such features suggest the existence of phase separation during cure. A binary interaction model in conjunction with chemical kinetic data and estimated solubility parameters was used to evaluate enthalpic interactions between the growing polymer network and monomers of the vinyl–ester system. The results indicate that the interaction energy becomes increasingly endothermic as cure progresses and that this energy is affected by the temperature of cure through differences in copolymerization behavior. Hence, in addition to entropic factors, the changes in enthalpic contribution to the Gibbs free energy suggest that the probability of phase separation increases with extent of cure and that its onset is potentially affected by cure temperature. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 725–744, 1999

High Temperature Bulk Copolymerization of Butyl Acrylate/Methyl Methacrylate: Reactivity Ratio Estimation

ABSTRACTIn order to extend the validity of existing mechanistic polymerization models, it is necessary to conduct experiments beyond typical temperature ranges. Bulk copolymerizations of butyl acrylate/methyl methacrylate were performed over an expanded temperature range (60 to 140°C) compared to most studies published to date which have focused on a more limited temperature range (60 to 80°C). From the large amount of collected data, reactivity ratios were estimated at five different temperatures. The reactivity ratios were estimated from low conversion copolymer composition data using the error-in-variables model method (EVM). The low conversion data were subsequently coupled with high conversion data and the reactivity ratios were re-estimated using non-linear parameter estimation based on the integrated copolymer composition equation. Using all of the available data, temperature-dependent expressions were developed for the reactivity ratios. The copolymer composition data conformed to the Mayo-Lewis k...

Photoinitiated copolymerisation of furfuryl methacrylate and N,N-dimethyl acrylamide

Copolymers of furfuryl methacrylate ( F) and N,N-dimethyl acrylamide ( A) were prepared by free radical photoinitiated polymerisation in bulk at 40°C, using 2,2-azobisisobutyronitrile (AIBN) as photoinitiator. The reactivity ratios of both monomers ( r F and r A) were determined according to the general copolymer composition equation by applying the Tidwell and Mortimer non-linear least squares fit. To this end initial approximated values of r F and r A were obtained by means of the Fineman-Ross and Kelen-Tüdos linearisation methods. The reactivity ratios obtained were r F = 2.06 and r A = 0.28. Also, kinetic parameters such as reaction rate ( R p) and copolymerisation quantum yield ( φ m) were determined for the above system over a wide composition interval, with molar fraction of F ranging from 0.1 to 0.9 in the monomer feed. The kinetics of photopolymerisation were followed using differential scanning photocalorimetry.

Further Improvement to the Analytical Solution of Binary Copolymer Composition Equation and Suggested Procedure for Deriving Monomer Reactivity Ratios

The previously published analytical method of Joshi and Joshi [1] has been improved by incorporating the principle of self-regression. The applicability of this procedure in estimating reactivity ratios from copolymerization experimental data has been demonstrated for two representative cases.

Intramolecular reactions in vinyl polymers as a means of investigation of the propagation step

The Flory-Wall expressions for the fraction of substituents remaining of a vinyl copolymer, when substituents are removed of random from adjacent 1.3 positions, are extended to the case of nonrandam copolymerization. A copolymer composition equation is desired for the case in which the type of monomer preceding the active free radical chain and affects the propagation reaction. The distribution of lengths of sequences in copolymers is discussed.

Main-Chain Lyotropic Liquid-Crystalline Elastomers. 1. Syntheses of Cross-Linked Polyisocyanate Gels Acquiring Liquid-Crystalline Behavior in the Swollen State

Copolymers of n-hexyl and allyl isocyanates were successfully synthesized using an organotitanium(IV) catalyst initiated polymerization. Viscosity measurements indicated that molecular weight increased with decrease in monomer/initiator ratio. Monomer reactivity ratios were calculated using the copolymer composition equation, and the resulting values indicated relative randomness in the copolymer. The liquid-crystalline behavior of these copolymers was studied with regard to their molecular weight, composition, and concentration. Radical cross-linking was extensively studied but yielded only very brittle gels. Consequently, hydrosilation cross-linking was investigated and did yield networks suitable for orientation in a novel technique for increasing the mechanical properties of polymer films. All the hydrosilation cross-linked gels exhibited brilliant mesomorphic birefringence under a cross- polarized microscope at low cross-link density. In addition, the glass transition temperatures of the hydrosilation cross-linked networks were found to be lower than those of their constituent polymers.

Solvent Effect on Free-Radical Chain Polymerization. 7. Kinetical Analysis of the Binary System Methyl Methacrylate/N-Vinylpyrrolidone in Bulk and in Model Solvents in Terms of the Reactant-Solvent Complex Model

The monomer system methyl methacrylate (MMA = M 1 )/N-vinylpyrrolidone (NVP = M 2 ) was copolymerized at 60 °C with azobis(isobutyronitrile) as the initiator in cyclohexane (c-H), methyl isobutyrate (MiB), and N-methylpyrrolidone (NMP) at the total monomer concentration 0.4 (mol.L -1 ). The relative reactivity ratios r i were estimated by the nonlinear least-squares curve fitting by Tidwell and Mortimer, and they depend on the nature of the solvent. For the description of this effect the reactant-solvent complex (RSC) model was taken into consideration. Since the analytical copolymer composition equation derived is inconvenient for very small r i values, the Monte Carlo method was used. It permits us to describe all tendencies correctly in terms of the RSC model. In the present paper the RSC model was tested for the first time in application to a binary copolymerization, whereby preevaluated relative reactivity parameters were used instead of fitting the model to experimental data. In this manner a check of the physical meaning of the model increments was achieved. The highest deviation between measured and calculated copolymer compositions amounted to 3-5 mol %. Solvents especially affect the resonance parameter Q of the monomers which changes 4-fold by a change from c-H to NMP. The polarity parameter e remains almost unchanged. Observed effects can be understood in terms of the molecular orbital (MO) energies of the reacting partners.

Living carbocationic copolymerizations. II. Reactivity ratios and microstructure of isobutylene/p‐methylstyrene copolymers

AbstractA novel method was developed for the quantitative description of copolymerization behavior, specifically for the derivation of reactivity ratios and micro‐ and macro‐compositions of monomer pairs with significantly different reactivities. The novelty of the method lies in the manner of generating instantaneous feed and copolymer composition data from experimentally readily obtainable cumulative copolymer compositions, although the latter drifts with progressing copolymerization. It is demonstrated that such copolymer systems can be described by two reactivity ratios, albeit the values are valid only over the narrow feed composition range within which they were determined. The great advantage of this method is that whereas the differential copolymer composition equation is strictly valid only at 0% conversion, the method produces corresponding instantaneous feed and copolymer compositions at any conversion. Assumptions or approximations are unnecessary to calculate reactivity ratios. Subsequently the procedure was applied to obtain reliable monomer reactivity ratios of isobutylene (IB)–p‐methylstyrene (pMeSt) copolymers, rIB and rpMest, prepared by living carbocationic copolymerizations with [IB]/[pMeSt] feeds compositions of 90:10 and 97:3 mol/mol, i.e., with feed compositions of industrial importance. According to our procedure, rIB = 0·74±0·11 and rpMeSt = 7·99±3·34. These reactivity ratios were then used to calculate overall IB–pMeSt copolymer compositions over the entire comonomer conversion range and to compare calculated with experimental compositions. The good quantitative agreement between calculated and experimental compositions indicates that the description of both macro‐ and micro‐compositions of IB–pMeSt copolymers obtained in the 90:10 and to 97:3 mol/mol feed composition range is satisfactory.

Some newer concepts on ethylene/α‐olefin copolymerization on heterogeneous Ziegler‐Natta catalysts

AbstractUnsteady diffusion kinetics, recently advanced by this laboratory, is applied to the examination of some polymerization and molecular chain structure problems. Hitherto deemed “anomalous” phenomena, such as the faster rate of copolymerization of ethylene/α‐olefin than the homopolymerization of ethylene and the enrichment in the incorporation of a higher α‐olefin in its copolymerization with ethylene by a lower α‐olefin, are reasonably explained by unsteady diffusion of monomers. Molecular chain structure of copolymers, such as compositional heterogeneity and its dependence on comonomer incorporation originates from the difference in diffusion coefficients of the monomers. A copolymer composition equation taking into consideration the unsteady diffusion was developed. In cases where simulated curves were compared with experimental curves, good agreements were found.

Derivation of Copolymer Composition Equation Through Kinetic Theory in Binary Copolymerization Systems with Antepenultimate Effect

Abstract A new treatment to characterize copolymer composition in binary copolymerization systems was developed by using a steady-state assumption for free radicals. It gives a copolymer composition equation solely through classical kinetic theory with the antepenultimate effect taken into account. This equation and its derivation procedure are compared with those previously published.