Monte Carlo simulation of diffusion effects on chain‐extension reactions

The diffusion effects on chain‐extension reactions using carboxyl‐terminated polyamide‐12 as a model reactant with bisoxazolines were investigated by the stochastic Monte Carlo method. Thus, complicated direct modeling and numerical calculations were avoided. The chain‐length dependence and detailed diffusive behavior were discussed in depth. The diffusion effects retarded the progress of chain‐extension reactions and led to lower coupling efficiency. The simulated results indicated that the diffusion effects could make the final molecular weight distributions wider. In the presence of diffusion and with the progress of the coupling efficiency, peaks in the evolution curves of the weight‐average molecular weight and valleys in the evolution curves of the polydispersity index were observed, respectively, when the coupling efficiency was low enough. These phenomena were different from those without diffusion effects and were analyzed in detail. The critical entanglement chain length had strong effects on the simulated results of the diffusion effects, especially when its value was near the average chain length. The results also showed that the effects of the reactant degradation made the molecular weight distribution of the reaction system wider and weakened the diffusion effects on the coupling reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2902–2911, 2006     

Substituent effects of N‐alkyl groups on thermally induced polymerization behavior of 1,3‐benzoxazines

Thermally induced polymerizations of a series of 1,3‐benzoxazines with a variety of substituents on the nitrogen atom were investigated in detail, particularly in the following three aspects of the polymerization: (1) N‐alkyl‐1,3‐benzoxazines are much more reactive than N‐phenyl‐1,3‐benzoxazine. (2) The polymerization rate depended on the bulkiness of the N‐substituent. The bulkier the substituent was, the slower the polymerization was. (3) The polymerizations accompanied weight loss due to the elimination of the corresponding imine (R‐N = CH₂), and its extent became larger when R was more bulky. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2777–2782, 2010     

Thiol‐ene photopolymerization of polymer‐derived ceramic precursors

The liquid, ceramic precursor monomer VL20 was copolymerized with a thiol monomer in a traditional radical thiol‐ene photopolymerization. Polymerization occurred via addition of the thiol functional group to the vinyl silazane functional group in a 1:1 ratio consistent with a step‐growth polymerization. Gelation occurred at a high conversion of functional groups (70%) consistent with an average molecular weight and functionality of 560 and 1.7, respectively, for VL20 monomers. Initiatorless photopolymerization of the thiol‐VL20 system also occurred upon irradiation at either 365 or 254 nm. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1752–1757, 2004     

New aliphatic poly(ester‐carbonates) based on 5‐methyl‐5‐allyloxycarbonyl‐1,3‐dioxan‐2‐one

The synthesis, characterization, and ring‐opening polymerization of a new cyclic carbonate monomer containing an allyl ester moiety, 5‐methyl‐5‐allyloxycarbonyl‐1,3‐dioxan‐2‐one (MAC), was performed for the first time. MAC was synthesized in five steps in good yield beginning from the starting material, 2,2‐bis(hydroxymethyl)propionic acid. Subsequent polymerization and copolymerizations of the new cyclic carbonate with rac‐lactide (rac‐LA) and ?‐caprolactone (CL) were attempted. Rac‐LA copolymerized well with MAC, but CL copolymerizations produced insoluble products. Oligomeric macroinitiators of MAC and rac‐LA were synthesized from stannous ethoxide, and both macroinitiators were used for the controlled ring‐opening polymerization of rac‐LA. The polymerization kinetics were examined by monitoring the disappearance of the characteristic C? O ring stretch of the monomer at 1240 cm^?1 with real‐time in situ Fourier transform infrared spectroscopy. Postpolymerization oxidation reactions were conducted to epoxidize the unsaturated bonds of the MAC‐functionalized polymers. Epoxide‐containing polymers may allow further organic transformations with various nucleophiles, such as amines, alcohols, and carboxylic acids. NMR was used for microstructure identification of the polymers, and size exclusion chromatography and differential scanning calorimetry were used to characterize the new functionalized poly(ester‐carbonates). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1978–1991, 2003     

Organometallic and enzymatic catalysis for ring opening copolymerization of ε‐caprolactone and 4‐methyl‐ε‐caprolactone

A series of copolymers containing ε‐caprolactone (CL) and 4‐methyl‐ε‐caprolactone (MeCL) were synthesized by ring‐opening polymerization (ROP) using Tin(II) bis(2‐ethylhexanoate)(Sn(Oct)₂) or Novozym 435 as catalyst. The molecular structure and weight of copolymers were determined by nuclear magnetic resonance (NMR) and size exclusion chromatography (SEC), respectively. Our kinetic study showed that the monomer reactivity ratios for CL (r₁) and MeCL (r₂) using Sn(Oct)₂ as catalyst were estimated to be near unity and r₁ × r₂ = 1, indicating the random distribution of the monomers in the final copolymer. The results of DSC and XRD consistently indicated that the copolymers were inclined to be amorphous with the increasing of MeCL fraction. Microspheres were prepared from copolymers and characterized by SEM. The preliminary degradability and biocompatibility studies on these copolymers were also assessed. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Decomposition of model alkoxyamines in simple and polymerizing systems. II. Diastereomeric N‐(2‐methylpropyl)‐N‐(1‐diethyl‐phosphono‐2,2‐dimethyl‐propyl)‐aminoxyl‐based compounds

Thermal reactions of the alkoxyamine diastereomers DEPN‐R′ [DEPN: N‐(2‐methylpropyl)‐N‐(1‐diethylphosphophono‐2,2‐dimethyl‐propyl)‐aminoxyl; R′: methoxy‐carbonylethyl and phenylethyl] with (R,R) + (S,S) and (R,S) + (S,R) configurations have been investigated by ¹H NMR at 100 °C. During the overall decay the diastereomers interconvert, and an analytical treatment of the combined processes is presented. Rate constants are obtained for the cleavage and reformation of DEPN‐R′ from NMR, electron spin resonance, and chemically induced dynamic nuclear polarization experiments also using 2,2,6,6‐tetramethylpiperidinyl‐1‐oxyl (TEMPO) as a radical scavenger. The rate constants depend on the diastereomer configuration and the residues R′. Simulations of the kinetics observed with styrene and methyl methacrylate containing solutions yielded rate constants for unimeric and polymeric alkoxyamines DEPN‐(M)_n‐R′. The results were compatible with the known DEPN mediation of living styrene and acrylate polymerizations. For methyl methacrylate the equilibrium constant of the reversible cleavage of the dormant chains DEPN‐(M)_n‐R′ is very large and renders successful living polymerizations unlikely. Mechanistic and kinetic differences of DEPN‐ and TEMPO‐mediated polymerizations are discussed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3264–3283, 2002     

Monte Carlo Simulation of Ethylene Copolymers: A Look into the Monomer Sequence Distribution

A comprehensive mathematical model was developed using Monte Carlo simulation to describe the mechanism of ethylene and α-olefin copolymerization. The model studies the polymerization mechanism using coordination catalysts and is able to predict molecular weight and detailed chemical composition distributions. This work is considered to be a useful tool that enables us to understand and described the monomer sequence distribution as a function of chain length in semi-batch polymerization reactors.     

A Parallelised High Performance Monte Carlo Simulation Approach for Complex Polymerisation Kinetics

A novel, parallelised approach to Monte Carlo simulations for the computation of full molecular weight distributions (MWDs) arising from complex polymerisation reactions is presented. The parallel Monte Carlo method constitutes perhaps the most comprehensive route to the simulation of full MWDs of multiple chain length polymer entities and can also provide detailed microstructural information. New fundamental insights have been developed with regard to the Monte Carlo process in at least three key areas: (i) an insufficient system size is demonstrated to create inaccuracies via poor representation of the most improbable events and least numerous species; (ii) advanced algorithmic principles and compiler technology known to computer science have been used to provide speed improvements and (iii) the parallelisability of the algorithm has been explored and excellent scalability demonstrated. At present, the parallel Monte Carlo method presented herein compares very favourably in speed with the latest developments in the h‐p Galerkin method‐based PREDICI software package while providing significantly more detailed microstructural information. It seems viable to fuse parallel Monte Carlo methods with those based on the h‐p Galerkin methods to achieve an optimum of information depths for the modelling of complex macromolecular kinetics and the resulting microstructural information.

     

Solubility of N2 in poly(α‐n‐hexyl‐β,L‐aspartate): Temperature and force‐field dependence

The solubility of N₂ in poly(α‐n‐hexyl‐β,L ‐aspartate), a stereoregular poly(β‐peptide), was investigated with atomistic Monte Carlo simulations. The structure of this material is intermediate between that of polymers able to form a three‐dimensional crystal lattice and that of liquid‐crystalline polymers with a biphasic distribution. The dependence of the calculated solubility coefficients on both the parameters of the force field and the temperature was examined. The results are compared with recently reported experimental data. Furthermore, the motion of the penetrant molecules within the polymer matrix was analyzed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2928–2936, 2003     

Batch emulsion copolymerization of 3‐O‐methacryloyl‐1,2:5,6‐di‐O‐isopropylidene‐α‐D‐glucofuranose and butyl acrylate: Synthesis and properties of the sugar latices

To obtain new polymer latices based on sugar derivative, batch emulsion copolymerizations of 3‐O‐methacryloyl‐1,2:5,6‐di‐O‐isopropylidene‐α‐D ‐glucofuranose (3‐MDG) and n‐butyl acrylate (BA) were carried out at 70 °C, with potassium persulfate as the initiator. 3‐MDG polymerizes faster than BA because of its higher reactivity ratio, r_(3‐MDG) = 1.94 versus r_(BA) = 0.54. The effect of the initial monomer composition on the polymerization rate and the thermal properties of the end copolymers was investigated. The overall rate of polymerization increases by enhancing the sugar content in the initial monomer composition. The glass‐transition temperature is linearly related to the sugar content in the copolymer. The influence of the type of surfactant showed that the particle size increases by changing from ionic to nonionic surfactant. Furthermore, the effect of the added acrylic acid (AA) on the rheological properties suggests that the sugar latices exhibit different non‐Newtonian flows depending on the pH of the latex and on the AA concentration on the particle surface. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 788–803, 2003     

Kinetics of the ring‐opening metathesis polymerization of a 7‐oxanorbornene derivative by Grubbs' catalyst

The kinetics of the initiation and propagation of the ring‐opening metathesis polymerization of exo,exo‐5,6‐bis(methoxycarbonyl)‐7‐oxabicyclo[2.2.1]hept‐2‐ene catalyzed by Grubbs' catalyst (Cl₂(PCy₃)₂Ru?CHPh) were measured by ultraviolet–visible and ¹H NMR spectroscopy, respectively. Activation parameters for these processes were also determined. Although the ratio of the rate constant of initiation to the rate constant of propagation was determined to be less than 1 for this system, this polymerization showed many of the characteristics of a living system, including low polydispersities. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2125–2131, 2003     

Synthesis and characterization of new organosoluble polyamides derived from bis[4‐(4‐carboxyphenoxy) phenyl]diphenylmethane

A new dicarboxylic acid containing a diphenylmethylene linkage, bis[4‐(4‐carboxyphenoxy)phenyl]diphenylmethane (BCAPD), was prepared from bis(4‐hydroxphenyl)diphenylmethane and p‐fluorobenzonitrile via an aromatic nucleophilic substitution reaction followed by hydrolysis. A series of novel polyamides were prepared by the direct polycondensation of BCAPD and various aromatic diamines. The polymers were produced with moderate to high inherent viscosities of 0.80–0.85 dL g^?1. Nearly all the polymers were readily soluble in polar solvents such as N‐methyl‐2‐pyrrolidinone, N,N‐dimethylacetamide, N,N‐dimethylformamide, and dimethyl sulfoxide, in less polar solvents such as pyridine and cyclohexanone, and in tetrahydrofuran. All the polymers were amorphous, and the polyamide films had a tensile strength and a tensile modulus greater than 80 MPa and 2.0 GPa, respectively. These polyamides had glass‐transition temperatures between 249 and 274 °C, and their temperatures at a 10% weight loss were 477–538 and 483–540 °C in nitrogen and air atmospheres, respectively. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1156–1161, 2001     

H‐transfer reaction during decomposition of N‐(2‐methylpropyl)‐ N‐(1‐diethylphosphono‐2,2‐dimethylpropyl)‐N‐oxyl (SG1)‐based alkoxyamines

Thermal decomposition of four tertiary N‐(2‐methylpropyl)‐N‐(1‐diethylphosphono‐2,2‐dimethylpropyl)‐N‐oxyl (SG1)‐based alkoxyamines (SG1‐C(Me)₂‐C(O)‐OR, R = Me, tBu, Et, H) has been studied at different experimental conditions using ¹H and ³¹P NMR spectroscopies. This experiment represents the initiating step of methyl methacrylate polymerization. It has been shown that H‐transfer reaction occurs during the decomposition of three alkoxyamines in highly degassed solution, whereas no products of H‐transfer are detected during decomposition of SG1‐MAMA alkoxyamine. The value of the rate constant of H‐transfer for alkoxyamines 1 (SG1‐C(Me)₂‐C(O)‐OMe) and 2 ( SG1‐C(Me)₂‐C(O)‐OtBu) has been estimated as 1.7 × 10³ M^?1s^?1. The high influence of oxygen on decomposition mechanism is found. In particular, in poorly degassed solutions, nearly quantitative formation of oxidation product has been observed, whereas at residual pressure of 10^?5 mbar, the main products originate from H‐atom transfer reaction. The acidity of the reaction medium affects the decomposition mechanism suppressing the H‐atom transfer. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Incubation period in the 2,2,4,4‐tetramethyl‐1‐piperidinyloxy‐mediated thermal autopolymerization of styrene: Kinetics and simulations

Mechanisms and simulations of the induction period and the initial polymerization stages in the nitroxide‐mediated autopolymerization of styrene are discussed. At 120–125 °C and moderate 2,2,4,4‐tetramethyl‐1‐piperidinyloxy (TEMPO) concentrations (0.02–0.08 M), the main source of radicals is the hydrogen abstraction of the Mayo dimer by TEMPO [with the kinetic constant of hydrogen abstraction (k_h)]. At higher TEMPO concentrations ([N?] > 0.1 M), this reaction is still dominant, but radical generation by the direct attack against styrene by TEMPO, with kinetic constant of addition k_ad, also becomes relevant. From previous experimental data and simulations, initial estimates of k_h ≈ 1 and k_ad ≈ 6 × 10^?7 L mol^?1 s^?1 are obtained at 125 °C. From the induction period to the polymerization regime, there is an abrupt change in the dominant mechanism generating radicals because of the sudden decrease in the nitroxide radicals. Under induction‐period conditions, the simulations confirm the validity of the quasi‐steady‐state assumption (QSSA) for the Mayo dimer in this regime; however, after the induction period, the QSSA for the dimer is not valid, and this brings into question the scientific basis of the well‐known expression k_th[M]³ (where [M] is the monomer concentration and k_th is the kinetic constant of autoinitiation) for the autoinitiation rate in styrene polymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 6962‐6979, 2006     

Theoretical Consideration of the Grafting of Polymer Chains onto Fullerene C60

Summary: For the first time, the kinetics and statistics of the formation of polymer stars by grafting linear macromolecules onto the fullerene C₆₀ are considered. Two kinetic models are put forward providing an explanation for some important experimentally observed peculiarities of these macromolecular reactions. The comparison of the results found from the solution of the kinetic equations and those obtained by Monte Carlo simulations demonstrates their good agreement. Due to the minimal number of the parameters involved, the theoretical approach proposed is rather convenient for the treatment of experimental data.

     

Biospecific Properties of Random Copolymers, 1

The kinetic study of copolymer synthesis is important to understand how a material is built and how it can get some particular properties. The radical copolymerization of one, two or more monomers can be simulated with classical analytic models, but can also be simulated by a Monte Carlo model that allows a bigger flexibility and is a lot easier to compute and use. We have shown that this Monte Carlo simulation gives the same results of the kinetic study of the terpolymerization as the analytic model, and it can create easily a bank of virtual copolymers for all the compositions needed to analyze the structure of the macromolecular chains in terms of sequences of monomers occurring as a function of the global composition. The search for the sequences is very simple to compute as it consists in a simple reading of the virtual chains previously simulated. This result can thus be applied to make appear a simple correlation between the distribution of functional groups and some specific observed biological activities of biospecific copolymers.

Simplified schema of the numerical virtual terpolymerization.     

The Kinetic Modeling of Strong Diffusion‐Limited Reaction with Cyclization for Three Isomers – Diallyl Ortho‐, Iso‐ and Tere‐Phthalate in a Bulk

Free radical polymerization kinetic in a bulk for three diallyl phthalate isomers – diallyl orthophthalate, diallyl isophthalate and diallyl terephthalate was investigated in a temperature range from 50 to 70 °C initiated with dicyclohexan peroxydicarbonate as initiator at three different initiator concentrations. Conversion points were measured using Fourier Transform Raman measurements. A new kinetic model for polymerization of three diallyl phthalate isomers was developed. It demands the inclusion of only two new kinetic parameters k_DegC and k_pc which were obtained as a ratio k_DegC/k_pc from an additional set of experiments conducted. Computed conversions from the proposed kinetic model show good agreement with the conversion and molecular weight measured data for all three investigated diallyl phthalate isomers.

     

Bayesian Modeling and Markov Chain Monte Carlo Simulations for a Kinetic Study of Homo‐ and Co‐ Polymerization Systems

A Bayesian modeling and Markov Chain Monte Carlo simulation was developed for a kinetic study of homopolymerization and copolymerization systems at the molecular scale. Two copolymerization models – the terminal unit model and the penultimate unit model – were considered. Prior estimates of the kinetic parameters were obtained by L₁‐norm robust statistics. Using the structure of experimental data through a likelihood function, Bayesian modeling was employed to update the prior estimates. The joint posterior probability regions and shimmer bands were calculated for updated reactivity ratios. A method for assessing the power of experimental data in discrimination between copolymerization models is presented. This method was validated for free radical polymerization in binary systems. The evolution of species and radical populations during the course of polymerization were determined. The computational time was considerably decreased by calculating the propagation step from lifetime of the polymer chain and local monomer concentration. To avoid inaccuracies in the results caused by poor choice or false computation of the time step, the time step between successive Monte Carlo events was adapted to the time scale of the fastest reaction. The simulation algorithm is exact, in the sense that it takes full account of the fluctuations and correlations.