The effect of direct interchange reactions on the MWD of condensation polymers

In this theoretical study, a relationship has been developed for the transient molecular-weight distribution (MWD) of a condensation polymer undergoing a direct interchange reaction. Direct interchange is one of several reactions which can take place in condensation polymers in the melt. When compared to the more well-known reactions of polycondensation, degradation, and interchange of an end-group with a condensation linkage, direct interchange has a more complex statistical effect on the MWD and is less commonly observed. However, these types of reactions can be quite important in some polymeric systems, such as in the reaction of poly (butylene terephthalate) with polycarbonate. The MWD relationship was developed from the species balance: The rate of accumulation of chains of a given molecular weight is equal to their rate of generation minus their rate of consumption. For this reaction, development of the generation term is quite complex; it is approached here by describing five probability situations which are determined by each possible combination of reactant and product chains. Example distributions computed from these equations show that different transient paths are followed under direct and end-group interchange, but that both reactions lead to the equilibrium most-probable distribution.     

Polyethylene with bimodal molecular weight distribution synthesized by 2,6-bis(imino)pyridyl complexes of Fe(II) activated with various activators

Polyethylenes with bimodal molecular weight distribution (MWD) were synthesized by 2,6-bis(imino)pyridyl complexes of Fe(II) combined with different activators, which were prepared from alkylaluminium. It is found that the molecular weight (MW) and MWD was influenced by not only iron complexes but activators as well. The activator plays key important role in determination of the MW and MWD of final polymer and the MWD shape could be regulated by selection of various activators and polymerization conditions. The study on the variation of the MWD with the polymerization time and fitting of bimodal MWD with two Flory distributions suggests that bimodal MWD is caused by chain transfer reaction to activator or two active sites.     

Monte carlo simulation of copolymerization by ester interchange reaction in miscible polyester blends

The effects of reaction variables on the degree of randomness in copolymers formed by ester interchange reaction in miscible polyester melt blends were systematically investigated using a Monte Carlo method. Three reaction variables such as the molecular weight difference between two component polymers, the blend ratio, and the reaction ratio of end attack to bond flip, were particularly considered on the cubic lattice model. Ester interchange reactions were assumed to take place during reptational chain motions. It was found that the copolymerization was dependent upon the molecular weight difference and reaction ratio: As the molecular weight difference becomes smaller and when both end attack and bond flip reactions are involved simultaneously, the copolymerization is accelerated. However, the blend ratio does not affect the copolymerization process. This result is discussed in relation to the polymer chain conformation for the ester interchange reaction. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1637–1645, 1998     

Narrow molecular weight distribution of condensation polymers achieved by adding monomers in many batches

The Z transform method has been used to calculate the molecular weight distribution (MWD) of condensation polymers. The MWD obtained by using Z transform is explicitly discrete. The method is illustrated for two cases: (1) further polycondensation of AB prepolymers with certain initial MWD, and (2) polycondensation of AB and Ar (r is the number of A type functional groups) monomers where AB monomers are added in several batches. In the latter case, it is found that the resulting MWD is much narrower than that of one-batch polycondensation. The trick of producing narrow MWDs of condensation polymers is merely a consequence of keeping AB monomer concentration as low as possible during the reaction in order to suppress the condensation reaction between monomeric AB molecules. The theoretical prediction has been confirmed by Monte Carlo simulation. Therefore, it provides a new possible technique for obtaining narrow MWD polymers through polycondensation reactions.     

Molecular Weight Distribution Simulation in Equilibrium Ring‐Opening Polymerization: A New Macroscopic Model

Compared with other types of polymerization, the molecular weight and its distribution (MWD) of equilibrium ring‐opening polymerization (EROP) are complicated and have not been extensively studied. By using statistic method, a series of equations based on polymerization mechanism is established to describe numbers of rings, chains, and active centers. Using this new model, the predicted results of polydimethylsiloxane synthesized by EROP agree well with experimental results. This model has advantages in molecule number, calculation speed, and stability when compared with the Monte Carlo simulation. It also has the potential to replace Monte Carlo simulation in MWD prediction.     

Monte Carlo simulation of size exclusion chromatography for branched polymers formed through free‐radical polymerization with chain transfer to polymer

The elution curves of size exclusion chromatography (SEC) for branched polymers formed through free‐radical polymerization that involves chain transfer to polymer were theoretically investigated by using a Monte Carlo method. We considered two types of measured molecular weight distribution (MWD), (1) the calibrated MWD relative to standard linear polymers, and (2) the MWD obtained by using a light scattering photometer (LS) in which the weight‐average molecular weight of polymers within the elution volume is determined directly. It was found that the calibrated MWD clearly underestimates the high molecular weight tail, and the measured distributions are narrower than the true MWD. On the other hand, the present simulation results showed that the LS method gives reasonable estimates of the true MWDs. The mean square radius of gyration of the polymer molecules having the same molecular weight was also investigated. The radii of gyration showed clear deviation from the Zimm‐Stockmayer equation^[1] because of the non‐random nature of branched structure and the difference in the primary chain length distribution.     

Size exclusion chromatography of branched polymers: Star and comb polymers

Monte Carlo simulations were conducted to estimate the elution curve of size exclusion chromatography (SEC). The present simulation can be applied to various types of branched polymers, as long as the kinetic mechanism of nonlinear polymer formation is given. We considered two types of detector systems, (1) a detector that measures the polymer concentration in the elution volume to determine the calibrated molecular weights, such as by using the differential refractive index detector (RI), and (2) a detector that determines the weight‐average molecular weight of polymers within the elution volume directly, such as a light scattering photometer (LS). For polydisperse star polymers, both detector systems tend to give a reasonable estimate of the true molecular weight distribution (MWD). On the other hand, for comb‐branched polymers, the RI detector underestimates the molecular weight of branched polymers significantly. The LS detector system improves the measured MWD, but still is not exact. The present simulation technique promises to establish various types of complicated reaction mechanisms for nonlinear polymer formation by using the SEC data quantitatively. In addition, the present technique could be used to reinvestigate a large amount of SEC data obtained up to the present to estimate the true MWD.     

不等活性缩聚反应动力学及其分子量分布Monte Carlo模拟

 将缩聚产物分子量分布（ＭＷＤ）的ＭｏｎｔｅＣａｒｌｏ方法和聚合反应动力学的ＭｏｎｔｅＣａｒｌｏ方法结合起来，可在研究聚合反应动力学的同时获得ＭＷＤ随时间的变化．将该方法用于研究非等活性的ＡＢ—ＡＡ型缩聚反应的动力学与实验结果十分一致．通过考察高活性ＡＡ单体加入后对其动力学行为和相应的ＭＷＤ的影响，作者提出了对聚苯撑醚砜的ＡＢ型缩聚合成中加快其反应速度和改进ＭＷＤ的实用方法．     

Origin of miscibility‐induced sequential reordering and crystallization‐induced sequential reordering in binary copolyesters: a Monte Carlo simulation

The effect of the repulsive interaction between the components of binary copolyesters on their sequence order was investigated with the Monte Carlo simulation method. The phase separation and ester‐interchange reactions were implemented simultaneously with a kind of one‐site bond fluctuation model. When the repulsive interaction energy was applied to the binary copolyesters, miscibility‐induced sequential reordering (MISR) was induced. The more repulsive the pair interaction was, the higher the sequence order was. During the MISR process, homoester‐interchange reactions became more favorable because of the repulsive interaction, accompanying the decrease of the interactional free energy. The sequence order resulting from MISR was independent of the relative trial ratio of phase separation to ester‐interchange reaction at a given value of interaction energy. Restoration of the sequence distribution was also simulated with and without the repulsive interaction between the components of the binary copolyesters to investigate the effect of MISR on the crystallization‐induced sequential reordering (CISR) process in binary copolyesters, where sequences with lengths longer than 6 were assumed to crystallize and could not take part in ester‐interchange reactions. The sequence distribution in the amorphous phase was restored via ester‐interchange reactions. When the repulsive interaction was applied to binary copolyesters during the CISR process, restoration of the sequence distribution was accelerated, indicating that MISR can accelerate the CISR process when a polyester blend shows upper critical solution temperature behavior. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1337–1347, 2001     

由一种新型非均相聚合方法制备的聚氯乙烯的分子结构

聚氯乙烯(PVC)树脂通常采用自由基本体聚合、悬浮聚合和乳液聚合方法制备.无链转移剂时,头-尾加成和PVC大分子自由基向单体链转移反应分别是链增长和链终止的主要方式,聚合温度成为影响PVC平均分子量及分子量分布的主要因素.     

不等活性缩聚反应动力学及其分子量分布Monte Carlo模拟

将缩聚产物分子量分布（ＭＷＤ）的ＭｏｎｔｅＣａｒｌｏ方法和聚合反应动力学的ＭｏｎｔｅＣａｒｌｏ方法结合起来，可在研究聚合反应动力学的同时获得ＭＷＤ随时间的变化．将该方法用于研究非等活性的ＡＢ—ＡＡ型缩聚反应的动力学与实验结果十分一致．通过考察高活性ＡＡ单体加入后对其动力学行为和相应的ＭＷＤ的影响，作者提出了对聚苯撑醚砜的ＡＢ型缩聚合成中加快其反应速度和改进ＭＷＤ的实用方法．     

Model hysteresis dimer molecule II: deductions from probability profile due to system coordinates

The hysteresis dimer reaction of the first sequel is applied to test the Gibbs density-in-phase hypothesis for a canonical distribution at equilibrium. The probability distribution of variously defined internal and external variables is probed using the algorithms described, in particular the novel probing of the energy states of a labeled particle where it is found that there is compliance with the Gibbs’ hypothesis for the stated equilibrium condition and where the probability data strongly suggests that an extended equipartition principle may be formulated for some specific molecular coordinates, whose equipartition temperature does not equal the mean system temperature and a conjecture concerning which coordinates may be suitable is provided. Evidence of violations to the mesoscopic nonequilibrium thermodynamics (MNET) assumptions used without clear qualifications for a canonical distribution for internal variables are described, and possible reasons outlined, where it is found that the free dimer and atom particle kinetic energy distributions agree fully with Maxwell–Boltzmann statistics but the distribution for the relative kinetic energy of bonded atoms does not. The principle of local equilibrium (PLE) commonly used in nonequilibrium theories to model irreversible systems is investigated through NEMD simulation at extreme conditions of bond formation and breakup at the reservoir ends in the presence of a temperature gradient, where for this study a simple and novel difference equation algorithm to test the divergence theorem for mass conservation is utilized, where mass is found to be conserved from the algorithm in the presence of flux currents, in contradiction to at least one aspect of PLE in the linear domain. It is concluded therefore that this principle can be a good approximation at best, corroborating previous purely theoretical results derived from the generalized Clausius Inequality, which proved that the PLE cannot be an exact principle for nonequilibrium systems.      

Investigation of the formation of poly(ethylene terephthalate) with model molecules: Kinetics and mechanism of the catalytic esterification and alcoholysis reactions. I. Carboxylic acid catalysis (monofunctional reactants)

Monofunctional compounds (benzoic acid, heptyl alcohol, and 2-butoxy-ethanol) were used to investigate the kinetics of the esterification and the alcoholysis reactions. Carboxylic acids (benzoic acid) are the only catalysts present in the reaction medium. The factors which influence the kinetics of the esterification reaction were studied: the nature of the carboxylic acid (substituents on the benzene ring), the nature of the alcohol, the composition of the reaction medium (alcohol alone or with another solvent, ester, or water). The results point out for an acyl type (A_AC2) mechanism. The alcoholysis reaction needs the presence of carboxylic acid as a catalyst to occur significantly. A similar mechanism is proposed for both reactions: nucleophilic attack by the oxygen atom of the alcohol at the ion pair formed by protonation of the acid (esterification reaction) or by protonation of the ester (alcoholysis).     

Comparison of Accuracy and Convergence Rate between Equilibrium and Nonequilibrium Alchemical Transformations for Calculation of Relative Binding Free Energy

Estimation of protein-ligand binding affinity within chemical accuracy is one of the grand challenges in structure-based rational drug design. With the efforts over three decades, free energy methods based on equilibrium molecular dynamics (MD) simulations have become mature and are nowadays routinely applied in the community of computational chemistry. On the contrary, nonequilibrium MD simulation methods have attracted less attention, despite their underlying rigor in mathematics and potential advantage in efficiency. In this work, the equilibrium and nonequilibrium simulation methods are compared in terms of accuracy and convergence rate in the calculations of relative binding free energies. The proteins studied are T4-lysozyme mutant L99A and COX-2. For each protein, two ligands are studied. The results show that the nonequilibrium simulation method can be competitively as accurate as the equilibrium method, and the former is more efficient than the latter by considering the convergence rate with respect to the cost of wall clock time. In addition, Bennett acceptance ratio, which is a bidirectional post-processing method, converges faster than the unidirectional Jarzynski equality for the nonequilibrium simulations.     

Formation of diethylene glycol as a side reaction during production of polyethylene terephthalate

Polymers of poly(ethylene terephthalate) (PET) always contain a certain amount of incorporated diethylene glycol (DEG), substituting the incorporated glycol. DEG is formed in a side reaction during the ester interchange of dimethyl terephthalate (DMT) with ethylene glycol or during direct esterification of terephthalic acid with ethylene glycol, and to a smaller extent during the polycondensation of the low-molecular material. DEG is formed via an unusual type of reaction: ester + alcohol → ether + acid. Some evidence of this type of reaction is given by the formation of dioxane in low molecular PET and of methyl Cellosolve and methyl carbitol during the ester interchange of DMT with ethylene glycol and diethylene glycol, respectively. The strongest support for this type of reaction, however, was obtained from kinetic data. Polyesters of low molecular weight with OH group contents ranging from 3 to 0.5 mole/kg were heated at 270°C in sealed tubes for 1–7 hr. The kinetic equation for the proposed reaction is: d[DEG]/dt = k[OH] [ester]. With the aid of one rate constant the formation of DEG in all esters could be described.     

Characterization of functionalized styrene-butadiene rubber by flow field-flow fractionation/light scattering in organic solvent

Flow field-flow fractionation (FlFFF) using an organic solvent as mobile phase has been effectively utilized for the separation and characterization of functionalized styrene-butadiene rubbers (SBR) that are polymerized and followed by coupling reaction in solution. Separation of broad molecular weight SBR was accomplished by an asymmetrical FlFFF channel in THF under field programming and the molecular weight distribution (MWD) of the SBR sample was determined by on-line measurement of light scattering. In this study, FlFFF has been utilized to characterize high-MW functionalized SBR from the low-MW non-functionalized molecules which were used for coupling reaction to produce high-MW functionalized SBRs, and to determine the coupling number of the functionalized SBRs depending on the type of the coupling reagents. The resulting MWD of the SBR samples prepared by the different coupling reagents (SnCl(4) and a polydimethylsiloxane compound) were compared.     

Equilibrium calculations of viscosity and thermal conductivity across a solid-liquid interface using boundary fluctuations

We calculate viscosity and thermal conductivity in systems of Lennard-Jones particles consisting of coexisting solid and liquid with different interface wetting properties using the recently developed equilibrium boundary fluctuation theory. We compare the slip length and equivalent liquid length obtained from these calculations with those obtained from nonequilibrium molecular dynamics. The equilibrium and nonequilibrium calculations of the slip length and the sum of the thermal equivalent lengths are in good agreement. We conclude that for both interfacial properties, the nonequilibrium simulations were probing the linear response. The significant dependence of the intrinsic equivalence length on the interfacial temperature difference used to generate the thermal gradient is explained as a consequence of the different thermodynamic states of the two interfaces.     

Comparison of reaction rates for helium plasmas calculated using nonequilibrium and equilibrium electron energy distribution functions

The electron energy distribution functions for helium plasmas have been calculated using the Boltzmann equation. Three characteristic temperatures of these distribution functions have been determined (from mean energy, the Einstein formula, and the logarithmic slope). The reaction rates for nonequilibrium and three equilibrium (corresponding to these three characteristic temperatures) distribution functions have been calculated and compared We have found that the use of equilibrium values for reaction rates of processes going from the ground state can lead to great errors in results, the use of equilibrium values for processes going from higher levels is possible for higher reduced electric fields, and there is no problem with using equilibrium values. for superelastic processes.     

Calculating fifth-order Raman signals for various molecular liquids by equilibrium and nonequilibrium hybrid molecular dynamics simulation algorithms

The fifth-order two-dimensional (2D) Raman signals have been calculated from the equilibrium and nonequilibrium (finite field) molecular dynamics simulations. The equilibrium method evaluates response functions with equilibrium trajectories, while the nonequilibrium method calculates a molecular polarizability from nonequilibrium trajectories for different pulse configurations and sequences. In this paper, we introduce an efficient algorithm which hybridizes the existing two methods to avoid the time-consuming calculations of the stability matrices which are inherent in the equilibrium method. Using nonequilibrium trajectories for a single laser excitation, we are able to dramatically simplify the sampling process. With this approach, the 2D Raman signals for liquid xenon, carbon disulfide, water, acetonitrile, and formamide are calculated and discussed. Intensities of 2D Raman signals are also estimated and the peak strength of formamide is found to be only five times smaller than that of carbon disulfide.     

Preparation of poly(ethylene terephthalate-co-isophthalate) by ester interchange reaction in the PET/PEI blend system

Optimum conditions for the synthesis of PEI of considerable molecular weight have been established. Poly(ethylene terephthalate-co-isophthalate) (PETI) has been prepared through the ester interchange reaction of a blend of poly(ethylene terephthalate) (PET) and poly(ethylene isophthalate) (PEI). NMR analysis has indicated that the PETI changes from a block-type copolymer to a random type copolymer as the ester interchange reaction proceeds. If the reaction is limited to 20 min, the resulting PETI is crystallizable. The effects of catalysts that have been used during the synthesis of PEI on the characteristics of PETI are also discussed. © 1997 John Wiley & Sons, Inc.