Molecular dynamics simulation of solvent-polymer interdiffusion: Fickian diffusion

The interdiffusion of a solvent into a polymer melt has been studied using large scale molecular dynamics and Monte Carlo simulation techniques. The solvent concentration profile and weight gain by the polymer have been measured as a function of time. The weight gain is found to scale as t(1/2), which is expected for Fickian diffusion. The concentration profiles are fit very well assuming Fick's second law with a constant diffusivity. The diffusivity found from fitting Fick's second law is found to be independent of time and equal to the self-diffusion constant in the dilute solvent limit. We separately calculated the diffusivity as a function of concentration using the Darken equation and found that the diffusivity is essentially constant for the concentration range relevant for interdiffusion.     

Reaction of nitrogen dioxide with polystyrene films

The reaction of nitrogen dioxide with thin polystyrene films has been investigated at 35°C with different partial pressures of NO₂ (0.1, 2, 15, 30, and 60 cm Hg) and at several temperatures (25, 35, 45 and 55°C). The films were thin enough (ca. 20 μ) so that the reaction was independent of the diffusion of gas into the polymer. The experimental results can be represented by a chain mechanism. The whole degradation process is controlled by the diffusion of polymer radicals out of cages. This diffusion in turn, is affected by the decrease in viscosity or decrease in weight-average molecular weight as degradation proceeds. This leads to an acceleration of the degradation process. A straight-line relationship between the logarithm of the reciprocal weight-average molecular weight and the logarithm of a reaction–time function was found. The dependence on the rate was substantiated by degrading polymer fractions. The energy of activation for the process is small, in agreement with a diffusion process for chain scission. Nitro and nitrite groups are incorporated along the backbone of polystyrene during exposure. The number of these polar side groups appears to pass through a maximum with time, as is evidenced by aggregation of polymer molecules in benzene solution only during the middle stage of the degradation. The final stage of the process is slowed down by retarder being produced. This retarder can be removed by reprecipitation of exposed polymer films. Degradation in solution is similar to that of films. Isotactic polystyrene shows less irregularities in its degradation curve than the atactic polymer. This is, presumably, due to its more homogeneous morphology, large molecular weight, and broader molecular size distribution. The plot of the degree of degradation versus time for the isotactic polymer can be satisfactorily approximated by a straight line.     

Intramolecular excimer formation in polymers: Pyrene Labelled Polyvinylacetate

The rate constant for intramolecular excimer formation between pyrenyl side-groups, in a polyvinylacetate chain at a mean separation of 200 bonds, has been measured as a function of molecular weight, solvent viscosity and solvent thermodynamic power. Above M = 1 × 10⁵, the rate constant is 1.4 × 10⁷ sec^?1 in low viscosity bad solvents. This value is about twenty times that for the rate constant of the analogous reaction between the two terminal groups in a chain with a mean end-to-end separation of 200 bonds. Increases of the viscosity and of the thermodynamic power of the solvent depress the rate constant, in agreement with the behaviour expected for a diffusion controlled reaction.     

甲基丙烯酸羟丙酯催化链转移聚合及其催化剂链转移常数的变化

采用COBF[bis(aqua)bis((difluoroboryl)dimethylglyoximato)cobalt(II)为催化剂,AIBN为引发剂,60℃下进行甲基丙烯酸β-羟丙酯的催化链转移自由基本体聚合,得到了端基含有双键的低分子量聚合物.分别用Mayo方程法和链长分布(CLD)方程法测算反应过程中催化剂的链转移常数,发现随着反应的进行,催化剂的链转移能力逐渐下降,表观链转移常数Csapp从反应初期的2000左右下降到600左右.这主要是由于反应初期形成了部分比较稳定的碳钴键,导致Csapp在一开始迅速下降,然后趋于缓慢;反应至中后期,由于粘度效应,表观链转移常数进一步降低到300以下.研究进一步发现,由CLD方程法所得的表观链转移常数值普遍低于由Mayo方程法所得的值,且高转化率时误差更大.这是因为GPC测得的是累积产物的分子量分布,对于中、高转化率情况,有必要将其转化为瞬时产物的值.由于累积产物的数均聚合度转化为瞬时产物的数均聚合度相对容易,因而Mayo方程法较适合于测算中、高转化率时的表观链转移常数.     

Branching kinetics of epoxy polymerization of 1, 4-butanediol diglycidyl ether with cis-1, 2-cyclohexanedicarboxylic anhydride

The copolymerization of an epoxy resin [1, 4-butanediol diglycidyl ether (DGEB) (Note a)] with an anhydride [cis-1, 2-cyclohexanedicarboxylic anhydride (CH)] in the presence of N, N-benzyldimethylamine (CA) as a catalyst produces a branched epoxy polymer. We show that the branching kinetics of the copolymerization reaction and the molecular weight distribution of the branched polymers can be approximated by using Smoluchowski's coagulation equation. In the simplest relevant application of this equation to our problem, the overall rate kernel w(u, v) that describes the branching probability in the equation turns out to be proportional to the sum of active sites on the two polymers with a time dependent coefficient. The molecular weight distribution (MWD) and the weight average molecular weight of the branched copolymers at different reaction stages before the gelation threshold are calculated theoretically. The calculated values are then compared with the experimental results obtained by using small angle X-ray scattering (SAXS), laser light scattering (LLS), and chemical analysis. Satisfactory agreement between experimental results and the use of the coagulation equation is attained when it is assumed that the distribution of epoxy polymer molecules is exponential in the number of branching points or, equivalently, active sites, at an early stage of the polymerization reaction.     

Kinetics of bimolecular chemical reaction by a modified diffusion equation

In order to describe the kinematical behavior of the bimolecular chmical reaction in a dilute solution of species characterized by a single diffusion coefficient and by some nonuniform spatial distribution of the active site, a diffusion equation with a simple sink term is derived by reducing the many-body problem to a one-body problem. The equation is normalized with the concentration of unreacted particles. The so-called second-order reaction rate constant can be calculated from the solution of the equation. The equation is applied to the intermolecular termination reaction of polymer radicals on the assumption of free draining. The reaction rate constant gradually decreases with time.     

Cationic Polymerization of Cyclic Sulfides

Abstract

The mechanism of the cationic polymerization of several thietanes and of propylene sulfide under the influence of triethyloxonium tetrafluoroborate in methylene chloride is described. The thietane polymerizations stop at limited conversions because of a termination reaction occurring between the reactive chain ends (cyclic sulfonium salts) and the sulfur atoms of the polymer chain. The maximum conversions obtained under identical conditions differ markedly for the different monomers. Ratios of rate constants of propagation (k_p) to rate constants of termination (k_t) have been calculated. The differences in k _p/k_t. values for the different monomers are explained in terms of differences in basicity and differences in steric hindrance of the monomers compared to the corresponding polymers. In the case of propylene sulfide it is proposed that the main termination reaction is the formation of 12-membered ring sulfonium salts by an intramolecular reaction of the third sulfur of the growing polymer chain with the reactive chain end (three-membered ring sulfonium salt). This terminated polymer is able to reinitiate the polymerization, for example, by reaction of a monomer molecule at the exocyclic carbon atom of the sulfonium salt function. The cyclic tetramer of propylene sulfide is formed in this reaction. After complete polymerization, formation of cyclic tetramer continues, probably via a backbiting mechanism. In methylene chloride as solvent, the absolute value of the rate constant of propagation for 3,3-dimethylthietane changes with changing concentration of initiator and by adding different amounts of indifferent electrolyte to the reaction mixture. From these changes, and assuming that the value of the dissociation constant of the growing chain-ends is close to values of dissociation constants of low molecular weight sulfonium salts, separate rate constants for propagation via free ions and ion-pairs were calculated. The propagation constant of free ions is about 70 times higher than that of ion pairs in methylene chloride at 20°C. Free ions and ion pairs are nearly equally reactive in nitrobenzene.     

Annealing during polymerization of crystalline poly(ethylene terephthalate)

Melt-crystallized poly(ethylene terephthalate) and etched oligomer lamellae from the same polymer have been annealed under vacuum at temperatures between 200 and 260°C and times between 3 and 48 hr. The annealed samples were analyzed through determination of viscosity-average molecular weight, x-ray low-angle spacing, density, heat of fusion, and variation of melting point with heating rate. In all cases it could be shown that the crystal lamellar surfaces remained chemically reactive. Chain folds and chain ends in the surface were converted by chemical reaction to tie molecules between different crystals or different locations on the same lamella.     

Dynamics of chain molecules. Intramolecular diffusion controlled reactions for a pair of terminal reactive groups

The first order intramolecular rate constant for the reaction between the terminal groups of flexible macromolecules is calculated in the partial draining case, following the theory formulated by Wilemski and Fixman for diffusion controlled reactions. Substantial differences with respect to the nondraining and free-draining limits are evidenced, and it is shown that the rate constant in the partial-draining case has relevant contributions from all the modes of the bead-spring chain. The effects of chain flexibility and hydrodynamic interaction in macromolecules of increasing molecular weight are examined. The effective diffusion constant of the end groups increases with both the flexibility and the length of the chain. Numerical results for polystyrene (PS) and polydimethylsiloxane (PDMS) are presented and employed to calculate the relative quantum yield for fluorescence quenching. For highly flexible chains, like PDMS, quenching effects are expected in a range of molecular weight well above the limit of validity of the bead-spring model. On the contrary, for more rigid polymers, like PS, the quenching can be observed only at molecular weights lower than this limit. The calculated behavior is compared with some experimental results recently obtained by the authors.     

Polyethylene networks crosslinked in solution: Preparation,elastic behavior,and oriented crystallization. I. Crosslinking in solution

A study has been made of the crosslinking of linear polyethylene in solution. Networks containing a low number of trapped entanglements and elastically ineffective chain ends were prepared by crosslinking high molecular weight linear polyethylene in 1,2,4-trichlorobenzene solutions with dicumyl peroxide at 120°C. No syneresis was observed during crosslinking except at high peroxide concentrations. The networks were characterized by swelling measurements, infrared spectroscopy, and differential scanning calorimetry. The crosslinking efficiency, calculated from swelling, was found to be proportional to the square of the polymer volume fraction. The proportionality constant was 0.8, indicating close to unit efficiency for undiluted polymer. Chemical modification of the polyethylene chains by attachment of peroxide and solvent fragments was of the order of one foreign unit per elastically active network chain, depending on peroxide and polymer concentration. Sol–gel analysis indicated that no chain scission occurred. These results are shown to be consistent with a “cage” mechanism for crosslinking. The possible topological consequence of this mechanism, preferential crosslinking of entanglements, is discussed. The concentration of trapped entanglements was also found to be proportional to the square of the polymer volume fraction. The proportionality constant corresponds to a molecular weight between entanglements of 4000 for the undiluted polymer, which is close to the value of 4200 found for networks prepared from the undiluted polymer. Since the results obtained are based mainly on the use of the swelling equation, different aspects of the applicability of this equation for the evaluation of the crosslinking process are discussed. As regards the reference dimensions, which should be known for a quantitative application of the elastic theory, the results strongly support the use of the dimensions of the network chains after completion of crosslinking.     

Reaction of a low‐molecular‐weight free radical with a flexible polymer chain: Kinetic studies on the OH + poly(N‐vinylpyrrolidone) model

This work addresses the issue of kinetics of diffusion‐controlled reactions of small radicals with macromolecules in solution. Attack of pulse‐generated hydroxyl radicals on poly(N‐vinylpyrrolidone)—PVP—chains of various molecular weight in water was used as the model reaction. Pulse radiolysis with spectrophotometric detection was applied to determine the rate constants by competition kinetics. The rate constant depends both on polymer concentration and on its molecular weight. In dilute solutions, a distinct dependence of the rate constant on the molecular weight is observed. In the studied range of molecular weight, the values of reaction radius, calculated using Smoluchowski equation on the basis of experimental kinetic data, are very close to the radius of gyration of polymer coils. We believe that radius of gyration, as an easily determined parameter, could possibly serve for predicting rate constants of diffusion‐controlled reactions of polymers with low‐molecular‐weight compounds in dilute solutions. With increasing polymer concentration and thus increasing spatial overlap of polymer coils the dependence of the rate constant on the molecular weight fades away, and the rate constant values increase with increasing concentration toward the value determined for low‐molecular‐weight model of PVP. Most steep increase approximately coincides with the hydrodynamic critical concentration of a given PVP sample, reflecting the change in reaction geometry from individual coils to a continuous matrix of interpenetrating chains. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 474–481, 2011     

Diffusion-controlled vinyl polymerization. I. The gel effect

It is well known that the reaction rate and molecular weight of vinyl polymers can change markedly during the course of polymerization and that these changes are due to the influence of diffusion on the termination reaction. The chain length dependence of the termination rate constant has been considered in this work and has resulted in a general method of treating the polymerization kinetics and molecular weight distribution. This method is independent of the form of the chain length dependency and is capable of dealing with both disproportionation and recombination modes of termination. A specific model for the termination rate constant with chain length dependence is proposed and is based on free volume theory and entanglement coupling. Master curves for the characteristics of the reaction rate and molecular weight distribution are presented with the application of this model.     

Friedel-Crafts crosslinking of polystyrene

Polystyrene may be crosslinked by p-dichloromethylbenzene (DCMB) in 1,2-dichloroethane solution with SnCl₄ as catalyst. Combined intra- and intermolecular crosslinking can be measured by evolution of hydrogen chloride and by an ultraviolet spectral method, and the results for the two methods are in excellent agreement. Intermolecular crosslinking may be calculated separately from number-average molecular weight measurements, so that the extent of intramolecular crosslinking may be deduced by difference. Rate equations for the overall, intermolecular, and intramolecular reactions have been obtained as follows: The anomalous behavior with respect to polystyrene concentration may be due to inhibition of the intramolecular reaction because of increasing interpenetration of polystyrene molecules as the concentration of polystyrene is increased. The rate constant for the intermolecular reaction, which shows “normal” kinetic behavior has been compared with values for the reaction of DCMB with the model compounds benzene, toluene, diphenylmethane, and benzyl chloride. The very much smaller value for polystyrene compared with the models has been accounted for in terms of adverse steric effects when the reaction is occurring in the polymer chain environment.     

Surface segregation and surface tension of polydisperse polymer melts

The effect of polydispersity on surface segregation of a lower molecular weight polymer component in a higher molecular weight linear polymer melt host is investigated theoretically. We show that the integrated surface excess zM of a polymer component of molecular weight M satisfies a simple relation zM=2Ue(M/Mw-1)phiM, where Mw is the weight averaged molecular weight, phiM is the polymer volume fraction, and Ue is the attraction of polymer chain ends to the surface. Ue is principally of entropic origin, but also reflects any energetic preference of chain ends to the surface. We further show that the surface tension gammaM of a polydisperse melt of high molar mass components depends on the number average degree of polymerization Mn as, gammaM=gammainfinity+2UerhobRT/Mn. The parameter gammainfinity is the asymptotic surface tension of an infinitely long polymer of the same chemistry, rhob is the bulk density of the polymer, R is the universal gas constant, and T is the temperature. The predicted gammaM compare favorably with surface tension values obtained from self-consistent field theory simulations that include equation of state effects, which account for changes in polymer density with molecular weight. We also compare the predicted surface tension with available experimental data.     

Molecular weight segregation induced by interfacial melt reactivity in polyamide 6/reactive rubber blends

Polyamide 6 (PA) and ethylene-propylene rubber with maleic functionality (EPMA) were blended in a batch mixer. EPMA anhydride groups react with amine chain ends of polyamide and form a grafted copolymer at the interface. The molecular weights of the grafted PA and of the free PA were measured. The molecular weight of the free PA decreases during the processing. This effect is due to the hydrolysis of the PA consecutively to its reaction with anhydride groups. The molecular weight of both grafted and free polyamide decreases during the processing. Moreover, the molecular weight of the grafted PA is lower than that of the free PA. At constant mixing time, a high conversion level produces grafted PA with a higher molecular weight. This is the result of molecular weight segregation for interfacial reaction. Small molecules react faster at the interface than larger ones. If we compare experimental results with model predictions, two segregation regimes are observed. For high shear and low EPMA concentrations, dispersion is very fast; the segregation only depends on molecular elasticity. In this case, the best correlation between model and experiment is obtained for low interfacial thicknesses. For low shear, or for EPMA concentrations close to the phase inversion composition, the segregation is more noticeable, which is mainly due to the diffusion of macromolecules through the brush of already grafted molecules. In this case, there is a clear competition between the compatibilization and the grafting reaction. Molecular weight segregation gives low ratio of the grafted PA molecular weight to the free PA molecular weight. This is detrimental to interfacial properties of the grafted copolymer formed by melt reactivity. Strategies are developed to improve this ratio in order to investigate its influence on the mechanical properties. © 1995 John Wiley & Sons, Inc.     

Mechanistic studies on the enzymatic transesterification of polyesters

The effect of solvents on the enzymatic transesterification of aliphatic polyesters has been investigated. It has been shown that the hydrophobicity and the polarity of the solvent have little effect on the reaction, however, the molecular weight of the product depends on the solubility of the product in the medium. Above a certain molecular weight, when the product is no longer soluble in the medium, transesterification does not occur. Deuterium NMR studies have shown that transesterification tends to take place at the ends of the polymer chain rather than at random along the polymer chain.     

Triethylaluminum as a concentration-dependent coinitiator and chain-transfer agent of free-radical polymerization of methyl methacrylate in the presence of benzoquinone

Yields in methyl methacrylate (MMA) polymerization as a function of triethylaluminum (TEA) concentration have been determined at a constant benzoquinone (BQ) concentration. The polymerization is negligible at [TEA]/[BQ] concentration ratios smaller than 1, but reaches a maximum yield and then decreases for larger TEA concentrations. Molecular weight measurements show a similar trend, although the maximum is shifted with respect to that corresponding to polymer yield. The existence of two reaction mechanisms is shown by rate measurements at constant initial concentrations. One is a fast reaction, over in a few minutes, which accounts for most of the yield after 30 min reaction time. The other is a slower photoinitiated reaction of the products of the fast reaction. The mechanism proposed is based on a chain-transfer reaction between the inhibitor radical, formed by the addition of the polymer radical (M·) to BQ and TEA, giving a reactive ethyl radical: The competition between a pair of reactions of TEA and BQ, i.e., a free-radical reaction corresponding to the conjugate addition and a molecular reaction leading to the BQ reduction product, is held responsible for the observed yield maximum, since the molecular reaction prevails at larger TEA concentrations. The observed drop in the molecular weight is the result of a chain-transfer reaction on TEA, i.e., the substitution of an ethyl group by the growing polymer radical.     

Modelling free-radical copolymerization kinetics—evaluation of the pseudo-kinetic rate constant method, 2. Molecular weight calculations for copolymers with long chain branching

The full moment equations and equations using pseudo-kinetic rate constants for binary copolymerization with chain transfer to polymer in the context of the terminal model have been developed and solved numerically for a batch reactor operating over a wide range of conditions. Calculated number- and weight-average molecular weights (M̄_n and M̄_w) were compared with those found using the pseudo-kinetic rate constant method (PKRCM). The results show that the weight-average molecular weights calculated using PKRCM are in agreement with those found using the method of full moments for binary copolymerization when polymeric radical fractions φ₁^˙ and φ₂^˙ of type 1 and 2 (radical centers are on monomer types 1 and 2 for a binary copolymerization) are calculated accounting for chain transfer to small molecules and polymer reactions in addition to propagation reactions. Errors in calculating M̄_w using PKRCM are not always negligible when polymer radical fractions are calculated neglecting chain transfer to small molecules and polymer. In this case, the relative error in M̄_w by PKRCM increases with increase in monomer conversion, extent of copolymer compositional drift and chain transfer to polymer rates. The errors in calculating M̄_w, however, vanish over the entire monomer conversion range for all polymerization conditions when chain transfer reactions are properly taken into account. It is theoretically proven that the pseudo-kinetic rate constant for chain transfer to polymer is valid for copolymerizations. One can therefore conclude that the pseudo-kinetic rate constant method is a valid method for molecular weight modelling for binary and multicomponent polymerizations.     

Reaction rate of crosslinkings by using a metallated polymer. II. Intermolecular and intramolecular crosslinkings at the second state

Lithium-metallated styrene–p-benzylstyrene copolymer was reacted with the branched polymer with chlorine groups at the pendant chain ends (multifunctional branched polymer) in tetrahydrofuran (THF) at 25°C. The rate constant was estimated from the changes in the concentration of metallated polymer by using photometrical measurements. The various reaction conditions were chosen and it became clear that the rate constants of intermolecular (k₂₀) and intramolecular (k_3intra) crosslinkings were derived separately at the second stage. k₂₀ showed a constant value in spite of the molecular weight of crosslinker chains and was about equal to the rate constant of the grafting. The rate of intramolecular crosslinking at the second stage increased with decreasing the molecular weight of pendant chains of multifunctional branched polymer.