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 in glassy polymers. II

The Fickian diffusion coefficient of methylene chloride in a glassy epoxy polymer is calculated with the use of Crank's model of discontinuous change of D with concentration C. The diffusion constant is obtained as 1.93 × 10^?6 cm²/sec. The swollen layer behind the advancing solvent front is essentially in the rubbery state of the same polymer. The case II swelling by benzene is discussed in terms of a convective transport arising from the partial stress (internal) tensor of the penetrant. The superposition of Fickian and case II diffusion found with mixtures of methylene chloride and benzene is also discussed briefly.     

Transport of organic vapors and liquids in poly(vinyl chloride)

This paper reviews research since 1980 on the equilibria and kinetics of transport of small organic molecules in rigid and plasticized PVC. The forms of both the solubility isotherms and the sorption kinetics are shown to change as the PVC/penetrant system undergoes a glass-rubber transition with an increase of either temperature or penetrant concentration. The isotherms are of “dual-mode” form (concave to the activity axis) for the glassy state, and show an inflection to Flory-Huggins form when the penetrant concentration exceeds C_g, the transition composition at the experimental temperature. The solubility at a given penetrant activity is governed primarily by the PVC/penetrant interaction parameter, χ. Sorption kinetics are Fickian for conditions producing small changes of concentration in either the glassy or rubbery state. For sorption into initially unplasticized PVC, kinetics are anomalous if the final penetrant concentration is between about C_g/2 and C_g, and Case II if C_g is exceeded. The magnitude of the Fickian diffusion coefficients depends largely on the geometric factors of molecular size and shape of the penetrant; this dependence is much steeper in the glassy than in the rubbery state. Recent results show that carbon dioxide displays both high diffusivity and substantial solubility in PVC under high pressure; this combination makes compressed CO₂ uniquely useful in accelerating the absorption of low-molecular-weight additives into PVC.     

Solubility,diffusivity, and mobility of n-pentane and ethanol in poly(1-trimethylsilyl-1-propyne)

The diffusion coefficient of ethanol and of n-pentane in PTMSP, at 27°C, was measured as a function of concentration up to a penetrant content of about 12% by weight, for polymer samples obtained through different processes; differential sorptions and desorptions with vapor phases were considered. In the case of ethanol a nonmonotonous behavior was observed for the diffusivity, while in the case of n-pentane the same property was found to monotonously decrease with increasing the penetrant content. The sorption isotherms were also reported, indicating that n-pentane exhibits a typical dual mode behavior, while ethanol follows an unusual s-shape curve. The chemical potential of the dissolved penetrants, calculated directly from the isotherms, shows the very different importance of the energetic interactions of the two penetrants with the polymer units. In spite of the remarkably different concentration dependencies observed for both solubility and diffusivity of the two penetrants, the mobility factors are in both cases monotonously decreasing with the penetrant concentration, and follow very similar trends. The significant differences observed for the concentration dependence of the diffusion coefficients are, thus, associated to the thermodynamic contributions, which are very different for n-pentane and ethanol. Different polymeric films, obtained through different solvent evaporation processes, show quite different solubility, diffusivity and mobility for both ethanol and n-pentane. On the other hand, the ratio between the mobility of the two penetrants as well as the slope of mobility as function of the concentration remains the same for all the different samples inspected. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35 : 2245–2258, 1997     

Molecular dynamics simulations of polymer transport in nanocomposites

Molecular dynamics simulations on the Kremer-Grest bead-spring model of polymer melts are used to study the effect of spherical nanoparticles on chain diffusion. We find that chain diffusivity is enhanced relative to its bulk value when polymer-particle interactions are repulsive and is reduced when polymer-particle interactions are strongly attractive. In both cases chain diffusivity assumes its bulk value when the chain center of mass is about one radius of gyration R(g) away from the particle surface. This behavior echoes the behavior of polymer melts confined between two flat surfaces, except in the limit of severe confinement where the surface influence on polymer mobility is more pronounced for flat surfaces. A particularly interesting fact is that, even though chain motion is strongly speeded up in the presence of repulsive boundaries, this effect can be reversed by pinning one isolated monomer onto the surface. This result strongly stresses the importance of properly specifying boundary conditions when the near surface dynamics of chains are studied.     

Noncontinuum effects on the mobility of nanoparticles in unentangled polymer solutions

The results for the diffusivity of nanoparticles in unentangled semidilute polymer solutions obtained using coarse‐grained simulations are presented. The results indicate that for particle sizes smaller than the polymer radius of gyration, the nanoparticle diffusivities deviate from Stokes–Einstein predictions and depend explicitly on the polymer radius of gyration and the polymer solution correlation lengths. Scaling ideas proposed are invoked for rationalizing such noncontinuum effects and demonstrate that the simulation results could be collapsed onto a single universal function of the depletion thickness, the polymer radius of gyration, and the particle radius. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2145–2150.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.     

Dissolution of rubbery and glassy polymers

A mathematical model is formulated for solvent dissolution of rubbery and glassy polymers. An exact solution to the problem is derived for the constant diffusivity case, and a weighted residual solution is developed for the case of a concentration-dependent diffusion coefficient. The solution is used to calculate concentration profiles, dissolution curves, dissolution half-times, and pseudointerface positions at various times. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2607–2614, 1998     

Properties of semidilute polymer solutions: Investigation of an optically labeled three-component system

A three-component system containing a polymer (2), a good solvent (1) for that polymer, and a second polymer (3) that is compatible with component (2) and isorefractive with the solvent (1) has been studied by static and dynamic light-scattering methods. In concentrated toluene (1) solutions of poly(vinyl methyl ether) (3), where appreciable chain overlap occurs and excluded-volume effects are reduced, polystyrene (2) may be studied in the dilute-solution limit. Consequently, these light-scattering measurements provide an explicit measure of both thermodynamic and hydrodynamic changes that occur as the total polymer concentration is increased from dilute to concentrated solution. Precise numerical coefficients, correct scaling exponents, the radius of gyration, and the effective hydrodynamic radius can be measured directly along with the observation of long-wave single-chain reptation motions and short-range cooperative motions in semidilute and concentrated solutions.     

Anomalous transport of penetrants in glassy polymers

Solutions are presented for the Fickian and non-Fickian equations describing the case of penetrant transport in a glassy polymer. Due to associated macromolecular relaxation, a sharp penetrant front is observed which separates the glassy core from the rubbery (gel-like) layer at the surface. Concentration profiles are compared and general comments about Fickian versus non-Fickian transport in polymers are made.     

Influence of reptation on localized diffusion in crystallizing polymers

Crystalline texture in polymer spherulites appears to be determined in part by interplay during solidification between interface morphology and the diffusion of species segregated at crystal growth fronts; these species are molecules of lower molecular weight (fractionation) or molecules of stereoirregular structure. Early discussions of this behavior were based upon assumption of a single diffusion coefficient in each case. However, it is now known that, because of reptation, each molecule in a polymer melt diffuses with a diffusion coefficient dependent on its individual molecular weight. In this paper, the influence of reptation upon concentration profiles and diffusion ranges is examined. It is shown that such influence is slight when segregated species have relatively narrow distributions of molecular weight, such as are typical when segregation involves fractionation or is mostly confined to fractionated stereoirregular species blended with crystallizable host polymer. With broad distributions, however, concentration profiles are significantly altered and long segregated molecules dominate morphologically important behavior. Meaningful average diffusion ranges can often be derived and related to appropriately averaged molecular weights of participating molecules. Morphological implications of the various results are outlined.     

Factors affecting the nodule size of asymmetric PMMA membranes

Several factors that may affect the surface nodule size of a polymeric membrane were under investigation. The increase of polymer concentration and molecular weight were found to increase the surface nodule size. The increase of casting temperature also resulted in an increase in nodule size. These results supported that the radius of gyration and the collision frequency between polymer chains were the key factors affecting the nodule size. However, when the radius of gyration was reduced by the use of a poor solvent or by pre-adding nonsolvent in the casting solution, the surface nodule size increased. It suggested that there existed other factors affecting the nodule size on membrane surface besides the gyration radius and the collision frequency of polymer chains. In this study, we found in most cases that the surface nodule size decreased along with the surface tension difference between the casting solution and the coagulant. To demonstrate the effect of surface tension, we examined the nodule size inside the membranes where the nodule formation was not significantly affected by the interfacial tension. Opposite to what was observed on the surface, the nodule size increased with the solvation power of the solvent. This result suggested that it was the interfacial tension that overpowered the gyration radius in affecting the surface nodule size.     

Determination of penetrant solubility from transient permeation measurements

The permeability coefficient for the transport of a gas, vapor, or liquid through a polymer film is the product of the penetrant solubility and a diffusion coefficient. A transient permeation experiment known as the time-lag technique can be used to separate this product, provided the diffusion coefficient is independent of penetrant concentration. In this well-known experiment the polymer is initially free of penetrant. A new transient permeation experiment where the polymer is initially saturated with penetrant is suggested here. A general mathematical proof is given to show that by using the results form these two transient experiments which have different initial conditions one can determine the penetrant solubility no matter how the diffusion coefficient depends on penetrant concentration. Also one can determine two different concentration averaged diffusion coefficients from the results.     

Mean-square radius of gyration of polymer chains

The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S²〉 = aM^b, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.     

Dynamics of liquid–liquid demixing: mesoscopic simulations of polymer solutions

In this article, the mesoscopic simulation method dissipative particle dynamics (DPD) is applied to study the dynamics of polymer–solvent liquid–liquid phase separation. It will be shown that the degree of branching has a pronounced effect on the radius of gyration and the centre of mass diffusion of the polymer. Based on the simulation results it can be concluded that the difference in chemical potential between the mixed and the demixed state is the main driving force behind the centre of mass diffusion (and thus phase separation), rather than the reduced radius of gyration due to to polymer chain collapse.     

Analysis of the kinetics of vapor absorption/desorption in/from silicone rubber and cellulose acetate membranes in the presence of stagnant boundary layers

The application of an interferometric technique (optical thickness meter, OTM) to the measurement of vapor sorption kinetics in both rubbery and glassy polymers is presented. In this technique, the membrane is formed by casting on a suitable glass surface and interferometry is applied in situ. The use of a carrier gas loaded with penetrant vapor introduced a stagnant boundary layer (SBL) effect which had to be corrected, in order to determine true sorption kinetics. The said SBL effect was estimated, on the basis of existing theory for the silicone rubber–methylene chloride (SR/MC) system and found to be more pronounced in the case of desorption. Upon correction for this effect, Fickian sorption curves were obtained; which yielded nearly constant values of the diffusion coefficient, not materially different for absorption and desorption, in line with theoretical expectation.Cellulose acetate–methylene chloride (CA/MC) was then studied as an example of a glassy polymer–vapor system, where the SBL effect distorts the absorption kinetic curve in the same way as the non-Fickian mechanism of sorption inherent in this kind of polymer–penetrant system. Here, the vapor sorption data were corrected using the results obtained from the Fickian SR/MC system. The corrected results were checked by comparison with independent data reflecting the true kinetic behavior of CA/MC, obtained with a vacuum balance apparatus (VBA), which is free of SBL effects. It is shown that this novel method of applying the SBL correction was reasonably successful in favorable circumstances, while a criterion is provided to identify cases where reasonably reliable correction is not possible.     

Interdiffusion of solvent into glassy polymer films: a molecular dynamics study

Large scale molecular dynamics and grand canonical Monte Carlo simulation techniques are used to study the behavior of the interdiffusion of a solvent into an entangled polymer matrix as the state of the polymer changes from a melt to a glass. The weight gain by the polymer increases with time t as t(1/2) in agreement with Fickian diffusion for all cases studied, although the diffusivity is found to be strongly concentration dependent especially as one approaches the glass transition temperature of the polymer. The diffusivity as a function of solvent concentration determined using the one-dimensional Fick's model of the diffusion equation is compared to the diffusivity calculated using the Darken equation from simulations of equilibrated solvent-polymer solutions. The diffusivity calculated using these two different approaches are in good agreement. The behavior of the diffusivity strongly depends on the state of the polymer and is related to the shape of the solvent concentration profile.     

Effects of polymer chain disentanglement on NMR properties. II. 13C magnetic relaxation in polystyrene

The transverse magnetic relaxation of ¹³C_α nuclei has been studied in concentrated solutions of polystyrene. The magnetic relaxation rate was measured as a function of molecular weight at several temperatures (313,318, and 323 K) and at several concentrations (0.53, 0.43, and 0.34 g/cm³). The spin-system response of these nuclei in natural abundance exhibits a characteristic evolution from pseudosolid properties to liquidlike one, induced by decreasing the molecular weight of polymer molecules. This evolution is analogous to that already observed in protons attached to polyisobutylene or polydimethylsiloxane chains; it is assumed to be induced by an increase of the disentanglement rate of polymer chains. The spin-system response may be considered as reflecting single-chain magnetic properties, because of the low concentration of ¹³CC_α nuclei, although all chains are in dynamic interaction with one another. The NMR disentanglement transition is interpreted in terms of a two-step motional averaging effect involving submolecules. A numerical analysis of NMR properties is given using a model of polymer chain relaxation based on a multiple-mode relaxation process, characterized by (i)a terminal relaxation time τ^v₁ depending upon M³, the molecular weight, and approximately proportional to the polymer concentration C (like the reptation time); (ii)a relaxation-time spectrum analogous to a Rouse spectrum; (iii)a terminal relaxation time τ^v₁ = 2.5 × 10^?2s for M = 2.5 × 10⁵, C = 0.53 g/cm³ in carbon tetrachloride at 313 K.