On the equation of state for thermal polymer solutions and melts with attractive interaction

We perform Monte Carlo simulations of a lattice model for polymer melts, i. e., the bond fluctuation model in three dimensions. By using an energy parameter that prefers relatively long bonds, the model exhibits a glass transition at low temperatures, in close qualitative similarity to experiment. We modify this model by adding an attractive interaction of variable strength. We demonstrate that a small interaction strength has only a very small effect on the static properties of the melt. For a fixed strength of the potential, the chemical potential is measured by a modified particle-insertion method over a large range of temperatures and densities. The osmotic pressure is obtained by thermodynamic integration. In contrast to the original version our extended model exhibits a positive thermal expansion.     

The glass transition in polymer melts

This paper presents some results of a Monte Carlo simulation for the glass transition in two- and three-dimensional polymer melts. The melt was simulated by the bond-fluctuation model on a d-dimensional cubic lattice which was combined with a two-level hamiltonian favouring long bonds in order to generate a competition between the energetic and topological constraints in the system. This competition prevents crystallization and makes the melt freeze in an amorphous structure as soon as the internal relaxation times match the observation time of the simulation set by the cooling rate. The freezing point of the melt, i.e the glass transition temperature T_g, thus depends upon the cooling rate and additionally upon the chain length of the polymers. The dependence of the glass transition temperature on the cooling rate was closely analysed in three and that on the chain length in both two and three dimensions, resulting in a non-linear relationship between T_g and the logarithm of the cooling rate and a linear relationship between T_g and the inverse chain length, respectively. In addition to this behaviour of the melt during the cooling process an example for the relaxational properties of the three-dimensional model is provided by a quantitative analysis of the incoherent intermediate scattering function in the framework of the idealized mode coupling theory.     

The effect of lattice compressibility on the thermodynamics of gas sorption in polymers

A compressible lattice model with holes, the glassy polymer lattice sorption model (GPLSM), was used to model the sorption of carbon dioxide, methane, and ethylene in glassy polycarbonate and carbon dioxide in glassy tetramethyl polycarbonate. For glassy polymers, an incompressible lattice model, such as the Flory–Huggins theory, requires concentration-dependent and physically unrealistic values for the lattice site volumes in order to satisfy lattice incompressibility. Rather than forcing lattice incompressibility, GPLSM was used and reasonable parameter values were obtained. The effect of conditioning on gas sorption in glassy polymers was analyzed quantitatively with GPLSM. The Henry's law constant decreases significantly upon gas conditioning, reflecting changes in the polymer matrix at infinite dilution. Treating the Henry's law constant as a hypothetical vapor pressure at infinite dilution, gas molecules in the conditioned polymer are less “volatile” than those in the unconditioned polymer. Flory–Huggins theory was used to model the sorption of carbon dioxide, methane, and ethylene in silicone rubber. Above the glass transition temperature, the criterion of lattice incompressibility for Flory-Huggins theory was satisfied with physically realistic and constant values for the lattice site volumes. © 1992 John Wiley & Sons, Inc.     

Monte Carlo simulation studies of the interfaces between polymeric and other solids as models for fiber-matrix interactions in advanced composite materials

As a coarse-grained model for dense amorphous polymer systems interacting with solid walls (i.e., the fiber surface in a composite), the bond fluctuation model of flexible polymer chains confined between two repulsive surfaces is studied by extensive Monte Carlo simulations. Choosing a potential for the length of an effective bond that favors rather long bonds, the full temperature region from ordinary polymer melts down to the glass transition is accessible. It is shown that in the supercooled state near the glass transition an “interphase” forms near the walls, where the structure of the melt is influenced by the surface. This “interphase” already shows up in static properties, but also has an effect on monomer mobilities and the corresponding relaxation behavior of the polymer matrix. The thickness of the interphase is extracted from monomer density oscillations near the walls and is found to be strongly temperature dependent. It is ultimately larger than the gyration radius of the polymer chains. Effects of shear deformation on this model are simulated by choosing asymmetric jump rates near the moving wall (large jump rate in the direction of motion, and a small rate against it). It is studied how this dynamic perturbation propagates into the bulk of the polymer matrix.     

Monte Carlo modelling of the polymer glass transition

We are proposing a lattice model with chemical input for the computer modelling of the polymer glass transition. The chemical input information is obtained by a coarse graining procedure applied to a microscopic model with full chemical detail. We use this information on Bisphenol-A-Polycarbonate to predict it's Vogel-Fulcher temperature out of a dynamic Monte Carlo Simulation. The microscopic structure of the lattice model is that of a genuine amorphous material, and the structural relaxation obeys the time temperature superposition.     

Molecular scale modeling of polymer imprint nanolithography

We present the results of large-scale molecular dynamics simulations of two different nanolithographic processes, step-flash imprint lithography (SFIL), and hot embossing. We insert rigid stamps into an entangled bead-spring polymer melt above the glass transition temperature. After equilibration, the polymer is then hardened in one of two ways, depending on the specific process to be modeled. For SFIL, we cross-link the polymer chains by introducing bonds between neighboring beads. To model hot embossing, we instead cool the melt to below the glass transition temperature. We then study the ability of these methods to retain features by removing the stamps, both with a zero-stress removal process in which stamp atoms are instantaneously deleted from the system as well as a more physical process in which the stamp is pulled from the hardened polymer at fixed velocity. We find that it is necessary to coat the stamp with an antifriction coating to achieve clean removal of the stamp. We further find that a high density of cross-links is necessary for good feature retention in the SFIL process. The hot embossing process results in good feature retention at all length scales studied as long as coated, low surface energy stamps are used.     

Direct observation of nanoparticle embedding into the surface of a polymer melt

Direct embedding of metal nanoparticles (NPs) into the surface of a polymer melt is observed by TEM and a new embedding mechanism proposed. Upon annealing above the glass transition temperature of polystyrene (PS), NPs (20 nm gold) are rapidly covered by a thin PS wetting layer, h* approximately 1.3-1.8 nm (i.e., about two or three monomers). Because it creates capillary pressure on a NP, this "universal" wetting layer is proposed to be responsible for NP embedding. The value of h* is independent of the molecular weight of PS and constant during the embedding process. The value of h* is found to be similar to the equilibrium wetting layer thickness of a polymer melt spreading on a metal substrate. Using a model that includes the spreading coefficient, long-range van der Waals interactions, and a chain-stretching penalty, h* is shown to be independent of the molecular weight of the polymer. Using this model and the measured value of h*, the interfacial energy between Au NP and PS is estimated to be 8.7 J/m2.     

Influence of the electrostatic interactions on thermophysical properties of polyimides: Molecular‐dynamics simulations

Revealing the way of how modification of the chemical structure of a polymer affects its macroscopic physical properties offers an opportunity to develop novel polymer materials with pre‐defined characteristics. To address this problem two thermoplastic polyimides, ULTEM? and EXTEM?, were simulated with small difference in chemical structures of monomer units, namely, the phenyl ring in ULTEM? was replaced by the diphenylsulphone group in EXTEM?. It is shown that such a small modification results in a drastic difference of the thermal properties: the glass transition temperature of EXTEM? is higher than that of ULTEM?. Our molecular‐dynamics simulations clearly demonstrated that it is the electrostatic interactions that are responsible for the observed difference in thermal properties of ULTEM? and EXTEM?: large partial charges of the sulphone group in the EXTEM? lead to strong dipole–dipole intra‐ and intermolecular interactions and correspondingly to an elevated glass transition temperature. © 2014 Wiley Periodicals, Inc. J. Polym. Sci. Part B: Polym. Phys. 2014 , 52, 640–646     

Effect of solvent on glass transition temperature in chemically modified polyvinyl chloride (PVC)

Polyvinylchloride has been chemically modified with sodium benzene thiolate at different temperatures, in solvents promoting the formation of polymer gels, in solvents favoring light polymer interactions and in the absence of solvent, that is, in the melt. From the¹³C-NMR results it is shown that the substitution reactions on PVC, in all media and temperatures studied, are stereospecific and the nature of substituted chlorines the same.The glass transition temperature of modified polymers has been studied by differential scanning calorimetry. The glass transition temperature of the modified polymers in the absence of solvent decreases linearly with degree of substitution. When the reaction is carried out in solvents containing carbonyl groups, such as diethyl malonate, cyclohexanone and 2-butanone, the evolution of the glass transition up to about 25% substitution does not follow the above behavior. At higher levels of substitution the evolution ofT _g is similar to that in the melt. For the ether-containing solvents, such as tetrahydrofurane and dioxane, the evolution lies between the two previous curves.When the reactions of PVC with sodium benzene thiolate are carried out in cyclohexanone at different temperatures, between 15–90°C, the evolution of the glass transition temperature with conversion is different for each temperature, and if the reaction temperature increases, the slope of the initial part moves to that in the absence of solvent.These results are related to the formation of PVC gels or interactions. As the nature and percentage of substituted chlorine for a given chemical composition are the same in all the solvents and conditions studied, we propose that Cl-atoms of isotactic and/or heterotactic configurations are implied in the formation of PVC gels or interactions.     

A theoretical interpretation of free volume at glass transition

We device a relaxed lattice model (RLM) to study the mechanism of glass transition,which unifies the cageeffects from particle-particle interaction and entropy.By analyzing entropy in RLM with considering the influence of interactions on equilibrium,we demonstrate that glass transition is a second-order phase transition.For a perfect onedimensional linked particle system like linear polymer under normal pressure,the free volume at glass transition is rigorously deduced out to be 2.6％,which provides a theoretical basis for the iso-free volume of 2.5％ given by Willian,Landel and Ferry (WLF) equation.Extending to system with dead particles linked with higher dimensions like branched or cross-linked chains under positive or negative pressure,free volume at glass transition is varied,based on which we construct a phase diagram of glass transition in the space of free volume-dead particle-pressure.This demonstrates that free volume is not the single parameter determining glass transition,while either dead particles like cross-linked points or external force fields like pressure can vary free volume at the glass transition.     

Volume Phase Transition of Polymer Networks in Polymeric Solvents

A strong concentration dependence of the solvent–polymer interaction parameter χ is known to be a requirement for the first‐order volume phase transition in uncharged polymer networks in solvents. Another possibility for the observation of phase transition in nonpolar networks is to increase the number of lattice sizes occupied by a solvent molecule. This possibility has been indicated earlier and is worked out in detail in this paper. Using the theory of swelling equilibrium, we examine the polymer network systems immersed in a polymer melt. The critical conditions for the phase transition in both uncharged and ionic networks are described.     

Free volume and oxygen transport in cold‐drawn polyesters

Poly(ethylene terephthalate) (PET), poly(ethylene terephthalate‐co‐4,4′‐bibenzoate) (PETBB55), and poly(ethylene 2,6‐naphthalate) (PEN) were cold‐drawn to achieve uniform extension without crystallization or stress whitening, and oxygen transport properties were studied at temperatures from 10 to 40 °C. Correlation of oxygen solubility and polymer specific volume made it possible to consider the oriented polyester as a one‐phase densified glass. Orientation was viewed as decreasing the amount of excess‐hole free volume and bringing the nonequilibrium polymer glass closer to the equilibrium condition. Between 10 and 40 °C, the amount of excess‐hole free volume in PET decreased as the polymer approached the glass transition temperature. In contrast, temperature changes in this range had little effect on the excess‐hole free volume in PETBB55 and PEN, which were well below their glass transition temperature. Gas diffusion was viewed as discrete jumps of the oxygen molecule between holes of excess‐free volume. The jump length was extracted from the activation energy for diffusion according to a channel‐formation model. The result agreed well with the hole spacing estimated from a simple lattice model using the hole density reported in the literature. Extending the lattice model to estimate the mean excess‐free volume hole radius from the fractional free volume resulted in good correlation with the hole radius obtained from positron annihilation lifetime spectroscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 493–504, 2004     

Transition of polymers from rubbery elastic state to fluid state

On increasing the temperature of a polymer, the transition of the polymer from a rubbery elastic state to a fluid state could occur. The transition temperature is termed the fluid temperature of the polymer, T _f, which has a direct relationship with the polymer molecular weight. As one of polymer parameters, T _f is as important as the glass transition temperature of a polymer, T _g. Moreover, special attention to T _f should be paid for polymer processing. In research on the transition of a polymer from a rubbery elastic state to a fluid state, the concept of T _f would be more reasonable and more effective than the concept of T _l,l because it is neglected in the concept of T _l,l in that the molecular weight of a polymer may affect the transition of the polymer. In this paper the discussion on the fluid temperature involves the characters of polymers, such as the deformation—temperature curve, the temperature range of the rubbery state and the shear viscosity of polymer melt. From the viewpoint of the cohesional state of polymers, the transition of a polymer from a rubbery elastic state to a fluid state responds to destruction and construction of the cohesional entanglement network in the polymer. The relaxing network of polymer melt would be worthy to be considered as an object of study. __________ Translated from Huaxue Tongbao (Chemistry), 2008,71(3) (in Chinese)     

Prediction of the glass transition temperature of polymers: A model based on the principle of corresponding states

The application of corresponding state principles to describe the properties of polymers is implicit in many of the fundamental studies of polymeric behavior. The seminal works of Prigogine, Hildebrand, Eyring, Flory, Gibbs, and DiMarzio in which multidimensional lattice representations and refined statistical mechanical approaches have been used are the basis for much of today's understanding of the thermodynamic behavior of polymers and their solutions. In this work the lattice energy of a polymer is defined in terms of reduced molecular parameters, and it is assumed that all polymers with the same functional form for their lattice energies will be in corresponding states. A reduced second order transition temperature is defined relative to a characteristic temperature T* = s?*/2kv* c, where the molecular parameters refer to the properties of the repeating segments of the polymer chain. Equations are derived that express the effects of molecular weight, plasticization, degree of crosslinking, and copolymerization on the second order (i.e., glass) transition temperature. In their limits, the equations are shown to reduce in form to equations derivable from free volume theory. They are also used to analyze successfully a variety of glass transition temperature data available in the literature on homogeneous uncrosslinked and crosslinked polymers, plasticized polymers, and random copolymers.     

Effect of pressure on the flow behavior of polybutene

The rheology of submicron thick polymer melt is examined under high normal pressure conditions by a recently developed photobleached‐fluorescence imaging velocimetry technique. In particular, the validity and limitation of Reynold equation solution, which suggests a linear through‐thickness velocity profile, is investigated. Polybutene (PB) is sheared between two surfaces in a point contact. The results presented in this work suggest the existence of a critical pressure below which the through‐thickness velocity profile is close to linear. At higher pressures however, the profile assumes a sigmoidal shape resembling partial plug flow. The departure of the sigmoidal profile from the linear profile increases with pressure, which is indicative of a second‐order phase/glass transition. The nature of the transition is confirmed independently by examining the pressure‐dependent dynamics of PB squeeze films. The critical pressure for flow profile transition varies with molecular weight, which is consistent with the pressure‐induced glass transition of polymer melt. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 708–715     

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.     

玻璃化转变的热力学理论错在哪里？

现行国内高分子物理学教科书上都介绍玻璃化转变的热力学理论,其把玻璃化转变描述成为一个二级相转变.但是现在人们已经普遍接受玻璃化转变的本质是一个动力学过程的观点.我们通过讨论玻璃化转变热力学理论的来历,试图弄清这一理论到底错在哪里.首先,该理论所基于的Kauzmann佯谬可能不是一个真正的佯谬;其次,半柔顺链高分子溶液的经典格子统计理论结果中所谓的熵灾难可能是出于对构型熵的错误理解所致.因此,把以上二者联系起来构成玻璃化转变热力学理论的基本假定就从根本上来说是不可靠的.     

The amount of immobilized polymer in PMMA SiO2 nanocomposites determined from calorimetric data

For semicrystalline polymers there is an ongoing debate at what temperature the immobilized or rigid amorphous fraction (RAF) devitrifies (relaxes). The question if the polymer crystals are melting first and simultaneously the RAF devitrifies or the RAF devitrifies first and later on the crystals melt cannot be answered easily on the example of semicrystalline polymers. This is because the crystals, which are the reason for the immobilization of the polymer, often disappear (melt) in the same temperature range as the RAF. For polymer nanocomposites the situation is simpler. Silica nanoparticles do not melt or undergo other phase transitions altering the polymer-nanoparticle interaction in the temperature range where the polymer is thermally stable (does not degrade). The existence of an immobilized fraction in PMMA SiO₂ nanocomposites was shown on the basis of heat capacity measurements at the glass transition of the polymer. The results were verified by enthalpy relaxation experiments below the glass transition. The immobilized layer is about 2 nm thick at low filler content if agglomeration is not dominant. The thickness of the layer is similar to that found in semicrystalline polymers and independent from the shape of the nanoparticles. Nanocomposites therefore offer a unique opportunity to study the devitrification of the immobilized fraction (RAF) without interference of melting of crystals as in semicrystalline polymers. It was found that the interaction between the SiO₂ nanoparticles and the PMMA is so strong that no devitrification occurs before degradation of the polymer. No gradual increase of heat capacity or a broadening of the glass transition was found. The cooperatively rearranging regions (CRR) are either immobilized or mobile. No intermediate states are found. The results obtained for the polymer nanocomposites support the view that the reason for the restricted mobility must disappear before the RAF can devitrify. For semicrystalline polymers this means that rigid crystals must melt before the RAF can relax.     

Interfacial properties of glassy polymer melts: A Monte Carlo study

The properties of the interface between a polymer melt and a solid wall are studied over a wide range of temperatures by dynamic Monte Carlo simulations. It is shown that in the supercooled state near the glass transition of the melt an “interphase” forms, the structure of which is influenced by the wall. The thickness of this interphase is determined from the monomer density profile near the surface and is strongly temperature dependent. At low glass-like temperatures it is larger than the bulk radius of gyration of the chains.     

高聚物从高弹态到流体态的转变

将高聚物由高弹态转变为流体态的转变温度命名为流动温度Tf,该转变温度与高聚物分子量密切相关.在高聚物从高弹态转变为流体态的研究中,由于T1.1的概念忽视对高聚物分子量的依赖性,因此采用Tf的概念更为合理.本文对高聚物的流动温度Tf的讨论涉及高聚物温度-形变曲线、高弹态温区、高聚物熔体剪切粘度.从高聚物凝聚态观点来看,高聚物熔体中凝聚缠结网络中的凝聚结点是分子链的局部向列相互作用使链单元间产生平行凝聚而形成的,而高聚物从高弹态到流体态的转变正是反映了高聚物熔体中凝聚缠结网络的物理交联点,即凝聚结点状态的变化.高聚物熔体可以流动,说明熔体中凝聚网络中的凝聚结点至少是可以在瞬间内打开的,升温使凝聚结点的解凝聚状态存在的时间加长,凝聚状态存在时间减短,当升高到某一温度时,在凝聚结点解凝聚状态的时间内,分子链通过内旋转使质量中心在外加力的方向上可以发生位移,此时高聚物从高弹态转变为流体态,而此时的温度就是流动温度Tf.对高聚物流体弛豫网络的研究,是一个很有前景的研究课题.