Structure as a function of relaxation in glassy polymers

Previously, amorphous glasses were simulated by carrying out energy minimization on initial conformations generated by growing polymer chains in a periodic cube. It was not known what degree of relaxation these simulated glasses possessed. The degree relaxation is determined by the thermal history of the bulk polymer and in turn determines numerous important properties. Constant stress molecular dynamics (CSMD) followed by energy minimization was used to simulate different thermal histories of an isotactic poly(propylene) glass. This simulation approach produced glasses in which the degree of energetic relaxation was a function of the thermal history. Based on the simulated cohesive energy density, the simulation using minimization alone produced a glass that was energetically annealed. However, the local geometry and x-ray structure factor indicate that it has a different structure than those obtained using CSMD followed by energy minimization and may not be structurally relaxed.     

Phase diagram of supercooled water confined to hydrophilic nanopores

We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature, and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhibits liquid and crystal-like behaviors, with abrupt crossovers between these regimes. For small pore radii, crystal-like behavior is unstable and water remains amorphous for all non-zero temperatures. At low enough temperatures, these states are glasses. Several experimental results for supercooled water can be understood in terms of the phase diagram we present.     

Coarse-grained Dynamics Simulation in Polymer Systems: from Structures to Material Properties

Polymers are widely used in our daily life and industry because of their intrinsic characteristics, such as multi-functionality, low cost, light mass, ease of processability, and excellent chemical stability. Polymers have multiscale space-time properties, which are mainly reflected in the fact that the properties of polymer systems depend not only on chemical structure and molecular properties, but also to a large extent on the aggregation state of molecules, that is, phase structure and condensed state structure. Thanks to the continuous development of simulation methods and the rapid improvement of scientific computation, computer simulation has played an increasingly important role in investigating the structure and properties of polymer systems. Among them, coarse-grained dynamics simulations provide a powerful tool for studying the self-assembly structure and dynamic behavior of polymers, such as glass transition and entanglement dynamics. This review summarizes the coarse-grained models and methods in the dynamic simulations for polymers and their composite systems based on graphics processing unit(GPU) algorithms, and discusses the characteristics, applications, and advantages of different simulation methods. Based on recent studies in our group, the main progress of coarse-grained simulation methods in studying the structure, properties and physical mechanism of polymer materials is reviewed. It is anticipated to provide a reference for further development of coarse-grained simulation methods and software suitable for polymer research.     

Relation between amorphous structure of polymers and penetrant diffusion: A molecular dynamics simulation

Molecular dynamics simulation has been performed for studying the relation between amorphous structure of polymers and penetrant diffusion. The self-diffusion coefficients of O₂ and He in various polymer models, which differ from each other in view of the amorphous structure, were calculated above their glass transition temperatures. The amorphous structure was characterized by considering the percolation of the unoccupied volume. A good correlation was found between the self-diffusion coefficients and the number of clusters in the unoccupied volume at the critical point of the percolation. Based on the simulated cluster size distribution at the critical point, we defined a parameter into which effects of both the amorphous structure and the penetrant size are well incorporated. It was confirmed that the penetrant diffusion is intimately associated with the amorphous structure of polymers.     

Modeling of polyethylene and poly (L-lactide) polymer blends and diblock copolymer: chain length and volume fraction effects on structural arrangement

Dissipative particle dynamics (DPD), a mesoscopic simulation approach, has been used to investigate the chain length effect on the structural property of the immiscible polyethylene (PE)/poly(L-lactide) (PLLA) polymer in a polymer blend and in a system with their diblock copolymer. In this work, the interaction parameter in DPD simulation, related to the Flory-Huggins interaction parameter chi, is estimated by the calculation of mixing energy for each pair of components in molecular dynamics simulation. The immiscibility property of PE and PLLA polymers induces the phase separation and exhibits different architectures at different volume fractions. In order to observe the structural property, the radius of gyration is used to observe the detailed arrangement of the polymer chains. It shows that the structure arrangement of a polymer chain is dependent on the phase structure and has a significantly different structural arrangement character for the very short chains in the homopolymer and copolymers. The chain length effect on the degree of stretching or extension of polymers has also been observed. As the chain length increases, the chain exhibits more stretching behavior at lamellae, perforated lamellae, and cylindrical configurations, whereas the chain exhibits a similar degree of stretching or extension at the cluster configuration.     

Characterization of annealed isotactic polypropylene in the solid state by 2D time‐domain 1H NMR

Two‐dimensional time‐domain ¹H NMR was used to investigate annealed isotactic polypropylene in the solid phase. The spin–lattice relaxation in the laboratory frame and in the rotating frame were correlated with the shape of the free induction decay to identify and characterize relaxation components over the temperature range −120 to 120 °C. Several phase transitions were observed, and three distinct solid phases, with different chain mobilities, were detected. Two of these phases were identified as regions with different mobilities within the crystalline phase. The third phase was characterized by a high degree of isotropy in molecular motion. This phase, identified as the amorphous phase, appeared as the polymer was heated above a low‐temperature (−45 °C) phase transition. All transitions observed at higher temperatures occurred exclusively in this phase. About one‐third of the polymer chains reside between crystalline lamellae, whereas the majority form amorphous regions outside fibrils of multilamellar structure. Furthermore, the glass‐to‐rubber transition, occurring above −15 °C, consists of three stages. During the first stage, between −15 °C and 15 °C, regions with an increased segment mobility (labeled intermediate phase) appear gradually within the amorphous phase. At 15 °C, the intermediate phase consists of ∼10% of the polymer units, or one‐third of the polymer units constituting the amorphous phase. Between 15 °C and 25 °C, the intermediate phase increases rapidly to 18%. This is associated with the appearance of semiliquid and liquid regions, likely within the intermediate phase. Polymer chain segments (and possibly entire chains) involved in the liquidlike phases exhibit heterogeneous molecular motion with a correlation frequency higher than 10⁶ Hz. These two stages of glass‐to‐rubber transition occur within amorphous regions outside multilamellar structures. The third stage of the glass transition, appearing above 70 °C, is associated with the upper glass transition and occurs within the interlamellar amorphous phase. Finally, on a timescale of 100 ms or less, spin diffusion does not couple the amorphous regions outside fibrils with crystalline and amorphous regions within multilamellar fibrils. However, on a timescale of hundreds of milliseconds to seconds, all different regions within isotactic polypropylene are partially coupled. It is proposed that the relative magnitude of the crystalline magnetization, as observed in the T_1ρ experiment, is a good measure of polymer crystallinity. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2487–2506, 2000     

Visualization of deformation-induced structural rearrangements in amorphous polymers

A technique is proposed for decorating amorphous polymers: Before the deformation (shrinkage) of an amorphous polymer, its surface is decorated with a thin metal coating. The subsequent deformation is accompanied by surface structure formation, which makes the processes that occur in the polymer visible. The proposed technique makes it possible to visualize and describe the mechanism of transfer of the polymer from the surface into the bulk and vice versa and to obtain direct information about the direction of the actual local stress. The technique makes it possible to obtain information about the topological heterogeneity of rubber networks, to reveal the features of structural rearrangements that occur during the cold rolling of amorphous polymers, and to describe the phenomenon of self-elongation during annealing of the oriented PET. These microscopic data explain the following features of the structural and mechanical behavior of glassy polymers from a unified viewpoint: stress relaxation in a polymer in the elastic (Hookean) region of the stress-strain curve, an increase in stress in a deformed glassy polymer during its isometric annealing below T _g, the low-temperature shrinkage of a deformed polymer glass in the strain range below its yield point, the storage of internal energy in a deformed glassy polymer in the strain range below the yield point, some anomalies of thermophysical properties, and some other features.     

On the molecular mobility in amorphous polymers, inorganic glasses, and amorphous metal alloys in the glass transition range

The transition of kinetic units (atoms or groups of atoms) in amorphous media from one quasi-equilibrium state to another is determined by fluctuations of both energy and entropy of the system. In the glass transition range of liquids and polymers, the entropic mechanism plays a determining role: the fluctuation of packing of particles turns out to be more important than accumulation of energy. Above the glass transition range, the energy mechanism begins to play a dominant role. The procedure that is currently used to calculate the constant for the Bartenev equation, which relates the relaxation time to the cooling rate at the glass transition temperature, leads to overestimated values. A procedure for the calculation of this parameter was proposed with allowance for the temperature dependence of the entropy of activation in the region of the liquid-glass transition. The use of this equation in the relaxation spectrometry of amorphous polymers, inorganic glasses, and amorphous metal alloys is discussed.     

Microstructural model for prediction of stress–strain curves of amorphous and semicrystalline elastomers

A fundamental microstructural model was developed to calculate the stress–strain curves of rubbery amorphous polymers and of semicrystalline polymers with a rubbery amorphous phase by numerical simulations. The rubbery amorphous phase was treated by using a version of the theory of rubber elasticity with finite extensibility. Physical entanglements and chemical crosslinks were both allowed. Slippage was implemented by a Monte Carlo algorithm controlled by kinetic parameters such as the activation energy and activation volume for slippage. The crystalline phase was treated in a very idealized manner, including a crude representation of tie chains but not taking the internal structure of the crystallites into account. A two-dimensional embodiment of the model was implemented into software. For amorphous polymers, while lacking truly quantitative accuracy, the model showed sufficiently good agreement with the experimental trends to be used as a qualitative or semiquantitative predictive tool, and it is currently being used in this manner. The more complex semicrystalline version was less accurate and will need to be improved in future work. Most of the limitations of the semicrystalline version could be ascribed unambiguously to specific simplifications made in the software implementation to reduce the amount of computer time required for the calculations. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2715–2739, 1997     

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.     

Structural approach to the study of deformation mechanism of amorphous polymers

A new microscopic procedure for the visualization of structural rearrangements in amorphous polymers during their deformation to high strains is described. This approach involves the deposition of thin (several nanometers) metallic coatings onto the surface of the deformed polymer. Subsequent deformation entails the formation of a relief in the deposited coating that can be studied by direct microscopic methods. The above phenomenon of relief formation provides information concerning the deformation mechanism of the polymer support. Experimental data obtained with the use of this procedure are reported, and this evidence allows analysis of the specific features of structural rearrangements during deformation of the amorphous polymer at temperatures above and below its glass transition temperature under the conditions of plane compression and stretching, uniaxial tensile drawing and shrinkage, rolling, and environmental crazing. This direct structural approach originally justified in the works by Academician V.A. Kargin appears to be highly efficient for the study of amorphous polymer systems.     

Thermally induced relaxation after plastic deformation of glassy systems in the excited state model

The low-temperature component of thermally induced recovery after a plastic deformation of amorphous polymers and silicate glasses is a result of the transition of such materials into an excited state with subsequent return of the disordered structure of the glass from the excited to the ground state. This process was satisfactorily interpreted within the framework of the excited state model.     

Athermal simulation of plastic deformation in amorphous solids at constant pressure

An algorithm is introduced for the molecular simulation of constant-pressure plastic deformation in amorphous solids at zero temperature. This allows to directly study the volume changes associated with plastic deformation (dilatancy) in glassy solids. In particular, the dilatancy of polymer glasses is an important aspect of their mechanical behavior. The new method is closely related to Berendsen's barostat, which is widely used for molecular dynamics simulations at constant pressure. The new algorithm is applied to plane strain compression of a binary Lennard-Jones glass. Conditions of constant volume lead to an increase of pressure with strain, and to a concommitant increase in shear stress. At constant (zero) pressure, by contrast, the shear stress remains constant up to the largest strains investigated (ε = 1), while the system density decreases linearly with strain. The linearity of this decrease suggests that each elementary shear relaxation event brings about an increase in volume which is proportional to the amount of shear. In contrast to the stress–strain behavior, the strain-induced structural relaxation, as measured by the self-part of the intermediate structure factor, was found to be the same in both cases. This suggests that the energy barriers that must be overcome for their nucleation continually grow in the case of constant-volume deformation, but remain the same if the deformation is carried out at constant pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2057–2065, 2004     

How did we find the rigid amorphous phase?

The first experimental evidence of the existence of the rigid amorphous phase was reported by Menczel and Wunderlich [1]: when trying to clarify the glass transition characteristics of the first main chain liquid crystalline polymers [poly(ethylene terephthalate-co-p-oxybenzoate) with 60 and 80 mol% ethylene terephthalate units] [2], the absence of the hysteresis peak at the lower temperature glass transition became evident when the sample of this copolymer was heated much faster than it had previously been cooled. Since this glass transition involved the ethylene terephthalate-rich segments of the copolymer, we searched for the source of the absence of the hysteresis peak in PET. There, the gradual disappearance of the hysteresis peak with increasing crystallinity was confirmed [1]. At the same time it was noted that the higher crystallinity samples showed a much smaller ΔC _p than could be expected on the basis of the crystallinity calculated from the heat of fusion (provided that the crystallinity concept works). Later it was confirmed that the hysteresis peak is also missing at the glass transition of nematic glasses of polymers. When checking other semicrystalline polymers, the sum of the amorphous content calculated from the ΔC _p at the glass transition, and the crystallinity calculated from the heat of fusion was far from 100% for a number of semicrystalline polymers. For most of these polymers, the sum of the amorphous content and the crystalline fraction was 0.7, meaning that ca. 30% rigid amorphous fraction was present in these samples after a cooling at 0.5 K min⁻¹ rate. Thus, the presence of the rigid amorphous phase was confirmed in five semicrystalline polymers: PET, Nylon 6, PVF, Nylon 66 and polycaprolactone [1]. Somewhat later poly(butylene terephthalate) and bisphenol-A polycarbonate [3] were added to this list.     

结晶高分子非晶区的结构及其动力学行为研究进展

非晶结构对结晶高分子材料结构和最终使用性能有非常重要的影响,但目前对半晶高分子中非晶结构的认识还不太清晰并且有待进一步完善.随着研究手段的发展,结晶高分子中非晶区结构及其动力学行为的研究受到越来越多的关注.本文简要概述了目前对结晶高分子中非晶相的研究进展,主要从结晶高分子中非晶区的结构﹑结晶高分子中非晶区的松弛行为﹑非晶相对结晶高分子性能的影响以及等温结晶过程中非晶相的结构演化这四个方面进行介绍,并对它们的研究现状进行了概述,同时指出了目前在这方面研究中存在的争议和问题.     

Direct crystallization of silicate–phosphate glasses of NaCaPO4–SiO2 system

The subject of the study was silicate–phosphate glasses of NaCaPO₄–SiO₂ system which are precursors of glass–crystalline materials. Glass–crystalline materials of NaCaPO₄–SiO₂ system obtained via crystallization of glasses belong to a group of the so-called bioactive materials. In order to obtain glass–crystalline materials with pre-established parameters, it is necessary to conduct crystallization of glasses at specific conditions. In order to design direct crystallization process properly, it is necessary to know the structure and microstructure of the glassy precursor. Microscopic investigation showed that liquation takes place in all the studied glasses. Based on DSC examinations, it has been found out that crystallization of the glasses of NaCaPO₄–SiO₂ system is a multistep process. The presence of several clearly separated exothermic peaks in DSC curves of investigated glasses makes it possible to crystallize only the separated phase with the matrix remaining amorphous or vice versa. Conducted detailed X-ray and spectroscopic studies of the materials obtained by heating in a gradient furnace (in the temperature specified on the basis of DSC) showed that separated phase and matrix crystallizes separately. Therefore, bioactive glass–crystalline materials can be obtained due to the existence of the phase separation phenomenon and pre-established sizes of the crystalline phase.     

Characterization of the motion of spin probes and spin labels in amorphous polymers with two-dimensional field-step ELDOR

The motion of nitroxide spin probes and spin labels in amorphous polymers is studied below the glass transition temperature with a two-dimensional pulsed electron double-resonance experiment. Polystyrene and a liquid crystalline side group polymer are studied using both spin probes and spin labels covalently bound to specific sites along the polymer chain. Two methyl acrylic polymers differing only in their side group structure and polyvinylacetate are compared and large differences in the molecular dynamics deduced from both the nuclear and the electron spin relaxation rates are observed as the glass transition is approached. The results demonstrate the complexity of small amplitude motion in simple polymers below the glass transition temperature and show that it is very sensitive to the packing in the polymer. © 1996 John Wiley & Sons, Inc.     

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.     

On the relaxation theory of glass transition in liquids

A method for calculating the constant in the main equation of glass transition (which relates the relxation time and the cooling rate near the glass transition temperature) with consideration given to the temperature dependence of the activation energy in this region is proposed. A modification of the main glass transition equation is considered. Application of this equation to the relaxation spectrometry of amorphous polymers and inorganic glasses is discussed.     

The elementary softening event in glassy systems in terms of the model of the excited state

The pressure dependence of the glass-transition temperature (glass-transition lines) is described through a relationship similar to the Clausius-Clapeyron equation. The criterion for the glass-liquid transition for polymer and other glasses is calculated. According to the proposed speculations, an elementary softening event in glasses is reduced to the critical deformation of interatomic (intermolecular) linkage, which corresponds to the maximum force of attraction between atoms. A glass (an amorphous polymer) softens when the mean energy of the thermal motion of the kinetic units responsible for the viscous flow is ∼3 times higher than the work of the ultimate deformation of the interatomic bond. The nature of structural changes occurring in the course of critical displacement (excitation) of kinetic units in liquids and glasses is discussed.