Chain Polymer Molecules Research Articles

A simulation approach to study of entropic elasticity properties of polymer chain molecules using atomic scale Monte-Carlo

This paper describes atomic scale Monte–Carlo studies of entropic elasticity properties of individual polymer chain molecules. An efficient numerical Monte –Carlo sampling approach is outlined and used to evaluate the entropic contribution to the total elastic force.Theoretic predictions of mechanical properties of polymer molecules, particularly complex bio-molecules (proteins, lipids, etc.), are difficult due to effects of entropic elasticity. Entropic elastic force can be a significant contributor to the free energy F of the polymer chain and can even exceed interatomic potential energy U under external mechanical load. Monte-Carlo based approach allows to achieve atomic resolution for molecular structure in contrast to analytical methods. Specific load-extension curves are obtained numerically for a group of molecules with degenerate potential energy profiles. Results of the atomistic modeling are compared with the limiting continuum model of the same type of polymers. The extent of the linear and nonlinear elastic regimes and dependence on the molecular weight and geometric parameters of the molecules are discussed. A significant divergence with the continuummodel behavior is observed at smaller bond angles for all elongationsof the molecule. Linearity of the entropic force exists in a wide range ofthe elongations, however, molecules with low gyration radii(densely packedpolymers) are linear mostly in extensionor unfolding, while very sparsely packed molecules are linear mostly in thecontraction mode. The achieved result cannot be reproduced withinthe settings of the continuum model and required an application of atomic scale Monte-Carlo approach developed by our group.

Modeling the construction of polymeric adsorbent media: Effects of counter-ions on ligand immobilization and pore structure

Molecular dynamics modeling and simulations are employed to study the effects of counter-ions on the dynamic spatial density distribution and total loading of immobilized ligands as well as on the pore structure of the resultant ion exchange chromatography adsorbent media. The results show that the porous adsorbent media formed by polymeric chain molecules involve transport mechanisms and steric resistances which cause the charged ligands and counter-ions not to follow stoichiometric distributions so that (i) a gradient in the local nonelectroneutrality occurs, (ii) non-uniform spatial density distributions of immobilized ligands and counter-ions are formed, and (iii) clouds of counter-ions outside the porous structure could be formed. The magnitude of these counter-ion effects depends on several characteristics associated with the size, structure, and valence of the counter-ions. Small spherical counter-ions with large valence encounter the least resistance to enter a porous structure and their effects result in the formation of small gradients in the local nonelectroneutrality, higher ligand loadings, and more uniform spatial density distributions of immobilized ligands, while the formation of exterior counter-ion clouds by these types of counter-ions is minimized. Counter-ions with lower valence charges, significantly larger sizes, and elongated shapes, encounter substantially greater steric resistances in entering a porous structure and lead to the formation of larger gradients in the local nonelectroneutrality, lower ligand loadings, and less uniform spatial density distributions of immobilized ligands, as well as substantial in size exterior counter-ion clouds. The effects of lower counter-ion valence on pore structure, local nonelectroneutrality, spatial ligand density distribution, and exterior counter-ion cloud formation are further enhanced by the increased size and structure of the counter-ion. Thus, the design, construction, and functionality of polymeric porous adsorbent media will significantly depend, for a given desirable ligand to be immobilized and represent the adsorption active sites, on the type of counter-ion that is used during the ligand immobilization process. Therefore, the molecular dynamics modeling and simulation approach presented in this work could contribute positively by representing an engineering science methodology to the design and construction of polymeric porous adsorbent media which could provide high intraparticle mass transfer and adsorption rates for the adsorbate biomolecules of interest which are desired to be separated by an adsorption process.

The test-particle induced inhomogeneous direct correlation functions and extensions of Widom's theorem: Impacts on the incremental chemical potentials and high-order correlation functions

We develop the potential distributions of several test particles to obtain a hierarchy of the nonuniform singlet direct correlation functions (s-DCFs). These correlation functions are interpreted as the segmental chemical potentials or works of insertion of successive test particles in a classical fluid. The development has several interesting consequences: (i) it extends the Widom particle insertion formula to higher-order theorems, the first member gives the chemical potential as in the original theorem, the second member gives the incremental energy for dimer formation, with higher members giving the energies for forming trimers, tetramers, etc. (ii) The second and third order s-DCFs can be related to the cavity distribution functions y((2)) and y((3)) in the liquid-state theory. Thus we can express the triplet cavity function y((3)) in terms of these s-DCFs in an exact form. This enables us to calculate, as an illustration of the above theoretical developments, the numerical values of the s-DCFs via Monte Carlo (MC) simulation data on hard spheres. We use these data to critically analyze the commonly used approximations, the Kirkwood superposition (KSA) and the linear approximation (LA) for triplet correlation functions. An improved rule over KSA and LA is proposed for triplet hard spheres in the rolling-contact configurations. (iii) The s-DCFs are naturally suited for analyzing the chain-incremental Ansatz or hypothesis in the calculation of the chemical potentials of polymeric chain molecules. The first few segments of a polymer chain have been shown from extensive Monte Carlo simulations to not obey this Ansatz. By examining the insertion energies of successive segments through the s-DCFs, we are able to quantitatively decipher the decay of the segmental chemical potentials for at least the first three segments. Comparison with MC data on 4-mer and 8-mer hard-sphere fluids shows commensurate behavior with the s-DCFs. In addition, an analytical density functional theory is derived, through the potential distribution theorem, for obtaining these nonuniform direct correlation functions.

Polymeric Prodrugs: Recent Achievements and General Strategies

It is well known that polymeric prodrug or polymer-drug conjugate is an effective and fast growing technique for improved use of drugs for therapeutic applications. Polymer conjugated drugs generally exhibit prolonged half-life, higher stability, water solubility, lower immunogenicity and antigenicity and specific targeting to tissues or cells. Polymers are used as carriers in polymeric prodrugs/macromolecular prodrugs for the delivery of drugs, proteins, targeting moieties, and imaging agents. The polymeric pro-drug can be regarded as drug delivery systems that exhibit their therapeutic activities by means of releasing smaller therapeutic drug molecules from a polymer chain molecule for a prolonged period of time which results in enhanced pharmacokinetic behaviour by increasing the t1/2, bioavailability, and hence prolonged pharmacological action. The potential of the polymer-drug conjugates have already been proved by success of many products in the market for the treatment of different diseases. A model for macromolecular pro-drugs was first proposed by Ringsdorf in the mid 1970s. The pro-drug shows particular properties determined by the macromolecule presence and manifested in the pharmacokinetic behaviour of the drug-polymer conjugate. This review deals with the Rational for design of polymer-drug conjugates, requirements for selection of drug candidate for polymeric prodrug, requirements for selecting polymers as candidate drug carriers, classification of polymers, design and synthesis of polymeric prodrugs, strategies to reduce steric hindrances exhibited by polymers and the bio-components, strategies to enhance the reactivity of polymer and the drug by incorporation of spacers and structure-activity relationship (SAR) of polymer-drug conjugates.

Biodegradable thermoresponsive polymeric magnetic nanoparticles: a new drug delivery platform for doxorubicin

The use of nanoparticles as drug delivery systems for anticancer therapeutics has great potential to revolutionize the future of cancer therapy. The aim of this study is to construct a novel drug delivery platform comprising a magnetic core and biodegrad- able thermoresponsive shell of tri-block-copolymer. Oleic acid-coated Fe3O4 nanoparticles and hydrophilic anticancer drug ''doxorubicin'' are encapsulated with PEO-PLGA-PEO (polyethylene oxide-poly D, L lac- tide-co-glycolide-polyethylene oxide) tri-block- copolymer. Structural, magnetic, and physical proper- ties of Fe3O4 core are determined by X-ray diffraction, vibrating sample magnetometer, and transmission electron microscopy techniques, respectively. The hydrodynamic size of composite nanoparticles is determined by dynamic light scattering and is found to be *36.4 nm at 25 C. The functionalization of magnetic core with various polymeric chain molecules and their weight proportions are determined by Fourier transform infrared spectroscopy and thermogravimet- ric analysis, respectively. Encapsulation of doxorubi- cin into the polymeric magnetic nanoparticles, its loading efficiency, and kinetics of drug release are investigated by UV-vis spectroscopy. The loading efficiency of drug is 89% with a rapid release for the initial 7 h followed by the sustained release over a period of 36 h. The release of drug is envisaged to occur in response to the physiological temperature by deswelling of thermoresponsive PEO-PLGA-PEO block-copolymer. This study demonstrates that tem- perature can be exploited successfully as an external parameter to control the release of drug.

Characterization of Molecular Motions and in Nafion® Fuel Cell Membranes by Dielectric Spectroscopy

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Electrospinning of Cyclodextrin–Pseudopolyrotaxane Nanofibers

Cyclodextrins (CDs) are distinctive molecules that can form noncovalent host–guest complexes with a variety of molecules to yield intriguing supramolecular structures. Electrospinning has gained enormous attention since this versatile technique enables production of multifunctional nanofibers made from various polymers, polymer blends, composites, and ceramics. Electrospun nanofibers containing cyclodextrin inclusion complexes are particularly attractive because of the unique properties obtained by combining the large surface area of a polymer nanofiber carrier with the specific chemical structure of the CD complex. Herein we report the first results from electrospinning cyclodextrin inclusion complexes and/or cyclodextrin pseudopolyrotaxanes. Cyclodextrins are cyclic oligosaccharides with a toroidshaped molecular structure consisting of a(1,4)-linked glucopyranose units (Figure 1a). The most common natural CDs have either six, seven, or eight glucopyranose units and are referred to as a-, b-, and g-cyclodextrins, respectively (Figure 1b). The hydrophobic cavity of CDs allows them to form host–guest complexes with various small molecules and macromolecules. The stability of CD complexes depends on many factors such as the size or shape match between host and guest, chemical environment, and the binding forces (e.g., hydrophobic interactions, van der Waals attractions, hydrogen bonding, and electrostatic interactions) between the host CD and guest molecules. Since the physical and chemical properties of incorporated guest compounds can be tailored by CD complexation, CDs are used in a variety of application areas, such as pharmaceuticals (e.g., enhancement of drug solubility and stability, bioavailability, controlled drug delivery, and reduction of drug toxicity), 15] functional food additives (stabilization of volatile or unstable flavors and masking or removal of unwanted tastes and odor), cosmetics and home or personal care (releasing fragrances and masking unpleasant odors), and textiles (stabilization and controlled release of textile additives). CD pseudopolyrotaxanes, formed by threading a polymer chain or long molecule through many CD rings, have fascinating supramolecular structures with unusual properties. It has been shown that CD pseudopolyrotaxanes can be formed with various synthetic polymers, biopolymers, conducting polymers, dyes, polypeptides, proteins, and enzymes, and that the huge variety of supramolecular structures are extremely useful in many diverse areas. The nanostructure or microstructure and the functionality of the guest molecules are altered when encapsulated by CD molecules; furthermore, CD rings assist the stabilization and protection of the guest molecules and can control or sustain their delivery. CDs are natural, nontoxic, and slowly biodegradable, and consequently CD polyrotaxanes are very attractive candidates for smart materials, controlled or sustained delivery systems, sensor devices, molecular switches, or other diagnostic systems. Electrospinning is as a versatile and cost-effective technique for producing multifunctional nanofibers. Nanofibers and their mats have several remarkable characteristics such as large surface area to volume ratios, pore sizes in the nanometer range, unique physical and mechanical properties, and the chemical, physical, and functional properties of the nanofiber surfaces are fairly easy to modify. It has been shown that the very interesting properties and the multifunctionality of the nanofibers make them favorable candidates for use in many areas including biotechnology (tissue engineering, controlled or sustained release systems), textiles (delivery and stabilization of additives) and membranes/filters. The incorporation of CD-pseudopolyrotaxanes into nanofibers is extremely interesting since such the resulting CDcomplex-containing nanowebs will have unique characterFigure 1. a) Chemical structure of a-CD; b) approximate dimensions of g-, b-, and a-CDs; schematic representation of packing structures of c) cage-type and d) channel-type a-CD crystals.

Below-Gap Excitation ofπ-Conjugated Polymer-Fullerene Blends: Implications for Bulk Organic Heterojunction Solar Cells

We used a variety of optoelectronic techniques such as broadband fs transient and cw photomodulation spectroscopies, electroabsorption, and short-circuit photocurrent in bulk heterojunctions organic solar cells for studying the photophysics in pi-conjugated polymer-fullerene blends with below-gap excitation. In contrast to the traditional view, we found that below-gap excitation, which is incapable of generating intrachain excitons, nevertheless efficiently generates polarons on the polymer chains and fullerene molecules. The polaron action spectrum extends deep inside the gap as a result of a charge-transfer complex state formed between the polymer chain and fullerene molecule. With appropriate design engineering the long-lived polarons might be harvested in solar cell devices.

Ergodicity breaking and conformational hysteresis in the dynamics of a polymer tethered at a surface stagnation point

We study the dynamics of long chain polymer molecules tethered to a plane wall and subjected to a stagnation point flow. Using a combination of theory and numerical techniques, including Brownian dynamics (BD), we demonstrate that a chain conformation hysteresis exists even for freely draining (FD) chains. Hydrodynamic interactions (HI) between the polymer and the wall are included in the BD simulations. We find qualitative agreement between the FD and HI simulations, with both exhibiting simultaneous coiled and stretched states for a wide range of fixed flow strengths. The range of state coexistence is understood by considering an equivalent projected equilibrium problem of a two state reaction. Using this formalism, we construct Kramers rate theory (from the inverse mean first passage time for a Markov process) for the hopping transition from coil to stretch and stretch to coil. The activation energy for this rate is found to scale proportionally to chain length or Kuhn step number. Thus, in the limit of infinite chain size the hopping rates at a fixed value of the suitably defined Deborah number approach zero and the states are "frozen." We present the results that demonstrate this "ergodicity breaking."

Measurement and Prediction of the Elongational Stress Growth in a Dilute Solution of DNA Molecules

We report the measurement of the elongational stress growth coefficient of a dilute solution of λ-phage DNA molecules in sugar and corn-syrup solvent mixtures under excess salt conditions. The stress growth is measured using a filament stretching rheometer, at strain rates far exceeding the inverse relaxation time of the DNA molecule. The DNA molecule is assumed to behave like a long chain polymer molecule under good solvent conditions, and the observed behavior is modeled using a bead-spring chain model for the DNA. Excluded-volume (EV) effects are accounted for by a narrow-Gaussian repulsive potential between the beads, hydrodynamic interactions (HI) between beads are approximated by the Rotne-Prager-Yamakawa tensor, and the finite length of the DNA molecule is treated by springs whose force-extension behavior mimics that of a wormlike chain. By combining a Brownian dynamics simulation of the chain along with the recently introduced method of successive fine graining [Sunthar, P.; Prakash, J. R. Macromolecules 2005, 38, 617], predictions of the stress growth coefficient are obtained which are insensitive to the microscopic interaction parameters for EV and HI.

Computer simulations of polymer chain structure and dynamics on a hypersphere in four-space

There is a rapidly growing interest in performing computer simulations in a closed space, avoiding periodic boundary conditions. To extend the range of potential systems to include also macromolecules, we describe an algorithm for computer simulations of polymer chain molecules on S3, a hypersphere in four dimensions. In particular, we show how to generate initial conformations with a bond angle distribution given by the persistence length of the chain and how to calculate the bending forces for a molecule moving on S3. Furthermore, we discuss how to describe the shape of a macromolecule on S3, by deriving the radius of gyration tensor in this non-Euclidean space. The results from both Monte Carlo and Brownian dynamics simulations in the infinite dilution limit show that the results on S3 and in R3 coincide, both with respect to the size and shape as well as for the diffusion coefficient. All data on S3 can also be described by master curves by suitable scaling by the corresponding values in R3. We thus show how to extend the use of spherical boundary conditions, which are most effective for calculating electrostatic forces, to polymer chain molecules, making it possible to perform simulations on S3 also for polyelectrolyte systems.

How Many Monomer Repeat Units are Necessary for Reliable Molecular Dynamics Simulation?

This study was an attempt to answer the question, “How many monomer repeat units are necessary in molecular dynamics simulation in order to obtain reliable (i.e. repeatable) solutions?” A series of numerical tests was conducted to provide an answer. Based on the numerical results, reliable solutions required approximately ten thousand monomer repeat units at minimum, which was the sum of the monomer units in every polymer chain molecule. It did not matter much whether there were longer chain polymer molecules in a small quantity or shorter chain polymer molecules in a large quantity. What was critical was the total number of monomer repeat units. For a particle reinforced composite that consists of metallic atoms embedded in a polymer matrix, the minimum number of total monomer repeat units in the polymer matrix was approximately five thousand for reliable solutions.

Theory of transport of long polymer molecules through carbon nanotube channels.

A theory of transport of long chain polymer molecules through carbon nanotube (CNT) channels is developed using the Fokker-Planck equation and direct molecular dynamics simulations. The mean transport or translocation time tau is found to depend on the chemical potential energy, the entropy, and the diffusion coefficient. A power law dependence tau approximately N2 is found, where N is the number of monomers in a molecule. For 10(5)-unit long polyethylene molecules, tau is estimated to be approximately 1 micros. The diffusion coefficient of long polymer molecules inside CNTs, like that of short ones, is found to be a few orders of magnitude larger than in ordinary silicate based zeolite systems.

Diffusion assisted end–to–end relaxation of a flexible Rouse polymer chain: Fluorescence quenching through a model energy transfer

The diffusion-influenced end–to–end conformational relaxation of a flexible polymer chain molecule (within the Rouse model) is investigated theoretically in the Markovian limit utilizing a generalized diffusion equation for the probability distribution of the end–to–end distance of a chain molecule, which has its origin in the Zwanzig’s treatment of Onsager’s theory of irreversible processes. The end–to–end diffusion dynamics of the chain molecule is considered to be probed by fluorescence resonance energy transfer between two chromophores, attached to the chain ends. The resulting diffusion equation with a sink term representing this energy transfer through a suitably modified Förster rate expression is solved numerically for equilibrium close/open conformations, and end–to–end irreversible ring opening or closure of the chain. Illustrative calculations and comparisons between the kinetics arising out of these conformations are presented to demonstrate the competitive interplay between the transfer sink strength, diffusion, and chain relaxation. From the numerical results for a variety of transfer parameters and end–to–end diffusion coefficients, it is found that a nonmonotonic distribution of reaction times is a confirmative signature for a cyclization transition, whereas a monotonic decay of distribution of the reaction times, as is always the case with the chain opening transition or with the equilibrium configuration (either closed or opened) of the chain, cannot also be ruled out for the cyclization transition. The knowledge of the distribution of energy-transfer distances is utilized to help delineate the features associated with the reaction time distribution during the end–to–end relaxation.

Comparative evaluation of the infrared transmission of polymer films

The total infrared (IR) transmission of polymer films is a very important property in engineering, which determines their suitability for a specific application at a given temperature level. Aiming to investigate the total IR transmission of various polymer material films of a particular thickness, an analysis is developed for the comparative evaluation of this very important physical property. Excitation of the radical bonds in randomly oriented, long chain polymer molecules by absorption of IR radiation usually causes a large number of sharp resonances at various wavelengths and is responsible for the characteristic shape of the spectral transmission plot for the particular polymer material. The comparative presentation of results shows that at least as far as the accuracy of the available data is concerned, the total transmission of a polymer film is determined by the specific spectral transmission characteristics of the material and may vary remarkably as a function of the radiant source temperature. According to the derived results, polymer films made of materials like plexiglass, mylar, kapton and fiberglass appear to be remarkably less transparent than other film materials like polypropylene or, even more, polyethylene, which are remarkably transparent, almost uniformly, within the wavelength region under consideration. This certainly determines the potential of the particular films for use in a specific application like the design of solar collector glazing systems or convection suppression windscreens in radiative cooling panels.

Structure of Water Sorbed into Poly(MEA-co-HEMA) Films As Examined by ATR−IR Spectroscopy

The structure of water sorbed into poly(2-methoxyethyl acrylate) (PMEA), poly(2-hydroxyethyl methacrylate) (PHEMA), and their copolymers (p(MEA/HEMA)) was investigated by attenuated total reflection infrared (ATR−IR) spectroscopy. The extinction coefficient of the OH stretching band of sorbed water (εOH) was calculated from the band area obtained by IR measurement and the amount of sorbed water obtained by thermogravimetric analysis. When the polymers contacted with water vapor (relative humidity = ∼55%), the εOH values were quite similar in all polymers. On the other hand, when the polymers contacted with liquid water, the εOH values were drastically changed by the content of 2-methoxyethyl acrylate (MEA). When the MEA content of the polymers was low (<60 mol %), the εOH value of the water sorbed into polymers in contact with liquid water was equal to that in contact with water vapor. In the higher MEA content (70−100 mol %), on the other hand, the εOH values of the water sorbed into polymers in contact with liquid water were 5−8 times larger than that in contact with water vapor. These results seemed to indicate that the interaction between the primary hydration water around the MEA-containing polymer chain and water molecules surrounding the primarily hydrating water is very weak. Such water with a large εOH value seemed to correspond to “cold-crystallizable” water, which has been observed by DSC as anomalous water other than intermediate and nonfreezable waters. Taking both the experimental results obtained in this work and those thermodynamically obtained previously into consideration, it was strongly suggested that the cold crystallization of water is generated by caging water molecules in a small space by the polymer chains with a small hydration region. The correlation between the εOH value and the blood compatibility of the copolymer was also discussed.

Swelling and deswelling transition of water-soluble poly(N-isopropylacrylamide) by a method of blob rescaling

The transition behavior of swelling and deswelling of water-soluble poly(N-isopropylacrylamide) was calculated by a decorated UNIQUAC model with blob concept. The deswelling behavior of hydrogels at high tem- peratures was also reported with shrinking volumes during the transition. Polymer chains were scaled within a directly interacting size as blobs, which are composed of a segmentalized polymer chain and solvent molecules and counted blobs of hypothetical components or segments. The interaction parameters of bulks, UNIQUAC interaction parameters, were approximated with temperature-independent site interaction energies following the blob renormalization trans- formation. The swelling gel transition volume at each given temperature was calculated with the decorated UNIQUAC model. The blob rescaling model successfully described the first order transition of swelling-deswelling behaviors.

Structure and Nonlinear Flow Behavior of Simple and Complex Fluids

The structure of a fluid as described by the pair-correlation function or by the static structure factor is modified by a viscous flow. This modification already exists in the linear flow regime (Newtonian behavior) but it becomes more pronounced at higher shear rates where non-Newtonian effects, such as a dependence of the viscosity on the shear rate and normal stress differences, prevail. Examples are presented for fluids composed of spherical particles, in particular, “simple fluids” and dense colloidal dispersions, and for “complex fluids” composed of nonspherical particles and polymeric chain molecules. Calculations based on kinetic equations for the pair-correlation function or for the orientational distribution function are compared with results obtained by nonequilibrium molecular dynamics (NEMD) computer simulations, as well as with rheological and neutron scattering experiments.

Free-volume change during the volume phase transition of polyacrylamide gel studied by positron annihilation: Solvent-composition dependence

Changes in the free-volume parameters of polyacrylamide (PAAm) gels during the volume phase transition (VPT) were studied with the positron annihilation lifetime technique. The VPT was induced through the variation of the solvent composition in a mixture of acetone and water. The PAAm gels containing 0 and 4 mol % carboxyl groups in their polymer chains were adapted to compare the effect of the presence of ionic groups on the microscopic environment. The change of the free-volume property is discussed on a nanoscopic scale, with attention paid to the interactions between the polymer chains and the solvent molecules. It is proven that the variations of the free-volume parameters correlate significantly with the VPT phenomenon. The results of the free volume for both gels are well-explained when an interaction parameter, εg, is assumed. The interpretation suggests that the state of the interactions among the components (the polymer chain, acetone, and water molecules) plays an important role in the change of the free volume of PAAm gels during the VPT. An increase of the dispersion of the free-volume size near the VPT point was observed for the ionized PAAm gel. The broadened size distribution of the free volume of the ionized PAAm gel around the VPT point lay between those of pure water and the corresponding mixed solvent, suggesting that a local minimum of the average free-volume size at the VPT point is caused by the increase of a specific interaction, hydrogen bonding. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 922–933, 2000

Graft Polymerization of Styrene on Mica: Formation and Behavior of Molecular Droplets and Thin Films

Cation-bearing peroxide free-radical initiators were attached to mica surfaces via ion exchange and used to polymerize styrene. Polystyrene chains grafted to the mica by growth from the surface resulted. Scanning electron microscopy showed distinct droplets on the surface. The droplets appear, from their size, to each consist of a single polymer chain molecule. The density of the droplets on the surface could be varied by varying the polymerization time. The droplets could be made to coalesce into thin films by increasing the grafting density, by heating, or by solvent treatment. Upon heating, the droplets appeared to spread on the surface at temperatures well below the normal glass transition temperature of polystyrene.