Polymer Glass Formation: Role of Activation Free Energy, Configurational Entropy, and Collective Motion

A closer examination of the nature of atomic motion in the interfacial region of crystals upon approaching melting

Although crystalline materials are often conceptualized as involving a static lattice configuration of particles, it has recently become appreciated that string-like collective particle exchange motion is a ubiquitous and physically important phenomenon in both the melting and interfacial dynamics of crystals. This type of collective motion has been evidenced in melting since early simulations of hard disc melting by Alder et al. [Phys. Rev. Lett. 11(6), 241-243 (1963)], but a general understanding of its origin, along with its impact on melting and the dynamics of crystalline materials, has been rather slow to develop. We explore this phenomenon further by focusing on the interfacial dynamics of a model crystalline Cu material using molecular dynamics simulations where we emphasize the geometrical nature and spatial extent of the atomic trajectories over the timescale that they are caged, and we also quantify string-like collective motion on the timescale of the fast β-relaxation time, τf, i.e., "stringlets." Direct visualization of the atomic trajectories in their cages over the timescale over which the cage persists indicates that they become progressively more anisotropic upon approaching the melting temperature Tm. The stringlets, dominating the large amplitude atomic motion in the fast dynamics regime, are largely localized to the crystal interfacial region and correspond to "excess" modes in the density of states that give rise to a "boson peak." Moreover, interstitial point defects occur in direct association with the stringlets, demonstrating a link between classical defect models of melting and more recent studies of melting emphasizing the role of this kind of collective motion.

Confinement effect of inter-arm interactions on glass formation in star polymer melts

We utilized molecular dynamic simulation to investigate the glass formation of star polymer melts in which the topological complexity is varied by altering the number of star arms (f). Emphasis was placed on how the "confinement effect" of repulsive inter-arm interactions within star polymers influences the thermodynamics and dynamics of star polymer melts. All the characteristic temperatures of glass formation were found to progressively increase with increasing f, but unexpectedly the fragility parameter KVFT was found to decrease with increasing f. As previously observed, stars having more than 5 or 6 arms adopt an average particle-like structure that is more contracted relative to the linear polymer size having the same mass and exhibit a strong tendency for intermolecular and intramolecular segregation. We systematically analyzed how varying f alters collective particle motion, dynamic heterogeneity, the decoupling exponent ζ phenomenologically linking the slow β- and α-relaxation times, and the thermodynamic scaling index γt. Consistent with our hypothesis that the segmental dynamics of many-arm star melts and thin supported polymer films should exhibit similar trends arising from the common feature of high local segmental confinement, we found that ζ increases considerably with increasing f, as found in supported polymer films with decreasing thickness. Furthermore, increasing f led to greatly enhanced elastic heterogeneity, and this phenomenon correlates strongly with changes in ζ and γt. Our observations should be helpful in building a more rational theoretical framework for understanding how molecular topology and geometrical confinement influence the dynamics of glass-forming materials more broadly.

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

Anomalous segmental dynamics of supercooled polyrotaxane melts: A computer simulation study

Polyrotaxanes, which consist of mechanically interlocked bonds with rings threaded onto soft polymer chains, exhibit unique mechanical properties and find applications in diverse fields. In this study, we investigate the anomalous segmental dynamics of supercooled polyrotaxane melts using coarse-grained molecular dynamics simulations. Our simulations reveal that the presence of rings effectively reduces the packing efficiency, resulting in well-contained local motion even below the glass transition temperature. We also observe variations in dynamical free volume, characterized by the Debye-Waller factor, which shows a minimum at a ring coverage of 0.1 on threading chains. Such a non-monotonic dependence on coverage shows great consistency in structural relaxation time and dynamic heterogeneity. Specifically, the high segmental mobility of threading linear chains at large coverage can be attributed to the increased dynamical free volume due to supported rigid rings. However, such anomalous segmental dynamics is limited to length scales smaller than one ring size. Beyond this characteristic length scale, the diffusion is dominated by topological constraints, which significantly reduce the mobility of polyrotaxanes and enhance the dynamic heterogeneity. These findings offer microscopic insights into the unique packing structures and anomalous segmental dynamics of supercooled polyrotaxane melts, facilitating the design of advanced materials based on mechanical interlocking polymers for various applications.

Competing Effects of Molecular Additives and Cross-Link Density on the Segmental Dynamics and Mechanical Properties of Cross-Linked Polymers

The introduction of molecular additives into thermosets often results in changes in their dynamics and mechanical properties that can have significant ramifications for diverse applications of this broad class of materials such as coatings, high-performance composites, etc. Currently, there is limited fundamental understanding of how such additives influence glass formation in these materials, a problem of broader significance in glass-forming materials. To address this fundamental problem, here, we employ a simplified coarse-grained (CG) model of a polymer network as a model of thermoset materials and then introduce a polymer additive having the same inherent rigidity and polymer-polymer interaction strength as the cross-linked polymer matrix. This energetically "neutral" or "self-plasticizing" additive model gives rise to non-trivial changes in the dynamics of glass formation and provides an important theoretical reference point for the technologically more important case of interacting additives. Based on this rather idealized model, we systematically explore the combined effect of varying the additive mass percentage (m) and cross-link density (c) on the segmental relaxation dynamics and mechanical properties of a model thermoset material with additives. We find that increasing the additive mass percentage m progressively decreases both the glass-transition temperature Tg and the fragility of glass formation, a trend opposite to increasing c so that these thermoset variables clearly have a competing effect on glass formation in these model materials. Moreover, basic mechanical properties (i.e., bulk, shear, and tensile moduli) likewise exhibit a competitive variation with the increase of m and c, which are strongly correlated with the Debye-Waller parameter ⟨u2⟩, a measure of material stiffness at a molecular scale. Our findings prove beneficial in the development of structure-property relationships for the cross-linked polymers, which could help guide the design of such network materials with tailored physical properties.

Approach to hyperuniformity in a metallic glass-forming material exhibiting a fragile to strong glass transition

We investigate a metallic glass-forming (GF) material (Al₉₀Sm₁₀) exhibiting a fragile-strong (FS) glass-formation by molecular dynamics simulation to better understand this highly distinctive pattern of glass-formation in which many of the usual phenomenological relations describing relaxation times and diffusion of ordinary GF liquids no longer apply, and where instead genuine thermodynamic features are observed in response functions and little thermodynamic signature is exhibited at the glass transition temperature, T_g. Given the many unexpected similarities between the thermodynamics and dynamics of this metallic GF material with water, we first focus on the anomalous static scattering in this liquid, following recent studies on water, silicon and other FS GF liquids. We quantify the "hyperuniformity index" H of our liquid, which provides a quantitative measure of molecular "jamming". To gain insight into the T-dependence and magnitude of H, we also estimate another more familiar measure of particle localization, the Debye-Waller parameter 〈u²〉 describing the mean-square particle displacement on a timescale on the order of the fast relaxation time, and we also calculate H and 〈u²〉 for heated crystalline Cu. This comparative analysis between H and 〈u²〉 for crystalline and metallic glass materials allows us to understand the critical value of H on the order of 10^-3 as being analogous to the Lindemann criterion for both the melting of crystals and the "softening" of glasses. We further interpret the emergence of FS GF and liquid-liquid phase separation in this class of liquids to arise from a cooperative self-assembly process in the GF liquid.

Molecular Mobility of Polymers at the Melting Transition

Melting of crystals is an archetypical first order phase transition. Albeit extensive efforts, the molecular origin of this process in polymers is still not clear. Experiments are complicated by the tremendous change in mechanical properties and the occurrence of parasitic phenomena masking the genuine material response. Here, we present an experimental procedure permitting to circumvent these issues by investigating the dielectric response of thin polymer films. Extensive measurements on several commercially available semicrystalline polymers allowed us to identify a genuine molecular process associated with the newly formed liquid phase. In line with recent observations of amorphous polymer melts, we show this mechanism─known as the slow Arrhenius process (SAP)─involves time scales longer than those characteristics of segmental mobility and has the same energy barrier of the flow of the melt.

Combined description of pressure-volume-temperature and dielectric relaxation of several polymeric and low-molecular-weight organic glass-formers using SL-TS2 approach

We apply our recently-developed mean-field "SL-TS2" (two-state Sanchez-Lacombe) model to simultaneously describe dielectric α-relaxation time, τ_α, and pressure-volume-temperature (PVT) data in four polymers (polystyrene, poly(methylmethacrylate), poly(vinyl acetate) and poly(cyclohexane methyl acrylate)) and four organic molecular glass formers (ortho-terphenyl, glycerol, PCB-62, and PDE). Previously, it has been shown that for all eight materials, the Casalini-Roland thermodynamical scaling, τ_α = f(Tvγsp) (where T is temperature and v_sp is specific volume) is satisfied (R. Casalini and C. M. Roland, Phys. Rev. E, 2004, 69(6), 62501). It has also been previously shown that the same scaling emerges naturally (for sufficiently low pressures) within the "SL-TS2" framework (V. V. Ginzburg, Soft Matter, 2021, 17, 9094-9106). Here, we fit the ambient pressure curves for the relaxation time and the specific volume as functions of temperature for the eight materials and observe a good agreement between theory and experiment. We then use the Casalini-Roland scaling to convert those results into "master curves", thus enabling predictions of relaxation times and specific volumes at elevated pressures. The proposed approach can be used to describe other glass-forming materials, both low-molecular-weight and polymeric.

Understanding the role of cross-link density in the segmental dynamics and elastic properties of cross-linked thermosets

Cross-linking is known to play a pivotal role in the relaxation dynamics and mechanical properties of thermoset polymers, which are commonly used in structural applications because of their light weight and inherently strong nature. Here, we employ a coarse-grained (CG) polymer model to systematically explore the effect of cross-link density on basic thermodynamic properties as well as corresponding changes in the segmental dynamics and elastic properties of these network materials upon approaching their glass transition temperatures (T_g). Increasing the cross-link density unsurprisingly leads to a significant slowing down of the segmental dynamics, and the fragility K of glass formation shifts in lockstep with T_g, as often found in linear polymer melts when the polymer mass is varied. As a consequence, the segmental relaxation time τ_α becomes almost a universal function of reduced temperature, (T - T_g)/T_g, a phenomenon that underlies the applicability of the "universal" Williams-Landel-Ferry (WLF) relation to many polymer materials. We also test a mathematical model of the temperature dependence of the linear elastic moduli based on a simple rigidity percolation theory and quantify the fluctuations in the local stiffness of the network material. The moduli and distribution of the local stiffness likewise exhibit a universal scaling behavior for materials having different cross-link densities but fixed (T - T_g)/T_g. Evidently, T_g dominates both τ_α and the mechanical properties of our model cross-linked polymer materials. Our work provides physical insights into how the cross-link density affects glass formation, aiding in the design of cross-linked thermosets and other structurally complex glass-forming materials.

Role of torsional potential in chain conformation, thermodynamics, and glass formation of simulated polybutadiene melts

For polymer chains, the torsional potential is an important intramolecular energy influencing chain flexibility and segmental dynamics. Through molecular dynamics simulations of an atomistic model for melts of cis-trans-1,4-polybutadiene (PBD), we explore the effect of the torsions on conformational properties (bond vector correlations and mean-square internal distances), fundamental thermodynamic quantities (density, compressibility, internal energy, and specific heat), and glass transition temperature T_g. This is achieved by systematically reducing the strength of the torsional potential, starting from the chemically realistic chain (CRC) model with the full potential toward the freely rotating chain (FRC) model without the torsional potential. For the equilibrium liquid, we find that the effect of the torsions on polymer conformations is very weak. Still weaker is the influence on the monomer density ρ and isothermal compressibility κ_T of the polymer liquid, both of which can be considered as independent of the torsional potential. We show that a van der Waals-like model proposed by Long and Lequeux [Eur. Phys. J. E 4, 371 (2001)] allows us to describe very well the temperature (T) dependence of ρ and κ_T. We also find that our data obey the linear relation between 1/k_BTρκ_T and 1/T (with the Boltzmann constant k_B) that has recently been predicted and verified on the experiment by Mirigian and Schweizer [J. Chem. Phys. 140, 194507 (2014)]. For the equilibrium liquid, simulations result in a specific heat, at constant pressure and at constant volume, which increases on cooling. This T dependence is opposite to the one found experimentally for many polymer liquids, including PBD. We suggest that this difference between simulation and experiment may be attributed to quantum effects due to hydrogen atoms and backbone vibrations, which, by construction, are not included in the classical united-atom model employed here. Finally, we also determine T_g from the density-temperature curve monitored in a finite-rate cooling process. While the influence of the torsional potential on ρ(T) is vanishingly small in the equilibrium liquid, the effect of the torsions on T_g is large. We find that T_g decreases by about 150 K when going from the CRC to the FRC model.

A β-NMR study of the depth, temperature, and molecular-weight dependence of secondary dynamics in polystyrene: Entropy–enthalpy compensation and dynamic gradients near the free surface

We investigated the depth, temperature, and molecular-weight (MW) dependence of the γ-relaxation in polystyrene glasses using implanted 8Li+ and β-detected nuclear magnetic resonance. Measurements were performed on thin films with MW ranging from 1.1 to 641 kg/mol. The temperature dependence of the average 8Li spin–lattice relaxation time [Formula: see text] was measured near the free surface and in the bulk. Spin–lattice relaxation is caused by phenyl ring flips, which involve transitions between local minima over free-energy barriers with enthalpic and entropic contributions. We used transition state theory to model the temperature dependence of the γ-relaxation, and hence [Formula: see text]. There is no clear correlation of the average entropy of activation [Formula: see text] and enthalpy of activation [Formula: see text] with MW, but there is a clear correlation between [Formula: see text] and [Formula: see text], i.e., entropy–enthalpy compensation. This results in the average Gibbs energy of activation, [Formula: see text], being approximately independent of MW. Measurements of the temperature dependence of [Formula: see text] as a function of depth below the free surface indicate the inherent entropic barrier, i.e., the entropy of activation corresponding to [Formula: see text] = 0, has an exponential dependence on the distance from the free surface before reaching the bulk value. This results in [Formula: see text] near the free surface being lower than the bulk. Combining these observations results in a model where the average fluctuation rate of the γ-relaxation has a “double-exponential” depth dependence. This model can explain the depth dependence of [Formula: see text] in polystyrene films. The characteristic length of enhanced dynamics is ∼6 nm and approximately independent of MW near room temperature.

Unraveling Sequence Effect on Glass Transition Temperatures of Discrete Unconjugated Oligomers

Sequence plays a critical role in enabling unique properties and functions of natural biomolecules, which has promoted the rapid advancement of synthetic sequence-defined polymers in recent decades. Particularly, investigation of short chain sequence-defined oligomers (also called discrete oligomers) on their properties has become a hot topic. However, most studies have focused on discrete oligomers with conjugated structures. In contrast, unconjugated oligomers remain relatively underexplored. In this study, three pairs of discrete oligomers with the same composition but different sequence for each pair are employed for investigating their glass transition temperatures (T_g s). The resultant T_g s of sequenced oligomers in each pair are found to be significantly different (up to 11.6 °C), attributable to variations in molecular packing as demonstrated by molecular dynamics and density function theory simulations. Intermolecular interaction is demonstrated to have less impact on T_g s than intramolecular interaction. The mechanistic investigation into two model dimers suggests that monomer sequence caused the difference in intramolecular rotational flexibility of the sequenced oligomers. In addition, despite having different monomer sequence and T_g s, the oligomers have very similar solubility parameters, which supports their potential use as effective oligomeric plasticizers to tune the T_g s of bulk polymer materials.

A Dynamically Correlated Network Model for the Collective Dynamics in Glass-Forming Molecular Liquids and Polymers

The non-Arrhenius behavior of segmental dynamics in glass-forming liquids is one of the most profound mysteries in soft matter physics. In this article, we propose a dynamically correlated network (DCN) model to understand the growing behavior of dynamically correlated regions during cooling, which leads to the viscous slowdown of supercooled liquids. The fundamental concept of the model is that the cooperative region of collective motions has a network structure that consists of string-like parts, and networks of various sizes interpenetrate each other. Each segment undergoes dynamical coupling with its neighboring segments via a finite binding energy. Monte Carlo simulations showed that the fractal dimension of the DCNs generated at different temperatures increased and their size distribution became broader with decreasing temperature. The segmental relaxation time was evaluated based on a power law with four different exponents for the activation energy of rearrangement with respect to the DCN size. The results of the present DCN model are consistent with the experimental results for various materials of molecular and polymeric liquids.

Glass transition of ion-containing polymer melts in bulk and thin films

Ion-containing polymers often are good glass formers, and the glass transition temperature is an important parameter to consider for practical applications, which prescribes the working temperature range for different mechanical and dynamic properties. In this work, we present a systematic molecular dynamics simulation study on the coupling of ionic correlations with the glass transition, based on a generic coarse-grained model of ionic polymers. The variation of the glass transition temperature is examined concerning the influence of the electrostatic interaction strength, charge fraction, and charge sequence. The interplay with the film thickness effect is also discussed. Our results reveal a few typical features about the glass transition process that are in qualitative agreement with previous studies, further highlighting the effects of counterion entropy at weak ionic correlations and physical crosslinking of ionic aggregates at strong ionic correlations. Detailed parametric dependencies are displayed, which demonstrate that introducing strong ionic correlations promotes vitrification while adopting a precise charge sequence and applying strong confinement with weak surface affinity reduce the glass transition temperature. Overall, our investigation provides an improved picture towards a comprehensive understanding of the glass transition in ion-containing polymeric systems from a molecular simulation perspective.