Relating dynamic free volume to cooperative relaxation in a glass-forming polymer composite.

There are a variety of complementary descriptions of the temperature dependence of the structural relaxation time τ in glass-forming materials, which we interpret positively as suggesting an underlying unified description. We examine the inter-relation between the string model, an outgrowth of the Adam and Gibbs approach that emphasizes collective particle exchange motion, and the localization model, which emphasizes the volume explored by particles in their caged states, a kind of dynamic "free volume." Each model of liquid dynamics is described by a limited set of parameters that must be interrelated if both descriptions simultaneously describe the relaxation behavior. We pursue the consequences of this idea by performing coarse-grained molecular simulations of polymer melts with additives of variable size and interaction strength with the polymer matrix, thereby significantly altering the relaxation of the composite material. Both the string and localization models describe our relaxation time data well, and a comparison of the model parameters allows us to relate the local caging scale ⟨u2⟩ (the Debye-Waller parameter) to the entropy of activation for molecular rearrangements in the string model, thereby developing a bridge between these seemingly disparate approaches to liquid dynamics.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory.

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

The effect of nanoparticle softness on the interfacial dynamics of a model polymer nanocomposite.

The introduction of soft organic nanoparticles (NPs) into polymer melts has recently expanded the material design space for polymer nanocomposites, compared to traditional nanocomposites that utilize rigid NPs, such as silica, metallic NPs, and other inorganic NPs. Despite advances in the fabrication and characterization of this new class of materials, the effect of NP stiffness on the polymer structure and dynamics has not been systematically investigated. Here, we use molecular dynamics to investigate the segmental dynamics of the polymer interfacial region of isolated NPs of variable stiffness in a polymer matrix. When the NP-polymer interactions are stronger than the polymer-polymer interactions, we find that the slowing of segmental dynamics in the interfacial region is more pronounced for stiff NPs. In contrast, when the NP-polymer interaction strength is smaller than the matrix interaction, the NP stiffness has relatively little impact on the changes in the polymer interfacial dynamics. We also find that the segmental relaxation time τα of segments in the NP interfacial region changes from values lower than to higher than the bulk material when the NP-polymer interaction strength is increased beyond a "critical" strength, reminiscent of a binding-unbinding transition. Both the NP stiffness and the polymer-surface interaction strength can thus greatly influence the relative segmental relaxation and interfacial mobility in comparison to the bulk material.

Reactive Molecular Dynamics Simulations of the Depolymerization of Polyethylene Using Graphene-Oxide-Supported Platinum Nanoparticles.

While plastic materials offer many benefits to society, the slow degradation and difficulty in recycling plastics raise important environmental and sustainability concerns. Traditional recycling efforts often lead to materials with inferior properties and correspondingly lower value, making them uneconomical to recycle. Recent efforts have shown promising chemical pathways for converting plastic materials into a wide range of value-added products, feedstocks or monomers. This is commonly referred to as "chemical recycling". Here, we use reactive molecular dynamics (MD) simulations to study the catalytic process of depolymerization of polyethylene (PE) using platinum (Pt) nanoparticles (NPs) in comparison to PE pyrolysis (thermal degradation). We apply a simple kinetic model to our MD results for the catalytic reaction rate as a function of temperature, from which we obtain the activation energy of the reaction, which shows the that the Pt NPs reduce the barrier for depolymerization. We further evaluate the molecular mass distribution of the reaction products to gain insight into the influence of the Pt NPs on reaction selectivity. Our results demonstrate the potential for the reactive MD method to help the design of recycling approaches for polymer materials.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films.

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH0 and entropy ΔS0 as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH0 in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u2(z)-3/2, where u2(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH0(z) and that ΔS0(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

Detecting bound polymer layers in attractive polymer-nanoparticle hybrids.

When polymer-nanoparticle (NP) attractions are sufficiently strong, a bound polymer layer with a distinct dynamic signature spontaneously forms at the NP interface. A similar phenomenon occurs near a fixed attractive substrate for thin polymer films. While our previous simulations fixed the NPs to examine the dilute limit, here, we allow the NP to move. Our goal is to investigate how NP mobility affects the signature of the bound layer. For small NPs that are relatively mobile, the bound layer is slaved to the motion of the NP, and the signature of the bound layer relaxation in the intermediate scattering function essentially disappears. The slow relaxation of the bound layer can be recovered when the scattering function is measured in the NP reference frame, but this process would be challenging to implement in experimental systems with multiple NPs. Instead, we use the counterintuitive result that the NP mass affects its mobility in the nanoscale limit, along with the more expected result that the bound layer increases the effective NP mass, to suggest that the signature of the bound polymer manifests as a change in NP diffusivity. These findings allow us to rationalize and quantitatively understand the results of recent experiments focused on measuring NP diffusivity with either physically adsorbed or chemically end-grafted chains.

Explaining the Sensitivity of Polymer Segmental Relaxation to Additive Size Based on the Localization Model.

We use molecular simulations to examine how the dynamics of a coarse-grained polymer melt are altered by additives of variable size and interaction strength with the polymer matrix. The effect of diluent size σ on polymer dynamics changes significantly when its size is comparable to the polymer segment size. For each σ, we show that the localization model (LM) quantitatively describes the dependence of the segmental relaxation time τ on temperature T in terms of dynamic free volume, quantified by the Debye-Waller factor ⟨u^{2}⟩. Within this model, we show that the additive size alone controls the functional form of the T dependence. The LM parameters reach asymptotic values when the diluent size exceeds the monomer size, converging to a limit applicable to macroscopic interfaces.

Predictive relation for the α-relaxation time of a coarse-grained polymer melt under steady shear.

We examine the influence of steady shear on structural relaxation in a simulated coarse-grained unentangled polymer melt over a wide range of temperature and shear rates. Shear is found to progressively suppress the α-relaxation process observed in the intermediate scattering function, leading ultimately to a purely inertially dominated ß-relaxation at high shear rates, a trend similar to increasing temperature. On the basis of a scaling argument emphasizing dynamic heterogeneity in cooled liquids and its alteration under material deformation, we deduce and validate a parameter-free scaling relation for both the structural relaxation time τα from the intermediate scattering function and the "stretching exponent" ß quantifying the extent of dynamic heterogeneity over the entire range of temperatures and shear rates that we can simulate.

Reconciling computational and experimental trends in the temperature dependence of the interfacial mobility of polymer films.

Many measurements have indicated that thin polymer films in their glass state exhibit a mobile interfacial layer that grows in thickness upon heating, while some measurements indicate the opposite trend. Moreover, simulations and limited measurements on glass-forming liquids at temperatures above the glass transition temperature Tg exhibit a growing interfacial mobility scale ξ upon cooling. To better understand these seemingly contradictory trends, we perform molecular dynamics simulations over a temperature regime for which our simulated polymer film enters a non-equilibrium glassy state and find that the relaxation time τα within the film interior, relative to the polymer-air interfacial layer, exhibits a maximum near the computational Tg. Correspondingly, we also observe that the interfacial mobility length scale exhibits a maximum near Tg, explaining the apparent reversal in the temperature dependence of this scale between the glass and liquid states. We show that the non-monotonic variation of ξ and the relative interfacial mobility to the film interior arise qualitatively from a non-monotonic variation of the gradient of the effective activation free energy of the film; we then obtain a quantitative description of this phenomenon by introducing a phenomenological model that describes the relaxation time layer-by-layer in the film for a temperature range both above and below Tg of the film as a whole. This analysis reveals that the non-monotonic trend in the relative interfacial mobility and ξ both arise primarily from the distinctive temperature dependence of relaxation in the interfacial layer, which apparently remains in local equilibrium over the whole temperature range investigated.

Dynamic heterogeneity and collective motion in star polymer melts.

While glass formation of linear chain polymer melts has widely been explored, comparatively little is known about glass formation in star polymer melts. We study the segmental dynamics of star polymer melts via molecular dynamics simulations and examine the cooperative nature of segmental motion in star melts. In particular, we quantify how the molecular architecture of star polymers, i.e., the number of arms and the length of those arms, affects the glass transition temperature Tg, the non-Gaussian nature of molecular displacements, the collective string-like motion of monomers, and the role of chain connectivity in the cooperative motion. Although varying the number of arms f and the molecular mass Ma of the star arms can significantly influence the average star molecular shape, all our relaxation data can be quantitatively described in a unified way by the string model of glass formation, an activated transport model that derives from the Adam-Gibbs model, where the degree of cooperative motion is identified with the average length L of string-like particle exchange motions observed in our simulations. Previous work has shown the consistency of the string model with simulations of linear polymers at constant volume and constant pressure, as well as for thin supported polymer films and nanocomposites with variable polymer-surface interactions, where there are likewise large mobility gradients as in the star polymer melts studied in the present paper.

What does the instantaneous normal mode spectrum tell us about dynamical heterogeneity in glass-forming fluids?

We examine the instantaneous normal mode spectrum of model metallic and polymeric glass-forming liquids. We focus on the localized modes in the unstable part of the spectrum [unstable localized (UL) modes] and find that the particles making the dominant contribution to the participation ratio form clusters that grow upon cooling in a fashion similar to the dynamical heterogeneity in glass-forming fluids, i.e., highly mobile (or immobile) particles form clusters that grow upon cooling; however, a comparison of the UL mode clusters to the mobile and immobile particle clusters indicates that they are distinct entities. We also show that the cluster size provides an alternate method to distinguish localized and delocalized modes, offering a significant practical advantage over the finite-size scaling approach. We examine the trajectories of particles contributing most to the UL modes and find that they have a slightly enhanced mobility compared to the average, and we determine a characteristic time quantifying the persistence time of this excess mobility. This time scale is proportional to the structural relaxation time τα of the fluid, consistent with a prediction by Zwanzig [Phys. Rev. 156, 190 (1967)] for the lifetime of collective excitations in cooled liquids. Evidently, these collective excitations serve to facilitate relaxation but do not actually participate in the motion associated with barrier crossing events governing activated transport. They also serve as a possible concrete realization of the "facilitation" clusters postulated in previous modeling of glass-forming liquids.

The interfacial zone in thin polymer films and around nanoparticles in polymer nanocomposites.

We perform coarse-grained simulations of model unentangled polymer materials to quantify the range over which interfaces alter the structure and dynamics in the vicinity of the interface. We study the interfacial zone around nanoparticles (NPs) in model polymer-NP composites with variable NP diameter, as well as the interfacial zone at the solid substrate and free surface of thin supported polymer films. These interfaces alter both the segmental packing and mobility in an interfacial zone. Variable NP size allows us to gain insight into the effect of boundary curvature, where the film is the limit of zero curvature. We find that the scale for perturbations of the density is relatively small and decreases on cooling for all cases. In other words, the interfaces become more sharply defined on cooling, as naively expected. In contrast, the interfacial mobility scale ξ for both NPs and supported films increases on cooling and is on the order of a few nanometers, regardless of the polymer-interfacial interaction strength. Additionally, the dynamical interfacial scale of the film substrate is consistent with a limiting value for polymer-NP composites as the NP size grows. These findings are based on a simple quantitative model to describe the distance dependence of relaxation that should be applicable to many interfacial polymer materials.

State variables for glasses: The case of amorphous ice.

Glasses are out-of-equilibrium systems whose state cannot be uniquely defined by the usual set of equilibrium state variables. Here, we seek to identify an expanded set of variables that uniquely define the state of a glass. The potential energy landscape (PEL) formalism is a useful approach within statistical mechanics to describe supercooled liquids and glasses. We use the PEL formalism and computer simulations to study the transformations between low-density amorphous ice (LDA) and high-density amorphous ice (HDA). We employ the ST2 water model, which exhibits an abrupt first-order-like phase transition from LDA to HDA, similar to that observed in experiments. We prepare a number of distinct samples of both LDA and HDA that have completely different preparation histories. We then study the evolution of these LDA and HDA samples during compression and decompression at temperatures sufficiently low that annealing is absent and also during heating. We find that the evolution of each glass sample, during compression/decompression or heating, is uniquely determined by six macroscopic properties of the initial glass sample. These six quantities consist of three conventional thermodynamic state variables, the number of molecules N, the system volume V, and the temperature T, as well as three properties of the PEL, the inherent structure (IS) energy EIS, the IS pressure PIS, and the average curvature of the PEL at the IS SIS. In other words, (N,V,T,EIS,PIS,SIS) are state variables that define the glass state in the case of amorphous ice. An interpretation of our results in terms of the PEL formalism is provided. Since the behavior of water in the glassy state is more complex than for most substances, our results suggest that these six state variables may be applicable to amorphous solids in general and that there may be situations in which fewer than six variables would be sufficient to define the state of a glass.

Collective Motion in the Interfacial and Interior Regions of Supported Polymer Films and Its Relation to Relaxation.

To understand the role of collective motion in the often large changes in interfacial molecular mobility observed in polymer films, we investigate the extent of collective motion in the interfacial regions of a thin supported polymer film and within the film interior by molecular dynamics simulation. Contrary to commonly stated expectations, we find that the extent of collective motion, as quantified by string-like molecular exchange motion, is similar in magnitude in the polymer-air interfacial layer as the film interior and distinct from the bulk material. This finding is consistent with Adam-Gibbs description of the segmental dynamics within mesoscopic film regions, where the extent of collective motion is related to the configurational entropy of the film as a whole rather than a locally defined extent of collective motion or configurational entropy.

The Stability of a Nanoparticle Diamond Lattice Linked by DNA.

The functionalization of nanoparticles (NPs) with DNA has proven to be an effective strategy for self-assembly of NPs into superlattices with a broad range of lattice symmetries. By combining this strategy with the DNA origami approach, the possible lattice structures have been expanded to include the cubic diamond lattice. This symmetry is of particular interest, both due to the inherent synthesis challenges, as well as the potential valuable optical properties, including a complete band-gap. Using these lattices in functional devices requires a robust and stable lattice. Here, we use molecular simulations to investigate how NP size and DNA stiffness affect the structure, stability, and crystallite shape of NP superlattices with diamond symmetry. We use the Wulff construction method to predict the equilibrium crystallite shape of the cubic diamond lattice. We find that, due to reorientation of surface particles, it is possible to create bonds at the surface with dangling DNA links on the interior, thereby reducing surface energy. Consequently, the crystallite shape depends on the degree to which such surface reorientation is possible, which is sensitive to DNA stiffness. Further, we determine dependence of the lattice stability on NP size and DNA stiffness by evaluating relative Gibbs free energy. We find that the free energy is dominated by the entropic component. Increasing NP size or DNA stiffness increases free energy, and thus decreases the relative stability of lattices. On the other hand, increasing DNA stiffness results in a more precisely defined lattice structure. Thus, there is a trade off between structure and stability of the lattice. Our findings should assist experimental design for controlling lattice stability and crystallite shape.

Diminishing Interfacial Effects with Decreasing Nanoparticle Size in Polymer-Nanoparticle Composites.

Using molecular simulations on model polymer nanocomposites at fixed filler loading, we show that interfacial polymer dynamics are affected less with decreasing nanoparticle (NP) size. However, the glass transition temperature T_{g} changes substantially more for an extremely small NP. The reason for this apparent contradiction is that the mean NP spacing decreases with decreasing particle size. Thus, all polymers are effectively interfacial for sufficiently small NPs, resulting in relatively large T_{g} shifts, even though the interfacial effects are smaller. For larger NPs, interfacial relaxations are substantially slower than the matrix for favorable NP-polymer interactions. The minority "bound" polymer dynamically decouples from the polymer matrix, and we only find small changes in T_{g} relative to that of the bulk polymer for large NPs. These results are used to organize a large body of relevant experimental data, and we propose an apparent universal dependence on the ratio of the face-to-face distance between the NPs and the chain radius of gyration.

Why we need to look beyond the glass transition temperature to characterize the dynamics of thin supported polymer films.

There is significant variation in the reported magnitude and even the sign of [Formula: see text] shifts in thin polymer films with nominally the same chemistry, film thickness, and supporting substrate. The implicit assumption is that methods used to estimate [Formula: see text] in bulk materials are relevant for inferring dynamic changes in thin films. To test the validity of this assumption, we perform molecular simulations of a coarse-grained polymer melt supported on an attractive substrate. As observed in many experiments, we find that [Formula: see text] based on thermodynamic criteria (temperature dependence of film height or enthalpy) decreases with decreasing film thickness, regardless of the polymer-substrate interaction strength ε. In contrast, we find that [Formula: see text] based on a dynamic criterion (relaxation of the dynamic structure factor) also decreases with decreasing thickness when ε is relatively weak, but [Formula: see text] increases when ε exceeds the polymer-polymer interaction strength. We show that these qualitatively different trends in [Formula: see text] reflect differing sensitivities to the mobility gradient across the film. Apparently, the slowly relaxing polymer segments in the substrate region make the largest contribution to the shift of [Formula: see text] in the dynamic measurement, but this part of the film contributes less to the thermodynamic estimate of [Formula: see text] Our results emphasize the limitations of using [Formula: see text] to infer changes in the dynamics of polymer thin films. However, we show that the thermodynamic and dynamic estimates of [Formula: see text] can be combined to predict local changes in [Formula: see text] near the substrate, providing a simple method to infer information about the mobility gradient.

String-like collective motion in the α- and ß-relaxation of a coarse-grained polymer melt.

Relaxation in glass-forming liquids occurs as a multi-stage hierarchical process involving cooperative molecular motion. First, there is a "fast" relaxation process dominated by the inertial motion of the molecules whose amplitude grows upon heating, followed by a longer time α-relaxation process involving both large-scale diffusive molecular motion and momentum diffusion. Our molecular dynamics simulations of a coarse-grained glass-forming polymer melt indicate that the fast, collective motion becomes progressively suppressed upon cooling, necessitating large-scale collective motion by molecular diffusion for the material to relax approaching the glass-transition. In each relaxation regime, the decay of the collective intermediate scattering function occurs through collective particle exchange motions having a similar geometrical form, and quantitative relationships are derived relating the fast "stringlet" collective motion to the larger scale string-like collective motion at longer times, which governs the temperature-dependent activation energies associated with both thermally activated molecular diffusion and momentum diffusion.

Valence, loop formation and universality in self-assembling patchy particles.

Patchy particles have emerged as an attractive model to mimic phase separation and self-assembly of globular proteins solutions, colloidal patchy particles, and molecular fluids where directional interactions are operative. In our previous work, we extensively explored the coupling of directional and isotropic interactions on both the phase separation and self-assembly in a system of patchy particles with five spots. Here, we extend this work to consider different patch valences and isotropic interaction strengths with an emphasis on self-assembly. Although the location of self-assembly transition lines in the temperature-density plane depend on a number of parameters, we find universal behavior of cluster size that is dependent only on the probability of a spot being bound, the patch valence, and the density. Using these principles, we quantify both the mass distribution and the shape for all clusters, as well as clusters containing loops. Following the logical implications of these results, combined with a simplified version of a mean-field theory that incorporates Flory-Stockmayer theory, we find a universal curve for the temperature dependence of cluster mass and a universal curve for the fraction of clusters that contain loops. As the curves are dependent on the particle valence, such results provide a method for parameterizing patchy particle models using experimental data.

Molecular rigidity and enthalpy-entropy compensation in DNA melting.

Enthalpy-entropy compensation (EEC) is observed in diverse molecular binding processes of importance to living systems and manufacturing applications, but this widely occurring phenomenon is not sufficiently understood from a molecular physics standpoint. To gain insight into this fundamental problem, we focus on the melting of double-stranded DNA (dsDNA) since measurements exhibiting EEC are extensive for nucleic acid complexes and existing coarse-grained models of DNA allow us to explore the influence of changes in molecular parameters on the energetic parameters by using molecular dynamics simulations. Previous experimental and computational studies have indicated a correlation between EEC and changes in molecular rigidity in certain binding-unbinding processes, and, correspondingly, we estimate measures of DNA molecular rigidity under a wide range of conditions, along with resultant changes in the enthalpy and entropy of binding. In particular, we consider variations in dsDNA rigidity that arise from changes of intrinsic molecular rigidity such as varying the associative interaction strength between the DNA bases, the length of the DNA chains, and the bending stiffness of the individual DNA chains. We also consider extrinsic changes of molecular rigidity arising from the addition of polymer additives and geometrical confinement of DNA between parallel plates. All our computations confirm EEC and indicate that this phenomenon is indeed highly correlated with changes in molecular rigidity. However, two distinct patterns relating to how DNA rigidity influences the entropy of association emerge from our analysis. Increasing the intrinsic DNA rigidity increases the entropy of binding, but increases in molecular rigidity from external constraints decreases the entropy of binding. EEC arises in numerous synthetic and biological binding processes and we suggest that changes in molecular rigidity might provide a common origin of this ubiquitous phenomenon in the mutual binding and unbinding of complex molecules.