Swelling and growth of polymers, membranes, and sponges

Atomistic Simulations of Polydisperse Lignin Melts Using Simple Polydisperse Residue Input Generator

Understanding the physics of lignin will help rationalize its function in plant cell walls as well as aiding practical applications such as deriving biofuels and bioproducts. Here, we present SPRIG (Simple Polydisperse Residue Input Generator), a program for generating atomic-detail models of random polydisperse lignin copolymer melts i.e., the state most commonly found in nature. Using these models, we use all-atom molecular dynamics (MD) simulations to investigate the conformational and dynamic properties of polydisperse melts representative of switchgrass (Panicum virgatum L.) lignin. Polydispersity, branching and monolignol sequence are found to not affect the calculated glass transition temperature, Tg. The Flory-Huggins scaling parameter for the segmental radius of gyration is 0.42 ± 0.02, indicating that the chains exhibit statistics that lie between a globular chain and an ideal Gaussian chain. Below Tg the atomic mean squared displacements are independent of molecular weight. In contrast, above Tg, they decrease with increasing molecular weight. Therefore, a monodisperse lignin melt is a good approximation to this polydisperse lignin when only static properties are probed, whereas the molecular weight distribution needs to be considered while analyzing lignin dynamics.

Coexistence of Crumpling and Flat Sheet Conformations in Two-Dimensional Polymer Networks: An Understanding of Aggrecan Self-Assembly

We investigate the conformational properties of self-avoiding two-dimensional (2D) ideal polymer networks with tunable mesh sizes as a model of self-assembled structures formed by aggrecan. Polymer networks having few branching points and large enough mesh tend to crumple, resulting in a fractal dimension of d_{f}≈2.7. The flat sheet behavior (d_{f}=2) emerges in 2D polymer networks having more branching points at large length scales; however, it coexists with crumpling conformations at intermediate length scales, a feature found in scattering profiles of aggrecan solutions. Our findings bridge the long-standing gap between theories and simulations of polymer sheets.

Molecular dynamics study of the swelling and osmotic properties of compact nanogel particles

Owing to their great importance in materials science and other fields, we investigate the solution and osmotic properties of uncharged compact nanogel particles over a wide range of solvent quality and particle concentration by molecular dynamics (MD) simulations. We characterize the osmotic pressure by estimating the second and third virial coefficients, and by extension, we identify the θ-point where the second virial coefficient vanishes. Calculations of the structure factor indicate that these particles are similar to macrogels in that the particle-like scattering profile disappears at moderate concentrations. We also find that improving the solvent quality enhances the spatial segmental uniformity, while significant heterogeneous structure arises near the θ-point. Well below the θ-point where the second osmotic virial coefficient vanishes, these heterogeneous structures become less prevalent as the particles tend to collapse. We also investigate the degree of swelling and structure of compact nanogel particles with a variable excluded volume interaction and gel particle concentration. The osmotic modulus and the scaling exponents in good and θ-point conditions of these gels are characteristic of interacting randomly branched polymers, i.e., "lattice animals".

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

Structure and conformational properties of ideal nanogel particles in athermal solutions

We investigate the conformational properties of "ideal" nanogel particles having a lattice network topology by molecular dynamics simulations to quantify the influence of polymer topology on the solution properties of this type of branched molecular architecture. In particular, we calculate the mass scaling of the radius of gyration (Rg), the hydrodynamic radius, as well as the intrinsic viscosity with the variation of the degree of branching, the length of the chains between the branched points, and the average mesh size within these nanogel particles under good solvent conditions. We find competing trends between the molecular characteristics, where an increase in mesh size or degree of branching results in the emergence of particle-like characteristics, while an increase in the chain length enhances linear polymer-like characteristics. This crossover between these limiting behaviors is also apparent in our calculation of the form factor, P(q), for these structures. Specifically, a primary scattering peak emerges, characterizing the overall nanogel particle size. Moreover, a distinct power-law regime emerges in P(q) at length scales larger than the chain size but smaller than Rg of the nanogel particle, and the Rg mass scaling exponent progressively approaches zero as the mesh size increases, the same scaling as for an infinite network of Gaussian chains. The "fuzzy sphere" model does not capture this feature, and we propose an extension to this popular model. These structural features become more pronounced for values of molecular parameters that enhance the localization of the branching segments within the nanogel particle.

Dynamic heterogeneity, cooperative motion, and Johari-Goldstein [Formula: see text]-relaxation in a metallic glass-forming material exhibiting a fragile-to-strong transition

We investigate the Johari-Goldstein (JG) [Formula: see text]-relaxation process in a model metallic glass-forming (GF) material ([Formula: see text]), previously studied extensively by both frequency-dependent mechanical measurements and simulation studies devoted to equilibrium properties, by molecular dynamics simulations based on validated and optimized interatomic potentials with the primary aim of better understanding the nature of this universal relaxation process from a dynamic heterogeneity (DH) perspective. The present relatively low temperature and long-time simulations reveal a direct correspondence between the JG [Formula: see text]-relaxation time [Formula: see text] and the lifetime of the mobile particle clusters [Formula: see text], defined as in previous DH studies, a relationship dual to the corresponding previously observed relationship between the [Formula: see text]-relaxation time [Formula: see text] and the lifetime of immobile particle clusters [Formula: see text]. Moreover, we find that the average diffusion coefficient D nearly coincides with [Formula: see text] of the smaller atomic species (Al) and that the 'hopping time' associated with D coincides with [Formula: see text] to within numerical uncertainty, both trends being in accord with experimental studies. This indicates that the JG [Formula: see text]-relaxation is dominated by the smaller atomic species and the observation of a direct relation between this relaxation process and rate of molecular diffusion in GF materials at low temperatures where the JG [Formula: see text]-relaxation becomes the prevalent mode of structural relaxation. As an unanticipated aspect of our study, we find that [Formula: see text] exhibits fragile-to-strong (FS) glass formation, as found in many other metallic GF liquids, but this fact does not greatly alter the geometrical nature of DH in this material and the relation of DH to dynamical properties. On the other hand, the temperature dependence of the DH and dynamical properties, such as the structural relaxation time, can be significantly altered from 'ordinary' GF liquids.

A comparative study of thermodynamic, conformational, and structural properties of bottlebrush with star and ring polymer melts

Thermodynamic, conformational, and structural properties of bottlebrush polymer melts are investigated with molecular dynamics simulations and compared to linear, regular star, and unknotted ring polymer melts to gauge the influence of molecular topology on polymer melt properties. We focus on the variation of the backbone chain length, the grafting density along the backbone, and the length of the side chains at different temperatures above the melt glass transition temperature. Based on these comparisons, we find that the segmental density, isothermal compressibility, and isobaric thermal expansion of bottlebrush melts are quantitatively similar to unknotted ring polymer melts and star polymer melts having a moderate number ( f = 5 to 6) of arms. These similarities extend to the mass scaling of the chain radius of gyration. Our results together indicate that the configurational properties of bottlebrush polymers in their melt state are more similar to randomly branched polymers than linear polymer chains. We also find that the average shape of bottlebrush polymers having short backbone chains with respect to the side chain length is also rather similar to the unknotted ring and moderately branched star polymers in their melt state. As a general trend, the molecular shape of bottlebrush polymers becomes more spherically symmetric when the length of the side chains has a commensurate length as the backbone chain. Finally, we calculate the partial static structure factor of the backbone segments and we find the emergence of a peak at the length scales that characterizes the average distance between the backbone chains. This peak is absent when we calculate the full static structure factor. We characterize the scaling of this peak with parameters characterizing the bottlebrush molecular architecture to aid in the experimental characterization of these molecules by neutron scattering.

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.

Polymer Nanosheets from Supramolecular Assemblies of Conjugated Linoleic Acid-High Surface Area Adsorbents from Renewable Materials

We present a strategy for robustly cross-linking self-assembled lamellar mesophases made from plant-derived materials to generate polymer nanosheets decorated with a high density of functional groups. We formulate a supramoleclar complex by hydrogen-bonding conjugated linoleic acid moieties to a structure-directing tribasic aromatic core. The resulting constructs self-assemble into a thermotropic lamellar mesophase. Photo-cross-linking the mesophase with the aid of an acrylate cross-linker yields a polymeric material with high-fidelity retention of the lamellar mesophase structure. Transmission electron microscopy images demonstrate the preservation of the large area, highly ordered layered nanostructures in the polymer. Subsequent extraction of the tribasic core and neutralization of the carboxyl groups by NaOH result in exfoliation of polymer nanosheets with a uniform thickness of ∼3 nm. The nanosheets have a large specific area of ∼800 m²/g, are decorated by negatively charged carboxylate groups at a density of 4 nm^-2, and exhibit the ability to readily adsorb positively charged colloidal particles. The strategy as presented combines supramolecular self-assembly with the use of renewable or sustainably derived materials in a scalable manner. The resulting nanosheets have potential for use as adsorbents and, with further development, rheology modifiers.

Self-assembly of polymer-grafted nanoparticles in solvent-free conditions

Grafting of polymer chains onto the surface of spherical nanoparticles leads to a hybrid type of fluid that exhibits properties of both particle suspensions and melts of star polymers-these properties being controlled by the relative dimensions of the grafted polymer chains to the nanoparticle diameter, D, and the number of the number of chains grafted on the nanoparticle surface, f. While polymer-grafted nanoparticles (GNP) of this kind typically have a spherical average shape after grafting even a moderate number of chains, their instantaneous molecular shape can fluctuate significantly due to the deformation of the grafted chains. Both simulations and measurements have previously revealed that these "conformationally polarizable" particles can exhibit self-assembly into large scale polymeric structures in both solution and in polymer melts, and we simulate polymer-grafted nanoparticles with D and temperature (T) variations without a dispersing solvent to better understand the nature of this self-assembly process. We observe a reversible self-assembly into linear and branched dynamic GNP structures, where the extent of the assembly and geometry depend on D and T, and we constructed a map capturing the GNP structural behavior with D and T variations. Since the shape of the GNPs appeared to be correlated with the occurrence of the GNP self-assembly, we quantified the average shape and a measure of shape fluctuations to better understand how molecular shape influences their propensity to self-assemble into different structural forms. Based on this framework, we describe the clustering process of the GNPs as an equilibrium polymerization phenomenon and we calculate the order parameter governing the dynamic clustering behavior of GNPs, the average mass of the clusters, size distribution, and the apparent fractal dimension of the clusters.

Coupling of isotropic and directional interactions and its effect on phase separation and self-assembly

The interactions of molecules and particles in solution often involve an interplay between isotropic and highly directional interactions that lead to a mutual coupling of phase separation and self-assembly. This situation arises, for example, in proteins interacting through hydrophobic and charged patch regions on their surface and in nanoparticles with grafted polymer chains, such as DNA. As a minimal model of complex fluids exhibiting this interaction coupling, we investigate spherical particles having an isotropic interaction and a constellation of five attractive patches on the particle's surface. Monte Carlo simulations and mean-field calculations of the phase boundaries of this model depend strongly on the relative strength of the isotropic and patch potentials, where we surprisingly find that analytic mean-field predictions become increasingly accurate as the directional interactions become increasingly predominant. We quantitatively account for this effect by noting that the effective interaction range increases with increasing relative directional to isotropic interaction strength. We also identify thermodynamic transition lines associated with self-assembly, extract the entropy and energy of association, and characterize the resulting cluster properties obtained from simulations using percolation scaling theory and Flory-Stockmayer mean-field theory. We find that the fractal dimension and cluster size distribution are consistent with those of lattice animals, i.e., randomly branched polymers swollen by excluded volume interactions. We also identify a universal functional form for the average molecular weight and a nearly universal functional form for a scaling parameter characterizing the cluster size distribution. Since the formation of branched clusters at equilibrium is a common phenomenon in nature, we detail how our analysis can be used in experimental characterization of such associating fluids.

Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path-integral, and finite-element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi-conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self-avoiding worm-like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex-shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (αE, αM) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient σ in the conductive and insulating particle limits, which are required to estimate σ in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for αE and αM that should be useful in materials design and characterization applications.

The relationship of dynamical heterogeneity to the Adam-Gibbs and random first-order transition theories of glass formation

We carefully examine common measures of dynamical heterogeneity for a model polymer melt and test how these scales compare with those hypothesized by the Adam and Gibbs (AG) and random first-order transition (RFOT) theories of relaxation in glass-forming liquids. To this end, we first analyze clusters of highly mobile particles, the string-like collective motion of these mobile particles, and clusters of relative low mobility. We show that the time scale of the high-mobility clusters and strings is associated with a diffusive time scale, while the low-mobility particles' time scale relates to a structural relaxation time. The difference of the characteristic times for the high- and low-mobility particles naturally explains the well-known decoupling of diffusion and structural relaxation time scales. Despite the inherent difference of dynamics between high- and low-mobility particles, we find a high degree of similarity in the geometrical structure of these particle clusters. In particular, we show that the fractal dimensions of these clusters are consistent with those of swollen branched polymers or branched polymers with screened excluded-volume interactions, corresponding to lattice animals and percolation clusters, respectively. In contrast, the fractal dimension of the strings crosses over from that of self-avoiding walks for small strings, to simple random walks for longer, more strongly interacting, strings, corresponding to flexible polymers with screened excluded-volume interactions. We examine the appropriateness of identifying the size scales of either mobile particle clusters or strings with the size of cooperatively rearranging regions (CRR) in the AG and RFOT theories. We find that the string size appears to be the most consistent measure of CRR for both the AG and RFOT models. Identifying strings or clusters with the "mosaic" length of the RFOT model relaxes the conventional assumption that the "entropic droplets" are compact. We also confirm the validity of the entropy formulation of the AG theory, constraining the exponent values of the RFOT theory. This constraint, together with the analysis of size scales, enables us to estimate the characteristic exponents of RFOT.

Concentration Dependence of Ring Polymer Conformations from Monte Carlo Simulations

The concentration dependence of the conformations of ring polymers is investigated by lattice Monte Carlo simulations and compared with that of linear polymers. The relative radii of gyration of linear polymers follow a universal master curve as a function of the scaled concentration for various chain lengths, with a scaling relationship ⟨R_g²⟩ ∼ ϕ^-0.25, which is consistent with scaling theory and neutron scattering experiments. Ring polymers of different lengths also follow a universal behavior with a broad crossover to a scaling behavior ⟨R_g²⟩ ∼ ϕ^-0.59 for long chains. The scaling relationship between the concentration dependence and the chain-length dependence of the radius of gyration implies ⟨R_g²⟩ ∼ N^0.72, indicating highly collapsed conformations for long-chain ring polymers in the melt.

Number of arm selection in two-dimensional diffusion processes

We introduce an algorithm to generate two-dimensional diffusion-limited star-branched aggregates (DLSA) attaching bi-functional monomers successively to a central colloidal particle with any desired number of reactive sites. The proposed algorithm produces star-shaped aggregates that grow forever and show a power law polydispersity in the chemical length of the arms near the central colloid. More interestingly, it gives rise to a number of arm selection consisting in that only a small number of arms (around five) define the final structure at relatively large distances from the central colloid, independently of the initial number of reactive sites and the size of the central colloid. We characterize the structure of the aggregates by means of the particle-particle correlation function, analyze its scaling properties and obtain the fractal dimension.

Multiscale mode dynamics of a tethered membrane

Stochastic dynamics of a tethered membrane with a bond-fluctuating coarse-grained Monte Carlo simulation shows, in addition to diffusion, nondiffusive behavior sensitive to the type of membrane, its size, and quality of the solvent. Motion of the membrane's center node is described by the variation of the mean-square displacement (R{n}{2}) with time step (t) , i.e., R{n}{2} proportional, variantt{2nu} with the exponent nu approximately 18-16 in the short time followed by subdiffusive power laws (i.e., nu approximately 15,110 ) in the intermediate time regimes before reaching diffusion nu=1. The crossover between in-plane wrinkle modes is identified from the segmental (node) motion of the membrane.

Symmetry, equivalence, and molecular self-assembly

Molecular self-assembly at equilibrium is fundamental to the fields of biological self-organization, the development of novel environmentally responsive polymeric materials, and nanofabrication. Our approach to understanding the principles governing this process is inspired by existing models and measurements for the self-assembly of actin, tubulin, and the ubiquitous icosahedral shell structures of viral capsids. We introduce a family of simple potentials that give rise to the self-assembly of linear polymeric, random surface ("membrane"), tubular ("nanotube"), and hollow icosahedral structures that are similar in many respects to their biological counterparts. The potentials involve equivalent particles and an interplay between directional (dipolar, multipolar) and short-range (van der Waals) interactions. Specifically, we find that the dipolar potential, having a continuous rotational symmetry about the dipolar axis, gives rise to chain formation, while particles with multipolar potentials, having discrete rotational symmetries (square quadrupole or triangular ring of dipoles or "hexapole"), lead to the self-assembly of open sheet, nanotube, and hollow icosahedral geometries. These changes in the geometry of self-assembly are accompanied by significant changes in the kinetics of the organization.