Energy Formulation for Infinite Structures: Order Parameter for Percolation, Critical Bonds, and Power-Law Scaling of Contact-Based Transport.

Investigating heterogeneous materials' microstructure, often simulated using periodic images, is crucial for understanding their physical traits. We propose a generic spring-based representation for periodic two-component structures. The equilibrium energy in this framework serves as an order parameter, offering an analytical expression for wrapping and introducing the concept of critical bonds. We show that these minimum bonds for depercolation can be efficiently detected. The number of critical bonds scales with system size, accurately capturing contact-based transport's scaling. This approach holds potential to analyze functional robustness of networks.

Ionic poly(dimethylsiloxane)-silica nanocomposites: Dispersion and self-healing.

Abstract: Poly(dimethylsiloxane) (PDMS)-based nanocomposites have attracted increasing attention due to their inherent outstanding properties. Nevertheless, the realization of high levels of dispersion of nanosilicas in PDMS represents a challenge arising from the poor compatibility between the two components. Herein, we explore the use of ionic interactions located at the interface between silica and a PDMS matrix by combining anionic sulfonate-functionalized silica and cationic ammonium-functionalized PDMS. A library of ionic PDMS nanocomposites was synthesized and characterized to highlight the impact of charge location, density, and molecular weight of ionic PDMS polymers on the dispersion of nanosilicas and the resulting mechanical reinforcement. The use of reversible ionic interactions at the interface of nanoparticles-polymer matrix enables the healing of scratches applied to the surface of the nanocomposites. Molecular dynamics simulations were used to estimate the survival probability of ionic cross-links between nanoparticles and the polymer matrix, revealing a dependence on polymer charge density. Impact statement: Poly(dimethylsiloxane) (PDMS) has been widely used in diverse applications due to its inherent attractive and multifunctional properties including optical transparency, high flexibility, and biocompatibility. The combination of such properties in a single polymer matrix has paved the way toward a wide range of applications in sensors, electronics, and biomedical devices. As a liquid at room temperature, the cross-linking of the PDMS turns the system into a mechanically stable elastomer for several applications. Nanofillers have served as a reinforcing agent to design PDMS nanocomposites. However, due to significant incompatibility between silica and the PDMS matrix, the dispersion of nanosilica fillers has been challenging. One of the existing strategies to improve nanoparticle dispersion consists of grafting oppositely charged ionic functional groups to the nanoparticle surface and the polymer matrix, respectively, creating nanoparticle ionic materials. Here, this approach has been explored further to improve the dispersion of nanosilicas in a PDMS matrix. The designed ionic PDMS nanocomposites exhibit self-healing properties due to the reversible nature of ionic interactions. The developed synthetic approach can be transferred to other kinds of inorganic nanoparticles dispersed in a PDMS matrix, where dispersion at the nanometer scale is a prerequisite for specific applications such as encapsulants for light-emitting diodes (LEDs). Supplementary information: The online version contains supplementary material available at 10.1557/s43577-022-00346-x.

Transport and nonequilibrium phase transitions in polygonal urn models.

We study the deterministic dynamics of N point particles moving at a constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback control on the particles, inverting the horizontal component of their velocities when their number in the channel exceeds a fixed threshold. Such a bounce-back mechanism is non-dissipative: it preserves volumes in phase space. An additional passive channel closes the billiard table forming a circuit in which a stationary current may flow. Under specific constraints on the geometry and on the initial conditions, the large N limit allows nonequilibrium phase transitions between homogeneous and inhomogeneous phases. The role of ergodicity in making a probabilistic theory applicable is discussed for both rational and irrational urns. The theoretical predictions are compared with the numerical simulation results. Connections with the dynamics of feedback-controlled biological systems are highlighted.

Insights from modeling into structure, entanglements, and dynamics in attractive polymer nanocomposites.

Conformations, entanglements and dynamics in attractive polymer nanocomposites are investigated in this work by means of coarse-grained molecular dynamics simulation, for both weak and strong confinements, in the presence of nanoparticles (NPs) at NP volume fractions φ up to 60%. We show that the behavior of the apparent tube diameter dapp in such nanocomposites can be greatly different from nanocomposites with nonattractive interactions. We find that this effect originates, based on a mean field argument, from the geometric confinement length dgeo at strong confinement (large φ) and not from the bound polymer layer on NPs (interparticle distance ID <2Rg) as proposed recently based on experimental measurements. Close to the NP surface, the entangled polymer mobility is reduced in attractive nanocomposites but still faster than the NP mobility for volume fractions beyond 20%. Furthermore, entangled polymer dynamics is hindered dramatically by the strong confinement created by NPs. For the first time using simulations, we show that the entangled polymer conformation, characterized by the polymer radius of gyration Rg and form factor, remains basically unperturbed by the presence of NPs up to the highest volume fractions studied, in agreement with various experiments on attractive nanocomposites. As a side-result we demonstrate that the loose concept of ID can be made a microscopically well defined quantity using the mean pore size of the NP arrangement.

Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?

An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible-infectious-recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.

Unified Analytic Expressions for the Entanglement Length, Tube Diameter, and Plateau Modulus of Polymer Melts.

By combining molecular dynamics simulations and topological analyses with scaling arguments, we obtain analytic expressions that quantitatively predict the entanglement length N_{e}, the plateau modulus G, and the tube diameter a in melts that span the entire range of chain stiffnesses for which systems remain isotropic. Our expressions resolve conflicts between previous scaling predictions for the loosely entangled [Lin-Noolandi, Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{3}], semiflexible [Edwards-de Gennes: Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{2}], and tightly entangled [Morse, Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{1+ϵ}] regimes, where ℓ_{K} and p are, respectively, the Kuhn and packing lengths. We also find that maximal entanglement (minimal N_{e}) coincides with the onset of local nematic order.

Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation.

The intriguing properties of magnetic nanoparticles have sparked a growing number of theoretical studies as well as practical applications. Here, we provide the first comprehensive study of the influence of interactions on the two main relaxation mechanisms: internal (Néel) and Brownian relaxation. While non-interacting magnetic nanoparticles show Debye behavior with an effective relaxation time, many authors use this model also for the interacting case. Since Néel relaxation is typically a thermally activated process on times scales that are many orders of magnitude larger than the underlying micromagnetic times, we use extensive computer simulations employing a Brownian dynamics/Monte-Carlo algorithm to show that dipolar interactions lead to significant deviations from the Debye behavior. We find that Néel and Brownian relaxation can be considered as independent processes for short enough times until dipolar interactions lead to a coupling of these mechanisms, making the interpretation more difficult. We provide mean-field arguments that describe these short and long-time, effective relaxation times well for weak up to moderate interaction strengths. Our findings about the coupling of Brownian and Néel process and the effective relaxation time provide an important theoretical insight that will have also important consequences for the interpretation of magnetic susceptibility measurements and magnetorelaxometry analysis.

Structure Elucidation of 2D Polymer Monolayers Based on Crystallization Estimates Derived from Tip-Enhanced Raman Spectroscopy (TERS) Polymerization Conversion Data.

Structural elucidation of 2D polymer monolayers proving long-range order is a challenge that limits the pace in which this recent field of polymer chemistry and of synthetic 2D materials develops. To overcome this bottleneck, we here present a method in which tip-enhanced Raman spectroscopy is combined with a random growth crystallization model to obtain global features from local spectroscopic information. Concretely, we prove the nature and determine the conversion number X of the cross-links for two new 2D homopolymers and one (of three) new 2D copolymers. Assuming random and in-plane growth, our model results in crystallinity degrees of 93.1% to 99.7% and mean radii of defect-free crystalline areas of 3-15 nm for conversion numbers of 84% < X < 98%. Thus, we provide strong evidence for the synthetic monolayer 2D materials presented that they qualify as 2D polymers and are therefore perfectly suited for in-depth studies both in a more fundamental direction as well as toward application. This example shows how our method can affect current research on covalent sheets.

Relaxation Behavior and Nonlinear Surface Rheology of PEO-PPO-PEO Triblock Copolymers at the Air-Water Interface.

Surface dilatational viscoelasticity of adsorbed layers of pluronics triblock copolymers at the air-water interface was measured using the oscillating barrier technique. The effect of molecular architecture and concentration on surface viscoelasticity was explored for two different types of pluronics with different degrees of hydrophobicity, Pluronic F-108 (Mw ≈ 14 600 g/mol) and Pluronic P-123 (Mw ≈ 5800 g/mol), the former exhibiting a larger hydrophilic to hydrophobic block length ratio. Frequency sweeps in the linear regime suggested that interfacial films of F-108 have higher surface limiting elasticity and larger in-plane and out-of-plane relaxation times at the same bulk concentration (the former possibly related to in-plane microstructure rearrangements, the latter to surface/bulk diffusion). Increasing the bulk concentration of pluronics from 1 to 100 µM led to a decrease in both in- and out-of-plane relaxation times. Large amplitude oscillatory dilatation (LAOD) tests were performed to capture nonlinear behavior of these interfacial films by means of elastic and viscous Lissajous plots. Nonlinearities in elastic responses were quantified through calculation of the strain-stiffening indices in extension SE and compression SC. Both pluronics exhibited strain softening in extension. In compression, P-123 showed strain-hardening and F-108 displayed a relatively linear response. Apparent strain hardening in extension was observed for the P-123 adsorbed film, at high strain, at a bulk concentration of 100 µM. However, at these strains, the response was dominated by the viscous contribution and calculation of strain rate-thickening factors in extension and compression showed that the overall response was strain rate-thinning in extension and strain rate-thickening in compression.

Can one determine the density of an individual synthetic macromolecule?

Dendronized polymers (DPs) are large and compact main-chain linear polymers with a cylindrical shape and cross-sectional diameters of up to ∼15 nm. They are therefore considered molecular objects, and it was of interest whether given their experimentally accessible, well-defined dimensions, the density of individual DPs could be determined. We present measurements on individual, deposited DP chains, providing molecular dimensions from scanning and transmission electron microscopy and mass-per-length values from quantitative scanning transmission electron microscopy. These results are compared with density values obtained from small-angle X-ray scattering on annealed bulk specimen and with classical envelope density measurements, obtained using hydrostatic weighing or a density gradient column. The samples investigated comprise a series of DPs with side groups of dendritic generations g = 1-8. The key findings are a very large spread of the density values over all samples and methods, and a consistent increase of densities with g over all methods. While this work highlights the advantages and limitations of the applied methods, it does not provide a conclusive answer to the question of which method(s) to use for the determination of densities of individual molecular objects. We are nevertheless confident that these first attempts to answer this challenging question will stimulate more research into this important aspect of polymer and soft matter science.

Gas-liquid phase equilibrium of a model Langmuir monolayer captured by a multiscale approach.

The gas-liquid expanded phase transition of a Langmuir monolayer happens at very low surface concentrations which makes this phenomenon extremely expensive to explore in finite three-dimensional (3D) atomistic simulations. Starting with a 3D model reference system of amphiphilic surfactants at a 2D vapor-liquid interface, we apply our recently developed approach (Phys. Chem. Chem. Phys., 2018, 20, 16238) and map the entire system to an effective 2D system of surfactant center-of-masses projected onto the interface plane. The coarse-grained interaction potential obtained via a force-matching scheme from the 3D simulations is then used to predict the 2D gas-liquid phase equilibrium of the corresponding Langmuir monolayer. Monte Carlo simulations in the Gibbs ensemble are performed to calculate areal densities, chemical potentials and surface pressures of the gaseous and liquid coexisting phases within the monolayer. We compare these simulations to the results of a 2D density functional approach based on Weeks-Chandler-Anderson perturbation theory. We furthermore use this approach to determine the density profiles across the equilibrium gas-liquid dividing line and the corresponding line tensions.

Dynamics and Wetting Behavior of Core-Shell Soft Particles at a Fluid-Fluid Interface.

We investigate the conformation, position, and dynamics of core-shell nanoparticles (CSNPs) composed of a silica core encapsulated in a cross-linked poly( N-isopropylacrylamide) shell at a water-oil interface for a systematic range of core sizes and shell thicknesses. We first present a free-energy model that we use to predict the CSNP wetting behavior at the interface as a function of its geometrical and compositional properties in the bulk phases, which is in good agreement with our experimental data. Remarkably, based on the knowledge of the polymer shell deformability, the equilibrium particle position relative to the interface plane, an often elusive experimental quantity, can be extracted by measuring its radial dimensions after adsorption. For all the systems studied here, the interfacial dimensions are always larger than in bulk and the particle core resides in a configuration, wherein it just touches the interface or is fully immersed in water. Moreover, the stretched shell induces a larger viscous drag at the interface, which appears to depend solely on the interfacial dimensions, irrespective of the portion of the CSNP surface exposed to the two fluids. Our findings indicate that tailoring the architecture of CSNPs can be used to control their properties at the interface, as of interest for applications including emulsion stabilization and nanopatterning.

What causes the anomalous aggregation in pluronic aqueous solutions?

Pluronic (PL) block copolymers have been widely used as delivery carriers, molecular templates for porous media, and process additives for affecting rheological behavior. Unlike most surfactant systems, where unimer transforms into micelle with increased surfactant concentration, anomalous large PL aggregates below the critical micelle concentration (CMC) were found throughout four types of PL (F108, F127, F88 and P84). We characterized their structures using dynamic light scattering and small-angle X-ray/neutron scattering. Molecular dynamics simulations suggest that the PPO segments, though weakly hydrophobic interaction (insufficient to form micelles), promote the formation of large aggregates. Addition of acid or base (e.g. citric acid, acetic acid, HCl and NaOH) in F108 solution significantly suppresses the aggregate formation for up to 20 days due to the repulsion force from the attached H3O+ molecules on the EO segment in both PEO and PL and the reduction of CMC through the salting out effect, respectively.

Size of graphene sheets determines the structural and mechanical properties of 3D graphene foams.

Graphene is recognized as an emerging 2D nanomaterial for many applications. Assembly of graphene sheets into 3D structures is an attractive way to enable their macroscopic applications and to preserve the exceptional mechanical and physical properties of their constituents. In this study, we develop a coarse-grained (CG) model for 3D graphene foams (GFs) based on the CG model for a 2D graphene sheet by Ruiz et al (2015 Carbon 82 103-15). We find that the size of graphene sheets plays an important role in both the structural and mechanical properties of 3D GFs. When their size is smaller than 10 nm, the graphene sheets can easily stack together under the influence of van der Waals interactions (vdW). These stacks behave like building blocks and are tightly packed together within 3D GFs, leading to high density, small pore radii, and a large Young's modulus. However, if the sheet sizes exceed 10 nm, they are staggered together with a significant amount of deformation (bending). Therefore, the density of 3D GFs has been dramatically reduced due to the loosely packed graphene sheets, accompanied by large pore radii and a small Young's modulus. Under uniaxial compression, rubber-like stress-strain curves are observed for all 3D GFs. This material characteristic is dominated by the vdW interactions between different graphene layers and slightly affected by the out-of-plane deformation of the graphene sheets. We find a simple scaling law [Formula: see text] between the density ρ and Young's modulus E for a model of 3D GFs. The simulation results reveal structure-property relations of 3D GFs, which can be applied to guide the design of 3D graphene assemblies with exceptional properties.

From intermediate anisotropic to isotropic friction at large strain rates to account for viscosity thickening in polymer solutions.

The steady-state extensional viscosity of dense polymeric liquids in elongational flows is known to be peculiar in the sense that for entangled polymer melts it monotonically decreases-whereas for concentrated polymer solutions it increases-with increasing strain rate beyond the inverse Rouse time. To shed light on this issue, we solve the kinetic theory model for concentrated polymer solutions and entangled melts proposed by Curtiss and Bird, also known as the tumbling-snake model, supplemented by a variable link tension coefficient that we relate to the uniaxial nematic order parameter of the polymer. As a result, the friction tensor is increasingly becoming isotropic at large strain rates as the polymer concentration decreases, and the model is seen to capture the experimentally observed behavior. Additional refinements may supplement the present model to capture very strong flows. We furthermore derive analytic expressions for small rates and the linear viscoelastic behavior. This work builds upon our earlier work on the use of the tumbling-snake model under shear and demonstrates its capacity to improve our microscopic understanding of the rheology of entangled polymer melts and concentrated polymer solutions.

A Two-Dimensional Polymer Synthesized at the Air/Water Interface.

A trifunctional, partially fluorinated anthracene-substituted triptycene monomer was spread at an air/water interface into a monolayer, which was transformed into a long-range-ordered 2D polymer by irradiation with a standard UV lamp. The polymer was analyzed by Brewster angle microscopy, scanning tunneling microscopy measurements, and non-contact atomic force microscopy, which confirmed the generation of a network structure with lattice parameters that are virtually identical to a structural model network based on X-ray diffractometry of a closely related 2D polymer. The nc-AFM images highlight the long-range order over areas of at least 300×300 nm2 . As required for a 2D polymer, the pore sizes are monodisperse, except for the regions where the network is somewhat stretched because it spans over protrusions. Together with a previous report on the nature of the cross-links in this network, the structural information provided herein leaves no doubt that a 2D polymer has been synthesized under ambient conditions at an air/water interface.

Assessing numerical methods for molecular and particle simulation.

We discuss the design of state-of-the-art numerical methods for molecular dynamics, focusing on the demands of soft matter simulation, where the purposes include sampling and dynamics calculations both in and out of equilibrium. We discuss the characteristics of different algorithms, including their essential conservation properties, the convergence of averages, and the accuracy of numerical discretizations. Formulations of the equations of motion which are suited to both equilibrium and nonequilibrium simulation include Langevin dynamics, dissipative particle dynamics (DPD), and the more recently proposed "pairwise adaptive Langevin" (PAdL) method, which, like DPD but unlike Langevin dynamics, conserves momentum and better matches the relaxation rate of orientational degrees of freedom. PAdL is easy to code and suitable for a variety of problems in nonequilibrium soft matter modeling; our simulations of polymer melts indicate that this method can also provide dramatic improvements in computational efficiency. Moreover we show that PAdL gives excellent control of the relaxation rate to equilibrium. In the nonequilibrium setting, we further demonstrate that while PAdL allows the recovery of accurate shear viscosities at higher shear rates than are possible using the DPD method at identical timestep, it also outperforms Langevin dynamics in terms of stability and accuracy at higher shear rates.

Self-assembled core-polyethylene glycol-lipid shell nanoparticles demonstrate high stability in shear flow.

A core-polyethylene glycol-lipid shell (CPLS) nanoparticle consists of an inorganic core coated with polyethylene glycol (PEG) polymers, surrounded by a lipid bilayer shell. It can be self-assembled from a PEGylated core with surface-tethered PEG chains, where all the distal ends are covalently bonded to lipid molecules. Upon adding free lipids, a complete lipid bilayer shell can be formed on the surface driven by the hydrophobic nature of lipid tails, leading to the formation of a CPLS nanoparticle. The stability of CPLS nanoparticles in shear flow has been systematically studied through large scale dissipative particle dynamics simulations. CPLS nanoparticles demonstrate higher stability and less deformation in shear flow, compared with lipid vesicles. Burst leakage of drug molecules inside lipid vesicles and CPLS NPs can be induced by the large pores at their tips. These pores are initiated by the maximum stress in the waist region. It further grows along with the tank-treading motion of vesicles or CPLS NPs in shear flow. However, due to the constraints applied by PEG polymers, CPLS NPs are less deformed than vesicles with comparable size under the same flow conditions. Thus, the less deformed CPLS NPs express a smaller maximum stress at waists, demonstrating higher stability. Pore formation at waists, evolving into large pores on vesicles, leads to the burst leakage of drug molecules and complete rupture of vesicles. In contrast, although similar drug leakage in CPLS nanoparticles can occur at high shear rates, pores initiated at moderate shear rates tend to be short-lived and close due to the constraints mediated by PEG polymers. This kind of 'self-healing' capability can be observed over a wide range of shear rates for CPLS nanoparticles. Our results suggest self-assembled CPLS nanoparticles to exhibit high stability during blood circulation without rapid drug leakage. These features make CPLS nanoparticles candidates for a promising drug delivery platform.

Non-constant link tension coefficient in the tumbling-snake model subjected to simple shear.

The authors of the present study have recently presented evidence that the tumbling-snake model for polymeric systems has the necessary capacity to predict the appearance of pronounced undershoots in the time-dependent shear viscosity as well as an absence of equally pronounced undershoots in the transient two normal stress coefficients. The undershoots were found to appear due to the tumbling behavior of the director u when a rotational Brownian diffusion term is considered within the equation of motion of polymer segments, and a theoretical basis concerning the use of a link tension coefficient given through the nematic order parameter had been provided. The current work elaborates on the quantitative predictions of the tumbling-snake model to demonstrate its capacity to predict undershoots in the time-dependent shear viscosity. These predictions are shown to compare favorably with experimental rheological data for both polymer melts and solutions, help us to clarify the microscopic origin of the observed phenomena, and demonstrate in detail why a constant link tension coefficient has to be abandoned.

Communication: Appearance of undershoots in start-up shear: Experimental findings captured by tumbling-snake dynamics.

Our experimental data unambiguously show (i) a damping behavior (the appearance of an undershoot following the overshoot) in the transient shear viscosity of a concentrated polymeric solution, and (ii) the absence of a corresponding behavior in the transient normal stress coefficients. Both trends are shown to be quantitatively captured by the bead-link chain kinetic theory for concentrated polymer solutions and entangled polymer melts proposed by Curtiss and Bird, supplemented by a non-constant link tension coefficient that we relate to the nematic order parameter. The observed phenomena are attributed to the tumbling behavior of the links, triggered by rotational fluctuations, on top of reptation. Using model parameters deduced from stationary data, we calculate the transient behavior of the stress tensor for this "tumbling-snake" model after startup of shear flow efficiently via simple Brownian dynamics. The unaltered method is capable of handling arbitrary homogeneous flows and has the promising capacity to improve our understanding of the transient behavior of concentrated polymer solutions.