Tuning the heat flow is fundamentally important for the design of advanced functional materials. Here, polymers are of particular importance because they provide different pathways for the energy transfer. More specifically, the heat flow between two covalently bonded monomers is over 100 times faster than between the two non-bonded monomers interacting via van der Waals (vdW) forces. Therefore, the delicate balance between these two contributions often provide a guiding tool for the tunability in thermal transport coefficient k of the polymeric materials. Traditionally most studies have investigated k in the linear polymeric materials, the recent interests have also been directed towards the highly cross-linked polymers (HCP). In this work, using the generic molecular dynamics simulations we investigate the factors effecting k of HCP. We emphasize on the importance of the cross-linking bond types and its influence on the network microstructure with a goal to provide a guiding principle for the tunability in k. While these simulation results are discussed in the context of the available experimental data, we also make predictions.
The stretchability of polymeric materials is critical to many applications such as stretchable electronics and soft robotics, yet the stretchability of conventional cross-linked linear polymers is limited by the entanglements between polymer chains. We show using molecular dynamics simulations that cross-linked ring polymers are significantly more stretchable than cross-linked linear polymers. Compared to linear polymers, the entanglements between ring polymers do not act as effective cross-links. As a result, the stretchability of cross-linked ring polymers is determined by the maximum extens…
Indentation is a common experimental technique to study the mechanics of polymeric materials. The main advantage of using indentation is because this provides a direct correlation between the microstructure and the small-scale mechanical response, which is otherwise difficult within the standard tensile testing. Here, majority of studies have investigated hydrogels, microgels and/or elastomers. However, a lesser investigated system is the indentation in highly cross-linked polymer (HCP) networks, where the complex network structure plays a key role in dictating their physical properties. In th…
Polymerization and formation of crosslinked polymer networks are important processes in manufacturing, materials fabrication, and in the case of hydrated polymer networks, synthesis of biomedical materials, drug delivery, and tissue engineering. While considerable research has been devoted to the modeling of polymer networks to determine averaged, mean-field, global properties, there are fewer studies that specifically examine the variance of the composition across "micro-regions" (composed of a large, but finite, number of polymer network strands) within the larger polymer network.Here, we ma…
Using video-microscopy imaging we demonstrate the existence of a short-ranged equilibrium attraction between heavy silica colloids diffusing on soft surfaces of cross-linked polymer gels. The inter-colloid potential can be tuned by changing the gel stiffness or by coating the colloids with a polymer layer. On sufficiently soft substrates, the interaction induced by the polymer matrix leads to large-scale colloidal aggregation. We correlate the in-plane interaction with a colloid-surface attraction.
Inspired to understand the complex spectrum of space-filling organizations the dsDNA genome within the capsid of bacterial viruses, we study a minimal, coarse-grained model of single chains densely-packed into a finite spherical volume. We build the three basic elements of the model--i) the absence of chain ends ii) the tendency of parallel-strand alignment and iii) a preference of uniform areal density of chain segments--into a polymer nematic theory for confined chains. Given the geometric constraints of the problem, we show that axially symmetric packings fall into one of three topologies: …
Reducing the complexity of cross-linked polymer networks by preserving their main macroscale properties, is key to understanding them, and a crucial issue is to relate individual properties of the polymer constituents to those of the reduced network. Here we study polymer networks in a good solvent, by considering star polymers as their unit elements, and first quantify the interaction between their centers of masses. We then reduce the complexity of a network by replacing sets of its bridged star polymers by equivalent effective soft particles with dense cores. Our coarse graining allows us t…
We calculate the free energy and the pressure of a weakly slip-linked Gaussian polymer chains. We show that the equilibrium statistics of a slip-linked system is different from one of the corresponding ideal chain system without any constraints by slip-links. It is shown that the pressure of a slip-linked system decreases compared with the ideal system, which implies that slip-linked chains spontaneously form aggregated cluster like compact structures. These are qualitatively consistent with previous theoretical analyses or multi chain simulations. We also show that repulsive potentials betwee…
The band structure and electronic properties in a series of vinylene-linked heterocyclic conducting polymers are investigated using density functional theory (DFT). In order to accurately calculate electronic band gaps, we utilize hybrid functionals with fully periodic boundary conditions to understand the effect of chemical functionalization on the electronic structure of these materials. The use of predictive first-principles calculations coupled with simple chemical arguments highlights the critical role that aromaticity plays in obtaining a low band gap polymer. Contrary to some approaches…
Polymer models are used to describe chromatin, which can be folded at different spatial scales by binding molecules. By folding, chromatin generates loops of various sizes. We present here a randomly cross-linked (RCL) polymer model, where monomer pairs are connected randomly. We obtain asymptotic formulas for the steady-state variance, encounter probability, the radius of gyration, instantaneous displacement and the mean first encounter time between any two monomers. The analytical results are confirmed by Brownian simulations. Finally, the present results can be used to extract the minimum n…
We investigate the behaviour of randomly cross-linked (co)polymer blends using a combination of replica theory and large-scale molecular dynamics simulations. In particular, we derive the analogue of the random phase approximation for systems with quenched disorder and show how the required correlation functions can be calculated efficiently. By post-processing simulation data for homopolymer networks we are able to describe neutron scattering measurements in heterogeneous systems without resorting to microscopic detail and otherwise unphysical assumptions. We obtain structure function data wh…
Structure, Dynamics and Hydrogen Transport in Amorphous Polymers: An Analysis of the Interplay Between Free Volume Element Distribution and Local Segmental Dynamics from Molecular Dynamics Simulations
Short fiber reinforced polymer composites have found extensive industrial and engineering applications owing to their unique combination of low cost, relatively easy processing and superior mechanical properties compared to their parent polymers. In this study, a coarse grained (CG) model of cross linked carbon nanotube (CNT) reinforced polymer matrix composites is developed. A characteristic feature of the CG model is the ability to capture the interactions between polymer chains, and nanotubes and polymer matrix. The dependence of the elastic properties of the composites on the mole fraction…
We present an extensive molecular dynamics (MD) simulation study of poly(ethylene oxide) (PEO) based densely cross-linked polymers, focussing on structural properties as well as the systems dynamics in the presence of lithium salt. Motivated by experimental findings for networks with short PEO strands we employ a combination of LiTFSI (Lithium bis(trifluoromethanesulfonyl)imide) and LiDFOB (Lithium difluoro(oxalato)borate). Recently, it has been shown that such multi-salt systems outperform classical single salt systems (Shaji et al., Energy Storage Materials, 2022, 44, 263). To analyse the mi…
We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and …
We explore the effect of random permanent cross-links on a system of directed polymers confined between two planes with their end-points free to slide on them. We treat the cross-links as quenched disorder and we use a semimicroscopic replica field theory to study the structure and elasticity of this system. Upon increasing the cross-link density, we get a continuous gelation transition signaled by the emergence of a finite in-plane localization length. The distribution of localization length turns out to depend on the height along the preferred direction of the directed polymers. The gelation…
Cross-linked polymer networks with orientational order constitute a wide class of soft materials and are relevant to biological systems (e.g., F-actin bundles). We analytically study the nonlinear force-extension relation of an array of parallel-aligned, strongly stretched semiflexible polymers with random cross-links. In the strong stretching limit, the effect of the cross-links is purely entropic, independent of the bending rigidity of the chains. Cross-links enhance the differential stretching stiffness of the bundle. For hard cross-links, the cross-link contribution to the force-extension …
We introduce an efficient, scalable Monte Carlo algorithm to simulate cross-linked architectures of freely-jointed and discrete worm-like chains. Bond movement is based on the discrete tractrix construction, which effects conformational changes that exactly preserve fixed-length constraints of all bonds. The algorithm reproduces known end-to-end distance distributions for simple, analytically tractable systems of cross-linked stiff and freely jointed polymers flawlessly, and is used to determine the effective persistence length of short bundles of semi-flexible worm-like chains, cross-linked t…
For a wide range of modern soft functional materials the selective transport of sub-nanometer-sized molecules (`penetrants') through a stimuli-responsive polymeric membrane is key to the desired function. In this study, we investigate the diffusion properties of penetrants ranging from non-polar to polar molecules and ions in a matrix of collapsed Poly(N-isopropylacrylamide) (PNIPAM) polymers in water by means of extensive molecular dynamics simulations. We find that the water distributes heterogeneously in fractal-like cluster structures embedded in the nanometer-sized voids of the polymer ma…
Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on molecular ring polymers are challenging due to their polydispersity in molecular weight and the presence of undesired side products such as chains. Here, we study an experimental model system for cyclic polymers, that consists of rings of flexibly-linked micron-sized colloids with $n$=4..8 segments. We characterize the conformations of these flexible colloidal rings and find that they are freely-jointed up to steric…
Semiflexible polymers such as filamentous actin play a vital role in the mechanical behavior of cells, yet the basic properties of cross-linked F-actin networks remain poorly understood. To address this issue, we have performed numerical studies of the linear response of homogeneous and isotropic two-dimensional networks subject to an applied strain at zero temperature. The elastic moduli are found to vanish for network densities at a rigidity percolation threshold. For higher densities, two regimes are observed: one in which the deformation is predominantly affine and the filaments stretch an…
Low-density "equilibrium" gels that consist of a percolated, kinetically arrested network of colloidal particles and are resilient to aging can be fabricated by restricting the number of effective bonds that form between the colloids. Valence-restricted patchy particles have long served as one archetypal example of such materials, but equilibrium gels can also be realized through a synthetically simpler and scalable strategy that introduces a secondary linker, such as a small ditopic molecule, to mediate the bonds between the colloids. Here, we consider the case where the ditopic linker molecu…
Using computer simulations, we study the dynamic arrest in a schematic model of colloid-polymer mixtures combining short-ranged attractions with long-ranged repulsions. The arrested gel is a dilute rigid network of colloidal particles bonded due to the strong attractions. Without repulsions, the gel forms at the spinodal through arrested phase separation. In the ergodic suspension at sufficiently high densities, colloidal clusters form temporary networks that percolate space. Recently [Nat. Commun. 7, 11817 (2016)], it has been proposed that the transition of these networks to directed percola…
While polymer solutions lack the mechanical stability only transiently cross-linked networks can fulfill the competing requirements of structural stability and maximal energy dissipation. Here, we show that transient cross-links entail local stress relaxation and energy dissipation in an intermediate elasticity dominated frequency regime. We quantify the mechanical response of a semi-flexible polymer network by experimentally tuning the off-rate of the transient cross-linker molecule and theoretically reproduce the measured frequency response by a model that is predicated on microscopic unbind…
In this work we focus on the dynamics of macromolecular networks formed by end-linking identical polymer stars. The resulting macromolecular network can then be viewed as consisting of spacers which connect branching points (the cores of the stars). We succeed in analyzing exactly, in the framework of the generalized Gaussian model, the eigenvalue spectrum of such networks. As applications we focus on several topologies, such as regular networks and dendrimers; furthermore, we compare the results to those found for regular hyperbranched structures. In so doing, we also consider situations in w…
Extra-terrestrial polymers of glycine with iron have been characterized by mass spectrometry to have a core mass of 1494Da with dominant rod-like variants at m/z 1567 and m/z 1639 [1]. Several principal macro-structural morphologies are observed in solvent extracts from CV3 class meteoritic material. The first is an extended sheet of linked triskelia containing the 1494Da core entity that encloses gas bubbles in the solvent [1]. A second is of fiber-like crystals found here, via X-ray diffraction, to be multiple-walled nanotubes made from a square lattice of the 1494Da polymer. A third is a di…
Coarse-graining to create minimalist models for dynamic, end-linked star-polymer networks
McKetta Department of Chemical Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校麦凯塔化学工程系）；Department of Chemical Engineering, Auburn University（奥本大学化学工程系）；Department of Chemical Engineering and Biointerfaces Institute, University of Michigan（密歇根大学生物界面研究所化学工程系）；McKetta Department of Engineering, The University of Texas at Austin（德克萨斯大学奥斯汀分校麦凯塔工程学院）
Inspired by how certain proteins "sense" knots and entanglements in DNA molecules, here we ask if there exist local geometric features that may be used as a read-out of the underlying topology of generic polymers. We perform molecular simulations of knotted and linked semiflexbile polymers and study four geometric measures to predict topological entanglements: local curvature, local density, local 1D writhe and non-local 3D writhe. We discover that local curvature is a poor predictor of entanglements. In contrast, segments with maximum local density or writhe correlate as much as 90% of the ti…
Ferrogels, i.e. swollen polymer networks into which magnetic particles are immersed, can be considered as "smart materials" since their shape and elasticity can be controlled by an external magnetic field. Using molecular dynamics simulations on the coarse-grained level we study a ferrogel in which the magnetic particles act as the cross-linkers of the polymer network. In a homogeneous external magnetic field the direct coupling between the orientation of the magnetic moments and the polymers by means of covalent bonds gives rise to a deformation of the gel, independent of the interparticle di…
Confined in two dimensional planes, polymer chains comprising dense monolayer solution are segregated from each other due to topological interaction. Although the segregation is inherent in two dimensions (2D), the solution may display different properties depending on the solvent quality. Among others, it is well known in both theory and experiment that the osmotic pressure ($Π$) in the semi-dilute regime displays solvent quality-dependent increases with the area fraction ($ϕ$) (or monomer concentration, $ρ$), that is, $Π\sim ϕ^3$ for good solvent and $Π\sim ϕ^8$ for $Θ$ solvent. The osmotic …
In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However, implementation of machine-learned approaches in material modeling has been modest due to the high-dimensionality of the data space, significant size of missing data, and limited convergence. This work proposes a framework to hire concepts from polymer science, statistical physics, and continuum mechanics to provide super-constrained machine-learning techniques of…
Molecular dynamic simulation enables one to correlate the evolution of the micro-structure with anisotropic stress when a material is subject to strain. The anisotropic stress due to a constant strain-rate load in a cross-linked polymer is primarily dependent on the mean-square bond length and mean-square bond angle. Excluded volume interactions due to chain stacking and spatial distribution also has a bearing on the stress response. The bond length distribution along the chain is not uniform. Rather, the bond lengths at the end of the chains are larger and uniformly decrease towards the middl…
This paper reports the first example of the degradable ROMP thermosetting materials catalysed by bio-derived acids and cutinase from Thermobifida cellulosilytica (Thc_Cut1). The ROMP thermosetting materials are based on norbornene dicarboximides containing acetal ester groups only in the crosslink moiety. The insoluble cross-linked materials were subjected to acid-catalysed hydrolysis using bio-derived acetic and citric acids as well as enzymatic degradation using Thc_Cut1, resulting in the materials becoming completely soluble in dichloromethane. 1H NMR and rheological analysis performed on m…
Motivated by the structure of networks of cross-linked cytoskeletal biopolymers, we study the orientationally ordered phases in two-dimensional networks of randomly cross-linked semiflexible polymers. We consider permanent cross-links which prescribe a finite angle and treat them as quenched disorder in a semi-microscopic replica field theory. Starting from a fluid of un-cross-linked polymers and small polymer clusters (sol) and increasing the cross-link density, a continuous gelation transition occurs. In the resulting gel, the semiflexible chains either display long range orientational order…
In this work a new strategy is proposed in order to build analytic and microscopic models of fluctuating polymer rings subjected to topological constraints. The topological invariants used to fix these constraints belong to a wide class of the so-called numerical topological invariants. For each invariant it is possible to derive a field theory that describes the statistical behavior of knotted and linked polymer rings following a straightforward algorithm. The treatment is not limited to the partition function of the system, but it allows also to express the expectation values of general obse…
We study the elastic deformations in a cross-linked polymer network film triggered by the binding of submicron particles with a sticky surface, mimicking the interactions of viral pathogens with thin films of stimulus-responsive polymeric materials such as hydrogels. From extensive Langevin Dynamics simulations we quantify how far the network deformations propagate depending on the elasticity parameters of the network and the adhesion strength of the particles. We examine the dynamics of the collective area shrinkage of the network and obtain some simple relations for the associated characteri…
We present an intuitive physical picture for fractures in nacre-type stratified materials via scaling arguments: strain distributions around a fracture are rather different depending on directions and size of fractures. We thus observe that viscoelastic effects are important for parallel fractures. These effect are taken into account via the simplest viscoelastic model for weakly cross-linked polymer. Within a certain limit, we find a trumpet crack shape similar to that in certain polymers and make predictions for the fracture energy of certain stratified materials in this mode.
Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers $Wi<<1$. Thickening coincides with the extreme elongation of a minority population of rings that grows with $Wi$. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower $Wi$ and are pulled tight and stabilized by the flow. Once linked, these composite object…
We study the friction between a flat solid surface where polymer chains have been end-grafted and a cross-linked elastomer at low sliding velocity. The contribution of isolated grafted chains' penetration in the sliding elastomer has been early identified as a weakly velocity dependent pull-out force. Recent experiments have shown that the interactions between the grafted chains at high grafting density modify the friction force by grafted chain. We develop here a simple model that takes into account those interactions and gives a limit grafting density beyond which the friction no longer incr…
Entropic phase separation in polymer--vitrimer melts
DICMaPI, Università degli Studî di Napoli Federico II（那不勒斯费德里科二世大学）；BSMA, IMCN, Université catholique de Louvain（天主教鲁汶大学）；MSE, University of Crete（克里特大学）；School of Mathematics, University of Leeds（利兹大学）
We study the adhesion between a cross-linked elastomer and a flat solid surface where polymer chains have been end-grafted. To understand the adhesive feature of such a system, one has to study both the origin of the grafted layer interdigitation with the network, and the end-grafted chains extraction out of the elastomer when it comes unstuck from the solid surface. We shall tackle here the first aspect for which we develop a partial interdigitation model that lets us analytically predict a critical surface grafting density $σ^{*} \simeq P^{1/10}N^{-{3/5}}$ beyond which the layer no longer in…
In-vivo DNA organization at large length scales ($\sim 100nm$) is highly debated and polymer models have proved useful to understand the principle of DNA-organization. Here, we show that $<2$% cross-links at specific points in a ring polymer can lead to a distinct spatial organization of the polymer. The specific pairs of cross-linked monomers were extracted from contact maps of bacterial DNA. We are able to predict the structure of 2 DNAs using Monte Carlo simulations of the bead-spring polymer with cross-links at these special positions. Simulations with cross-links at random positions along…
Levan is a bacterial homopolysaccharide, which consists of beta-2,6 linked beta-D-fructose monomers. Because of its structural properties and its health promoting effects, levan is a promising functional ingredient for the food, cosmetic and pharma industry. The properties of levan have been reported to be linked to its molecular weight. For a better understanding of how its molecular weight determines its polymer conformation in aqueous solution, levan produced by the food grade acetic acid bacterium Gluconobacter albidus TMW 2.1191 was analysed over a broad molecular weight range using dynam…
Stick-slip, manifest as intermittent tangential motion between two solids, is a well-known friction instability that occurs in a number of natural and engineering systems. In the context of adhesive polymer interfaces, this phenomenon has often been solely associated with Schallamach waves, which are termed slow waves due to their low propagation speeds. We study the dynamics of a model polymer interface using coupled force measurements and high speed \emph{in situ} imaging, to explore the occurrence of stick-slip linked to other slow wave phenomena. Two new waves---slip pulse and separation p…
We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau v…
Entangled polymers are deformed by a strong shear flow. The shape of the polymer, called the form factor, is measured by small angle neutron scattering. However, the real-space molecular structure is not directly available from the reciprocal-space data, due to the phase problem. Instead, the data has to be fitted with a theoretical model of the molecule. We approximate the unknown structure using piecewise straight segments, from which we derive an analytical form factor. We fit it to our data on a semi-dilute entangled polystyrene solution under in situ shear flow. The character of the defor…
Ionic electro-active polymers (E.A.P.) is an active material consisting in a polyelectrolyte (for example Nafion). Such material is usually used as thin film sandwiched between two platinum electrodes. The polymer undergoes large bending motions when an electric field is applied across the thickness. Conversely, a voltage can be detected between both electrodes when the polymer is suddenly bent. The solvent-saturated polymer is fully dissociated, releasing cations of small size. We used a continuous medium approach. The material is modelled by the coexistence of two phases; it can be considere…
