Determining the Mesh Size of Polymer Solutions via the Pore Size Distribution

Nanoscopic Interfacial Hydrogel Viscoelasticity Revealed from Comparison of Macroscopic and Microscopic Rheology

Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for an interfacial shell around tracers with viscoelastic properties that deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable to the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is applicable to different kinds of viscoelastic fluids and particles.

Conformational and static properties of tagged chains in solvents: effect of chain connectivity in solvent molecules

Polymer chains immersed in different solvent molecules exhibit diverse properties due to multiple spatiotemporal scales and complex interactions. Using molecular dynamics simulations, we study the conformational and static properties of tagged chains in different solvent molecules. Two types of solvent molecules were examined: one type consisted of chain molecules connected by bonds, while the other type consisted of individual bead molecules without any bonds. The only difference between the two solvent molecules lies in the chain connectivity. Our results show a compression of the tagged chains with the addition of bead or chain molecules. Chain molecule confinement induces a stronger compression compared to bead molecule confinement. In chain solvent molecules, the tagged chain's radius of gyration reached a minimum at a monomer volume fraction of ∼0.3. Notably, the probability distributions of chain size remain unchanged at different solvent densities, irrespective of whether the solvent consists of beads or polymers. Furthermore, as solvent density increases, a crossover from a unimodal to a bimodal distribution of bond angles is observed, indicating the presence of both compressed and expanded regions within the chain. The effective monomer-solvent interaction is obtained by calculating the partial radial distribution function and the potential of the mean force. In chain solvents, the correlation hole effect results in a reduced number of nearest neighbors around tagged monomers compared to bead solvents. The calculation of pore size distribution reveals that the solvent nonhomogeneity induced by chain connectivity leads to a broader distribution of pore sizes and larger pore dimensions at low volume fractions. These findings provide a deeper understanding of the conformational behavior of polymer chains in different solvent environments.

Dilute gel networks vs. clumpy gels in colloidal systems with a competition between repulsive and attractive interactions

Using Brownian dynamics simulations we study gel-forming colloidal systems. The focus of this article lies on the differences of dense and dilute gel networks in terms of structure formation both on a local and a global level. We apply reduction algorithms and observe that dilute networks and dense gels differ in the way structural properties like the thickness of strands emerge. We also analyze the percolation behavior and find that two different regimes of percolation exist which might be responsible for structural differences. In dilute networks we confirm that solidity is mainly a consequence of pentagonal bipyramids forming in the network. In dense gels, tetrahedral structures also influence solidity.

Chromatin phase separated nanoregions explored by polymer cross-linker models and reconstructed from single particle trajectories

Phase separated domains (PSDs) are ubiquitous in cell biology, representing nanoregions of high molecular concentration. PSDs appear at diverse cellular domains, such as neuronal synapses but also in eukaryotic cell nucleus, limiting the access of transcription factors and thus preventing gene expression. We develop a generalized cross-linker polymer model, to study PSDs: we show that increasing the number of cross-linkers induces a polymer condensation, preventing access of diffusing molecules. To investigate how the PSDs restrict the motion of diffusing molecules, we compute the mean residence and first escaping times. Finally, we develop a method based on mean-square-displacement of single particle trajectories to reconstruct the properties of PSDs from the continuum range of anomalous exponents. We also show here that PSD generated by polymers do not induces a long-range attracting field (potential well), in contrast with nanodomains at neuronal synapses. To conclude, PSDs can result from condensed chromatin organization, where the number of cross-linkers controls molecular access.

Arabinoxylan in Water through SANS: Single-Chain Conformation, Chain Overlap, and Clustering

Using small-angle neutron scattering (SANS), we examine the structure and conformational behavior of wheat arabinoxylan (AX) prepared at various concentrations in a sodium phosphate aqueous buffer. As for another major hemicellulose, xyloglucan, we observe a small number of large clusters surrounded by AX chains that behave exactly as a polymer in good solvent with a Flory exponent ν = 0.588. The fit of the data at high q-values to a standard worm-like chain model gives the persistence length lp = 45 Å and cross section of the chains 2Rc = 11-12 Å. In addition, using a dedicated modeling approach, we extract from the SANS data at the intermediate q-range the correlation length ξ of the solutions in the semidilute regime. The decay of ξ with concentration follows a scaling law that further confirms the self-avoiding statistical behavior of the AX chains. This first comprehensive study about the properties of water-soluble AX at different length scales may help in the development of products and processes involving AX as a substitute for fossil carbon molecules.

Dynamics of chromosome organization in a minimal bacterial cell

Computational models of cells cannot be considered complete unless they include the most fundamental process of life, the replication and inheritance of genetic material. By creating a computational framework to model systems of replicating bacterial chromosomes as polymers at 10 bp resolution with Brownian dynamics, we investigate changes in chromosome organization during replication and extend the applicability of an existing whole-cell model (WCM) for a genetically minimal bacterium, JCVI-syn3A, to the entire cell-cycle. To achieve cell-scale chromosome structures that are realistic, we model the chromosome as a self-avoiding homopolymer with bending and torsional stiffnesses that capture the essential mechanical properties of dsDNA in Syn3A. In addition, the conformations of the circular DNA must avoid overlapping with ribosomes identitied in cryo-electron tomograms. While Syn3A lacks the complex regulatory systems known to orchestrate chromosome segregation in other bacteria, its minimized genome retains essential loop-extruding structural maintenance of chromosomes (SMC) protein complexes (SMC-scpAB) and topoisomerases. Through implementing the effects of these proteins in our simulations of replicating chromosomes, we find that they alone are sufficient for simultaneous chromosome segregation across all generations within nested theta structures. This supports previous studies suggesting loop-extrusion serves as a near-universal mechanism for chromosome organization within bacterial and eukaryotic cells. Furthermore, we analyze ribosome diffusion under the influence of the chromosome and calculate in silico chromosome contact maps that capture inter-daughter interactions. Finally, we present a methodology to map the polymer model of the chromosome to a Martini coarse-grained representation to prepare molecular dynamics models of entire Syn3A cells, which serves as an ultimate means of validation for cell states predicted by the WCM.

Effects of solvent conditions on the self-assembly of heterotrimeric collagen-like peptide (CLP) triple helices: a coarse-grained simulation study

We perform coarse-grained (CG) molecular dynamics (MD) simulations to investigate the self-assembly of collagen-like peptide (CLP) triple helices into fibrillar structures and percolated networks as a function of solvent quality. The focus of this study is on CLP triple helices whose strands are different lengths (i.e., heterotrimers), leading to dangling 'sticky ends'. These 'sticky ends' are segments of the CLP strands that have unbonded hydrogen-bonding donor/acceptor sites that drive heterotrimeric CLP triple helices to physically associate with one another, leading to assembly into higher-order structures. We use a validated CG model for CLP in implicit solvent and capture varying solvent quality through changing strength of attraction between CG beads representing the amino acids in the CLP strands. Our CG MD simulations show that, at lower CLP concentrations, CLP heterotrimers assemble into fibrils and, at higher CLP concentrations, into percolated networks. At higher concentrations, decreasing solvent quality causes (i) the formation of heterogeneous network structures with a lower degree of branching at network junctions and (ii) increases in the diameter of network strands and pore sizes. We also observe a nonmonotonic effect of solvent quality on distances between network junctions due to the balance between heterotrimer end-end associations driven by hydrogen bonding and side-side associations driven by worsening solvent quality. Below the percolation threshold, we observe that decreasing solvent quality leads to the formation of fibrils composed of multiple aligned CLP triple helices, while the number of 'sticky ends' governs the spatial extent (radius of gyration) of the assembled fibrils.

Structure-Thermodynamic Relationship of a Polysaccharide Gel (Alginate) as a Function of Water Content and Counterion Type (Na vs Ca)

Biofilms are the predominant mode of microbial life on Earth, and so a deep understanding of microbial communities─and their impacts on environmental processes─requires a firm understanding of biofilm properties. Because of the importance of biofilms to their microbial inhabitants, microbes have evolved different ways of engineering and reconfiguring the matrix of extracellular polymeric substances (EPS) that constitute the main non-living component of biofilms. This ability makes it difficult to distinguish between the biotic and abiotic origins of biofilm properties. An important route toward establishing this distinction has been the study of simplified models of the EPS matrix. This study builds on such efforts by using atomistic simulations to predict the nanoscale (≤10 nm scale) structure of a model EPS matrix and the sensitivity of this structure to interpolymer interactions and water content. To accomplish this, we use replica exchange molecular dynamics (REMD) simulations to generate all-atom configurations of ten 3.4 kDa alginate polymers at a range of water contents and Ca-Na ratios. Simulated systems are solvated with explicitly modeled water molecules, which allows us to capture the discrete structure of the hydrating water and to examine the thermodynamic stability of water in the gels as they are progressively dehydrated. Our primary findings are that (i) the structure of the hydrogels is highly sensitive to the identity of the charge-compensating cations, (ii) the thermodynamics of water within the gels (specific enthalpy and free energy) are, surprisingly, only weakly sensitive to cation identity, and (iii) predictions of the differential enthalpy and free energy of hydration include a short-ranged enthalpic term that promotes hydration and a longer-ranged (presumably entropic) term that promotes dehydration, where short and long ranges refer to distances shorter or longer than ∼0.6 nm between alginate strands.

Structure and elasticity of model disordered, polydisperse, and defect-free polymer networks

The elasticity of disordered and polydisperse polymer networks is a fundamental problem of soft matter physics that is still open. Here, we self-assemble polymer networks via simulations of a mixture of bivalent and tri- or tetravalent patchy particles, which result in an exponential strand length distribution analogous to that of experimental randomly cross-linked systems. After assembly, the network connectivity and topology are frozen and the resulting system is characterized. We find that the fractal structure of the network depends on the number density at which the assembly has been carried out, but that systems with the same mean valence and same assembly density have the same structural properties. Moreover, we compute the long-time limit of the mean-squared displacement, also known as the (squared) localization length, of the cross-links and of the middle monomers of the strands, showing that the dynamics of long strands is well described by the tube model. Finally, we find a relation connecting these two localization lengths at high density and connect the cross-link localization length to the shear modulus of the system.

Voronoi tessellation-based algorithm for determining rigorously defined classical and generalized geometric pore size distributions

The geometric pore size distribution (PSD) P(r) as function of pore radius r is an important characteristic of porous structures, including particle-based systems, because it allows us to analyze adsorption behavior, the strength of materials, etc. Multiple definitions and corresponding algorithms, particularly in the context of computational approaches, exist that aim at calculating a PSD, often without mentioning the employed definition and therefore leading to qualitatively very different and apparently incompatible results. Here, we analyze the differences between the PSDs introduced by Torquato et al. and the more widely accepted one provided by Gelb and Gubbins, here denoted as T-PSD and G-PSD, respectively, and provide rigorous mathematical definitions that allow us to quantify the qualitative differences. We then extend G-PSD to incorporate the ideas of coating, which is significant for nanoparticle-based systems, and of finite probe particles, which is crucial to micro and mesoporous particles. We derive how the extended and classical versions are interrelated and how to calculate them properly. We next analyze various numerical approaches used to calculate classical G-PSDs and may be used to calculate the generalized G-PSD. To this end, we propose a simple yet sufficiently complicated benchmark for which we calculate the different PSDs analytically. This approach allows us to completely rule out a recently proposed algorithm based on radical Voronoi tessellation. Instead, we find and prove that the output of a grid-free classical Voronoi tessellation, namely, the properties of its triangulated faces, can be used to formulate an algorithm, which is capable of calculating the generalized G-PSD for a system of monodisperse spherical particles (or points) to any precision, using analytical expressions. The Voronoi-based algorithm developed and provided here has optimal scaling behavior and outperforms grid-based approaches.

Structural and dynamical properties of dilute gel networks in colloid-polymer mixtures

The competition of short-ranged depletion attraction and long-ranged repulsion between colloidal particles in colloid-polymer mixtures leads to the formation of heterogeneous gel-like structures. Our special focus will be on the states where the colloids arrange in thin strands that span the whole system and that we will refer to as dilute gel networks. These states occur at low packing fractions for attractions that are stronger than those at both the binodal line of the equilibrium gas-liquid phase separation and the directed percolation transition line. By using Brownian dynamics simulations, we explore the formation, structure, and aging dynamics of dilute gel networks. The essential connections in a dilute gel network are determined by constructing reduced networks. We compare the observed properties to those of clumpy gels or cluster fluids. Our results demonstrate that both the structure and the (often slow) dynamics of the stable or meta-stable heterogeneous states in colloid-polymer mixtures possess distinct features on various length and time scales and thus are richly diverse.

Development of Coarse-Grained Models for Poly(4-vinylphenol) and Poly(2-vinylpyridine): Polymer Chemistries with Hydrogen Bonding

In this paper, we identify the modifications needed in a recently developed generic coarse-grained (CG) model that captured directional interactions in polymers to specifically represent two exemplary hydrogen bonding polymer chemistries-poly(4-vinylphenol) and poly(2-vinylpyridine). We use atomistically observed monomer-level structures (e.g., bond, angle and torsion distribution) and chain structures (e.g., end-to-end distance distribution and persistence length) of poly(4-vinylphenol) and poly(2-vinylpyridine) in an explicitly represented good solvent (tetrahydrofuran) to identify the appropriate modifications in the generic CG model in implicit solvent. For both chemistries, the modified CG model is developed based on atomistic simulations of a single 24-mer chain. This modified CG model is then used to simulate longer (36-mer) and shorter (18-mer and 12-mer) chain lengths and compared against the corresponding atomistic simulation results. We find that with one to two simple modifications (e.g., incorporating intra-chain attraction, torsional constraint) to the generic CG model, we are able to reproduce atomistically observed bond, angle and torsion distributions, persistence length, and end-to-end distance distribution for chain lengths ranging from 12 to 36 monomers. We also show that this modified CG model, meant to reproduce atomistic structure, does not reproduce atomistically observed chain relaxation and hydrogen bond dynamics, as expected. Simulations with the modified CG model have significantly faster chain relaxation than atomistic simulations and slower decorrelation of formed hydrogen bonds than in atomistic simulations, with no apparent dependence on chain length.