Excluded Volume Interactions Research Articles

The Kinetics of Polymer Brush Growth in the Frame of the Reaction Diffusion Front Formalism.

We studied the properties of a reaction front that forms in irreversible reaction-diffusion systems with concentration-dependent diffusivities during the synthesis of polymer brushes. A coarse-grained model of the polymerization process during the formation of polymer brushes was designed and investigated for this purpose. In this model, a certain amount of initiator was placed on an impenetrable surface, and the "grafted from" procedure of polymerization was carried out. The system consisted of monomer molecules and growing chains. The obtained brush consisted of linear chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions only. The simulations were carried out for high rafting densities of 0.1, 0.3, and 0.6 and for reaction probabilities of 0.02, 0.002, and 0.0002. Simulations were performed by means of the Monte Carlo method while employing the Dynamic Lattice Liquid model. Some universal behavior was found, i.e., irrespective of reaction rate and grafting density, the width of the reaction front as well as the height of the front show for long times the same scaling with respect to time. During the formation of the polymer layer despite the observed difference in dispersion of chain lengths for different grafting densities and reaction rates at a given layer height, the quality of the polymer layer does not seem to depend on these parameters.

Electrolytes in conducting nanopores: Revisiting constant charge and constant potential simulations.

Simulating electrolyte-electrode systems poses challenges due to the need to account for the electrode's response to ion movements in order to maintain a constant electrode potential, which slows down the simulations. To circumvent this, computationally more efficient constant charge (CC) simulations are sometimes employed. However, the accuracy of CC simulations in capturing the behavior of electrolyte-electrode systems remains unclear, especially for microporous electrodes. Herein, we consider electrolyte-filled slit nanopores and systematically analyze the in-pore ion structure and diffusivity using CC and constant potential simulations. Our results indicate that CC simulations provide comparable pore occupancies at high bulk ion densities and for highly charged pores, but they fail to accurately describe the ion structure and dynamics, particularly in quasi-2D (single-layer) pores and at low ion densities. We attribute these results to the superionic state emerging in conducting nanoconfinement and its interplay with excluded volume interactions.

Achiral hard bananas assemble double-twist skyrmions and blue phases.

Skyrmions are topologically protected, vortex-like structures found in various condensed-matter systems including helical ferromagnets and liquid crystals, typically arising from chiral interactions. Using extensive particle-based simulations, we demonstrate that non-chiral hard banana-shaped particles, governed solely by excluded-volume interactions, spontaneously stabilize skyrmion structures through the bend-flexoelectric effect. Under thin confinement, we observe the formation of quasi-2D layers of isolated skyrmions or dense skyrmion lattices. These structures, comprising a racemic mixture of left- and right-handed skyrmions, show resilience against thermal fluctuations while remaining responsive to external fields, offering intriguing possibilities for manipulation. We also find that the size of these skyrmions can be adjusted by the dimensions and curvature of the banana-shaped particles. In the absence of geometric frustration due to confinement, a blue phase III may emerge, characterized by a 3D network of chiral skyrmion filaments of the nematic director field within an isotropic background. Our findings provide valuable insights into stabilizing skyrmion lattices and blue phases, showcasing non-Gaussian fluid-like dynamics in systems of achiral hard particles. Furthermore, they highlight the remarkable capacity of these complex fluids in designing advanced functional materials with diverse applications in photonics and memory devices.

Analytical Model to Deduce the Conformational and Dynamical Behavior in Dendrimers: A Review.

This review utilizes an optimized Rouse-Zimm discrete hydrodynamic model and the preaveraged Oseen tensor, which accurately consider hydrodynamic interactions to study model dendrimers. We report the analytical theories that have been previously developed for the creation of generalized analytical models for dendrimers. These generalized theories were used to assess the conformational and dynamical behavior of the dendrimers. By including stiffness in the bonds, the neglect of excluded volume interactions may be somewhat offset. This is true at least in the case of short spacers. While the topological limitations on the directions and orientations of the individual bond vectors in dendrimers implement semiflexibility, the intensity of these contacts was determined by the potential geometric orientations of the bonds, and later on the excluded volume interactions in dendrimers, which were described in terms of the effective co-volume between nearest non-bonded monomers and modeled using the delta function pseudopotential. With the aid of the models developed, the authors condensed various conformational and dynamic properties of dendrimers that depend on their degree of semiflexibility and the strength of the excluded volume. These analyses came to the conclusion that the flexible dendrimer in one limit and the earlier described freely rotating model of dendrimers in the other constitute a highly generalized way of capturing a wide range of conformations in the developed mathematical model in dendrimers.

Influence of swelling on the elasticity of polymer networks cross-linked in the melt state: Test of the localization model of rubber elasticity.

The elasticity of polymer networks, formed by cross-linking high molecular mass polymers in the melt state and then swollen by a solvent, involves contributions from both the presence of cross-link network junctions and the interchain interactions associated with the combined effect of excluded volume interactions and topological constraints that become modified when the network is swollen. We test the capacity of the previously developed localization model of rubber elasticity, a mean field "tube model," to describe changes in elasticity observed in classical experimental studies of the mechanical properties of this type of network. In order to obtain a satisfactory comparison to the experiments, it was found to be necessary to account for the independently observed tendency of the network junctions to become localized in the network with appreciable swelling, as well as the interchain interactions emphasized in previous discussions of the localization model.

A molecular perspective on the emergence of long-range polar order from an isotropic fluid

The ferroelectric nematic phase (NF) has quickly become the most studied system in liquid crystal research. In this work, we investigate the origin of such polar structure by studying a compound for which the NF phase directly follows the isotropic liquid phase on cooling, making it a particularly interesting system. Our experimental results evidence the presence of polar correlations already in the high-temperature phase, in which ferroelectric order can be induced under a sufficiently strong electric field. In the NF phase, molecular dynamics and polar correlations are investigated through detailed dynamic dielectric measurements, while second harmonic generation experiments evidence a large value of the main coefficient of the second order dielectric susceptibility tensor. Lastly, experimentally determined parameters are employed for calculations based on a recently proposed theoretical model for the stability of the NF phase. The obtained results suggest that the parallel alignment of dipoles is driven by a subtle interplay between electrostatic and excluded volume interactions.

Combinatorics and topological weights of chromatin loop networks.

Polymer physics models suggest that chromatin spontaneously folds into loop networks with transcription units (TUs), such as enhancers and promoters, as anchors. Here we use combinatoric arguments to enumerate the emergent chromatin loop networks, both in the case where TUs are labeled and where they are unlabeled. We then combine these mathematical results with those of computer simulations aimed at finding the inter-TU energy required to form a target loop network. We show that different topologies are vastly different in terms of both their combinatorial weight and energy of formation. We explain the latter result qualitatively by computing the topological weight of a given network-i.e., its partition function in statistical mechanics language-in the approximation where excluded volume interactions are neglected. Our results show that networks featuring local loops are statistically more likely with respect to networks including more nonlocal contacts. We suggest our classification of loop networks, together with our estimate of the combinatorial and topological weight of each network, will be relevant to catalog three-dimensional structures of chromatin fibers around eukaryotic genes, and to estimate their relative frequency in both simulations and experiments.

Excluded volume effects on tangentially driven active ring polymers.

The conformational and dynamical properties of active ring polymers are studied by numerical simulations. The two-dimensionally confined polymer is modeled as a closed bead-spring chain, driven by tangential forces, put in contact with a heat bath described by the Brownian multiparticle collision dynamics. Both phantom polymers and chains comprising excluded volume interactions are considered for different bending rigidities. The size and shape are found to be dependent on persistence length, driving force, and bead mutual exclusion. The lack of excluded volume interactions is responsible for a shrinkage of active rings when increasing driving force in the flexible limit, while the presence induces a moderate swelling of chains. The internal dynamics of flexible phantom active rings shows activity-enhanced diffusive behavior at large activity values while, in the case of self-avoiding active chains, it is characterized by active ballistic motion not depending on stiffness. The long-time dynamics of active rings is marked by rotational motion whose period scales as the inverse of the applied tangential force, irrespective of persistence length and beads' self-exclusion.

Cell deformability drives fluid-to-fluid phase transition in active cell monolayers.

Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for tissue homeostasis and stable developmental processes. However, large-scale simulations of deformable cells have been restricted to those of polygonal-shaped cells, limiting our understanding of populations of arbitrarily deformable cells, such as mesenchymal, amoeboid cells, and nonconfluent epithelial cells. Here, we present an efficient approach for simulating large populations of nonpolygonally deformable cells with considerably higher computational efficiency than existing methods. Using the method, we demonstrate that the densely packed active cell population interacting via excluded volume interactions exhibits a fluid-to-fluid transition. An experimentally measurable index of topological defects, defined using the number of neighboring cells, is also proposed to characterize this transition. This study provides a flexible approach to tissue-scale cell population and a broader perspective on the biological fluid phases.

Active osmoticlike pressure on permeable inclusions.

We use a standard minimal active Brownian model to investigate the osmotic-like effective pressure generated by active fluids on fixed hollow inclusions. These inclusions are enclosed by a permeable (albeit nonflexible) membrane, and the interior and exterior regions of the inclusions have different particle motility strengths. We consider both rectangular and disklike inclusions and analyze the effects of various system parameters, such as excluded volume interaction between active particles, hardness of membrane, and active particle density, on the effective pressure produced on the enclosing membrane. We focus on the range of intermediate to high motility strengths and analyze the effective pressure in the steady state. Our findings for the active pressure produced in the interior and exterior regions of the inclusion indicate that the pressure is higher in the region with lower motility due to the relatively stronger accumulation of active particles.

Excluded volume induces buckling in optically driven colloidal rings

In our combined experimental, theoretical, and numerical work, we study the out-of-equilibrium deformations in a shrinking ring of optically trapped, interacting colloidal particles. Steerable optical tweezers are used to confine dielectric microparticles along a circle of discrete harmonic potential wells, and to reduce the ring radius at a controlled quench speed. We show that excluded-volume interactions are enough to induce particle sliding from their equilibrium positions and nonequilibrium zigzag roughening of the colloidal structure. Our work unveils the underlying mechanism of interfacial deformation in radially driven microscopic discrete rings. Published by the American Physical Society 2024

Effect of counterion size on polyelectrolyte conformations and thermodynamics.

We present a theoretical model to study the effect of counterion size on the effective charge, size, and thermodynamic behavior of a single, isolated, and flexible polyelectrolyte (PE) chain. We analyze how altering counterion size modifies the energy and entropy contributions to the system, including the ion-pair free energy, excluded volume interactions, entropy of free and condensed ions, and dipolar attraction among monomer-counterion pairs, which result in competing effects challenging intuitive predictions. The PE self-energy is calculated using the Edwards-Muthukumar Hamiltonian, considering a Gaussian monomer distribution for the PE. The condensed ions are assumed to be confined within a cylindrical volume around the PE backbone. The dipolar and excluded volume interactions are described by the second and third virial coefficients. The assumption of freely rotating dipoles results in a first-order coil-globule transition of the PE chain. A more realistic, weaker dipolar attraction, parameterized in our theory, shifts it to a second-order continuous transition. We calculate the size scaling-exponent of the PE and find exponents according to the relative dominance of the electrostatic, excluded volume, or dipolar effects. We further identify the entropy- and energy-driven regimes of the effective charge and conformation of the PE, highlighting the interplay of free ion entropy and ion-pair energy with varying electrostatic strengths. The crossover strength, dependent on the counterion size, indicates that diminishing sizes favor counterion condensation at the expense of free ion entropy. The predictions of the model are consistent with trends in simulations and generalize the findings of the point-like counterion theories.

Nonmonotonic polymer translocation kinetics through nanopores under changing surface-polymer interactions.

Understanding the dynamics of polymers in confined environments is pivotal for diverse applications ranging from polymer upcycling to bioseparations. In this study, we develop an entropic barrier model using self-consistent field theory that considers the effect of attractive surface interactions, solvation, and confinement on polymer kinetics. In this model, we consider the translocation of a polymer from one cavity into a second cavity through a single-segment-width nanopore. We find that, for a polymer in a good solvent (i.e., excluded volume, u0 > 0), there is a nonmonotonic dependence of mean translocation time (τ) on surface interaction strength, ɛ. At low ɛ, excluded volume interactions lead to an energetic penalty and longer translocation times. As ɛ increases, the surface interactions counteract the energetic penalty imposed by excluded volume and the polymer translocates faster through the nanopore. However, as ɛ continues to increase, an adsorption transition occurs, which leads to significantly slower kinetics due to the penalty of desorption from the first cavity. The ɛ at which this adsorption transition occurs is a function of the excluded volume, with higher u0 leading to an adsorption transition at higher ɛ. Finally, we consider the effect of translocation across different size cavities. We find that the kinetics for translocation into a smaller cavity speeds up while translocation to a larger cavity slows down with increasing ɛ due to higher surface contact under stronger confinement.

Pressure Anisotropy in Polymer Brushes and Its Effects on Wetting.

Polymer brushes, coatings consisting of densely grafted macromolecules, experience an intrinsic lateral compressive pressure, originating from chain elasticity and excluded volume interactions. This lateral pressure complicates a proper definition of the interface and, thereby, the determination and interpretation of the interfacial tension and its relation to the wetting behavior of brushes. Here, we study the link among grafting-induced compressive lateral pressure in polymer brushes, interfacial tension, and brush wettability using coarse-grained molecular dynamics simulations. We focus on grafting densities and polymer-liquid affinities such that the polymer and liquid do not tend to mix. For these systems, a central result is that the liquid contact angle is independent of the grafting density, which implies that the grafting-induced lateral compressive pressure in the brush does not influence its wettability. Although the definition of brush interfacial tensions is complicated by the grafting-induced pressure, the difference in the interfacial tension between wet and dry brushes is perfectly well-defined. We confirm explicitly from Young's law that this difference offers an accurate description of the brush wettability. We then explore a method to isolate the grafting-induced contribution to the lateral pressure, assuming the interfacial tension is independent of grafting density. This scenario indeed allows disentanglement of interfacial and grafting effects for a broad range of parameters, except close to the mixing point. We separately discuss the latter case in light of autophobic dewetting.

Nonmonotonic dynamics of nuclear-to-cellular volume ratio under osmotic shocks

How the nuclear size dynamically scales with the cellular size during osmotic shock treatments remains controversial. We develop a dynamic model by incorporating the typical interactions between polydisperse biomolecules and the mechanical elasticity of the cytoplasm and nucleoplasm to investigate this long-standing critical issue. We find the nontrivial phenomenon that the nuclear-to-cellular volume ratio can vary nonmonotonically with time, instead of maintaining a constant as usually known, under the osmotic shocks. Combining simulations and analytical argument, we validly account for this nonmonotonic dynamic behavior, and identify its essential regulatory mechanism to be the collaboration of the excluded volume interactions between the polydisperse biomolecules and the spatial constraint from the nuclear envelope on the macromolecule diffusions. Our results agree well with the published experiments for cellular and nuclear size controls of the protoplasts. Our model offers energetic insight in characterizing biology-associated dynamic processes such as macromolecular crowding, and biophase separation occurring in cytoplasm and nucleoplasm. Published by the American Physical Society 2024

Self–dual solutions of a field theory model of two linked rings

In this work the connection established in [7,8] between a model of two linked polymers rings with fixed Gaussian linking number forming a 4-plat and the statistical mechanics of non-relativistic anyon particles is explored. The excluded volume interactions have been switched off and only the interactions of entropic origin arising from the topological constraints are considered. An interpretation from the polymer point of view of the field equations that minimize the energy of the model in the limit in which one of the spatial dimensions of the 4-plat becomes very large is provided. It is shown that the self-dual contributions are responsible for the long-range interactions that are necessary for preserving the global topological properties of the system during the thermal fluctuations. The non self-dual part is also related to the topological constraints, and takes into account the local interactions acting on the monomers in order to prevent the breaking of the polymer lines. It turns out that the energy landscape of the two linked rings is quite complex. Assuming as a rough approximation that the monomer densities of half of the 4-plat are constant, at least two points of energy minimum are found. Classes of non-trivial self-dual solutions of the self-dual field equations are derived. One of these classes is characterized by densities of monomers that are the squared modulus of holomorphic functions. The second class is obtained under some assumptions that allow to reduce the self-dual equations to an analog of the Gouy-Chapman equation for the charge distribution of ions in a double layer capacitor. In the present case, the spatial distribution of the electric potential of the ions is replaced by the spatial distribution of the fictitious magnetic fields associated with the presence of the topological constraints. In the limit in which two of the spatial dimensions are large in comparison with the third one, we provide exact formulas for the conformations of the monomer densities of the 4-plat by using the elliptic, hyperbolic and trigonometric solutions of the sinh-Gordon and cosh-Gordon equations which have been used for instance in the construction of classical string solutions in AdS3 and dS3 [9].

Microscopic interactions control a structural transition in active mixtures of microtubules and molecular motors

Microtubules and molecular motors are essential components of the cellular cytoskeleton, driving fundamental processes in vivo, including chromosome segregation and cargo transport. When reconstituted in vitro, these cytoskeletal proteins serve as energy-consuming building blocks to study the self-organization of active matter. Cytoskeletal active gels display rich emergent dynamics, including extensile flows, locally contractile asters, and bulk contraction. However, it is unclear how the protein-protein interaction kinetics set their contractile or extensile nature. Here, we explore the origin of the transition from extensile bundles to contractile asters in a minimal reconstituted system composed of stabilized microtubules, depletant, adenosine 5'-triphosphate (ATP), and clusters of kinesin-1 motors. We show that the microtubule-binding and unbinding kinetics of highly processive motor clusters set their ability to end-accumulate, which can drive polarity sorting of the microtubules and aster formation. We further demonstrate that the microscopic time scale of end-accumulation sets the emergent time scale of aster formation. Finally, we show that biochemical regulation is insufficient to fully explain the transition as generic aligning interactions through depletion, cross-linking, or excluded volume interactions can drive bundle formation despite end-accumulating motors. The extensile-to-contractile transition is well captured by a simple self-assembly model where nematic and polar aligning interactions compete to form either bundles or asters. Starting from a five-dimensional organization phase space, we identify a single control parameter given by the ratio of the different component concentrations that dictates the material-scale organization. Overall, this work shows that the interplay of biochemical and mechanical tuning at the microscopic level controls the robust self-organization of active cytoskeletal materials.

Capillary action and stationary currents in scalar active matter

Active matter consists of particles (motile microorganism or active colloids) that consume nutrients or fuel and convert it into a persistent motion, has received a lot of attention due to its intrinsic out-of-equilibrium character on the microscale [1]. The simplest representatives of active matter are spherically symmetric, active Brownian particles (ABPs) [2] without alignment, however, with excluded volume interactions [3,4].

Endocytosis efficiency and targeting ability by the cooperation of nanoparticles.

Cooperative wrapping of nanoparticles (NPs) with small sizes is an important pathway for the uptake of NPs by cell membranes. However, the cooperative wrapping efficiency and the effects of NPs' rigidity remain ambiguous. With the aid of computer simulations, we show that the complete wrapping mechanism of cooperative endocytosis is that the aggregation of NPs leads to greater wrapping forces than the single NP case, which triggers the increase of the wrapping degree and in turn further increases the wrapping forces until they are finally fully taken up. The effects of the NP size, initial distance, interaction strength, arrangement and stiffness on cooperative endocytosis were systematically studied. The cooperative wrapping efficiency increases as the NP radius increases. Hexagonal close packed NPs have the highest internalization efficiency. When the interactions are strong, softer NPs exhibit higher endocytosis efficiency. We further propose two strategies by combining NPs with different wrapping properties for targeting applications. By combining two NPs decorated with different types of ligands, the combination NPs can only be fully endocytosed by the cell membrane with two cognate types of receptors and adhere to the normal cell membrane with only one type of receptor. We also design composite NPs using a large NP non-covalently decorated with several small NPs. By harnessing the competition between the ligand-receptor interactions and the excluded volume interactions between the small NPs and the lipid membrane, the composite NPs have targeting ability towards the cancer cell membrane. The design concept of combining NPs with different wrapping properties for drug targeting applications may be very promising in biomedicine.

Development of soy protein isolate gels added with Tremella polysaccharides and psyllium husk powder as 3D printing inks for people with dysphagia.

The aim of this study was to investigate the feasibility of soy protein isolate (SPI) gels added with Tremella polysaccharides (TPs) and psyllium husk powder (PHP) as 3D printing inks for developing dysphagia-friendly food and elucidate the potential mechanism of TPs and PHP in enhancing the printing and swallowing performance of SPI gels. The results indicated that the SPI gels with a TP : PHP ratio of 3 : 7 could be effectively used as printing inks to manufacture dysphagia-friendly food. The addition of TPs increased the free water content, resulting in a decrease in the viscosity of the SPI gels, which, in turn, reduced the line width of the 3D-printed product and structural strength of the gel system. The addition of PHP increased disulfide bond interactions and excluded volume interactions, which determined the mechanical strength of SPI gels and increased the line width of the printed product. The synergistic effects between TPs and PHP improved the printing precision and structural stability. This study presents meaningful insights for the utilization of 3D printing in the creation of dysphagia-friendly food using protein-polysaccharide complexes.