Dissipative particle dynamics for systems with high density of charges: Implementation of electrostatic interactions

Instability of membranes containing ionizable cationic lipids: Effects of the repulsive range of headgroups and tail structures

The stability of membranes formed by ionizable cationic lipids, which constitute the primary components in lipid nanoparticles capable of endosomal escape, is explored using coarse-grained dissipative particle dynamics. Three types of ionizable model lipids with different tail structures are considered. Endosome acidification causes the ionization of lipids, leading to an increased repulsive range between their headgroups. When electrostatic repulsion is modeled as a conservative force with a long-range cutoff distance (rc,HH), the membrane and vesicle experience a loss of structural integrity and develop holes as rc,HH is beyond a critical value, which varies with the tail structure. When Coulombic repulsion is explicitly incorporated and intensified, a fully ionized lipid membrane undergoes a loss of structural integrity, displaying a qualitative similarity to the effect observed with the increase in rc,HH on the membrane stability. Qualitatively similar results are obtained for partially ionized membranes as the fraction of charged lipids increases. The stability of a mixed lipid membrane containing both ionizable and conventional lipids is also investigated. The disruption of the bilayer structure occurs for a sufficiently high charged fraction. The membrane instability can be attributed to the decrease in the packing parameter, which significantly deviates from unity as the interaction range increases.

Design, preparation, and characterization of lubricating polymer brushes for biomedical applications

The lubrication modification of biomedical devices significantly enhances the functionality of implanted interventional medical devices, thereby providing additional benefits for patients. Polymer brush coating provides a convenient and efficient method for surface modification while ensuring the preservation of the substrate's original properties. The current research has focused on a "trial and error" method to finding polymer brushes with superior lubricity qualities, which is time-consuming and expensive, as obtaining effective and long-lasting lubricity properties for polymer brushes is difficult. This review summarizes recent research advances in the biomedical field in the design, material selection, preparation, and characterization of lubricating and antifouling polymer brushes, which follow the polymer brush development process. This review begins by examining various approaches to polymer brush design, including molecular dynamics simulation and machine learning, from the fundamentals of polymer brush lubrication. Recent advancements in polymer brush design are then synthesized and potential avenues for future research are explored. Emphasis is placed on the burgeoning field of zwitterionic polymer brushes, and highlighting the broad prospects of supramolecular polymer brushes based on host-guest interactions in the field of self-repairing polymer brush applications. The review culminates by providing a summary of methodologies for characterizing the structural and functional attributes of polymer brushes. It is believed that a development approach for polymer brushes based on "design-material selection-preparation-characterization" can be created, easing the challenge of creating polymer brushes with high-performance lubricating qualities and enabling the on-demand creation of coatings. STATEMENT OF SIGNIFICANCE: Biomedical devices have severe lubrication modification needs, and surface lubrication modification by polymer brush coating is currently the most promising means. However, the design and preparation of polymer brushes often involves "iterative testing" to find polymer brushes with excellent lubrication properties, which is both time-consuming and expensive. This review proposes a polymer brush development process based on the "design-material selection-preparation-characterization" strategy and summarizes recent research advances and trends in the design, material selection, preparation, and characterization of polymer brushes. This review will help polymer brush researchers by alleviating the challenges of creating polymer brushes with high-performance lubricity and promises to enable the on-demand construction of polymer brush lubrication coatings.

The conformational phase diagram of charged polymers in the presence of attractive bridging crowders

Using extensive molecular dynamics simulations, we obtain the conformational phase diagram of a charged polymer in the presence of oppositely charged counterions and neutral attractive crowders for monovalent, divalent, and trivalent counterion valencies. We demonstrate that the charged polymer can exist in three phases: (1) an extended phase for low charge densities and weak polymer-crowder attractive interactions [Charged Extended (CE)]; (2) a collapsed phase for high charge densities and weak polymer-crowder attractive interactions, primarily driven by counterion condensation [Charged Collapsed due to Intra-polymer interactions [(CCI)]; and (3) a collapsed phase for strong polymer-crowder attractive interactions, irrespective of the charge density, driven by crowders acting as bridges or cross-links [Charged Collapsed due to Bridging interactions [(CCB)]. Importantly, simulations reveal that the interaction with crowders can induce collapse, despite the presence of strong repulsive electrostatic interactions, and can replace condensed counterions to facilitate a direct transition from the CCI and CE phases to the CCB phase.

Effect of the counterion size on microphase separation in charged-neutral diblock copolymers

In this work, the question of the influence of the counterion size on the self-assembly in melts of diblock copolymers with one charged block was studied using coarse-grained molecular dynamics simulations. It was assumed that the blocks were fully compatible, i.e., the Flory-Huggins parameter χ between them was equal to 0. Due to the presence of correlation attraction (electrostatic cohesion) between the charged species, the systems with all types of counterions underwent transitions to ordered states, forming various morphologies, including lamellae, perforated lamellae, and hexagonally packed cylinders. Phase diagrams were constructed by varying the chain composition f_c and locating the order-disorder transition positions in terms of the electrostatic strength parameter λ (dimensionless Bjerrum length). Despite having a rather large ion size mismatch, the systems with smaller counterions demonstrated an even better tendency to form microphase separated states than the systems with larger ones. It was found that the differences between the phase diagrams of the systems with different counterions can be roughly rationalized by using coordinates (volume fraction of the charged block φ_c-modified interaction parameter λ*). The latter parameter assumes that the electrostatic energy is simply inversely proportional to the characteristic distance between the ions of different signs. Such an approach appeared to be rather effective and allowed the diagrams obtained for different counterion sizes to almost coincide. The results of this work suggest that the counterion size can be used as a tool to control the system morphology as well as the effective incompatibility between the blocks.

Notes on the Treatment of Charged Particles for Studying Cyclotide/Membrane Interactions with Dissipative Particle Dynamics

Different charge treatment approaches are examined for cyclotide-induced plasma membrane disruption by lipid extraction studied with dissipative particle dynamics. A pure Coulomb approach with truncated forces tuned to avoid individual strong ion pairing still reveals hidden statistical pairing effects that may lead to artificial membrane stabilization or distortion of cyclotide activity depending on the cyclotide's charge state. While qualitative behavior is not affected in an apparent manner, more sensitive quantitative evaluations can be systematically biased. The findings suggest a charge smearing of point charges by an adequate charge distribution. For large mesoscopic simulation boxes, approximations for the Ewald sum to account for mirror charges due to periodic boundary conditions are of negligible influence.

DPD Modelling of the Self- and Co-Assembly of Polymers and Polyelectrolytes in Aqueous Media: Impact on Polymer Science

This review article is addressed to a broad community of polymer scientists. We outline and analyse the fundamentals of the dissipative particle dynamics (DPD) simulation method from the point of view of polymer physics and review the articles on polymer systems published in approximately the last two decades, focusing on their impact on macromolecular science. Special attention is devoted to polymer and polyelectrolyte self- and co-assembly and self-organisation and to the problems connected with the implementation of explicit electrostatics in DPD numerical machinery. Critical analysis of the results of a number of successful DPD studies of complex polymer systems published recently documents the importance and suitability of this coarse-grained method for studying polymer systems.

The effect of explicit polarity on the conformational behavior of a single polyelectrolyte chain

In this work using dissipative particle dynamics simulations with explicit treatment of polar species we demonstrate that the molecular nature of dielectric media has a significant impact on swelling and collapse of a polyelectrolyte chain in a dilute solution. We show that the small-scale effects related to the presence of polar species lead to the intensification of the electrostatic interactions when the charges are close to each other and/or their density is high enough. As a result, the electrostatic strength , usually regarded as the main parameter governing the polyelectrolyte chain collapse, does not have a universal meaning: the value of λ at which the coil-to-globule transition occurs is found to be dependent on the specific fixed value of the solvent bulk permittivity ε while varying the monomer unit charge Q and vice versa. This effect is observed even when the backbone and the counterions have the same polarity as the solvent beads, i.e. no dielectric mismatch is present. The reason for such behavior is rationalized in terms of the "effective" dielectric permittivity ε^eff which depends on the volume fraction φ of charged units inside the polymer chain volume; using ε^eff instead of ε collapses all data onto one master curve describing the chain shrinking with λ. Furthermore, it is shown that a polar chain adopts less swollen conformations in the polyelectrolyte regime and collapses more easily compared to a non-polar chain.

An Enhanced Scheme for Multiscale Modeling of Thermomechanical Properties of Polymer Bulks

While multiscale modeling significantly enhances the capability of molecular simulations of polymer systems, it is well realized that the systematically derived coarse-grained (CG) models generally underestimate the thermomechanical properties. In this work, a charge-based mapping scheme has been adopted to include explicit electrostatic interactions and benchmarked against two typical polymers, atactic poly(methyl methacrylate) (PMMA) and polystyrene (PS). The CG potentials are parameterized against the oligomer bulks of nine monomers per chain to match the essential structural features and the two basic pressure-volume-temperature (PVT) properties, which are obtained from the all-atomistic (AA) molecular dynamics (MD) simulations at a single elevated temperature. The so-parameterized CG potentials are extended with the MD method to simulate the two polymer bulks of one hundred monomers per chain over a wide temperature range. Without any scaling, all the simulated results, including mass densities and bulk moduli at room temperature, thermal expansion coefficients at rubbery and glassy states, and glass transition temperatures (T_g), compare well with the corresponding experimental data. The proposed scheme not only contributes to realistically simulating various thermomechanical properties of both apolar and polar polymers but also allows for directly simulating their electrical properties.

Two contributions to the dielectric response of polar liquids

In this Note, we study the total conservative force {instead of pure electrostatic force as it was carried out in the work by Gavrilov [J. Chem. Phys. 152, 164101 (2020)]} acting on two charges in a polar liquid using dissipative particle dynamics and coarse-grained molecular dynamics simulations. We show that such force (instead of the electrostatic force) obeys Coulomb's law at large distances between the charges. Apparently, the dielectric response of a polar liquid (at least, within such coarse-grained models) can be decomposed into two contributions: the reorientation of the dipoles (i.e., electrostatic contribution) and the density redistribution (i.e., volume interaction contribution).

The ENUF method-Ewald summation based on nonuniform fast Fourier transform: Implementation, parallelization, and application

Computer simulations of model systems are widely used to explore striking phenomena in promising applications spanning from physics, chemistry, biology, to materials science and engineering. The long range electrostatic interactions between charged particles constitute a prominent factor in determining structures and states of model systems. How to efficiently calculate electrostatic interactions in simulation systems subjected to partial or full periodic boundary conditions has been a grand challenging task. In the past decades, a large variety of computational schemes has been proposed, among which the Ewald summation method is the most reliable route to accurately deal with electrostatic interactions between charged particles in simulation systems. In addition, extensive efforts have been done to improve computational efficiencies of the Ewald summation based methods. Representative examples are approaches based on cutoffs, reaction fields, multi-poles, multi-grids, and particle-mesh schemes. We sketched an ENUF method, an abbreviation for the Ewald summation method based on the nonuniform fast Fourier transform technique, and have implemented this method in particle-based simulation packages to calculate electrostatic energies and forces at micro- and mesoscopic levels. Extensive computational studies of conformational properties of polyelectrolytes, dendrimer-membrane complexes, and ionic fluids demonstrated that the ENUF method and its derivatives conserve both energy and momentum to floating point accuracy, and exhibit a computational complexity of O N log N with optimal physical parameters. These ENUF based methods are attractive alternatives in molecular simulations where high accuracy and efficiency of simulation methods are needed to accelerate calculations of electrostatic interactions at extended spatiotemporal scales.

Influence of Charges on the Behavior of Polyelectrolyte Microgels Confined to Oil-Water Interfaces

The role of electrostatics on the interfacial properties of polyelectrolyte microgels has been discussed controversially in the literature. It is not yet clear if, or how, Coulomb interactions affect their behavior under interfacial confinement. In this work, we combine compression isotherms, atomic force microscopy imaging, and computer simulations to further investigate the behavior of pH-responsive microgels at oil-water interfaces. At low compression, charged microgels can be compressed more than uncharged microgels. The in-plane effective area of charged microgels is found to be smaller in comparison to uncharged ones. Thus, the compressibility is governed by in-plane interactions of the microgels with the interface. At high compression, however, charged microgels are less compressible than uncharged microgels. Microgel fractions located in the aqueous phase interact earlier for charged than for uncharged microgels because of their different swelling perpendicular to the interface. Therefore, the compressibility at high compression is controlled by out-of-plane interactions. In addition, the size of the investigated microgels plays a pivotal role. The charge-dependent difference in compressibility at low compression is only observed for small but not for large microgels, while the behavior at high compression does not depend on the size. Our results highlight the complex nature of soft polymer microgels as compared to rigid colloidal particles. We clearly demonstrate that electrostatic interactions affect the interfacial properties of polyelectrolyte microgels.

Dissipative particle dynamics for systems with polar species: Interactions in dielectric media

In this work, we develop a method for simulating polar species in the dissipative particle dynamics (DPD) method. The main idea behind the method is to treat each bead as a dumb-bell, i.e., two sub-beads kept at a fixed distance, instead of a point-like particle. The relation between the bead dipole moment and the bulk dielectric permittivity was obtained. The interaction force of single charges in polar liquid showed that the effective dielectric permittivity is somewhat smaller than that obtained for the bulk case at large separation between the charges. In order to understand the reasons behind the observed drop in the dielectric permittivity, we calculate the electric field of an isolated charge in a polar liquid; no permittivity drop is observed for this case. We can assume that the behavior observed for the force is due to the fact that the probing point is always associated with the charged bead, which is a force center, which essentially leads to a non-homogeneous density distribution around it on average; this is not the case when the field is measured. The interaction of a single charge with an interface between two liquids with different permittivities was studied after that; the model is found to correctly reproduce the "mirror image" effects. Finally, we show why it is necessary to treat the polar species in DPD explicitly by investigating the behavior of a charged colloidal particle at a liquid-liquid interface.

Phase Behavior of Melts of Diblock-Copolymers with One Charged Block

In this work, we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory-Huggins χ parameters were equal to 0. We showed that the charge- correlation attraction solely can cause microphase separation with a long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter λ (dimensionless Bjerrum length). The obtained phase diagram was compared to the phase diagram of "equivalent" neutral diblock-copolymers with the non-zero χ-parameter between the beads of different blocks. The neutral copolymers were constructed by grafting the counterions to the corresponding co-ions of the charged block with further switching off the electrostatic interactions. Surprisingly, the differences between these phase diagrams are rather subtle; the same phases in the same order are observed, and the positions of the order-disorder transition ODT points are similar if the λ-parameter is considered as an "effective" χ-parameter. Next, we studied the position of the ODT for lamellar structure depending on the chain length N. It turned out that while for the uncharged diblock copolymer the product χcrN was almost independent of N, for the diblock copolymers with one charged block we observed a significant increase in λcrN upon increasing N. This can be attributed to the fact that the counterion entropy prevents the formation of ordered structures, and its influence is more pronounced for longer chains since they undergo the transition to ordered structures at smaller values of λ, when the electrostatic energy becomes comparable to kbT. This was supported by studying the ODT in diblock-copolymers with charged blocks and counterions cross-linked to the charged monomer units. The ODT for such systems was observed at significantly lower values of λ, with the difference being more pronounced at longer chain lengths N. The fact that the microphase separation is observed even at zero Flory-Huggins parameter can be used for the creation of "high-χ" copolymers: The incorporation of charged groups (for example, ionic liquids) can significantly increase the segregation strength. The diffusion of counterions in the obtained ordered structures was studied and compared to the case of a system with the same number of charged groups but a homogeneous structure; the diffusion coefficient along the lamellar plane was found to be higher than in any direction in the homogeneous structure.

Computer study of the solubilization of polymer chains in polyelectrolyte complex cores of polymeric nanoparticles in aqueous media

The formation and structure of nanoparticles containing non-polar polymer chains solubilized in interpolyelectrolyte complex (IPC) cores and the partitioning of non-polar chains between bulk solvent and IPC cores were studied by coarse-grained computer simulations. The choice of the model system was inspired by experimental results published by van der Burgh et al. (Langmuir, 2004, 20, 1073-1084). The dissipative particle dynamics (DPD) simulations reproduced the structure and basic features of co-assembled nanoparticles described by experimentalists well at the semi-quantitative coarse-grained level and revealed new properties of co-assembled particles. The simulated co-assemblies were used as reference systems for the solubilization studies. Their results show that non-polar polymers (electrically neutral and compatible with core-forming chains) solubilize easily in IPC cores. They intermix with polyelectrolyte blocks in cores and do not hinder, but, on the contrary, they slightly promote the electrostatic co-assembly.

Dynamic simulations of many-body electrostatic self-assembly

Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process.This article is part of the theme issue 'Modern theoretical chemistry'.

Effect of counterion excluded volume on the conformational behavior of polyelectrolyte chains

Conformational behavior of a single strongly charged polyelectrolyte chain in a dilute solution is studied by molecular dynamics simulations. The novel feature of the model is variation of the excluded volume of counterions for investigating its effect on the chain conformation, especially in low-polar media. It has been confirmed that the chain with conventional counterions collapses into a dense globule with increasing electrostatic interactions. However, if the counterions are bulky enough, they prevent the chain collapse even in media with strong electrostatic interactions. They stay bound in the vicinity of the backbone of the chain that adopts a swollen conformation. In this conformation, the scaling relation for the polymer dimensions with the chain length is the same as for neutral macromolecules in a good solvent, however the polyelectrolyte chain complexed with bulky counterions has a larger gyration radius than its uncharged analogue due to the excluded volume of the counterions contributing to the chain rigidity. Study of the counterion mobility has shown that, similar to the conventional counterions, the bulky counterions do not form stable ion pairs with ions on the polymer chain even in media with strong electrostatic interactions, but rather freely move along the chain backbone. In solutions containing mixtures of counterions with a bimodal size distribution, the conformations of linear polyelectrolytes depend considerably on the fraction of bulky counterions. Furthermore, a kind of intramolecular microphase separation can take place within a polyelectrolyte globule with the formation of a core-shell particle: the smaller counterions concentrate within the globular core while the bulkier counterions form a shell on the globule surface. The stability of the core-shell globule depends on the relative size of the counterions as well as their fractions in the solution. Thus, fine tuning of the balance between the counterion excluded volume and the electrostatic interactions opens new ways for controlling the conformational behavior of polyelectrolytes.

Development of Coarse-Grained Liquid-Crystal Polymer Model with Efficient Electrostatic Interaction: Toward Molecular Dynamics Simulations of Electroactive Materials

Liquid-crystal polymers (LCPs) are well known materials for functional sensor and actuators, because of their high-responsiveness to an electric field. Owing to their complex physical nature, however, the prediction of the functions of LCPs is a challenge. To attack this problem from a molecular point of view, a simulation study is a promising approach. In this work, for future applications of molecular dynamics simulations to problems involving an electric field, we develop an LCP model which consists of coarse-grained mesogenic molecules and smeared charges. For the smearing function of the electrostatic force, the Gauss error function is introduced. This smearing is optimized to attain a reasonable accuracy for phase transition phenomena of liquid crystal while numerical instabilities arising from the singularity of the Coulomb potential are circumvented. For swelling systems, our LCP model exhibits the characteristics of both liquid crystals and unentangled polymer chains; orientational order of the mesogenic units and Rouse-like relaxation dynamics. Our coarse-grained LCP model successfully incorporates electric charges and dipoles and is therefore applicable to problems concerning an electric field.

Regimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solvent

We perform extensive molecular dynamics simulations of a highly charged, collapsed, flexible polyelectrolyte chain in a poor solvent for the case when the electrostatic interactions, characterized by the reduced Bjerrum length l_B, are strong. We find the existence of several sub-regimes in the dependence of the gyration radius of the chain R_g on l_B characterized by R_g ∼ l. In contrast to a good solvent, the exponent γ for a poor solvent crucially depends on the size and valency of the counterions. To explain the different sub-regimes, we generalize the existing counterion fluctuation theory by including a more complete account of all possible volume interactions in the free energy of the polyelectrolyte chain. We also show that the presence of condensed counterions modifies the effective attraction among the chain monomers and modulates the sign of the second virial coefficient under poor solvent conditions.