Dissipative Particle Dynamics Study of the pH-Dependent Behavior of Poly(2-vinylpyridine)-block-poly(ethylene oxide) Diblock Copolymer in Aqueous Buffers

Changes in Ion Concentrations upon the Binding of Short Polyelectrolytes on Phospholipid Bilayers: Computer Study Addressing Interesting Physiological Consequences

This computer study was inspired by the experimental observation of Y. Qian et al. published in ACS Applied Materials and Interfaces, 2018 that the short positively charged β-peptide chains and their oligomeric analogues efficiently suppress severe medical problems caused by antimicrobial drug-resistant bacteria despite them not penetrating the bacterial membrane. Our coarse-grained molecular dynamics (dissipative particle dynamics) simulations confirm the tentative explanation of the authors of the experimental study that the potent antimicrobial activity is a result of the entropically driven release of divalent ions (mainly magnesium ions essential for the proper biological function of bacteria) into bulk solution upon the electrostatic binding of β-peptides to the bacterial membrane. The study shows that in solutions containing cations Na⁺, Ca²⁺ and Mg²⁺, and anions Cl⁻, the divalent cations preferentially concentrate close to the membrane and neutralize the negative charge. Upon the addition of positively charged oligomer chains (models of β-peptides and their analogues), the oligomers electrostatically bind to the membrane replacing divalent ions, which are released into bulk solvent. Our simulations indicate that the entropy of small ions (which controls the behavior of synthetic polyelectrolyte solutions) plays an important role in this and also in other similar biologically important systems.

Adsorption of amphiphilic grafted polymers as polymer corrosion inhibitors: insights from mesoscopic simulations

The homogeneous covering of amphiphillic polymer molecules onto metallic surfaces is of great importance for corrosion inhibitor applications. Lyophillic side chains grafted onto a lyophobic backbone act as anchors that allow the molecule to absorb at the metallic surface preventing the exposure with the solvent. Coarse-grained simulations are used to study the sorption and conformation behaviour of amphiphillic grafted polymers for corrosion inhibition. The backbone insolubility is found to play a key role in the sorption and conformation behaviour in the dilute limit. For finite concentrations, moderate backbone solubility and moderate molecule concentrations achieve optimal surface coverage, while highly a lyophobic backbone leads to bulk-like structures as a consequence of aggregation.

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.

Dual-responsive zwitterion-modified nanopores：a mesoscopic simulation study

In this work, dissipative particle dynamics simulation was carried out to investigate the intelligent switching effect of nanopores grafted by the zwitterionic polymer brushes poly(carboxybetaine) with excellent antifouling property. The...

Multiscale simulations of polyzwitterions in aqueous bulk solutions and brush array configurations

Zwitterionic polymers are very promising candidates for antifouling materials that exhibit high chemical stability as compared to polyethylene glycol-based systems. A number of simulation and experimental studies have emerged over recent years for the investigation of sulfobetaine-based zwitterionic polymers. Investigating the structural and thermodynamic properties of such polymers requires access to broad time and length regimes, thus necessitating the development of multiscale simulation strategies. The present article advocates a mesoscopic dissipative particle dynamics (DPD) model capable of addressing a wide range of time and length scales. The mesoscopic force field was developed hand-in-hand with atomistic simulations based on the OPLS force field through a bottom-up parameterization procedure that matches the atomistically calculated strand-length, strand-angle and pair distribution functions. The DPD model is validated against atomistic simulations conducted in this work, and against relevant atomistic simulation studies, theoretical predictions and experimental correlations from the literature. Properties examined include the conformations of SPE polymers in dilute bulk aqueous solution, the density profile and thickness of brush arrays as functions of the grafting density and chain length. In addition, we compute the potential of mean force of an approaching hydrophilic or hydrophobic foulant via umbrella sampling as a function of its position relative to the poly-zwitterion-covered surface. The aforementioned observables lead to important insights regarding the conformational tendencies of grafted polyzwitterions and their antifouling properties.

Temperature-responsive morphology formation of a PS-b-PI copolymer: a dissipative particle dynamics simulation study

Self-assembly responsiveness to stimuli of polystyrene-block-polyisoprene (PS-b-PI) diblock copolymer materials is explored by means of classical molecular dynamics (MD) and dissipative particle dynamics (DPD) simulations. A concerted relationship between the parameters achieved from atomistic and DPD simulations is obtained for this molecular recognition as clearly pronounced in a phase transition. Effects of temperature, model size and composition on the morphological formation were systematically investigated for the diblock copolymeric system. Structural changes resulting in the evolution of rheology as well as an equilibrium ordered structure were analyzed in terms of order parameters and radial distribution functions. From our models, various morphologies were observed including discrete clusters (sphere-liked morphology), connected clusters (gyroid-liked morphology), hexagonally packed cylinders (HEX), connected cylinders, irregular cylinders, perfect lamellae, perforated lamellae and defected lamellae. Based on this finding, a bottom-up multi-scale simulation of the PS-b-PI diblock copolymer provides a link between equilibrium copolymeric morphologies and the crucial parameters.

Ionic Transport and Robust Switching Properties of the Confined Self-Assembled Block Copolymer/Homopolymer in Asymmetric Nanochannels

The self-assembly of block copolymers in a confined space has been proven to be a facile and robust strategy for fabricating assembled structures with various potential applications. Herein, we employed a new pH-responsive polymer self-assembly method to regulate ion transport inside artificial nanochannels. The track-etched asymmetric nanochannels were functionalized with PS_22k-b-P4VP_17k/hPS_4k blend polymers, and the ionic conductance and rectification properties of the proposed system were investigated. The pH-actuated changes in the surface charge and wettability resulted in the selective pH-gated ionic transport behavior. The designed system showed a good switching property to the pH stimulus and could recover during the repetitive experiments. The gating ability of the polymer-nanochannel system increased with increasing the weight of the homopolymer, and the proposed platform demonstrated robust stability and reusability. Numerical and the dissipative particle dynamics simulations were implemented to emulate the pH-dependent self-assembling behavior of diblock copolymers in a confined space, which were consistent with the experimental observations. As an example of the self-assembly of polymers in nanoconfinements, this work provides a facile and robust strategy for the regulation of ion transport in synthetic nanochannels. Meanwhile, this work can be further extended to design artificial smart nanogates for various applications such as mass delivery and energy harvesting.

Solubilization of Charged Porphyrins in Interpolyelectrolyte Complexes: A Computer Study

Using coarse-grained dissipative particle dynamics (DPD) with explicit electrostatics, we performed (i) an extensive series of simulations of the electrostatic co-assembly of asymmetric oppositely charged copolymers composed of one (either positively or negatively charged) polyelectrolyte (PE) block A and one water-soluble block B and (ii) studied the solubilization of positively charged porphyrin derivatives (P+) in the interpolyelectrolyte complex (IPEC) cores of co-assembled nanoparticles. We studied the stoichiometric mixtures of 137 A10+B25 and 137 A10-B25 chains with moderately hydrophobic A blocks (DPD interaction parameter aAS=35) and hydrophilic B blocks (aBS=25) with 10 to 120 P+ added (aPS=39). The P+ interactions with other components were set to match literature information on their limited solubility and aggregation behavior. The study shows that the moderately soluble P+ molecules easily solubilize in IPEC cores, where they partly replace PE+ and electrostatically crosslink PE- blocks. As the large P+ rings are apt to aggregate, P+ molecules aggregate in IPEC cores. The aggregation, which starts at very low loadings, is promoted by increasing the number of P+ in the mixture. The positively charged copolymers repelled from the central part of IPEC core partially concentrate at the core-shell interface and partially escape into bulk solvent depending on the amount of P+ in the mixture and on their association number, AS. If AS is lower than the ensemble average ⟨AS⟩n, the copolymer chains released from IPEC preferentially concentrate at the core-shell interface, thus increasing AS, which approaches ⟨AS⟩n. If AS>⟨AS⟩n, they escape into the bulk solvent.

Phase behavior of AB/CD diblock copolymer blends via coarse-grained simulation

The phase diagram of equimolar blends of AB and CD diblock copolymers has been studied using dissipative particle dynamics. All unlike blocks interacted with the same χ, except for the B-C interaction, for which χ_BC < 0 in order to prevent macrophase separation. The BC interaction was able to prevent macrophase separation except for low volume fractions of B and C (φ_BC⪅ 0.1) and relatively equal fractions of A and D. For high φ_BC (φ_BC⪆ 0.92), a disordered state was obtained. For all microphase separated states the shapes/morphologies were described by the ratios of the eigenvalues of the radius of gyration tensor and their sphericity. These were used to classify the domains as forming sphere, cylinders, lamellae, or branched/gyroidal structures. For φ_BC < 0.5 the BC domains acted as an interfacial region which compatibilized the A and D domains, while for φ_BC > 0.5 the BC domain filled in the space between A and D domains. Several interesting structures were formed including a novel connected/branched spheres morphology, hierarchical lamellae, concentric spheres/cylinders, and a combination of cylinders/lamellae. Comparisons are made with the linear diblock and linear triblock phase diagrams.

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.

Adsorption of amphiphilic graft copolymers in solvents selective for the grafts on a lyophobic surface: a coarse-grained simulation study

The sorption of graft copolymers on surfaces attractive only for the backbone and its effect on the conformational behavior of adsorbed/desorbed chains in solvents good for the grafts and poor for the backbone was studied by coarse-grained computer simulations.

A dissipative particle dynamics simulation study on phase diagrams for the self-assembly of amphiphilic hyperbranched multiarm copolymers in various solvents

Self-assembly of amphiphilic hyperbranched multiarm copolymers (HMCs) has shown great potential for preparing all kinds of delicate supramolecular structures in all scales and dimensions in solution. However, theoretical studies on the influencing factors for the self-assembly of HMCs have been greatly lagging behind. The phase diagram of HMCs in selective solvents is very necessary but has not been disclosed up to now. Here, the self-assembly of HMCs with different hydrophilic fractions in various solvents was studied systematically by using dissipative particle dynamics (DPD) simulations. Three morphological phase diagrams are constructed and a rich variety of morphologies, ranging from spherical micelles, worm-like micelles, membranes, vesicles, vesosomes, small micellar aggregates (SMAs), and aggregates of spherical and worm-like micelles to helical micelles, are obtained. In addition, both the self-assembly mechanisms and the dynamic processes for the formation of these self-assemblies have been systematically investigated. The simulation results are consistent with available experimental observations. Besides, several novel structures, like aggregates of spherical and worm-like micelles, vesosomes and helical micelles, are firstly discovered for HMC self-assembly. We believe the current work will extend the knowledge on the self-assembly of HMCs, especially on the control of supramolecular structures and on fabricating novel self-assemblies.

Dynamics of Charged Species in Ionic-Neutral Block Copolymer and Surfactant Complexes

Structure-property relationships of ionic block copolymer (BCP) surfactant complexes are critical toward the progress of favorable engineering design of efficient charge-transport materials. In this article, molecular dynamics simulations are used to understand the dynamics of charged-neutral BCP and surfactant complexes. The dynamics are examined for two different systems: charged-neutral double-hydrophilic and hydrophobic-hydrophilic block copolymers with oppositely charged surfactant moieties. The dynamics of the surfactant head, tails, and charges are studied for five different BCP volume fractions. We observe that the dynamics of the different species solely depend on the balance between electrostatic and entropic interactions between the charged species and the neutral monomers. The favorable hydrophobic-hydrophobic interactions and the unfavorable hydrophobic-hydrophilic interactions determine the mobilities of the monomers. The dynamical properties of the charge species influence complex formation. Structural relaxations exhibit length-scale dependent behavior, with slower relaxation at the radius of gyration length-scale and faster relaxation at the segmental length-scale, consistent with previous results. The dynamical analysis correlates ion-exchange kinetics to the self-assembly behavior of the complexes.

A self-consistent mean-field model for polyelectrolyte gels

We present a novel approach to modeling polyelectrolyte gels, exploiting the analogy between star-branched polymers and polymer networks as a computationally inexpensive yet reliable alternative to full-scale simulations. In the numerical mean-field model of a star-like polymer we modify the boundary conditions to represent an infinite network. We validate the predictions of our new model against a coarse-grained simulation model. We also validate it against a phenomenological analytical model which has been previously shown to agree with simulations in a limited range of parameters. The mean-field model explicitly considers local density gradients and agrees with the simulation results in a broad range of parameters, beyond that of the analytical model. Finally, we use the mean-field model for predictions of the swelling behaviour of weak polyelectrolyte gels under different pH conditions. We demonstrate that the local density gradients are important and that the ionization of the weak polyelectrolyte gel is significantly suppressed. Under the studied conditions the effective pK_A is about one unit higher than that of the free monomer. This shift in the effective pK_A stems from the different pH values inside and outside the gel.

Flow and aggregation of rod-like proteins in slit and cylindrical pores coated with polymer brushes: an insight from dissipative particle dynamics

We use a meso-scale dissipative particle dynamics method to simulate the flow and aggregation of rod-like protein solutions through pores grafted with a solvent-sensitive polymer brush. The coated pores can control protein permeability and aggregation by a stretch-to-collapse conformational transition of the brush polymers in response to changes in the solvent quality. The protein solutions mimic aqueous glycoprotein solutions and proteins are represented as rod-like objects formed by coarse-grain beads. The model further employs two types of beads to represent the existence of cystein-like terminal groups in real glycoproteins and mimic the aggregation of real glycoproteins in aqueous solutions. We vary the solvent quality with respect to the brush chains and study the flow and aggregation of rod-like proteins in the slit and cylindrical pores as the brush polymers undergo the stretch-to-collapse transition. The results show that stretched brush chains close the pore, hamper proteins' flow and promote proteins' aggregation. The collapsed brush chains open the pores for proteins' flow and suppress their aggregation. Therefore, we observe more than a ten-fold reduction in the permeation rate of proteins in both pore geometries. Finally, due to pore confinement, larger proteins' aggregates are formed in the slit pore than in the cylindrical pore, while more pronounced orientation of proteins in the flow direction is seen in the cylindrical pore than in the slit pore.

Computer Simulation Studies on the pH-Responsive Self-Assembly of Amphiphilic Carboxy-Terminated Polyester Dendrimers in Aqueous Solution

This paper investigates the pH-responsive self-assembly of an amphiphilic carboxyl-terminated polyester dendrimer, H20-COOH, in aqueous solution using the dissipative particle dynamics method. The electrostatic interactions were described by introducing the explicit interaction between the smeared charges on ionized polymer beads and the counterions. The results show that the self-assemblies could change from unimolecular micelles, microphase-separated small micelles, wormlike micelles, sheetlike micelles, and small vesicles to large vesicles with the decrease in the degree of ionization (α) of carboxylic acid groups. In addition, the detailed self-assembly mechanisms and the molecular packing models have also been disclosed for each self-assembly stages. Interestingly, the wormlike micelles are found to change from linear to branched when α decreases from 0.182 to 0.109. The current work might serve as a comprehensive understanding on the effect of carboxylic acid groups on the self-assembly behaviors of dendritic polymers.

Architectural evolution of phase domains in shape memory polyurethanes by dissipative particle dynamics simulations

The MDI phase in SMPUs develops a framework with netpoints evolving from spheres, to linked-spheres, linked-cylinders, and then to linked-bi-crossing-cylinders.

Self-organization of hydrophobic-capped triblock copolymers with a polyelectrolyte midblock: a coarse-grained molecular dynamics simulation study

We present the results of a Langevin dynamics simulation study of micellar organization and hydrogel formation in the solutions of coarse-grained ABA copolymer chains. Polymer chains are modeled as bead-spring chains of Lennard-Jones particles by explicit treatment of ionic species in implicit solvent. The studied copolymer is composed of a polyelectrolyte midblock flanked by two hydrophobic endblocks. We explore the self-assembly of copolymer solutions at a fixed polymer concentration and temperature upon systematic variation of the midblock charge fraction, valency of neutralizing counterions, and the stiffness and length of hydrophobic endblocks. Minimization of the surface energy, conformational entropy of the midblock chains, electrostatic repulsion of midblock charges, and the translational entropy of counterions are found to play central roles in controlling the self-organization features of copolymer solutions. Flower-like micelles with A-blocks forming the core of spherical aggregates and B-blocks constituting the micelle corona are established for the neutral midblocks. Increasing the charge content of B chains lowers the fraction of loop conformations and yields a spanning hydrogel network with midblocks bridging the hydrophobic clusters. Counterion valence is shown to exert a strong effect on the micelle size and network structure. The increase in the rigidity of terminal A-blocks increases the fraction of bridging chains and results in the formation of a hydrogel network with bundle-like hydrophobic domains. Longer endblocks are shown to increase the hydrophobic cluster size and enhance the bridged midblock fraction. The qualitative agreement between the experimental and theoretical studies is also discussed. The comprehensive molecular picture provides a framework for the future studies of stimuli-responsive copolymer systems.

The electrostatic co-assembly in non-stoichiometric aqueous mixtures of copolymers composed of one neutral water-soluble and one polyelectrolyte (either positively or negatively charged) block: a dissipative particle dynamics study

The electrostatic co-assembly in non-stoichiometric aqueous mixtures of diblock copolymers.

The self-assembly of copolymers with one hydrophobic and one polyelectrolyte block in aqueous media: a dissipative particle dynamics study

The reversible self-assembly of copolymers with one hydrophobic and one polyelectrolyte block.

Modeling Aggregation of Ionic Surfactants Using a Smeared Charge Approximation in Dissipative Particle Dynamics Simulations

Using dissipative particle dynamics (DPD) simulations, we explore the specifics of micellization in the solutions of anionic and cationic surfactants and their mixtures. Anionic surfactant sodium dodecyl sulfate (SDS) and cationic surfactant cetyltrimethylammonium bromide (CTAB) are chosen as characteristic examples. Coarse-grained models of the surfactants are constructed and parameterized using a combination of atomistic molecular simulation and infinite dilution activity coefficient calibration. Electrostatic interactions of charged beads are treated using a smeared charge approximation: the surfactant heads and dissociated counterions are modeled as beads with charges distributed around the bead center in an implicit dielectric medium. The proposed models semiquantitatively describe self-assembly in solutions of SDS and CTAB at various surfactant concentrations and molarities of added electrolyte. In particular, the model predicts a decline in the free surfactant concentration with the increase of the total surfactant loading, as well as characteristic aggregation transitions in single-component surfactant solutions caused by the addition of salt. The calculated values of the critical micelle concentration reasonably agree with experimental observations. Modeling of catanionic SDS-CTAB mixtures show consecutive transitions to worm-like micelles and then to vesicles caused by the addition of CTAB to micellar solution of SDS.

The structure and interaction mechanism of a polyelectrolyte complex: a dissipative particle dynamics study

The mechanism of complex formation of two oppositely charged linear polyelectrolytes dispersed in a solvent is investigated by using dissipative particle dynamics (DPD) simulation. In the polyelectrolyte solution, the size of the cationic polyelectrolyte remains constant while the size of the anionic chain increases. We analyze the influence of the anionic polyelectrolyte size and salt effect (ionic strength) on the conformational changes of the chains during complex formation. The behavior of the radial distribution function, the end-to-end distance and the radius of gyration of each polyelectrolyte is examined. These results showed that the effectiveness of complex formation is strongly influenced by the process of counterion release from the polyelectrolyte chains. The radius of gyration of the complex is estimated using the Fox-Flory equation for a wormlike polymer in a theta solvent. The addition of salts in the medium accelerates the complex formation process, affecting its radius of gyration. Depending on the ratio of chain lengths a compact complex or a loosely bound elongated structure can be formed.

Origami with ABC Triblock Terpolymers Based on Glycopolymers: Creation of Virus-Like Morphologies

Morphologies, that resemble viruses, were created using a single ABC triblock terpolymer poly(2-acryloylethyl-α-d-mannopyranoside)-b-poly(n-butyl acrylate)-b-poly(4-vinylpyridine) (PAcManA₇₀-b-PBA₃₆₉-b-PVP₃₇₀). Morphologies ranging from flower-like micelles, cylindrical micelles, raspberry-like morphologies to nanocaterpillars were obtained by adjusting the pH value during the self-assembly process. The resulting nanoparticles had an abundance of mannose on the surface, which were recognized by the mannose receptors of RAW264.7, a macrophage cell line that can be used as a model for virus entry.

Mesoscale modelling of environmentally responsive hydrogels: emerging applications

We review recent advances in mesoscale computational modeling, focusing on dissipative particle dynamics, used to probe stimuli-sensitive behavior of hydrogels.