Nanotribology of biopolymer brushes in aqueous solution using dissipative particle dynamics simulations: an application to PEG covered liposomes in a theta solvent

Effect of amphiphilic polymers on phase separating binary mixtures: A DPD simulation study

We present the phase separation dynamics of a binary (AB), simple fluid (SF), and amphiphilic polymer (AP) mixture using dissipative particle dynamics simulation at d = 3. We study the effect of different AP topologies, including block copolymers, ring block copolymers (RCP), and miktoarm star polymers, on the evolution morphologies, dynamic scaling functions, and length scale of the AB mixture. Our results demonstrate that the presence of APs leads to significantly different evolution morphologies in SF. However, the deviation from dynamical scaling is prominent, mainly for RCP. Typically, the characteristic length scale for SF follows the power law R(t) ∼ tϕ, where ϕ is the growth exponent. In the presence of high AP, we observe diffusive growth (ϕ → 1/3) at early times, followed by saturation in length scale (ϕ → 0) at late times. The extent of saturation varies with constraints imposed on the APs, such as topology, composition ratio, chain length, and stiffness. At lower composition ratios, the system exhibits inertial hydrodynamic growth (ϕ → 2/3) at asymptotic times without clearly exhibiting the viscous hydrodynamic regime (ϕ → 1) at earlier times in our simulations. Our results firmly establish the existence of hydrodynamic growth regimes in low surfactant-influenced phase separation kinetics of binary fluids and settle the related ambiguity in d = 3 systems.

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

Modeling of Branched Thickening Polymers under Poiseuille Flow Gives Clues as to How to Increase a Solvent's Viscosity

The viscosity enhancement of a solvent produced by the addition of thickening branched polymers is predicted as a function of polymer concentration, branch length and persistence length, and strength of the covalent bonding interactions. Nonequilibrium, stationary-state Poiseuille numerical simulations are performed using the dissipative particle dynamics model to obtain the viscosity of the fluid. It is found that the clustering of the polymers into aggregates increases the viscosity and that it is more strongly affected by the strength of the bonding interactions. General scaling relationships are found for the viscosity as a function of the variables studied, which are expected to be useful for the design and synthesis of new viscosifying polymers. It is argued that our results can be applied to aqueous thickeners, of importance for colloidal fluids such as paints and coatings and also for nonpolar fluids such as supercritical CO₂, which is a promising nonhydraulic fracking fluid also useful in enhanced oil recovery.

Liquid and Droplet Transport in Brush-Coated Cylindrical Nanochannels: Brush-Assisted Droplet Formation

We study, by coarse-grained molecular dynamics simulations, equilibrium and flow properties of a liquid in cylindrical nanochannels, coated with polymer brushes. The parameters of the interaction potential model confer a chemical incompatibility between brush monomers and liquid particles. First, we study cylindrical channels whose radii are larger than the brush height and a continuous column of liquid forms at the center of the channel. These results are contrasted to the limiting case in which the radius of the cylinder is comparable to the brush height. In this second case, the grafted polymers interact across the channel and "close" it. We observe a train of droplets as the stable liquid morphology. The droplet size is comparable to the cylinder radius. By applying a constant body force onto the liquid, we induce a Poiseuille-like flow and investigate the morphology and flow rate as a function of driving force. Upon increasing the driving force, we encounter a nonequilibrium transition from a closed channel with slowly moving droplets to a flowing liquid thread at the center. The switching between these two states is reversible.

Combined Experimental and Simulation Studies of Cross-Linked Polymer Brushes under Shear

We have studied the effect of cross-linking on the tribological behavior of polymer brushes using a combined experimental and theoretical approach. Tribological and indentation measurements on poly(glycidyl methacrylate) brushes and gels in the presence of dimethylformamide solvent were obtained by means of atomic force microscopy. To complement experiments, we have performed corresponding molecular dynamics (MD) simulations of a generic bead-spring model in the presence of explicit solvent and cross-linkers. Our study shows that cross-linking leads to an increase in friction between polymer brushes and a counter-surface. The coefficient of friction increases with increasing degree of cross-linking and decreases with increasing length of the cross-linker chains. We find that the brush-forming polymer chains in the outer layer play a significant role in reducing friction at the interface.

Lubrication in polymer-brush bilayers in the weak interpenetration regime: Molecular dynamics simulations and scaling theories

We conduct molecular dynamics (MD) simulations and develop scaling laws to quantify the lubrication behavior of weakly interpenetrated polymer brush bilayers in the presence of an external shear force. The weakly interpenetrated regime is characterized by 1<d_{g}/d_{0}<2, where d_{g} is the gap between the opposing surfaces (where the brushes are grafted) and d_{0} is the unperturbed brush height. MD simulations predict that in the shear thinning regime, characterized by a larger shear force or a large Weissenberg number (W), R_{g}^{2}∼W^{0.19} and η∼W^{-0.38}, where R_{g} is the chain extension in the direction of the shear and η is the viscosity. These scaling behaviors, which are distinctly different from that witnessed in strongly compressed regime (for such a regime, characterized by d_{g}/d_{0}<1, R_{g}^{2}∼W^{0.53}, and η∼W^{-0.46}), match excellently with those predicted by our scaling theory.

Polyelectrolyte brush bilayers in weak interpenetration regime: Scaling theory and molecular dynamics simulations

We employ molecular dynamics (MD) simulations and develop scaling theories to quantify the equilibrium behavior of polyelectrolyte (PE) brush bilayers (BBLs) in the weakly interpenetrated regime, which is characterized by d_{0}<d_{g}<2d_{0}, where d_{g} is the gap between the opposing plates where the PE brushes are grafted and d_{0} is the unperturbed height of a PE brush grafted at a single plate. Scaling predictions establish that, for the weakly interpenetrated osmotic PE BBLs δ∼N^{1/2}(2-d_{g}/d_{0})^{1/2} (where δ is the interpenetration length and N is the number of Kuhn segments in PE brush). MD simulations excellently recover this dependence of δ on N and the extent of interpenetration (quantified by d_{g}/d_{0}). These predictions, unlike the existing studies, establish a finite interpenetration for all values of d_{g}/d_{0} as long as d_{g}<2d_{0}. Finally, we quantify the monomer and counterion concentration distributions and point out that these two distributions may quantitatively deviate from each other at locations very close to the channel centerline, where the interpenetration-induced monomer concentration can be significantly low.

Self-assembled core-polyethylene glycol-lipid shell nanoparticles demonstrate high stability in shear flow

A core-polyethylene glycol-lipid shell (CPLS) nanoparticle consists of an inorganic core coated with polyethylene glycol (PEG) polymers, surrounded by a lipid bilayer shell. It can be self-assembled from a PEGylated core with surface-tethered PEG chains, where all the distal ends are covalently bonded to lipid molecules. Upon adding free lipids, a complete lipid bilayer shell can be formed on the surface driven by the hydrophobic nature of lipid tails, leading to the formation of a CPLS nanoparticle. The stability of CPLS nanoparticles in shear flow has been systematically studied through large scale dissipative particle dynamics simulations. CPLS nanoparticles demonstrate higher stability and less deformation in shear flow, compared with lipid vesicles. Burst leakage of drug molecules inside lipid vesicles and CPLS NPs can be induced by the large pores at their tips. These pores are initiated by the maximum stress in the waist region. It further grows along with the tank-treading motion of vesicles or CPLS NPs in shear flow. However, due to the constraints applied by PEG polymers, CPLS NPs are less deformed than vesicles with comparable size under the same flow conditions. Thus, the less deformed CPLS NPs express a smaller maximum stress at waists, demonstrating higher stability. Pore formation at waists, evolving into large pores on vesicles, leads to the burst leakage of drug molecules and complete rupture of vesicles. In contrast, although similar drug leakage in CPLS nanoparticles can occur at high shear rates, pores initiated at moderate shear rates tend to be short-lived and close due to the constraints mediated by PEG polymers. This kind of 'self-healing' capability can be observed over a wide range of shear rates for CPLS nanoparticles. Our results suggest self-assembled CPLS nanoparticles to exhibit high stability during blood circulation without rapid drug leakage. These features make CPLS nanoparticles candidates for a promising drug delivery platform.

Compression of polymer brushes in the weak interpenetration regime: scaling theory and molecular dynamics simulations

We employ scaling theory and Molecular Dynamics (MD) simulations to probe the compression of the semi-dilute polymer brush bilayers (BBLs) in the weak interpenetration (IP) regime. Such a regime is characterized by two layers of interacting polymer brushes grafted on opposing planar surfaces having a separation d_g, such that d₀ < d_g < 2d₀, with d₀ being the unperturbed brush height. Currently, scaling theories are known for polymer BBLs with a much larger degree of IP (i.e., d_g < d₀) - in such regimes, the brush height can be quantified by the corresponding IP length δ. On the other hand, we show that in the weak IP regime, the brush height is not solely dictated by δ. We develop new scaling theories to show that δ in this weak IP regime is different from that in the strong IP regime. Secondly, we establish that the compressed brush height in this weakly IP regime can be described as d ∼ N^χ with χ < 1 and varying monotonically with d_g/d₀. MD simulations are carried out to quantify δ and χ and the results match excellently with our new scaling theory predictions. Finally, we establish that our scaling theory can reasonably predict the experimentally witnessed variation of the interaction energy dictating the compressive force between the interpenetrating brushes in this weakly IP regime.

Scaling features of the tribology of polymer brushes of increasing grafting density around the mushroom-to-brush transition

Nonequilibrium coarse-grained, dissipative particle dynamics simulations of complex fluids, made up of polymer brushes tethered to planar surfaces immersed in a solvent yield nonmonotonic behavior of the friction coefficient as a function of the polymer grating density on the substrates, Γ, while the viscosity shows a monotonically increasing dependence on Γ. This effect is shown to be independent of the degree of polymerization, N, and the size of the system. It arises from the composition and the structure of the first particle layer adjacent to each surface that results from the confinement of the fluid. Whenever such layers are made up of as close a proportion of polymer beads to solvent particles as there are in the fluid, the friction coefficient shows a minimum, while for disparate proportions the friction coefficient grows. At the mushroom-to-brush transition (MBT) the viscosity scales with an exponent that depends on the characteristic exponent of the MBT (6/5) and the solvent quality exponent (ν=0.5, for θsolvent), but it is independent of the polymerization degree (N). On the other hand, the friction coefficient at the MBT scales as μ∼N^{6/5}, while the grafting density at the MBT scales as Γ∼N^{-6/5} when friction is minimal, in agreement with previous scaling theories. We argue these aspects are the result of cooperative phenomena that have important implications for the understanding of biological brushes and the design of microfluidics devices, among other applications of current academic and industrial interest.

Polymer-brush lubrication: a review of recent theoretical advances

This review compiles recent theoretical advances to describe compressive and shear forces of polymer-brush bilayers, which consist of two opposing brushes in contact. Such model systems for polymer-brush lubrication are frequently used as a benchmark to gain insight into biological problems, e.g., synovial joint lubrication. Based on scaling theory, I derive conformational and collective properties of polymer-brush bilayers in equilibrium and out-of-equilibrium situations, such as shear forces in the linear and nonlinear response regimes of stationary shear and under non-stationary shear. Furthermore, I discuss the influence of macromolecular inclusions and electrostatic interactions on polymer-brush lubrication. Comparisons to alternative analytical approaches, experiments and numerical results are performed. Special emphasis is given to methods for simulating polymer-brush bilayers using molecular dynamics simulations.

Brushes of semiflexible polymers in equilibrium and under flow in a super-hydrophobic regime

We performed molecular dynamics simulations to study the equilibrium and flow properties of a liquid in a nano-channel with confining surfaces coated with a layer of grafted semiflexible polymers. The coverage spans a wide range of grafting densities from essentially isolated chains to dense brushes. The end-grafted polymers were described by a bead spring model with a harmonic potential to include the bond stiffness of the chains. We varied the rigidity of the chains, from fully flexible polymers to rigid rods, in which the configurational entropy of the chains is negligible. The brush-liquid interaction was tuned to obtain a super-hydrophobic channel, in which the liquid did not penetrate the polymer brush, giving rise to a Cassie-Baxter state. Equilibrium properties such as brush height and bending energy were measured, varying the grafting density and the stiffness of the polymers. We also studied the characteristics of the brush-liquid interface and the morphology of the polymer chains supporting the liquid for different bending rigidities. Non-equilibrium simulations were performed, moving the walls of the channel in opposite directions at constant speed, obtaining a Couette velocity profile in the bulk liquid. The molecular degrees of freedom of the polymers were studied as a function of the Weissenberg number. Also, the violation of the no-slip boundary condition and the slip properties were analyzed as a function of the shear rate, grafting density and bending stiffness. At high grafting densities, a finite slip length independent of the shear rate or bending constant was found, while at low grafting densities a very interesting non-monotonic dependence on the bending constant is observed.

Hyperscaling relationship between the interfacial tension of liquids and their correlation length near the critical point

Interfaces involving coexisting phases in condensed matter are essential in many phenomena: wetting, nucleation, morphology, phase separation kinetics, membranes, phase coexistence in nanomaterials, etc. The majority of analytical theories available use concepts derived from mean field artifacts which do not describe adequately these systems. Satisfactory numerical simulation of interfaces at the atomistic to mesoscopic scale is still a challenge. In the present work, the interfacial tension between mixtures of organic solvents and water is obtained from mesoscopic computer simulations. The temperature dependence of the interfacial tension is found to obey a scaling law with an average critical exponent μ = 1.23. Additionally, we calculate the evolution of the correlation length, defined as the thickness of the interface between the immiscible fluids, as a function of temperature and find that it obeys also a scaling law with an average critical exponent being ν = 0.67. Finally, we show that the comparison of μ and ν for these binary mixtures constitutes the first test of Widom's hyperscaling relationship between these exponents in 3d, expressed as μ = ν (d - 1). Based on these values and those for the 3d Ising model it is argued that both systems belong to the same universality class, which opens up the way for the calculation of new scaling exponents.