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.

Pressure responsive gating in nanochannels coated by semiflexible polymer brushes.

We study by coarse-grained molecular-dynamics simulations the liquid flow in a slit channel with the inner walls coated by semiflexible polymer brushes. The distance between walls is close enough such that polymers grafted to opposing walls interact among each other and form bundles across the channel in poor solvent conditions. The solvent is simulated explicitly, including particles that fill the interior of the channel. The system is studied in equilibrium and under flow, by applying a constant body force on each particle of the system. A non-linear relation between external force and flow rate is observed, for a particular set of parameters. This non-linear response is linked to a morphological change of the polymer brushes. For large enough forces, the bundle structures formed across the channel break as the chains lean in the direction of the flow, and clear the middle of the channel. This morphological alteration of the polymer configurations translates in a sudden increase in the flow rate, acting as a pressure-responsive gate. The relation between flow and external force is investigated for various parameters, such as grafting density, quality of the solvent and polymer bending rigidity. We observe a non-monotonic dependence of the flow as a function of the polymer rigidity, and find an optimum value for the persistence length. We also find that the force threshold at which the morphological changes happen in the polymer brush, depends linearly on the grafting density. These findings can lead to new flow control techniques in micro and nano-fluidic devices.

Droplet Transport in a Nanochannel Coated by Hydrophobic Semiflexible Polymer Brushes: The Effect of Chain Stiffness.

We study the influence of chain stiffness on droplet flow in a nanochannel, coated with semiflexible hydrophobic polymers by means of nonequilibrium molecular dynamics simulations. The studied system is then a moving droplet in the slit channel, coexisting with its vapor and subjected to periodic boundary conditions in the flow direction. The polymer chains, grafted by the terminal bead to the confining walls, are described by a coarse-grained model that accounts for chain connectivity, excluded volume interactions and local chain stiffness. The rheological, frictional and dynamical properties of the brush are explored over a wide range of persistence lengths. We find a rich behavior of polymer conformations and concomitant changes in the friction properties over the wide range of studied polymer stiffnesses. A rapid decrease in the droplet velocity was observed as the rigidity of the chains is increased for polymers whose persistence length is smaller than their contour length. We find a strong relation between the internal dynamics of the brush and the droplet transport properties, which could be used to tailor flow properties by surface functionalization. The monomers of the brush layer, under the droplet, present a collective "treadmill belt" like dynamics which can only be present due the existence of grafted chains. We describe its changes in spatial extension upon variations of polymer stiffness, with bidimensional velocity and density profiles. The deformation of the polymer brushes due to the presence of the droplet is analyzed in detail. Lastly, the droplet-gas interaction is studied by varying the liquid to gas ratio, observing a 16% speed increase for droplets that flow close to each other, compared to a train of droplets that present a large gap between consecutive droplets.

Fluctuation-induced forces between rings threaded around a polymer chain under tension.

We characterize the fluctuation properties of a polymer chain under external tension and the fluctuation-induced forces between two ring molecules threaded around the chain. The problem is relevant in the context of fluctuation-induced forces in soft-matter systems, features of liquid interfaces, and to describe the properties of polyrotaxanes and slide-ring materials. We perform molecular-dynamics simulations of the Kremer-Grest bead-spring model for the polymer and a simple ring-molecule model in the canonical ensemble. We study transverse fluctuations of the stretched chain as a function of chain stretching and in the presence of ring-shaped threaded molecules. The fluctuation spectra of the chains are analyzed in equilibrium at constant temperature, and the differences in the presence of two-ring molecules are compared. For the rings located at fixed distances, we find an attractive fluctuation-induced force between the rings, proportional to the temperature and decaying with the ring distance. We characterize this force as a function of ring distance, chain stretching, and ring radius, and we measure the differences between the free chain spectrum and the fluctuations of the chain constrained by the rings. We also compare the dependence and range of the force found in the simulations with theoretical models coming from different fields.

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.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations.

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

Mean properties and free energy of a few hard spheres confined in a spherical cavity.

We use analytical calculations and event-driven molecular dynamics simulations to study a small number of hard sphere particles in a spherical cavity. The cavity is also taken as the thermal bath so that the system thermalizes by collisions with the wall. In that way, these systems of two, three, and four particles, are considered in the canonical ensemble. We characterize various mean and thermal properties for a wide range of number densities. We study the density profiles, the components of the local pressure tensor, the interface tension, and the adsorption at the wall. This spans from the ideal gas limit at low densities to the high-packing limit in which there are significant regions of the cavity for which the particles have no access, due the conjunction of excluded volume and confinement. The contact density and the pressure on the wall are obtained by simulations and compared to exact analytical results. We also obtain the excess free energy for N = 4, by using a simulated-assisted approach in which we combine simulation results with the knowledge of the exact partition function for two and three particles in a spherical cavity.

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

We undertake the investigation of sheared polymer chains grafted onto flat surfaces to model liposomes covered with polyethylene glycol brushes as a case study for the mechanisms of efficient drug delivery in biologically relevant situations, for example, as carriers for topical treatments of illnesses in the human vasculature. For these applications, specific rheological properties are required, such as low viscosity at high shear rates, to improve the transport of the liposomes. Therefore, extensive non-equilibrium, coarse-grained dissipative particle dynamics simulations of polymer brushes of various lengths and shear rates are performed to obtain the average viscosity and the friction coefficient of the system as functions of the shear rate and polymerization degree under theta-solvent conditions, and we find that the brushes experience considerable shear thinning at large shear rates. The viscosity (η) and the friction coefficient (µ) are shown to obey the scaling laws η ∼ γ dot above (-0.31) and µ ∼ γ dot above (0.69) at high shear rates (γ dot above) in a theta solvent, irrespective of the degree of polymerization of brushes. These results confirm recent scaling predictions and reproduce very well trends in measurements of the viscosity at a high shear rate (γ dot above) of red blood cells in a liposome containing medium.

Mixed brush of chemically and physically adsorbed polymers under shear: inverse transport of the physisorbed species.

We study mixed brushes under shear flow by molecular dynamics simulation with an explicit solvent. The primary brush is formed by chemically grafting polymers to a solid substrate, the secondary brush is comprised of shorter, physically end-adsorbed molecules that can laterally diffuse. By virtue of the immobility of the grafted end-points of the primary brush, its individual macromolecules perform a cyclic motion. If there is a well defined solvent-brush interface, this cyclic motion of the primary brush molecules will collectively result in the reversal of the flow inside of the primary brush. This backflow, linear in the shear rate, gives rise to the transport of the shorter, physically end-adsorbed molecules in the opposite direction of the solvent flow. We discuss which conditions are necessary to observe this counter-intuitive phenomenon. Comparing Poiseuille and Couette flow we demonstrate that the magnitude of the local shear rate at the brush-liquid interface dictates the cyclic motion and concomitant inversion of transport but that these universal effects are independent of the type of driving the flow.

Comparison of ternary bilayer mixtures with asymmetric or symmetric unsaturated phosphatidylcholine lipids by coarse grained molecular dynamics simulations.

We studied the phase behavior of various ternary bilayer mixtures composed of cholesterol, an unsaturated lipid, and a fully saturated lipid, by means of molecular dynamics simulations of the MARTINI coarse grain model. We aimed at comparing lateral organization and local properties of bilayers containing phosphatidylcholine (PC) lipids, either with two unsaturated tails (symmetric), or one unsaturated and one saturated tail (asymmetric), as the low-melting component of the mixture. The number of unsaturations per chain was systematically varied in both classes of unsaturated lipids, to account for its consequences in segregation. In the asymmetric unsaturated PCs, the saturated tail was kept identical to the hydrophobic chains of the fully saturated lipid component. Membranes with a symmetric or an asymmetric unsaturated lipid, with the same kind of unsaturated chain, show different phase behavior. Symmetric polyunsaturated PCs set the separation in two phases. Instead, the asymmetric polyunsaturated lipids induced nonideal mixing of components in single-phase bilayers. A significative drop of temperature, within the accessible temperature range, enhances the segregation in mixtures with the more unsaturated asymmetric PC, but still within a single phase. This different phase behavior between membranes with symmetric and asymmetric unsaturated PCs is also observed for lipids with the same total number of unsaturations. On the other hand, the degree of unsaturation per se enhances the segregation, by increasing the composition fluctuations in single-phase membranes with asymmetric PC lipids, and raising the line tension in the two-phase bilayer mixtures with symmetric polyunsaturated PCs. Dynamic clusters of unsaturated asymmetric lipids can be identified. The clusters show no correlation between leaflets, as observed for the phase domains in mixtures with the symmetric polyunsaturated PCs. Interestingly, we found that asymmetric PC lipids have a preferential orientation such that their saturated tails increase their density toward the periphery of the clusters, facing regions enriched in the fully saturated lipids and cholesterol. The degree of unsaturation increases the cluster size and also enhances the anisotropy of the orientation. The surface density of cholesterol follows a gradient that favors its interaction with the saturated tails. Such gradients in composition lead to gradients in order parameters, such as the conformational order and the area of the tails, which increases away from the unsaturated lipid clusters. We compared, in addition, differences in hydrophobic length mismatch between acyl chains of the low-melting and high-melting components, in mixtures containing either symmetric or asymmetric unsaturated lipids.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems.

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Polyunsaturated and saturated phospholipids in mixed bilayers: a study from the molecular scale to the lateral lipid organization.

Polyunsaturated lipids are remarkably flexible molecules, with a great influence on the membrane structure and dynamics, affecting from mechanical properties to domain segregation. In this work, we studied phospholipid mixtures of dipalmitoylphosphatidylcholine (DPPC) and diunsaturated phosphatidylcholine lipids (diunsPC) of different lengths, by means of molecular dynamic simulations of a coarse-grained interaction model. These diunsPC:DPPC binary mixtures show nonideal behavior characterized by one mixed phase with composition fluctuations on a length scale of nanometers. Motivated by this observation, we studied comprehensively the characteristics of molecular structure as a function of the compositional gradient. We analyzed orientational order profiles, density distributions, and pair-pair correlation functions between the molecule residues. We observed that, in diunsPC-enriched regions, DPPC tails become expanded and disordered, especially toward the membrane center. On the other hand, in the more condensed DPPC-enriched patches, diunsaturated acyl chains become displaced toward the interface instead of stretching along the membrane normal. From the comparison of the two diunsPC lipids of different tail length, we measured that the presence of a longer terminal saturated segment induces better mixing with DPPC, and most interestingly eliminates the up-down composition correlation measured with the shorter tail-diunsPC. At molecular level, there is a reduced redistribution of densities and changes in the local order as a function of composition. We interpret these results as indicative that the packing incompatibility between polyunsaturated and saturated lipids rules their mixing behavior.

Frictional forces between strongly compressed, nonentangled polymer brushes: molecular dynamics simulations and scaling theory.

By means of molecular dynamics simulations and scaling theory we study the response of opposing polymer brushes to constant shear motion under good solvent conditions. Model systems that contain explicit solvent molecules (Lennard-Jones dimers) are compared to solvent-free systems while varying of the distance between the grafted layers and their molecular parameters, chain length and grafting density. Our study reveals a power-law dependence of macroscopic transport properties on the Weissenberg number, W, beyond linear response. For instance, we find that the kinetic friction constant scales as mu approximately W(0.57) for large values of W. We develop a scaling theory that describes our data and previous numerical data including recent experiments.

Comparison of dissipative particle dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems.

In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.

Static and dynamic properties of the interface between a polymer brush and a melt of identical chains.

Molecular-dynamics simulations of a short-chain polymer melt between two brush-covered surfaces under shear have been performed. The end-grafted polymers which constitute the brush have the same chemical properties as the free chains in the melt and provide a soft deformable substrate. Polymer chains are described by a coarse-grained bead-spring model, which includes excluded volume and backbone connectivity of the chains. The grafting density of the brush layer offers a way of controlling the behavior of the surface without altering the molecular interactions. We perform equilibrium and nonequilibrium molecular-dynamics simulations at constant temperature and volume using the dissipative particle dynamics thermostat. The equilibrium density profiles and the behavior under shear are studied as well as the interdigitation of the melt into the brush, the orientation on different length scales (bond vectors, radius of gyration, and end-to-end vector) of free and grafted chains, and velocity profiles. The obtained boundary conditions and slip length show a rich behavior as a function of grafting density and shear velocity.

Advanced practice nursing role: nurse practitioner.

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