Unconventional ordering behavior of semi-flexible polymers in dense brushes under compression

Heat flow through a liquid-vapor interface in a nano-channel: the effect of end-grafting polymers on a wall

Heat transfer through a liquid-vapor interface is a complex phenomenon and crucially relevant in heat-removal and cryogenic applications. The physical coupling among confining walls, liquid and vapor phases is very important for controlling or improving cooling rates or condensation efficiency. Surface modification is a promising route, which has been explored to taylor the heat transfer through confined two-phase systems. We use coarse-grained molecular-dynamics simulations to study the heat transfer through a nano-confined liquid-vapor interface as a function of fluid filling. We set up a stationary heat flow through a liquid-vapor interface, stabilized with the liquid in contact with a colder wall and a vapor in contact with a hotter wall. For these physical conditions, we perform extensive simulations by progressively increasing the number of fluid particles, i.e. the channel filling, and measure the fluid distribution in the channel, density, pressure and temperature profiles We also compare the heat flux behavior between a bare-surfaces nano-channel and others where the hot surface was coated with end-grafted polymers, with different wetting affinities and bending properties. We take extreme cases of polymer properties to obtain a general picture of the polymer effect on the heat transfer, as compared with the bare surfaces. We find that walls covered by end-grafted solvophylic polymers change the heat flux by a factor of 6, as compared with bare walls, if the liquid phase is in contact with the polymers. Once the liquid wets the coated wall, the improve on heat flux is smaller and dominated by the grafting density. We also find that for a wall coated with stiff polymers, the jump in heat flux takes place at a significantly lower channel filling, when the polymers' free ends interact with the liquid surface. Interestingly, the morphology of the polymers induces a 'liquid bridge' between the liquid phase and the hot wall, through which heat is transported with high (liquid-like) thermal conductivity.

The responsive behaviors of bilayer membrane under uniaxial mechanical probe

In experiments, atomic force microscopy technology was used to measure the modulus of the membrane. However, these studies mainly focus on the linear responsive behavior. In the present work, a theoretical study is performed to show the nonlinear responsive behavior, which includes the stretching induced structural transitions. It demonstrates that the structural transition of the bilayer membrane takes place during the stretching process of the mechanical probe. A vertical cylindrical micelle can be obtained by stretching the membrane under deep compression conditions, and the cylindrical micelle can grow continuously along the axial direction. Moreover, under shallow compression conditions, the probe pulls a spherical micelle from the membrane, and then, the membrane returns to flatness. A comprehensive study is performed to show the mechanism of the responsive behaviors of the structural transition during the compression and stretching processes. When the probe acts on the B-rich layer, it is more likely to pull out a regular micelle. However, when the probe acts on the bottom A-rich layer, complex vesicles are more likely to be pulled out from the bilayer membrane. This study provides a comprehensive diagram of the mechanical responsive behavior of the membrane, which would be a guide for an experiment of biomembranes and the design of new self-assembled structures.

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.

Buckling a Semiflexible Polymer Chain under Compression

Instability and structural transitions arise in many important problems involving dynamics at molecular length scales. Buckling of an elastic rod under a compressive load offers a useful general picture of such a transition. However, the existing theoretical description of buckling is applicable in the load response of macroscopic structures, only when fluctuations can be neglected, whereas membranes, polymer brushes, filaments, and macromolecular chains undergo considerable Brownian fluctuations. We analyze here the buckling of a fluctuating semiflexible polymer experiencing a compressive load. Previous works rely on approximations to the polymer statistics, resulting in a range of predictions for the buckling transition that disagree on whether fluctuations elevate or depress the critical buckling force. In contrast, our theory exploits exact results for the statistical behavior of the worm-like chain model yielding unambiguous predictions about the buckling conditions and nature of the buckling transition. We find that a fluctuating polymer under compressive load requires a larger force to buckle than an elastic rod in the absence of fluctuations. The nature of the buckling transition exhibits a marked change from being distinctly second order in the absence of fluctuations to being a more gradual, compliant transition in the presence of fluctuations. We analyze the thermodynamic contributions throughout the buckling transition to demonstrate that the chain entropy favors the extended state over the buckled state, providing a thermodynamic justification of the elevated buckling force.

Loss of bottlebrush stiffness due to free polymers

A recently introduced DNA-bottlebrush system, which is formed by the co-assembly of DNA with a genetically engineered cationic polymer-like protein, is subjected to osmotic stress conditions. We measured the inter-DNA distances by X-ray scattering. Our co-assembled DNA-bottlebrush system is one of the few bottlebrushes known to date that shows liquid crystalline behaviour. The alignment of the DNA bottlebrushes was expected to increase with imposed pressure, but interestingly this did not always happen. Molecularly detailed self-consistent field calculations targeted to complement the experiments, focused on the role of molecular crowding on the induced persistence length lp due to the side chains and the cross-sectional width D of the molecular bottlebrushes. Both the thickness as well as the backbone persistence length drop with increasing protein-polymer bulk concentrations and dramatic effects are found above the overlap threshold. The flexibilisation is more significant and therefore the bottlebrush aspect ratio, lp/D, decreases with protein-polymer concentration. This loss in aspect ratio is yet another argument why molecular bottlebrushes rarely order in anisotropic phases and may explain why bottlebrushes are excellent lubricants.

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.

Compression induced phase transition of nematic brush: A mean-field theory study

Responsive behavior of polymer brush to the external compression is one of the most important characters for its application. For the flexible polymer brush, in the case of low grafting density, which is widely studied by the Gaussian chain model based theory, the compression leads to a uniform deformation of the chain. However, in the case of high grafting density, the brush becomes anisotropic and the nematic phase will be formed. The normal compression tends to destroy the nematic order, which leads to a complex responsive behaviors. Under weak compression, chains in the nematic brush are buckled, and the bending energy and Onsager interaction give rise to the elasticity. Under deep compression, the responsive behaviors of the nematic polymer brush depend on the chain rigidity. For the compressed rigid polymer brush, the chains incline to re-orientate randomly to maximize the orientational entropy and its nematic order is destroyed. For the compressed flexible polymer brush, the chains incline to fold back to keep the nematic order. A buckling-folding transition takes place during the compressing process. For the compressed semiflexible brush, the chains are collectively tilted to a certain direction, which leads to the breaking of the rotational symmetry in the lateral plane. These responsive behaviors of nematic brush relate to the properties of highly frustrated worm-like chain, which is hard to be studied by the traditional self-consistent field theory due to the difficulty to solve the modified diffusion equation. To overcome this difficulty, a single chain in mean-field theory incorporating Monte Carlo simulation and mean-field theory for the worm-like chain model is developed in present work. This method shows high performance for entire region of chain rigidity in the confined condition.

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.

Semiflexible polymer brushes and the brush-mushroom crossover

Semiflexible polymers end-grafted to a repulsive planar substrate under good solvent conditions are studied by scaling arguments, computer simulations, and self-consistent field theory. Varying the chain length N, persistence length lp, and grafting density σg, the chain linear dimensions and distribution functions of all monomers and of the free chain ends are studied. Particular attention is paid to the limit of very small σg, where the grafted chains behave as "mushrooms" no longer interacting with each other. Unlike a flexible mushroom, which has a self-similar structure from the size (a) of an effective monomer up to the mushroom height (h/a ∝ N(v), ν ≈ 3/5), a semiflexible mushroom (like a free semiflexible chain) exhibits three different scaling regimes, h/a ∝ N for contour length L = Na < lp, a Gaussian regime, h/a ∝ (Llp)(1/2)/a for lp ≪ L ≪ R* ∝ (lp(2)/a), and a regime controlled by excluded volume, h/a ∝ (lp/a)(1/5)N(ν). The semiflexible brush is predicted to scale as h/a ∝ (lpaσg)(1/3)N in the excluded volume regime, and h/a ∝ (lpa(3)σ(2))(1/4)N in the Gaussian regime. Since in the volume taken by a semiflexible mushroom excluded-volume interactions are much weaker in comparison to a flexible mushroom, there occurs an additional regime where semiflexible mushrooms overlap without significant chain stretching. Moreover, since the size of a semiflexible mushroom is much larger than the size of a flexible mushroom with the same N, the crossover from mushroom to brush behavior is predicted to take place at much smaller densities than for fully flexible chains. The numerical results, however, confirm the scaling predictions only qualitatively; for chain lengths that are relevant for experiments, often intermediate effective exponents are observed due to extended crossovers.