We have explored a model for adsorption of water into slit-like nanochannels with two walls chemically modified by grafted polymer layers forming brushes. A version of density functional method is used as theoretical tools. The water-like fluid model adopted from the work of Clark et al. [Mol. Phys., 2006, 104, 3561] adequately reproduces the bulk vapour-liquid coexistence envelope. The polymer layer consists of chain molecules in the framework of pearl-necklace model. Each chain molecule is chemically bonded to the pore walls by a single terminating segment. Our principal focus is in the study of the dependence of polymer layer height on grafting density and in the microscopic structure of the interface between adsorbed fluid and brushes. Thermal response of these properties upon adsorption is investigated in detail. The results are of importance to understand shrinking and swelling of the molecular brushes in the nanochannels.
Polymer Brushes and Grafted Polymers: AI/ML-Driven Synthesis, Simulation, and Characterization towards autonomous SDL
Oak Ridge National Laboratory（橡树岭国家实验室）；Department of Chemical and Biomolecular Engineering, University of Tennessee at Knoxville（田纳西大学诺克斯维尔分校化学与生物分子工程系）
We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by use of self-consistent field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate an existence of repulsive energy barrier of several $k_{B}T$, which can be interpreted by separating the interaction energy into three parts: colloids-polymer interfacial energy, entropic contribution due to ``depletion zone" overlap of colloidal particles, and entropically elasti…
A coarse-grained model to describe the lateral structure of a one-component polymer brush is presented. In this model, a single polymer chain is described by just two coordinates, namely the position of the grafted monomer, and the monomer on the non-grafted end. Due to its simplicity, the lateral arrangement of large numbers of structural units, each unit containing hundreds of polymers, can be analyzed. We consider here the corresponding low-energy configurations. Provided the grafting density is large enough, the latter all feature hexagonal order, even when the grafted monomers are distrib…
We report a simulation study for bottle-brush polymers grafted on a rigid backbone. Using a standard coarse-grained bead-spring model extensive molecular dynamics simulations for such macromolecules under good solvent conditions are performed. We consider a broad range of parameters and present numerical results for the monomer density profile, density of the untethered ends of the grafted flexible backbones and the correlation function describing the range that neighboring grafted bottle-brushes are affected by the presence of the others due to the excluded volume interactions. The end beads …
We study the influence of chain stiffness on droplet flow in a nano-channel, coated with semiflexible hydrophobic polymers by means of non-equilibrium 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 properti…
In this paper, we present a molecular theory analysis of ions and potential distribution, degree of ionization of polyelectrolyte (PE) brushes, velocity profile, volumetric flow rate, ionic selectivity, ionic conduction and advection by electroosmotic flow in poly-acid (PA)/poly-base (PB) grafted nanopores. The generated conformations by the Rotational Isomeric State model are used in performing the minimization of the free energy functional of the system including the effects of the Born energy arising from the variation of permittivity, pH of the electrolyte, grafting density of weak PE brus…
Bottle brushes are polymeric macromolecules made of a linear polymeric backbone grafted with side chains. The choice of the grafting density σg, the length ns the grafted side chains and their chemical nature fully determines the properties of each macromolecule, such as its elasticity and its folding behaviour. Typically, experimental bottle brushes are systems made of tens of thousands of monomeric units, rendering a computational approach extremely expensive, especially in the case of bottle brush solutions. A proper coarse graining description of these macromolecules thus appears essential…
Percolation phenomena of homopolymer brushes on a planar substrate are simulated using the molecular Monte Carlo method in 3 dimensions. The grafted polymers are isolated from each other at extremely low grafting density, whereas a continuous polymer layer covers the whole substrate when the density rises to extremely high values. This indicates that percolation clusters of the grafted polymers, bridging both the edges of the substrate, appear at an intermediate density. We construct phase diagrams of this percolation phenomenon. Critical phenomena at the transition are also studied.
Via computer simulations, we demonstrate how a densely grafted layer of polymers, a {\it brush}, could be turned into an efficient switch through chemical modification of some of its end-monomers. In this way, a surface coating with reversibly switchable properties can be constructed. We analyze the fundamental physical principle behind its function, a recently discovered surface instability, and demonstrate that the combination of a high grafting density, an inflated end-group size and a high degree of monodispersity are conditions for an optimal functionality of the switch.
We probe, using the Surface Forces Apparatus, the thermal response of poly(N-isopropylacrylamide) (PNIPAM) brushes of various grafting densities, grown from plasma-activated mica by means of surface-initiated polymerization. We thus show that dense thermoresponsive brushes collapse gradually as temperature is increased, and that grafting density greatly affects their ability to swell: the swelling ratio of the brushes, which characterizes the thickness variation between the swollen and the collapsed state, is found to decrease from $\sim 7$ to $\sim 3$ as the number of grafted chains per unit …
Polydisperse brushes obtained by reversible radical chain polymerization reaction onto a solid substrate with surface-attached initiators, are studied by means of an off-lattice Monte Carlo algorithm of living polymers (LP). Various properties of such brushes, like the average chain length and the conformational orientation of the polymers, or the force exerted by the brush on the opposite container wall, reveal power-law dependence on the relevant parameters. The observed molecular weight distribution (MWD) of the grafted LP decays much more slowly than the corresponding LP bulk system due to…
Large scale Monte Carlo simulations of dense layers of grafted polymer chains in good solvent conditions are used to explore the relaxation of a polymer brush. Monomer displacements are analyzed for the directions parallel and perpendicular to the grafting plane. Auto-correlation functions of individual segments or chain sections are monitored as function of time. We demonstrate that the terminal relaxation time $τ$ of grafted layers well in the brush regime grows exponentially with degree of polymerization $N$ of the chains, $τ\propto N^{3}\exp(N/N_{e})$, with $N_{e}$ the entanglement degree …
Theories of strongly stretched polymer brushes, particularly the parabolic brush theory, are valuable for providing analytically tractable predictions for the thermodynamic behavior of surface-grafted polymers in a wide range of settings. However, the parabolic brush limit fails to describe polymers grafted to convex, curved substrates, such as the surfaces of spherical nanoparticles or the interfaces of strongly segregated block copolymers. It has been previously shown that strongly-stretched, curved brushes require a boundary layer devoid of free chain ends, requiring modifications of the th…
The organization of nano-particles inside grafted polymer layers is governed by the interplay of polymer-induced entropic interactions and the action of externally applied fields. Earlier work had shown that strong external forces can drive the formation of colloidal structures in polymer brushes. Here we show that external fields are not essential to obtain such colloidal patterns: we report Monte Carlo and Molecular dynamics simulations that demonstrate that ordered structures can be achieved by compressing a `sandwich' of two grafted polymer layers, or by squeezing a coated nanotube, with n…
We describe the design of micropatterned surfaces for single cell studies, based on thermoresponsive polymer brushes. We show that brushes made of poly(N-isopropylacrylamide) grafted at high surface density display excellent protein and cell anti-adhesive properties. Such brushes are readily patterned at the micron scale via deep UV photolithography. A proper choice of the adhesive pattern shapes, combined with the temperature-dependent swelling properties of PNIPAM, allow us to use the polymer brush as a microactuator which induces cell detachment when the temperature is reduced below 32degC.
I consider the ordering of dilute platelet additives when incorporated into an end-grafted polymer brush. The competition between wetting interactions and the anisotropic stress environment of the interior of the brush causes these platelet additives to either remain suspended at the outer edge of the brush laying flat against the brush surface (as bits of confetti at rest on the ground), or to invade the interior of the brush in which case the platelets stand end-on and in some cases protrude above the outer edge of the brush. The orientation of the additives is controlled by the ratio of the…
Planar brushes formed by end-grafted semiflexible polyampholyte chains, each chain containing equal number of positively and negatively charged monomers is studied using molecular dynamics simulations. Keeping the length of the chains fixed, dependence of the average brush thickness and equilibrium statistics of the brush conformations on the grafting density and the salt concentration are obtained with various sequences of charged monomers. When similarly charged monomers of the chains are arranged in longer blocks, the average brush thickness is smaller and dependence of brush properties on …
The structural phase behavior of polymer brushes, single-component linear homopolymers grafted onto a planar substrate, is studied using the molecular Monte Carlo method in 3 dimensions. When simulation parameters of the system are set in regions of macrophase separation of solution for the corresponding non-grafted homopolymers, the grafted polymers also prefer segregation. However, macrophase separation is disallowed due to the spatially-fixed grafting points of the polymers. Such constraints on the grafting are similar to connecting points between blocks of non-grafted diblock copolymers at…
We describe a microscope-based optical setup that allows us to perform space-and time-resolved measurements of the spectral reflectance of transparent substrates coated with ultrathin films. This technique is applied to investigate the behavior in water of thermosensitive polymer brushes made of poly(N-isopropylacrylamide) grafted on glass. We show that spectral reflectance measurements yield quantitative information about the conformation and axial structure of the brushes as a function of temperature. We study how molecular parameters (grafting density, chain length) affect the hydra-tion st…
We demonstrate a novel route of spatially organizing the colloid arrangements on the polymer-grafted substrate by use of self-consistent field and density functional theories. We find that grafting of polymers onto a substrate can effectively control spatial dispersions of deposited colloids as a result of the balance between colloidal settling force and entropically elastic force of brushes, and colloids can form unexpected ordered structures on a grafting substrate. The depositing process of colloidal particles onto the elastic "soft" substrate includes two steps: brush-mediated one-dimensio…
Neutral or charged polymers that are densely end-grafted to surfaces form brush-like structures and are highly stretched under good-solvent conditions. We discuss and compare relevant results from scaling models, self-consistent-field methods and MD simulation techniques and concentrate on the conceptual simple case of planar substrates. For neutral polymers the main quantity of interest is the brush height and the polymer density profile, which can be well predicted from self-consistent calculations and simulations. Charged polymers (polyelectrolytes) are of practical importance since they ar…
The stretching of brushes of long polymers grafted to a planar surface is investigated byMonte Carlo simulations in the limit of very high grafting densities, as achieved in recent experiments. The monomer density profiles are shown to deviate considerably from the parabolic limiting form predicted by self-consistent field theory. A rapid transition is observed from parabolic to fully stretched polymers, characterized by a dramatic change in the end-monomer height distribution and by a clear cross-over in the slope of the brush height versus scaled grafting density.
We consider a polymer brush grafted to a surface (acting as an electrode) and bearing a charged group at its free end. Using a second distant electrode, the brush is subject to a constant electric field. Based on a coarse-grained continuum model, we calculate the average brush height and find that the brush can stretch or compress depending on the applied field and charge end-group. We further look at an undulation mode of the flat polymer brush and find that the electrostatic energy scales linearly with the undulation wavenumber, $q$. Competition with surface tension, scaling as $q^2$, tends …
In the present work, we study the equilibrium conformations of linear polyelectrolytes tethered onto a spherical, oppositely charged core in equilibrium with an ionic reservoir of fixed concentration. Particular focus is placed on the situation of stretched chains, where the monomer concentration is known to display an inverse square-law decay far away from the spherical surface, which is then further extrapolated all the way down to the grafting core. While the equilibrium distributions of mobile ions are computed in the framework of a classical Density Functional Theory (cDFT) that incorpora…
The structural features of polystyrene brushes grafted on spherical silica nanoparticles immersed in polystyrene are investigated by means of a Monte Carlo methodology based on polymer mean field theory. The nanoparticle radii (either 8 nm or 13 nm) are held constant, while the grafting density and the lengths of grafted and matrix chains are varied systematically in a series of simulations. The primary objective of this work is to simulate realistic nanocomposite systems of specific chemistry at experimentally accessible length scales and study the structure and scaling of the grafted brush. …
We explore the effect of an attractive interaction between parallel-aligned polymers, which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength…
Polymer brushes normally swell in a good solvent and collapse in a poor solvent. An abnormal response of polymer brushes, so-called co-nonsolvency, is the phenomenon where the brush counter-intuitively collapses in a good solvent mixture. In this work, we employed molecular dynamics simulations to investigate the structural properties of the grafted polymers on the occurrence of co-nonsolvency. Brushes with various grafting densities were considered to study the effect of topological excluded volumes on the co-nonsolvency. We found that the brush height follows a novel scaling behavior of the …
There is ample evidence that polymer brushes reduce friction between surfaces. Several industrial applications take advantage of this fact, such as those in plastic bag production, where the brushes act as slip agents; however, the complex mechanisms that give rise to such reduction of friction are not yet fully understood. In this work we report coarse grained, dissipative particle dynamics simulations carried out for surfaces functionalized with erukamide brushes, a polymer commonly used in the plastics industry as a slip agent between surfaces. We calculate their rheological properties, suc…
From glycosylated cell surfaces to sterically stabilized liposomes, polymers attached to membranes attract biological and therapeutic interest. Can the scaling laws of polymer "brushes" describe the physical properties of these coats? We delineate conditions where the Alexander - de Gennes theory of polymer brushes successfully describes the intermembrane distance vs. applied osmotic stress data of Kenworthy et al. for PEG-grafted multilamellar liposomes [Biophys. J. (1995) 68:1921]. We establish that the polymer density and size in the brush must be high enough that, in a bulk solution of equ…
The interactions between spherical colloids covered with end-grafted polymers (brushes) immersed in a polymer melt are studied theoretically. We show that attractive enthalpic interactions between the two polymer species, characterized by a negative Flory parameter (chi<0), can stabilize the colloidal dispersion. The stabilizing mechanism is a result of a structural change from a dry brush, where the melt chains do not penetrate deeply into the brush, to a wet brush, where the free chains penetrate the brush and force the grafted chains to extend into the melt.
A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions, by Molecular Dynamics methods and density functional theory. With increasing chain length the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both sin…
We undertake the investigation of sheared polymer chains grafted on 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 rate to improve the transport of the liposomes. Therefore non - equilibrium, DPD simulations of polymer brushes of various length and shear rates are performed to obt…
We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $ξ\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a disk), the lateral extension $u_S$ of the border chains follows the scaling law $u_S = ξϕ(S/ξ)$. The scaling function $ϕ(x)$ is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small $x$, $ϕ(x)$ decays as a power law in agreement with simple argument…
We grafted polyacrylic acid brushes containing cysteine side chains at a defined surface density on planar lipid membranes. Specular X-ray reflectivity data indicated that the addition of Cd2+ ions induces the compaction of the polymer brush layer and modulates the adhesion of lipid vesicles. The critical threshold level inducing the switch from non-wetting to partial wetting state, [Cd2+] = 0.25 mM, was determined by microinterferometry. The interactions between vesicles and brushes were evaluated by height fluctuations of the membrane in contact with brushes and the shape of vesicles near th…
Using a coarse-grained bead-spring model for semi-flexible macromolecules forming a polymer brush, structure and dynamics of the polymers is investigated, varying chain stiffness and grafting density. The anchoring condition for the grafted chains is chosen such that their first bonds are oriented along the normal to the substrate plane. Compression of such a semi-flexible brush by a planar piston is observed to be a two-stage process: for small compressions the chains contract by "buckling" deformation whereas for larger compression the chains exhibit a collective (almost uniform) bending def…
Using self-consistent field and density-functional theories, we first investigate colloidal self-assembling of colloid/polymer films confined between two soft surfaces grafted by polymers. With the increase of colloidal concentrations, the film undergoes a series of transitions from disordered liquid $\to$ sparse square $\to$ hexagonal (or mixed square-hexagonal) $\to$ dense square $\to$ cylindric structures in plane, which results from the competition between the entropic elasticity of polymer brushes and the steric packing effect of colloidal particles. A phase diagram displays the stable re…
In this paper, we study the electrostatics of pH-responsive polyelectrolyte-grafted spherical particles by using a strong stretching theory that takes into account the excluded volume interaction and the density of chargeable sites on the polyelectrolyte molecules. Based on the free energy formalism, we obtain self-consistent field equations for determining the structure and electrostatics of spherical polyelectrolyte brushes. First, we find that the smaller the radius of the inner core, the longer the height of the polyelectrolyte brush. Then, we also prove that an increase in excluded volume…
We present a Monte Carlo study of the surface anchoring of a nematic fluid on swollen layers of grafted liquid crystalline chain molecules. The liquid crystalline particles are modeled by soft repulsive ellipsoids, and the chains are made of the same particles. An appropriately modified version of the configurational bias Monte Carlo algorithm is introduced, which removes and redistributes chain bonds rather than whole monomers. With this algorithm, a wide range of grafting densities could be studied. The substrate is chosen such that it favors a planar orientation (parallel to the surface). D…
We performed molecular dynamics simulations to study 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 an 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 in…
The extent of coupling between the folding of a protein and its binding to a substrate varies from protein to protein. Some proteins have highly structured native states in solution, while others are natively disordered and only fold fully upon binding. In this Letter, we use Monte Carlo simulations to investigate how disordered polymer chains grafted around a binding site affect the folding and binding of three model proteins. The protein that approaches the substrate fully folded is more hindered during the binding process than those whose folding and binding are cooperative. The polymer cha…
Ordering nanoparticles into a desired super-structure is often crucial for their technological applications. We use molecular dynamics simulations to study the assembly of nanoparticles in a polymer brush randomly grafted to a planar surface as the solvent evaporates. Initially, the nanoparticles are dispersed in a solvent that wets the polymer brush. After the solvent evaporates, the nanoparticles are either inside the brush or adsorbed at the surface of the brush, depending on the strength of the nanoparticle-polymer interaction. For strong nanoparticle-polymer interactions, a 2-dimensional …
We report a theoretical study of ion size effect on various properties in a soft nanochannel with pH-dependent charge density. We develop a free energy based mean-field theory taking into account ion size as well as pH-dependence of charged polyelectrolyte layer grafted on a rigid surface in an electrolyte. The influence of ion size on properties in a soft nanochannel is evaluated by numerically calculating ion number densities and electrostatic potential. We demonstrate that unlike in point-like ions, for finite sizes of ions, a uniform distribution of chargeable sites within the polyelectrol…
We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a contro…
The application of a polymer brush in sensing, actuation, self-folding, among others acutely depends on the tuneable bending of a brush-grafted substrate caused by the stress in the brush. However, the stress in a stimuli-responsive brush has not been investigated. In this work, we study the stress in the stimuli-responsive planar polymer brushes of neutral water-soluble polymers with low to very high graft densities using strong stretching theory (SST). First, SST with the Langevin force-extension relation for a polymer chain is extended to the study of stimuli-responsive brushes. Stress prof…
The adsorption of a bottle-brush polymer end-grafted with one chain end of its backbone to a flat substrate surface is studied by Monte Carlo simulation of a coarse-grained model, that previously has been characterized in the bulk, assuming a dilute solution under good solvent conditions. Applying the bond fluctuation model on the simple cubic lattice, we vary the backbone chain length $N_b$ from $N_b=67$ to $N_b = 259$ effective monomeric units, the side chain length $N$ from N=6 to N=48, and the grafting density $σ=1$, i.e., parameters that correspond well to the experimentally accessible ra…
In this paper, we have studied polystyrene (PS) and polyethylene (PE) stiffness by 3-dimensional Langevin Molecular Dynamics simulation. Hard polymers have a very small bending, and thus, their end-to-end distance is more than soft polymers. Quantum dot lasers can be established as colloidal particles dipped in a liquid and grafted by polymer brushes to maintain the solution. Here by a study on molecular structures of PS and PE, we show that the principle reason lies on large phenyl groups around the backbone carbons of PS, rather than a PE with Hydrogen atoms. Our results show that the mean r…
Chain-like macromolecules (polymers) show characteristic adsorption properties due to their flexibility and internal degrees of freedom, when attracted to surfaces and interfaces. In this review we discuss concepts and features that are relevant to the adsorption of neutral and charged polymers at equilibrium, including the type of polymer/surface interaction, the solvent quality, the characteristics of the surface, and the polymer structure. We pay special attention to the case of charged polymers (polyelectrolytes) that have a special importance due to their water solubility. We present a su…
