Mesoscale simulations of the behavior of charged polymer brushes under normal compression and lateral shear forces

Dissipative particle dynamics (DPD) was used to investigate the behavior of two opposing end-grafted charged polymer brushes in aqueous media under normal compression and lateral shear. The effect of polymer molecular weight, degree of ionization, grafting density, ionic strength, and compression on the polymer conformation and the resulting shear force between the opposing polymer layers were investigated. The simulations were carried out for the poly(tert-butyl methacrylate)-block-poly(sodium sulfonate glycidyl methacrylate) copolymer, referred as PtBMA-b-PGMAS, end-attached to a hydrophobic surface for comparison with previous experimental data. Mutual interpenetration of the opposing end-grafted chains upon compression is negligible for highly charged polymer brushes for compression ratios ranging from 2.5 to 0.25. Under electrostatic screening effects or for weakly charged polymer brushes, a significant mutual interpenetration was measured. The variation of interpenetration thickness with separation distance, grafting density, and polymer size follows the same scaling law as the one observed for two opposing grafted neutral brushes in good solvent. However, compression between two opposing charged brushes results in less interpenetration relative to neutral brushes when considering equivalent grafting density and molecular weight. The friction coefficient between two opposing polymer-coated surfaces sliding past each other is shown to be directly correlated with the interpenetration thickness and more specifically to the number of polymer segments within the interpenetration layer.     

Neutral and charged polymer brushes at solid surfaces

Neutral and charged polymer brushes covalently attached to planar solid surfaces were generated by using self-assembled monolayers of an azo initiator and radical chain polymerization in situ. The brushes were characterized by FTIR-spectroscopy, optical waveguide-spectroscopy and Ellipsometry. Especially the film thicknesses of surface bound polyelectrolyte (PEL) monolayers were measured by optical waveguide spectroscopy (OWS) as a function of the humidity of the environment. The PEL brushes show strong increases in thickness as well as strong decrease of the refractive index of the surface attached layer due to water incorporation caused by the exposure to the humid environment. Additionally the behavior of neutral as well as charged brushes in contact with solvent was investigated by using multiple-angular-scans of ellipsometry in a total internal reflectance setup. The scaling behavior of the brush height as a function of the graft density of the attached polymer molecules was investigated for the neutral brush as well as for the PEL brush system.     

Architecture and solution properties of amphiphilic polymer brushes with peripheral charged ions

Functionalized poly(ethylene oxide) (PEO) macromonomers (alpha -tertiary amino and omega -methacryloyl groups) were prepared by ring-opening polymerization of live PEO anions end-capped with styrene oxide using 2-[2-(N ,N -dimethylamino)-ethoxy]ethanol potassium alkoxides as an initiator with methacryloyl chloride. PEO brushes were synthesized by free-radical homopolymerization of such PEO macromonomers. These brushes were converted into peripherally charged brushes by quaternization. We studied the solution properties of both types of brushes from the viewpoint of charge effect. It was found from dynamic light scattering (DLS) that the polymer brushes formed a single macromolecule in solution due to crowding of side chains. It was speculated from angular dependence measurements that the polymer brushes with large aspect ratios took a geometrical anisotropic conformation such as a cylinder. In methanol with a low dielectric constant, radius of gyration (R(G)), and cross-sectional radius of gyration (R(G,C)) of the polymer brushes with charged side chains were smaller than those of the polymer brushes without charges. In a solvent with a low dielectric constant such as methanol, ionic groups do not dissociate and condense. On the other hand, these physical values in an aqueous solution were somewhat larger than those of the polymer brushes without charges. In water with a high dielectric constant, peripherally charged brushes were strongly stabilized by electric double layers.     

Normal and frictional forces between surfaces bearing polyelectrolyte brushes

Normal and shear forces were measured as a function of surface separation, D, between hydrophobized mica surfaces bearing layers of a hydrophobic-polyelectrolytic diblock copolymer, poly(methyl methacrylate)- block-poly(sodium sulfonated glycidyl methacrylate) copolymer (PMMA- b-PSGMA). The copolymers were attached to each hydrophobized surface by their hydrophobic PMMA moieties with the nonadsorbing polyelectrolytic PSGMA tails extending into the aqueous medium to form a polyelectrolyte brush. Following overnight incubation in 10 (-4) w/v aqueous solution of the copolymer, the strong hydrophobic attraction between the hydrophobized mica surfaces across water was replaced by strongly repulsive normal forces between them. These were attributed to the osmotic repulsion arising from the confined counterions at long-range, together with steric repulsion between the compressed brush layers at shorter range. The corresponding shear forces on sliding the surfaces were extremely low and below our detection limit (+/-20-30 nN), even when compressed down to a volume fraction close to unity. On further compression, very weak shear forces (130 +/- 30 nN) were measured due to the increase in the effective viscous drag experienced by the compressed, sliding layers. At separations corresponding to pressures of a few atmospheres, the shearing motion led to abrupt removal of most of the chains out of the gap, and the surfaces jumped into adhesive contact. The extremely low frictional forces between the charged brushes (prior to their removal) is attributed to the exceptional resistance to mutual interpenetration displayed by the compressed, counterion-swollen brushes, together with the fluidity of the hydration layers surrounding the charged, rubbing polymer segments.     

A simple theory of the interaction between polymer brushes immersed in a supercritical fluid

We use a simple two-order parameter model to describe the interaction between the brushes of polymers terminally attached to flat surfaces immersed in a supercritical solvent. Our approach makes it possible to take into account the high compressibility of the supercritical solvent, which proves to give a significant contribution to the disjoining force acting between polymer brushes. Our theory explains why the interaction between brushes can change from repulsive to attractive with decreasing solvent density. This theoretical finding is verified by making a comparison with recent computer simulations. A reasonably good agreement between the results of the present theory and the simulations is found.     

Soft effective interactions between weakly charged polyelectrolyte chains

We apply extensive molecular dynamics simulations and analytical considerations in order to study the conformations and the effective interactions between weakly charged, flexible polyelectrolyte chains in salt-free conditions. We focus on charging fractions lying below 20%, for which case there is no Manning condensation of counterions and the latter can be thus partitioned in two states: those that are trapped within the region of the flexible chain and the ones that are free in the solution. We examine the partition of counterions in these two states, the chain sizes and the monomer distributions for various chain lengths, finding that the monomer density follows a Gaussian shape. We calculate the effective interaction between the centers of mass of two interacting chains, under the assumption that the chains can be modeled as two overlapping Gaussian charge profiles. The analytical calculations are compared with measurements from molecular dynamics simulations. Good quantitative agreement is found for charging fractions below 10%, where the chains assume coil-like configurations, whereas deviations develop for charge fraction of 20%, in which case a conformational transition of the chain towards a rodlike configuration starts to take place.     

Enhancing the ionic conductivity in a composite polymer electrolyte with ceramic nanoparticles anchored to charged polymer brushes

Polymer electrolytes a re essential for next-gene ration lithium batteries because of their excellent safety record.However,low ionic conductivity is the main obstacle restricting their commercial application.Composites with nanoparticles are a promising route to overcome this obstacle.In this work,lithium polystyrene sulfonate brushes(LiPSS)is anchored to silicon dioxide nanoparticles with chemical bonding using atom transfer radial polymerization(SI-ATRP).The composite polymer electrolytes are made by mixing vinylene carbonate and nanoparticles via a facile in situ polymerization process.The ionic conductivity of composite polymer electrolytes is improved to 7.2×10^-4 S/cm at room temperature,which is attributed to the low degree of crystallinity of polymer electrolyte and the fast ion transport on the surfaces of polymer brush layers that act as a conductive network.The composite polymer electrolytes show a wide electrochemical window of approximately 4.5 V vs.Li^+/Li and excellent cycling performance retention of approximately 95%after 100 cycles at ambient temperature.The results also prove that surface groups of ceramic na noparticles are an important way to increase the electrochemical properties of composite polymer electrolytes.     

Effect of temperature on the frictional forces between polystyrene brushes

Normal and shear forces between opposing polystyrene (PS) brushes made from preferentially assembled PS–polyvinylpyridine diblock copolymers were measured in toluene and in near‐theta cyclohexane at 32, 40, and 50 °C, using a modified surface forces apparatus. In cyclohexane, over the temperature window probed, the normal forces of interaction are repulsive and the range of those force profiles changes only slightly; however, for both of the PS brushes studied, the onset of shear forces in near‐theta cyclohexane is strongly influenced by changes in temperature: As the temperature is increased, the onset of the frictional interactions between the brushes in cyclohexane shifts to smaller distances, approaching the distances where frictional forces are observed for brushes in the good solvent toluene. The pattern of behavior seen in the frictional response between the limits of good and theta condition is attributed to composition fluctuations, which increase near the theta condition because of the decrease in excluded volume interactions. These fluctuations may give rise to increased drag during shearing motion because of interfacial roughness or interchain coupling across the brush–brush interface. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 649–655, 2006     

Competing forces in the interaction of polyelectrolytes with charged interfaces

In this review, we discuss the competition of non-DLVO forces in the adsorption of polyelectrolytes onto charged surfaces. We consider two particularly illustrative problems, namely the adsorption of polyelectrolytes onto similarly charged surfaces and the reversal of surface charge by adsorption of polyelectrolytes. Emphasis is made on how simulation results help to understand relevant experimental situations.     

Electric forces induced by a charged colloid particle attached to the water-nonpolar fluid interface

Here, we solve the problem about the electric field of a charged dielectric particle, which is adsorbed at the water-nonpolar fluid (oil, air) boundary. The solution of this problem is a necessary step for the theoretical prediction of the electrodipping force acting on such particle, as well as of the electrostatic repulsion and capillary attraction between two adsorbed particles. In accordance with the experimental observations, we consider the important case when the surface charges are located at the particle-nonpolar fluid boundary. To solve the electrostatic problem, the Mehler-Fock integral transform is applied. In the special case when the dielectric constants of the particle and the nonpolar fluid are equal, the solution is obtained in a closed analytical form. In the general case of different dielectric constants, the problem is reduced to the numerical solution of an integral equation, which is carried out by iterations. The long-range asymptotics of the solution indicates that two similar particles repel each other as dipoles, whose dipole moments are related to the particle radius, contact angle, dielectric constant and surface charge density. The investigated short-range asymptotics ensures accurate calculation of the electrodipping force. For a fast and convenient application of the obtained results, the derived physical dependencies are tabulated as functions of the contact angle and the dielectric constants.     

Responsive and patterned polymer brushes

While polymer brush systems continue to grow in popularity, so does their complexity and sophistication. Advances in polymerization and specific functionalization methods have led to novel applications in diverse research fields. The marriage of top‐down lithography with bottom‐up brush processing is becoming increasingly important in the development and progress of nanotechnology. The aim of this review is to examine different approaches taken to generate tailored polymer brush systems through surface‐initiated polymerizations as well as patterning techniques. Detaching polymer brushes to create free‐standing membranes is also highlighted and discussed in terms of methods and characterization. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013 , 51, 1457–1472     

Effective interaction between charged nanoparticles and DNA

We investigate the effective interaction mediated by salt ions between charged nanoparticles (NPs) and DNA. DNA is modeled as an infinite cylinder with a constant surface charge in an implicit solvent. Monte Carlo simulations are used to compute the free energy of the system described in the framework of the primitive model of electrolytes, which accounts for excluded volumes of salt ions. A mean-field Poisson-Boltzmann theory also allows us to compute the free energy and provides us with explicit formulae for its main characteristics (position and depth of the minimum). We intend here to identify the physical parameters that have a major impact on the NP-DNA interaction, in an attempt to evaluate physico-chemical properties which could play a role in genotoxicity or, which could be exploited for therapeutic use. Thus, we investigate the influence on the effective interaction of: the shape of the nanoparticle, the magnitude of the nanoparticle charge and its distribution, the value of the pH of the solution, the magnitude of Van der Waals interactions depending on the nature of the constitutive material of the NP (metal vs. dielectric). We show that for positively charged concave NPs the effective interaction is repulsive at short distance, so that it presents a minimum at distance from the DNA. This short-range repulsion is specific to indented particles and is a robust property that holds for a large range of materials and charge densities.     

Interaction forces between adsorbed polymer layers

The interaction forces between adsorbed polymer layers were investigated. Two types of graft copolymers that were adsorbed on hydrophobic surfaces have been investigated: (i) a graft copolymer consisting of polymethylmethacrylate/polymethacrylic acid back bone (the B chain) on which several poly(ethylene oxide) chains are grafted (to be referred to as PMMA/PEO_n); and (ii) a graft copolymer consisting of inulin (linear polyfructose with degree of polymerization > 23) (the A chain) on which several C₁₂ chains are grafted (INUTEC SP1). In the first case adsorbed layers of the graft copolymer were obtained on mica sheets and the interaction forces were measured using the surface force apparatus. In the second case the interaction forces were measured using Atomic Force Microscopy (AFM). For this purpose a hydrophobically modified glass sphere was attached to the tip of the cantilever of the AFM and the glass plate was also made hydrophobic. Both the sphere and the glass plate contained an adsorbed layer of INUTEC SP1.In the surface forces apparatus one essentially measures the energy E(D)–distance D curves for the graft copolymer of PMMA/PEO_n between mica surfaces bearing the graft copolymer and this could be converted to interaction energy between flat surfaces. Using the de Gennes scaling theory, it is possible to calculate the interaction energy between the polymer layers. The same graft copolymer was used in latex dispersions and the high frequency modulus G′_∝ was measured as a function of the volume fraction ? of the dispersion. This high frequency modulus could be related to the potential of mean force. In this way one could compare the results obtained from rheology and those obtained from direct measurement of interaction forces.In the AFM method, the interaction forces are measured in the contact area between two surfaces, i.e. a spherical glass particle and a glass plate. Both glass spheres and plates were hydrophobized using dichlorodimethylsilane. Results were obtained for adsorbed layers of INUTEC SP1 in water and in the presence of various concentrations of Na₂SO₄ (0.3, 0.8, 1.0 and 1.5 mol dm^{− 3}). All results showed a rapid increase of force with a decrease of separation distance and the forces were still repulsive up to the highest Na₂SO₄ concentration. This explains the high stability of dispersions when using INUTEC SP1 as stabilizer.     

Surface forces between bottlebrush polymer layers

In this review, I summarize recent experimental investigations of surface and friction forces between bottlebrush structure macromolecules including biolubricants and biomimetic ones by direct force measurements. I also discuss recent experimental investigations of synergy in lubrication in which a question, ‘How do lubricants act together?’, is aimed to be answered. Lastly, challenges and opportunities for developing efficient lubricating systems are outlined.     

Long-range interaction between heterogeneously charged membranes

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the electrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased.     

Effect of pH and hydration on the normal and lateral interaction forces between alumina surfaces

Interaction forces between alumina surfaces were measured using an AFM-colloid probe method at different pHs. For an alpha-alumina-sapphire system at acidic pH, the force curve exhibited a well-defined repulsive barrier and an attractive minimum. At basic pH, the interactive force was repulsive at all separations with no primary minimum. Lateral force measurements under the same conditions showed that frictional forces were nearly an order of magnitude smaller at basic pH than those observed at acidic pH. This behavior was attributed to the hydration of the alumina surface. Normal and lateral force measurements with the strongly hydrated rho-alumina surfaces supported these findings.     

Polymer-induced depletion interaction between weakly attractive plates

Lattice Monte Carlo simulations have been employed to calculate depletion interaction of excluded volume chains in a weakly attractive slit, particularly in the region around the critical point of adsorption. The simulations were performed under full equilibrium conditions where a dilute solution in a slit was in contact with the reservoir. The free energy of confinement deltaA, the force f, and the relative pressurepI/pE on the slit walls were calculated as a function of slit width D and the attraction strength epsilon. The depletion region in the pressure profile pI/pE vs D is reduced by an increase in the attraction potential epsilon in a manner resembling the influence of polymer concentration. At the critical point of adsorption epsilonc the depletion interaction vanishes both in the pressure pI/pE and in the intraslit concentration profile phiI(x). The parameters used to assess the stability of colloidal dispersions such as the depletion potential W(D) (an integral of the net pressure deltap) reach a unique value at the critical condition. A monotonic repulsive profilepI vs D was found for chains trapped in the slit at restricted equilibrium. The mean dimensions (R2) of chains compressed in attractive slits feature a distinct minimum at intermediate slit widths.     

Ion-specific forces between a colloidal nanoprobe and a charged surface

We investigate the effect of ion-specific potentials on the force between a nanoprobe attached to a cantilever tip, and a charged surface. The probe is treated as a spherical nanoparticle with constant charge. A modified Poisson-Boltzmann equation in bispherical coordinates is used to address this problem in a more quantitative way. We predict that the ion-specific series of measured forces depend on the sign and magnitude of surface charge densities.     

Double layer interaction between two plates with polyelectrolyte brushes

When polyelectrolyte chains are grafted to colloidal particles, the electric field between particles is affected by the charges of the chains. In some previous theoretical attempts, the charge density of the polyelectrolyte chains per unit length was considered constant, and its effect was accounted for by introducing an additional constant charge density into the unidimensional Poisson-Boltzmann equation, which was evaluated assuming that it is uniformly distributed in the polyelectrolyte volume of the brush. In this paper, a more detailed model is employed for the calculation of the electrical potential between two plates on which polyelectrolyte brushes are present. In this model, the polyelectrolyte chain is viewed as a rigid cylinder, on the surface of which charges are generated through the dissociation of ionizable sites and adsorption of the cations of the electrolyte. To each of the chains an atmosphere is attached which for simplicity is assumed cylindrical. In the brush region, the electrical potential is described by a two-dimensional Poisson-Boltzmann equation, while in the region free of polyelectrolyte chains by a unidimensional Poisson-Boltzmann equation. Such a model is physically suitable when the charges of the chains are sufficiently large for the repulsion they generate to ensure that the chains are fully extended. Such cases are quite frequent, because relatively low charges lead to an almost complete extension of the chains. In this paper, both the plate surface and the surface of the cylinders are considered charged. The effects of electrolyte concentration, pH, brush thickness and chain coverage density on the repulsion between plates are examined.     

Friction and forces between cellulose model surfaces: a comparison

Four different cellulose model surfaces, and one silica surface, have been studied by means of atomic force microscopy (AFM). The normal interactions have been found to consist of a longer range double layer force with a short range steric interaction, the nature of which is extensively discussed. Both the surface charge and range of the steric force depend on the type of cellulose substrate used, as does the magnitude of the adhesion. Studies of friction reveal that surface roughness is the determining factor for the friction coefficient, with which it increases monotonically. The absolute value, however, is determined by the surface chemistry. All studied cellulose surfaces show similar behavior in response to xyloglucan addition.