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.     

Friction and normal interaction forces between irreversibly attached weakly charged polymer brushes

Polyelectrolyte brushes were built on mica by anchoring polystyrene-poly(acrylic acid) (PS-b-PAA) diblock copolymers at a controlled surface density in a polystyrene monolayer covalently attached to OH-activated mica surfaces. Compared to physisorbed polymer brushes, these irreversibly attached charged brushes allow the polymer grafting density to remain constant upon changes in environmental conditions (e.g., pH, salt concentration, compression, and shear). The normal interaction and friction forces as a function of surface separation distance and at different concentrations of added salt (NaCl) were investigated using a surface forces apparatus. The interaction force profiles were completely reversible both on loading and receding and were purely repulsive. For a constant polymer grafting density, the influence of the polyelectrolyte charges and the Debye screening effect on the overall interaction forces was investigated. The experimental interaction force profiles agree very well with scaling models developed for neutral and charged polymer brushes. The variation of the friction force between two PAA brushes in motion with respect to each other as a function of surface separation distance appeared to be similar to that observed with neutral brushes. This similarity suggests that the increase in friction is associated with an increase in mutual interpenetration upon compression as observed with neutral polymers. The effect of the PAA charges and added ions was more significant on the repulsive normal forces than on the friction forces. The reversible characteristics of the normal force profiles and friction measurements confirmed the strong attachment of the PAA brushes to the mica substrate. High friction coefficients (ca 0.3) were measured at relatively high pressures (40 atm) with no surface damage or polymer removal.     

Linear shear viscoelasticity of confined,end-attached polymers in a near-theta solvent

Diblock copolymers of polystyrene and polyvinylpyridine, end-attached to mica by the traditional method of selecting one block to be insoluble and the other block to be soluble in the solvent, were studied with surface-force experiments while immersed in trans-decalin, a near-theta solvent for the polystyrene block, with special attention given to the small-amplitude shear viscoelastic response. The relaxation time, defined as the inverse frequency at which the effective loss modulus equaled the effective storage modulus, was studied not only as a function of the film thickness but also as a function of the grafting density. The relaxation times started to slow in direct proportion to diminishing surface separation when the surface separation took the value D ≈ L_o/3 (where L_o is the thickness of the uncompressed end-attached layer). Attempts to make comparisons with available theories met with limited success. To test experimentally the origin of this shear viscoelastic slowdown, similar measurements were made with adsorbed polystyrene with a molecular weight similar to that of the polystyrene moiety of the diblock copolymer, and it was found that high magnitudes of the effective viscoelastic shear moduli appeared only when the compression was much larger. In a control experiment in which interpenetration between opposed end-attached chains was precluded, we also studied the case of adsorbed polystyrene–polyvinylpyridine on one side and a bare mica surface on the other side, and the effective viscoelastic shear forces were reduced by nearly 1 order of magnitude. By inference, in the opposed diblock copolymer systems, we attributed the slowdown of the relaxation times with decreasing film thickness to the interpenetration of end-attached chains. Additional comments are made regarding the ratio of shear forces to compressive forces, which is called the small-strain friction coefficient. This is believed to be the first quantification of the linear-response relaxation time of end-attached polymer layers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3487–3496, 2005     

Stress-induced polymer deformation in shear flows

By means of dynamic Monte Carlo simulation of bulk lattice polymers in Couette shear flow, it was demonstrated that in addition to velocity gradient the constant driving forces acting as the activation aspect of shear stresses can also raise polymer deformation. Moreover, enhancing driving forces in a flow without any velocity gradient can reproduce nonNewtonian fluid behaviors of long-chain polymers. The simulations of Poiseuille shear flow with a gradient of shear stresses show that, the velocity gradient dominates small deformation in the flow layers of low shear stresses, while the shear stress dominates large deformation in the flow layers of high shear stresses. This result implies that the stress-induced deformation could be mainly responsible for the occurrence of non-Newtonian fluid behaviors of real polymers at high shear rates.     

Monte Carlo simulation study of the kinetics of brush formation by irreversible adsorption of telechelic polymers onto a solid substrate

The irreversible adsorption of telechelic polymer chains from solution and melts onto solid substrates has been studied using the bond fluctuation Monte Carlo model. Complex brush formation kinetics dominated by diffusion of chains to the substrate at short times (diffusion-limited regime or DLR) and by penetration of chains through the maturing brush at longer times (penetration-limited regime or PLR) were observed. During the entire adsorption process, the rate of chain adsorption decreases monotonically with time. In the DLR, characterized by a maximum in the concentration of singly bound chains and a rapidly increasing fraction of doubly bound chains (loops), this decrease is due primarily to the depletion of free chains near the substrate and the formation of concentration gradients of free (nonadsorbed) chains in the bulk solution. The DLR and PLR are separated by an intermediate regime during which the brush becomes dominated by doubly bound chains and both penetration of the maturing brush and diffusion of chains to the brush surface play a role in determining the kinetics of brush growth. The PLR is characterized by steep gradients of free chains within the growing brush and the disappearance of concentration gradients for free chains in the bulk solution. In the PLR, the concentration of singly bound chains is low and decreases slowly while surface coverage and the fraction of doubly bound chains increase slowly. The rates of adsorption of new chains and the formation of loops in the PLR slow dramatically with increasing surface coverage and increasing chain length and less dramatically with decreasing bulk concentration.     

Direct measurement of shear forces between polymer-bearing surfaces sliding past each other

We have used a recently developed surface force balance to measure, with extreme sensitivity, both lateral and normal forces between interacting surfaces, for the case of simple liquids and particularly with surface-attached polymers. The presence of polymers on the surfaces reduces drastically the force required to maintain them in sliding motion, under a given normal load, relative to the bare surface case. We believe this is due to the long range steric repulsion which can sustain a large normal load while maintaining a very fluid interfacial layer. The effect is much more marked for end-tethered chains in a good solvent than for adsorbed chains in a θ-solvent. This is attributed to the different extents of interpenetration of the compressed polymer layers.     

Constitutive equations for the flow behavior of entangled polymeric systems: application to star polymers

A semimicroscopic derivation is presented of equations of motion for the density and the flow velocity of concentrated systems of entangled polymers. The essential ingredient is the transient force that results from perturbations of overlapping polymers due to flow. A Smoluchowski equation is derived that includes these transient forces. From this, an equation of motion for the polymer number density is obtained, in which body forces couple the evolution of the polymer density to the local velocity field. Using a semimicroscopic Ansatz for the dynamics of the number of entanglements between overlapping polymers, and for the perturbations of the pair-correlation function due to flow, body forces are calculated for nonuniform systems where the density as well as the shear rate varies with position. Explicit expressions are derived for the shear viscosity and normal forces, as well as for nonlocal contributions to the body force, such as the shear-curvature viscosity. A contribution to the equation of motion for the density is found that describes mass transport due to spatial variation of the shear rate. The two coupled equations of motion for the density and flow velocity predict flow instabilities that will be discussed in more detail in a forthcoming publication.     

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.     

Interfacial friction and adhesion of polymer brushes

A bead-probe lateral force microscopy (LFM) technique is used to characterize the interfacial friction and adhesion properties of polymer brushes. Our measurements attempt to relate the physical structure and chemical characteristics of the brush to their properties as thin-film, tethered lubricants. Brushes are synthesized at several chain lengths and surface coverages from polymer chains of polydimethylsiloxane (PDMS), polystyrene (PS), and a poly(propylene glycol)-poly(ethylene glycol) block copolymer (PPG/PEG). At high surface coverage, PDMS brushes manifest friction coefficients (COFs) that are among the lowest recorded for a dry lubricant film (μ ≈ 0.0024) and close to 1 order of magnitude lower than the COF of a bare silicon surface. Brushes synthesized from higher molar mass chains exhibit higher friction forces than those created using lower molar mass polymers. Increased grafting density of chains in the brush significantly reduces the COF by creating a uniform surface of stretched chains with a decreased surface viscosity. Brushes with lower surface tension and interfacial shear stresses manifest the lowest COF. In particular, PDMS chains exhibit COFs lower than PS by a factor of 3.7 and lower than PPG/PEG by a factor of 4.7. A scaling analysis conducted on the surface coverage (σ) in relation to the fraction (ε) of the friction force developing from adhesion predicts a universal relation ε ~ σ(4/3), which is supported by our experimental data.     

Molecular simulation of the frictional behavior of polymer-on-polymer sliding

Molecular simulations of the sliding processes of polymer-on-polymer systems were performed to investigate the surface and subsurface deformations and how these affect tribological characteristics of nanometer-scale polymer films. It is shown that a very severe deformation is localized to a band of material about 2.5 nm thick at the interface of the polymer surfaces. Outside of this band, the polymer films experience a uniform shear strain that reaches a finite steady-state value of close to 100%. Only after the polymer films have achieved this steady-state shear strain do the contacting surfaces of the films show significant relative slippage over each other. Because severe deformation is limited to a localized band much thinner than the polymeric films, the thickness of the deformation band is envisaged to be independent of the film thickness and hence frictional forces are expected to be independent of the thickness of the polymer films. A strong dependency of friction on interfacial adhesion, surface roughness, and the shear modulus of the sliding system was observed. Although the simulations showed that frictional forces increase linearly with contact pressure, adhesive forces contribute significantly to the overall friction and must therefore be accounted for in nanometer-scale friction. It is also shown that the coefficient of friction is lower for lower-density polymers as well as for polymers with higher molecular weights.     

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.     

Nonlinear dynamics of melted polymer layers

A theory for non-linear rheology of molten polymer layers between solid surfaces in the Rouse regime is discussed. It is shown that the effect of finite extensibility of polymer chains leads to the characteristic 1/3 power law for the shear stress vs. shear velocity in the regime of high velocities. It is also shown that bridging polymer fragments connecting the two surfaces play an important role for the rheology if the effective monomer friction in the immediate vicinity of the surfaces is much higher than far from the surfaces. In particular we predict that shear stress is decreasing with shear velocity u in a limited range between u₁ and u, _min. This effect results in a possibility of stick-slip periodical dynamics of the layer under a constant imposed velocity.     

固体~1H-NMR表征玻璃态高分子链的缠结、互穿及链间邻近度

系统回顾了缠结定义的演化及对其表征的各种方法,比较了这些方法的特点和不足.在以往研究的基础上,发展了一套在分子尺度上表征玻璃态高分子链互穿的方法.该方法结合高速魔角和偶极滤波,用固体1H-NMR探测互穿区域的质子信号,表征了玻璃态聚苯乙烯的链互穿程度.该方法在0.5 nm尺度范围内测定了分子链间的距离,且与以往方法相比,该方法具有耗时短、需要样品量少、灵敏度和信噪比高等优点.     

A molecular simulation study of the structure and tribology of polymer brushes: Comparison of behavior in theta and good solvents

Implicit solvent Brownian dynamics simulations of the structure and tribology of opposing polymer-brush covered surfaces have been carried out as a function of surface separation and solvent quality. Consistent with experiment, shear forces were found to be greater under theta solvent conditions than in a good solvent at equal relative separations (normalized by the respective height of the brushes in theta and good solvents). Much higher relative compression is required before the onset of significant shear forces in good solvent compared to theta solvent. The dependence of shear force for a given relative separation on solvent quality can be accounted for by differences in interpenetration of the brushes. When compared as a function of absolute surface separation, greater interpenetration and greater shear force are observed at large separations for the brushes in good solvent than in theta solvent, consistent with the greater brush height in good solvent. At shorter separations, corresponding to moderate to high compression, brush-brush interactions result in significant deformation of the brushes. In this regime, greater interpenetration and greater shear forces are observed in theta solvent at a given separation, in qualitative agreement with experiment.     

Atomic force microscopy study of the interaction between adsorbed poly(ethylene oxide) layers: effects of surface modification and approach velocity

The interaction forces between layers of the triblock copolymer Pluronic F108 adsorbed onto hydrophobic radio frequency glow discharge (RFGD) thin film surfaces and hydrophilic silica, in polymer-free 0.15 M NaCl solution, have been measured using the atomic force microscope (AFM) colloid probe technique. Compression of Pluronic F108 layers adsorbed on the hydrophobic RFGD surfaces results in a purely repulsive force due to the steric overlap of the layers, the form of which suggests that the PEO chains adopt a brush conformation. Subsequent fitting of these data to the polymer brush models of Alexander-de Gennes and Milner, Witten, and Cates confirms that the adsorbed Pluronic F108 adsorbs onto hydrophobic surfaces as a polymer brush with a parabolic segment density profile. In comparison, the interaction between Pluronic F108 layers adsorbed on silica exhibits a long ranged shallow attractive force and a weaker steric repulsion. The attractive component is reasonably well described by van der Waals forces, but polymer bridging cannot be ruled out. The weaker steric component of the force suggests that the polymer is less densely packed on the surface and is less extended into solution, existing as polymeric isolated mushrooms. When the surfaces are driven together at high piezo ramp velocities, an additional repulsive force is measured, attributable to hydrodynamic drainage forces between the surfaces. In comparing theoretical predictions of the hydrodynamic force to the experimentally obtained data, agreement could only be obtained if the flow profile of the aqueous solution penetrated significantly into the polymer brush. This finding is in line with the theoretical predictions of Milner and provides further evidence that the segment density profile of the adsorbed polymer brush is parabolic. A velocity dependent additional stepped repulsive force, reminiscent of a solvation oscillatory force, is also observed when the adsorbed layers are compressed under high loads. This additional force is presumably a result of hindered drainage of water due to the presence of a high volume fraction of polymer chains between the surfaces.     

Dynamics of free chains in polymer nanocomposites

The dynamics of entangled polymeric chains in a polymer filled with nanoparticles is studied by means of molecular dynamics simulations of a model system. The primary objective is to study to what extent the reptation of polymers not in direct contact with fillers is modified with respect to the neat material. To this end, two systems are considered: A regular filled material in which the filler-polymer affinity is controlled, and a system in which the beads in contact with the filler at the beginning of the production phase of the simulation are tethered to the filler surface. This second system represents the limit case of long polymer-filler attachment time. In this case attention is focused on the free chains of the melt. The dynamics in the two models is different. In the filled system uniform slowing down for all Rouse modes is observed. The effect varies monotonically with the filler-polymer affinity. Up to saturation, this behavior may be captured by usual models with an effective, affinity-dependent, friction coefficient. In the system with grafted chains, the free chain Rouse dynamics is identical to that in the neat material, except for the longest modes which are significantly slowed down. More interestingly, the dynamics of the free chains depends in a nonmonotonic way on the polymer-filler affinity, although the free chains do not come in direct contact with the filler. This effect is due to small changes in the structure of the polydisperse brush upon modification of the affinity. Specifically, the density of the brush and the amount of interpenetration of free and grafted chains depend on the filler-polymer affinity. The use of a reptation model with modified tube diameter to capture this behavior is discussed.     

A Study of the Authophobic Dewetting in Thin Polymer Films

We have investigated the dewetting behaviour of a thin polystyrene film on top of cross-linked network of the same polymer. By changing the cross-linking density, the dynamic of the dewetting is modified. The behaviour of the contact angle and dewetting velocity can be related to the interfacial width between the polymers. We observe moreover that while the lost of entropy of the network connected to the penetration of the free chains will favour the dewetting; the possible presence of “connectors” between the layers will tend to stabilize the wetting. By modifying the entropy of the mesh by swelling the cross-linked system with a reservoir of the same polymer, the mesh is saturated and a stable interface without interdiffusion between the layers is obtained: in this case a constant contact angle and slippage length are obtained. Networks with higher cross-linking density are more difficult in general to swell – the mesh size is smaller - and the complete saturation is not reached.     

Correlation between conformation change of polyelectrolyte brushes and lubrication

We directly monitor the absolute separation profiles that function as film thickness between a single glass disk and the charged polyelectrolyte brushes decorated steel slider in water using a home-made slider-on-disk apparatus, which reflects the structural conformation variations and interactions of polymer brushes under externally applied pressure, in addition to probing the relative variation of friction forces under different applied loads and sliding velocities. We find that the polyelectrolyte brushes modified surfaces can sustain high pressure and have extremely low friction coefficients(around 0.006 at pressures of 0.13 MPa; 0.5-0.6 without brushes). The water-lubrication characteristics are correlated to the structural conformation changes of the polyelectrolyte brushes that are mainly governed by electrostatic interactions and the osmotic pressure of counterions inside the polymer chains, which can be used to support and distribute the normal pressure. The apparent thickness of the brush decreases with the increase of loading forces, an increase in the ionic strength causes the polymer chains collapse, and the friction forces increase. This fundamental research is of great importance to understand the mechanical and structural properties of polyelectrolyte brushes and their influences on the tribological behaviors, and helps to design friction/lubrication-controlled surface/interface by taking advantage of polyelectrolyte brushes.     

Friction of single polymers at surfaces

Atomic force microscope (AFM) single molecule force spectroscopy has been used to investigate the friction coefficient of individual polymers adsorbed onto a solid support. The polymer chains were covalently attached to an AFM tip and were allowed to adsorb on a mica surface. Different polymers (ssDNA, polyallylamine) were chosen to cover a range of friction coefficients. During the experiment, the AFM tip was retracted in- and off-plane which results, depending on the chosen conditions, in a desorption of the polymer from the surface, a sliding across the surface, or a combination of both. Thus, the obtained force-extension spectra reveal detailed information on the mobility of a polymer chain on a surface under experimentally accessible conditions. This study demonstrates that absorbed polymers with comparable desorption forces may exhibit drastically different in plane mobility.     

平行壁面间平衡聚合物吸附行为的自洽场分析

采用自洽场理论研究了平衡聚合物在平行壁面间的吸附规律.结果表明,平衡聚合物的吸附行为可根据壁面吸附强度划分为弱吸附和强吸附两个区间.在强吸附区间,平衡聚合物可以形成明确的吸附层,增大吸附强度能够引起平均分子链长的陡增,但不会改变链长分布的指数形式.平衡聚合物的长链分子在强吸附条件下较短链分子更靠近吸附壁面,在弱吸附条件下,则更接近体系中心.通过计算壁面压强发现:在弱吸附作用下,吸附壁面始终受到分子链的推斥作用;在强吸附作用下,分子链对壁面的作用随壁面间距的加大由推斥转变为吸引.平衡聚合物的溶解性和排空效应以及壁面吸附作用之间存在竞争关系,加大排除体积作用参数会引起分子链密度分布的均一化和壁面承受压强的降低.