Self‐Consistent Brownian Dynamics Simulation of an Anisotropic Brush Under Shear Flow

Summary: The behavior of an anisotropic polymer brush under a lateral shear flow is considered in the framework of a hybrid method combining a self‐consistent field approach and Brownian dynamics simulation. It is shown that such a flow can induce the compression of an anisotropic brush at shear rates much smaller than those which induce the compression of a conventional isotropic brush. Moreover, a lateral flow can initiate a thermotropic collapse which occurs as an LC phase transition. This collapse takes place at higher temperatures than in the absence of the flow. This can help to find brush compression experimentally. The variation of the internal structure of a brush (density, order parameter, and director orientation profiles, distribution of terminal groups) is also investigated. An anomalous effect of brush densification and ordering near the outer surface is observed. At large shear rates the distribution of chains over their deformation has a bimodal character: one fraction of chains is strongly stretched and another fraction remains unperturbed by the flow. Average characteristics of a brush were compared with predictions of the lattice theory for the box model where the lateral force is applied to chain ends. Satisfactory agreement was observed.

Polymer brush under an influence of lateral flow.     

Normal and Lateral Deformation of Lyotropically Ordered Polymer Brush

Summary: Planar polymer brush formed by semirigid chains of freely jointed rigid segments and immersed into a solvent is considered. Brush collapse induced by deterioration of the solvent quality and its deformation by external normal or lateral force is studied. It is demonstrated that these three different situations can be described in the framework of the common approach. It is shown that the collapse is accompanied by liquid‐crystalline (LC) ordering within the brush. The LC transition can be jump‐like (the first order) or continuous, depending on the segment's aspect ratio and grafting density. Transition point is investigated in detail, the corresponding phase diagrams are calculated. It is shown that the phase diagrams of a normally deformed brush have different structures, with a narrow ‘leg’ in the good solvent region for sparsely grafted brush, with two coexistence regions and a triple point, in addition, for shorter segment length or without these features if the chains are densely grafted. For the laterally deformed brush, phase diagrams have similar structures with a critical point in the good solvent regime.

Polymer brush subjected to deformation by normal (top) and lateral (bottom) external force.     

Normal and shear forces between a polyelectrolyte brush and a solid surface

The diblock copolymer poly(methyl methacrylate)‐b‐poly(sodium sulfonated glycidyl methacrylate) (PMMA‐b‐PSGMA) was end‐attached by its hydrophobic block (PMMA) onto mica hydrophobized by a stearic trimethylammonium iodide (STAI) layer, to form a polyelectrolyte brush immersed in water. With a surface force balance (SFB), we extended earlier measurements between two such brush layers for the case of normal and shear forces at different shear rates, surface separation, and compressions between one mica surface coated with STAI or a STAI‐diblock layer against a bare mica surface. After coating one of the surfaces with STAI, a long range attraction that results in a jump into an adhesive flat contact between the hydrophobic and hydrophilic surfaces was observed. A very different behavior was seen after forming the polyelectrolyte brush on the STAI‐coated surface. The long range attraction was replaced by repulsion, accompanied by very low friction during shear (ca. three orders of magnitude lower than with adsorbed polyelectrolytes). On further compression, a weak attraction to the adhesive contact was observed. From the final surface–surface contact separation, we deduce that most of the polyelectrolyte diblock brush layer was squeezed out from the gap, leaving the STAI layer and a small amount of the polymer attached to the surface. Stick‐sliding behavior was seen while applying shear, suggesting a dissipation mechanism caused by the trapped polyelectrolyte. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 193–204, 2005     

Polyelectrolyte brushes

The simple scaling theory of weakly-charged polyelectrolyte brush (the layer of polyelectrolyte chains grafted at one end onto an impermeable surface) immersed into a good solvent has been developed.The asymptotic scaling dependences of the free layer thickness on charge density and solvent strength are obtained. The behavior of polyelectrolyte brush subjected to normal and tangential external forces is considered. New “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness in contrast to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to external normal stretching force. This force in the case of polyelectrolyte brush is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges.     

Theory of Liquid-crystalline Ordering in Polymer Brushes

Summary: We present a review of the works devoted to investigation of LC ordering in polymer brushes. This series has been carried out by the group of T. M. Birshtein and covers the following aspects of the problem: thermotropic LC phase transition in LCP brushes, microphase segregation, homeotropic and planar LC phases, LC polymer in LC solvent, lyotropic LCP brushes, LC transitions under normal or lateral force (shear flow). Analytical theory is developed for simplified model of polymer brush with accounting for thermotropic attraction in Mayer-Saupe approximation and lyotropic repulsion in DiMarzio formalism; numerical calculations are fulfilled in self-consistent field approximation (method of Scheutjens and Fleer). Brownian dynamics simulations are applied for modeling polymer brush in a shear flow.     

Shear of a planar polyelectrolyte brush

The behavior of a planar polyelectrolyte brush subjected to normal and tangential external forces is considered. A new “polyelectrolyte effect” is predicted: shear of a free polyelectrolyte brush leads to a decrease in brush thickness contrary to the case of a free neutral brush. Such behavior is equivalent to that of a neutral brush subjected to an external normal stretching force. In the case of a polyelectrolyte brush this force is created by the osmotic pressure of mobile counterions neutralizing grafted chain charges. Addition of salt diminishes the polyelectrolyte effect and changes the sign of correlation between brush thickness and tangential deformation.     

Monte carlo simulations of polydisperse polymers grafted on spherical surfaces

This article presents effects of polydispersity in polymers grafted on spherical surfaces on grafted polymer chain conformations, grafted layer thickness, and free‐end monomer distribution within the grafted layer. At brush‐like grafting densities, as polydispersity index (PDI) increases, the scaling exponent of radius of gyration of grafted chains approaches that of a single chain grafted on the same nanoparticle, because polydispersity alleviates monomer crowding within the brush. At high PDI, the chains shorter than the number average chain length, N_n, have more compressed conformations, and the chains longer than N_n overall stretch less than in the monodisperse case. As seen in polydisperse flat brushes at high grafting densities, the grafted layer thickness on spherical nanoparticle increases with PDI. Polydispersity eliminates the region near the surface devoid of free‐end monomers seen in monodisperse cases, and it reduces the width of free‐end monomer distribution and shifts the free‐end monomer distribution close to the surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Stimuli‐responsive diblock copolymer brushes via combination of “click chemistry” and living radical polymerization

pH‐ and temperature‐responsive poly(N‐isopropylacrylamide‐block?4‐vinylbenzoic acid) (poly(NIPAAm‐b‐VBA)) diblock copolymer brushes on silicon wafers have been successfully prepared by combining click reaction, single‐electron transfer‐living radical polymerization (SET‐LRP), and reversible addition‐fragmentation chain‐transfer (RAFT) polymerization. Azide‐terminated poly(NIPAAm) brushes were obtained by SET‐LRP followed by reaction with sodium azide. A click reaction was utilized to exchange the azide end group of a poly(NIPAAm) brushes to form a surface‐immobilized macro‐RAFT agent, which was successfully chain extended via RAFT polymerization to produce poly(NIPAAm‐b‐VBA) brushes. The addition of sacrificial initiator and/or chain‐transfer agent permitted the formation of well‐defined diblock copolymer brushes and free polymer chains in solution. The free polymer chains were isolated and used to estimate the molecular weights and polydispersity index of chains attached to the surface. Ellipsometry, contact angle measurements, grazing angle‐Fourier transform infrared spectroscopy, and X‐ray photoelectron spectroscopy were used to characterize the immobilization of initiator on the silicon wafer, poly(NIPAAm) brush formation via SET‐LRP, click reaction, and poly(NIPAAm‐b‐VBA) brush formation via RAFT polymerization. The poly(NIPAAm‐b‐VBA) brushes demonstrate stimuli‐responsive behavior with respect to pH and temperature. The swollen brush thickness of poly(NIPAAm‐b‐VBA) brush increases with increasing pH, and decreases with increasing temperature. These results can provide guidance for the design of smart materials based on copolymer brushes. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 2677–2685     

Stochastic dynamics simulation of grafted polymer brushes under shear deformation

We present results of computer simulations of polymer brushes (layers of polymer chains attached at one end onto an impermeable planar surface) under shear deformation at constant shear rate. As the first stage of calculations the behavior of a single brush was studied. The monomer density profile, the distribution of the chain ends, the positions and orientations of different monomers along the chain were calculated. Dimensions of the polymer chains as functions of the shear rate were obtained for different grafting densities. An increase in the brush thickness over the grafting plane with an increase in the shear rate as predicted by the theory of Barrat was observed. However, the magnitude of the effect appears to be small. We explain this by finite extensibility of the grafted chains.     

Free Energy of a Non‐Gaussian Polymer Brush

An analytical theory describing layers of polymer chains grafted to a planar surface (i.e. polymer brush) is developed. We consider a brush of chains with finite extensibility (or non‐Gaussian brush) within the framework of molecular field theory. An analytical solution for free energy of the brush and a few other brush characteristics are obtained and studied. Comparison with other known models of a brush is also made.

Chain extensibility E(x, y) for Gaussian model (dashed lines) and BCC model (solid lines) for a few chain end positions y (numbers near curves).     

Synthesis of novel polypyromellitimides with n‐alkyloxy side chains and their liquid‐crystal aligning property

New well‐defined brush polypyromellitimides with n‐octyloxy and n‐dodecyloxy side chains were prepared by two‐step polycondensations of 3,6‐di(n‐alkyloxy)pyromellitic dianhydrides with various conventional aromatic diamines. Their structures and properties were investigated and compared with those of polyimides without the side chains. The alkyloxylated poly(amic acid)s had inherent viscosities of 0.45–1.09 dL/g. The polyimides showed enhanced solubility in organic solvents and had layered structures in the solid state. As the side‐chain length increased from n‐octyloxy to n‐dodecyloxy, the extent of layered structure formation increased, whereas the glass‐transition temperature and thermal resistance decreased. As for the liquid‐crystal (LC) aligning ability measured with 4‐n‐pentyl‐4′‐cyanobiphenyl on rubbed thin‐film surfaces, all the side‐chain polyimides revealed homogeneous LC alignment parallel to the rubbing direction with distinctively higher pretilt angles than those of the polyimides without the side chains. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3130–3142, 2004     

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.     

A Langevin dynamics simulation study of the tribology of polymer loop brushes

The tribology of surfaces modified with doubly bound polymer chains (loops) has been investigated in good solvent conditions using Langevin dynamics simulations. The density profiles, brush interpenetration, chain inclination, normal forces, and shear forces for two flat substrates modified by doubly bound bead-necklace polymers and equivalent singly bound polymers (twice as many polymer chains of 12 the molecular weight of the loop chains) were determined and compared as a function of surface separation, grafting density, and shear velocity. The doubly bound polymer layers showed less interpenetration with decreasing separation than the equivalent singly bound layers. Surprisingly, this difference in interpenetration between doubly bound polymer and singly bound polymer did not result in decreased friction at high shear velocity possibly due to the decreased ability of the doubly bound chains to deform in response to the applied shear. However, at lower shear velocity, where deformation of the chains in the flow direction is less pronounced and the difference in interpenetration is greater between the doubly bound and singly bound chains, some reduction in friction was observed.     

Grafted polymers under strong shear: Scaling and non-equilibrium Monte Carlo studies

End-grafted polymer chains exposed to strong shear solvent flow in the x-direction are investigated by a non-equilibrium Monte Carlo method using the bond-fluctuating model. The solvent flow is modelled by an enhanced jump rate of monomers in the flow direction. Under strong enough shear flow, the shear force is non-linear with the blob size ζ depending on the shear force and not on the monomer volume fraction ϕ. For the case of a grafted single chain, our data on the end-to-end distance of the polymer for a wide range of shear rate γ agree well with the proposed scaling form and compare reasonably well with the Langevin force law in the extreme strong shear case. Also the scaling for the blob size is derived with ζ = aN^vK(γN^2+v) for some scaling function K, and verified by our simulation data. For the case of a polymer brush, we derive the crossover force scale F^* separating the weak and strong shear regime with F^*a/(kT) = ϕ^v/(3v−1) where v is the usual self-avoiding walk exponent. For the case of a polymer brush under strong shear, the velocity profile, v(z), inside and above the brush is calculated analytically by treating the flow as in a porous medium and solving the Brinkman equation. The solution of the velocity profile is then combined with non-equilibrium Monte Carlo simulation data which allow a self-consistent determination of the chain end-to-end length and the incline angle of the chain. Also we derive the scaling form for the positions x(n) of the nth monomer and verify it by our simulation data. We further obtain an analytical expression for x(n) in terms of the effective viscosity η of the model, given by F = ηav(z). The effective viscosity is also found from our simulation to be ηa²/(kT) ≃ 0.02 ± 0.005.     

Investigating the chain conformations of spin‐coated polymer thin films by ToF‐SIMS depth profiling

Thin films of bromine‐terminated poly(bisphenol A octane ether) (BA‐C10) were prepared using 1,2‐dichlorobenzene (ODCB) as the solvent. The organization of the chains in these amorphous polymer films was evaluated using time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) depth profiling. For the thin films, the bifunctional polymer chains were folded and anchored to the substrate via their two Br end groups and a polymer brush of chain loops was formed on the substrate. As the film thickness increased, polymer chains in a random coil conformation were found to reside on the top of the polymer brush. Depth profiling revealed that the polymer chains were densely packed at the interface. Moreover, the polymer films showed thermal stability, implying strong interactions between the end groups and the substrate. Copyright © 2015 John Wiley & Sons, Ltd.     

Ordered nanostructures at two different length scales mediated by temperature: A triphenylene‐containing mesogen‐jacketed liquid crystalline polymer with a long spacer

A mesogen‐jacketed liquid crystalline polymer (MJLCP) containing triphenylene (Tp) moieties in the side chains with 12 methylene units as spacers (denoted as PP12V) was synthesized. Its liquid crystalline (LC) phase behavior was studied with a combination of solution ¹H NMR, solid‐state NMR, gel permeation chromatography, thermogravimetric analysis, polarized light microscopy, differential scanning calorimetry, and one‐ and two‐dimensional wide‐angle X‐ray diffraction. By simply varying the temperature, two ordered nanostructures at sub‐10‐nm length scales originating from two LC building blocks were obtained in one polymer. The low‐temperature phase of the polymer is a hexagonal columnar phase (Φ_H, a = 2.06 nm) self‐organized by Tp discotic mesogens. The high‐temperature phase is a nematic columnar phase with a larger dimension (a′ = 4.07 nm) developed by the rod‐like supramolecular mesogen—the MJLCP chain as a whole. A re‐entrant isotropic phase is found in the medium temperature range. Partially homeotropic alignment of the polymer can be achieved when treated with an electric field, with the polymer in the Φ_H phase developed by the Tp moieties. The incorporation of Tp moieties through relatively long spacers (12 methylene units) disrupts the ordered packing of the MJLCP at low temperatures, which is the first case for main‐chain/side‐chain combined LC polymers with MJLCPs as the main‐chain LC building block to the best of our knowledge. The relationship of the molecular structure and the novel phase behavior of PP12V has implications in the design of LC polymers containing nanobuilding blocks toward constructing ordered nanostructures at different length scales. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 295–304     

Controlled sub‐10‐nanometer poly(N‐isopropyl‐acrylamide) layers grafted from silicon by atom transfer radical polymerization

Surface‐initiated atom transfer radical polymerization (SI‐ATRP) was used to graft poly(N‐isopropylacrylamide) (PNIPAM) brush layers with a controllable thickness in the 10‐nm range from silicon substrates. The rate of polymerization of N‐isopropylacrylamide was tuned by the [Cu(II)]₀/[Cu(I)]₀ ratio between the deactivating and activating species. The polymer layer thickness was characterized by atomic force microscopy (AFM) and ellipsometry. PNIPAM layers with a dry thickness between 5.5 and 16 nm were obtained. Time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) confirmed that the chemical structure is PNIPAM brushes. Analysis of the AFM data showed that our procedure leads to polymer grafts in the “mushroom‐to‐brush” transition regime.     

Theoretical implications of the elastic modulus discontinuity in rubber networks

The existence of a discontinuity in the modulus of rubber as the strain transitions from compression to extension is strongly suggested by multiple experiments. Classical rubber elasticity theories, however, do not admit such behavior. Here, we investigate a modification of the assumptions of classical elasticity theory to reconcile this discrepancy. We present an analysis of the consequences of assuming that chain forces are nonzero only for chain extension relative to the unstrained state, in contrast to the classical elasticity theory, which assumes that the chain force is directly proportional to the chain end‐to‐end distance (an entropic spring). Assuming an affine transformation of the network node coordinates, we derive two modulus discontinuity factors between compression and extension: D₁, based on the differing number of network chains being extended and D₂, based on the average differential chain extension. The discontinuities arise due to geometric effects, inherent in the affine transformation between compressive and extensive strains. We find that D₁, the ratio of the numbers of participating chains (compressive/extensive = 1.37), suffices to account for the experimentally observed modulus discontinuity in natural rubber of 1.34. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1795–1798, 2010     

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.     

Nanotribology of surface-grafted PEG layers in an aqueous environment

The lubrication properties of adsorbed poly(L-lysine)-graft-poly(ethylene glycol) in aqueous buffer solution were studied with the surface forces apparatus. In general, the polymer brushes revealed extremely low friction forces. Two distinct regimes could be identified. In response to lateral shear, the friction forces of intact polymer films at moderate loads were below the detection limit. At high loads, when the films were compressed to about 10% of the original equilibrium film thickness, the friction showed a reversible increase with load. Under certain conditions, film destruction was observed, immediately followed by a dramatic increase in the frictional force and an expansion of the adsorbed brush layer. By the addition of free polymer to the buffer solution, the resistance of the polymer brushes to abrasion was dramatically increased by readsorption of the polymer following friction-induced desorption. This self-healing capacity and the extremely low friction of the adsorbed copolymer films contribute to their excellent properties as lubricant additives for water-based lubrication under boundary conditions.