Friction between ring polymer brushes

Molecular conformations of dumbbell-shaped polymers in good solvent

We study conformational properties of diluted dumbbell polymers composed of two rings attached to both ends of a linear spacer segment. Our investigation involves analytical methods of field theory and bead-spring coarse-grained molecular dynamics simulations. We focus on the influence of the relative length of the spacer segment to the length of side rings on the shape and the relative size of dumbbells as compared to linear polymers of equal mass. We find that dumbbells with short spacers exhibit a significantly more compact structure than linear polymers. Conversely, as the spacer length increases, the influence of the side rings on the size of the dumbbells becomes negligible. Consequently, dumbbell molecules with long spacers attain a size comparable to corresponding linear chains. Our analytical theory accurately predicts a quantitative conformational crossover between the behaviors of short-spacer and long-spacer dumbbells, which is further confirmed by our numerical simulations.

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

Compression and interpenetration of adsorption-active brushes

Compression and interpenetration of two opposing polymer brushes formed by end-grafted adsorption-active chains are studied by the numerical self-consistent field approach and by analytical theory. For sufficiently strong polymer-surface attraction, a fraction of chains in the adsorption-active brush condenses into a near-surface layer, while the remaining ones form the outer brush with reduced effective grafting density. Analysis shows that the normal pressure in adsorption-active brushes can be understood in terms of the effective grafting density concept although the pressure at small separations is affected by the presence of the dense adsorbed phase. We propose a simple theory modification that accounts for this effect. We also formulate a procedure for extracting the value of the effective grafting density directly from the pressure vs separation curves by inverting the equation of state. In contrast to the normal pressure, the interpenetration of the two opposing adsorption-active brushes demonstrates a much more intricate behavior. At weak to moderate compressions, the effective grafting density concept works well but fails spectacularly at small interbrush separations. We identify two interpenetration regimes for adsorption-active brushes: (i) at separations larger than the ideal Gaussian coil size N^1/2, the overlap of the two brushes is concentrated in the mid-plane region, in the same way as in brushes grafted onto non-attractive surfaces; (ii) at separations less than N^1/2, the brush overlap is strongly enhanced in the wall regions where the attractive interaction plays an important role both in generating the dense layer for the "proper" brush and in attracting the "foreign" chains.

Conformational properties of hybrid star-shaped polymers comprised of linear and ring arms

We study the influence of arm architecture on the conformational properties of hybrid star-shaped macromolecules called rosette polymers containing linear and ring grafts connected to a central branching point in a good solvent regime. We utilize analytical methods and molecular dynamics simulations to determine the estimates for the relative size ratios of these polymers with respect to linear chains and starlike polymers composed of the same number of solely linear arms and equal molecular weights. The results of numerical simulations corroborate our theoretical prediction that rosette polymers undergo conformational compactification with increasing functionality of grafted rings. Our results quantitatively describe the impact of the complex architecture of the molecules with excluded volume on their effective size measures.

Gold nanoparticles endowed with low-temperature colloidal stability by cyclic polyethylene glycol in ethanol

The colloidal stability of metal nanoparticles is tremendously dependent on the thermal behavior of polymer brushes. Neat polyethylene glycol (PEG) presents an unconventional upper critical solution temperature in ethanol, where phase segregation and crystallization coexist. This thermal behavior translated to a PEG brush has serious consequences on the colloidal stability in ethanol of gold nanoparticles (AuNPs) modified with PEG brushes upon cooling. We observed that AuNPs (13 nm diameter) stabilized with conventional linear PEG brushes (M_n = 6 and 11 kg mol^-1) in ethanol suffer from reversible phase separation upon a temperature drop over the course of a few hours. However, the use of a polymer brush with cyclic topology as a stabilizer prevents sedimentation, ensuring the colloidal stability in ethanol at -25 °C for, at least, four months. We postulate that temperature-driven collapse of chain brushes promotes the interpenetration of linear chains, causing progressive AuNP sedimentation, a process that is unfavorable for cyclic polymer brushes whose topology prevents chain interpenetration. This study reinforces the notion about the importance of polymer topology on the colloidal stability of AuNPs.

Thermoresponsive Nanoparticles with Cyclic-Polymer-Grafted Shells Are More Stable than with Linear-Polymer-Grafted Shells: Effect of Polymer Topology, Molecular Weight, and Core Size

Polymer brush-grafted superparamagnetic iron oxide nanoparticles can change their aggregation state in response to temperature and are potential smart materials for many applications. Recently, the shell morphology imposed by grafting to a nanoparticle core was shown to strongly influence the thermoresponsiveness through a coupling of intrashell solubility transitions and nanoparticle aggregation. We investigate how a change from linear to cyclic polymer topology affects the thermoresponsiveness of poly(2-isopropyl-2-oxazoline) brush-grafted superparamagnetic iron oxide nanoparticles. Linear and cyclic polymers with three different molecular weights (7, 18, and 24.5 kg mol-1) on two different core sizes (3.7 and 9.2 nm) and as free polymer were investigated. We observed the critical flocculation temperature (CFT) during temperature cycling dynamic light scattering experiments, the critical solution temperature (CST), and the transition enthalpy per monomer during differential scanning calorimetry measurements. When all conditions are identical, cyclic polymers increase the colloidal stability and the critical flocculation temperature compared to their linear counterparts. Furthermore, the cyclic polymer shows only one uniform transition, while we observe multiple transitions for the linear polymer shells. We link the single transition and higher colloidal stability to the absence in cyclic PiPrOx shells of a dilute outer part where the particle shells can interdigitate.

Surface science of cosmetic substrates, cleansing actives and formulations

The development of shampoo and cleansing formulations in cosmetics is at a crossroads due to consumer demands for better performing, more natural products and also the strong commitment of cosmetic companies to improve the sustainability of cosmetic products. In order to go beyond traditional formulations, it is of great importance to clearly establish the science behind cleansing technologies and appreciate the specificity of cleansing biological surfaces such as hair and skin. In this review, we present recent advances in our knowledge of the physicochemical properties of the hair surface from both an experimental and a theoretical point of view. We discuss the opportunities and challenges that newer, sustainable formulations bring compared to petroleum-based ingredients. The inevitable evolution towards more bio-based, eco-friendly ingredients and sustainable formulations requires a complete rethink of many well-known physicochemical principles. The pivotal role of digital sciences and modelling in the understanding and conception of new ingredients and formulations is discussed. We describe recent numerical approaches that take into account the specificities of the hair surface in terms of structuration, different methods that study the adsorption of formulation ingredients and finally the success of new data-driven approaches. We conclude with practical examples on current formulation efforts incorporating bio-surfactants, controlling foaming and searching for new rheological properties.

Topological Polymer Chemistry Enters Materials Science: Expanding the Applicability of Cyclic Polymers

Polymer-topology effects can alter technologically relevant properties when cyclic macromolecules are applied within diverse materials formulations. These include coatings, polymer networks, or nanostructures for delivering therapeutics. While substituting linear building blocks with cyclic analogues in commonly studied materials is itself of fundamental interest, an even more fascinating observation has been that the introduction of physical or chemical boundaries (e.g., a grafting surface or cross-links) can amplify the topology-related effects observed when employing cyclic polymer-based precursors for assembling multidimensional objects. Hence, the application of cyclic polymers has enabled the fabrication of coatings with enhanced biorepellency and superior lubricity, broadened the tuning potential for mechanical properties of polymer networks, increased the thermodynamic stability, and altered the capability of loading and releasing drugs within polymeric micelles.

Bioinert and Lubricious Surfaces by Macromolecular Design

The modification of a variety of biomaterials and medical devices often encompasses the generation of biopassive and lubricious layers on their exposed surfaces. This is valid when the synthetic supports are required to integrate within physiological media without altering their interfacial composition and when the minimization of shear stress prevents or reduces damage to the surrounding environment. In many of these cases, hydrophilic polymer brushes assembled from surface-interacting polymer adsorbates or directly grown by surface-initiated polymerizations (SIP) are chosen. Although growing efforts by polymer chemists have been focusing on varying the composition of polymer brushes in order to attain increasingly bioinert and lubricious surfaces, the precise modulation of polymer architecture has simultaneously enabled us to substantially broaden the tuning potential for the above-mentioned properties. This feature article concentrates on reviewing this latter strategy, comparatively analyzing how polymer brush parameters such as molecular weight and grafting density, the application of block copolymers, the introduction of branching and cross-links, or the variation of polymer topology beyond the simple, linear chains determine highly technologically relevant properties, such as biopassivity and lubrication.

Surface Density Variation within Cyclic Polymer Brushes Reveals Topology Effects on Their Nanotribological and Biopassive Properties

While topology effects by cyclic polymers in solution and melts are well-known, their translation into the interfacial properties of polymer "brushes" provides new opportunities to impart enhanced surface lubricity and biopassivity to inorganic surfaces, above and beyond that expected for linear analogues of identical composition. The impact of polymer topology on the nanotribological and protein-resistance properties of polymer brushes is revealed by studying linear and cyclic poly(2-ethyl-2-oxazoline) (PEOXA) grafts presenting a broad range of surface densities and while shearing them alternatively against an identical brush or a bare inorganic surface. The intramolecular constraints introduced by the cyclization provide a valuable increment in both steric stabilization and load-bearing capacity for cyclic brushes. Moreover, the intrinsic absence of chain ends within cyclic adsorbates hinders interpenetration between opposing brushes, as they are slid over each other, leading to a reduction in the friction coefficient (μ) at higher pressures, a phenomenon not observed for linear grafts. The application of cyclic polymers for the modification of inorganic surfaces generates films that outperform both the nanotribological and biopassive properties of linear brushes, significantly expanding the design possibilities for synthetic biointerfaces.

Lubrication in polymer-brush bilayers in the weak interpenetration regime: Molecular dynamics simulations and scaling theories

We conduct molecular dynamics (MD) simulations and develop scaling laws to quantify the lubrication behavior of weakly interpenetrated polymer brush bilayers in the presence of an external shear force. The weakly interpenetrated regime is characterized by 1<d_{g}/d_{0}<2, where d_{g} is the gap between the opposing surfaces (where the brushes are grafted) and d_{0} is the unperturbed brush height. MD simulations predict that in the shear thinning regime, characterized by a larger shear force or a large Weissenberg number (W), R_{g}^{2}∼W^{0.19} and η∼W^{-0.38}, where R_{g} is the chain extension in the direction of the shear and η is the viscosity. These scaling behaviors, which are distinctly different from that witnessed in strongly compressed regime (for such a regime, characterized by d_{g}/d_{0}<1, R_{g}^{2}∼W^{0.53}, and η∼W^{-0.46}), match excellently with those predicted by our scaling theory.

Lattice self-consistent field calculations of ring polymer brushes

We reported the first systematic study using lattice self-consistent field (LSCF) calculations of ring homopolymer brushes grafted onto a flat and homogeneous surface and immersed in an explicit and athermal solvent, which are either uncompressed, compressed by a flat and impenetrable surface, or compressed by an identical brush. Our results clearly show that ring brushes are slightly less stretched than, thus nearly but not completely identical to, the "equivalent" linear brushes having half the chain length and double the grafting density. Our LSCF results are consistent with the molecular simulation results reported in the literature (Reith et al., Europhys. Lett., 2011, 95, 28003; Erbas and Paturej, Soft Matter, 2015, 11, 3139), except that Erbas and Paturej reported that the normal pressure of two opposing ring brushes is only half of the "equivalent" linear brushes at melt density.

Polyelectrolyte brush bilayers in weak interpenetration regime: Scaling theory and molecular dynamics simulations

We employ molecular dynamics (MD) simulations and develop scaling theories to quantify the equilibrium behavior of polyelectrolyte (PE) brush bilayers (BBLs) in the weakly interpenetrated regime, which is characterized by d_{0}<d_{g}<2d_{0}, where d_{g} is the gap between the opposing plates where the PE brushes are grafted and d_{0} is the unperturbed height of a PE brush grafted at a single plate. Scaling predictions establish that, for the weakly interpenetrated osmotic PE BBLs δ∼N^{1/2}(2-d_{g}/d_{0})^{1/2} (where δ is the interpenetration length and N is the number of Kuhn segments in PE brush). MD simulations excellently recover this dependence of δ on N and the extent of interpenetration (quantified by d_{g}/d_{0}). These predictions, unlike the existing studies, establish a finite interpenetration for all values of d_{g}/d_{0} as long as d_{g}<2d_{0}. Finally, we quantify the monomer and counterion concentration distributions and point out that these two distributions may quantitatively deviate from each other at locations very close to the channel centerline, where the interpenetration-induced monomer concentration can be significantly low.

Design and characterization of ultrastable, biopassive and lubricious cyclic poly(2-alkyl-2-oxazoline) brushes

Bilayer films featuring cyclic, poly(2-alkyl-2-oxazoline) brush interfaces display excellent biopassivity, lubrication and long-term stability in chemically harsh aqueous environments.

Attraction between Opposing Planar Dipolar Polymer Brushes

We use a field theory approach to study the effects of permanent dipoles on interpenetration and free energy changes as a function of distance between two identical planar polymer brushes. Melts (i.e., solvent-free) and solvated brushes made up of polymers grafted on nonadsorbing substrates are studied. In particular, the weak coupling limit of the dipolar interactions is considered, which leads to concentration-dependent pairwise interactions, and the effects of orientational order are neglected. It is predicted that a gradual increase in the dipole moment of the polymer segments can lead to attractive interactions between the brushes at intermediate separation distances. Because classical theory of polymer brushes based on the strong stretching limit (SSL) and the standard self-consistent field theory (SCFT) simulations using the Flory's χ parameter always predicts repulsive interactions at all separations, our work highlights the importance of dipolar interactions in tailoring and accurately predicting forces between polar polymeric interfaces in contact with each other.

Compression of polymer brushes in the weak interpenetration regime: scaling theory and molecular dynamics simulations

We employ scaling theory and Molecular Dynamics (MD) simulations to probe the compression of the semi-dilute polymer brush bilayers (BBLs) in the weak interpenetration (IP) regime. Such a regime is characterized by two layers of interacting polymer brushes grafted on opposing planar surfaces having a separation d_g, such that d₀ < d_g < 2d₀, with d₀ being the unperturbed brush height. Currently, scaling theories are known for polymer BBLs with a much larger degree of IP (i.e., d_g < d₀) - in such regimes, the brush height can be quantified by the corresponding IP length δ. On the other hand, we show that in the weak IP regime, the brush height is not solely dictated by δ. We develop new scaling theories to show that δ in this weak IP regime is different from that in the strong IP regime. Secondly, we establish that the compressed brush height in this weakly IP regime can be described as d ∼ N^χ with χ < 1 and varying monotonically with d_g/d₀. MD simulations are carried out to quantify δ and χ and the results match excellently with our new scaling theory predictions. Finally, we establish that our scaling theory can reasonably predict the experimentally witnessed variation of the interaction energy dictating the compressive force between the interpenetrating brushes in this weakly IP regime.

Influence of Chain Stiffness, Grafting Density and Normal Load on the Tribological and Structural Behavior of Polymer Brushes: A Nonequilibrium-Molecular-Dynamics Study

We have performed coarse-grained molecular-dynamics simulations on both flexible and semiflexible multi-bead-spring model polymer brushes in the presence of explicit solvent particles, to explore their tribological and structural behaviors. The effect of stiffness and tethering density on equilibrium-brush height is seen to be well reproduced within a Flory-type theory. After discussing the equilibrium behavior of the model brushes, we first study the shearing behavior of flexible chains at different grafting densities covering brush and mushroom regimes. Next, we focus on the effect of chain stiffness on the tribological behavior of polymer brushes. The tribological properties are interpreted by means of the simultaneously recorded density profiles. We find that the friction coefficient decreases with increasing persistence length, both in velocity and separation-dependency studies, over the stiffness range explored in this work.

Polymer-brush lubrication: a review of recent theoretical advances

This review compiles recent theoretical advances to describe compressive and shear forces of polymer-brush bilayers, which consist of two opposing brushes in contact. Such model systems for polymer-brush lubrication are frequently used as a benchmark to gain insight into biological problems, e.g., synovial joint lubrication. Based on scaling theory, I derive conformational and collective properties of polymer-brush bilayers in equilibrium and out-of-equilibrium situations, such as shear forces in the linear and nonlinear response regimes of stationary shear and under non-stationary shear. Furthermore, I discuss the influence of macromolecular inclusions and electrostatic interactions on polymer-brush lubrication. Comparisons to alternative analytical approaches, experiments and numerical results are performed. Special emphasis is given to methods for simulating polymer-brush bilayers using molecular dynamics simulations.