Determination of end-adsorbed polymer density profiles by neutron reflectometry

Illuminating the nanostructure of diffuse interfaces: Recent advances and future directions in reflectometry techniques

Diffuse soft matter interfaces take many forms, from end-tethered polymer brushes or adsorbed surfactants to self-assembled layers of lipids. These interfaces play crucial roles across a multitude of fields, including materials science, biophysics, and nanotechnology. Understanding the nanostructure and properties of these interfaces is fundamental for optimising their performance and designing novel functional materials. In recent years, reflectometry techniques, in particular neutron reflectometry, have emerged as powerful tools for elucidating the intricate nanostructure of soft matter interfaces with remarkable precision and depth. This review provides an overview of selected recent developments in reflectometry and their applications for illuminating the nanostructure of diffuse interfaces. We explore various principles and methods of neutron and X-ray reflectometry, as well as ellipsometry, and discuss advances in their experimental setups and data analysis approaches. Improvements to experimental neutron reflectometry methods have enabled greater time resolution in kinetic measurements and elucidation of diffuse structure under shear or confinement, while innovation in analysis protocols has significantly reduced data processing times, facilitated co-refinement of reflectometry data from multiple instruments and provided greater-than-ever confidence in proposed structural models. Furthermore, we highlight some significant research findings enabled by these techniques, revealing the organisation, dynamics, and interfacial phenomena at the nanoscale. We also discuss future directions and potential advancements in reflectometry techniques. By shedding light on the nanostructure of diffuse interfaces, reflectometry techniques enable the rational design and tailoring of interfaces with enhanced properties and functionalities.

Nanoscopic Interfacial Hydrogel Viscoelasticity Revealed from Comparison of Macroscopic and Microscopic Rheology

Deviations between macrorheological and particle-based microrheological measurements are often considered to be a nuisance and neglected. We study aqueous poly(ethylene oxide) (PEO) hydrogels for varying PEO concentrations and chain lengths that contain microscopic tracer particles and show that these deviations reveal the nanoscopic viscoelastic properties of the particle-hydrogel interface. Based on the transient Stokes equation, we first demonstrate that the deviations are not due to finite particle radius, compressibility, or surface-slip effects. Small-angle neutron scattering rules out hydrogel heterogeneities. Instead, we show that a generalized Stokes-Einstein relation, accounting for an interfacial shell around tracers with viscoelastic properties that deviate from bulk, consistently explains our macrorheological and microrheological measurements. The extracted shell diameter is comparable to the PEO end-to-end distance, indicating the importance of dangling chain ends. Our methodology reveals the nanoscopic interfacial rheology of hydrogels and is applicable to different kinds of viscoelastic fluids and particles.

Adsorption Characteristics and Mechanical Responses of Lubricants Containing Polymer Additives under Fluid Lubrication with a Narrow Gap

The adsorption behavior of poly(methyl acrylate) (PMA)-based polymer additives and their mechanical response under fluid lubrication in narrow gaps were investigated by using neutron reflectometry, microchannel devices, and the narrow gap viscometer. The surface adsorption layer formed by the polymer additive in a stationary field that was investigated by neutron reflectometry was only about 3 nm thick. On the other hand, when the sample oil containing the polymer additive was flowed into the microchannel device with channels about 500 nm deep, the adsorption layer grew over a long period of time and eventually formed a layer that appeared to be more than 100 nm thick. The mechanical response was measured during one-directional rotation with a constant gap length by using the narrow gap viscometer. The results showed that the effective viscosity increased in the low shear rate range. The same behavior was also observed in the reciprocating rotational tests, where the mechanical response showed a distinctive distortion only when the shear rate was low near 0 rpm. The results of the neutron reflectometer, incorporating the narrow gap viscometer, showed no effect of the rotational speed with regard to the structure of the homogeneous layer over a large area. However, the discrepancy between the reflectivity profile and the fitting curve became progressively more pronounced with time, confirming the formation of inhomogeneous structures with time. It is finally suggested that the inhomogeneous structure is due to the formation of local aggregates by PMA molecules, and it acts as flow resistance only in the low shear rate, resulting in an increase in effective viscosity.

Predicting Polymer Brush Behavior in Solvents Using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is utilized to study the effects of temperature on polymer brushes. The brushes are represented by a discrete energy spectrum, and energy degeneracies obtained through the replica-exchange Wang-Landau algorithm. The SEAQT equation of motion is applied to the density of states to establish a unique kinetic path from an initial thermodynamic state to a stable equilibrium state. The kinetic path describes the brush's evolution in state space, as it interacts with a thermal reservoir. The predicted occupation probabilities along the kinetic path are used to determine the expected thermodynamic and structural properties. The polymer density profile of a polystyrene brush in cyclohexane solvent is predicted using the equation of motion, and it agrees qualitatively with the experimental density profiles. The Flory-Huggins parameter chosen to describe brush-solvent interactions affects the solvent distribution in the brush but has a minimal impact on the polymer density profile. Three types of nonequilibrium kinetic paths with differing amounts of entropy production are considered: a heating path, a cooling path, and a heating-cooling path. Properties such as tortuosity, radius of gyration, brush density, solvent density, and brush chain conformations are calculated for each path.

Shaping the Structure and Response of Surface-Grafted Polymer Brushes via the Molecular Weight Distribution

Breadth in the molecular weight distribution is an inherent feature of synthetic polymer systems. While in the past this was typically considered as an unavoidable consequence of polymer synthesis, multiple recent studies have shown that tailoring the molecular weight distribution can alter the properties of polymer brushes grafted to surfaces. In this Perspective, we describe recent advances in synthetic methods to control the molecular weight distribution of surface-grafted polymers and highlight studies that reveal how shaping this distribution can generate novel or enhanced functionality in these materials.

Quantifying the robustness of the neutron reflectometry technique for structural characterization of polymer brushes

Neutron reflectometry is the foremost technique for in situ determination of the volume fraction profiles of polymer brushes at planar interfaces. However, the subtle features in the reflectometry data produced by these diffuse interfaces challenge data interpretation. Historically, data analyses have used least-squares approaches that do not adequately quantify the uncertainty of the modeled profile and ignore the possibility of other structures that also match the collected data (multimodality). Here, a Bayesian statistical approach is used that permits the structural uncertainty and multimodality to be quantified for polymer brush systems. A free-form model is used to describe the volume fraction profile, minimizing assumptions regarding brush structure, while only allowing physically reasonable profiles to be produced. The model allows the total volume of polymer and the profile monotonicity to be constrained. The rigor of the approach is demonstrated via a round-trip analysis of a simulated system, before it is applied to real data examining the well characterized collapse of a thermoresponsive brush. It is shown that, while failure to constrain the interfacial volume and consider multimodality may result in erroneous structures being derived, carefully constraining the model allows for robust determination of polymer brush compositional profiles. This work highlights that an appropriate combination of flexibility and constraint must be used with polymer brush systems to ensure the veracity of the analysis. The code used in this analysis is provided, enabling the reproduction of the results and the application of the method to similar problems.

How Dissociation of Carboxylic Acid Groups in a Weak Polyelectrolyte Brush Depend on Their Distance from the Substrate

A weak polyelectrolyte brush is composed of a layer of polyacids or polybases grafted by one end of their chains to a substrate surface. For such brush layers immersed in an aqueous solution, the dissociation behavior of the acidic or basic groups and the structural and physical properties of the brush layer will thus be strongly dependent on the environmental conditions. For a polyacid brush layer consisting of, e.g., poly(acrylic acid), this means that the chains in the brush layer will be charged at high pH and uncharged at low pH. However, theoretical scaling laws not only foresee the structural changes occurring in response to the pH-induced dissociation behavior but also how the dissociation behavior of the brush layer depends on the ionic strength of the aqueous solution and the density of acidic groups within the brush layer. We have herein employed spectroscopic ellipsometry and a quartz crystal microbalance with dissipation monitoring (QCM-D) to experimentally evaluate the theoretically predicted dissociation and structural behavior of PAA brushes. Spectroscopic ellipsometry allows us to study the brush thickness as a function of pH and ionic strength, while QCM-D gives us an opportunity to investigate the swelling behavior of PAA brushes at various penetration depths of propagating acoustic waves. Our studies show that the dissociation degree of the carboxylic acid groups in a PAA brush increases with increasing distance from the substrate. Moreover, the ionic strength enhances carboxylic acid dissociation, such that a higher ionic strength leads to a narrower distribution and higher average dissociation degree. In conclusion, our results provide an experimental verification of the theoretically predicted gradient in the degree of dissociation of the acid groups in weak polyacid brush layers and shows that at a pH value equal to approximately the average pK_a value of the brush, the state of the acid groups varies from being almost uncharged to almost fully dissociated depending on the ionic strength and vertical position in the brush.

Polymer on Top: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting

Well-defined polymer strands covalently tethered onto solid substrates determine the properties of the resulting functional interface. Herein, the current approaches to determine quantitative grafting densities are assessed. Based on a brief introduction into the key theories describing polymer brush regimes, a user's guide is provided to estimating maximum chain coverage and-importantly-examine the most frequently employed approaches for determining grafting densities, i.e., dry thickness measurements, gravimetric assessment, and swelling experiments. An estimation of the reliability of these determination methods is provided via carefully evaluating their assumptions and assessing the stability of the underpinning equations. A practical access guide for comparatively and quantitatively evaluating the reliability of a given approach is thus provided, enabling the field to critically judge experimentally determined grafting densities and to avoid the reporting of grafting densities that fall outside the physically realistic parameter space. The assessment is concluded with a perspective on the development of advanced approaches for determination of grafting density, in particular, on single-chain methodologies.

Structure and elasticity of bush and brush-like models of the endothelial glycocalyx

The endothelial glycocalyx (EG), a sugar-rich layer that lines the luminal surface of blood vessels, is an important constituent of the vascular system. Although the chemical composition of the EG is fairly well known, there is no consensus regarding its ultrastructure. While previous experiments probed the properties of the layer at the continuum level, they did not provide sufficient insight into its molecular organisation. In this work, we investigate the EG mechanics using two simple brush and bush-like simulation models, and use these models to describe its molecular structure and elastic response to indentation. We analyse the relationship between the mechanical properties of the EG layer and several molecular parameters, including the filament bending rigidity, grafting density, and the type of ultrastructure . We show that variations in the glycan density determine the elasticity of the EG for small deformations, and that the normal stress may be effectively dampened by the EG layer, preventing the stress from being transferred to the cell membrane. Furthermore, our bush-like model allows us to evaluate the forces and energies required to overcome the mechanical resistance of the EG.

Scaling Behavior and Segment Concentration Profile of Densely Grafted Polymer Brushes Swollen in Vapor

The scaling of the thickness, hs, of a densely grafted polymer brush of chain length N and grafting density σ swollen in vapor agrees quantitatively with the scaling reported by Kuhl et al. for densely grafted brushes swollen in liquid. Deep in the brush, next to the substrate, the shape of the segment concentration profile is the same whether the brush is swollen by liquid or by vapor. Differences in the segment concentration profile are manifested primarily in the swollen brush interface with the surrounding fluid. The interface of the polymer brush swollen in vapor is much more abrupt than that of the same brush swollen in liquid. This has implications for the compressibility of the swollen brush surface and for fluctuations at that surface.

Polymer brush-based optical device with multiple responsivities

Poly(N-isopropylacrylamide) brush-based optical materials were fabricated, and the tunability of their optical properties characterized.

Morphological control of grafted polymer films via attraction to small nanoparticle inclusions

Control of the morphologies of polymer films and layers by addition of nanosize particles is a novel technique for design of nanomaterials and is also at the core of some important biological processes. In order to facilitate the analysis of experimental data and enable predictive engineering of such systems, solid theoretical understanding is necessary. We study theoretically and computationally the behavior of plane-grafted polymer layers (brushes) in athermal solvent, decorated with small nanoparticle inclusions, using mean field theory and coarse-grained simulations. We show that the morphology of such layers is very sensitive to the interaction between the polymers and the nanoparticles and to the nanoparticle density. In particular, the mean field model shows that for a certain range of parameters, the nanoparticles induce a sharp transition in the layer height, accompanied by a sharp increase in the number of adsorbed nanoparticles. At other parameter values, the layer height depends smoothly on the nanoparticle concentration. Predictions of the theoretical model are verified by Langevin dynamics simulations. The results of the paper are in qualitative agreement with experiments on in vitro models of biological transport and suggest strategies for morphological control of nanocomposite materials.

Stimuli-Responsive Polymer Brushes for Flow Control through Nanopores

Responsive polymers attached to the inside of nano/micro-pores have attracted great interest owing to the prospect of designing flow-control devices and signal responsive delivery systems. An intriguing possibility involves functionalizing nanoporous materials with smart polymers to modulate biomolecular transport in response to pH, temperature, ionic concentration, light or electric field. These efforts open up avenues to develop smart medical devices that respond to specific physiological conditions. In this work, an overview of nanoporous materials functionalized with responsive polymers is given. Various examples of pH, temperature and solvent responsive polymers are discussed. A theoretical treatment that accounts for polymer conformational change in response to a stimulus and the associated flow-control effect is presented.

Shear-induced metastable states of end-grafted polystyrene

The in situ molecular scale response of end-grafted polystyrene to shear against a deuterated polystyrene melt was investigated with neutron reflectometry. The derived grafted polystyrene density profiles showed that the grafted polystyrene was retained on the quartz wafer during the measurements. The profiles suggested that the end-grafted polystyrene response to shear results in a series of metastable states, rather than equilibrium states assumed in the current theory. Except for some possible extension and/or contraction of the grafted polystyrene with shear, there was no obvious correlation between the grafted polymer structure and the shear thinning behavior observed in these samples.

Voltage-induced swelling and deswelling of weak polybase brushes

We have investigated a novel method of remotely switching the conformation of a weak polybase brush using an applied voltage. Surface-grafted polyelectrolyte brushes exhibit rich responsive behavior and show great promise as "smart surfaces", but existing switching methods involve physically or chemically changing the solution in contact with the brush. In this study, high grafting density poly(2-(dimethylamino)ethyl methacrylate) (PDMAEMA) brushes were grown from silicon surfaces using atom transfer radical polymerization. Optical ellipsometry and neutron reflectivity were used to measure changes in the profiles of the brushes in response to DC voltages applied between the brush substrate and a parallel electrode some distance away in the surrounding liquid (water or D(2)O). Positive voltages were shown to cause swelling, while negative voltages in some cases caused deswelling. Neutron reflectometry experiments were carried out on the INTER reflectometer (ISIS, Rutherford Appleton Laboratory, UK) allowing time-resolved measurements of polymer brush structure. The PDMAEMA brushes were shown to have a polymer volume fraction profile described by a Gaussian-terminated parabola both in the equilibrium and in the partially swollen states. At very high positive voltages (in this study, positive bias means positive voltage to the brush-bearing substrate), the brush chains were shown to be stretched to an extent comparable to their contour length, before being physically removed from the interface. Voltage-induced swelling was shown to exhibit a wider range of brush swelling states in comparison to pH switching, with the additional advantages that the stimulus is remotely controlled and may be fully automated.

Reflectivity Studies on Adsorbed Block Copolymers Under Shear

We report neutron reflectivity data on (poly)styrene-(poly)ethylene oxide (PS-PEO) diblock copolymers adsorbed onto quartz from the selective solvent deuterated cyclohexane (a non-solvent for PEO and a poor solvent for PS). The PEO "anchor block" adsorbs strongly to form a thin layer on the quartz substrate, while the PS chains dangle into the solvent. We find that under static conditions the density profile of the PS block in a poor solvent can be well described by a Schultz function which is indicative of a polymer "mushroom." Furthermore, we have studied the same system under shear at shear rates from 0-400s-l. We find that there is a dramatic increase in the thickness of the PS layer under shear in cyclohexane and that the relaxation time from the shear-on profile back to the static profile is on the order of several days.

Chemical grafting of silane end-functionalized polymer on silicon surfaces

X-ray and neutron reflectivity was used to determine the kinetics of adsorption and characterize the concentration profile of a low molecular weight trichlorosilane endfunctionalized polystyrene adsorbed onto polished silicon wafers. Higher adsorbed amounts were obtained from a cyclohexane solution of the polymer rather than toluene, with kinetics that followed a stretched exponential behavior. For moderately high grafting densities the polymer concentration profile in deuterated toluene (a good solvent) was best modelled using a small tailed parabola. In deuterated cyclohexane (a poor solvent) the brush profile steepened but was substantially smoother than a step, while in D20 (a non-solvent) it became step-like.

The Los Alamos Neutron Science Center neutron rheometer in the cone and plate geometry to examine tethered polymers/polymer melt interfaces via neutron reflectivity

Although several other neutron rheometers have been built to study soft matter under nonequilibrium conditions, none of them have the ability to measure the structure and behavior of the polymeric interfacial regions in highly viscous polymer melts which require high torques/high strain rates and high temperatures. A neutron rheometer in the cone and plate geometry has been constructed at the Los Alamos Neutron Science Center to rectify this lack of experimental instrumentation. It is also the first-of-its-kind to perform neutron reflectivity studies concurrently with rheological measurements. The details of both the development and testing of the Los Alamos Neutron Science Center neutron rheometer in the cone and plate configuration are described. Proof of principle neutron reflectivity results of end-grafted polystyrene against an identical melt under shear are presented, showing qualitatively that the structural attributes of the end-grafted polymer change when exposed to shear.

Polymer brushes on periodically nanopatterned surfaces

Structural properties of polymer brushes tethered on a periodically nanopatterned substrate are investigated by computer simulations. The substrate consists of an alternating succession of two different types of equal-width parallel stripes, and the polymers are end-tethered selectively on every second stripe. Three distinct morphologies of the nanopatterned brush have been identified, and their range of stability has been determined in terms of a single universal parameter that combines the grafting density, the polymer length, and the stripe width. We propose scaling relations for the average brush height and for the architectural properties of the outer surface of the nanopatterned brush under good solvent conditions. Our analysis provides guidelines for fabricating well-defined and tunable nanopatterned polymeric films.

Surface force confinement cell for neutron reflectometry studies of complex fluids under nanoconfinement

In this paper, we describe the construction of a new neutron surface force confinement cell (NSFCC). The NSFCC is equipped with hydraulically powered in situ, temporally stable, force control system for simultaneous neutron reflectometry studies of nanoconfined complex fluid systems. Test measurements with deuterated toluene confined between two opposing diblock copolymer (polystyrene+poly 2-vinylpyridine) coated quartz substrates demonstrate the capabilities of the NSFCC. With increasing hydraulically applied force, a series of well-defined decreasing separations were observed from neutron reflectivity measurements. No noticeable changes in the hydraulic pressure used for controlling the surface separation were observed during the measurements, demonstrating the high stability of the apparatus. This newly designed NSFCC introduces a higher level of control for studies of confinement and consequent finite size effects on nanoscale structure in a variety of complex fluid and soft condensed matter systems.

Viscoelastic response and profile of adsorbed molecules probed by quartz crystal microbalance

The acoustic responses of molecular films with continuous viscoelastic profiles adsorbed on solid-liquid interfaces probed by quartz crystal microbalance (QCM) are analyzed using a continuum mechanics model. The numerically calculated results show that the shift of resonant frequency and the change of dissipation factor of a QCM are determined mostly by the change of viscoelastic profile of the layers in solution adjacent to the quartz-solution interface due to the adsorbed molecular film. For films with the same amount of absorbed mass, the changes in resonant frequency and the dissipation factor vary approximately linearly with the width of the film-solution interface in the profiles. Other viscoelastic properties of the adsorbed films are also affected by the profiles.

Polymer brushes in solvents of variable quality: Molecular dynamics simulations using explicit solvent

The structure and thermodynamic properties of a system of end-grafted flexible polymer chains grafted to a flat substrate and exposed to a solvent of variable quality are studied by molecular dynamics methods. The macromolecules are described by a coarse-grained bead-spring model, and the solvent molecules by pointlike particles, assuming Lennard-Jones-type interactions between pairs of monomers (epsilon(pp)), solvent molecules (epsilon(ss)), and solvent monomer (epsilon(ps)), respectively. Varying the grafting density sigma(g) and some of these energy parameters, we obtain density profiles of solvent particles and monomers, study structural properties of the chain (gyration radius components, bond orientational parameters, etc.), and examine also the profile of the lateral pressure P( parallel)(z), keeping in the simulation the normal pressure P( perpendicular) constant. From these data, the reduction of the surface tension between solvent and wall as a function of the grafting density of the brush has been obtained. Further results include the stretching force on the monomer adjacent to the grafting site and its variation with solvent quality and grafting density, and dynamic characteristics such as mobility profiles and chain relaxation times. Possible phase transitions (vertical phase separation of the solvent versus lateral segregation of the polymers into "clusters," etc.) are discussed, and a comparison to previous work using implicit solvent models is made. The variation of the brush height and the interfacial width of the transition zone between the pure solvent and the brush agrees qualitatively very well with corresponding experiments.