Kinetically Controlled Site-Specific Self-assembly of Hairy Colloids.

The solvophobicity-driven directional self-assembly of polymer-coated gold nanorods is a well-established phenomenon. Yet, the kinetics of this process, the origin of site-selectivity in the self-assembly, and the interplay of (attractive) solvophobic brush interactions and (repulsive) electrostatic forces are not fully understood. Herein, we use a combination of time-resolved (vis/NIR) extinction spectroscopy and finite-difference time-domain (FDTD) simulations to determine conversion profiles for the assembly of gold nanorods with polystyrene shells of distinct thicknesses into their (tip-to-tip) self-assembled structures. In particular, we demonstrate that the assembly process is highly protracted compared with diffusion-controlled rates, and we find that the assembly rate varies for different thickness values of the polymer shell. Our findings were rationalized using coarse-grained molecular dynamics simulations, which also corroborated the tip-to-tip preference in the self-assembly process, albeit with a uniform polymer coating. Utilizing the knowledge of quantified conversion rates for distinct colloidal species, we designed coassembling systems with different brush thicknesses, featuring "narcissistic" self-sorting behavior. This provides new perspectives for high-level supracolloidal self-assembly.

A nanofluidic system based on cylindrical polymer brushes: how to control the size of nanodroplets.

In molecular dynamics simulations we investigate the self-organized formation of droplets from a continuous flow of incoming nanoparticles. This transformation is facilitated by a cylindrical channel that is decorated with a polymer brush in a marginally poor solvent. We analyze droplet formation and propagation by means of simple scaling arguments which are tested in the simulations. Polymer brushes in marginally poor solvents serve as a pressure feedback system, exhibit a collapse transition under the moderate pressure of the incident flow, without the need for additional external stimuli, and finally close spontaneously after droplet passage. Our results qualitatively demonstrate the control of polymer brushes over continuous fluids and droplet formation, and its effectiveness as a means of fluid control can be used to design nanofluidic rectification devices that operate reliably under moderate pressure.

Theoretical analysis of the elastic free energy contributions to polymer brushes in poor solvent: A refined mean-field theory.

We consider polymer brushes in poor solvent that are grafted onto planar substrates and onto the internal and external surfaces of a cylinder using molecular dynamics simulation, self-consistent field (SCF), and mean-field theory. We derive a unified expression for the mean field free energy for the three geometrical classes. While for low grafting densities, the effect of chain elasticity can be neglected in poor solvent conditions, it becomes relevant at higher grafting densities and, in particular, for concave geometries. Based on the analysis of the end monomer distribution, we introduce an analytical term that describes the elasticity as a function of grafting density. The accuracy of the model is validated with molecular dynamics simulations as well as SCF computations and shown to yield precise values for the layer thickness over a wide range of system parameters. We further apply this model to analyze the gating behavior of switchable brushes inside nanochannels.

Chemotaxis of Cargo-Carrying Self-Propelled Particles.

Active particles with their characteristic feature of self-propulsion are regarded as the simplest models for motility in living systems. The accumulation of active particles in low activity regions has led to the general belief that chemotaxis requires additional features and at least a minimal ability to process information and to control motion. We show that self-propelled particles display chemotaxis and move into regions of higher activity if the particles perform work on passive objects, or cargo, to which they are bound. The origin of this cooperative chemotaxis is the exploration of the activity gradient by the active particle when bound to a load, resulting in an average excess force on the load in the direction of higher activity. Using a new theoretical model, we capture the most relevant features of these active-passive dimers, and in particular we predict the crossover between antichemotactic and chemotactic behavior. Moreover, we show that merely connecting active particles to chains is sufficient to obtain the crossover from antichemotaxis to chemotaxis with increasing chain length. Such an active complex is capable of moving up a gradient of activity such as provided by a gradient of fuel and to accumulate where the fuel concentration is at its maximum. The observed transition is of significance to protoforms of life, enabling them to locate a source of nutrients even in the absence of any supporting sensomotoric apparatus.

FRET-Integrated Polymer Brushes for Spatially Resolved Sensing of Changes in Polymer Conformation.

Polymer brush surfaces that alter their physical properties in response to chemical stimuli have the capacity to be used as new surface-based sensing materials. For such surfaces, detecting the polymer conformation is key to their sensing capabilities. Herein, we report on FRET-integrated ultrathin (<70 nm) polymer brush surfaces that exhibit stimuli-dependent FRET with changing brush conformation. Poly(N-isopropylacrylamide) polymers were chosen due their exceptional sensitivity to liquid mixture compositions and their ability to be assembled into well-defined polymer brushes. The brush transitions were used to optically sense changes in liquid mixture compositions with high spatial resolution (tens of micrometers), where the FRET coupling allowed for noninvasive observation of brush transitions around complex interfaces with real-time sensing of the liquid environment. Our methods have the potential to be leveraged towards greater surface-based sensing capabilities at intricate interfaces.

Design of binary polymer brushes with tuneable functionality.

Using coarse grained molecular dynamics simulations, we study how functionalized binary brushes may be used to create surfaces whose functionality can be tuned. Our model brushes consist of a mixture of nonresponsive polymers with functionalized responsive polymers. The functional groups switch from an exposed to a hidden state when the conformations of the responsive polymers change from extended to collapsed. We investigate quantitatively which sets of brush parameters result in optimal switching in functionality, by analyzing to which extent the brush conformation allows an external object to interact with the functional groups. It is demonstrated that brushes with species of comparable polymer lengths, or with longer responsive polymers than nonresponsive polymers, can show significant differences in their functionality. In the latter case, either the fraction of responsive polymers or the total grafting density has to be reduced. Among these possibilities, a reduction of the fraction of responsive polymers is shown to be most effective.

Linear response approach to active Brownian particles in time-varying activity fields.

In a theoretical and simulation study, active Brownian particles (ABPs) in three-dimensional bulk systems are exposed to time-varying sinusoidal activity waves that are running through the system. A linear response (Green-Kubo) formalism is applied to derive fully analytical expressions for the torque-free polarization profiles of non-interacting particles. The activity waves induce fluxes that strongly depend on the particle size and may be employed to de-mix mixtures of ABPs or to drive the particles into selected areas of the system. Three-dimensional Langevin dynamics simulations are carried out to verify the accuracy of the linear response formalism, which is shown to work best when the particles are small (i.e., highly Brownian) or operating at low activity levels.

Directional transport of colloids inside a bath of self-propelling walkers.

We present a setup in which passive colloids inside a solvent are moved to the boundaries of the container. The directional transport is facilitated by self-propelling microparticles ("walkers") with an activity gradient, which reduces their propulsion in the vicinity of bounding walls. An attractive interaction leads to the adsorption of walkers onto the colloid-surfaces in regions of low walker activity. It is shown that the activity gradient generates a free energy gradient which in turn acts as a driving force on the passive colloids. We carry out molecular dynamics simulations and present approaches to a theoretical description of the involved processes. Although the simulation data are not reproduced on a fully quantitative level, their qualitative features are covered by the model. The effect described here may be applied to facilitate a directional transport of drugs or to eliminate pollutants.

Mixed brush made of 4-arm stars and linear chains: MD simulations.

We investigate the structural properties of binary polymer brushes, composed of functional 4-armed star polymers and chemically identical linear polymers of different molecular weights. The molecular dynamics simulations confirm recent self-consistent field studies, in which a considerable potential of these systems for the design of switchable surfaces has been claimed. The length of the linear chains serves as a control parameter, which, while passing over a critical value, induces a sharp transition of the molecular conformation. We investigate these transitions at different grafting densities and summarize our findings in a phase diagram. The temperature dependence of the brush structure is investigated in a non-selective solvent, and non-trivial variations of the surface composition are observed. The quantity of these latter effects would be insufficient to build switchable systems, and we argue that a minor quantity of solvent selectivity would suffice to enable the desired feature of an environment-responsive coating.

Polyelectrolyte brushes in external fields: molecular dynamics simulations and mean-field theory.

A mean-field model is developed to predict the layer-thickness of sparse and salt-free polyelectrolyte brushes, exposed to an external electric field, which attracts the polyelectrolytes to the substrate. In molecular dynamics simulations, it is shown that a fraction of polymers collapses entirely to screen the charge of the substrate. The remaining brushes are then treated as field-free brushes at reduced grafting density. The mean-field model may thus be applied to field-free brushes, both in their osmotic and their weak charge regimes. It yields simple, closed equations for the brush height and for the partition of counterions in- and outside the brushes, and accurately reproduces simulation data of the collapse of the brushes during the crossover between both charge regimes.

Counterion-mediated protein adsorption into polyelectrolyte brushes.

We present molecular dynamics simulations of the interaction of fullerene-like, inhomogeneously charged proteins with polyelectrolyte brushes. A motivation of this work is the experimental observation that proteins, carrying an integral charge, may enter like-charged polymer brushes. Simulations of varying charge distributions on the protein surfaces are performed to unravel the physical mechanism of the adsorption. Our results prove that an overall neutral protein can be strongly driven into polyelectrolyte brush whenever the protein features patches of positive and negative charge. The findings reported here give further evidence that the strong adsorption of proteins is also driven by entropic forces due to counterion release, since charged patches on the surface of the proteins can act as multivalent counterions of the oppositely charged polyelectrolyte chains. A corresponding number of mobile co- and counterions is released from the brush and the vicinity of the proteins so that the entropy of the total system increases.

Performance of binoculars: Berek's model of target detection.

A model of target detection thresholds, first presented by Max Berek of Leitz, is fitted into a simple set of closed equations. These are combined with a recently published universal formula for the human eye's pupil size to yield a versatile formalism that is capable of predicting binocular performance gains. The model encompasses target size, contrast, environmental luminance, binocular's objective diameter, magnification, angle of view, transmission, stray light, and the observer's age. We analyze performance parameters of various common binocular models and compare the results with popular approximations to binocular performance, like the well-known twilight index. The formalisms presented here are of interest in military target detection as well as in civil applications such as hunting, surveillance, object security, law enforcement, and astronomy.

Molecular dynamics simulations of polyelectrolyte brushes under poor solvent conditions: origins of bundle formation.

Molecular dynamics simulations are applied to investigate salt-free planar polyelectrolyte brushes under poor solvent conditions. Starting above the Θ-point with a homogeneous brush and then gradually reducing the temperature, the polymers initially display a lateral structure formation, forming vertical bundles of chains. A further reduction of the temperature (or solvent quality) leads to a vertical collapse of the brush. By varying the size and selectivity of the counterions, we show that lateral structure formation persists and therefore demonstrate that the entropy of counterions being the dominant factor for the formation of the bundle phase. By applying an external compression force on the brush we calculate the minimal work done on the polymer phase only and prove that the entropy gain of counterions in the bundle state, as compared to the homogeneously collapsed state at the same temperature, is responsible for the lateral microphase segregation. As a consequence, the observed lateral structure formation has to be regarded universal for osmotic polymer brushes below the Θ-point.

Comparison of different thermostat settings in the implicit solvent approach for nanoparticles through brush-decorated nanopores.

Nanoparticles (NPs) that are forcefully driven through a brush-decorated nanochannel form a nonequilibrium system with a rich physical behavior, including a dynamical phase transition between two modes of propagation that correspond to either separate clusters of NPs or a continuous flow channel. The peculiar properties of this system make it an ideal benchmark candidate for a comparison of three thermostat settings, the dissipative particle dynamics (DPD), the Langevin (LGV) dynamics, and a modified LGV setup, denoted as LGV^{-}, in which the thermostatting is disabled in the direction of the driving force. We demonstrate that the choice of the thermostat has little influence on the conformations of NPs, and that, due to differences in the dissipation modes, notable differences arise in their dynamical properties, such as effective friction constants and average velocities. This also includes differences in the coupling between NP clusters and the surrounding brush and affects the corresponding phase diagrams of the two propagation modes. We conclude that the conventional DPD and LGV thermostats yield results that display a reasonable degree of coincidence, but we cannot recommend the use of the LGV^{-} algorithm for the present system.

Depletion Strategies for Crystallized Layers of Two-Dimensional Nanosheets to Enhance Lithium-Ion Conductivity in Polymer Nanocomposites.

The assembly of long-range aligned structures of two-dimensional nanosheets (2DNSs) in polymer nanocomposites (PNCs) is in urgent need for the design of nanoelectronics and lightweight energy-storage materials of high conductivity for electricity or heat. These 2DNS are thin and exhibit thermal fluctuations, leading to an intricate interplay with polymers in which entropic effects can be exploited to facilitate a range of different assemblies. In molecular dynamics simulations of experimentally studied 2DNSs, we show that the layer-forming crystallization of 2DNSs is programmable by regulating the strengths and ranges of polymer-induced entropic depletion attractions between pairs of 2DNSs, as well as between single 2DNSs and a substrate surface, by exclusively tuning the temperature and size of the 2DNS. Enhancing the temperature supports the 2DNS-substrate depletion rather than crystallization of 2DNSs in the bulk, leading to crystallized layers of 2DNSs on the substrate surfaces. On the other hand, the interaction range of the 2DNS-2DNS depletion attraction extends further than the 2DNS-substrate attraction whenever the 2DNS size is well above the correlation length of the polymers, which results in a nonmonotonic dependence of the crystallization layer on the 2DNS size. It is demonstrated that the depletion-tuned crystallization layers of 2DNSs contribute to a conductive channel in which individual lithium ions (Li ions) migrate efficiently through the PNCs. This work provides statistical and dynamical insights into the balance between the 2DNS-2DNS and 2DNS-substrate depletion interactions in polymer-2DNS composites and highlights the possibilities to exploit depletion strategies in order to engineer crystallization processes of 2DNSs and thus to control electrical conductivity.

Numerical evidences for a free energy barrier in starlike polymer brushes.

The existence of a free energy barrier, which prohibits the upward motion of retracted molecules into the surface region of starlike polymer brushes, is analyzed through molecular dynamics simulations in good solvent. This barrier emerges at moderate and high grafting densities, as a result of a density-discontinuity at the branching points of the highly stretched starlike molecules. The vertical force profiles of brushes of varying densities are taken with the help of a probe-particle that is gradually moved into the brush, and the results are compared with the density profiles and their negative gradients which generate the local osmotic pressures. Chain expulsion simulations, supported by scaling theory, are conducted to understand the dynamics of individual molecules inside the brushes. We prove that the flip-rates between retracted and extended states, being of relevance for the generation of efficiently switchable, environment-responsive brush layers, are determined by the elastic tension of the stretched molecules.

Screening confinement of entanglements: Role of a self-propelling end inducing ballistic chain reptation.

Synthetic and natural nanomaterials with self-propelling mechanisms continue to be explored to boost chain mobility beyond normal reptation in the crowded environments of entangled chains. Here we employ scaling theory and numerical simulations to demonstrate that activating one chain end of a singular or isolated chain boosts entanglement-constrained chain reptation from the one-dimensional diffusive mobility as described by the de Gennes-Edwards-Doi model to ballistic motion along the entanglement tube contour. The active chain is effectively screened from the constraint of entanglements on length scales exceeding the tube size.

Active colloidal molecules in activity gradients.

We consider a rigid assembly of two active Brownian particles, forming an active colloidal dimer, in a gradient of activity. We show analytically that depending on the relative orientation of the two particles the active dimer accumulates in regions of either high or low activity, corresponding to, respectively, chemotaxis and antichemotaxis. Certain active dimers show both chemotactic and antichemotactic behavior, depending on the strength of the activity. Our coarse-grained Fokker-Planck approach yields an effective potential, which we use to construct a nonequilibrium phase diagram that classifies the dimers according to their tactic behavior. Moreover, we show that for certain dimers a higher persistence of the motion is achieved similar to the effect of a steering wheel in macroscopic devices. This work could be useful for designing autonomous active colloidal structures which adjust their motion depending on the local activity gradients.

Mechanofluorescent Polymer Brush Surfaces that Spatially Resolve Surface Solvation.

Polymer brushes, consisting of densely end-tethered polymers to a surface, can exhibit rapid and sharp conformational transitions due to specific stimuli, which offer intriguing possibilities for surface-based sensing of the stimuli. The key toward unlocking these possibilities is the development of methods to readily transduce signals from polymer conformational changes. Herein, we report on single-fluorophore integrated ultrathin (<40 nm) polymer brush surfaces that exhibit changing fluorescence properties based on polymer conformation. The basis of our methods is the change in occupied volume as the polymer brush undergoes a collapse transition, which enhances the effective concentration and aggregation of the integrated fluorophores, leading to a self-quenching of the fluorophores' fluorescence and thereby reduced fluorescence lifetimes. By using fluorescence lifetime imaging microscopy, we reveal spatial details on polymer brush conformational transitions across complex interfaces, including at the air-water-solid interface and at the interface of immiscible liquids that solvate the surface. Furthermore, our method identifies the swelling of polymer brushes from outside of a direct droplet (i.e., the polymer phase with vapor above), which is controlled by humidity. These solvation-sensitive surfaces offer a strong potential for surface-based sensing of stimuli-induced phase transitions of polymer brushes with spatially resolved output in high resolution.

Chain stiffness boosts active nanoparticle transport in polymer networks.

Recent advances in technologies such as nanomanufacturing and nanorobotics have opened new pathways for the design of active nanoparticles (NPs) capable of penetrating biolayers for biomedical applications, e.g., for drug delivery. The coupling and feedback between active NP motility (with large stochastic increments relative to passive NPs) and the induced nonequilibrium deformation and relaxation responses of the polymer network, spanning scales from the NP to the local structure of the network, remain to be clarified. Using molecular dynamics simulations, combined with a Rouse mode analysis of network chains and position and velocity autocorrelation functions of the NPs, we demonstrate that the mobility of active NPs within cross-linked, concentrated polymer networks is a monotonically increasing function of chain stiffness, contrary to passive NPs, for which chain stiffness suppresses mobility. In flexible networks, active NPs exhibit a behavior similar to passive NPs, with a boost in mobility proportional to the self-propulsion force. These results are suggestive of design strategies for active NP penetration of stiff biopolymer matrices.