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.

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.

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.

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.

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.

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.

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.

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.

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.

Pseudo-chemotaxis of active Brownian particles competing for food.

Active Brownian particles (ABPs) are physical models for motility in simple life forms and easily studied in simulations. An open question is to what extent an increase of activity by a gradient of fuel, or food in living systems, results in an evolutionary advantage of actively moving systems such as ABPs over non-motile systems, which rely on thermal diffusion only. It is an established fact that within confined systems in a stationary state, the activity of ABPs generates density profiles that are enhanced in regions of low activity, which is thus referred to as 'anti-chemotaxis'. This would suggest that a rather complex sensoric subsystem and information processing is a precondition to recognize and navigate towards a food source. We demonstrate in this work that in non-stationary setups, for instance as a result of short bursts of fuel/food, ABPs do in fact exhibit chemotactic behavior. In direct competition with inactive, but otherwise identical Brownian particles (BPs), the ABPs are shown to fetch a larger amount of food. We discuss this result based on simple physical arguments. From the biological perspective, the ability of primitive entities to move in direct response to the available amount of external energy would, even in absence of any sensoric devices, encompass an evolutionary advantage.

Mechanical Strength Management of Polymer Composites through Tuning Transient Networks.

The addition of transient networks to polymer composites marks a new direction toward the design of novel materials, with numerous biomedical and industrial applications. The network structure connected by transient cross-links (CLs) relaxes as time evolves, which results in the stretching release of polymer strands between transient CLs during strain. Using molecular dynamics simulations, we measure directly the stress-strain curves of double polymer networks (DPNs), containing both transient and permanent components, at different strain rates. Lifetime and density of transient CLs control the relaxation spectrum of transient networks and determine the mechanical properties of DPNs. A Rouse mode analysis reveals that at high strain rates the mechanical strength of DPNs is defined jointly by the cross-linking structures of permanent and transient networks. At low strain rates, the cross-linking structure of transient network relaxes, leaving the permanent component of the network as a sole contributor to the mechanical strength of DPNs. The transient network is shown to facilitate a dissipation of energy at higher strain rates and prevents a rupture of the network, while the permanent network preserves the structural integrity of the composite at low strain rates. This study provides computational and theoretical foundations for designing polymer composites with desirable mechanical strength and toughness by means of tuning transient networks.

Nanoparticle Loading of Unentangled Polymers Induces Entanglement-Like Relaxation Modes and a Broad Sol-Gel Transition.

We combine molecular dynamics simulations, imaging and data analysis, and the Green-Kubo summation formula for the relaxation modulus G(t) to elicit the structure and rheology of unentangled polymer-nanoparticle composites distinguished by small NPs and strong NP-monomer attraction, εNPM ≫ kBT. A reptation-like plateau emerges in G(t) beyond a terminal relaxation time scale as the volume fraction, cNP, of NPs increases, coincident with a structure transition. A condensed phase of NP-aggregates forms, tightly interlaced with thin sheets of polymer chains, the remaining phase consisting of free chains void of NPs. Rouse mode analyses are applied to the two individual phases, revealing that long-wavelength Rouse modes in the aggregate phase are the source of reptation-like relaxation. Imaging reveals chain motion confined within the thin sheets between NPs and exhibits a 2D analogue of classical reptation. In the NP-free phase, Rouse modes relax indistinguishable from a neat polymer melt. The Fourier transform of G(t) reveals a sol-gel transition across a broad frequency spectrum, tuned by cNP and εNPM above critical thresholds, below which all structure and rheological transitions vanish.

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.

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.

Pseudochemotaxis in inhomogeneous active Brownian systems.

We study dynamical properties of confined, self-propelled Brownian particles in an inhomogeneous activity profile. Using Brownian dynamics simulations, we calculate the probability to reach a fixed target and the mean first passage time to the target of an active particle. We show that both these quantities are strongly influenced by the inhomogeneous activity. When the activity is distributed such that high-activity zone is located between the target and the starting location, the target finding probability is increased and the passage time is decreased in comparison to a uniformly active system. Moreover, for a continuously distributed profile, the activity gradient results in a drift of active particle up the gradient bearing resemblance to chemotaxis. Integrating out the orientational degrees of freedom, we derive an approximate Fokker-Planck equation and show that the theoretical predictions are in very good agreement with the Brownian dynamics simulations.

Nanoparticles of Various Degrees of Hydrophobicity Interacting with Lipid Membranes.

Using coarse-grained molecular dynamics simulations, we study the passive translocation of nanoparticles with a size of about 1 nm and with tunable degrees of hydrophobicity through lipid bilayer membranes. We observe a window of translocation with a sharp maximum for nanoparticles having a hydrophobicity in between hydrophilic and hydrophobic. Passive translocation can be identified as diffusive motion of individual particles in a free energy landscape. By combining direct sampling with umbrella-sampling techniques we calculate the free energy landscape for nanoparticles covering a wide range of hydrophobicities. We show that the directly observed translocation rate of the nanoparticles can be mapped to the mean-escape-rate through the calculated free energy landscape, and the maximum of translocation can be related with the maximally flat free energy landscape. The limiting factor for the translocation rate of nanoparticles having an optimal hydrophobicity can be related with a trapping of the particles in the surface region of the membrane. Here, hydrophobic contacts can be formed but the free energy effort of insertion into the brush-like tail regions can still be avoided. The latter forms a remaining barrier of a few kBT and can be spontaneously surmounted. We further investigate cooperative effects of a larger number of nanoparticles and their impact on the membrane properties such as solvent permeability, area per lipid, and the orientation order of the tails. By calculating the partition of nanoparticles at the phase boundary between water and oil, we map the microscopic parameter of nanoparticle hydrophobicity to an experimentally accessibly partition coefficient. Our studies reveal a generic mechanism for spherical nanoparticles to overcome biological membrane-barriers without the need of biologically activated processes.

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.

Tuning Adsorption Duration To Control the Diffusion of a Nanoparticle in Adsorbing Polymers.

Controlling the nanoparticle (NP) diffusion in polymers is a prerequisite to obtain polymer nanocomposites (PNCs) with desired dynamical and rheological properties and to achieve targeted delivery of nanomedicine in biological systems. Here we determine the suppression mechanism of direct NP-polymer attraction to hamper the NP mobility in adsorbing polymers and then quantify the dependence of the effective viscosity ηeff felt by the NP on the adsorption duration τads of polymers on the NP using scaling theory analysis and molecular dynamics simulations. We propose and confirm that participation of adsorbed chains in the NP motion break up at time intervals beyond τads due to the rearrangement of polymer segments at the NP surface, which accounts for the onset of Fickian NP diffusion on a time scale of t ≈ τads. We develop a power law, ηeff ∼ (τads)ν, where ν is the scaling exponent of the dependence of polymer coil size on the chain length, which leads to a theoretical basis for the design of PNCs and nanomedicine with desired applications through tuning the polymer adsorption duration.

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.