Chemical herding as a multiplicative factor for top-down manipulation of colloids.

Colloidal particles can create reconfigurable nanomaterials, with applications such as color-changing, self-repairing, and self-regulating materials and reconfigurable drug delivery systems. However, top-down methods for manipulating colloids are limited in the scale they can control. We consider here a new method for using chemical reactions to multiply the effects of existing top-down colloidal manipulation methods to arrange large numbers of colloids with single-particle precision, which we refer to as chemical herding. Using simulation-based methods, we show that if a set of chemically active colloids (herders) can be steered using external forces (i.e., electrophoretic, dielectrophoretic, magnetic, or optical forces), then a larger set of colloids (followers) that move in response to the chemical gradients produced by the herders can be steered using the control algorithms given in this paper. We also derive bounds that predict the maximum number of particles that can be steered in this way, and we illustrate the effectiveness of this approach using Brownian dynamics simulations. Based on the theoretical results and simulations, we conclude that chemical herding is a viable method for multiplying the effects of existing colloidal manipulation methods to create useful structures and materials.

Ready, Set, Grow: From Micelles to Giant Vesicles via Biocatalytic Activation.

Controlling physicochemical processes that drive changes in supramolecular aggregates is an important objective toward creating artificial soft micro- and nanomachines. Previous research explored the morphology control of membrane-based materials subjected to externally imposed chemical stimuli. Here, we modulate the microscale morphology of pH-responsive assemblies by using biocatalysis to internally generate changes in global pH. Catalytic reactions offer flexibility in the mechanism and rate at which stimuli are introduced to responsive assemblies, ultimately enabling precision and control over size and morphology. We observed, by dynamic light scattering and fluorescence microscopy, substantial microscale differences between assemblies subjected to manually titrated pH changes compared to biocatalytically activated pH changes, including the growth of giant vesicles from micelles. Coarse-grained molecular dynamics simulations of these metastable self-assembled structures provided insight into the thermodynamics and kinetics of the preferred structures. These results demonstrate the feasibility of using biocatalytic reactions to modulate the size and morphology of supramolecular assemblies, from micelles to giant vesicles.

Coarsening dynamics of ternary polymer solutions with mobility and viscosity contrasts.

Using phase-field simulations, we investigate the bulk coarsening dynamics of ternary polymer solutions undergoing a glass transition for two models of phase separation: diffusion only and with hydrodynamics. The glass transition is incorporated in both models by imposing mobility and viscosity contrasts between the polymer-rich and polymer-poor phases of the evolving microstructure. For microstructures composed of polymer-poor clusters in a polymer-rich matrix, the mobility and viscosity contrasts significantly hinder coarsening, effectively leading to structural arrest. For microstructures composed of polymer-rich clusters in a polymer-poor matrix, the mobility and viscosity contrasts do not impede domain growth; rather, they change the transient concentration of the polymer-rich phase, altering the shape of the discrete domains. This effect introduces several complexities to the coarsening process, including percolation inversion of the polymer-rich and polymer-poor phases-a phenomenon normally attributed to viscoelastic phase separation.

Nonsolvent-induced phase separation inside liquid droplets.

Nonsolvent-induced phase separation (NIPS) is a popular method for creating polymeric particles with internal microstructure, but many fundamental questions remain surrounding the kinetics of the complex coupled mass transfer and phase separation processes. In this work, we use simulations of a phase-field model to examine how (i) finite domain boundaries of a polymer droplet and (ii) solvent/nonsolvent miscibility affect the NIPS process. To isolate the effects of phase separation kinetics and solvent/nonsolvent mass transfer on the NIPS process, we study two different cases. First, we investigate droplet concentrations that originate inside the two-phase region, where phase separation kinetics alone governs the microstructure. Second, we investigate the effects of solvent/nonsolvent mass transfer by studying droplet concentrations that begin outside the two-phase region, where both phase separation kinetics and mass transfer play a role. In both cases, we find that qualitative NIPS behavior is a strong function of the relative location of the initial droplet composition with respect to the phase diagram. We also find that polymer/nonsolvent miscibility competes with solvent/nonsolvent miscibility in driving NIPS kinetic behavior. Finally, we examine polymer droplets undergoing solvent/nonsolvent exchange and find that the model predicts droplets that shrink with nearly Fickian diffusion kinetics. We conclude with a brief perspective on the state of simulations of NIPS processes and some recommendations for future work.

Steering particles via micro-actuation of chemical gradients using model predictive control.

Biological systems rely on chemical gradients to direct motion through both chemotaxis and signaling, but synthetic approaches for doing the same are still relatively naïve. Consequently, we present a novel method for using chemical gradients to manipulate the position and velocity of colloidal particles in a microfluidic device. Specifically, we show that a set of spatially localized chemical reactions that are sufficiently controllable can be used to steer colloidal particles via diffusiophoresis along an arbitrary trajectory. To accomplish this, we develop a control method for steering colloidal particles with chemical gradients using nonlinear model predictive control with a model based on the unsteady Green's function solution of the diffusion equation. We illustrate the effectiveness of our approach using Brownian dynamics simulations that steer single particles along paths, such as circle, square, and figure-eight. We subsequently compare our results with published techniques for steering colloids using electric fields, and we provide an analysis of the physical parameter space where our approach is useful. Based on these findings, we conclude that it is theoretically possible to explicitly steer particles via chemical gradients in a microfluidics paradigm.

Active control of equilibrium, near-equilibrium, and far-from-equilibrium colloidal systems.

The development of top-down active control over bottom-up colloidal assembly processes has the potential to produce materials, surfaces, and objects with applications in a wide range of fields spanning from computing to materials science to biomedical engineering. In this review, we summarize recent progress in the field using a taxonomy based on how active control is used to guide assembly. We find there are three distinct scenarios: (1) navigating kinetic pathways to reach a desirable equilibrium state, (2) the creation of a desirable metastable, kinetically trapped, or kinetically arrested state, and (3) the creation of a desirable far-from-equilibrium state through continuous energy input. We review seminal works within this framework, provide a summary of important application areas, and present a brief introduction to the fundamental concepts of control theory that are necessary for the soft materials community to understand this literature. In addition, we outline current and potential future applications of actively-controlled colloidal systems, and we highlight important open questions and future directions.

A phase field model for dynamic simulations of reactive blending of polymers.

A facile way to generate compatibilized blends of immiscible polymers is through reactive blending of end-functionalized homopolymers. The reaction may be reversible or irreversible depending on the end-groups and is affected by the immiscibility and transport of the reactant homopolymers and the compatibilizing copolymer product. Here we describe a phase-field framework to model the combined dynamics of reaction kinetics, diffusion, and multi-component thermodynamics on the evolution of the microstructure and reaction rate in reactive blending. A density functional with no fitting parameters, which is obtained by adapting a framework of Uneyama and Doi and qualitatively agrees with self-consistent field theory, is used in a diffusive dynamics model. For a symmetric mixture of equal-length reactive polymers mixed in equal proportions, we find that depending on the Flory χ parameter, the microstructure of an irreversibly reacting blend progresses through a rich evolution of morphologies, including from two-phase coexistence to a homogeneous mixture, or a two-phase to three-phase coexistence transitioning to a homogeneous blend or a lamellar copolymer. The emergence of a three-phase region at high χ leads to a previously unreported reaction rate scaling. For a reversible reaction, we find that the equilibrium composition is a function of both the equilibrium constant for the reaction and the χ parameter. We demonstrate that phase-field models are an effective way to understand the complex interplay of thermodynamic and kinetic effects in a reacting polymer blend.

Semiflexible oligomers crystallize via a cooperative phase transition.

Semicrystalline polymers are ubiquitous, yet despite their fundamental and industrial importance, the theory of homogeneous nucleation from a melt remains a subject of debate. A key component of the controversy is that polymer crystallization is a non-equilibrium process, making it difficult to distinguish between effects that are purely kinetic and those that arise from the underlying thermodynamics. Due to computational cost constraints, simulations of polymer crystallization typically employ non-equilibrium molecular dynamics techniques with large degrees of undercooling that further exacerbate the coupling between thermodynamics and kinetics. In a departure from this approach, in this study, we isolate the near-equilibrium nucleation behavior of a simple model of a melt of short, semiflexible oligomers. We employ several Monte Carlo methods and compute a phase diagram in the temperature-density plane along with two-dimensional free energy landscapes (FELs) that characterize the nucleation behavior. The phase diagram shows the existence of ordered nematic and crystalline phases in addition to the disordered melt phase. The minimum free energy path in the FEL for the melt-crystal transition shows a cooperative transition, where nematic order and monomer positional order move in tandem as the system crystallizes. This near-equilibrium phase transition mechanism broadly agrees with recent evidence that polymer stiffness plays an important role in crystallization but differs in the specifics of the mechanism from several recent theories. We conclude that the computation of multidimensional FELs for models that are larger and more fine-grained will be important for evaluating and refining theories of homogeneous nucleation for polymer crystallization.

Using reactive dissipative particle dynamics to understand local shape manipulation of polymer vesicles.

Biological cells have long been of interest to researchers due to their capacity to actively control their shape. Accordingly, there is significant interest in generating simplified synthetic protocells that can alter their shape based on an externally or internally generated stimulus. To date, most progress has been made towards controlling the global shape of a protocell, whereas less is known about generating a local shape change. Here, we seek to better understand the possible mechanisms for producing local morphological changes in a popular protocell system, the block copolymer vesicle. Accordingly, we have combined Dissipative Particle Dynamics (DPD) and the Split Reactive Brownian Dynamics algorithm (SRBD) to produce a simulation tool that is capable of modeling the dynamics of self-assembled polymer structures as they undergo chemical reactions. Using this Reactive DPD or RDPD method, we investigate local morphological change driven by either the microinjection of a stimulus or an enzymatically-produced stimulus. We find that sub-vesicle-scale morphological change can be induced by either a solvent stimulus that swells the vesicle membrane, or by a reactant stimulus that alters the chemistry of the block polymer in the membrane corona. Notably, the latter method results in a more persistent local deformation than the former, which we attribute to the slower diffusion of polymer chains relative to the solvent. We quantify this deformation and show that it can be modulated by altering the interaction parameter of the parts of the polymer chain that are affected by the stimulus.

Mechanisms of Asymmetric Membrane Formation in Nonsolvent-Induced Phase Separation.

We report the first simulations of nonsolvent-induced phase separation (NIPS) that predict membrane microstructures with graded asymmetric pore size distribution. In NIPS, a polymer solution film is immersed in a nonsolvent bath, enriching the film in nonsolvent, and leading to phase separation that forms a solid polymer-rich membrane matrix and polymer-poor membrane pores. We demonstrate how mass-transfer-induced spinodal decomposition, thermal fluctuations, and glass-transition dynamics-implemented with mobility contrast between the polymer-rich and polymer-poor phases-are essential to the formation of asymmetric membrane microstructures. Specifically, we show that the competition between the propagation of the phase-separation and glass-transition fronts determines the degree of pore-size asymmetry. We also explore the sensitivity of these microstructures to the initial film composition, and compare their formation in 2D and 3D.

Mass-transfer driven spinodal decomposition in a ternary polymer solution.

Nonsolvent induced phase separation (NIPS) is a widely occuring process used in industrial membrane production, nanotechnology and Nature to produce microstructured polymer materials. A variety of process-dependent morphologies are produced when a polymer solution is exposed to a nonsolvent that, following a period where mass is exchanged, precipitates and solidifies the polymer. Despite years of investigation, both experimental and theoretical, many questions surround the pathways to the microstructures that NIPS can produce. Here, we provide simulation results from a model that simultaneously captures both the processess of solvent/nonsolvent exchange and phase separation. We show that the time it takes the nonsolvent to diffuse to the bottom of the film is an important timescale, and that phase separation is possible at times both much smaller and much larger than this scale. Our results include both one-dimensional simulations of the mass transfer kinetics and two- and three-dimensional simulations of morphologies at both short and long times. We find good qualitative agreement with experimental heuristics, but we conclude that an additional model for the vitrification process will be key for fully explaining experimental observations of microstructure formation.

Marangoni Flows during Nonsolvent Induced Phase Separation.

Motivated by the much discussed, yet unexplained, presence of macrovoids in polymer membranes, we explore the impact of Marangoni flows in the process of nonsolvent induced phase separation. Such flows have been hypothesized to be important to the formation of macrovoids, but little quantitative evidence has been produced to date. Using a recently developed multifluid phase field model, we find that roll cells indicative of a solutal Marangoni instability are manifest during solvent/nonsolvent exchange across a stable interface. However, these flows are weak and subsequently do not produce morphological features that might lead to macrovoid formation. By contrast, initial conditions that lead to an immediate precipitation of the polymer film coincide with large Marangoni flows that disturb the interface. The presence of such flows suggests a new experimental and theoretical direction in the search for a macrovoid formation mechanism.

A multi-fluid model for microstructure formation in polymer membranes.

We develop a multi-fluid model for a ternary polymer solution using the Rayleighian formalism of Doi and Onuki, and give an efficient pseudo-spectral method for solving both the diffusion and momentum equations that result. Subsequently, we find that the numerical simulation is capable of describing systems at the micron length-scale and easily reaches millisecond time-scales. In addition, we characterize the model thermodynamics and kinetics including the (i) phase behavior, (ii) structure of the interfaces, (iii) mutual diffusion coefficients, (iv) bulk spinodal decomposition kinetics with and without hydrodynamics and (v) spinodal decomposition in the presence of an interface with a non-solvent bath. We obtain good qualitative agreement with the expected thermodynamic and kinetic behavior. We also show that a linear stability analysis of the diffusion equation quantitatively predicts the fastest growing mode obtained from simulation and gives insight into the phase separation process relevant for the evolution of microstructure in phase-separating ternary polymer solutions.

Interplay between chain stiffness and excluded volume of semiflexible polymers confined in nanochannels.

The properties of channel-confined semiflexible polymers are determined by a complicated interplay of chain stiffness and excluded volume effects. Using Pruned-Enriched Rosenbluth Method (PERM) simulations, we study the equilibrium properties of channel-confined polymers by systematically controlling chain stiffness and excluded volume. Our calculations of chain extension and confinement free energy for freely jointed chains with and without excluded volume show excellent agreement with theoretical predictions. For ideal wormlike chains, the extension is seen to crossover from Odijk behavior in strong confinement to zero-stretching, bulk-like behavior in weak confinement. In contrast, for self-avoiding wormlike chains, we always observe that the linear scaling of the extension with the contour length is valid in the long-chain limit irrespective of the regime of confinement, owing to the coexistence of stiffness and excluded volume effects. We further propose that the long-chain limit for the extension corresponds to chain lengths wherein the projection of the end-to-end distance along the axis of the channel is nearly equal to the mean span parallel to the axis. For DNA in nanochannels, this limit was identified using PERM simulations out to molecular weights of more than 1 megabase pairs; the molecular weight of λ-DNA is found to exhibit nearly asymptotic fractional extension for channels sizes used commonly in experiments.

Hydrodynamics of DNA confined in nanoslits and nanochannels.

Modeling the dynamics of a confined, semi exible polymer is a challenging problem, owing to the complicated interplay between the configurations of the chain, which are strongly affected by the length scale for the confinement relative to the persistence length of the chain, and the polymer-wall hydrodynamic interactions. At the same time, understanding these dynamics are crucial to the advancement of emerging genomic technologies that use confinement to stretch out DNA and "read" a genomic signature. In this mini-review, we begin by considering what is known experimentally and theoretically about the friction of a wormlike chain such as DNA confined in a slit or a channel. We then discuss how to estimate the friction coefficient of such a chain, either with dynamic simulations or via Monte Carlo sampling and the Kirk-wood pre-averaging approximation. We then review our recent work on computing the diffusivity of DNA in nanoslits and nanochannels, and conclude with some promising avenues for future work and caveats about our approach.

Is DNA a Good Model Polymer?

The details surrounding the cross-over from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the Pruned-Enriched Rosenbluth Method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains (≈ 1,000,000 base pairs depending on the choice of size metric) are required to reach flexible, swollen non-draining coils. Furthermore, our results indicate that the commonly used model polymer λ-DNA (48,500 base pairs) does not exhibit "ideal" scaling, but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.

Entropic depletion of DNA in triangular nanochannels.

Using Monte Carlo simulations of a touching-bead model of double-stranded DNA, we show that DNA extension is enhanced in isosceles triangular nanochannels (relative to a circular nanochannel of the same effective size) due to entropic depletion in the channel corners. The extent of the enhanced extension depends non-monotonically on both the accessible area of the nanochannel and the apex angle of the triangle. We also develop a metric to quantify the extent of entropic depletion, thereby collapsing the extension data for circular, square, and various triangular nanochannels onto a single master curve for channel sizes in the transition between the Odijk and de Gennes regimes.

Modeling the relaxation time of DNA confined in a nanochannel.

Using a mapping between a Rouse dumbbell model and fine-grained Monte Carlo simulations, we have computed the relaxation time of λ-DNA in a high ionic strength buffer confined in a nanochannel. The relaxation time thus obtained agrees quantitatively with experimental data [Reisner et al., Phys. Rev. Lett. 94, 196101 (2005)] using only a single O(1) fitting parameter to account for the uncertainty in model parameters. In addition to validating our mapping, this agreement supports our previous estimates of the friction coefficient of DNA confined in a nanochannel [Tree et al., Phys. Rev. Lett. 108, 228105 (2012)], which have been difficult to validate due to the lack of direct experimental data. Furthermore, the model calculation shows that as the channel size passes below approximately 100 nm (or roughly the Kuhn length of DNA) there is a dramatic drop in the relaxation time. Inasmuch as the chain friction rises with decreasing channel size, the reduction in the relaxation time can be solely attributed to the sharp decline in the fluctuations of the chain extension. Practically, the low variance in the observed DNA extension in such small channels has important implications for genome mapping.

Revisiting blob theory for DNA diffusivity in slitlike confinement.

Blob theory has been widely applied to describe polymer conformations and dynamics in nanoconfinement. In slit confinement, blob theory predicts a scaling exponent of 2/3 for polymer diffusivity as a function of slit height, yet a large body of experimental studies using DNA produce a scaling exponent significantly less than 2/3. In this work, we develop a theory that predicts that this discrepancy occurs because the segment correlation function for a semiflexible chain such as DNA does not follow the Flory exponent for length scales smaller than the persistence length. We show that these short length scale effects contribute significantly to the scaling for the DNA diffusivity, but do not appreciably affect the scalings for static properties. Our theory is fully supported by Monte Carlo simulations, quantitative agreement with DNA experiments, and the results reconcile this outstanding problem for confined polymers.