Development of a New Coarse-Grained Model to Simulate Assembly of Cellulose Chains Due to Hydrogen Bonding.

In this work, we present a new coarse-grained (CG) model that captures the directional hydrogen bonding interactions that drive cellulose chains to assemble into ordered aggregates. This CG model balances the incorporation of chemical details at the monomer level needed to represent directional interactions and the coarse-graining needed to capture large length scales and time scales associated with macromolecular assembly. We validate this CG model by first comparing the cellulose single-chain structure in the CG molecular dynamics (MD) simulations with that in atomistic MD simulations. We also compare the hydrogen bonding pattern, interchain distance, and interchain orientation seen in assembled cellulose chains observed in CG MD simulations with those seen in experimental crystal structures of cellulose. Upon validation, we present the aggregation behavior of cellulose chains with "silenced" hydrogen bonding site interactions to mimic cellulose chains that are chemically modified at the donor and acceptor hydrogen bonding sites (e.g., methylcellulose). We expect this type of CG model to be useful in predicting the morphology of cellulose chains in solution under a wide range of solution conditions and chemical modifications.

Computational Reverse-Engineering Analysis for Scattering Experiments on Amphiphilic Block Polymer Solutions.

In this paper, we present a computational reverse-engineering analysis for scattering experiments (CREASE) based on genetic algorithms and molecular simulation to analyze the structure within self-assembled amphiphilic polymer solutions. For a given input comprised of scattering intensity profiles and information about the amphiphilic polymers in solution, CREASE outputs the structure of the self-assembled micelles (e.g., core and corona diameters, aggregation number) as well as the conformations of the amphiphilic polymer chains in the micelle (e.g., blocks' radii of gyration, chain radii of gyration, monomer concentration profiles). First, we demonstrate CREASE's ability to reverse-engineer self-assembled nanostructures for scattering profiles obtained from molecular simulations (or in silico experiments) of generic coarse-grained bead-spring polymer chains in an implicit solvent. We then present CREASE's outputs for scattering profiles obtained from small-angle neutron scattering (SANS) experiments of poly(d-glucose carbonate) block copolymers in solution that exhibit assembly into spherical nanoparticles. The success of this method is demonstrated by its ability to replicate, quantitatively, the results from in silico experiments and by the agreement in micelle core and corona sizes obtained from microscopy of the in vitro solutions. The primary strength of CREASE is its ability to analyze scattering profiles without an off-the-shelf scattering model and the ability to provide chain and monomer level structural information that is otherwise difficult to obtain from scattering and microscopy alone.

Coarse-grained molecular dynamics simulations of α-1,3-glucan.

In this paper we present a computational study of aggregation in aqueous solutions of α-1,3-glucan captured using a coarse-grained (CG) model that can be extended to other polysaccharides. This CG model captures atomistic geometry (i.e., relative placement of the hydrogen bonding donors and acceptors within the monomer) of the α-1,3-glucan monomer, the directional interactions due to the donor-acceptor hydrogen bonds, and their effect on aggregation of multiple α-1,3-glucan chains without the extensive computational resources needed for simulations with atomistic models. Using this CG model, we conduct molecular dynamics simulations to assess the effect of varying α-1,3-glucan chain length and hydrogen bond interaction strengths on the aggregation of multiple chains at finite concentrations in implicit solvent. We quantify the hydrogen bonding strength needed for multiple chains to aggregate, the distribution of inter- and intra-chain hydrogen bonds within the aggregate and in some cases, the shapes of the aggregate. We also explore the effect of substitution/silencing of some randomly selected or specific hydrogen bonding sites in the chain on the aggregation and aggregate structure. In the unmodified α-1,3-glucan solution, the inter-chain hydrogen bonds cause the chains to aggregate into sheets. Random silencing of hydrogen bonding donor sites only increases the hydrogen bond strength needed for aggregation but retains the same aggregate structure as the unmodified chains. Specific silencing of the hydrogen-bonding site on the C6 carbon leads to the chains aggregating into planar sheets that then fold over to form hollow cylinders at intermediate hydrogen bond strength - 4.7 to 5.3 kcal mol-1. These cylindrical aggregates assemble end-to-end to form larger aggregates at higher hydrogen bond strengths.

Shear-Induced Alignment of Janus Particle Lamellar Structures.

Control over the alignment of colloidal structures plays a crucial role in advanced reconfigurable materials. In this work, we study the alignment of Janus particle lamellar structures under shear flow via Brownian dynamics simulations. Lamellar alignment (orientation relative to flow direction) is measured as a function of the Péclet number (Pe)-the ratio of the viscous shear to the Brownian forces-the particle volume fraction, and the strength of the anisotropic interaction potential made dimensionless with thermal energy. Under conditions where lamellar structures are formed, three orientation regimes are observed: (1) random orientation for very small Pe, (2) parallel orientation-lamellae with their normals parallel to the direction of the velocity gradient-for intermediate values of Pe, and (3) perpendicular orientation-lamellae with their normals parallel to the vorticity direction-for large Pe. To understand the alignment mechanism, we carry out a scaling analysis of competing torques between a pair of particles in the lamellar structure. Our results suggest that the change of parallel to perpendicular orientation is independent of the particle volume fraction and is caused by the hydrodynamic and Brownian torques on the particles overcoming the torques resulting from the interparticle interactions. This initial study of shear-induced alignment on lamellar structures formed by Janus colloidal particles also opens the door for future applications where a reversible actuator for structure orientation is required.

Phase diagram of Janus particles: The missing dimension of pressure anisotropy.

Brownian dynamics simulations of single-patch Janus particles under sedimentation equilibrium reveal that the phases found at fixed temperature and volume fraction are extremely sensitive to small changes in lateral box dimension. We trace this sensitivity to an uncontrolled parameter, namely, the pressure component parallel to the hexagonally ordered layers formed through sedimentation. We employ a flexible-cell constant-pressure scheme to achieve explicit control over this usually overlooked parameter, enabling the estimation of phase behavior under given pressure anisotropy. Our results show an increase in the stability range of an orientationally ordered lamellar phase with lateral layer compression and suggest a novel mechanism to control solid-solid phase transitions with negligible change in system volume, thus showing prospect for design of novel structures and switchable crystals from anisotropic building blocks.

Rotator-to-Lamellar Phase Transition in Janus Colloids Driven by Pressure Anisotropy.

We demonstrate through Brownian dynamics simulations a phase transition in plastic crystalline assemblies of Janus spheres through controlled pressure anisotropy. When the pressure in plane with hexagonally ordered layers is increased relative to that normal to the layers, a rapid first-order rotator-to-lamellar transition of Janus sphere orientation occurs at constant temperature. We show that the underlying mechanism closely follows the Maier-Saupe theory, originally developed for isotropic-to-nematic transition in positionally disordered materials but here applied to positionally ordered ones. Since the transition involves almost no translational diffusion or volume change, and occurs rapidly by particle rotation, the results should help guide the design of rapidly switchable colloidal crystals.

Rich Janus colloid phase behavior under steady shear.

We study the assembly of single-patch colloidal Janus particles under steady shear flow via Brownian dynamics simulations. In the absence of flow, by varying the Janus patch size and the range and strength of the anisotropic interaction potential, Janus colloids form different aggregates such as micelles, wormlike clusters, vesicles and lamellae. Under shear flow we observe rearrangement, deformation, and break-up of aggregates. At small and intermediate Péclet (Pe) numbers-the ratio between shear and Brownian forces-the competition between rearrangement, deformation, and break-up favors the growth of micelles and vesicles increasing mean cluster size, which is consistent with a previous numerical study of Janus particles under shear. This initial shear-induced growth causes micelles and vesicles to reach a maximum cluster size at Pe ≈ 1 and Pe ≈ 10, respectively. After this growth micelles dissociate continuously to reach a dilute colloidal "gas phase" at Pe ≈ 10 while vesicles dissociate into micelles with high aspect ratio at Pe ≈ 10 and finally break-up into a gas phase at Pe ≈ 30. Wormlike clusters initially break-up into micelles with high aspect ratio at Pe ≈ 0.1, and proceed to finally reach a gas phase at Pe ≈ 10. Lamellae initially break into smaller lamellae that align with the flow in the velocity-velocity-gradient plane and finally break-up into a gas phase at Pe ≈ 100. The different cluster sizes and morphologies observed as functions of interaction range, Janus patch size, interaction strength, and shear rate, open new actuation routes for reconfigurable materials and applications.

Kinetic modeling and design of colloidal lock and key assembly.

We investigate the kinetics of colloidal lock and key particle assembly by modeling transitions between free, non-specifically and specifically (dumbbells) bound pairs to enable the rapid formation of specific pairs. We expand on a model introduced in a previous publication (Colón-Meléndez et al., 2015) to account for the shape complementarity between the lock and the key particle. Specifically we develop a theory to predict free energy differences between specific and non-specific states based on the interaction potential between arbitrary surfaces and apply this to the interaction of a spherical key particle with the concave dimple surface. Our results show that a lock particle dimple slightly wider than the key particle radius results in optimal binding, but also show escape rates much smaller than those observed in experimental measurements described in the paper cited above. We assess the possible sources of error in experiments and in analysis, including spatial and temporal resolution of the confocal microscopy method used to measure kinetic coefficients, the polydispersity of the lock dimple size, and the sedimentation of the particles in a quasi-two-dimensional layer. We find that the largest sources of variation are in the limited temporal resolution of the experiments, which we account for in our theory, and in the quasi-two-dimensional nature of the experiment that leads to misidentification of non-specific pairs as specific ones. Accounting for these sources of variation results in very good quantitative agreement with experimental data.

Binding kinetics of lock and key colloids.

Using confocal microscopy and first passage time analysis, we measure and predict the rates of formation and breakage of polymer-depletion-induced bonds between lock-and-key colloidal particles and find that an indirect route to bond formation is accessed at a rate comparable to that of the direct formation of these bonds. In the indirect route, the pocket of the lock particle is accessed by nonspecific bonding of the key particle with the lock surface, followed by surface diffusion leading to specific binding in the pocket of the lock. The surprisingly high rate of indirect binding is facilitated by its high entropy relative to that of the pocket. Rate constants for forward and reverse transitions among free, nonspecific, and specific bonds are reported, compared to theoretical values, and used to determine the free energy difference between the nonspecific and specific binding states.

Colloidal crystal grain boundary formation and motion.

The ability to assemble nano- and micro- sized colloidal components into highly ordered configurations is often cited as the basis for developing advanced materials. However, the dynamics of stochastic grain boundary formation and motion have not been quantified, which limits the ability to control and anneal polycrystallinity in colloidal based materials. Here we use optical microscopy, Brownian Dynamic simulations, and a new dynamic analysis to study grain boundary motion in quasi-2D colloidal bicrystals formed within inhomogeneous AC electric fields. We introduce "low-dimensional" models using reaction coordinates for condensation and global order that capture first passage times between critical configurations at each applied voltage. The resulting models reveal that equal sized domains at a maximum misorientation angle show relaxation dominated by friction limited grain boundary diffusion; and in contrast, asymmetrically sized domains with less misorientation display much faster grain boundary migration due to significant thermodynamic driving forces. By quantifying such dynamics vs. compression (voltage), kinetic bottlenecks associated with slow grain boundary relaxation are understood, which can be used to guide the temporal assembly of defect-free single domain colloidal crystals.

Phase behavior of Janus colloids determined by sedimentation equilibrium.

We investigate the phase behavior of short-range interacting isotropic particles and single-patch Janus particles via simulations of sedimentation equilibrium, which allows for a rapid assessment of the equation of state and phase behavior directly from simulation. The methodology is tested against results by traditional methods and is found to yield good agreement for isotropic interactions. The method is then used to study single-patch Janus particles with different interaction strengths and patch sizes with particle area coverage greater than ∼0.63. Our results show an interplay between translational and orientational order. We observe a lamellar phase, a fluid phase and a rotator close-packed structure. The lamellar phase is shown to have a different range of stability than previously observed in simulation studies for systems of similar and longer-ranged interactions.

Self-consistent colloidal energy and diffusivity landscapes in macromolecular solutions.

We report a dynamic analysis to simultaneously measure colloidal forces and hydrodynamic interactions in the presence of both adsorbed and unadsorbed macromolecules. A Bayesian inference method is used to self-consistently obtain the position-dependent potential energy (i.e., energy landscape) and diffusivity (i.e., diffusivity landscape) from measured colloidal trajectories normal to a wall. Measurements are performed for particles and surfaces with adsorbed polyethylene oxide (PEO) copolymer as a function of unadsorbed PEO homopolymer concentration. Energy landscapes are well described by a steric repulsion between adsorbed brushes and depletion attraction due to unadsorbed macromolecules. Diffusivity landscapes show agreement with predicted short-range permeable brush models and long-range mobilities determined by the bulk solution viscosity. Lower than expected mobilities in the vicinity of overlapping depletion layers are attributed to interactions of adsorbed and unadsorbed macromolecules altering nonconservative lubrication forces.

Anomalous silica colloid stability and gel layer mediated interactions.

Total internal reflection microscopy (TIRM) is used to measure SiO2 colloid ensembles over a glass microscope slide to simultaneously obtain interactions and stability as a function of pH (4-10) and NaCl concentration (0.1-100 mM). Analysis of SiO2 colloid Brownian height excursions yields kT-scale potential energy vs separation profiles, U(h), and diffusivity vs separation profiles, D(h), and determines whether particles are levitated or irreversibly deposited (i.e., stable). By including an impermeable SiO2 "gel layer" when fitting van der Waals, electrostatic, and steric potentials to measured net potentials, gel layers are estimated to be ~10 nm thick and display an ionic strength collapse. The D(h) results indicate consistent surface separation scales for potential energy profiles and hydrodynamic interactions. Our measurements and model indicate how SiO2 gel layers influence van der Waals (e.g., dielectric properties), electrostatics (e.g., shear plane), and steric (e.g., layer thickness) potentials to understand the anomalous high ionic strength and high pH stability of SiO2 colloids.

Colloidal cluster crystallization dynamics.

The crystallization dynamics of a colloidal cluster is modeled using a low-dimensional Smoluchowski equation. Diffusion mapping shows that two order parameters are required to describe the dynamics. Using order parameters as metrics for condensation and crystallinity, free energy, and diffusivity landscapes are extracted from brownian dynamics simulations using bayesian inference. Free energy landscapes are validated against Monte Carlo simulations, and mean first-passage times are validated against dynamic simulations. The resulting model enables a low-dimensional description of colloidal crystallization dynamics.

A Smoluchowski model of crystallization dynamics of small colloidal clusters.

We investigate the dynamics of colloidal crystallization in a 32-particle system at a fixed value of interparticle depletion attraction that produces coexisting fluid and solid phases. Free energy landscapes (FELs) and diffusivity landscapes (DLs) are obtained as coefficients of 1D Smoluchowski equations using as order parameters either the radius of gyration or the average crystallinity. FELs and DLs are estimated by fitting the Smoluchowski equations to Brownian dynamics (BD) simulations using either linear fits to locally initiated trajectories or global fits to unbiased trajectories using Bayesian inference. The resulting FELs are compared to Monte Carlo Umbrella Sampling results. The accuracy of the FELs and DLs for modeling colloidal crystallization dynamics is evaluated by comparing mean first-passage times from BD simulations with analytical predictions using the FEL and DL models. While the 1D models accurately capture dynamics near the free energy minimum fluid and crystal configurations, predictions near the transition region are not quantitatively accurate. A preliminary investigation of ensemble averaged 2D order parameter trajectories suggests that 2D models are required to capture crystallization dynamics in the transition region.

Charged micelle depletion attraction and interfacial colloidal phase behavior.

Ensemble total internal reflection microscopy (TIRM) is used to directly measure the evolution of colloid-surface depletion attraction with increasing sodium dodecyl sulfate (SDS) concentration near the critical micelle concentration (CMC). Measured potentials are well described by a modified Asakura-Oosawa (AO) depletion potential in addition to electrostatic and van der Waals contributions. The modified AO potential includes effects of electrostatic interactions between micelles and surfaces via effective depletant dimensions in an excluded volume term and partitioning in an osmotic pressure term. Directly measured colloid-surface depletion potentials are used in Monte Carlo (MC) simulations to capture video microscopy (VM) measurements of micelle-mediated quasi-two-dimensional phase behavior including fluid, crystal, and gel microstructures. Our findings provide information to develop more rigorous and analytically simple models of depletion attraction in charged micellar systems.

Concentrated diffusing colloidal probes of Ca2+-dependent cadherin interactions.

We report video microscopy measurements and inverse simulation analyses of specific Ca(2+)-dependent interactions between N-cadherin fragments attached to supported lipid bilayer-coated silica colloids in quasi-2D concentrated configurations. Our results include characterization of the bilayer formation and fluidity and the attachment of active extracellular cadherin fragments on bilayers. Direct measurements of interaction potentials show nonspecific macromolecular repulsion between cadherin fragments in the absence of Ca(2+) and irreversible bilayer fusion via cadherin-mediated attraction at >100 µM Ca(2+). Analysis of Ca(2+)-dependent N-cadherin bond formation in quasi-2D concentrated configurations using inverse Monte Carlo and Brownian Dynamics simulations show measurable attraction starting at 0.1 µM Ca(2+), a concentration significantly below previously reported values.

Fokker-Planck analysis of separation dependent potentials and diffusion coefficients in simulated microscopy experiments.

Total internal reflection microscopy (TIRM) and video microscopy (VM) are methods for nonintrusively measuring weak colloidal interactions important to many existing and emerging applications. Existing analyses of TIRM measured single particle trajectories can be used to extract particle-surface potentials and average particle diffusion coefficients. Here we develop a Fokker-Planck (FP) formalism to simultaneously extract both particle-surface interaction potentials and position dependent diffusion coefficients. The FP analysis offers several advantages including capabilities to measure separation dependent hydrodynamic interactions and nonequilibrium states that are not possible with existing analyses. The FP analysis is implemented to analyze Brownian dynamic simulations of single particle TIRM and VM experiments in several configurations. Relative effects of spatial and temporal sampling on the correct interpretation of both conservative and dissipative forces are explored and show a broad range of applicability for accessible experimental systems. Our results demonstrate the ability to extract both static and dynamic information from microscopy measurements of isolated particles near surfaces, which provides a foundation for further investigation of particle ensembles and nonequilibrium systems.

Spatially controlled reversible colloidal self-assembly.

We studied the localized self-assembly of colloidal crystals on a topographically patterned substrate. A competition between particle and pattern interactions provided the ability to reversibly assemble quasi-two-dimensional colloidal crystals on a periodic landscape. The assembly process was visualized and controlled in real-space and real-time using video microscopy. Independent measurements and computer simulations were used to quantify all interactions controlling self-assembly. Steady-state studies characterized spatially inhomogeneous, coexisting fluid and crystal microstructures at various stages of assembly. Microstructures arise from a balance of local sedimentation equilibria within potential energy features and a tunable pairwise depletion attraction between colloids. Transient colloidal crystal self-assembly occurred via a quasiequilibrium process as characterized by continuously evolving spatial profiles of local density, bond orientational order, and self-diffusivities.

Interfacial colloidal crystallization via tunable hydrogel depletants.

We demonstrate an approach using temperature-dependent hydrogel depletants to thermoreversibly tune colloidal attraction and interfacial colloidal crystallization. Total internal reflection and video microscopy are used to measure temperature-dependent depletion potentials between approximately 2 microm silica colloids and surfaces as mediated by approximately 0.2 microm poly-N-isopropylacrylamide (PNIPAM) hydrogel particles. Measured depletion potentials are modeled using the Asakura-Oosawa theory while treating PNIPAM depletants as swellable hard spheres. Monte Carlo simulations using the measured potentials predict reversible, quasi-2D crystallization and melting at approximately 27 degrees C in quantitative agreement with video microscopy images of measured microstructures (i.e., radial distribution functions) over the temperature range of interest (20-29 degrees C). Additional measurements of short-time self-diffusivities display excellent agreement with predicted diffusivities by considering multibody hydrodynamic interactions and using a swellable hard sphere model for the PNIPAM solution viscosity. Our findings demonstrate the ability to quantitatively measure, model, and manipulate kT-scale depletion attraction and phase behavior as a means of formally engineering interfacial colloidal crystallization.