Self-consistent colloidal energy and diffusivity landscapes in macromolecular solutions

Direct measurements & simplified models of colloidal interactions & diffusion with adsorbed macromolecules

We report total internal reflection microscopy measurements of 3D trajectories of ensembles of micron sized colloidal particles near interfaces with and without adsorbed macromolecules. Evanescent wave scattering reveals nanometer scale motion normal to planar surfaces and sub-diffraction limit lateral motion is resolved via image analysis. Equilibrium and non-equilibrium analyses of particle trajectories reveal self-consistent position dependent energies (energy landscapes) and position dependent diffusivities (diffusivity landscapes) both perpendicular and parallel to interfaces. For bare colloids and surfaces, electrostatic and hydrodynamic interactions are accurately quantified with established analytical theories. For colloids and surfaces with adsorbed macromolecules, conservative forces are accurately quantified with models for interactions between brush layers, whereas directly measured position dependent diffusivities require novel models of spatially varying permeability within adsorbed layers. Agreement between spatially resolved interactions and diffusivities and rigorous simplified models provide a basis to consistently interpret, predict, and design colloidal transport in the presence of adsorbed macromolecules for diverse applications.

Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook

Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Besides discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.

Dynamic interfaces for contact-time control of colloidal interactions

Understanding pairwise interactions between colloidal particles out of equilibrium has a profound impact on dynamical processes such as colloidal self assembly. However, traditional colloidal interactions are effectively quasi-static on colloidal timescales and cannot be modulated out of equilibrium. A mechanism to dynamically tune the interactions during colloidal contacts can provide new avenues for self assembly and material design. In this work, we develop a framework based on polymer-coated colloids and demonstrate that in-plane surface mobility and mechanical relaxation of polymers at colloidal contact interfaces enable an effective, dynamic interaction. Combining analytical theory, simulations, and optical tweezer experiments, we demonstrate precise control of dynamic pair interactions over a range of pico-Newton forces and seconds timescales. Our model helps further the general understanding of out-of-equilibrium colloidal assemblies while providing extensive design freedom via interface modulation and nonequilibrium processing.

Impact of the inner solute structure on the electrostatic mean-field and strong-coupling regimes of macromolecular interactions

The structural diversity of the solute molecules involved in biomolecular processes necessitates the characterization of the forces between charged macromolecules beyond the point-ion description. From the field-theoretic partition function of an electrolyte confined between two anionic membranes, we derive a contact-value identity valid for general intramolecular solute structure and electrostatic coupling strength. In the electrostatic mean-field regime, the inner charge spread of the solute particles is shown to induce the twofold enhancement of the short-range Poisson-Boltzmann level membrane repulsion and a longer-range depletion attraction. Our contact theorem indicates that the twofold repulsion enhancement by solute size is equally present in the opposite strong-coupling regime of linear and spherical solute molecules. Upon the inclusion of the dielectric contrast between the electrolyte and the interacting membranes, the emerging polarization forces substantially amplify the solute specificity of the macromolecular interactions. Namely, the finite size of the dumbbell-like solute particles composed of similar terminal charges weakens the intermembrane repulsion. However, the extended structure of the solute molecules carrying opposite elementary charges such as ionized atoms and zwitterionic molecules enhances the membrane repulsion by several factors. We also show that these polarization forces can extend the range of the solute structure effects up to intermembrane distances exceeding the solute size by an order of magnitude. This radical alteration of the intermembrane interactions by the salt structure identifies the solute specificity as a key ingredient of the thermodynamic stability in colloidal systems.

Blood Protein Exclusion from Polymer Brushes

We report interactions between adsorbed copolymers of poly(ethylene glycol) (PEG) in the presence of two abundant blood proteins, serum albumin and an immunoglobulin G, up to physiological blood concentrations. We directly and nonintrusively measure interactions between PEG triblock copolymers (PEG-PPO-PEG) adsorbed to hydrophobic colloids and surfaces using Total Internal Reflection Microscopy, which provides kT- and nanometer-scale resolution of interaction potentials (energy vs separation). In the absence of protein, adsorbed PEG copolymer repulsion is consistent with dimensions and architectures of PEG brushes on both colloids and surfaces. In the presence of proteins, we observe concentration dependent depletion attraction and no change to brush repulsion, indicating protein exclusion from PEG brushes. Because positive and negative protein adsorption are mutually exclusive, our observations of concentration dependent depletion attraction with no change to brush repulsion unambiguously indicate the absence of protein coronas at physiological protein concentrations. These findings demonstrate a direct sensitive approach to determine interactions between proteins and particle/surface coatings important to diverse biotechnology applications.

The Curvature Effect on the Diffusion of Single Brownian Squares on a Cylindrical Surface in the Presence of Depletion Attractions

The diffusion of single micron-sized Brownian square platelets on cylindrical surfaces with different radii of curvature in the presence of depletion attractions was studied experimentally by video microscopy. The translational motion of a square is found to be diffusive along the axial direction of the cylinder but sub-diffusive along the circumferential direction due to the confinement induced by gravity, while its rotational motion displays a sub-diffusive behavior due to the confinement induced by orientation-dependent depletion attractions. Such a confinement effect decreases as the radius of curvature increases and can be tuned both through surface curvatures and/or depletion attractions. Our work provides a new way to control the translational and rotational dynamics of anisotropic particles through curved surfaces in the presence of depletion attractions.

Synergistic Polymer-Surfactant-Complex Mediated Colloidal Interactions and Deposition

Total internal reflection microscopy (TIRM) is used to directly, sensitively, and simultaneously measure colloidal interactions, dynamics, and deposition for a broad range of polymer-surfactant compositions. A deposition state diagram containing comprehensive information about particle interactions, trajectories, and deposition behavior is obtained for polymer-surfactant compositions covering four decades in both polymer and surfactant concentrations. Bulk polymer-surfactant phase behavior and surface properties are characterized to provide additional information to interpret mechanisms. Materials investigated include cationic acrylamide-acrylamidopropyltrimonium copolymer (AAC), sodium lauryl ether sulfate (SLES) surfactant, silica colloids, and glass microscope slides. Measured colloid-substrate interaction potentials and deposition behavior show nonmonotonic trends vs polymer-surfactant composition and appear to be synergistic in the sense that they are not easily explained as the superposition of single-component-mediated interactions. Broad findings show that at some compositions polymer-surfactant complexes mediate bridging and depletion attractions that promote colloidal deposition, whereas other compositions produce electrosteric repulsion that deters colloidal deposition. These findings illustrate mechanisms underlying colloid-surface interactions in polymer-surfactant mixtures, which are important to controlling selective colloidal deposition in multicomponent formulation applications.

Measurements of Particle-Surface Interactions in Both Equilibrium and Nonequilibrium Systems

Total internal reflection microscopy (TIRM) is a passive technique that measures colloidal interactions in aqueous solution. A traditional Boltzmann method requires that particles must fluctuate around equilibrium positions for a long time. A method based on multiparticle tracking and drift velocity method was developed to measure interactions in both equilibrium and nonequilibrium systems. This method relaxed the limitation of the traditional Boltzmann method and do not require any external force like optical tweezer. Theoretical predictions of particle sedimentation under the influence of various forces were investigated to determine the proper particle size and solution properties. We found that the polystyrene (PS) particle with a size of 2.1 μm took the longest time to finish sedimentation, and 5% (w/w) sucrose was chosen to suppress the Brownian motion. For single and ensemble particles in equilibrium, the experimental diffusion coefficients and potential energy profiles were consistent with the theoretical prediction. In nonequilibrium experiments, the van der Waals force between the bare/hybrid particles and flat surface was measured, and the silica shell acted to strengthen the van der Waals attraction. This method extends the application of TIRM to nonequilibrium systems without any active control. Moreover, the silica-coated PS core-shell hybrid particles facilitate surface modification with a variety of active chemicals. It would be a great advantage to measure all kinds of long-range interactions between surface-modified particles and surface in aqueous solution with TIRM.

Direct Measurements of kT-Scale Capsule-Substrate Interactions and Deposition Versus Surfactants and Polymer Additives

We report a novel approach to directly measure the interactions and deposition behavior of functional capsule delivery systems on glass substrates versus the concentration of an anionic surfactant sodium lauryl ether sulfate (SLES) and a cationic acrylamide-acrylamidopropyltrimonium copolymer (AAC). Analyses of three-dimensional optical microscopy trajectories were used to quantify lateral diffusive dynamics, deposition lifetimes, and potentials of mean force for different solution conditions. In the absence of additives, negatively charged capsule surfaces yield electrostatic repulsion with the negatively charged substrate, which inhibits deposition. With an increasing SLES concentration below the critical micelle concentration (CMC), capsule-substrate electrostatic repulsion is mediated by the charged surfactant solution that decreases the Debye length. Above the SLES CMC, depletion attraction causes enhanced deposition until eventually depletion repulsion inhibits deposition at concentrations ∼10 wt %. Addition of an ACC causes deposition via capsule-substrate bridging at all concentrations; the weakest deposition occurs at intermediate AAC concentrations from a competition of steric repulsion and attraction via a few extended bridges. The novel measurements and models of capsule interactions and deposition on substrates in this work provide a basis to fundamentally understand and rationally design complex rinse-off cleansing formulations with optimal characteristics.

Interfacial colloidal rod dynamics: Coefficients, simulations, and analysis

Colloidal rod diffusion near a wall is modeled and simulated based on a constrained Stokesian dynamic model of chains-of-spheres. By modeling colloidal rods as chains-of-spheres, complete diffusion tensors are computed for colloidal rods in bulk media and near interfaces, including hydrodynamic interactions, translation-rotation coupling, and all diffusion modes in the particle and lab frames. Simulated trajectories based on the chain-of-spheres diffusion tensor are quantified in terms of typical experimental quantities such as mean squared positional and angular displacements as well as autocorrelation functions. Theoretical expressions are reported to predict measured average diffusivities as well as the crossover from short-time anisotropic translational diffusion along the rod's major axis to isotropic diffusion. Diffusion modes are quantified in terms of closed form empirical fits to model results to aid their use in interpretation and prediction of experiments involving colloidal rod diffusion in interfacial and confined systems.

Interfacial and Confined Colloidal Rod Diffusion

Optical microscopy is used to measure translational and rotational diffusion of colloidal rods near a single wall, confined between parallel walls, and within quasi-2D porous media as a function of rod aspect ratio and aqueous solution ionic strength. Translational and rotational diffusivities are obtained as rod particles experience positions closer to boundaries and for larger aspect ratios. Models based on position dependent hydrodynamic interactions quantitatively capture diffusivities in all geometries and indicate particle-wall separations in agreement with independent estimates based on electrostatic interactions. Short-time translational diffusion in quasi-2D porous media is insensitive to porous media area fraction, which appears to arise from a balance of hydrodynamic hindrance and enhanced translation due to parallel alignment along surfaces. Findings in this work provide a basis to interpret and predict interfacial and confined colloidal rod transport relevant to biological, environmental, and synthetic material systems.

Diffusing Colloidal Probes of kT-Scale Biomaterial-Cell Interactions

In the optimization of applied biomaterials, measurements of their interactions with cell surfaces are important to understand their influence on specific and nonspecific cell surface adhesion, internalization pathways, and toxicity. In this study, a novel approach using dark field video microscopy with combined real-time particle and cell tracking allows the trajectories of biomaterial-coated colloids to be monitored in relation to their distance from cell perimeters. Dynamic and statistical mechanical analyses enable direct measurement of colloid-cell surface association lifetimes and interaction potentials mediated by biomaterials. Our analyses of colloidal transport showed polyethylene glycol (PEG) and bovine serum albumin (BSA) lead to net repulsive interactions with cell surfaces, while dextran and hyaluronic acid (HA) lead to reversible and irreversible association to the cell surface, respectively. Our results demonstrate how diffusing colloidal probes can be used for nonobtrusive, sensitive measurements of biomaterial-cell surface interactions important to therapeutics, diagnostics, and tissue engineering.

Diffusing colloidal probes of cell surfaces

Measurements and analyses are reported to quantify dynamic and equilibrium interactions between colloidal particles and live cell surfaces using dark field video microscopy. Two-dimensional trajectories of micron-sized polyethylene glycol (PEG)-coated silica colloids relative to adherent epithelial breast cancer cell perimeters are determined allowing measurement of position dependent diffusivities and interaction potentials. PEG was chosen as the material system of interest to assess non-specific interactions with cell surfaces and establishes a basis for investigation of specific interactions in future studies. Analysis of measured potential energies on cell surfaces reveals the spatial dependence in cell topography. With the measured cell topography and models for particle-cell surface hydrodynamic interactions, excellent agreement is obtained between theoretical and measured colloidal transport on cell surfaces. Quantitative analyses of association lifetimes showed that PEG coatings act to stabilize colloids above the cell surface through net repulsive, steric interactions. Our results demonstrate a self-consistent analysis of diffusing colloidal probe interactions due to conservative and non-conservative forces to characterize biophysical cell surface properties.

A colloid model system for interfacial sorption kinetics

Particle adsorption to an interface may be a complicated affair, motivating detailed measurements of various processes involved, to discover better understanding of the role of particle characteristics and solution conditions on adsorption coverage and rate. Here we use micron size colloids with a weak interfacial interaction potential as a model system to track particle motion and measure the rates of desorption and adsorption. The colloid-interface interaction strength is tuned to be less than 10 kBT so that it is comparable to many nanoscale systems of interest such as proteins at interfaces. The tuning is accomplished using a combination of depletion, electrostatic, and gravitational forces. The colloids transition between an entropically trapped adsorbed state and a desorbed state through Brownian motion. Observations are made using an light-emitting diode (LED)-based total internal reflection microscopy (TIRM) setup. The observed adsorption and desorption rates are compared to theoretical predictions based on the measured interaction potential and near-wall particle diffusivity. The results demonstrate that diffusion dynamics play a significant role when the barrier energy is small. This experimental system will allow for the future study of more complex dynamics such as nonspherical colloids and collective effects at higher concentrations.

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.