Modeling photo-generated charge extraction in bulk heterojunction nanoparticles.

We present a drift-diffusion model for predicting currents generated through the absorption of solar energy inside bulk heterojunction organic nanoparticles, which are, for example, promising nanomaterials for photo-catalytic water splitting. By coupling a model of the internal microstructure of the nanoparticle with the electronic properties, we show how different characteristics of the microstructure influence the efficiency of the conversion of solar energy into electrical energy. Our model provides a foundation for using computational modeling to optimize the design of photocatalytic nanoparticles.

Hot soup! Correlating the severity of liquid scald burns to fluid and biomedical properties.

Burns caused by hot drinks and soups can be both debilitating and costly, especially to pediatric and geriatric patients. This research is aimed at better understanding the fluid properties that can influence the severity of skin burns. We use a standard model which combines heat transfer and biomedical equations to predict burn severity. In particular, experimental data from a physical model serves as the input to our numerical model to determine the severity of scald burns as a consequence of actual fluid flows. This technique enables us to numerically predict the heat transfer from the hot soup into the skin, without the need to numerically estimate the complex fluid mechanics and thermodynamics of the potentially highly viscous and heterogeneous soup. While the temperature of the soup is obviously is the most important fact in determining the degree of burn, we also find that more viscous fluids result in more severe burns, as the slower flowing thicker fluids remain in contact with the skin for longer. Furthermore, other factors can also increase the severity of burn such as a higher initial fluid temperature, a greater fluid thermal conductivity, or a higher thermal capacity of the fluid. Our combined experimental and numerical investigation finds that for average skin properties a very viscous fluid at 100°C, the fluid must be in contact with the skin for around 15-20s to cause second degree burns, and more than 80s to cause a third degree burn.

Simulating the co-encapsulation of drugs in a "smart" core-shell-shell polymer nanoparticle.

A coarse-grained lattice Monte Carlo method is used to simulate co-encapsulation and delivery of both a hydrophilic and hydrophobic drug from polymer nanoparticles. In particular, core-shell-shell polymer nanoparticles with acid-labile bonds are simulated, and the preferential release of the encapsulated drugs near more acidic tumors is captured. While these simple models lack the molecular details of a real system, they can reveal interesting insights concerning the effects of entropy and enthalpy in these systems.

Propulsion and trapping of microparticles by active cilia arrays.

We model the transport of a microscopic particle via a regular array of beating elastic cilia, whose tips experience an adhesive interaction with the particle's surface. At optimal adhesion strength, the average particle velocity is maximized. Using simulations spanning a range of cilia stiffness and cilia-particle adhesion strength, we explore the parameter space over which the particle can be "released", "propelled", or "trapped" by the cilia. We use a lower-order model to predict parameters for which the cilia are able to "propel" the particle. This is the first study that shows how both stiffness and adhesion strength are crucial for manipulation of particles by active cilia arrays. These results can facilitate the design of synthetic cilia that integrate adhesive and hydrodynamic interactions to selectively repel or trap particulates. Surfaces that are effective at repelling particulates are valuable for antifouling applications, while surfaces that can trap and, thus, remove particulates from the solution are useful for efficient filtration systems.

Mathematical modeling of microtubule dynamics: insights into physiology and disease.

Computer models of microtubule dynamics have provided the basis for many of the theories on the cellular mechanics of the microtubules, their polymerization kinetics, and the diffusion of tubulin and tau. In the three-dimensional model presented here, we include the effects of tau concentration and the hydrolysis of GTP-tubulin to GDP-tubulin and observe the emergence of microtubule dynamic instability. This integrated approach simulates the essential physics of microtubule dynamics in a cellular environment. The model captures the structure of the microtubules as they undergo steady state dynamic instabilities in this simplified geometry, and also yields the average number, length, and cap size of the microtubules. The model achieves realistic geometries and simulates cellular structures found in degenerating neurons in disease states such as Alzheimer disease. Further, this model can be used to simulate microtubule changes following the addition of antimitotic drugs which have recently attracted attention as chemotherapeutic agents.

Designing oscillating cilia that capture or release microscopic particles.

We use computational modeling to capture the three-dimensional interactions between oscillating, synthetic cilia and a microscopic particle in a fluid-filled microchannel. The synthetic cilia are elastic filaments that are tethered to a substrate and are actuated by a sinusoidal force, which is applied to their free ends. The cilia are arranged in a square pattern, and a neutrally buoyant particle is initially located between these filaments. Our computational studies reveal that, depending on frequency of the beating cilia, the particle can be either driven downward toward the substrate or driven upward and expelled into the fluid above the cilial layer. This behavior mimics the performance of biological cilia used by certain marine animals to extract suspended food particles. The findings uncover a new route for controlling the deposition of microscopic particles in microfluidic devices.

"Bending to stretching" transition in disordered networks.

From polymer gels to cytoskeletal structures, random networks of elastic material are commonly found in both materials science and biology. We present a three-dimensional micromechanical model of these networks and identify a "bending-to-stretching" transition. We characterize this transition in terms of concentration scaling laws, the stored elastic energy, and affinity measurements. Understanding the relationship between microscopic geometry and macroscopic mechanics will elucidate, for example, the mechanical properties of polymer gel networks or the role of semiflexible network mechanics in cells.

Drug diffusion from polymer core-shell nanoparticles.

Polymer core-shell nanoparticles are attractive drug-delivery systems because the drug can be encapsulated inside the core, while the shell properties can be assigned to optimise drug-delivery needs. An elegant approach to such particles is to use polymer gels, which have swelling properties that depend upon conditions such as pH. In this way swelling of the shell, and the drug release, can be targeted to occur at the desired location. We use computer simulations to capture the deformation of polymer core-shell nanoparticles and, subsequently, the drug diffusion from the core of these structures. In particular, we investigate the effects of shell swelling on drug-release rates, where the expanding shell leaves more free space for the drug to diffuse out of the core. Furthermore, we introduce enthalpic interactions and investigate both the physical and chemical barriers to drug release. Therefore, through a combination of structural and fluid simulations we can capture the physics of polymer core-shell nanoparticles and their uses for drug delivery.

Multiscale model of miscible polymer blends in porous media: from flow fields to concentration fluctuations.

We have developed a multiscale approach for simulating the concentration fluctuations in a miscible blend subject to complex flow dynamics. We first simulate the hydrodynamics of a fluid as it flows through porous media. In particular, we monitor the velocity gradients as a function of time for a fluid "particle" as it follows a tortuous path through the system. Next, we evolve the structure factor of the spatial concentration fluctuations subject to this flow environment. The velocity gradients experienced by this fluid particle can result in elongation and rotation of the concentration fluctuations. In this manner, we couple the macroscopic flow fields in porous media with the microscopic concentration fluctuations in the polymer blend. We find a close correlation between the tortuous pathways, the velocity gradients in the fluid, and the perturbance of the structure factor from it quiescent state. Furthermore, we find that the concentrations tend to elongate towards the flow direction or at an acute angle with the flow direction.

Stress-guided self-assembly in Dutcher films.

Dutcher films consist of a layer of liquid sandwiched between two solid capping layers and can spontaneously self-assemble to form corrugated surfaces. The interplay between the attractive van der Waals forces across the film, and the elastic forces due to the deformation of the capping layers, produces well-defined periodic undulations. We show how computer simulations can capture both the formation of undulations in Dutcher films and the correct periodicity. Furthermore, we simulate Dutcher films which are either compressed or stretched, resulting in the promotion or suppression of undulation growth. In this manner, applied deformations can be shown to guide the self-assembly process in Dutcher films and result in the formation of highly oriented surface corrugations over large distances.

Structural evolution and control of Dutcher films.

We report on numerical simulations of late stage undulation growth in Dutcher films. Dutcher films are ultrathin trilayer films consisting of a fluid layer sandwiched in between two solid layers. The van der Waals forces acting across the film can result in the spontaneous formation of surface undulations and corrugations. The complex interplay between the van der Waals forces, the elastic deformation of the solid layers and the fluid dynamics of the sandwiched fluid essentially selects a wavelength of undulation which grows most rapidly. We show how the lateral deformations in the solid layers can be obtained from the elastic stretching free energy as a function of the height variations. Furthermore, these lateral deformations can be shown to contribute to a pressure normal to the film which influences the dynamics of fluctuation growth. By taking into consideration the large-amplitude elastic stretching effects we simulate the late stages of undulation growth including the contact between the upper and lower solid layers. As the area of contact between the solid layers increases the fluid is corralled into isolated pockets. Because our numerical model captures the full elasticity of the solid layers we show how internal forces can be incorporated into the system. As a demonstration, we simulate the effects of thermal mismatch between a small region of the film and the surrounding matrix and show how concentric grooves can be formed in Dutcher films.

Computational phlebology: the simulation of a vein valve.

We present a three-dimensional computer simulation of the dynamics of a vein valve. In particular, we couple the solid mechanics of the vein wall and valve leaflets with the fluid dynamics of the blood flow in the valve. Our model captures the unidirectional nature of blood flow in vein valves; blood is allowed to flow proximally back to the heart, while retrograde blood flow is prohibited through the occlusion of the vein by the valve cusps. Furthermore, we investigate the dynamics of the valve opening area and the blood flow rate through the valve, gaining new insights into the physics of vein valve operation. It is anticipated that through computer simulations we can help raise our understanding of venous hemodynamics and various forms of venous dysfunction.

Modeling the morphology and mechanical properties of sheared ternary mixtures.

Through a combination of simulation techniques, we determine both the structural evolution and mechanical properties of blends formed from immiscible ternary mixtures. In this approach, we first use the lattice Boltzmann method to simulate the phase separation dynamics of A/B/C fluid mixtures for varying compositions within the spinodal region. We also investigate the effect of an imposed shear on the phase ordering of the mixture. We assume that the fluid is quenched sufficiently rapidly that the phase-separated structure is preserved in the resultant solid. Then, the output from our morphological studies serves as the input to the lattice spring model, which is used to simulate the elastic response of solids to an applied deformation. These simulations reveal how the local stress and strain fields and the global Young's modulus depend on the composition of the blend and the stiffness of the components. By comparing the results for the sheared and unsheared cases, we can isolate optimal processing conditions for enhancing the mechanical performance of the blends. Overall, the findings provide fundamental insight into the relationship between structure, processing, and properties for heterogeneous materials and can yield guidelines for formulating blends with the desired macroscopic mechanical behavior.

Newtonian fluid meets an elastic solid: coupling lattice Boltzmann and lattice-spring models.

We integrate the lattice Boltzmann model (LBM) and lattice spring model (LSM) to capture the coupling between a compliant bounding surface and the hydrodynamic response of an enclosed fluid. We focus on an elastic, spherical shell filled with a Newtonian fluid where no-slip boundary conditions induce the interaction. We calculate the "breathing mode" oscillations for this system and find good agreement with analytical solutions. Furthermore, we simulate the impact of the fluid-filled, elastic shell on a hard wall and on an adhesive surface. Understanding the dynamics of fluid-filled shells, especially near adhesive surfaces, can be particularly important in the design of microcapsules for pharmaceutical and other technological applications. Our studies reveal that the binding of these capsules to specific surfaces can be sensitive to the physical properties of both the outer shell and the enclosed fluid. The integrated LBM-LSM methodology opens up the possibility of accurately and efficiently capturing the dynamic coupling between fluid flow and a compliant bounding surface in a broad variety of systems.

Creating structures in polymer blends via a dissolution and phase-separation process.

We show how three-dimensional structures can be formed in polymer blends from pre-existing structures. "Tape" of one polymer is inserted into a matrix of an alternative polymer to form an array of parallelepipeds. We subject this regular structure to partial dissolution in the one-phase region, before quenching the system into the two-phase region. The interplay between dissolution and phase separation can result in complex hierarchic structures. In particular, arrays of microchannels of one polymer species can be formed inside the other polymer.

Effect of hydrodynamic interactions on the evolution of chemically reactive ternary mixtures.

We investigate the structural evolution of an A/B/C ternary mixture in which the A and B components can undergo a reversible chemical reaction to form C. We developed a lattice Boltzmann model for this ternary mixture that allows us to capture both the reaction kinetics and the hydrodynamic interactions within the system. We use this model to study a specific reactive mixture in which C acts as a surfactant, i.e., the formation of C at the A/B interface decreases the interfacial tension between the A and B domains. We found that the dynamics of the system is different for fluids in the diffusive and viscous regimes. In the diffusive regime, the formation of a layer of C at the interface leads to a freezing of the structural evolution in the fluid; the values of the reaction rate constants determine the characteristic domain size in the system. In the viscous regime, where hydrodynamic interactions are important, interfacial reactions cause a slowing down of the domain growth, but do not arrest the evolution of the mixture. The results provide guidelines for controlling the morphology of this complex ternary fluid.

Using nanoparticles to create self-healing composites.

The need for viable materials for optical communications, display technologies, and biomedical engineering is driving the creation of multilayer composites that combine brittle materials, such as glass, with moldable polymers. However, crack formation is a critical problem in composites where thin brittle films lie in contact with deformable polymer layers. Using computer simulations, we show that adding nanoparticles to the polymers yields materials in which the particles become localized at nanoscale cracks and effectively form "patches" to repair the damaged regions. Through micromechanics simulations, we evaluate the properties of these systems in the undamaged, damaged, and healed states and determine optimal conditions for harnessing nanoparticles to act as responsive, self-assembled "band aids" for composite materials. The results reveal situations where the mechanical properties of the repaired composites can potentially be restored to 75%-100% of the undamaged material.

Simulating the morphology and mechanical properties of filled diblock copolymers.

We couple a morphological study of a mixture of diblock copolymers and spherical nanoparticles with a micromechanical simulation to determine how the spatial distribution of the particles affects the mechanical behavior of the composite. The morphological studies are conducted through a hybrid technique, which combines a Cahn-Hilliard (CH) theory for the diblocks and a Brownian dynamics (BD) for the particles. Through these "CH-BD" calculations, we obtain the late-stage morphology of the diblock-particle mixtures. The output of this CH-BD model serves as the input to the lattice spring model (LSM), which consists of a three-dimensional network of springs. In particular, the location of the different phases is mapped onto the LSM lattice and the appropriate force constants are assigned to the LSM bonds. A stress is applied to the LSM lattice, and we calculate the local strain fields and overall elastic response of the material. We find that the confinement of nanoparticles within a given domain of a bicontinous diblock mesophase causes the particles to percolate and form essentially a rigid backbone throughout the material. This continuous distribution of fillers significantly increases the reinforcement efficiency of the nanoparticles and dramatically increases the Young's modulus of the material. By integrating the morphological and mechanical models, we can isolate how modifications in physical characteristics of the particles and diblocks affect both the structure of the mixture and the macroscopic behavior of the composite. Thus, we can establish how choices made in the components affect the ultimate performance of the material.