By some estimates, nearly 80% of the world lives with water insecurity. Water desalination is a method of generating potable water that is free from rainfall constraints, but with current membranes, desalination is an expensive and energy intensive process. Two-dimensional crystals, like graphene, hold unique promise for ultrahigh throughput semipermeable membranes in water desalination, but the water transport mechanisms through them remain poorly understood.
Using porous graphene as both a specific model system and an analog to other two-dimensional crystals, our group has developed theory, simulation, and analysis techniques to understand how hydrophobicity impacts aqueous transport in these materials. The central problem that theory faces is one of vastly different competing scales. The gradients in pressure and density that drive flow are macroscopic, but the pores embedded in sheets that exclude ions with high fidelity are so small that they only admit about two water molecules at a time. Thus the motion of a few molecules bottlenecks the macroscopic current. This disparity in interacting scales challenges continuum hydrodynamic models, which are trustworthy away from equilibrium but are dubious at atomic length scales.
Drawing on foundational principles in equilibrium statistical mechanics, loosely speaking, “maximal freedom under minimal constraint,” we derived classical equations of motion for atomistic molecular dynamics simulations that are consistent with dynamical constraints on both the kinetic temperature and mass current. Based on the constraint methodology, we call this method “Gaussian Dynamics.” Drawing on our previous work that showed how electrical doping can tune the hydrophobic effect on graphene, a prediction recently verified in experiments, we used Gaussian Dynamics to examine the hydrophobic effect for water passing through nanoscale pores in doped graphene. In applications to water desalination, one might expect that a more hydrophilic crystal would be preferable to a hydrophobic one because a hydrophobic crystal exhibits a wetting penalty. But a surprising conclusion of our work is that the thermodynamics of the hydrophobic effect give an incomplete description of water transport dynamics, and that hydrophobicity can both help and hinder water transport through two-dimensional crystals. Small changes in the intermolecular interactions between the sheet and the water molecules, both in form and strength, change transport mechanisms and rates for aqueous transport qualitatively.
Our Gaussian Dynamics method is quite general and allows access to a host of problems where both hydrodynamic and atomistic degrees of freedom are important but have remained difficult to address at microscopic scales using computer simulation. We are currently using Gaussian Dynamics to study capacitive desalination, crystal nucleation under fluid flow, and friction-induced melting of ice.
Novel approaches in solar energy conversion and storage require theories capable of describing electronic systems, sometimes strongly interacting, in a dissipative condensed phase environment. In contrast to the Marcus scenario, many of these cases cannot be described as single electron transfer events. One important example is singlet fission, which is a photo-induced interconversion process where one singlet converts into two triplet excitons. My group developed the first microscopic quantum relaxation theory of singlet fission for dimers in the condensed phase. While our work was so early in the field that electronic structure theory had not yet caught up, the model we articulated underpins the most successful theories of singlet fission in the condensed phase. In separate work, we studied how the polarity and disorder of a surface that adsorbs chromophore molecules stabilizes the intermolecular dimer structures thought to promote efficient singlet fission in dye-sensitized solar cells.
Until very recently, singlet fission was observed to be more efficient in crystalline phases than in analog molecular dimers. To understand this, my group developed a theory of singlet fission in ideal crystals. This work shows how collective effects in crystals that have no counterpart in dimers, like exciton localization, can lead to efficient singlet fission in crystals. This work also applies recent advances in quantum information theory to quantify the role of entanglement and statistical dependence between the two triplet excitons that are products of the fission process.
Strong interactions between electrons can lead to interesting outcomes that are extraordinarily challenging to describe theoretically. An example is in carbon nanotubes, which are essentially one-dimensional objects. In metallic nanotubes, this low dimensional confinement forces electrons to interact so strongly that they form a novel phase of quantum matter called a Luttinger liquid. The Luttinger liquid theory predicted several results in electron transport that were confirmed by experiments. But because the theory was not straightforward to apply to a semiconducting system, it was virtually absent in discussions of optical phenomena. We extended the Luttinger liquid theory for transport to describe the optical excitations in semiconducting carbon nanotubes by developing a nonperturbative quantum field theory. Our theory shows how the excitons that dominate the optical spectra in carbon nanotubes can be reduced to excitations of noninteracting harmonic oscillators. When compared to experiment, the theory nearly quantitatively predicts the scaling law between the optical transition energy and the tube radius for dozens of measured transitions. This work also addresses how multiple-exciton generation, an analog to singlet fission in carbon nanotubes, scales with nanotube aspect ratio. More fundamentally, our work showed that the Luttinger liquid is a fragile state that collapses even in a weakly semiconducting nanotube. The excitations of the electron density lose the long-range character of the Luttinger liquid and become particle-like, rationalizing why more orthodox numerical electronic structure methods based on quasiparticle theories, like the GW approximation and Bethe-Salpeter equation, are applicable to semiconducting carbon nanotubes.
In its original form, Gibbs-Boltzmann statistical mechanics cannot describe “active matter,” such as living, driven, or self-propelled systems. Contemporary models of swarming and flocking behaviors, where self-propelled objects like rods spontaneously form patterns, are conceptually simple but practically complicated. While these models can imitate pattern formation they do a poor job explaining how or why it occurs.
To what extent do flocking transitions have an underlying thermodynamic origin and to what extent is the transition to a flocked state a purely dynamical phenomenon? To help answer this question, my group devised a simple two-dimensional lattice model, which we called the “panic model,” that displays robust spontaneous ordering even though it is a thermodynamic ideal gas. Our work shows that flocking transitions can be purely dynamical in nature even though the phenomenology of the pattern formation mechanisms, like nucleation and growth, bear striking resemblance to those encountered in thermodynamic phase transitions. In the panic model the irreversible spontaneous flocking transitions derive from the violation of detailed balance for active systems.
Glasses and active systems form the bookends of dynamically arrested states in nonequilibrium systems, but both exhibit myriad stable states that are kinetically estranged from one another. We thought it would be interesting to study a mixture of the two systems, so we generalized the canonical Sherrington-Kirkpatrick spin glass model and analyzed it by modifying the replica trick. Perhaps most interestingly, there is a region in the phase diagram where the interactions between the inactive and active phase can overpower the frustrated interactions of the glassy inactive state. When this happens, the glass melts under cooling. We are currently looking to see if this phenomenon, called reentrance, occurs in molecular analogs by designing molecular dynamics simulations for mixtures of active and glassy colloids. Our work shows that the interactions between frustrated and active phases may provide subtle, unusual, and previously unanticipated ways for systems to alter their mechanical properties by amplifying small fluctuations in the active phase. The results of our efforts in this area may well have applications to materials science and to cellular and tissue bioengineering.