We are a computational and theoretical chemistry research group in the Department of Chemistry at the University of Wisconsin-Madison and a part of the Theoretical Chemistry Institute. Our interests lie in understanding the structure and dynamics of complex fluids in solution and in complex environments using the methods of equilibrium and non-equilibrium statistical mechanics. More specifically, our current research focuses on using liquid state theory, computer simulation, and machine learning to understand the structure, dynamics, and phase behavior of macromolecular liquids.

We use two complementary approaches: a phenomenological approach where we devise simple models to obtain insight into complex behavior and a bottom-up approach where we parameterize atomistic force-fields, then coarse-grain these to obtain realistic but efficient models for the molecular simulation of complex fluids. The main computer simulation techniques we employ are molecular dynamics, Brownian dynamics, and Monte Carlo methods. Our research is interdisciplinary, and we collaborate with experimentalists in the department as well as scientists in chemical engineering, physiology, and food science.

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Multi-scale modeling: From atoms to the continuum

Multi-scale modeling

Computational studies play an important role in our understanding of complex fluids. They can provide physical insight and molecular information that is hard to obtain from experiment. The most important part of a computer simulation is the choice of molecule model. In classical models each molecule is represented by a collection of sites.  In an atomistic model each site represents a single atom, in a united atom model each site represents one heavy atom and associated hydrogen atoms, and in coarse-grained models each site represents several heavy atoms.

The choice of model depends on the problem and the relevant physics.  More detailed models more faithfully represent the physical system.  However, they are computationally intensive and cannot efficiently sample all configurations.  The process of coarse-graining results in a hierarchy of models that sample increasingly more efficiently, but are less representative of the system, and are likely to be less transferable to other conditions or molecules.

Force Field Development

The starting point is the development of a fully polarizable atomistic model for the system.  In our group we use symmetry adapted perturbation theory (SAPT) based on quantum density functional theory (DFT) as a starting point and then empirically introduce additional sites and interactions to reproduce the behavior of hydrogen bonding systems.  DFT-SAPT has unique advantages for force-field development, including its inherent energy decomposition and prediction of non-covalent interaction energies with comparable accuracy to coupled-cluster.

The robust and transferable character of the SAPT force fields is largely due to the parameterization methodology, in which all asymptotic interaction parameters are obtained from monomer properties.  The static polarizabilities are converted to a shell-model (Drude oscillators), for ease of implementation in standard MD simulation packages.  Dispersion coefficients are then generated from the frequency-dependent polarizabilities, and the remaining force field parameters, namely short-range terms describing exchange-repulsion and charge penetration (and potentially charge-transfer), are fit to the residual of the asymptotic force field description and SAPT intermolecular interaction energies of dimer species.

We make adjustments to the SAPT force field protocol to treat hydrogen bonding systems.  We add additional sites to better represent the angular dependence of the interaction, adjust the polarizability to reproduce crystal properties, and adjust short-ranged interactions to better reproduce the liquid structure as observed in first principles molecular dynamics simulations.  The resulting approach gives excellent results, for example, for urea water mixtures.

Hierarchical Coarse-Graining

We develop a hierarchy of coarse-grained models using a “top-down” approach.  We vary the polarization and atomistic resolution of functional groups and parameterize the models using SAPT to the same DFT calculations.   The approach has been successful in the study of room temperature ionic liquids.

BMW-MARTINI: Bottom-Up Coarse-Graining

An alternative approach is to start with a heuristic simpler representation and adjust the force fields to reproduce experimental data.  In the MARTINI approach 4 heavy atoms are mapped to a single site with the parameters obtained by comparing to experiment.  Our group has developed a coarse-grained force field for simulations of lipids, peptides, and polymers.  The basis is the big multipole water (BMW) model.

The new BMW-MARTINI force field reproduces many fundamental membrane properties and also yields improved energetics (when compared to the original MARTINI force-field) for the interactions between charged amino acids with lipid membranes, especially at the membrane/water interface. The simulations emphasize the importance of a reasonable description of the electrostatic properties of water in coarse-grained simulations.

Machine learning

Machine Learning

We use a number of supervised and un-supervised machine learning (ML) methods to study the phase behavior of complex fluids and the conformational properties of macromolecules.

Convolutional neural network

An example is the convolutional neural network (CNN) model for the phase behavior of the Widom Rowlinson mixture and symmetric polymer blends.  In our implementation the co-ordinates are mapped onto a grid and the CNN is used to classify the configuration.  The neural network is trained with mixed and phase separated configurations (at high and low temperature respectively).  At other temperatures the network is used to predict the probability that a configuration is mixed.  The transition temperature is when this probability is 0.5.

The method is quantitatively accurate when compared to traditional simulations, and we have used it to obtain the phase diagram of polymers in ionic liquids.

Unsupervised and supervised methods

The CNN method described above is a supervised method: The network is trained on known phase points and used to classify unknown configurations.  This is similar to how one would determine if a picture was that of a dog or cat, based on a training of the net on known pictures.  Unsupervised methods do not require training but rather focus on how correlations within the dataset change with conditions, such as temperature.  We use both classes of methods in our work.

Principal Component Axis (PCA) is unsupervised method that does not involve any parameters or fitting.  It is used to reduce the dimensionality of the dataset by considering the so-called “principal components”.   A large data set, such as the positions of all molecules is mapped onto two linear and uncorrelated variables.  The t-stochastic neighbor embedding (tSNE) method is similar to the PCA but uses a stochastic algorithm to cluster points according to their distance to other points.

For the two-dimension Ising model, both unsupervised and supervised methods are accurate for the critical point.  In this model, each lattice point contains a spin that can take on values of either +1 or -1.  If neighboring spins have the same value, it contributes -J to the energy.  At high temperatures, the system is disordered, and it undergoes a second order phase transition at a reduced temperature of T=2.269.

The table below shows that all the methods are accurate, but the unsupervised methods are the most reliable.

We are using these methods to study the phase behavior in other systems, as well as the conformational transitions in macromolecules and the growth of dendrites in Lithium metal batteries.

Polyelectrolytes and Coacervates

Polyelectrolytes and Polymer Coacervates

Polyelectrolytes are an important and interesting class of soft matter. Their fundamental interest arises from the fascinating range of properties they can display.  For example, single polyelectrolyte chains are predicted to display a wide range of conformations including rods, globules, pearl-necklace structures, torii, and helices depending on the balance between electrostatic and solvent induced interactions and the local chemistry of the molecules.  Their practical importance arises from the large number of applications; the worldwide production of super-absorbent polymers alone was 850000 metric tons in 1999.  They are also important as biological molecules such as proteins, sugars, and nucleic acids. The study of polyelectrolytes therefore spans diverse areas and has seen active research

Polymer coacervates are composed of charged polymers (polyions), usually one positively charged species and one negatively charged species, their associated counterions, and added salt. They display liquid-liquid phase separation that is affected by many factors such as ionic strength, pH, the molecular weight of the polyions, and temperature. Coacervates can also be formed with protein/polymer and colloid/polymer mixtures, and with polyampholytes.

Coacervates have generated interest in various fields because of their diverse applications in coatings, adhesives, drug carriers, and functional membranes, where both phase separation and self-assembly play an important role.  The drive to create hybrid materials requires a chemically detailed understanding of the fundamental interactions and quantitative descriptions of, for example, the concentrations of the complex and supernatant solution, and conformational properties of the polymers.

Coacervates are also of biological importance.  Proteins and nucleic acids undergo liquid- liquid phase separation in cells and form assemblies or condensates that function as membrane-less organelles in cells. These organelles, such as nucleoli, Cajal bodies, and stress granules, have been implicated in a number of biological processes such as gene regulation, and signal transduction. These micron-sized spherical “droplets” are found throughout the cell and can concentrate nucleic acids and proteins, the latter in a sequence dependent fashion. It has also been suggested that they might play a role in the origin of life, because these droplets can form in the absence of lipids, and the nucleic acids could have promoted catalysis in the early universe.

We are studying polyelectrolyte solutions and polymer coacervates using computer simulations on multiple scales, as well as liquid state theory (integral equations and classical density functional theory).  Studying the same system at several levels of resolution allows us to reach long lengthscales and timescales while validating results at lower resolution by comparing to those at higher resolution.

A widely studied polyelectrolyte solution is sodium polystyrene sulfonate (NaPSS) in water.  One can think of several resolutions of models for this system.  The model that most faithfully represents the real geometry is that atomistic model.  In this model all the atoms of the polymer, as well as counterions and water molecules are represented as sites.  Simulations using this model are very computationally intensive, however, and not feasible for long chains.  The MARTINI coarse-grained model groups four water molecules into a single site.  In the traditional MARTINI approach, four heavy atoms are grouped into a single site, but for PSS we choose one site for the backbone, three sites for the ring, and one for the sulfonate group.

There are some surprises at this level of modeling.  For example, a single PSS chain is rod-like when all monomers are sulfonated (f=1) as expected, but collapses into a cylinder, not sphere, when the degree of sulfonation is decreased.

Further simplifications including replacing the styrene ring with a rigid bond, and by modeling the entire polymer as a linear chain.

Polymer coacervates form when two species of opposite charge are mixed. Of interest in this case is the phase behavior, conformational properties, and dynamic properties of the mixture.

Electrolytes for Lithium Battery Applications

Electrolytes for Lithium battery applications

Improving lithium-ion battery performance is of technological importance due to increased demand for consumer electronics and the increasing electrification of automobiles.  Understanding the effect of chemical detail on the performance is of fundamental interest because the only design parameters are the solvent and anion type.  Solvents for battery electrolytes should have a large dielectric constant, to promote salt dissociation, and low viscosity to increase ion diffusion.  Mixtures of carbonate molecules have these characteristics.  A number of salt species have been considered as potential candidates for battery electrolytes. Lithium bis(trifluoromethane) sulfonimide (TFSI) is a promising ion, because it is electrically stable and has a large conductivity.  However, the chemically similar trifluoromethanesulfonate ion (OTf) does not provide the necessary performance as an electrolyte.  In our group we are using computer simulation of atomistic models to test various candidates for solvent and anion for battery applications.

A challenging and longstanding problem is the formation of Lithium dendrites in batteries.  We are using very coarse models in an effort to elucidate the general principles behind dendrite formation and growth.  In a simple model where the Lithium ions are spheres, and the rest of the electrolyte is a continuum we find that the important effects are due to the self-diffusion constant and the local electric field.   The dendrites transform from a cauliflower to broccoli shape as the diffusion constant and electric field decrease.  We are working towards obtaining a molecular explanation by connecting these studies to the simulation studies using more detailed molecular models.

Ionic liquids

Room temperature ionic liquids and deep eutectic solvents

The behavior of polymers is complex solvents, such as room temperature ionic liquids or deep eutectic solvents, is interesting from both a fundamental and practical perspective.   The fundamental interest arises from the fascinating sensitivity of polymer behavior to the solvent conditions.  The practical interest arises from the possibility of using the polymer as a scaffold for the working fluid solvent, or from the possibility of fabricating nanostructured materials by tuning the solvent properties.

Ionic liquids (ILs) are usually composed of a large organic cation and a small organic or inorganic anion and are liquid at room temperature (hence they are often referred to as room temperature ionic liquids or RTILs).  They possess a number of interesting and important physical properties such as low volatility, non-flammability, high conductivity, and thermal and chemical stability.  They have generated considerable excitement for their varied potential applications, as solvents for synthesis and catalysis, as electrolytes, as media for separations, as sorption media for gas absorption, and as lubricants.  The fundamental interest and technological importance of ionic liquids has resulted in an exponential growth in studies devoted to understanding their physical chemistry.  A widely studied example of an ionic liquid is 1-Butyl-3-methylimidazolium tetrafluoroborate ([BMIM][BF4]).

Deep eutectic solvents (DES) are obtained via the complexation of a quaternary ammonium salt with a hydrogen bond donor.  This results in a depression of the freezing point similar to what is seen in eutectic mixtures of metals.  A classic DES, called reline, is a mixture of choline chloride (ChCl) and urea.  ChCl and urea have melting points of 302oC and 133oC, respectively, but a 1:2 molar ratio (reline) has a melting point of 12oC3a.  DESs have many of the properties of ILs including non-volatility, conductivity, and biodegradability.  They do not suffer from toxicity and cost issues.    Many DES are obtained from natural sources; ChCl is extracted from biomass and used as an additive in chicken feed. reline costs approximately $4/kg.  This is much cheaper than the ionic liquid [BMIM][BF4], which costs $7000/kg.

Force field development

In our group, we have developed a first-principle, physically motivated force field for [BMIM][BF4], reline, and the polyethylene oxide (PEO) based on symmetry-adapted perturbation theory.  For BMIM][BF4], the predictions (from molecular dynamics simulations) of the liquid density, enthalpy of vaporization, diffusion coefficients, viscosity, and conductivity are in excellent agreement with experiment, with no adjustable parameters.  The explicit energy decomposition inherent in the force field enables a quantitative analysis of the important physical interactions in these systems.  We find that polarization is crucial and there is little evidence for charge transfer.  We also argue that the often-used procedure of scaling down charges in molecular simulations of ionic liquids is unphysical for [BMIM][BF4].

We make adjustments to the SAPT force field protocol to treat hydrogen bonding systems such as DES.  We add additional sites to better represent the angular dependence of the interaction, adjust the polarizability to reproduce crystal properties, and adjust short-ranged interactions to better reproduce the liquid structure as observed in first principles molecular dynamics simulations.  The resulting approach gives excellent results, for example, for urea water mixtures.

We develop a hierarchy of coarse-grained models using a “top-down” approach.  We vary the polarization and atomistic resolution of functional groups and parameterize the models using SAPT to the same DFT calculations.   The approach has been successful in the study of room temperature ionic liquids.  A series of coarse-grained models are shown below where the orange sites are Drude particles (for polarizability) and grey sites are hydrogen atoms.  The united atom representation (UA_AA) is as accurate as the fully polarizable atomistic model (AA_AP) while being an order of magnitude more computationally efficient.

Conformational properties and phase behavior

The UA_AA model allows one to perform multi microsecond molecular dynamics simulations. This is necessary because the conformational relaxation correlation times are of the order of 100 ns.  The average conformational properties are in good agreement with experiment and the simulations provide further insight.  For example, there are two conformational motifs in PEO corresponding to ring-like (crown ether) and extended structures.

We have used a deep neural network model to obtain the phase behavior of PEO in various ionic liquids,

Ongoing work involves study the behavior of a variety of polymers in various ionic liquids with an aim of obtaining optimal electrolytes for battery applications.