Research Interests

My research efforts focus on understanding processes in complex soft materials. In particular, I am interested in pattern and shape formation in multi-components solid and liquid membranes and self-assembly of complex, nanocomposite materials at nano-scales.
I have an extensive experience with molecular dynamics and Monte Carlo methods and scientific software development. Part of my research is devoted to the development of new simulation techniques and their implementation on specialized, high performance hardware, like modern graphics cards (scientific GPU programming).

Research Highlights

DNA-driven assembly of nanoparticles

Over past decade there has been a tremendous development in the field of guided assembly of nano-composite materials. DNA molecules have been extensively used in this process for their controllable selectivity in binding and their biocompatibility. With this bottom-up approach, spherical nucleic acid gold nanoparticle conjugates can be used as artificial "atoms", where the oligonucleotides connecting the nanoparticles are “chemical bonds” that can be used to create novel one-, two-, and three-dimensional superlattices. We use molecular dynamics simulations to study the crystallization of spherical nucleic-acid (SNA) gold nanoparticle conjugates, guided by sequence-specific DNA hybridization events. Binary mixtures of SNA gold nanoparticle conjugates (inorganic core diameter in the 8–15 nm range) are shown to assemble into BCC, CsCl, AlB2, and Cr3Si crystalline structures, depending upon particle stoichiometry, number of immobilized strands of DNA per particle, DNA sequence length, and hydrodynamic size ratio of the conjugates involved in crystallization. These data have been used to construct phase diagrams that are in excellent agreement with experimental data from wet-laboratory studies.

Curvature-driven shapes of liquid vesicles

We study closed liquid membranes that segregate into three phases due to differences in the chemical and physical properties of its components. The shape and in-plane membrane arrangement of the phases are coupled through phase-specific bending energies and line tensions. We use simulated annealing Monte Carlo simulations to find low-energy structures, allowing both phase arrangement and membrane shape to relax. The three-phase system is the simplest one in which there are multiple interface pairs, allowing us to analyze interfacial preferences and pairwise distinct line tensions. We observe the system's preference for interface pairs that maximize differences in spontaneous curvature. From a pattern selection perspective, this acts as an effective attraction between phases of most disparate spontaneous curvature. We show that this effective attraction is robust enough to persist even when the interface between these phases is the most penalized by line tension. This effect is driven by geometry and not by any explicit component-component interaction.

Coarse-grained simulations of charged lipid bilayers

By combining Molecular Dynamics simulations and analytical arguments we investigate the elastic properties of charged lipid bilayers. We show that electrostatic interactions between the head groups can lead to solidification of the lipid bilayer that would otherwise be in a liquid state if the charges were absent. All elastic parameters of the bilayer such as the bending rigidity and the two-dimensional bulk modulus and Young's modulus are found to depend on the values of the charges assigned to the lipid head groups. To extract Young's modulus and bulk modulus we fit the Molecular Dynamics data to a standard elastic model for lipid bilayers. Moreover, we analytically obtain the dependence of the Young's modulus on the relative strengths of electrostatic and van der Waals interactions in the zero temperature limit.

  • R. Sknepnek, G. Vernizzi, M. Olvera de la Cruz
    Charge renormalization of bilayer elastic properties
    submitted to J. Chem. Phys. (2012)

Shapes of multicomponent elastic membranes

Membranes are an essential part of all biological systems. Most notable examples include the cell membrane, a complex barrier that separates interior of a cell from its environment, the nuclear envelope, a thin layer encompassing nuclei of all eukaryotic cells, the mitochondrial membrane, etc. At physiological conditions, lipid membranes are typically in a liquid state, that is, lipid molecules are mobile and diffuse within the bilayer. Such membrane cannot sustain a shear deformation. However, if the membrane is cooled below gelation temperature or cross linked via suitable polymerization technique, it crystalizes into an essentially two-dimensional solid. Resistance to shear results in unique physical properties, central to a number of biological processes and of potential importance for nano-technology.
Shape of a crystalline vesicle is primarily determined by the interplay of two parameters, bending rigidity, i.e., resistance of the membrane to bend, and the Young modulus, i.e., its resistance to stretch. In the regime of strong bending rigidity and low Young modulus a homogeneous vesicle will be spherical, while for large Young modulii and low bending, the vesicle will buckle into an icosahedral shape. Biological membranes are rarely homogeneous and are rather built of components with very different elastic properties. We study the shape of vesicles made of two different components with very different elastic properties. Depending on the relative concentration of two components and the strength of line tension between them, we find a very rich set of shapes, very different from spheres and icosahedra observed in single-component systems.

Charge-driven collapse of nano-cages

Long-range nature of electrostatic forces can have profound effects on the shape and properties of nano-size elastic containers, like nanocages. Due to their small size, electrostatic interaction is strong over distances comparable to the cage radius and can lead to drastic changes of the shape, including the total collapse of the structure. Using Monte Carlo simulations, we demonstrate that small charged nanocages can undergo reversible changes of shapes by modifying the ionic conditions including salt concentration, pH, and dielectric permittivity of the medium. We analyze structures with various charge stoichiometric ratios. At zero or low charge densities, the shape of the cage is determined by its elastic properties, and the surface charge pattern is dictated by the globally fixed geometry. As the charge density per molecule increases, the shape is strongly affected by the electrostatic forces. In this regime, the shape of the nanocage is controlled by the charge distribution.

Numerical simulations on the GPUs

Ever-growing demand for realistic video games triggered a rapid development of highly sophisticated, inexpensive graphics cards. These devices are designed to perform an enormous amount of computations and easily reach floating point speeds of 1TFLOPS (1012 floating point operations per second). Recently, this computational power has become available for scientific computations. Most notable example is molecular dynamics, for which GPU implementations have been reported with speedups in excess of 100 times compared to the standard CPU codes. A highly parallel architecture of modern graphics processors requires existing methods to be redesigned and new algorithms to be developed in order to fully harvest the computational power of the device.
We have recently implemented in the HOOMD Blue graphics card molecular dynamics package a long-range electrostatic interaction method based on the orientation-averaged Ewald sum scheme, introduced by Yakub and Ronchi. Our implementation reaches a speedup of up to 80 times compared to an optimized CPU version of the traditional Ewald sum available in commonly used packages, like LAMMPS. Thermodynamic and structural properties of monovalent and divalent hydrated salts in bulk are calculated for a wide range of ionic concentrations. An excellent agreement between the two methods was found at the level of electrostatic energy, heat capacity, radial distribution functions, and integrated charge of the electrolytes.

Binding of Aniline Ligands and CdSe Quantum Dots

Using 1H NMR spectroscopy we measured the equilibrium constants for the solution-phase binding of two para-substituted aniline molecules (R-An), p-methoxyaniline (MeO-An) and p-bromoaniline (Br-An), to colloidal 4.1-nm CdSe quantum dots (QDs). Changes in the chemical shifts of the aromatic protons located ortho to the amine group on R-An were used to construct a binding isotherm for each R-An/QD system. These isotherms fit to a Langmuir function to yield Ka, the equilibrium constant for binding of the R-An ligands to the QDs; Ka ≈ 150 M-1 and Gads ≈ -19 kJ/mol for both R = MeO and R = Br. 31P NMR indicated that the native octylphosphonate ligands (OPA), which, by inductively-coupled plasma atomic emission spectroscopy cover 90% of the QD surface, are not displaced upon binding of R-An. The MeOAn ligand quenches the photoluminescence of the QDs at much lower concentrations than does Br-An; the observation, therefore, that Ka,MeO-An ≈ Ka,Br-An shows that this difference in quenching efficiencies is due solely to differences in the nature of the electronic interactions of the bound R-An with the excitonic state of the QD.
Without any attraction,the native OPA ligands would tend to maximize their entropy and form a uniform, approximately 1.5-nm thick brush-like layer. In order to reach the QD surface, ligands have to diffuse through the OPA coating, so their ability to bind is suppressed. As the hydrophobicity of the OPA ligands is increased, OPA chains cluster into bundles. This process involves a loss of entropy that is compensated by the enthalpic stabilization gained through a reduction of contact with the solvent. Regions between separate bundles open up, revealing surface sites that are now accessible to the R-An molecules.

Nanoparticle assembly via functionalized triblocks

Triblock coplymers are made by joing polymers of two different types in a structure AnBmAn, where n and m are degrees of polymerization of polymers A and B respectively. Triblocks can be modified by covalently attaching functional groups with affinity for nanoparticles. By controlling the affinity for nanoparticles functiolaized triblock copolymers can be used to control self-assembly of nanoparticles into a number of two and three dimensional ordered structures. Using coarse grained molecular dynamics simulations we show that under reasonable assumptions about the coplymer/nanoparticle interaction one could realize a large number of stable ordered structures, including unusual square and bicontinuous triply periodic (gyroid) orderings. Our simulations prove that in principal functionalized block copolymers can provide a simple and robust tool to control self-assembly at nanometer length scales.

Older project in hard condensed matter theory

Multiband superconductivity

Recent discovery of superconductivity in FeAs based compounds has attracted a lot of attention due to its rather large transition temperature. Although possible, it is unlikely that the superconducting pairing is caused by typical electron-lattice interaction responsible for the conventional superconductivity. Observation of antiferromagnetic ordering in undopped systems at ambient pressure suggest that spin fluctuations might be the primary mechanism of superconductivity in these compounds. The glue that keeps Cooper pairs together is provided by bosonic collective paramagnon excitations of the electron liquid, a role played by phonons in the conventional superconductivity. Nuclear magnetic resonace experiments indicate existence of nodes in the superconducting gap, while angle resolved photoemission spectroscopy find nodeless, weakly unisotropic gap at the Fermi surface. This suggests that there are multiple gap values originating in different electron bands. Using many-body fluctuation exchange (FLEX) calulation we determine the anisotropy of the spin fluctuation induced pairing gap on the Fermi surface of the FeAs based superconductors as function of the exchange and Hund's coupling J.

Universality of Mott transitions

Band theory of solids predicts that materials with a single electron per unit cell are metals. However experiments show that in general this is not the case. There are two competing energy scales, on-site Coluomb repulsion U, and kinetic energy represented by the bandwidth W. Coulomb repulsion prefers configurations with single electron site occupancy, while kinetic part prefers electrons hopping between sites. For U less that some critical value Uc, knetic term dominates and material is a metal. If the on-site Coloumb repulsion reaches the critical value, it becomes energetically unfavorable for electrons to move, and material is an insulator. This metal-insulator phase transition is known Mott transition. At sufficiently high temperatures, when no symmetry is broken, the Mott transition is characterized by paramagnetic insulating and metallic phases, whose coexistence terminates at a second-order critical point. In this work we explain in a consistent manner the set of seemingly conflicting experiments on the finite temperature Mott critical point, and demonstrate that the Mott transition is in the Ising universality class.