We derive the coarse-grained interactions between DNA nucleotides from ab initio total-energy calculations based on density functional theory (DFT). The interactions take into account base and sequence specificity, and are decomposed into physically distinct contributions that include hydrogen bonding, stacking interactions, backbone, and backbone-base interactions. The interaction energies of each contribution are calculated from DFT for a wide range of configurations and are fitted by simple analytical expressions for use in the coarse-grained model, which reduces each nucleotide into two sites. This model is not derived from experimental data, yet it successfully reproduces the stable B-DNA structure and gives good predictions for the persistence length. It may be used to realistically probe dynamics of DNA strands in various environments at the μs time scale and the μm length scale.

The complexity of the coupling between soft particle deformation and fluid perturbation has limited studies of soft particle hydrodynamics to dilute suspensions. A hybrid Brownian dynamics-lattice Boltzmann method is presented that models nondilute soft spherical deformable particle (DP) suspensions in flow. Dependences on particle size and density are investigated for suspensions with over 100 DP. Multi-DP interactions lead to complex dependence of particle distributions on concentration and flow rate. Flow-induced DP migration toward channel center for DP in narrow channels is found. In wide channels, off-center peaks in the center of mass distribution for DP are found. The migration of DP leads to faster average speed of DP than the flow, which can be exploited for fractionating DPs of different sizes.

Nanoparticles (NP) tethered with DNA strands can self-assemble into highly organized structures through complementary bonding of base pairs. Such materials are promising building blocks for the bottom-up nanotechnology. This thesis investigates (a) the phase diagram of NP tethered with four DNA strands, (b) lattice models that reveal the insights behind the unusual phase behavior, and (c) a theoretical description for the self-assembly. All of our studies are based on a combination of theory and simulations. We report the discovery of a hierarchy of amorphous networked phases that has never been observed in other materials. The mechanism behind the multitude of phases is studied in detail using various approaches. Lastly, we present a comprehensive theoretical framework that quantitatively describes the equilibrium clustering and dynamics, as well as the self-assembly kinetics. The theoretical predictions yield striking agreement with our molecular modeling.

Nanoparticles tethered with DNA strands are promising building blocks for bottom-up nanotechnology, and a theoretical understanding is important for future development. Here we build on approaches developed in polymer physics to provide theoretical descriptions for the equilibrium clustering and dynamics, as well as the self-assembly kinetics of DNA-linked nanoparticles. Striking agreement is observed between the theory and molecular modeling of DNA-tethered nanoparticles.

Nanoparticles (NP) functionalized with single-stranded DNA (ssDNA) offer a route to custom-designed, self-assembled nanomaterials with potentially unusual properties. The bonding selectivity of DNA guarantees one-to-one binding to form double-stranded DNA (dsDNA), and an appropriate base sequence results in head-to-tail binding linking NP into networks. We explore the phase behavior and structure of a model for NP functionalized with between 3 and 6 short ssDNA through simulations of a coarse-grained molecular model, allowing us to examine both the role of the number of attached strands (valency) and their relative orientations. The NP assemble into networks where the number of NP links is controlled by the number of attached strands. The large length scale of the DNA links relative to the core NP size opens the possibility for the formation of interpenetrating networks that give rise to multiple thermodynamically distinct states. We find that the 3-functionalized NP have only a single phase transition between a dilute solution of NPs and an assembled network state. 4-Functionalized NP (with tetrahedral symmetry) exhibit four amorphous phases, or polyamorphism, each higher density phase consisting of an additional interpenetrating network. The two investigated geometries of 5-functionalized NP both exhibit two phase transitions and three amorphous phases. Like the 4-functionalized NP, the highest density phase consists of interpenetrating networks, demonstrating that regular symmetry is not a prerequisite for interpenetration to produce thermodynamically distinct phases. The width of the coexistence regions for all phase transitions increases with increasing functionality. Finally, for 6-functionalized NP with octahedral symmetry, the possibility of observing disordered phases with significantly bonded particles is preempted by the formation of ordered crystal phases. Interestingly, the extreme softness of the potential combined with the directional interaction allows for the formation of (at least) six distinct crystalline structures (i.e., polymorphism) consisting of up to six interpenetrating simple cubic lattices.

We study simple lattice systems to demonstrate the influence of interpenetrating bond networks on phase behavior. We promote interpenetration by using a Hamiltonian with a weakly repulsive interaction with nearest neighbors and an attractive interaction with second-nearest neighbors. In this way, bond networks will form between second-nearest neighbors, allowing for two (locally) distinct networks to form. We obtain the phase behavior from analytic solution in the mean-field approximation and exact solution on the Bethe lattice. We compare these results with exact numerical results for the phase behavior from grand canonical Monte Carlo simulations on square, cubic, and tetrahedral lattices. All results show that these simple systems exhibit rich phase diagrams with two fluid-fluid critical points and three thermodynamically distinct phases. We also consider including third-nearest-neighbor interactions, which give rise to a phase diagram with four critical points and five thermodynamically distinct phases. Thus the interpenetration mechanism provides a simple route to generate multiple liquid phases in single-component systems, such as hypothesized in water and observed in several model and experimental systems. Additionally, interpenetration of many such networks appears plausible in a recently considered material made from nanoparticles functionalized by single-strands of DNA.

Nanoparticles and colloids functionalized by four single strands of DNA can be thought of as designed analogs to tetrahedral network-forming atoms and molecules, with a difference that the attached DNA strands allow for control of the length scale of bonding relative to the core size. We explore the behavior of an experimentally realized model for nanoparticles functionalized by four single strands of DNA (a tetramer), and show that this single-component model exhibits a rich phase diagram with at least three critical points and four thermodynamically distinct amorphous phases. We demonstrate that the additional critical points are part of the Ising universality class, like the ordinary liquid–gas critical point. The dense phases consist of a hierarchy of interpenetrating networks, reminiscent of a woven cloth. Thus, bonding specificity of DNA provides an effective route to generate new nano-networked materials with polyamorphic behavior. The concept of network interpenetration helps to explain the generation of multiple liquid phases in single-component systems, suggested to occur in some atomic and molecular network-forming fluids, including water and silica.