Fernando Vargas Lara

Stability of DNA-linked nanoparticle crystals: Effect of number of strands, core size, and rigidity of strand attachment

Three-dimensional ordered lattices of nanoparticles (NPs) linked by DNA have potential applications in novel devices and materials, but most experimental attempts to form crystals result in amorphous packing. Here we use a coarse-grained computational model to address three factors that impact the stability of bcc and fcc crystals formed by DNA-linked NPs : (i) the number of attached strands to the NP surface, (ii) the size of the NP core, and (iii) the rigidity of the strand attachment. We find that allowing mobility in the attachment of DNA strands to the core NP can very slightly increase or decrease melting temperature T(M). Larger changes to T(M) result from increasing the number of strands, which increases T(M), or by increasing the core NP diameter, which decreases T(M). Both results are consistent with experimental findings. Moreover, we show that the behavior of T(M) can be quantitatively described by the model introduced previously [F. Vargas Lara and F. W. Starr, Soft Matter, 7, 2085 (2011)].

Stability of DNA-linked nanoparticle crystals I: Effect of linker sequence and length

The creation of three-dimensional, crystalline-ordered nanoparticle (NP) structures linked by DNA has proved experimentally challenging. Here we aim to systematically study parameters that influence the relative thermodynamic and kinetic stability of such crystals. To avoid experimental bottlenecks and directly control molecular-scale parameters, we carry out molecular dynamics simulations of a coarse-grained model in which short DNA strands (6 to 12 bp) are tethered to a NP core. We examine the influence of the number of bases per strand L, number of linking bases and the number of spacer bases s on the stability of crystal states. We also consider the effect of using a single linking NP type versus a binary linking system. We explicitly compute the free energy, entropy, and melting point TM for BCC and FCC lattices. We show that binary systems are preferable for generating BCC lattices, while a single NP type generates the most stable FCC crystals. We propose a simple model for short DNA strands that can account for TM of all our data. The model also indicates that the heat of fusion between crystal and amorphous phases grows linearly with , providing a route to maximize the relative crystal stability.

Intrinsic conductivity of carbon nanotubes and graphene sheets having a realistic geometry

The addition of carbon nanotubes (CNTs) and graphene sheets (GSs) into polymeric materials can greatly enhance the conductivity and alter the electromagnetic response of the resulting nanocomposite material. The extent of these property modifications strongly depends on the structural parameters describing the CNTs and GSs, such as their shape and size, as well as their degree of particle dispersion within the polymeric matrix. To model these property modifications in the dilute particle regime, we determine the leading transport virial coefficients describing the conductivity of CNT and GS composites using a combination of molecular dynamics, path-integral, and finite-element calculations. This approach allows for the treatment of the general situation in which the ratio between the conductivity of the nanoparticles and the polymer matrix is arbitrary so that insulating, semi-conductive, and conductive particles can be treated within a unified framework. We first generate ensembles of CNTs and GSs in the form of self-avoiding worm-like cylinders and perfectly flat and random sheet polymeric structures by using molecular dynamics simulation to model the geometrical shapes of these complex-shaped carbonaceous nanoparticles. We then use path-integral and finite element methods to calculate the electric and magnetic polarizability tensors (αE, αM) of the CNT and GS nanoparticles. These properties determine the conductivity virial coefficient σ in the conductive and insulating particle limits, which are required to estimate σ in the general case in which the conductivity contrast Δ between the nanoparticle and the polymer matrix is arbitrary. Finally, we propose approximate relationships for αE and αM that should be useful in materials design and characterization applications.

Conformational nature of DNA–grafted chains on spherical gold nanoparticles

We investigate the conformational state of a simple, coarse–grained molecular model for single–stranded DNA chains (ssDNA) grafted onto spherical symmetric gold nanoparticles (NPs) and of the grafted layer as a whole by molecular dynamic simulations. In particular, we compare the radius of gyration (Rg) of an individual grafted chain to its value in solution and we use path–integration to estimate the change δRh of the hydrodynamic radius of ssDNA–grafted NPs (Rh) from the hydrodynamic radius of the bare gold NP core (R = 5.0 nm) for a range of grafted chains (N), chain lengths (L), and persistence lengths (lp) relevant to experimental studies of these NPs. We find the ssDNA chain size is not greatly perturbed from its free solution value so that the molecular cartoon of a brush–like layer involving highly extended ssDNA chains is an unrealistic model of the interfacial structure of ssDNA–grafted NPs under the solution conditions normally investigated.

Knot Energy, Complexity, and Mobility of Knotted Polymers

The Coulomb energy EC is defined by the energy required to charge a conductive object and scales inversely to the self–capacity C, a basic measure of object size and shape. It is known that C is minimized for a sphere for all objects having the same volume, and that C increases as the symmetry of an object is reduced at fixed volume. Mathematically similar energy functionals have been related to the average knot crossing number 〈m〉, a natural measure of knot complexity and, correspondingly, we find EC to be directly related to 〈m〉 of knotted DNA. To establish this relation, we employ molecular dynamics simulations to generate knotted polymeric configurations having different length and stiffness, and minimum knot crossing number values m for a wide class of knot types relevant to the real DNA. We then compute EC for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈EC〉 is directly proportional to 〈m〉. Finally, we calculate estimates of the ratio of the hydrodynamic radius, radius of gyration, and the intrinsic viscosity of semi–flexible knotted polymers in comparison to the linear polymeric chains since these ratios should be useful in characterizing knotted polymers experimentally.

Universal interrelation between measures of particle and polymer size

The characterization of many objects involves the determination of a basic set of particle size measures derived mainly from scattering and transport property measurements. For polymers, these basic properties include the radius of gyration Rg, hydrodynamic radius Rh, intrinsic viscosity [η], and sedimentation coefficient S, and for conductive particles, the electric polarizability tensor αE and self-capacity C. It is often found that hydrodynamic measurements of size deviate from each other and from geometric estimates of particle size when the particle or polymer shape is complex, a phenomenon that greatly complicates both nanoparticle and polymer characterizations. The present work explores a general quantitative relation between αE, C, and Rg for nanoparticles and polymers of general shape and the corresponding properties η, Rh, and Rg using a hydrodynamic-electrostatic property interrelation.

Hydrodynamic radius fluctuations in model DNA–grafted nanoparticles

We utilize molecular dynamics simulations (MD) and the path-integration program ZENO to quantify hydrodynamic radius (Rh) fluctuations of spherical symmetric gold nanoparticles (NPs) decorated with single-stranded DNA chains (ssDNA). These results are relevant to understanding fluctuation-induced interactions among these NPs and macromolecules such as proteins. In particular, we explore the effect of varying the ssDNA-grafted NPs structural parameters, such as the chain length (L), chain persistence length (lp), NP core size (R), and the number of chains (N) attached to the nanoparticle core. We determine Rh fluctuations by calculating its standard deviation (σRh ) of an ensemble of ssDNA-grafted NPs configurations generated by MD. For the parameter space explored in this manuscript, σRh shows a peak value as a function of N, the amplitude of which depends on L, lp and R, while the broadness depends on R.

Topological rigidification of flexible polymers in solution

We use molecular dynamic simulations on a coarse-grained model for flexible polymers in solution to study how molecular topology affects the intrinsic rigidity of polymeric chains. In particular, we study how polymeric “topological complexity”, defined by the minimum number of crossing in knotted polymers, m and polymer functionality, f, or arm number in regular star polymers, affects the chain rigidity measured through the determination of the chain persistence length, lp. We find that increasing these topological constraints leads to a progressive increase in lp. These topologically induced changes in rigidity, which also occur in the polymer melt state, have significant relevance for understanding the miscibility of topologically constrained polymers and regulating binding strength in biological macromolecules.