Paul N. Patrone

Kilohertz Rotation of Nanorods Propelled by Ultrasound, Traced by Microvortex Advection of Nanoparticles

We measure the microvortical flows around gold nanorods propelled by ultrasound in water using polystyrene nanoparticles as optical tracers. We infer the rotational frequencies of such nanomotors assuming a hydrodynamic model of this interaction. In this way, we find that nanomotors rotate around their longitudinal axes at frequencies of up to ≈ 2.5 kHz, or ≈ 150 000 rpm, in the planar pressure node of a half-wavelength layered acoustic resonator driven at ≈ 3 MHz with an acoustic energy density of <10 J·m(-3). The corresponding tangential speeds of up to ≈ 2.5 mm·s(-1) at a nanomotor radius of ≈ 160 nm are 2 orders of magnitude faster than the translational speeds of up to ≈ 20 μm·s(-1). We also find that rotation and translation are independent modes of motion within experimental uncertainty. Our study is an important step toward understanding the behavior and fulfilling the potential of this dynamic nanotechnology for hydrodynamically interacting with biological media, as well as other applications involving nanoscale transport, mixing, drilling, assembly, and rheology. Our results also establish the fastest reported rotation of a nanomotor in aqueous solution.

Bayesian calibration of coarse-grained forces: Efficiently addressing transferability

Generating and calibrating forces that are transferable across a range of state-points remains a challenging task in coarse-grained (CG) molecular dynamics. In this work, we present a coarse-graining workflow, inspired by ideas from uncertainty quantification and numerical analysis, to address this problem. The key idea behind our approach is to introduce a Bayesian correction algorithm that uses functional derivatives of CG simulations to rapidly and inexpensively recalibrate initial estimates f0 of forces anchored by standard methods such as force-matching. Taking density-temperature relationships as a running example, we demonstrate that this algorithm, in concert with various interpolation schemes, can be used to efficiently compute physically reasonable force curves on a fine grid of state-points. Importantly, we show that our workflow is robust to several choices available to the modeler, including the interpolation schemes and tools used to construct f0. In a related vein, we also demonstrate that our approach can speed up coarse-graining by reducing the number of atomistic simulations needed as inputs to standard methods for generating CG forces.

Modeling line-edge roughness in lamellar block copolymer systems

Block copolymers oer an appealing alternative to current lithographic techniques with regard to fabrication of the next generation micro-processors. However, if copolymers are to be useful on an industrial manufacturing scale, they must meet or exceed lithography specications for placement and line edge roughness (LER) of resist features. Here we discuss a eld theoretic approach to modeling the LER of lamellar microdomain interfaces in a strongly segregated block copolymer system; specically, we derive a formula for the LER as a functions of the Flory Huggins parameter and the index of polymerization N. Our model is based on the Leibler-Ohta-Kawasaki energy functional. We consider a system with a nite number of phase separated microdomains and also show how the LER depends on distance of the microdomain interface from the system boundary. Our results suggest that in order to meet target LER goals at the 15 nm, 11 nm, and 6 nm nodes, must be increased by a factor of at least 5 above currently attainable values.

Beyond histograms: Efficiently estimating radial distribution functions via spectral Monte Carlo

Despite more than 40 years of research in condensed-matter physics, state-of-the-art approaches for simulating the radial distribution function (RDF) g(r) still rely on binning pair-separations into a histogram. Such methods suffer from undesirable properties, including subjectivity, high uncertainty, and slow rates of convergence. Moreover, such problems go undetected by the metrics often used to assess RDFs. To address these issues, we propose (I) a spectral Monte Carlo (SMC) quadrature method that yields g(r) as an analytical series expansion and (II) a Sobolev norm that assesses the quality of RDFs by quantifying their fluctuations. Using the latter, we show that, relative to histogram-based approaches, SMC reduces by orders of magnitude both the noise in g(r) and the number of pair separations needed for acceptable convergence. Moreover, SMC reduces subjectivity and yields simple, differentiable formulas for the RDF, which are useful for tasks such as coarse-grained force-field calibration via iterat...

Connection of Kinetic Monte Carlo Model for Surfaces to One-Step Flow Theory in 1+1 Dimensions

The Burton--Cabrera--Frank (BCF) theory of step flow has been recognized as a valuable tool for describing nanoscale evolution of crystal surfaces. We formally derive a single-step BCF-type model from an atomistic, kinetic Monte Carlo (KMC) model of a crystal surface in 1+1 dimensions without external material deposition. Through an averaging procedure, consistent with Boltzmann statistics, we introduce definitions of the continuous quantities of the BCF theory, i.e., the step position and density of adsorbed atoms (adatoms), as expectation values taken over the discrete probabilities of the KMC model. The equations of our BCF-type model describe the time evolution of these expectation values. A central idea of our approach is to exploit the observation that the number of adatoms on a surface is typically small at experimentally relevant temperatures. Accordingly, we (i) show that our BCF-type theory arises from a KMC model in which only one adatom is allowed to move, and (ii) characterize corrections to ...

Block-copolymer healing of simple defects in a chemoepitaxial template

Using the Leibler-Ohta-Kawasaki (LOK) phase-field model of block copolymers (BCPs), we characterize how a chemoepitaxial template with parallel lines of arbitrary width affects the BCP microdomain shape. We apply boundary conditions that account for the interactions of the polymers with the templated substrate and a neutral top-coat. We derive formulas for the monomer density and the microdomain interface profile of periodic, lamellar BCP melts whose template lines are wider or narrower than the bulk microdomain width. For such systems, our analysis (i) shows that mass conservation causes the microdomain interfaces to oscillate about their bulk positions and (ii) determines the length scale λ over which these oscillations decay away from the substrate.

Steric Hindrance of Crystal Growth: Nonlinear Step Flow in 1+1 Dimensions

By linking atomistic and mesoscopic scales, we formally show how a local steric effect can hinder crystal growth and lead to a buildup of adsorbed atoms (adatoms) on a supersaturated, (1+1)-dimensional surface. Starting from a many-adatom master equation of a kinetic restricted solid-on-solid (KRSOS) model with external material deposition, we heuristically extract a coarse-grained, mesoscale description that defines the motion of a line defect (i.e., a step) in terms of statistical averages over KRSOS microstates. Near thermodynamic equilibrium, we use error estimates to show that this mesoscale picture can deviate from the standard Burton-Cabrera-Frank (BCF) step flow model in which the adatom flux at step edges is linear in the adatom supersaturation. This deviation is caused by the accumulation of adatoms near the step, which block one another from being incorporated into the crystal lattice. In the mesoscale picture, this deviation manifests as a significant contribution from many-adatom microstates to the corresponding statistical averages. We carry out kinetic Monte Carlo simulations to numerically demonstrate how certain parameters control the aforementioned deviation. From these results, we discuss empirical corrections to the BCF model that amount to a nonlinear relation for the adatom flux at the step. We also discuss how this work could be used to understand the kinetic interplay between accumulation of adatoms and step motion in recent experiments of ice surfaces.

The role of data analysis in uncertainty quantification: case studies for materials modeling

In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that can propagate into final predictions in unexpected ways. Thus, modelers require data analysis tools that (i) address the problems posed by simulated data, and (ii) facilitate uncertainty quantification. In this manuscript, we discuss three case studies in materials modeling where careful data analysis can be leveraged to address specific instances of these issues. As a unifying theme, we highlight the idea that attention to physical and mathematical constraints surrounding the generation of computational data can significantly enhance its analysis.

Small fluctuations in epitaxial growth via conservative noise

We study the combined effect of growth (material deposition from above) and nearest-neighbor entropic and force-dipole interactions in a stochastically perturbed system of N line defects (steps) on a vicinal crystal surface in 1+1 dimensions. First, we formulate a general model of conservative white noise and derive simplified formulas for the terrace width distribution and terrace width correlations in the limit N → ∞ for small step fluctuations. Our general result expresses terrace width correlations as an interplay of noise covariance and step interaction strength. Second, we apply our formalism to two specific noise models which stem, respectively, from (i) the fluctuation-dissipation theorem for diffusion of adsorbed atoms; and (ii) the phenomenological consideration of deposition-flux-induced asymmetric attachment and detachment of atoms at step edges. In both cases of noise, we find that terrace width correlations decay exponentially with the step number difference; this behavior leads to vanishing correlations in the macroscopic limit. Our analysis may be used to (i) determine the noise in quasi-one-dimensional surfaces and (ii) assess the validity of previous mean field approximations.