Hydrodynamic friction and the capacitance of arbitrarily shaped objects

Toward a Unified Description of the Electrostatic Assembly of Microgels and Nanoparticles

The interplay of soft responsive particles, such as microgels, with nanoparticles (NPs) yields highly versatile complexes that show great potential for applications, ranging from plasmonic sensing to catalysis and drug delivery. However, the microgel-NP assembly process has not been investigated so far at the microscopic level, thus hindering the possibility of designing such hybrid systems a priori. In this work, we combine state-of-the-art numerical simulations with experiments to elucidate the fundamental mechanisms taking place when microgel-NP assembly is controlled by electrostatic interactions and the associated effects on the structure of the resulting complexes. We find a general behavior where, by increasing the number of interacting NPs, the microgel deswells up to a minimum size after which a plateau behavior occurs. This occurs either when NPs are mainly adsorbed to the microgel corona via the folding of the more external chains or when NPs penetrate inside the microgel, thereby inducing a collective reorganization of the polymer network. By varying microgel properties, such as fraction of cross-linkers or charge, as well as NP size and charge, we further show that the microgel deswelling curves can be rescaled onto a single master curve, for both experiments and simulations, demonstrating that the process is entirely controlled by the charge of the whole microgel-NP complex. Our results thus have a direct relevance in fundamental materials science and offer novel tools to tailor the nanofabrication of hybrid devices of technological interest.

Scaling relations for sound scattering by a lattice of hard inclusions in a soft mediuma)

Soft elastic materials embedded with resonant inclusions are widely used as acoustic coatings for maritime applications. A versatile analytical framework for resonance scattering of sound waves in a soft material by a lattice of hard inclusions of complex shape is presented. Analogies from hydrodynamics and electrostatics are employed to derive universal scaling relations for a small number of well-known lumped parameters that map resonant scattering of a complex-shaped hard inclusion to that of a sphere. Multiple scattering of waves between inclusions in proximity is also considered. The problem is then treated using an effective medium theory, viz, a layer of hard inclusions is modeled as a homogenized layer with some effective properties. The acoustic performance of hard inclusions for a range of shapes with spheres of the same volume are compared. Results obtained using this approach are in good agreement with finite element simulations.

Structure of swollen hollow polyelectrolyte nanogels with inhomogeneous cross-link distribution

HYPOTHESIS

Recently, it has become possible to synthesize hollow polyelectrolyte nano- and microgels. The shell permeability can be controlled by external stimuli, while the cavity can serve as a storage place for guest molecules. However, there is a lack of a detailed understanding at the molecular level regarding the role of the network topology, inhomogeneities of the distribution of cross-links, and the impact of the electrostatics on the structural response of hollow microgel to external stimuli. To bridge these gaps, molecular dynamics (MD) of computer simulations are used.

EXPERIMENTS

Here, we propose a fresh methodology to create realistic hollow microgel particles in silico. The technique involves a gradual change in the average local length of subchains depending on the distance to the center of mass of the microgel particles resulting in the microgels with a non-uniform distribution of cross-linking species. In particular, a series of microgels with (i) a highly cross-linked inner part of the shell and gradually decreased cross-linker concentration towards the periphery, (ii) microgels with loosely cross-linked inner and outer parts, as well as (iii) microgels with a more-or-less homogeneous structure, have been created and validated. Counterions and salt ions are taken into account explicitly, and electrostatic interactions are described by the Coulomb potential.

FINDINGS

Our studies reveal a strong dependence of the microgel swelling response on the network topology. Simple redistribution of cross-links plays a significant role in the structure of the microgels, including cavity size, microgel size, fuzziness, and extension of the inner and outer parts of the microgels. Our results indicate the possibilities of qualitative justification of the structure of the hollow microgels in the experiments by measuring the relative change in the size of the sacrificial core to the size of the cavity and by estimation of a power law function, [Formula: see text] , of the hydrodynamic radius of the hollow microgels as a function of added salt concentration.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

Ligand Locking on Quantum Dot Surfaces via a Mild Reactive Surface Treatment

At the outermost surface of colloidal QDs are organic surface ligands which dynamically bind and release in solution to control the growth kinetics, control the size/shape of the crystals, passivate surface states, and provide colloidal stability through favorable interactions with the solvent. However, the dynamicity comes at the expense of the stability of the QD suspension. Here, we show that ligands can be permanently locked on the QD surface by a thin layer of an inert metal oxide which forms within the ligand shell, over the headgroup. By interrogating the surface chemistry with different spectroscopic methods, we prove the ligand locking on the QD surface. As a result, an exceptional stability of the coated QD inks is achieved in a wide concentration range, even in the presence of chemically competing surface ligands in solution. We anticipate that this critical breakthrough will benefit different areas related to colloidal QDs, spanning from single-particle studies to displays and solar cells and biological applications. Furthermore, the same chemistry could be easily translated to surface treatments of bulk materials and thin films.

Archaeal chromatin 'slinkies' are inherently dynamic complexes with deflected DNA wrapping pathways

Eukaryotes and many archaea package their DNA with histones. While the four eukaryotic histones wrap ~147 DNA base pairs into nucleosomes, archaeal histones form ‘nucleosome-like’ complexes that continuously wind between 60 and 500 base pairs of DNA (‘archaeasomes’), suggested by crystal contacts and analysis of cellular chromatin. Solution structures of large archaeasomes (>90 DNA base pairs) have never been directly observed. Here, we utilize molecular dynamics simulations, analytical ultracentrifugation, and cryoEM to structurally characterize the solution state of archaeasomes on longer DNA. Simulations reveal dynamics of increased accessibility without disruption of DNA-binding or tetramerization interfaces. Mg²⁺ concentration influences compaction, and cryoEM densities illustrate that DNA is wrapped in consecutive substates arranged 90^o out-of-plane with one another. Without ATP-dependent remodelers, archaea may leverage these inherent dynamics to balance chromatin packing and accessibility.

All animals, plants and fungi belong to a group of living organisms called eukaryotes. The two other groups are bacteria and archaea, which include unicellular, microscopic organisms. All three groups have genes, which are typically stored on long strands of DNA. Eukaryotes have so much DNA that they use proteins called histones to help package and organize it inside each cell. Archaea also have simplified histones that help store their DNA, and studying these proteins could reveal how eukaryotic histones first evolved.

In eukaryotes, groups of eight histones form a short cylinder that organizes a small section of DNA into a structure called a nucleosome. Each cell needs hundreds of thousands of nucleosomes to arrange its DNA. Eukaryotic cells also contain other proteins that release pieces of DNA from histones so that their genetic information can be used. The histones in Archaea don’t form discrete nucleosomes, instead, they coil DNA into ‘slinky-like’ shapes. It’s still unclear how DNA packing in archaea works and how it differs from eukaryotes.

Bowerman, Wereszczynski and Luger used computer simulations, biochemistry and cryo-electron microscopy to study the histones from archaea. The archaeal ‘slinky-like’ histone structures are more flexible than nucleosomes, and can open and close like clamshells. This flexibility allows the information in the genomes of Archaea to be easily accessed, so, unlike in eukaryotes, archaeal cells may not need other proteins to release the DNA from the histones.

The ability to package DNA allows cells to contain many more genes, so evolving histones was a vital step in the evolution of eukaryotic life, including the appearance of animals. Archaeal histones may reflect early versions of histones in eukaryotes, and can be used to understand how DNA packing has evolved. Furthermore, a greater understanding of Archaea may help better explain their role in health and global ecosystems, and allow their use in industrial applications.

CsPbBr3 Quantum Dots 2.0: Benzenesulfonic Acid Equivalent Ligand Awakens Complete Purification

The stability and optoelectronic device performance of perovskite quantum dots (Pe-QDs) are severely limited by present ligand strategies since these ligands exhibit a highly dynamic binding state, resulting in serious complications in QD purification and storage. Here, a "Br-equivalent" ligand strategy is developed in which the proposed strong ionic sulfonate heads, for example, benzenesulfonic acid, can firmly bind to the exposed Pb ions to form a steady binding state, and can also effectively eliminate the exciton trapping probability due to bromide vacancies. From these two aspects, the sulfonate heads play a similar role as natural Br ions in a perfect perovskite lattice. Using this approach, high photoluminescence quantum yield (PL QY) > 90% is facilely achieved without the need for amine-related ligands. Furthermore, the prepared PL QYs are well maintained after eight purification cycles, more than five months of storage, and high-flux photo-irradiation. This is the first report of high and versatile stabilities of Pe-QD, which should enable their improved application in lighting, displays, and biologic imaging.

Influence of Branching on the Configurational and Dynamical Properties of Entangled Polymer Melts

We probe the influence of branching on the configurational, packing, and density correlation function properties of polymer melts of linear and star polymers, with emphasis on molecular masses larger than the entanglement molecular mass of linear chains. In particular, we calculate the conformational properties of these polymers, such as the hydrodynamic radius R h , packing length p, pair correlation function g ( r ) , and polymer center of mass self-diffusion coefficient, D, with the use of coarse-grained molecular dynamics simulations. Our simulation results reproduce the phenomenology of simulated linear and branched polymers, and we attempt to understand our observations based on a combination of hydrodynamic and thermodynamic modeling. We introduce a model of "entanglement" phenomenon in high molecular mass polymers that assumes polymers can viewed in a coarse-grained sense as "soft" particles and, correspondingly, we model the emergence of heterogeneous dynamics in polymeric glass-forming liquids to occur in a fashion similar to glass-forming liquids in which the molecules have soft repulsive interactions. Based on this novel perspective of polymer melt dynamics, we propose a functional form for D that can describe our simulation results for both star and linear polymers, covering both the unentangled to entangled polymer melt regimes.

A radial calibration window for analytical ultracentrifugation

Analytical ultracentrifugation (AUC) is a first-principles based method for studying macromolecules and particles in solution by monitoring the evolution of their radial concentration distribution as a function of time in the presence of a high centrifugal field. In sedimentation velocity experiments, hydrodynamic properties relating to size, shape, density, and solvation of particles can be measured, at a high hydrodynamic resolution, on polydisperse samples. In a recent multilaboratory benchmark study including data from commercial analytical ultracentrifuges in 67 laboratories, the calibration accuracy of the radial dimension was found to be one of the dominant factors limiting the accuracy of AUC. In the present work, we develop an artifact consisting of an accurately calibrated reflective pattern lithographically deposited onto an AUC window. It serves as a reticle when scanned in AUC control experiments for absolute calibration of radial magnification. After analysis of the pitch between landmarks in scans using different optical systems, we estimate that the residual uncertainty in radial magnification after external calibration with the radial scale artifact is ≈0.2 %, of similar magnitude to other important contributions after external calibration such as the uncertainty in temperature and time. The previous multilaboratory study had found many instruments with errors in radial measurements of 1 % to 2 %, and a few instruments with errors in excess of 15 %, meaning that the use of the artifact developed here could reduce errors by 5-to 10-fold or more. Adoption of external radial calibration is thus an important factor for assuring accuracy in studies related to molecular hydrodynamics and particle size measurements by AUC.

Effect of the scaffold microenvironment on cell polarizability and capacitance determined by probabilistic computations

In living systems, it is frequently stated that form follows function by virtue of evolutionary pressures on organism development, but in the study of how functions emerge at the cellular level, function often follows form. We study this chicken versus egg problem of emergent structure-property relationships in living systems in the context of primary human bone marrow stromal cells cultured in a variety of microenvironments that have been shown to cause distinct patterns of cell function and differentiation. Through analysis of a publicly available catalog of three-dimensional (3D) cell shape data, we introduce a family of metrics to characterize the 'form' of the cell populations that emerge from a variety of diverse microenvironments. In particular, measures of form are considered that are expected to have direct significance for cell function, signaling and metabolic activity: dimensionality, polarizability and capacitance. Dimensionality was assessed by an intrinsic measure of cell shape obtained from the polarizability tensor. This tensor defines ellipsoids for arbitrary cell shapes and the thinnest dimension of these ellipsoids, P 1, defines a reference minimal scale for cells cultured in a 3D microenvironment. Polarizability governs the electric field generated by a cell, and determines the cell's ability to detect electric fields. Capacitance controls the shape dependence of the rate at which diffusing molecules contact the surface of the cell, and this has great significance for inter-cellular signaling. These results invite new approaches for designing scaffolds which explicitly direct cell dimensionality, polarizability and capacitance to guide the emergence of new cell functions derived from the acquired form.

Knot Energy, Complexity, and Mobility of Knotted Polymers

The Coulomb energy E C 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 E C 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 E C for all these knotted polymers using the program ZENO and find that the average Coulomb energy 〈E C〉 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.

Friction factor for aerosol fractal aggregates over the entire Knudsen range

We develop an approach for computing the hydrodynamic friction tensor and scalar friction coefficient for an aerosol fractal aggregate in the transition regime. Our approach involves solving the Bhatnagar-Gross-Krook equation for the velocity field around a sphere and using the velocity field to calculate the force on each primary sphere in the aggregate due to the presence of the other spheres. It is essentially an extension of Kirkwood-Riseman theory from the continuum flow regime to the entire Knudsen range (Knudsen number from 0.01 to 100 based on the primary sphere radius). Our results compare well to published direct simulation Monte Carlo results, and they converge to the correct continuum and free molecule limits. Our calculations for clusters with up to 100 spheres support the theory that aggregate slip correction factors collapse to a single curve when plotted as a function of an appropriate aggregate Knudsen number. This self-consistent-field approach calculates the friction coefficient very quickly, so the approach is well-suited for testing existing scaling laws in the field of aerosol science and technology, as we demonstrate for the adjusted sphere scaling method.

Quantifying intra- and extracellular aggregation of iron oxide nanoparticles and its influence on specific absorption rate

A promising route to cancer treatment is hyperthermia, facilitated by superparamagnetic iron oxide nanoparticles (SPIONs). After exposure to an alternating external magnetic field, SPIONs generate heat, quantified by their specific absorption rate (SAR, in W g(-1) Fe). However, without surface functionalization, commercially available, high SAR SPIONs (EMG 308, Ferrotec, USA) aggregate in aqueous suspensions; this has been shown to reduce SAR. Further reduction in SAR has been observed for SPIONs in suspensions containing cells, but the origin of this further reduction has not been made clear. Here, we use image analysis methods to quantify the structures of SPION aggregates in the extra- and intracellular milieu of LNCaP cell suspensions. We couple image characterization with nanoparticle tracking analysis and SAR measurements of SPION aggregates in cell-free suspensions, to better quantify the influence of cellular uptake on SPION aggregates and ultimately its influence on SAR. We find that in both the intra- and extracellular milieu, SPION aggregates are well-described by a quasifractal model, with most aggregates having fractal dimensions in the 1.6-2.2 range. Intracellular aggregates are found to be significantly larger than extracellular aggregates and are commonly composed of more than 10(3) primary SPION particles (hence they are "superaggregates"). By using high salt concentrations to generate such superaggregates and measuring the SAR of suspensions, we confirm that it is the formation of superaggregates in the intracellular milieu that negatively impacts SAR, reducing it from above 200 W g(-1) Fe for aggregates composed of fewer than 50 primary particles to below 50 W g(-1) for superaggregates. While the underlying physical mechanism by which aggregation leads to reduction in SAR remains to be determined, the methods developed in this study provide insight into how cellular uptake influences the extent of SPION aggregation, and enable estimation of the reduction of SAR brought about via uptake induced aggregation.

Highly Dynamic Ligand Binding and Light Absorption Coefficient of Cesium Lead Bromide Perovskite Nanocrystals

Lead halide perovskite materials have attracted significant attention in the context of photovoltaics and other optoelectronic applications, and recently, research efforts have been directed to nanostructured lead halide perovskites. Collodial nanocrystals (NCs) of cesium lead halides (CsPbX3, X = Cl, Br, I) exhibit bright photoluminescence, with emission tunable over the entire visible spectral region. However, previous studies on CsPbX3 NCs did not address key aspects of their chemistry and photophysics such as surface chemistry and quantitative light absorption. Here, we elaborate on the synthesis of CsPbBr3 NCs and their surface chemistry. In addition, the intrinsic absorption coefficient was determined experimentally by combining elemental analysis with accurate optical absorption measurements. (1)H solution nuclear magnetic resonance spectroscopy was used to characterize sample purity, elucidate the surface chemistry, and evaluate the influence of purification methods on the surface composition. We find that ligand binding to the NC surface is highly dynamic, and therefore, ligands are easily lost during the isolation and purification procedures. However, when a small amount of both oleic acid and oleylamine is added, the NCs can be purified, maintaining optical, colloidal, and material integrity. In addition, we find that a high amine content in the ligand shell increases the quantum yield due to the improved binding of the carboxylic acid.

Acceleration and Parallelization of ZENO/Walk-on-Spheres

This paper describes our on-going work to accelerate ZENO, a software tool based on Monte Carlo methods (MCMs), used for computing material properties at nanoscale. ZENO employs three main algorithms: (1) Walk on Spheres (WoS), (2) interior sampling, and (3) surface sampling. We have accelerated the first two algorithms. For the sake of brevity, the paper will discuss our work on the first one only as it is the most commonly used and the acceleration techniques were similar in both cases. WoS is a Brownian motion MCM for solving a class of partial differential equations (PDEs). It provides a stochastic solution to a PDE by estimating the probability that a random walk, which started at infinity, will hit the surface of the material under consideration. WoS is highly effective when the problem's geometry is additive, as this greatly reduces the number of walk steps needed to achieve accurate results. The walks start on the surface of an enclosing sphere and can make much larger jumps than in a direct simulation of Brownian motion. Our current implementation represents the molecular structure of nanomaterials as a union of possibly overlapping spheres. The core processing bottleneck in WoS is a Computational Geometry one, as the algorithm repeatedly determines the distance from query point to the material surface in each step of the random walk. In this paper, we present results from benchmarking spatial data structures, including several open-source implementations of k-D trees, for accelerating WoS algorithmically. The paper also presents results from our multicore and cluster parallel implementation to show that it exhibits linear strong scaling with the number of cores and compute nodes; this implementation delivers up to 4 orders of magnitude speedup compared to the original FORTRAN code when run on 8 nodes (each with dual 6-core Intel Xeon CPUs) with 24 threads per node.

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.

Confronting the complexity of CNT materials

The morphology of commercially available carbon nanotube materials is often much more complex than the term "carbon nanotube" (CNT) would imply. Commercial CNT materials are typically composed of roughly spherical CNT domains having a highly ramified internal structure and a size on the order of microns. Clearly, such structures cannot reasonably be modeled as "rods". To address this problem, we first perform molecular dynamics simulations (MD) to generate structures similar to those measured experimentally, based on the presumptions that CNT domains are composed of worm-like cylinders having observed persistence lengths and that these CNTs are confined to spherical domains having the observed average domain size. This simple model generates structures remarkably similar to those observed experimentally. We then consider numerical path-integral computations to calculate the self-capacitance C and intrinsic conductivity [σ]∞ of these CNT rich domains. This information is then incorporated in a generalized effective medium theory to estimate the conductivity of bulk composite materials composed of these complex-shaped "particles". We term these CNT structures "tumbleweeds", given their evident morphological similarity to this naturally occurring growth form. Based on this model, we find that the conductivity percolation threshold of the tumbleweeds can be quite low, despite their quasi-spherical average shape. We also examine the structure factor S(q) of the CNT-rich domains as function of the number N of CNTs within them, to aid in the structural characterization of CNT nanocomposites. The structure factor S(q) of our model tumbleweed is found to resemble that of hyperbranched, star and dendrimer polymers, and also domain structures observed in polyelectrolytes. Commercial CNT materials at high loading should then have physical features in common with suspension of "soft" colloidal particles by virtue of their deformability and roughly spherical shape.

High-speed, high-purity separation of gold nanoparticle-DNA origami constructs using centrifugation

DNA origami is a powerful platform for assembling gold nanoparticle constructs, an important class of nanostructure with numerous applications. Such constructs are assembled by the association of complementary DNA oligomers. These association reactions have yields of <100%, requiring the development of methods to purify the desired product. We study the performance of centrifugation as a separation approach by combining optical and hydrodynamic measurements and computations. We demonstrate that bench-top microcentrifugation is a simple and efficient method of separating the reaction products, readily achieving purities of >90%. The gold nanoparticles play a number of critical roles in our system, functioning not only as integral components of the purified products, but also as hydrodynamic separators and optical indicators of the reaction products during the purification process. We find that separation resolution is ultimately limited by the polydispersity in the mass of the gold nanoparticles and by structural distortions of DNA origami induced by the gold nanoparticles. Our study establishes a methodology for determining the design rules for nanomanufacturing DNA origami-nanoparticle constructs.

Accounting for biological aggregation in heating and imaging of magnetic nanoparticles

Aggregation is a known consequence of nanoparticle use in biology and medicine; however, nanoparticle characterization is typically performed under the pretext of well-dispersed, aqueous conditions. Here, we systematically characterize the effects of aggregation on the alternating magnetic field induced heating and magnetic resonance (MR) imaging performance of iron oxide nanoparticles (IONPs) in non-ideal biological systems. Specifically, the behavior of IONP aggregates composed of ~10 nm primary particles, but with aggregate hydrodynamic sizes ranging from 50 nm to 700 nm, was characterized in phosphate buffered saline and fetal bovine serum suspensions, as well as in gels and cells. We demonstrate up to a 50% reduction in heating, linked to the extent of aggregation. To quantify aggregate morphology, we used a combination of hydrodynamic radii distribution, intrinsic viscosity, and electron microscopy measurements to describe the aggregates as quasifractal entities with fractal dimensions in the 1.8-2.0 range. Importantly, we are able to correlate the observed decrease in magnetic field induced heating with a corresponding decrease in longitudinal relaxation rate (R1) in MR imaging, irrespective of the extent of aggregation. Finally, we show in vivo proof-of-principle use of this powerful new imaging method, providing a critical tool for predicting heating in clinical cancer hyperthermia.

Coulomb-influenced collisions in aerosols and dusty plasmas

In aerosol and dusty plasma systems, the behavior of suspended particles (grains) is often strongly influenced by collisions occurring between ions and particles, as well as between particles themselves. In determining the collision kernel or collision rate coefficient for such charged entities, complications arise in that the collision process can be completely described neither by continuum transport mechanics nor by free molecular (ballistic) mechanics; that is, collisions are transition regime processes. Further, both the thermal energy and the potential energy between colliding entities can strongly influence the collision rate and must be considered. Flux-matching theory, originally developed by Fuchs, is frequently applied for calculation of collision rate coefficients under these circumstances. However, recent work suggests that crucial assumptions in flux-matching theory are not appropriate to describe transition regime collisions in the presence of potential interactions. Here, we combine dimensional analysis and mean first passage time calculations to infer the collision kernel between dilute charged entities suspended in a light background gas at thermal equilibrium. The motion of colliding entities is described by a Langevin equation, and Coulombic interactions are considered. It is found that the dimensionless collision kernel for these conditions, H, is a function of the diffusive Knudsen number, Kn(D) (in contrast to the traditional Knudsen number), and the potential energy to thermal energy ratio, Ψ(E). For small and large Kn(D), it is found that the dimensionless collision kernels inferred from mean first passage time calculations collapse to the appropriate continuum and free molecular limiting forms, respectively. Further, for repulsive collisions (Ψ(E) negative) or attractive collisions with Ψ(E)<0.5, calculated results are in excellent agreement with flux-matching theory predictions, and the dimensionless collision kernel can be determined conveniently via use of the H(Kn(D)) relationship found for hard-sphere collisions with modified definitions of H and Kn(D) to account for potential energy. However, for Ψ(E)>0.5, it is found that flux-matching theory predictions substantially underestimate the collision kernel. We find that the collision process in this regime is governed by the minimum of Kn(D) and Kn(Ψ) (Kn(Ψ) = 3Kn(D)/2Ψ(E)), and based on calculations, propose a function H(Kn(D), Kn(Ψ)) for collision kernel evaluation. The situations for which Ψ(E)>0.5 apply to singly charged nanoparticles and multiply charged submicrometer and supermicrometer particles, and are thus prevalent in both aerosol and dusty plasma environments.

Characterizing string-of-pearls colloidal silica by multidetector hydrodynamic chromatography and comparison to multidetector size-exclusion chromatography, off-line multiangle static light scattering, and transmission electron microscopy

The string-of-pearls-type morphology is ubiquitous, manifesting itself variously in proteins, vesicles, bacteria, synthetic polymers, and biopolymers. Characterizing the size and shape of analytes with such morphology, however, presents a challenge, due chiefly to the ease with which the "strings" can be broken during chromatographic analysis or to the paucity of information obtained from the benchmark microscopy and off-line light scattering methods. Here, we address this challenge with multidetector hydrodynamic chromatography (HDC), which has the ability to determine, simultaneously, the size, shape, and compactness and their distributions of string-of-pearls samples. We present the quadruple-detector HDC analysis of colloidal string-of-pearls silica, employing static multiangle and quasielastic light scattering, differential viscometry, and differential refractometry as detection methods. The multidetector approach shows a sample that is broadly polydisperse in both molar mass and size, with strings ranging from two to five particles, but which also contains a high concentration of single, unattached "pearls". Synergistic combination of the various size parameters obtained from the multiplicity of detectors employed shows that the strings with higher degrees of polymerization have a shape similar to the theory-predicted shape of a Gaussian random coil chain of nonoverlapping beads, while the strings with lower degrees of polymerization have a prolate ellipsoidal shape. The HDC technique is contrasted experimentally with multidetector size-exclusion chromatography, where, even under extremely gentle conditions, the strings still degraded during analysis. Such degradation is shown to be absent in HDC, as evidenced by the fact that the molar mass and radius of gyration obtained by HDC with multiangle static light scattering detection (HDC/MALS) compare quite favorably to those determined by off-line MALS analysis under otherwise identical conditions. The multidetector HDC results were also comparable to those obtained by transmission electron microscopy (TEM). Unlike off-line MALS or TEM, however, multidetector HDC is able to provide complete particle analysis based on the molar mass, size, shape, and compactness and their distributions for the entire sample population in less than 20 min.

Influence of variable hydrodynamic interaction strength on the transport properties of coiled polymers

We have computed the hydrodynamic radius Rh and intrinsic viscosity [eta] of a large number of random coil polymer models by path integration. We examine the effects of chain length, solvent quality, monomer size and shape, and chain stiffness on the approach of these transport properties to the limit of large molecular mass. For many of the models, we have also calculated the ensemble-averaged solvent velocity field in the vicinity of the coil as it moves with constant drift velocity under the action of an external force. Naive scaling arguments predict alpha=nu and beta=3(nu-1) , where alpha , beta , and nu are the exponents controlling the chain length behavior of Rh , [eta] , and Rg , respectively. We present evidence for a "draining crossover" that quantifies the slow convergence of the transport properties to their asymptotic scaling behavior. Indeed, the convergence is so slow that effective alpha and beta exponents rarely agree with the naive predictions at typical molecular masses. For the same chain models, Rg converges rapidly to its asymptotic behavior, indicating that the effect is not due to a crossover from theta to swollen behavior, as often stated. Solvent quality, monomer size, and chain stiffness all influence the draining crossover. Our results call into question the common practice of extracting metrical data, e.g., characteristic ratios, directly from polymer solution transport properties.

Crowding induced self-assembly and enthalpy-entropy compensation

We develop a general virial expansion to describe the influence of molecular additives on the equilibrium self-assembly of proteins or other supermolecularly assembling species M in solution. When specialized to high molar mass polymer additives, the cross-virial coefficient between the polymer and M, which dominates this effect, is found to vanish at a particular temperature T_{Theta} corresponding to an enthalpy-entropy compensation condition. Specifically, the increased stability of the assembled form of M, due to the modification of the entropy of the assembly by repulsive polymer-protein interactions, is progressively compensated by attractive interactions that alter the enthalpy of assembly.

Improved path integration method for estimating the intrinsic viscosity of arbitrarily shaped particles

In previous work, we have established that the intrinsic viscosity [eta] of an object is nearly proportional to the average electrical polarizability tensor alphae = tr(alphae)/3 of a conducting object having the same shape, or equivalently, to the intrinsic conductivity [sigma]=alphae/V , which characterizes the conductivity of a dilute mixture of randomly oriented conducting objects (V being the volume of the object). This hydrodynamic-electrostatic analogy is useful because alphae can be determined accurately and efficiently by numerical path integration for objects of arbitrary shape. Here, we show that the uncertainty in [eta] can be reduced to a relatively small value (< 1.5% relative uncertainty) by utilizing additional information from the full tensor alphae, rather than just its average. Specifically, we determine the exact constant of proportionality between [eta] and [sigma] for triaxial ellipsoids as a function of the ratios of the eigenvalues of alphae and apply this relation to particles of general shape. In addition to an improved estimation of [eta] , the ratios of the components of alphae provide useful measures of particle anisotropy. We also present an improved method for applying the technique to flexible particles, which requires performing a conformational ensemble average. Conformational averages of alphae generate systematic errors that can be avoided by performing the conformational average at an earlier stage in the computation.

Numerical path integration technique for the calculation of transport properties of proteins

We present a new technique for the computation of both the translational diffusivity and the intrinsic viscosity of macromolecules, and apply it here to proteins. Traditional techniques employ finite element representations of the surface of the macromolecule, taking the surface to be a union of spheres or of polygons, and have computation times that are O(m(3)) where m is the number of finite elements. The new technique, a numerical path integration method, has computation times that are only O(m). We have applied the technique to approximately 1000 different protein structures. The computed translational diffusivities and intrinsic viscosities are, to lowest order, proportional respectively to N(-1/3)(R) and N(0)(R), where N(R) is the number of amino acid residues in the protein. Our calculations also show some correlation with the shape of the molecule, as represented by the ratio m(2)/m(3), where m(2) and m(3) are, respectively, the middle and the smallest of the three principal moments of inertia. Comparisons with a number of experimental results are also performed, with results generally consistent to within experimental error.

Intrinsic viscosity and the electrical polarizability of arbitrarily shaped objects

The problem of calculating the electric polarizability tensor alpha(e) of objects of arbitrary shape has been reformulated in terms of path integration and implemented computationally. The method simultaneously yields the electrostatic capacity C and the equilibrium charge density. These functionals of particle shape are important in many materials science applications, including the conductivity and viscosity of filled materials and suspensions. The method has been validated through comparison with exact results (for the sphere, the circular disk, touching spheres, and tori), it has been found that 10(6) trajectories yield an accuracy of about four and three significant figures for C and alpha(e), respectively. The method is fast: For simple objects, 10(6) trajectories require about 1 min on a PC. It is also versatile: Switching from one object to another is easy. Predictions have also been made for regular polygons, polyhedra, and right circular cylinders, since these shapes are important in applications and since numerical calculations of high stated accuracy are available. Finally, the path-integration method has been applied to estimate transport properties of both linear flexible polymers (random walk chains of spheres) and lattice model dendrimer molecules. This requires probing of an ensemble of objects. For linear chains, the distribution function of C and of the trace (alpha(e)), are found to be universal in a size coordinate reduced by the chain radius of gyration. For dendrimers, these distribution functions become increasingly sharp with generation number. It has been found that C and alpha(e) provide important information about the distribution of molecular size and shape and that they are important for estimating the Stokes friction and intrinsic viscosity of macromolecules.

Antigen-antibody diffusion-limited binding kinetics for biosensors. A fractal analysis

A fractal analysis is made for antigen-antibody binding kinetics for different biosensor applications available in the literature. Both types of examples are considered wherein: (1) the antigen is in solution and the antibody is immobilized on the fiberoptic surface, and (2) the antibody is in solution and the antigen is immobilized on the fiberoptic surface. For example, when the antibody is immobilized on the surface, an increase in the antigen Clostridium botulinum toxin A concentration in solution leads to (1) a decrease in the fractal dimension value or state of disorder, and (2) a higher rate constant for binding on the fiberoptic surface. An analysis of the effect of the influence of different parameters on the fractal dimension values for a particular example, such as varying treatments or incubation procedures, helps provide insights into the conformational states and reactions occurring on the fiberoptic surface. The analysis of the different example taken together provides novel physical insights into the state of "disorder" and reactions occurring on the surface. Such types of analysis should help contribute toward manipulating the reactions occurring on the fiberoptic surfaces in desired directions.