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The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation.
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The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a singular logarithmic dependence on $h$. We derive a general form for this energy in terms of the singular capacitance of two spheres in near contact $c(h)$, together with nonsingular geometric features of the cluster. Using this form, we determine the energies of various clusters, finding that more compact clusters are more stable. These energies are proposed to be significant for metal-semiconductor binary nanoparticle lattices found experimentally. We sketch how these effects should dictate the relative abundances of metal nanoparticle clusters in nonpolar solvents.
Electrostatic reaction inhibition in heterogeneous catalysis emerges if charged reactants and products are adsorbed on the catalyst and thus repel the approaching reactants. In this work, we study the effects of electrostatic inhibition on the reaction rate of unimolecular reactions catalyzed on the surface of a spherical model nanoparticle by using particle-based reaction-diffusion simulations. Moreover, we derive closed rate equations based on approximate Debye-Smoluchowski rate theory, valid for diffusion-controlled reactions, and a modified Langmuir adsorption isotherm, relevant for reaction-controlled reactions, to account for electrostatic inhibition in the Debye-Huckel limit. We study the kinetics of reactions ranging from low to high adsorptions on the nanoparticle surface and from the surface- to diffusion-controlled limits for charge valencies 1 and 2. In the diffusion-controlled limit, electrostatic inhibition drastically slows down the reactions for strong adsorption and low ionic concentration, which is well described by our theory. In particular, the rate decreases with adsorption affinity, because in this case the inhibiting products are generated at high rate. In the (slow) reaction-controlled limit, the effect of electrostatic inhibition is much weaker, as semi-quantitatively reproduced by our electrostatic-modified Langmuir theory. We finally propose and verify a simple interpolation formula that describes electrostatic inhibition for all reaction speeds (`diffusion-influenced reactions) in general.
Radiative heat transfer (RHT) and radiative thermal energy (RTE) for 2D nanoparticle ensembles are investigated in the framework of many-body radiative heat transfer theory. We consider nanoparticles made of different materials: metals (Ag), polar dielectrics (SiC) or insulator-metallic phase-change materials (VO$_2$). We start by investigating the RHT between two parallel 2D finite-size square-lattice nanoparticle ensembles, with particular attention to many-body interactions (MBI) effects. We systematically analyze the different physical regimes characterizing the RHT. When $pll lambda_T$, a multiple scattering of the electromagnetic field inside the systems gives rise to a MBI regime. MBI effects manifest themselves in different ways, depending on $d$: (a) if $d > lambda_T$, due to the pure intra-ensemble MBI inside each 2D ensemble, the total heat conductance is less affected, and the thermal conductance spectrum manifests a single peak which is nonetheless shifted with respect to the one typical of two isolated nanoparticles. (b) if $d < lambda_T$, there is a strong simultaneous intra- and inter-ensemble MBI. In this regime there is a direct quantitative effect on the heat conductance, in addition to a qualitative effect on the thermal conductance spectrum which now manifests a new second peak. As for the RTE, to correctly describe the radiation emitted by metallic nanoparticles, we derive an expression of the Poynting vector including also magnetic contribution, in addition to the electric one. By analyzing both periodic and non-periodic ensembles, we show that the RTE emitted by a single 2D nanoparticle ensemble is sensitive to the particle distribution. As instance, we see that the RTE emitted by 2D concentric ring-configuration ensemble has an inhibition feature near the center of the ensemble.
Devices made from two dimensional materials such as graphene and transition metal dichalcogenides exhibit remarkable electronic properties of interest to many subdisciplines of nanoscience. Owing to their 2D nature, their quality is highly susceptible to contamination and degradation when exposed to the ambient environment. Protecting the 2D layers by encapsulation between hexagonal boron nitride layers significantly improves their quality. Locating these samples within the encapsulant and assessing their integrity prior to further processing then becomes challenging. Here we show that conductive scanning probe techniques such as electrostatic force and Kelvin force microscopy makes it possible to visualize the encapsulated layers, their charge environment and local defects including cracks and bubbles on the sub-micrometer scale. Our techniques are employed without requiring electrical contact to the embedded layer, providing valuable feedback on the local electronic quality prior to any device etching or electrode deposition. We show that these measurement modes, which are simple extensions of atomic force microscopy, are perfectly suited for imaging encapsulated conductors and their local charge environments.
Magnetic nanoparticles are useful in many medical applications because they interact with biology on a cellular level thus allowing microenvironmental investigation. An enhanced understanding of the dynamics of magnetic particles may lead to advances in imaging directly in magnetic particle imaging (MPI) or through enhanced MRI contrast and is essential for nanoparticle sensing as in magnetic spectroscopy of Brownian motion (MSB). Moreover, therapeutic techniques like hyperthermia require information about particle dynamics for effective, safe, and reliable use in the clinic. To that end, we have developed and validated a stochastic dynamical model of rotating Brownian nanoparticles from a Langevin equation approach. With no field, the relaxation time toward equilibrium matches Einsteins model of Brownian motion. In a static field, the equilibrium magnetization agrees with the Langevin function. For high frequency or low amplitude driving fields, behavior characteristic of the linearized Debye approximation is reproduced. In a higher field regime where magnetic saturation occurs, the magnetization and its harmonics compare well with the effective field model. On another level, the model has been benchmarked against experimental results, successfully demonstrating that harmonics of the magnetization carry enough information to infer environmental parameters like viscosity and temperature.
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