Producing two-dimensional dust clouds and clusters using a movable electrode for complex plasma and fundamental physics experiments.

We report a Bidirectional Electrode Control Arm Assembly (BECAA) for precisely manipulating dust clouds levitated above the powered electrode in RF plasmas. The reported techniques allow the creation of perfectly 2D dust layers by eliminating off-plane particles by moving the electrode from outside the plasma chamber without altering the plasma conditions. The tilting and moving of electrodes using BECAA also allows the precise and repeatable elimination of dust particles one by one to achieve any desired number of grains N without trial and error. Simultaneously acquired top and side view images of dust clusters show that they are perfectly planar or 2D. A demonstration of clusters with N = 1-28 without changing the plasma conditions is presented to show the utility of BECAA for complex plasma and statistical physics experimental design. Demonstration videos and 3D printable part files are available for easy reproduction and adaptation of this new method to repeatably produce 2D clusters in existing RF plasma chambers.

Neutral gas pressure dependence of ion-ion mutual neutralization rate constants using Landau-Zener theory coupled with trajectory simulations.

In this computational study, we describe a self-consistent trajectory simulation approach to capture the effect of neutral gas pressure on ion-ion mutual neutralization (MN) reactions. The electron transfer probability estimated using Landau-Zener (LZ) transition state theory is incorporated into classical trajectory simulations to elicit predictions of MN cross sections in vacuum and rate constants at finite neutral gas pressures. Electronic structure calculations with multireference configuration interaction and large correlation consistent basis sets are used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of background gas on ion transport. For H+ - H- and Li+ - H(D)-, our approach quantitatively agrees with measured speed-dependent cross sections for up to ∼105 m/s. For the ion pair Ne+ - Cl-, our predictions of the MN rate constant at ∼1 Torr are a factor of ∼2 to 3 higher than the experimentally measured value. Similarly, for Xe+ - F- in the pressure range of ∼20 000-80 000 Pa, our predictions of the MN rate constant are ∼20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently capture the effect of gas pressure on MN reactions advanced here provides avenues for the inclusion of additional nonclassical effects in future work.

Experimental demonstration that a free-falling aerosol particle obeys a fluctuation theorem.

We investigate the fluctuating motion of an aerosol particle falling in air. Using a Millikan-like setup, we tracked a 1-µm sphere falling at its terminal velocity. We observe occurrences of particles undergoing upward displacements against the force of gravity, so that negative work is done briefly. These negative-work events have a probability that is shown to obey the work fluctuation theorem. This experimental confirmation of the theorem's applicability to aerosols leads us to develop and demonstrate an application: an in situ measurement of an aerosol particle's mass.

Nanoparticle collisions in the gas phase in the presence of singular contact potentials.

Collisional growth and ionization is commonplace for gas phase nanoparticles (i.e., in aerosols). Nanoparticle collisions in atmospheric pressure environments occur in the mass transfer transition regime, and further attractive singular contact potentials (which arise when modeling nanoparticles as condensed matter and for which the potential energy approaches -∞ when two entities contact) often have a non-negligible influence on collision processes. For these reasons collision rate calculations for nanoparticles in the gas phase are not straightforward. We use mean first passage time calculations to develop a simple relationship to determine the collision rate in the gas phase, accounting for the influences of both the transition regime and singular contact potentials (specifically the non-retarded van der Waals and image potentials). In the presented analysis, methods to determine the degree of enhancement in collision rate due to attractive singular potentials in the continuum (diffusive) regime, η(C), and the degree of enhancement in the free molecular (ballistic) regime, η(FM), are first reviewed. Accounting for these enhancement factors, with mean first passage time calculations it is found that the collision rate for gas phase nanoparticles with other gas phase entities can be determined from a relationship between the dimensionless collision rate coefficient, H, and the diffusive Knudsen number, Kn(D), i.e., the ratio of the mean collision persistence distance to the collision length scale. This coincides with the H(Kn(D)) relationship found to appropriately describe collisions between entities interacting via a hard-sphere potential, but with η(C) and η(FM) incorporated into the definitions of both H and Kn(D), respectively. The H(Kn(D)) relationship is compared to the predictions of flux matching theory, used prevalently in prior work for collision rate calculation, and through this comparison it is found that at high potential energy to thermal energy ratios, flux matching theory predictions underestimate the true collision rate. Finally, a series of experimental measurements of nanoparticle-nanoparticle collision rates are compared to the determined H(Kn(D)) expression, considering that nanoparticles interact via non-retarded van der Waals potentials. Very good agreement is found with collision rates inferred from experiments, with almost all measured values from four separate studies within 25% of model predictions.

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.

Collision limited reaction rates for arbitrarily shaped particles across the entire diffusive Knudsen number range.

Aerosol particle reactions with vapor molecules and molecular clusters are often collision rate limited, hence determination of particle-vapor molecule and particle-molecular cluster collision rates are of fundamental importance. These collisions typically occur in the mass transfer transition regime, wherein the collision kernel (collision rate coefficient) is dependent upon the diffusive Knudsen number, Kn(D). While this alone prohibits analytical determination of the collision kernel, aerosol particle- vapor molecule collisions are further complicated when particles are non-spherical, as is often the case for particles formed in high temperature processes (combustion). Recently, through a combination of mean first passage time simulations and dimensional analysis, it was shown that the collision kernel for spherical particles and vapor molecules could be expressed as a dimensionless number, H, which is solely a function of Kn(D). In this work, it is shown through similar mean first passage times and redefinitions of H and Kn(D) that the H(Kn(D)) relationship found for spherical particles applies for particles of arbitrary shape, including commonly encountered agglomerate particles. Specifically, it is shown that to appropriately define H and Kn(D), two geometric descriptors for a particle are necessary: its Smoluchowski radius, which defines the collision kernel in the continuum regime (Kn(D)→0) and its orientationally averaged projected area, which defines the collision kernel in the free molecular regime (Kn(D)→∞). With these two parameters, as well as the properties of the colliding vapor molecule (mass and diffusion coefficient), the particle-vapor molecule collision kernel in the continuum, transition, and free molecular regimes can be simply calculated using the H(Kn(D)) relationship.