Image Charge Model Research Articles

An Experimental Study and a Numerical Modelling of Microdroplets Charged in a Helium Atmospheric Pressure Plasma Jet

A droplet passing through a low temperature plasma acquires a net negative charge, Q, and the droplet floating potential increases negatively until positive and negative charge fluxes are balanced. Subsequently electrons arrive at the droplet with a very low net electron energy. Low energy electrons (LEE) may play an important role in for example water chemistry, DNA damage (e.g. in radiotherapy) and electron-initiated nanomaterials synthesis [1]. However obtaining true LEE (< 5 eV) sources compatible with liquid water has not been possible to date. In a previous study, we have shown extremely fast and enhanced metal salt reactions within droplets and it is thought LEE reactions from charge on the droplets was the major contributor, in comparison to radiolysis and electron-beam studies [2]. Charging models of collisional high pressure plasmas have received little experimental validation, especially for particles in the size range (microns) where droplets can survive the plasma-induced evaporation. Measuring the small charge on fast moving droplets, however, in a high plasma RF noise environment presents very significant challenges. We present an experimental study of microdroplets charged in a helium atmospheric pressure plasma jet (APPJ) and, along with numerical modelling, determine the dependence of droplet charge, Q, on droplet diameter (D) and plasma conditions e.g. electron density, ne, and temperature, Te. Our measurements were carried out on aerosol droplet streams under various plasma conditions (power and flow) using a 4 mm plate collector. Without droplets, the collector assumed a mean positive potential. This is likely due to the effect of the upstream plasma potential which is estimated at ~12 V, assuming a Te of 2 eV. The background signal variation due to noise and other sources was ~250 mV. With the addition of droplets, the collector mean potential decreased due to the impact of the negative charge flux. At the maximum power, floating potential (VF) is a factor of ~100 greater at 3 mm collector distance compared to 15 mm. On the addition of droplets, the characteristics remain similar at 3 mm but at 15 mm, the potential remains positive until a much higher power. An image charge model [3] was used to obtain charge per droplet estimates from stream of droplets based on droplet rate and size distribution. High resolution imaging was used to obtain droplet statistics at the edge of the capillary. Here, the maximum droplet rate was ~ 5 x 104 s-1 [4]. The voltage – charge calibration factor, obtained from simulation, varies from 4.6 – 7.6 nV per electron, depending on velocity. The average value of charge per droplet can be obtained from the net potential obtained at different powers. The possible influence of the plasma gas flow (Q2) and liquid delivery rate (QL) on collector potential was explored and maximum charging capability was found to occur around a total gas flow of 3.5 slm and for lower QL values.

(Digital Presentation) Measurements of the Average Droplet Charge Using a Low Density Stream of Microdroplets in Atmospheric Pressure Plasma Jet

A droplet passing through a low temperature plasma acquires a net negative charge, Q, and the droplet floating potential increases negatively until positive and negative charge fluxes are balanced. Subsequently electrons arrive at the droplet with a very low net electron energy. Low energy electrons (LEE) may play an important role in for example water chemistry, DNA damage (e.g. in radiotherapy) and electron-initiated nanomaterials synthesis [1]. However obtaining true LEE (< 5 eV) sources compatible with liquid water has not been possible to date. In a previous study, we have shown extremely fast and enhanced metal salt reactions within droplets and it is thought LEE reactions from charge on the droplets was the major contributor, in comparison to radiolysis and electron-beam studies [2]. Charging models of collisional high pressure plasmas have received little experimental validation, especially for particles in the size range (microns) where droplets can survive the plasma-induced evaporation. Measuring the small charge on fast moving droplets, however, in a high plasma RF noise environment presents very significant challenges. We present an experimental study of microdroplets charged in a helium atmospheric pressure plasma jet (APPJ) and, along with numerical modelling, determine the dependence of droplet charge, Q, on droplet diameter (D) and plasma conditions e.g. electron density, ne, and temperature, Te. Our measurements were carried out on aerosol droplet streams under various plasma conditions (power and flow) using a 4 mm plate collector. Without droplets, the collector assumed a mean positive potential. This is likely due to the effect of the upstream plasma potential which is estimated at ~12 V, assuming a Te of 2 eV. The background signal variation due to noise and other sources was ~250 mV. With the addition of droplets, the collector mean potential decreased due to the impact of the negative charge flux. At the maximum power, floating potential (VF) is a factor of ~100 greater at 3 mm collector distance compared to 15 mm. On the addition of droplets, the characteristics remain similar at 3 mm but at 15 mm, the potential remains positive until a much higher power. An image charge model [3] was used to obtain charge per droplet estimates from stream of droplets based on droplet rate and size distribution. High resolution imaging was used to obtain droplet statistics at the edge of the capillary. Here, the maximum droplet rate was ~ 5 x 104 s-1 [[4]]. The voltage – charge calibration factor, obtained from simulation, varies from 4.6 – 7.6 nV per electron, depending on velocity. The average value of charge per droplet can be obtained from the net potential and is shown in Figure 1 for low and high powers. The possible influence of the plasma gas flow (Q2) and liquid delivery rate (QL) on collector potential was explored and maximum charging capability was found to occur around a total gas flow of 3.5 slm and for lower QL values. [1] Léon Sanche, ‘Cancer Treatment: Low-Energy Electron Therapy’, Nature Materials, 14.9 (2015), 861–63 https://doi.org/10.1038/nmat4333 [2] Paul Maguire et al., ‘Continuous In-Flight Synthesis for On-Demand Delivery of Ligand-Free Colloidal Gold Nanoparticles’, Nano Letters, 17.3 (2017), 1336–43 https://doi.org/10.1021/acs.nanolett.6b03440 [3] E. Borzabadi and A. G. Bailey, ‘The Measurement of Charge on Microscopic Particles’, Journal of Physics E: Scientific Instruments, 12.12 (1979), 1137–38 https://doi.org/10.1088/0022-3735/12/12/005 [4] Paul Maguire et al., ‘Controlled Microdroplet Transport in an Atmospheric Pressure Microplasma’, Applied Physics Letters, 106.22 (2015) https://doi.org/10.1063/1.4922034 Figure 1

High-Resolution Detection of Rock-Forming Minerals by Permittivity Measurements with a Near-Field Scanning Microwave Microscope.

The identification of the minerals composing rocks and their dielectric characterization is essential for the utilization of microwave energy in the rock industry. This paper describes the use of a near-field scanning microwave microscope with enhanced sensitivity for non-invasive measurements of permittivity maps of rock specimens at the micrometer scale in non-contact mode. The microwave system comprises a near-field probe, an in-house single-port vectorial reflectometer, and all circuitry and software needed to make a stand-alone, portable instrument. The relationship between the resonance parameters of the near-field probe and the dielectric properties of materials was determined by a combination of classical cavity perturbation theory and an image charge model. The accuracy of this approach was validated by a comparison study with reference materials. The device was employed to determine the permittivity maps of a couple of igneous rock specimens with low-loss and high-loss minerals. The dielectric results were correlated with the minerals comprising the samples and compared with the dielectric results reported in the literature, with excellent agreements.

Competition between Coulomb and van der Waals Interactions in Xe-Cs^{+} Aggregates on Cu(111) Surfaces.

Microscopic insight into interactions is a key for understanding the properties of heterogenous interfaces. We analyze local attraction in noncovalently bonded Xe-Cs^{+} aggregates and monolayers on Cu(111) as well as repulsion upon electron transfer. Using two-photon photoemission spectroscopy, scanning tunneling microscopy, and coupled cluster calculations combined with an image-charge model, we explain the intricate impact Xe has on Cs^{+}/Cu(111). We find that attraction between Cs^{+} and Xe counterbalances the screened Coulomb repulsion between Cs^{+} ions on Cu(111). Furthermore, we observe that the Cs 6s electron is repelled from Cu(111) due to xenon's electron density. Together, this yields a dual, i.e., attractive or repulsive, response of Xe depending on the positive or negative charge of the respective counterparticle, which emphasizes the importance of the Coulomb interaction in these systems.

Metal screening effect on energy levels at metal/organic interface: Precise determination of screening energy using photoelectron and inverse-photoelectron spectroscopies

The energy level alignment at the metal/organic interface greatly affects the charge injection/extraction efficiency of electrodes in organic semiconductor devices. The charge carrier in the vicinity of the metal surface should be stabilized by the screening effect of the metal surface, thereby resulting in the narrowing of the energy gap (highest occupied molecular orbital (HOMO)--lowest unoccupied molecular orbital (LUMO) gap) and modifying the energy level alignment at the metal/organic interface. However, this metal screening effect has not been fully clarified because there has been no precise way to quantitatively evaluate the experimental values. In this study, we employed ultraviolet photoelectron spectroscopy (UPS), metastable atom electron spectroscopy (MAES), and low-energy inverse photoelectron spectroscopy (LEIPS) to examine the quasi--layer-by-layer grown film of perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) on the atomically flat metal surface of Ag(111) and Au(111). By applying a procedure we established recently, we precisely evaluated the energy of the metal screening effect. The results demonstrate that the screening effect of the metal surface modifies the charge injection/collection barrier at the metal/organic interface by as much as 0.25 eV. We found that the PTCDA thickness dependent screening effect is precisely reproduced by the image charge model.

Monte Carlo simulation of random dopant fluctuation in C–V characteristics using image charge model and adequately determined length scale

In recent years, it has been under discussion how the distribution of discrete dopant ions affects the performance of electron devices. In particular, dopant ions near the interface may not be surrounded by a sufficient number of carriers to achieve full screening. In addition, the screening effect is modeled assuming equilibrium, which cannot be validated. Therefore, the device modeling of the screening effect must be refined to cover the entire range of applied voltages. In the present work, we adequately define the length scale covering the entire voltage region in the capacitance–voltage (C–V) characteristics. Furthermore, we propose an image charge model for residual long-range potential of dopant ions near the interface. The Monte Carlo simulation of random dopant fluctuation in the C–V characteristics of 100 samples of MOS capacitors demonstrates that the main contributor to random dopant fluctuation is the location fluctuation of discrete dopant ions.

Effects of Thickness on the Responses of Piezoresponse Force Microscopy for Piezoelectric Film/Substrate Systems

Piezoresponse force microscopy (PFM) extends the conventional nano-indentation technique and has become one of the most widely used methods to determine the properties of small scale piezoelectric materials. Its accuracy depends largely on whether a reliable analytical model for the corresponding properties is available. Based on the coupled theory and the image charge model, a rigorous analysis of the film thickness effects on the electromechanical behaviors of PFM for piezoelectric films is presented. When the film is very thick, analytical solutions for the surface displacement, electric potential, image charge, image charge distance, and effective piezoelectric coefficient are obtained. For the infinitely thin (IT) film case, the corresponding closed-form solutions are derived. When the film is of finite thickness, a single parameter semi-empirical formula agreeing well with the numerical results is proposed for the effective piezoelectric coefficient. It is found that if the film thickness effect is not taken into account, PFM can significantly underestimate the effective piezoelectric coefficient compared to the half space result. The effects of the ambient dielectric property on PFM responses are also explored. Humidity reduces the surface displacement, broadens the radial distribution peak, and greatly enlarges the image charge, resulting in reduced effective piezoelectric coefficient. The proposed semi-empirical formula is also suitable to describe the thickness effects on the effective piezoelectric coefficient of thin films in humid environment. The obtained results can be used to quantitatively interpret the PFM signals and enable the determination of intrinsic piezoelectric coefficient through PFM measurement for thin films.

Reply to “Molecular mechanics models for the image charge”

We have considered the system investigated by Steinmann et al. by means of the image charge model originally proposed in Iori and Corni, J. Comput. Chem. 2008, 29, 1656. Qualitatively correct results are obtained, that compare favorably with the relevant analytical benchmarks. We show that the effect of the asymmetry of the rod model can be controlled, when needed, as originally suggested, that is, by shorter rods. This strategy does not increase neither the complexity of the model nor its computational cost. © 2017 Wiley Periodicals, Inc.

Molecular mechanics models for the image charge, a comment on “including image charge effects in the molecular dynamics simulations of molecules on metal surfaces”

We re-investigate the image charge model of Iori and Corni (Iori and Corni, J. Comput. Chem. 2008, 29, 1656). We find that a simple symmetrization of their model allows to obtain quantitatively correct results for the electrostatic interaction of a water molecule with a metallic surface. This symmetrization reduces the magnitude of the electrostatic interaction to less than 10% of the total interaction energy. © 2017 Wiley Periodicals, Inc.

Near field enhancement of TiO2 nanoparticle array on different substrates for femtosecond laser processing

Optical near field enhancement on substrate can be achieved by localizing femtosecond laser energy with nanoparticles. The enhanced field is located in the region between nanoparticles and the substrate. The localized femtosecond optical field is of great significance for fabricating the micro/nano structure with characteristic size beyond the diffraction limit. Up to now, femtosecond processing nanohole assisted by particle array is only possible for metal particle (Au) and low-refractive-index dielectric polystyrene particle. However, previous research results show that it cannot be realized for metal particle arrays (Au) to form periodic nanohole arrays, and it is limited for polystyrene particle to choose the corresponding substrate. In this paper, a novel method is proposed, in which high refractive index TiO2 arrayed particles are placed on the substrate to achieve laser induced near field enhancement. This makes feasible the nanoscale processing beyond the diffraction limit. In this paper, near field distributions of TiO2 particle array on Si, Pt and SiO2 substrates are simulated by the finite-difference time-domain (FDTD) method. The results show that TiO2 particles concentrate the laser energy to a region with a diameter of 100 nm around the particle and the near field enhancement is 140 times higher than the incident laser intensity, which is beneficial to fabricating the nanostructure of super diffraction limit, such as sub-hundred nanometer nanohole ablation by femtosecond laser. For Si substrate, the near field enhancement is only about 30% lower for TiO2 particle array than that for single TiO2 particle. In order to explore the influence mechanism of the substrate material parameters on the near field enhancement of TiO2 nanoparticle array, we further simulate the enhancement factor for the substrates of different refractive indices. It is found that the near field is enhanced with the increase of substrate refractive index, and this is attributed to an increased interaction of the particle with the near field of substrate and the scattering effect in which the TiO2 particle supports forward near field intensity pattern. Moreover, the image charge model is introduced to analyze the effect of substrate optical parameters on local field enhancement. Results in this paper can be applied to most metals as well as dielectric substrate surfaces, and they open a new way for femtosecond laser near field nano-processing with characteristic size beyond the diffraction limit.

Surface-sensitive measurement of dielectric screening via atom and electron manipulations

Dielectric screening is essential in determining semiconductor properties. Its assessment on the surface, however, is beyond the capability of conventional techniques due to their lack of surface sensitivity. Here we present the surface-sensitive measurement of the dielectric screening by using scanning tunneling microscopy and spectroscopy. Both single-atom and single-electron manipulations on the B $\ensuremath{\delta}$-doped Si(111) surface unravel that the dielectric screening on this surface is much in excess of what the classical image-charge model predicts, which we ascribe to the strained bonds and the ionic character of the surface layers. Also, as an exemplary application of the measured screening parameters, we demonstrate determining the ionization state of a surface defect from the defect-induced band bending.

Width and Crystal Orientation Dependent Band Gap Renormalization in Substrate-Supported Graphene Nanoribbons.

The excitation energy levels of two-dimensional (2D) materials and their one-dimensional (1D) nanostructures, such as graphene nanoribbons (GNRs), are strongly affected by the presence of a substrate due to the long-range screening effects. We develop a first-principles approach combining density functional theory (DFT), the GW approximation, and a semiclassical image-charge model to compute the electronic band gaps in planar 1D systems in weak interaction with the surrounding environment. Application of our method to the specific case of GNRs yields good agreement with the range of available experimental data and shows that the band gap of substrate-supported GNRs are reduced by several tenths of an electronvolt compared to their isolated counterparts, with a width and orientation-dependent renormalization. Our results indicate that the band gaps in GNRs can be tuned by controlling screening at the interface by changing the surrounding dielectric materials.

Charge transfer energies of benzene physisorbed on a graphene sheet from constrained density functional theory

Constrained density functional theory (CDFT) is used to evaluate the energy level alignment of a benzene molecule as it approaches a graphene sheet. Within CDFT the problem is conveniently mapped onto evaluating total energy differences between different charge-separated states, and it does not consist in determining a quasi-particle spectrum. We demonstrate that the simple local density approximation provides a good description of the level aligmnent along the entire binding curve, with excellent agreement to experiments at an infinite separation and to GW calculations close to the bonding distance. The method also allows us to explore the effects due to the presence of graphene structural defects and of multiple molecules. In general all our results can be reproduced by a classical image charge model taking into account the finite dielectric constant of graphene.

Asymptotic Effective Piezoelectric Coefficient Solution of Piezoresponse Force Microscopy for a Transversely Isotropic Piezoelectric Film

Based on the coupled theory, a simple explicit solution of piezoresponse force microscopy (PFM) in determining the effective piezoelectric coefficient for an ultra-thin transversely isotropic piezoelectric film bonded to a rigid conducting substrate is obtained, using the Taylor expansion and homogeneous assumption. And it is found to be exactly the same as the well-known result for the case of piezoelectric thin film clamped between flat rigid electrodes for homogeneous external electric field. The electric charge and the distance from the image charge model are also derived and the influences of the film thickness and substrate permittivity on the effective piezoelectric coefficient are then discussed. The obtained results can be used to quantitatively interpret the PFM signals and directly detect the piezoelectric constant through PFM for an ultra-thin film or supply important information for constructing a reliable formula to describe the thickness effect.

Charged hydrophobic colloids at an oil-aqueous phase interface.

Hydrophobic poly(methyl methacrylate) (PMMA) colloidal particles, when dispersed in oil with a relatively high dielectric constant, can become highly charged. In the presence of an interface with a conducting aqueous phase, image-charge effects lead to strong binding of colloidal particles to the interface, even though the particles are wetted very little by the aqueous phase. We study both the behavior of individual colloidal particles as they approach the interface and the interactions between particles that are already interfacially bound. We demonstrate that using particles which are minimally wetted by the aqueous phase allows us to isolate and study those interactions which are due solely to charging of the particle surface in oil. Finally, we show that these interactions can be understood by a simple image-charge model in which the particle charge q is the sole fitting parameter.

Electronic, structural, and substrate effect properties of single-layer covalent organic frameworks.

Recently synthesized two-dimensional covalent organic frameworks (COFs) exhibit high surface area, large pore size, and unique structural architectures, making them promising materials for various energy applications. Here, a total of nine COFs structures, including two deposited on a hexagonal boron nitride substrate, are investigated using density functional theory, quasi-particle many-body theory within the GW approximation, and an image charge model. The structures considered belong to two major families (thiophene-based COF-n (T-COF-n) and tetrakis (4-aminophenyl) porphyrin-x (TAPP-x)) differing from the presence of B-O or C=N linkers. While T-COF-n structures are shown to constitute planar networks, TAPP-x systems can display non-negligible corrugation due to the out-of-plane rotation of phenyl rings. We find that the electronic properties do not differ significantly when altering the chain molecules within each family. Many-body effects are shown to lead to large band-gap increase while the presence of the substrate yields appreciable reductions of the gaps, due to substrate polarization effects.

Uncertainties in the permittivity of thin films extracted from measurements with near field microwave microscopy calibrated by an image charge model

The microwave microscope is a device which utilises near fields to characterise material properties of samples on length scales smaller than the operating wavelength. The errors associated with extracting the permittivity of a high permittivity thin film on a low permittivity substrate from measurements using such a device are found to be of the order of 25% when using a widely used image charge model of the tip-sample interaction. The uncertainties arise from the model-based extraction of the permittivity from the raw frequency shift data, and in the current case are shown to come from the assumption in the model that the tip of the microwave probe can be modelled as a sphere.The raw data from the microscope contain random uncertainties of the order of 1% and reveal variations in the properties of the thin film with sub-wavelength resolution demonstrating the microwave microscope as a sub-wavelength characterisation technique for thin films.

Coulomb Fission in Dielectric Dication Clusters: Experiment and Theory on Steps That May Underpin the Electrospray Mechanism

A series of five molecular dication clusters, (H2O)n(2+), (NH3)n(2+), (CH3CN)n(2+), (C5H5N)n(2+), and (C6H6)n(2+), have been studied for the purpose of identifying patterns of behavior close to the Rayleigh instability limit where the clusters might be expected to exhibit Coulomb fission. Experiments show that the instability limit for each dication covers a range of sizes and that on a time scale of 10(-4) s ions close to the limit can undergo either Coulomb fission or neutral evaporation. The observed fission pathways exhibit considerable asymmetry in the sizes of the charged fragments, and are associated with kinetic (ejection) energies of ~0.9 eV. Coulomb fission has been modeled using a theory recently formulated to describe how charged particles of dielectric materials interact with one another (Bichoutskaia et al. J. Chem. Phys. 2010, 133, 024105). The calculated electrostatic interaction energy between separating fragments accounts for the observed asymmetric fragmentation and for the magnitudes of the measured ejection energies. The close match between theory and experiment suggests that a significant fraction of excess charge resides on the surfaces of the fragment ions. The experiments provided support for a fundamental step in the electrospray ionization (ESI) mechanism, namely the ejection from droplets of small solvated charge carriers. At the same time, the theory shows how water and acetonitrile may behave slightly differently as ESI solvents. However, the theory also reveals deficiencies in the point-charge image-charge model that has previously been used to quantify Coulomb fission in the electrospray process.

Electronic structure of assembled graphene nanoribbons: Substrate and many-body effects

Experimentally measured electronic band gaps of atomically sharp straight and chevronlike armchair graphene nanoribbons (GNRs) adsorbed on a gold substrate are smaller than theoretically predicted quasiparticle band gaps of their free-standing counterparts [Linden et al., Phys. Rev. Lett. 108, 216801 (2012)]. The influence of the substrate on electronic properties of both straight and chevronlike GNRs is here investigated including many-body effects beyond semilocal density-functional theory. The predicted small electron transfer from a straight or chevronlike GNR to the gold surface is found to lead to a surface polarization at the GNR-metal interface responsible for a significant reduction of the quasiparticle band gap of the GNR. This reduction is quantified using a semiclassical image charge model. By considering both quasiparticle and surface polarization corrections, we obtain theoretical band gaps that are consistent with experimental ones for gold-supported GNRs.

Treating highly charged carbon and fullerene clusters as dielectric particles

A model, recently developed for treating interactions between charged particles of dielectric materials (Bichoutskaia et al., J. Chem. Phys., 2010, 133, 024105), has been applied in an analysis of experimental data on the stability and fragmentation of highly charged carbon and fullerene clusters. Fragmentation data take the form of kinetic energy measurements that accompany the Coulomb fission of highly charged carbon clusters. For many of the examples chosen there is good agreement between the calculated and experimental results; however, the degree of uncertainty in some of the experimental data means that subtle features predicted by the model cannot be verified. When compared with an image charge model, treating carbon particles as a dielectric material reveals significant differences in the nature of the interaction potential.