Quantification of the dielectric constant of single non-spherical nanoparticles from polarization forces: eccentricity effects

Abstract

We analyze by means of finite-element numerical calculations the polarization force between a sharp conducting tip and a non-spherical uncharged dielectric nanoparticle with the objective of quantifying its dielectric constant from electrostatic force microscopy (EFM) measurements. We show that for an oblate spheroid nanoparticle of given height the strength of the polarization force acting on the tip depends linearly on the eccentricity, e, of the nanoparticle in the small eccentricity and low dielectric constant regimes (1 < e < 2 and 1 < ε(r) < 10), while for higher eccentricities (e > 2) the dependence is sub-linear and finally becomes independent of e for very large eccentricities (e > 30). These results imply that a precise account of the nanoparticle shape is required to quantify EFM data and obtain the dielectric constants of non-spherical dielectric nanoparticles. Experimental results obtained on polystyrene, silicon dioxide and aluminum oxide nanoparticles and on single viruses are used to illustrate the main findings.

Fast Label‐Free Nanoscale Composition Mapping of Eukaryotic Cells Via Scanning Dielectric Force Volume Microscopy and Machine Learning

“…[46,47] The nanoelongations have heights in the range ≈100-200 nm, and widths in the range ≈500-700 nm. For these dimensions, finite size effects can be relevant, [46] and hence the dielectric constant value extracted can depend on the actual size of the nanostructure, as we demonstrated for the case of nanoparticles and virus particles, [47] bacterial cells, [17,18,20] square slab thin films [46] and bacterial flagella. [19] While the height of the nanostructure can be accurately determined from the topographic image, its width is affected by tip convolution effects, which tend to increase it.…”

“…For these nanostructures the relevance of tip convolution and finite size effects should be analyzed, as discussed elsewhere. [ 46,47 ] The nanoelongations have heights in the range ≈100–200 nm, and widths in the range ≈500–700 nm. For these dimensions, finite size effects can be relevant, [ 46 ] and hence the dielectric constant value extracted can depend on the actual size of the nanostructure, as we demonstrated for the case of nanoparticles and virus particles, [ 47 ] bacterial cells, [ 17,18,20 ] square slab thin films [ 46 ] and bacterial flagella.…”

“…This fact can produce dielectric constant values systematically lower than the actual values. [ 47 ] However, applying tip‐convolution analysis to nanostructures with nonregular geometries, like the cell membrane nanoelongations, is very complex, and in general, it cannot be done in an unambiguous way. The fact that the nanoelongations show an almost uniform dielectric constant value (ε 1 ≈ 2 ± 0.4) despite its relatively irregular shape and size constitutes an indication that finite size and tip convolution effects are probably not very relevant in the present case.…”

Characterizing Dielectric Permittivity of Nanoscale Dielectric Films by Electrostatic Micro-Probe Technology: Finite Element Simulations

“…In the modeling of planar dielectrics, the sample is usually constructed as laterally infinite to reduce the influence of plane size on the probe-induced electrostatic force. Although the accurately quantitative analysis cannot be carried out with the simplified model, the tested data from probe detection can be physically interpreted, which is qualified to represent the finite lateral dimension of dielectric nanofilm [27]. Under the action of electrostatic force, the electrostatic probe fluctuates up and down with the change of the sample surface profile and causes substantial vibrations of microcantilever during the EFM scanning process.…”

Sizing single nanoscale objects from polarization forces

“…The proposed method consists in measuring the electric polarization of single nano-objects by EFM, and then use a multiparameter quantification algorithm to retrieve the dimensions of the nano-object that best reproduces the measured electric polarization (by assuming the dielectric constant of the object to be known, see discussion). The dependence of the electric polarization of an object on its shape and size is a well-known property of polarizable materials 34,35 . The quantification algorithm to extract the physical dimensions of the nano-object from the measured polarization forces is inspired in the method developed earlier to measure the dielectric constant of nanoscale objects 36 , but generalized to the much more complex situation of multiple parameter extraction (here the width and height).…”