Frequency-dependent force between ac-voltage-biased plates in electrolyte solutions.

We analyze the frequency dependence of the force between ac-voltage-biased plates in electrolyte solutions. To this end we solve analytically the Poisson-Nernst-Planck transport model in the dilute concentration and low voltage regime for a 1:1 symmetric electrolyte with blocking electrodes under a dc+ac applied voltage. The total force, which is the resultant of the electric and osmotic forces, shows a complex dependence on plate separation, frequency, ion concentration, and compact layer properties, different from that predicted from electrostatic current models or equivalent circuit models, due to the relevance of the osmotic force contribution in almost the whole range of frequencies. For the total dc force, we show that it decays at fixed ion concentration, linearly with plate separation for separations larger than a few times the Debye screening length. This linear dependence is due to the assumption about the conservation of the number of ions in the system. Moreover, the 1ω and 2ω ac harmonics of the total force show a broad peak at intermediate frequencies; it is centered at about the inverse of the charging time of the double layer capacitance, and covers the frequency range between the inverse of the diffusion time and the inverse of the electrolyte dielectric relaxation time. Finally, the 1ω ac harmonic component attains its high frequency asymptotic value at frequencies much higher than the inverse of the electrolyte dielectric relaxation time due to the very slow relaxation of the osmotic 1ω harmonic component at high frequencies. The derived analytical expressions for the total force remain valid up to voltages of the order of the thermal voltage, as has been assessed by means of numerical calculations. The numerical calculations are also used to explore the onset of higher force harmonics for larger applied voltages. Understanding the frequency dependence of the force acting on voltage-biased plates in electrolyte solutions can be of relevance for electrical actuation strategies in microelectromechanical systems and for the interpretation of some emerging electric scanning probe force microscopy techniques operating in electrolyte solutions.

Sizing single nanoscale objects from polarization forces.

Sizing natural or engineered single nanoscale objects is fundamental in many areas of science and technology. To achieve it several advanced microscopic techniques have been developed, mostly based on electron and scanning probe microscopies. Still for soft and poorly adhered samples the existing techniques face important challenges. Here, we propose an alternative method to size single nanoscale objects based on the measurement of its electric polarization. The method is based on Electrostatic Force Microscopy measurements combined with a specifically designed multiparameter quantification algorithm, which gives the physical dimensions (height and width) of the nanoscale object. The proposed method is validated with ~50 nm diameter silver nanowires, and successfully applied to ~10 nm diameter bacterial polar flagella, an example of soft and poorly adhered nanoscale object. We show that an accuracy comparable to AFM topographic imaging can be achieved. The main advantage of the proposed method is that, being based on the measurement of long-range polarization forces, it can be applied without contacting the sample, what is key when considering poorly adhered and soft nanoscale objects. Potential applications of the proposed method to a wide range of nanoscale objects relevant in Material, Life Sciences and Nanomedicine is envisaged.