Debye length | EPFL Graph Search

In plasmas and electrolytes, the Debye length \lambda_{\rm D} (Debye radius or Debye–Hückel screening length), is a measure of a charge carrier's net electrostatic effect in a solution and how far its electrostatic effect persists. With each Debye length the charges are increasingly electrically screened and the electric potential decreases in magnitude by 1/e. A Debye sphere is a volume whose radius is the Debye length. Debye length is an important parameter in plasma physics, electrolytes, and colloids (DLVO theory). The corresponding Debye screening wave vector k_{\rm D}=1/\lambda_{\rm D} for particles of density n, charge q at a temperature T is given by k_{\rm D}^2=4\pi n q^2/(k_{\rm B}T) in Gaussian units. Expressions in MKS units will be given below. The analogous quantities at very low temperatures (T \to 0) are known as the Thomas–Fermi length and the Thomas–Fermi wave vector. They

Sheath collapse at critical shallow angle due to kinetic effects

Alessandro Geraldini

The Debye sheath is known to vanish completely in magnetised plasmas for a sufficiently small electron gyroradius and small angle between the magnetic field and the wall. This angle depends on the current onto the wall. When the Debye sheath vanishes, there is still a potential drop between the wall and the plasma across the magnetic presheath. The magnetic field angle corresponding to the predicted sheath collapse is shown to be much smaller than previous estimates, scaling with the electron-ion mass ratio and not with the square root of the mass ratio. This is shown to be a consequence of the kinetic electron and finite ion orbit width effects, which are not captured by fluid models. The wall potential with respect to the bulk plasma at which the Debye sheath vanishes is calculated. Above this wall potential, it is possible that the Debye sheath will invert.

IOP Publishing Ltd2022

Interaction of polyelectrolytes with oppositely charged surfaces

Vesela Malinova

Despite progress during the last decade, the behavior of charged macromolecules, polyelectrolytes, including their interactions is not yet completely understood. In particular, interactions with oppositely charged surfaces, which play a significant role in many practical applications and are of central importance in life processes, need more investigation. This situation has motivated the selection of the topic of this doctoral thesis. The study is dedicated to interactions of positively charged polyelectrolytes with negatively charged surfaces considering two types of surfaces, flat amphiphile monolayers and porous surfaces of microspheres. The research aimed at quantitative evaluation of the influence of macromolecular dimensions, chemical structure, electrostatic parameters, and surface characteristics on the adsorption process. As a prerequisite, a series of poly(vinylbenzyltrialkylammonium chloride) model polyelectrolytes has been synthesized. The characteristics were five defined contour lengths with three different types of substituents at the quaternary ammonium group each in addition to uniform charge density and narrow chain length distribution. The final polyelectrolytes were the quaternization products of precursors synthesized by controlled radical polymerization. Two experimental techniques were employed to quantify the influence of chemical, macromolecular, and electrostatic parameters as well as geometrical characteristics on the adsorption of polyelectrolytes on porous microsphere surfaces. These were adsorption on microspheres suspended in aqueous phase and microspheres packed in a chromatography column. During the first technique the total surface comes immediately in contact with the polyelectrolyte molecules, whereas the second technique followed the rules of chromatography. For the first time, the contour length of the polyelectrolyte, the Debye length, the pore dimensions, as well as the chemical structure were likewise considered in a comprehensive study to describe the interaction of polyelectrolytes with well-characterized porous surfaces. A polyelectrolyte charge to surface charge ratio was defined and served to classify different adsorption behavior. Three models have been proposed to illustrate the adsorption behavior based on experimental findings and model calculations. The first one identifies the Debye length in addition to the contour length as dominating parameter, which decides whether a polyelectrolyte molecule can enter a pore or not. The second quantifies the influence of the contour length. Finally, the third describes the concentration influence on the type of molecule organization, layer formation, on the outer surface or inside of pores with diameters exceeding considerably the contour length. For amphiphile monolayer, for the first time, the influence of chain length and substituent at the quaternary ammonium group on the adsorption process was quantified. Based on the surface pressure, pressure-area and pressure-time isotherms measured, a model describing the monolayer arrangement on polyelectrolyte solutions was proposed. A second model correlates the increase of the area per amphiphile molecule and the decrease of the surface pressure with the size and hydrophobicity of the substituents. In addition chain length influence was evident. The results of the thesis contribute to progress in basic research in the field of polyelectrolytes, while also an impact on technical applications such as surface modification, chromatographic processes or improvement of materials is expected. Precise data for comparison with theoretical model calculations are provided, which were not available before.

EPFL2005

A fully-implicit Particle-In-Cell Monte Carlo Collision code for the simulation of inductively coupled plasmas

Stefano Mattei, Minh Quang Tran

We present a fully-implicit electromagnetic Particle-In-Cell Monte Carlo collision code, called NINJA, written for the simulation of inductively coupled plasmas. NINJA employs a kinetic enslaved Jacobian-Free Newton Krylov method to solve self-consistently the interaction between the electromagnetic field generated by the radio-frequency coil and the plasma response. The simulated plasma includes a kinetic description of charged and neutral species as well as the collision processes between them. The algorithm allows simulations with cell sizes much larger than the Debye length and time steps in excess of the Courant-Friedrichs-Lewy condition whilst preserving the conservation of the total energy. The code is applied to the simulation of the plasma discharge of the Linac4 H- ion source at CERN. Simulation results of plasma density, temperature and EEDF are discussed and compared with optical emission spectroscopy measurements. A systematic study of the energy conservation as a function of the numerical parameters is presented. (C) 2017 The Authors. Published by Elsevier Inc.

2017

Interaction of polyelectrolytes with oppositely charged surfaces

Vesela Malinova

EPFL2005