9 research outputs found
Density functional theory of electrowetting
The phenomenon of electrowetting, i.e., the dependence of the macroscopic
contact angle of a fluid on the electrostatic potential of the substrate, is
analyzed in terms of the density functional theory of wetting. It is shown that
electrowetting is not an electrocapillarity effect, i.e., it cannot be
consistently understood in terms of the variation of the substrate-fluid
interfacial tension with the electrostatic substrate potential, but it is
related to the depth of the effective interface potential. The key feature,
which has been overlooked so far and which occurs naturally in the density
functional approach is the structural change of a fluid if it is brought into
contact with another fluid. These structural changes occur in the present
context as the formation of finite films of one fluid phase in between the
substrate and the bulk of the other fluid phase. The non-vanishing Donnan
potentials (Galvani potential differences) across such film-bulk fluid
interfaces, which generically occur due to an unequal partitioning of ions as a
result of differences of solubility contrasts, lead to correction terms in the
electrowetting equation, which become relevant for sufficiently small substrate
potentials. Whereas the present density functional approach confirms the
commonly used electrocapillarity-based electrowetting equation as a good
approximation for the cases of metallic electrodes or electrodes coated with a
hydrophobic dielectric in contact with an electrolyte solution and an ion-free
oil, a significantly reduced tendency for electrowetting is predicted for
electrodes coated with a dielectric which is hydrophilic or which is in contact
with two immiscible electrolyte solutions.Comment: Submitte
Order of wetting transitions in electrolyte solutions
For wetting films in dilute electrolyte solutions close to charged walls we
present analytic expressions for their effective interface potentials. The
analysis of these expressions renders the conditions under which corresponding
wetting transitions can be first- or second-order. Within mean field theory we
consider two models, one with short- and one with long-ranged solvent-solvent
and solvent-wall interactions. The analytic results reveal in a transparent way
that wetting transitions in electrolyte solutions, which occur far away from
their critical point (i.e., the bulk correlation length is less than half of
the Debye length) are always first-order if the solvent-solvent and
solvent-wall interactions are short-ranged. In contrast, wetting transitions
close to the bulk critical point of the solvent (i.e., the bulk correlation
length is larger than the Debye length) exhibit the same wetting behavior as
the pure, i.e., salt-free, solvent. If the salt-free solvent is governed by
long-ranged solvent-solvent as well as long-ranged solvent-wall interactions
and exhibits critical wetting, adding salt can cause the occurrence of an
ion-induced first-order thin-thick transition which precedes the subsequent
continuous wetting as for the salt-free solvent.Comment: Submitte
Three-phase contact line and line tension of electrolyte solutions in contact with charged substrates
The three-phase contact line formed by the intersection of a liquid-vapor
interface of an electrolyte solution with a charged planar substrate is studied
in terms of classical density functional theory applied to a lattice model. The
influence of the substrate charge density and of the ionic strength of the
solution on the intrinsic structure of the three-phase contact line and on the
corresponding line tension is analyzed. We find a negative line tension for all
values of the surface charge density and of the ionic strength considered. The
strength of the line tension decreases upon decreasing the contact angle via
varying either the temperature or the substrate charge density
Wetting in electrolyte solutions
Wetting of a charged substrate by an electrolyte solution is investigated by
means of classical density functional theory applied to a lattice model. Within
the present model the pure, i.e., salt-free solvent, for which all interactions
are of the nearest-neighbor type only, exhibits a second-order wetting
transition for all strengths of the substrate-particle and the
particle-particle interactions for which the wetting transition temperature is
nonzero. The influences of the substrate charge density and of the ionic
strength on the wetting transition temperature and on the order of the wetting
transition are studied. If the substrate is neutral, the addition of salt to
the solvent changes neither the order nor the transition temperature of the
wetting transition of the system. If the surface charge is nonzero, upon adding
salt this continuous wetting transition changes to first-order within the wide
range of substrate surface charge densities and ionic strengths studied here.
As the substrate surface charge density is increased, at fixed ionic strength,
the wetting transition temperature decreases and the prewetting line associated
with the first-order wetting transition becomes longer. This decrease of the
wetting transition temperature upon increasing the surface charge density
becomes more pronounced by decreasing the ionic strength.Comment: submitte
Benetzungsphänomene in Elektrolytlösungen
The present study analyzes wetting phenomena in electrolyte solutions. They are investigated by means of classical density functional theory. First, the wetting of a charged substrate by an electrolyte solution is studied with emphasis on the influence of the substrate charge density and of the ionic strength on the wetting transition temperature and on the order of the wetting transition. The corresponding models consist of solvent particles, anions, and cations. Two mean field approaches are used:
(1) A lattice model (Chap. 3) within which particles occupy the sites of a semi-infinite simple cubic lattice. Each site is either empty or occupied by a single particle and the particles interact among each other via an attractive nearest-neighbor interaction which is taken to be the same for all pairs of particles. In addition, ion pairs interact via the Coulomb potential. The substrate can carry a homogeneous surface charge density and additionally attracts particles in the first layer adjacent to it.
(2) A continuum model (Chap. 4) with short- and long-ranged solvent-solvent and substrate-solvent interactions and with ions interacting among each other and with the wall only via the electrostatic field.
For the lattice model, the pure, i.e., salt-free, solvent exhibits a second-order wetting transition for all strengths of the substrate-particle and the particle-particle interactions for which the wetting transition temperature is nonzero. If the substrate is neutral, the addition of salt to the solvent changes neither the order nor the transition temperature of the wetting transition of the system. On the other hand, if the surface charge is nonzero, upon adding salt this continuous wetting transition changes to first-order within the range of substrate surface charge densities and ionic strengths considered here. As the substrate surface charge density is increased, for fixed ionic strength, the wetting transition temperature decreases. Moreover, the wetting transition temperature decreases when the ionic strength is decreased for fixed surface charge density.
For the continuum model, expressions for the effective interface potential are derived analytically. The analysis of these expressions renders the conditions under which corresponding wetting transitions can be first- or second-order. The analytic results reveal in a transparent way that wetting transitions in electrolyte solutions, which occur far away from their critical point (i.e., the bulk correlation length is less than half of the Debye length), are always first-order if the solvent-solvent and solvent-wall interactions are short-ranged. In contrast, wetting transitions close to the bulk critical point of the solvent (i.e., the bulk correlation length is larger than the Debye length) exhibit the same wetting behavior as the pure, i.e., salt-free, solvent. If the salt-free solvent is governed by long-ranged solvent-solvent as well as long-ranged substrate-solvent interactions and exhibits critical wetting, adding salt can cause the occurrence of an ion-induced first-order thin-thick transition which precedes the subsequent continuous wetting as for the salt-free solvent.
The phenomenon of electrowetting, i.e., the dependence of the macroscopic contact angle of a fluid on the electrostatic potential of the substrate, is studied in Chap. 5 for a vertical parallel plate capacitor in contact with two immiscible fluids, where at least one of the two fluids is an electrolyte solution. Here, the possibility of the formation of films of microscopic thickness on the substrates, widely ignored in the context of electrowetting, is taken into account. This approach allows one to transparently derive the electrowetting equation. The derivation shows that electrowetting is a consequence of the voltage-dependence of the depth of the effective interface potential.
Finally, the line tension and the three-phase contact line structure of a drop of an electrolyte solution on a charged substrate are investigated within the lattice model in Chap. 6. For the pure solvent, the equilibrium liquid-gas interface profile approaches its asymptote from above, as expected for second-order wetting transitions and the line tension depends linearly on the contact angle the drop makes with the substrate. For the electrolyte solution, the equilibrium liquid-gas interface profile approaches its asymptote from below as expected for first-order wetting transitions. When the contact angle is changed by varying the temperature while keeping the surface charge fixed, the line tension increases as the temperature is increased, i.e, as the contact angle is decreased. When the contact angle is changed by varying the surface charge density at fixed temperature, the line tension increases as the surface charge is increased. The equilibrium structure of the three-phase contact line for different charge densities has been calculated.In der vorliegenden Arbeit werden Benetzungsphänomene in Elektrolytlösungen mittels klassischer Dichtefunktionaltheorie untersucht. Zunächst wird der Einfluss der Oberflächenladungsdichte und der Ionenstärke auf die Übergangstemperatur und die Ordnung des Benetzungsübergangs beim Benetzen eines elektrisch geladenen Substrats durch eine Elektrolytlösung studiert. Die hier betrachteten Elektrolytösungen bestehend aus drei Teilchensorten: Lösungsmittel, Anionen und Kationen. Es werden zwei verschiedene Molekularfeld-Näherungen verwendet:
(1) Ein Gitter-Modell (Kapitel 3), in welchem die Gitterplätze eines halbunendlichen einfach-kubischen Gitters entweder leer oder von nur einem Teilchen besetzt sind. Alle direkt benachbarten Teilchen wechselwirken attraktiv miteinander. Zusätzlich wechselwirken Ionen durch das Coulomb-Potential miteinander. Das Substrat kann eine homogene Oberflächenladung tragen und zusätzlich wirkt es attraktiv auf die Fluid-Teilchen in der direkt angrenzenden Schicht.
(2) Ein Kontinuum-Modell (Kapitel 4) mit kurz- und langreichweitigen Wechselwirkungen, in welchem die Ionen miteinander und mit der Wand ausschließ lich mittels des elektrostatischen Felds wechselwirken.
Für das Gitter-Modell, die reine, d.h. salzfreie, Lösung zeigt einen Benetzungsübergang zweiter Ordnung bei allen Stärken der Substrat-Fluid- und der Fluid-Fluid-Wechselwirkung, bei denen die Benetzungstemperatur über dem absoluten Nullpunkt liegt. Bei einem elektrisch neutralen Substrat ändert die Zugabe von Salz zur Lösung weder die Temperatur noch die Ordnung des Benetzungsübergangs. Ist as Substrat hingegen geladen, ändert sich für die hier betrachteten Ladungsdichten und Ionenstärken der kontinuierliche Benetzungsübergang in einen erster Ordnung. Bei konstanter Ionenstärke sinkt die Benetzungstemperatur mit steigender Oberflächenladungsdichte. Außerdem sinkt die Benetzungstemperatur bei konstanter Oberflächenladungsdichte mit abnehmender Ionenstärke.
Innerhalb des Kontinuummodells wurden analytische Ausdrücke für das effektive Grenzflächenpotential hergeleitet. Eine Analyse dieser Ausdrücke gibt Aufschluss über die Bedingungen, unter welchen Benetzungsübergänge von erster Ordnung oder kontinuierlich sein können. Die analytischen Ergebnisse zeigen, dass Benetzungsübergänge in Elektrolytlösungen weit entfernt vom kritischen Punkt (d.h. die Korrelationslänge beträgt weniger als die Hälfte der Debye-Länge) bei ausschließ lich kurzreichweitigen Wechselwirkungen stets von erster Ordnung sind. Dagegen zeigen Benetzungsübergänge in der Nähe des kritischen Punkts (d.h. die Korrelationslänge ist größer als die Debye-Länge) dasselbe Benetzungsverhalten wie das reine, d.h. salzfreie, Lösungsmittel. Wenn das salzfreie Lösungsmittel durch langreichweitige Wechselwirkungen beschrieben wird und einen kritischen Benetzungsübergang aufweist, kann das Hinzufügen von Salz das Auftreten eines ioneninduzierten dünn-dick Übergangs erster Ordnung bewirken, der anschließ endem kontinuierlichem Benetzen vorausgeht, wie beim salzfreien Lösungsmittel.
Das Phänomen "electrowetting", d.h. die Abhängigkeit des makroskopischen Kontaktwinkels eines Fluids vom elektrostatischen Potential des Substrats, wird in Kapitel 5 für den Fall eines vertikalen Plattenkondensators in Kontakt mit zwei nicht mischbaren Fluiden untersucht, von denen mindestens eine eine elektrolytische Lösung ist. Dabei wird die weithin ignorierte Möglichkeit berücksichtigt, dass sich Benetzungsfilme mikroskopischer Dicke auf dem Substrat bilden können. Dieser Ansatz erlaubt es die sogenannte "electrowetting equation" herzuleiten. Diese Herleitung zeigt, dass "electrowetting" eine Folge der Spannungsabhängigkeit der Tiefe des effektiven Grenzflächenpotentials ist.
Schließlich wurden die Linienspannung und die Struktur der Dreiphasenkontaktlinie eines Tropfens elektrolytischer Lösung auf einem geladenen Substrat innerhalb des Gittermodells in Kapitel 6 untersucht. Im Falle des reinen Lösungsmittels nähert sich das Grenzflächenprofil zwischen Flüssigkeit und Gas seiner Asymptoten "von oben" an, wie dies für kontinuierliche Benetzungsübergänge erwartet wird, und die Linienspannung hängt linear vom Kontaktwinkel ab, den der Tropfen mit dem Substrat bildet. Im Fall der elektrolytischen Lösung nähert sich das Grenzflächenprofil zwischen Flüssigkeit und Gas seiner Asymptoten "von unten" an, wie dies für Benetzungsübergänge erster Ordnung zu erwarten ist. Wenn der Kontaktwinkel durch Temperaturerhöhung bei konstanter Oberflächenladung verringert wird, erhöht sich die Linienspannung. Wenn der Kontaktwinkel durch Erhöhung der Oberflächenladungsdichte bei konstanter Temperatur verringert wird, erhöht sich die Linienspannung.Die Gleichgewichtsstruktur der Dreiphasenkontaktlinie wurde für verschiedene Ladungsdichten berechnet