22 research outputs found
On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
We show that to account for the full spectrum of surface fluctuations from
low scattering vector qd << 1 (classical capillary wave theory) to high qd > 1
(bulk-like fluctuations), one must take account of the interface's bending
rigidity at intermediate scattering vector qd = 1, where d is the molecular
diameter. A molecular model is presented to describe the bending correction to
the capillary wave model for short-ranged and long-ranged interactions between
molecules. We find that the bending rigidity is negative when the Gibbs
equimolar surface is used to define the location of the fluctuating interface
and that on approach to the critical point it vanishes proportionally to the
interfacial tension. Both features are in agreement with Monte Carlo
simulations of a phase-separated colloid-polymer system.Comment: 18 pages, 11 figures, accepted for publication in The Journal of
Chemical Physic
The existence of a bending rigidity for a hard sphere liquid near a curved hard wall: Helfrich or Hadwiger?
In the context of Rosenfeld's Fundamental Measure Theory, we show that the
bending rigidity is not equal to zero for a hard-sphere fluid in contact with a
curved hard wall. The implication is that the Hadwiger Theorem does not hold in
this case and the surface free energy is given by the Helfrich expansion
instead. The value obtained for the bending rigidity is (1) an order of
magnitude smaller than the bending constant associated with Gaussian curvature,
(2) changes sign as a function of the fluid volume fraction, (3) is independent
of the choice for the location of the hard wall.Comment: 19 pages, 5 figures, to appear in Physical Review
On the spectrum of fluctuations of a liquid surface: From the molecular scale to the macroscopic scale
We show that to account for the full spectrum of surface fluctuations from
low scattering vector qd 1
(bulk-like fluctuations), one must take account of the interface's bending
rigidity at intermediate scattering vector qd = 1, where d is the molecular
diameter. A molecular model is presented to describe the bending correction to
the capillary wave model for short-ranged and long-ranged interactions between
molecules. We find that the bending rigidity is negative when the Gibbs
equimolar surface is used to define the location of the fluctuating interface
and that on approach to the critical point it vanishes proportionally to the
interfacial tension. Both features are in agreement with Monte Carlo
simulations of a phase-separated colloid-polymer system.Comment: 18 pages, 11 figures, accepted for publication in The Journal of
Chemical Physic
Density Functional Theory of a Curved Liquid-Vapour Interface: Evaluation of the rigidity constants
It is argued that to arrive at a quantitative description of the surface
tension of a liquid drop as a function of its inverse radius, it is necessary
to include the bending rigidity k and Gaussian rigidity k_bar in its
description. New formulas for k and k_bar in the context of density functional
theory with a non-local, integral expression for the interaction between
molecules are presented. These expressions are used to investigate the
influence of the choice of Gibbs dividing surface and it is shown that for a
one-component system, the equimolar surface has a special status in the sense
that both k and k_bar are then the least sensitive to a change in the location
of the dividing surface. Furthermore, the equimolar value for k corresponds to
its maximum value and the equimolar value for k_bar corresponds to its minimum
value. An explicit evaluation using a short-ranged interaction potential
between molecules, shows that k is negative with a value around minus 0.5-1.0
kT and that k_bar is positive with a value which is a bit more than half the
magnitude of k. Finally, for dispersion forces between molecules, we show that
a term proportional to log(R)/R^2 replaces the rigidity constants and we
determine the (universal) proportionality constants.Comment: 28 pages; 5 figures; accepted for publication in J. Phys.: Condens.
Matter (2013
Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples
acceptedVersio
Description of the fluctuating colloid-polymer interface
To describe the full spectrum of surface fluctuations of the interface
between phase-separated colloid-polymer mixtures from low scattering vector q
(classical capillary wave theory) to high q (bulk-like fluctuations), one must
take account of the interface's bending rigidity. We find that the bending
rigidity is negative and that on approach to the critical point it vanishes
proportionally to the interfacial tension. Both features are in agreement with
Monte Carlo simulations.Comment: 5 pages, 3 figures, 1 table. Accepted for publication in Phys. Rev.
Let
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Tolman lengths and rigidity constants of multicomponent fluids: Fundamental theory and numerical examples
The curvature dependence of the surface tension can be described by the Tolman length (first-order correction) and the rigidity constants (second-order corrections) through the Helfrich expansion. We present and explain the general theory for this dependence for multicomponent fluids and calculate the Tolman length and rigidity constants for a hexane-heptane mixture by use of square gradient theory. We show that the Tolman length of multicomponent fluids is independent of the choice of dividing surface and present simple formulae that capture the change in the rigidity constants for different choices of dividing surface. For multicomponent fluids, the Tolman length, the rigidity constants, and the accuracy of the Helfrich expansion depend on the choice of path in composition and pressure space along which droplets and bubbles are considered. For the hexane-heptane mixture, we find that the most accurate choice of path is the direction of constant liquid-phase composition. For this path, the Tolman length and rigidity constants are nearly linear in the mole fraction of the liquid phase, and the Helfrich expansion represents the surface tension of hexane-heptane droplets and bubbles within 0.1% down to radii of 3 nm. The presented framework is applicable to a wide range of fluid mixtures and can be used to accurately represent the surface tension of nanoscopic bubbles and droplets
Correspondence between the pressure expressions and van der Waals theory for a curved surface
We investigate the apparent contradiction between the pressure expressions, or ‘‘mechanical
expressions,’’ and the van der Waals squared-gradient expressions for the curvature coefficients
k/R0 , k, and k¯. We show that, in the context of the mean-field theory discussed, both types of
expression are indeed equivalent, with the differences only being caused by the thermodynamic
conditions used to vary the curvature