1,738 research outputs found
Geometric view of the thermodynamics of adsorption at a line of three-phase contact
We consider three fluid phases meeting at a line of common contact and study
the linear excesses per unit length of the contact line (the linear adsorptions
Lambda_i) of the fluid's components. In any plane perpendicular to the contact
line, the locus of choices for the otherwise arbitrary location of that line
that makes one of the linear adsorptions, say Lambda_2, vanish, is a
rectangular hyperbola. Two of the adsorptions, Lambda_2 and Lambda_3, then both
vanish when the contact line is chosen to pass through any of the intersections
of the two corresponding hyperbolas Lambda_2 = 0 and Lambda_3 = 0. There may be
two or four such real intersections. It is required, and is confirmed by
numerical examples, that a certain expression containing \Lambda_{1(2,3)}, the
adsorption of component 1 in a frame of reference in which the adsorptions
Lambda_2 and Lambda_3 are both 0, is independent of which of the two or four
intersections of Lambda_2 = 0 and Lambda_3 = 0 is chosen for the location of
the contact line. That is not true of Lambda_{1(2,3)} by itself; while the
adsorptions and the line tension together satisfy a linear analog of the Gibbs
adsorption equation, there are additional, not previously anticipated terms in
the relation that are required by the line tension's invariance to the
arbitrary choice of location of the contact line. The presence of the
additional terms is confirmed and their origin clarified in a mean-field
density-functional model. The additional terms vanish at a wetting transition,
where one of the contact angles goes to 0
Liquid drop in a cone - line tension effects
The shape of a liquid drop placed in a cone is analyzed macroscopically.
Depending on the values of the cone opening angle, the Young angle and the line
tension four different interfacial configurations may be realized. The phase
diagram in these variables is constructed and discussed; it contains both the
first- and the second-order transition lines. In particular, the tricritical
point is found and the value of the critical exponent characterizing the
behaviour of the system along the line of the first-order transitions in the
neighbourhood of this point is determined.Comment: 11 pages, 4 figure
Model of Hydrophobic Attraction in Two and Three Dimensions
An earlier one-dimensional lattice model of hydrophobic attraction is
extended to two and three dimensions and studied by Monte Carlo simulation. The
solvent-mediated contribution to the potential of mean force between
hydrophobic solute molecules and the solubility of the solute are determined.
As in the earlier model, an inverse relation is observed between the strength
and range of the hydrophobic attraction. The mean force no longer varies
monotonically with distance, as it does in one dimension, but has some
oscillations, reflecting the greater geometrical complexity of the lattice in
the higher dimensions. In addition to the strong attraction at short distances,
there is now also a local minimum in the potential of depth about at a
distance of three lattice spacings in two dimensions and one of depth about
at a distance of two lattice spacings in three dimensions. The solubility
of the solute is found to decrease with increasing temperature at low
temperatures, which is another signature of the hydrophobic effect and also
agrees with what had been found in the one-dimensional model.Comment: 4 pages, 4 figures, submitted to J. Chem. Phy
Molecular correlations and solvation in simple fluids
We study the molecular correlations in a lattice model of a solution of a
low-solubility solute, with emphasis on how the thermodynamics is reflected in
the correlation functions. The model is treated in Bethe-Guggenheim
approximation, which is exact on a Bethe lattice (Cayley tree). The solution
properties are obtained in the limit of infinite dilution of the solute. With
, , and the three pair correlation functions
as functions of the separation (subscripts 1 and 2 referring to solvent and
solute, respectively), we find for lattice steps that
. This illustrates a general
theorem that holds in the asymptotic limit of infinite . The three
correlation functions share a common exponential decay length (correlation
length), but when the solubility of the solute is low the amplitude of the
decay of is much greater than that of , which in turn is
much greater than that of . As a consequence the amplitude of the
decay of is enormously greater than that of . The
effective solute-solute attraction then remains discernible at distances at
which the solvent molecules are essentially no longer correlated, as found in
similar circumstances in an earlier model. The second osmotic virial
coefficient is large and negative, as expected. We find that the
solvent-mediated part of the potential of mean force between solutes,
evaluated at contact, , is related in this model to the Gibbs free energy
of solvation at fixed pressure, , by , where is the coordination number of the lattice, the
pressure, and the volume of the cell associated with each lattice site. A
large, positive associated with the low solubility is thus
reflected in a strong attraction (large negative at contact), which is the
major contributor to the second osmotic virial coefficient. In this model, the
low solubility (large positive ) is due partly to an unfavorable
enthalpy of solvation and partly to an unfavorable solvation entropy, unlike in
the hydrophobic effect, where the enthalpy of solvation itself favors high
solubility, but is overweighed by the unfavorable solvation entropy.Comment: 9 pages, 2 figure
Line adsorption in a mean-field density functional model
Recent ideas about the analog for a three-phase contact line of the Gibbs adsorption equation for interfaces are illustrated in a mean-field density-functional model. With the infinitesimal change in the line tension that accompanies the infinitesimal changes in the thermodynamic field variables and with the line adsorptions, the sum , unlike its surface analog, is not 0. An equivalent of this sum in the model system is evaluated numerically and analytically. A general line adsorption equation, which the model results illustrate, is derived.</p
Symmetry effects and equivalences in lattice models of hydrophobic interaction
We establish the equivalence of a recently introduced discrete model of the
hydrophobic interaction, as well as its extension to continuous state
variables, with the Ising model in a magnetic field with temperature-dependent
strength. In order to capture the effect of symmetries of the solvent particles
we introduce a generalized multi-state model. We solve this model - which is
not of the Ising type - exactly in one dimension. Our findings suggest that a
small increase in symmetry decreases the amplitude of the solvent-mediated part
of the potential of mean force between solute particles and enhances the
solubility in a very simple fashion. High symmetry decreases also the range of
the attractive potential. This weakening of the hydrophobic effect observed in
the model is in agreement with the notion that the effect is entropic in
origin.Comment: 19 pages, 2 figure
Fluctuations in Mass-Action Equilibrium of Protein Binding Networks
We consider two types of fluctuations in the mass-action equilibrium in
protein binding networks. The first type is driven by relatively slow changes
in total concentrations (copy numbers) of interacting proteins. The second
type, to which we refer to as spontaneous, is caused by quickly decaying
thermodynamic deviations away from the equilibrium of the system. As such they
are amenable to methods of equilibrium statistical mechanics used in our study.
We investigate the effects of network connectivity on these fluctuations and
compare them to their upper and lower bounds. The collective effects are shown
to sometimes lead to large power-law distributed amplification of spontaneous
fluctuations as compared to the expectation for isolated dimers. As a
consequence of this, the strength of both types of fluctuations is positively
correlated with the overall network connectivity of proteins forming the
complex. On the other hand, the relative amplitude of fluctuations is
negatively correlated with the abundance of the complex. Our general findings
are illustrated using a real network of protein-protein interactions in baker's
yeast with experimentally determined protein concentrations.Comment: 4 pages, 3 figure
The Dynamics of the One-Dimensional Delta-Function Bose Gas
We give a method to solve the time-dependent Schroedinger equation for a
system of one-dimensional bosons interacting via a repulsive delta function
potential. The method uses the ideas of Bethe Ansatz but does not use the
spectral theory of the associated Hamiltonian
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