46047-G5
Surfactant adsorption and self-assembly at solid/liquid interfaces
The surface tension, gamma, between a liquid and a solid is a
fundamental ingredient in the behavior and control of a wide range of
systems. For example, nanoparticles can be directed to self-assemble
into thin films at an oil/water interface by manipulating the
solid/water and solid/oil surface tensions. Since these assemblies
stabilize water-in-oil or oil-in-water droplets, they hold great
promise for encapsulation and tunable delivery strategies, and crude
oil recovery.
However, it is not possible to measure gamma by experiment. This is
discussed by Binks and Clint (Langmuir 2002, 18, 1270-1273) who
estimate the surface tensions on theoretical grounds. Such estimates
are approximate due to the many assumptions used. In contrast,
computer simulations offer the possibility of accurately computing
such surface tensions. We used three methods to compute the
solid/liquid surface tension for flat solids.
The contact angle of a static droplet of liquid on a flat solid
surface represents a state of mechanical equilibrium, and as such is
determined by a balance between three interfacial tensions: the
liquid/vapor surface tension, the solid/vapor surface tension, and the
solid/liquid interfacial tension. The equilibrium relation between
these quantities is known as Young's equation, which relates the
interaction energies between the pairs of phases to the contact angle
at which the three phases meet.
However, Young's equation is only valid for macroscopic droplets. For
microscopic droplets, the contact angle is influenced by the
three-phase solid/liquid/vapor contact line, which contributes an
additional energy per unit length called the line tension, tau. The
modified Young's equation accounts for the effect of line tension,
where R is the radius of the base of the droplet (in contact with the
solid): (gamma_lv)(cos theta_R) = gamma_sl - gamma_sv + tau/R (Eq. 1).
This equation can be related to the macroscopic contact angle in
Young’s equation by cos theta_R = cos theta + tau/(gamma_lv * R)
(Eq. 2).
Hence a plot of cos theta_R versus 1/(gamma_lv * R) yields a straight
line with slope tau and intercept cos theta. We carried out this
procedure for different size droplets using molecular dynamics
simulations, and published these results. Clearly something is wrong:
this contact angle data disagrees with the other two methods we used
to measure the solid/liquid surface tension. The accuracy of the other
methods is beyond doubt: the pressure tensor method is the most widely
used method in the simulation literature, and the solvation free
energy method follows directly from the thermodynamic definition of
surface tension.
We understand the reason for the failure of the contact angle method:
Equation (1) assumes that the surface tension gamma corresponds to a
flat liquid/vapor interface, but it is well-known that there are
curvature corrections to this surface tension. Hence Equation (2)
cannot be used and the extrapolation formula is invalid. We are
currently devising methods to measure the curvature corrections to the
liquid/vapor surface tension.
This is an important problem because experimentalists use this
extrapolation procedure to measure solid/liquid surface tensions, yet
we have shown that this method is inconsistent with the accepted
simulation methods to measure surface tension. The simulation
procedures and the new physics we observed have significantly impacted
the scientific development of the PI and the students involved in this
work, and we are excited to continue working on this important
problem.
