The City College and The Graduate Center of

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Wetting of hydrophobic substrates by aqueous
surfactant solutions A classical molecular
dynamics study
A doctoral research proposal by
Jonathan D. Halverson1
Under the faculty advisement of
J. Koplik2, A. Couzis1, C. Maldarelli1
Department of Chemical Engineering1, Department
of Physics2
The Benjamin Levich Institute of Physico-chemical
Hydrodynamics
The City College and The Graduate Center of
The City University of New York
Second Examination
September 16, 2004
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Wetting phenomena
According to hydrodynamic theory, a drop on a
flat surface assumes the shape of a spherical cap
The Young equation relates the contact angle ? of
a sessile drop to the various interfacial
tensions
where ?SV is the solid-vapor tension, ? is the
liquid-vapor tension, and ?SL is the solid-liquid
tension.
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Surfactants
A molecule formed by the bonding of a hydrophilic
group to a lipophilic group is said to be
amphiphilic due to its attraction for both water
and oil phases. Amphiphilic molecules are driven
towards interfaces making them interface- or
surface-active agents or surfactants.
CH3(CH2)11OSO3Na
Surfactant molecules display a rich phase
behavior above a critical concentration.
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Motivation
In the application of paint, ink, a herbicide
solution, or a coating to a hydrophobic surface
it is important for the fluid to completely wet
the surface.
Surfactants may be used to enhance the wetting of
aqueous solutions on hydrophobic substrates.
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Objectives
Elucidate the mechanism by which surfactants
enhance the spreading of aqueous solutions on
hydrophobic solid substrates. Offer a molecular
explanation as to why some surfactant molecules
are more effective than others. Identify
alternative surfactants that would be expected to
enhance wetting.
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Outline

• Surfactants
• Molecular simulation of wetting systems

• Wetting of a Lennard-Jones solid by water
• Wetting of graphite by water
• Wetting of a semi-infinite, continuous
  Lennard-Jones solid by a water-alcohol solution
• Wetting of a semi-infinite, continuous
  Lennard-Jones solid by a water-surfactant solution

• Simulation challenges
• Proposed research

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(Fatty) Alcohol surfactants
Alcohols with long alkyl chains are the simplest
nonionic surfactant molecules. Linear alcohols
have the chemical formula CH3(CH2)nOH.
CH3(CH2)17OH
CH3CH2OH
Alcohols do not exhibit surfactant phase behavior
(i.e., they do not form molecular aggregates or
micelles).
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Polyoxyethylene surfactants
Polyoxyethylene (POE) compounds are the most
important nonionic surfactants in commercial
use. POE surfactants with an alkyl ether link
have the chemical formula CiEj, where Ci is
CH3(CH2)i-1 and Ej is (OCH2CH2)jOH.
C12E2
A methyl-capped polymethylene chain serves as the
hydrophobic moiety. A hydroxyl-terminated
polyoxyethylene chain serves as the hydrophilic
moiety.
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Superspreaders
Trisiloxane alkoxylate surfactants have superior
wetting properties. They have been shown to
increase the wetted area of a sessile drop by 25
times in comparison to conventional organic
surfactants. Trisiloxane ethoxylate surfactants
consist of oxyethylene groups (-OCH2CH2-) which
act as the hydrophile while the nonpolar
trisiloxane groups (-SiOSiOSi-) serves as the
hydrophobe.
Nikolov, A. D., et al.
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Introduction to molecular simulation
Molecular dynamics simulation is the numerical
solution of Newtons equations of motion for a
system of interacting molecules in 3-dimensions
Intermolecular interactions (U2) are computed by
summing over all pairs of interactions sites.
Intramolecular interactions (U3 and U4) arise
from valence and dihedral angle potentials.
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TIP3P water geometry
Mass and electron distributions are modeled as
point masses and point charges. Bond lengths and
the valence angle are kept fixed using RATTLE.
Molecular parameters rOH 0.9572 Å, ?
104.52º, qO -0.834 e, qH 0.417 e, and sOO
3.15061 Å.
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TIP3P water potential
The potential energy of interaction between a
pair of TIP3P water molecules is
There is one Lennard-Jones interaction and nine
Coulomb interactions between each pair of water
molecules.
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TIP3P water versus experiment
This simple potential function reproduces many
properties of ambient liquid water.
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Water on Lennard-Jones substrate
An equilibrated drop of 1000 TIP3P water
molecules at 298 K is placed in the vicinity of a
solid substrate. Water interacts with substrate
atoms through a L-J potential.
The microscopic contact angle is found to be
117º. The contact angle is found by assuming the
drop forms a spherical cap of uniform density.
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Water on graphite (validation)
Other workers have studied the interaction of
water and graphite. Lennard-Jones parameters have
been found for the SPC/E water model that
reproduce the equilibrium contact anglea. Good
agreement is observed.
a
The left imagea features 2000 SPC/E water
molecules on graphite while the right imageb
shows 900 TIP3P water molecules on a graphene
sheet.
aT. Werder, J. H. Walther, R. L. Jaffe, T.
Halicioglu, P. Koumoutsakos, J. Phys. Chem. B,
107, 1345 (2003).
bM. Lundgren, N. L. Allen, T. Cosgrove, N.
George, Langmuir, 18, 10462 (2002).
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Simplified substrate interaction
Comparison of real versus half space solids
The solid is assigned the Lennard-Jones
parameters of a TraPPE CH2 united atom (?S 3.95
Å, ?S 0.382 kJ/mole). The number density is
taken as ?S 3 ?O-3.
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Simplified substrate interaction
The potential energy of interaction between a
Lennard-Jones atom and a semi-infinite,
continuous Lennard-Jones solid (or half space) of
density??S is
According to the Lorentz-Berthelot combining
rules
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Water-ethanol simulation
While ethanol is fully soluble in water it
preferentially adsorbs at the liquid-vapor and
solid-liquid interfaces (NH2O 1000, NCH3CH2OH
168).
The alcohol is found to decrease the contact
angle by lowering ?LV and ?SL.
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Surfactant model
The polyoxyethylene surfactant C12E2 or
CH3(CH2)11(OCH2CH2)2OH is sparingly soluble in
water.
The united atom approximation is applied to each
CH2 and CH3 group. Partial charges are assigned
to the nine atoms of the surfactant head group.
Valence angle potential
Dihedral angle potential
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Water-C12E2 simulation
The animations below feature 2000 TIP3P water
molecules and 36 C12E2 molecules interacting on a
continuous Lennard-Jones solid at 298 K.
(side view)
(bottom view)
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Water-C12E2 simulation
Surfactant molecules are distributed around the
contact line with their backbones orientated in
the radial direction. Only head groups are found
inside of the drop.
(birds eye view)
(solvent removed)
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Simulation challenges
The figures on the preceding slide reveal two
challenges that must be overcome

• The size of the drop is too small. Surfactant
  molecules consist of 10 of the drop.
• The use of a truncated Coulomb potential may
  introduce artifacts.

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Overview of proposed research
These shortcomings can be overcome by the
following

• Simulate large systems where the contact angle is
  independent of drop size
• Compute long-range interactions using the fast
  multipole algorithm
• Use a proper model for the solid substrate
• Study various types of surfactants
• Compute properties
• What can be learned from these simulations?

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Large-scale simulation
The following inequality may be used to guide
decisions concerning the drop size
The radius of curvature of the sessile drop must
be much greater than the thickness of the
liquid-vapor and solid-liquid interfaces.
If the above inequality is satisfied then a bulk
region will exist in the center of the drop.
Also, the contact angle should be independent of
molecule numbers in this regime.
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Large-scale simulation
Simulations must be conducted in the regime where
the contact angle is independent of drop size.
The area per surfactant molecule should be a
constant.
Cases (d), (c), and maybe (b) are sufficiently
large for the surfactants considered in this work.
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Parallel simulation
Large molecular systems must be simulated. A
single-processor computer code will take too long
to run. By parallelizing the computer code
simulations can be completed in reasonable times.
Parallel simulations using the spatial and
particle decomposition approaches have been
completed for water in free space using a
shifted-force potential.
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Long-range interactions
It is necessary to compute long-range or Coulomb
interactions accurately. The use of a truncated
Coulomb potential may give rise to artificial
behavior. The amount of computation associated
with the direct calculation (i.e., every particle
interacts with every other particle) is O(N2).
This approach is not feasible for large
systems. The fast multipole algorithm (FMA) by
Greengard and Rokhlin (1987) may be used to
compute long-range interactions to within
round-off error. The computational complexity of
the method is O(N).
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Fast multipole algorithm
The basic idea of the method is that a particle
interacts with the multipole expansion of a
distant group instead of with each individual
member of the group. Once the multipole
coefficients for each box have been computed,
interactions are computed using three translation
operators shifting the center of a multipole
expansion, converting a multipole expansion into
a local expansion, and shifting the center of a
local expansion.
A hierarchical decomposition of space is used to
determine distant groups.
Rigorous error bounds have been analytically
derived for the FMA.
Board, J. et al.
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Fast multipole algorithm (3-d)
Suppose N charges are located with a sphere of
radius a centered about the origin. For any point
outside of this sphere, the electrostatic
potential is
Suppose N charges are located outside of a sphere
of radius a centered about the origin. For any
point inside this sphere, the electrostatic
potential is
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Substrate models
The solid-liquid interaction is as important as
the liquid-liquid interaction. An acceptable
solid model must be used. Graphite may be a
thoughtful choice. Workers have found
Lennard-Jones parameters for the water-graphite
interaction that reproduce the macroscopic
contact angle. This was done for SPC/E
water. Lattice atoms have been kept fixed in
position. Is lattice atom motion important for
the wetting systems considered in this work? Can
a model of a hydrophobic solid of industrial
importance be found?
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Surfactant models
The computational machinery will soon be in place
to simulate a series of homologs (C8E2,C9E2, ,
CnE2), ethoxylogs (C12E2, C12E3, , C12En), and
linear alcohol solutions. Work will continue on
these surfactant classes. Ionic surfactants such
as sodium dodecyl sulphate may also be studied.
Numerous models of ionic surfactants have been
published. Potential functions for the
superspreaders are not currently available.
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Property calculations
Before useful generalizations regarding the role
of surfactants on wetting processes can be made,
well-defined properties of each system must be
examined. Candidate properties include the
microscopic contact angle, base radius or wetted
area, surfactant concentration field, interfacial
thickness, radius of curvature, orientational
distribution of surfactant backbones, and many
structural properties. Based on the molecular
trajectories and property calculations,
commentary of the role played by surfactant
molecules on wetting processes will be given.
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Summary
Preliminary work on a droplet of water containing
surfactant molecules was found to give
qualitatively correct behavior. Large-scale
molecular dynamics simulations may be used to
elucidate the mechanism by which surfactants
enhance the wetting of aqueous solutions on
hydrophobic solid substrates. The properties of
the surfactant molecules responsible for the
enhanced wetting may also be gotten from this
technique. Long-range interactions must be
properly treated. An appropriate model of the
solid substrate must be used.
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Acknowledgements
Funding provided by NSF IGERT Graduate Research
Fellowship