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Wetting of hydrophobic substrates by aqueous surfactant solutions: A classical molecular dynamics study. An ongoing doctoral research project by. Jonathan D. Halverson 1. Under the faculty advisement of. J. Koplik 2 , A. Couzis 1 , C. Maldarelli 1.

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slide1

Wetting of hydrophobic substrates by aqueous surfactant solutions: A classical molecular dynamics study

An ongoing doctoral research project 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

American Institute of Chemical Engineers

Austin Convention Center, Austin, TX

November 11, 2004

slide2

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 θ of a sessile drop to the various interfacial tensions:

where γSVis the solid-vapor tension, γis the liquid-vapor tension, and γSLis the solid-liquid tension.

slide3

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.

slide4

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.

slide5

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.
  • Use the new information to suggest forms of new surfactants or mixtures.
slide6

Outline

  • Surfactants
  • Molecular simulation of wetting systems:
  • Wetting of graphite by water
  • Wetting of graphite by water-alcohol solutions
  • Wetting of graphite by water-poly(oxyethylene) surfactant solutions
  • Simulation challenges
slide7

(Fatty) Alcohol surfactants

Alcohols with long alkyl chains are the simplest nonionic surfactant molecules.

Linear alcohols have the chemical formula CH3(CH2)nOH.

CH3CH2OH

CH3(CH2)17OH

Alcohols do not exhibit surfactant phase behavior (i.e., they do not form molecular aggregates or micelles).

slide8

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.

slide9

Molecular dynamics simulation

Intermolecular or nonbonded interactions (U2) are computed by summing over all pairs of interaction sites. Intramolecular interactions (U3 and U4) arise from valence and dihedral angle potentials.

A finite system is simulated. A soft repulsive potential is used to prevent the drop from evaporating.

slide10

SPC/E water model

Mass and electron distributions are modeled as point masses and point charges. Bond lengths and the valence angle are kept fixed using RATTLE.

Parameters: rOH = 1.0 Å, θ = 109.47º, qO = -0.8476 e, qH = 0.4238 e, σOO = 3.166 Å, and eOO = 650.2 J/mole.

slide11

SPC/E water potential

The potential energy of interaction between a pair of SPC/Ec water molecules is

There is one Lennard-Jones interaction and nine Coulomb interactions between each pair of water molecules. The cutoff distance is taken as rc = 13 Å.

cH. J. C. Berendsen, J. R. Grigera, T. P. Straatsma, J. Phys. Chem., 91, 6269 (1987).

slide12

SPC/E water versus experiment

This simple interaction potential reproduces many properties of ambient liquid water.

slide13

Water-graphite interaction

Water interacts with atoms in the lattice through a Lennard-Jones interaction with eCO = 392.0 J/mole and sCO = 3.19 Å. Workersa have determined the parameters to reproduce the equilibrium contact angle of 86.

Lattice atoms are kept fixed in position. The experimental interlayer distance of 3.41 Å is used.

aT. Werder, J. H. Walther, R. L. Jaffe, T. Halicioglu, P. Koumoutsakos, J. Phys. Chem. B, 107, 1345 (2003).

slide14

Wetting of graphite by water

A cluster of water molecules spontaneously takes on the shape of a sphere in vacuum. The equilibrated drop of 2197 SPC/E water molecules at 298 K is placed in the vicinity of two graphene sheets:

The contact angle of the sessile drop is seen to fluctuate. A soft potential maintains a vapor pressure.

slide15

Vertical distribution of water

The solid substrate induces structure on the fluid in the vicinity of the substrate.

Water is first found 2.5 Å away from the graphite lattice.

slide16

Contact angle measurement

The liquid-vapor interface occurs where the density falls to half the bulk value of the liquid.

The contact angle is found to be 82.6.

slide17

Water on graphite

Several contact angle measurements have been made for water on graphite.

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).

slide18

polyoxyethylene/alcohol model

Head groups are modeled using the OPLS force field. Partial electrical charges are assigned to the atoms of the surfactant/alcohol head group.

The united atom approximation is applied to each CH2 and CH3 group. The TraPPE force field is used.

Valence angle potential:

Combining rules:

Dihedral angle potential:

slide19

Water-C3E0 simulation

Nwater = 4096, Nsurfactant = 240

(top view)

(bottom view)

slide23

Water-C3E0 simulation

At 20 Å away from the surface, water is found to exist in bulk. Few propanol molecules are found in bulk.

slide24

Water-C3E0 simulation

Nwater = 4096, Nsurfactant = 480

(top view)

(bottom view)

slide25

Previous: CH3(CH2)2OH

Current: CH3(CH2)3OH

Water-C4E0 simulation

Nwater = 4096, Nsurfactant = 240

(top view)

(bottom view)

slide26

Previous: CH3(CH2)3OH

Current: CH3(CH2)4OH

Water-C5E0 simulation

Nwater = 4096, Nsurfactant = 240

(top view)

(bottom view)

slide27

Previous: CH3CH2CH2(CH2)2OH

Current: CH3CH2O(CH2)2OH

Water-C2E1 simulation

Nwater = 4096, Nsurfactant = 240

(top view)

(bottom view)

slide28

Water-C6E0 simulation

Nwater = 4096, Nsurfactant = 121

(top view)

(bottom view)

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.

slide29

Water-C6E0 simulation

At 20 Å away from the surface, water is found to exist in bulk. Few hexanol molecules are found in bulk.

slide33

Water-C3E1 simulation

The radial density profile was determined for a system of water and C3E1 in vacuum by averaging for 200 ps.

slide34

Previous: CH3(CH2)2CH2(CH2)2OH

Current: CH3(CH2)2O(CH2)2OH

Water-C3E1 simulation

Nwater = 4096, Nsurfactant = 121

(top view)

(bottom view)

slide38

Water-C3E1

At 20 Å away from the surface, water is found to exist in bulk. Few surfactant molecules are found in bulk.

slide39

Surfactant distributions

Two distinct peaks are seen in the vertical distribution of surfactant molecules. Alcohols have a higher first peak.

slide40

Water distributions

Surfactant changes the vertical distribution of water molecules.

slide41

Combined wetting results

A plot of the center-of-mass vertical coordinate versus time reveals that negligible to no increased wetting is observed.

slide42

Simulation challenges

The radius of curvature of the sessile drop must be much greater than the thickness of the liquid-vapor and solid-liquid interfaces.

Cases (d), (c), and maybe (b) are sufficiently large for the surfactants considered in this work.

slide43

Simulation challenges

The number of water molecules consisting of a sessile drop may be related to the contact angle q and radius of curvature R:

The number of surfactant molecules consisting of a sessile drop may be related to the various concentrations and radius of curvature R:

slide44

Conclusions

Simulations of aqueous surfactant droplets on graphite gave the physically correct molecular behavior.

Low-molecular weight alcohols and polyethoxylate surfactants are found at the contact line and vapor-liquid interface. As the length of the hydrocarbon chain increases these molecules become directed radially from the center of the drop.

The solid-liquid surface concentration is low in all cases. Surfactant molecules are not seen to diffuse from the contact line or bulk to this interface.

A significant increase in wetting is not observed in any of the cases considered.

slide45

Future work

The perils of a truncated Coulomb potential have been well-documented. Electrostatic interactions will be computed using the 3-d fast multipole algorithm. An implementation of the 2-d version has been completed.

To allow for larger systems the computer code will be parallelized using either the spatial or domain decomposition techniques. A parallel code for water using a truncated potential has been completed.

slide46

Acknowledgements

Funding provided by NSF IGERT Graduate Research Fellowship

slide47

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.