University of Oklahoma Institute for Applied Surfactant Research

1
University of OklahomaInstitute for Applied
Surfactant Research

• Reproducing Microemulsion Phase Behavior with the
  
• Net-Average Curvature Model

Jeff Harwell, Edgar Acosta, Erika Szekeres, and
David A. Sabatini
2
Outline

• Motivation
• Background (phase behavior, curvature/phase
  behavior relationship, models of microemulsions,
  critical scaling)
• Net-average curvature model drop radius
• net curvature expression scaling to critical
  point, SAD, critical exponent
• average curvature expression statistical droplet
  concept of water/oil, limiting
• Interfacial tension model (interfacial rigidity
  concept)
• Solution flow diagram
• Model results (drop radius/salinity benzene and
  limonene, phase vol TCE, extension for mixtures
  (2 slides), non-ionics-IFT, ternary diagram for
  saturated, ternary for non-saturated (Type IV)
• Summary

3
Motivation

• Why model microemulsions?
• To predict
• Solubilization / aggregate size
• Interfacial tension
• Phase behavior (Winsor Type I-III-II and IV
  phase transitions)
• Important to which applications?
• Remediation of oil contaminated aquifers /
  enhanced oil recovery
• Replacement of organic solvents
• Detergency
• Nanoscale aggregates formed by polymerization or
  precipitation
• Microemulsion drug delivery

4
Microemulsion Phase Behavior
Optimum Formulation (S, ?, ?)
S
Tetrachloroethylene (PCE) - 4 Sodium dihexyl
sulfosuccinate (AMA) - NaCl phase behavior study
5
Phase behavior - Curvature

0
-
Curvature (H 1/R)
Decreasing O/W Curvature
6
Microemulsions Models

• Types of models
• (1) Free energy of the bent surfactant film
  (Kegel, Overbeek and Lekkerkerker ACRS model by
  Adelman, Cates, Roux, and Safran, 1986)
• (2) Molecular thermodynamic model (Ruckenstein
  and Nagarajan, 1982)
• (3) Statistical mechanical models (microscopic
  models and interfacial models Gompper, Shick,
  Widom, Ginzburg - Landau, 1940-1970)
• (4) Lattice Monte Carlo Models (Care, 1987
  ,Larson, 1985 and Mattice,1994)
• Problems with models
• (1) (2) Complex equations with difficult to
  estimate parameters
• (3) (4) Over-simplified models for real
  systems
• Our model readily available parameters,
• simple to solve

7
Critical Scaling Law
Applies for second order (continuous) phase
transformations, where dependent variable
vanish/diverge at critical point, without
discontinuous change. On molecular level there is
no abrupt change between ordered / disordered
structures. Evans, Wennerstrom The colloidal
Domain. Where Physics, Chemistry, and Biology
Meet. 2nd, 1999, pp.489 Bellocq in Handbook of
Microemulsion Science and Technology, P. Kumar
and K. L. Mittal Eds. 1999, pp. 171
8
Net Curvature Model

• Critical point optimum formulation

• Scaling exponent

Critical Scaling law
Kelvin equation
? Length scale - radius of the droplet (Rd)
Hypothesis
9
Net Curvature Model

• Hypothesis

Surfactant Affinity Difference
(Salager, J. L. in Encyclopedia of Emulsion
Technology. Becher, P. Editor. Marcel Dekker, New
York, 1988, Vol 3, Chap. 3.)

• Ionic surfactants

• Nonionic surfactants

10
Net Curvature Model

• Statistical approach to structure
• Statistical distribution of coexistent water
• and oil droplets in middle phase systems
• droplet size limited by entropy effects -

• Net curvature

• Average curvature

11
Interfacial Rigidity Concept

• Surface free energy of bare o/w droplet

• Interfacial rigidity of surfactant self-assembly

12
Flow Diagram
Net - Average Curvature Model
Type I
Type II
Interfacial Tension
Type III
Independent variable salinity
13
Modeling Radius of Oil Droplets

• Net curvature

Salinity
does not include surfactant length
Surfactant 4 wt sodium dihexyl sulfosuccinate
14
Modeling Phase Volumes Effect of Temperature
Dwarakanath, V. Pope, Gary A. Environ. Sci.
Technol. 2000, 34, 4842
L 10 Å ? 51 Å

• The length parameter L is
• Independent of Temperature
• Independent of the Oil
• Proportional to the extended length of the
  surfactant

15
Modeling Selective Solubilization of Oil
Mixtures

• Two Important variables salinity (for ionic
  surfactants)
• oil
  composition

• Total solubilization core interfacial
  solubilization

from net-average curvature model
16
Modeling Selective Solubilization of Oil Mixtures

• Optimum salinity model
• Optimum characteristic length model

17
Modeling Selectivity

• Interfacial solubilization

• Selectivity

Benzene - limonene oil mixture 4 wt Sodium
dihexyl sulfosuccinate No salt, T 23 C
18
Modeling Interfacial Tension Non-Ionic Surfactant
Microemulsions
Stolen, T. and Strey, R. J.
Chem. Phys. 1997, 106(20), 8606
Net-average Curvature Model
C10 E5 - Octane microemulsion
Interfacial rigidity model
L 20 Å ? 230 Å T 25C Er 3
KBT cT0.054
19
Modeling Ternary Phase Diagram
Nonionic surfactants
H Kuneida and Stig Friberg, Bull Chem. Soc. Jpn.
541010 (1981)
T21.5 C
C8E3 -Decane Microemulsion
L 16 Å ? 40 Å T 21.5C cT0.064
Net-average Curvature Model
L2
L1
L3
L5
L4
D
20
Modeling Ternary Phase Diagram
Nonionic surfactants
H Kuneida and Stig Friberg, Bull Chem. Soc. Jpn.
541010 (1981)
T15.8 ºC
C8E3 -Decane Microemulsion
L 16 Å ? 40 Å T 21.5C cT0.064
Net-average Curvature Model
21
Modeling Ternary Phase Diagram
Nonionic surfactants
H Kuneida and Stig Friberg, Bull Chem. Soc. Jpn.
541010 (1981)
T26 ºC
C8E3 -Decane Microemulsion
L 16 Å ? 40 Å T 21.5C cT0.064
Net-average Curvature Model
22
Modeling Fish Diagram Anionic surfactants
Net-average Curvature Model
L 10 Å ? 55 Å S normalized

• Model simplifications
• constant
• constant
• when surfactant concentration changes

23
Summary

• Critical scaling theory is used to model
  microemulsions
• Model assumptions
• Critical point is the optimum formulation
• SAD is used as the reduced field variable
• Scaling exponent by analogy with
  the Kelvin equation
• Bicontinuous microemulsions are coexistent
  water/oil droplets
• Interfacial rigidity of surfactant film
  determines the IFT between microemulsion and an
  excess phase

24
Summary

• Model predictions for anionic surfactant systems
• Droplet sizes
• Phase volumes in saturated microemulsions
• Selective solubilization of polar-nonpolar oil
  mixtures
• Fish phase diagram
• Model predictions for non-ionic surfactant
  systems
• Interfacial tension
• Ternary phase diagrams at different temperatures

25
References

• Acosta, E. Szekeres, E. Sabatini, D. A.
  Harwell, J. H. Net-Average Curvature Model for
  Solubilization and Supersolubilization in
  Surfactant Microemulsions. Langmuir 2003, 19,
  186
• Acosta, E. Szekeres, E. Sabatini, D. A.
  Harwell, J. H. Modeling Microemulsion
  Solubilization and Interfacial Tension The
  Net-average Curvature Model. AIChE Annual
  Meeting, Nov.2002
• Szekeres, E. Acosta, E. Sabatini, D. A.
  Harwell, J. H. A Two-State Model for Selective
  Solubilization in Water-Surfactant-Mixed Oil
  Systems. AIChE Annual Meeting, Nov. 2002
• Szekeres, E. Acosta, E. Sabatini, D. A.
  Harwell, J. H. A Two-State Model for Selective
  Solubilization of Benzene-Limonene Mixture Using
  Sodium Dihexyl Sulfosuccinate Microemulsions (In
  preparation)