Micellization Thermodynamics

20120201

• Wrap up Blankschtein & Puvvada• Project guidance• Continue with student presentations

Micellization Thermodynamics

• (continued) Review of seminal paper– Puvvada and Blankschtein “Molecular-

thermodynamic approach to predict micellization, phase behavior and phase separation of micellar solutions. I. Application to nonionic surfactants” J. Chem. Phys. 1990, 92, 6, 3710.

continuing …

• Finish discussion of the model– Computational scheme

• Discuss P&B’s evaluation of the thermo. properties

• Model predictions and comparison with experiments

Equilibrium state of micellar system fully specified by the time averaged:• Minor radius of the micellar core, lc

• Number of surfactant molecules in the micelle, n

• The geometrical shape of the micelle, Sh

Time averaged variables are used since micelles fluctuate.

Computational strategy

• For each of the 3 micelle shapes– Spheres– Cylinders– Disks / bilayers (turned out not to be favored in case

examined by P & B)

• The free energy of micellization, gmic, is computed and minimized with respect to lc

• An interpolation scheme is used to account for finite n for cylinders or disks

Model contains 3 molecular parameters which must be specified:

• nc – a known property of the hydrocarbon chains

• δ – evaluated from experimental results based on 11 carbon chain hydrocarbons

• ah – estimated from the volume of the head group and its end to end length

Determining n

• For spheres a zero growth model is used • For cylinders and disks an interpolation is

made between the infinite n idealized case and the equivalent spherical micelle,

cylgsphgn

ncylgng micmic

sphmicmic

***

*

gw/hc , contribution of moving the hydrocarbon tail from water to the hydrocarbon core, is the largest contributor to gmic

As ah increases, the steric contribution ,gst, increases with the increase being larger for cylinders than for spheres.

>>> larger head groups favor sphericalover cylindrical micelles

The hydrocarbon tail anchoring contribution increases with increasing nc; is larger for spheres than for cylinders

Hydrocarbon/water interface creation term depends mostly on the shape and varies little beyond that.

Optimum lc is somewhat larger for spherical rather than cylindrical micelles

Evaluation of Thermodynamic Properties

• Free energy expressions• Apply multiple chemical equilibrium

principle– Yields micellar size distribution

• Find critical micelle concentration– Defined by break in the monomer mole fraction

versus total surfactant concentration curve

Free energy expressions

molecule water a and molecule

surfactant a of volumeebetween th ratio theis

parametern interactio theis ,

surfactantfraction volume theis

mers-in surfactantfraction mol theis

(total) surfactantfraction mol theis

where

2

11ln

20

PTC

mX

X

CXXXkT

m

mmww

Free energy expressions, cont.

112

1

11ln

2

0

nC

XXnXkTm

mnnn

Micelle size distribution

kT

nngXX

n

micnn

n

exp

gives that requiring

1

1

Critical Micelle Concentration

• Found from break in monomer mol fraction versus total surfactant mol fraction curve

• Result is the same for each shape

kT

ShgX mic

CMC

1exp

*

Comparison with experimental data

• CMC – As a function of EO count in headgroup for CmEn

nonionic surfactants– As a function of T for CmEn nonionic surfactants

– As a function of nc for alkyl glucosides

• Critical parameters (Tc and Xc) for CmEn nonionic surfactants

• Osmotic compressibility for C12E8

Project guidance• Literature review of general area of interest

– Status/progress report due 2/15– Draft due 2/22 (substantially complete)

• Assessment of the “state of the art” in your specific area of interest– Status/progress report due 2/29– Draft due 3/7 (substantially complete)

• Identification of research/development needs and/or opportunities– Status/progress report due 3/21– Draft due 3/28 (substantially complete)

• Ideas for meeting one (or some closely related) of the needs/opportunities– Status / progress report due 4/4– Draft due 4/11 (substantially complete)

• Final project report – With all four of the above major parts– Due 4/25