micellization thermodynamics
DESCRIPTION
Surfactant scienceTRANSCRIPT
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20120201
• Wrap up Blankschtein & Puvvada• Project guidance• Continue with student presentations
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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.
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continuing …
• Finish discussion of the model– Computational scheme
• Discuss P&B’s evaluation of the thermo. properties
• Model predictions and comparison with experiments
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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.
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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
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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
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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
***
*
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gw/hc , contribution of moving the hydrocarbon tail from water to the hydrocarbon core, is the largest contributor to gmic
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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
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The hydrocarbon tail anchoring contribution increases with increasing nc; is larger for spheres than for cylinders
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Hydrocarbon/water interface creation term depends mostly on the shape and varies little beyond that.
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Optimum lc is somewhat larger for spherical rather than cylindrical micelles
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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
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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
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Free energy expressions, cont.
112
1
11ln
2
0
nC
XXnXkTm
mnnn
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Micelle size distribution
kT
nngXX
n
micnn
n
exp
gives that requiring
1
1
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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
*
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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
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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