Thermodynamics of Micelle Formation of Ionic Surfactants

1
Thermodynamics of Micelle Formation of Ionic
Surfactants

• James Taylor
• Tommy Mitchell
• ?Gm

2
What is a Surfactant?

• Surface active agents
• Wetting agents
• Lower surface tension in solution
• Adsorbing at the liquid-gas interface
• Allows greater spreading and lower interfacial
  tension between liquids

3
Classification of surfactants

• Anionic Net negative formal charge at the head.
• SDS Sodium dodecyl sulfate.
• Denatures secondary structure and non-disulfide
  linkages in proteins.
• Cationic Net positive formal charge at the head.
• CPC Cetylpyridinium chloride.
• Antiseptic used in mouth washes and toothpaste.

4
What is a Micelle?

• Aggregated surfactant molecules
• Very ordered, relatively low entropy
• Have hydrophobic and hydrophilic properties
• Hydrophilic heads
• Hydrophobic tails

5
Micelle Formation

• CMC Critical Micelle Concentration
• System Dependent
• CMT Critical Micelle Temperature
• System Dependent
• Micelles form when
• The concentration of surfactant is greater than
  the CMC.
• The temperature of the system is greater than the
  CMT.

6
Mathematics used to calculate thermodynamic
properties

• ?Gm, ?Hm, ?Sm, ?CP

7
?Gm Vant Hoff Method

• Nonionic micellization
• Ionic micellization must account for binding of
  counterions to the charged micelles
• XCMC is The CMC on molefraction unit
• n is the aggregation number
• m is the of counterions bound per micelle
• fm/n

0, low weightage
8
How is ? Where is the
negative?

• It is all taken into account in the derivation,
  as follows
• At equilibrium, the equation between monomers and
  micelle is,
• N AM(aq) ? (AM)N
• Therefore the potential energies at equilibrium
  are,
• N µeq(AM) ? µeq(AM)N
• And by definition,
• µ µºRTln(x)
• So,
• Nµº(AM) RTln(x(AM)) µº((AM)NRTln(x(AMN))

9
Derivation cont.

• Rearrangement gives,
• Nµº(AM) - µº(AM)N NRTln(x(AMN))- RTln(x(AM))
• Which is equal to,
• ?Gmº RTln(x(AMN))- (RT/N)ln(x(AM))
• Assuming N is large, then,
• ?Gmº RTln(x(AMN))
• And x(AMN)XCMC ,Therefore,
• ?Gmº RTlnXCMC

0, when N is large
10
?Gm Ionic micellization significance of f

• When f 1(f m/n), there is no charge on the
  micelle
• The ?Gm is twice that of non-ionic micellization

11
?Hm Vant Hoff Method

• For nonionic micellization
• For ionic micellization

0, Low Weightage
12
?Sm Vant Hoff Method

• For both non-ionic and ionic micellization
• Once ?Gm ?Hm have been determined, calculating
  ?Sm is trivial based on the definition of Gibbs
  Free Energy

13
Summary of basic equations for calculating
thermodynamic properties
Nonionic micellization
Ionic micellization
Both types of micellization
14
Polynomial forms XCMC and f are functions of
temperature

• Plots of lnXCMC vs. T and f vs. T are not linear

XCMC
15
Using the polynomial forms to calculate ?Hm, and
?CP

• ?Hm becomes,
• And using
• ?CP becomes,

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Kresheck XCMC and f are functions of temperature

• Therefore,
• And using ,
  

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Thermodynamic Importance

• Formation results from a balance between entropy
  and enthalpy
• Driving force Hydrophobic effect
• Reduction of Entropy
• Enthalpy???

18
Isothermal Titration Calorimetry

• The Instrument
• Reference Cell
• composed of thermal conducting material, eg, Gold
• Surrounded by an adiabatic jacket
• Sample Cell
• Samples are titrated into cell in quantitative
  amount
• Thermopile circuits
• Used to detect the difference between cells.

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Isothermal Titration Calorimetry

• ITC Can directly measure,
• Binding Affinity, Ka
• Enthalpy Changes, ?H
• ITC Can indirectly measure,
• Gibbs Free Energy, ?G
• Changes in Entropy, ?S
• Changes in heat capacity, ?CP

20
Experimental
21
Materials

• SDS Sodium Dodecyl Sulfate
• AOT Dioctyl Sulfosuccinate (sodium salt)
• CPC Cetyl Pyridinium Chloride

22
Methods

• Conductance Method
• Aliquots of concentrated surfactant were titrated
  into a wide mouth test tube fitted with a
  conductometer
• Conductance was measure following each aliquot.

23
Methods

• Surface Tension
• Aliquots of concentrated surfactant were titrated
  into a wide mouth test tube fitted with a
  platinum ring tensionmeter.
• Surface tension was measured following each
  aliquot.

24
Methods

• Microcalorimetric
• Aliquots (5-20?L) of concentrated surfactant were
  added to the water containing sample cell.
• Heat flow from solution was measured using OMEGA
  ITC microcalorimeter following each addition of
  surfactant.

25
Results
26
Determination of the CMC of CPC Conductometric
method
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Determination of the CMC of AOT Tensiometric
method
28
Determination of the CMC of AOT
Microcalorimetric method

• A) heat flow vs time
• B) enthalpy change per mole of SDS vs SDS
• C) differential enthalpy change with respect to
  concentration vs SDS

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Micellization

• SDS CPC
• Show increased exothermicity and decreased
  critical micelle concentration with increased
  sodium chloride concentration.
• AOT
• Shows increased endothermicity and decreased
  critical micelle concentration with increased
  sodium chloride concentration

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SDS
31
CPC
32
AOT
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CPC Micellization
34
?Hm (CPC)

• a) Microcalorimetry
• b) Microcalorimetry, Vant Hoff Method not
  considering f
• c) Microcalorimetry, Vant Hoff Method
  considering f
• d) Conductometry, Vant Hoff Method considering f

35
?Sm (CPC)

• e) Microcalorimetry
• f) Microcalorimetry, Vant Hoff Method not
  considering f
• g) Microcalorimetry, Vant Hoff Method
  considering f
• h) Conductometry, Vant Hoff Method considering f

36
?Cpm (CPC)

• i) Microcalorimetry
• j) Microcalorimetry, Vant Hoff Method not
  considering f
• k) Microcalorimetry, Vant Hoff Method
  considering f
• l) Conductometry, Vant Hoff Method considering f

37
AOT Micellization
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?Hm (AOT)

• a) Microcalorimetry
• b) Microcalorimetry, Vant Hoff Method

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?Sm (AOT)

• a) Microcalorimetry
• b) Microcalorimetry, Vant Hoff Method

40
?Cpm (AOT)

• a) Microcalorimetry
• b) Microcalorimetry, Vant Hoff Method

41
SDS Micellization

• ?Hm
• Microcalorimetry Vant Hoff
• With and without f
• Conductometry Vant Hoff
• With and without f
• ?Sm
• Microcalorimetry Vant Hoff
• With and without f
• Conductometry Vant Hoff
• With and without f
• ?Cpm
• Microcalorimetry Vant Hoff
• With and without f
• Conductometry Vant Hoff
• With and without f

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?Hm (SDS)
43
?Sm (SDS)
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?Cpm (SDS)
45

• http//pubs.acs.org/isubscribe/journals/jpcbfk/105
  /i51/figures/jp0123029f00009.html

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Temperature-dependent CMC of SDS

• a) Blume et al. Microcalorimetry
• B) Microcalorimetry
• C) Conductometry
• D) Geddard conductometry

47
Microcalorimetric determination of ?Hm