1

Fall, 2013

Ch 4. Solubility and Adsorption – Potential

Energy Approach

Instructor: J.-W. John ChengMech. Engr. Dept., Nat’l Chung Cheng Univ.

Interfacial Physics and Thin-Film Processing

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Outline 4.1 Solubility of Like Molecules in a Medium 4.2 Solubility of Unlike Molecules in a 3rd Medium 4.3 Adsorption – Interaction between Solution and Solid Surface 4.4 Limitations of Potential Energy Approach Reference

Israelachvili, J. N., Intermolecular and Surface Forces, 2nd ed., 1991, Chapter 9

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van der Waals between Unlike Molecules

d2

d1

i2

i1

o2

o1

d2

d1

i2

i1

o2

o16

d12

i12

o12

d12

i12

o1266

VDW12

62021

2102012201

2102

22

21VDW

12

CCCCCCCCCCCCr1

CCCCCCr1

rC

r41

2h3uu

kT3uu2)r(w

Recall van der Waals between like molecules

)r(C)r(C)r(CCCCr1

rC

r41

4h3u2

kT3u2)r(w

d1

i1

o1

d1

i1

o166

VDW1

620

12012

101

41VDW

1

Recall van der Waals between unlike molecules

4

4.1 Hildebrand and Hanson Solubility Theories – A Free

Energy Approach

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Scenario – Description & Analysis Assumption: a dilute solution with solute A

and solvent B

dB

dA

iB

iA

oB

oA

VDWABdisp

CCCCCC2

w2w

dB

dA

iB

iA

oB

oA

VDWB

VDWAas

CCCCCC

www

0CCCCCC

www2

dB

dA

2iB

iA

2oB

oA

dispas

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Discussion Q1. What is the reference state with potential =

0? Q2. Does above analysis also take into account

the situation when there are more than one attachment of solvent B to a solute A, e.g., as shown in the 2D hexagonal compact lattice?

ABB

BBB

B

A2.

ABB

BBB

BB

BB

ABB

BBB

BB

BB

+ ABB

ABB

BB

BB

BBB

BBB

BB

BB

+

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Discussion w=was–wdisp 0 like molecules tend to self associate But entropy increase in dispersion state against self associate Thus, simple potential energy analysis can not tell precisely whether good dissolution of A in B will occur One can only say

When w 0, dissolution is likely to occur When w is much negative, self association is more likely to occur, i.e., solute A insoluble in solvent B

contd

8

4.2 Solubility of Unlike Molecules in a 3rd Medium

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Scenario – Description A dilute solution of two unlike solute

molecules A & B in solvent C1 2

3

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Potential Energy Analysis

d

CdB

iC

iB

oC

oB

dC

dA

iC

iA

oC

oA

VDWBC

VDWACdisp

CCCCCC2

CCCCCC2

w2w2w

A, B dispersed

AB associated

d

CiC

oC

dB

dA

iB

iA

oB

oA

VDWC

VDWABas AB

CCC2

CCCCCC2

w2w2w

nC

nBd,i,on

nC

nAdispas AB12 CCCC2www

21

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Potential Energy Analysis

d

CdB

iC

iB

oC

oB

dC

dA

iC

iA

oC

oA

VDWBC

VDWACdisp

CCCCCC2

CCCCCC2

w2w2w

A, B dispersed

AA, BB associated

d

CiC

oC

dB

iB

oB

dA

iA

oA

VDWC

VDWB

VDWAas BBAA,

CCC2

CCCCCC

w2www

d,i,on

2nC

nB

2nC

nAdispas BBAA,13 CCCCwww

contd31

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Potential Energy Analysis

AA, BB associated

d

CiC

oC

dB

iB

oB

dA

iA

oA

VDWC

VDWB

VDWAas BBAA,

CCC2

CCCCCC

w2www

d,i,on

2nB

nAasABas BBAA,23 CCwww

contd

AB associated

d

CiC

oC

dB

dA

iB

iA

oB

oA

VDWC

VDWABas AB

CCC2

CCCCCC2

w2w2w

2 3

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Potential Energy Analysis contd n

CnBd,i,on

nC

nA12 CCCC2w

d,i,on

2nC

nB

2nC

nA13 CCCCw

d,i,on

2nB

nAasABas BBAA,23 CCwww

1 2

3

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Discussion An interesting observation regarding transition

from the state of dispersed (1) to AB associated (2) Take only d-component of w12 as an illustration d

CdB

dC

dA

d12 CCCC2w

situation comment

“solute A in middle”

< 0 favoring immiscibility

“solute B in middle”

< 0 favoring immiscibility

“solvent C in middle”

> 0 favoring dissolution

dB

dA

dC

dC

dA

dB

CCC

CCC

dA

dB

dC

dC

dB

dA

CCC

CCC

dA

dC

dB

dB

dC

dA

CCC

CCC

d12w

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Discussion Most favorable state: self associations of AA, BB,

CC Although simple potential energy analysis can

not tell precisely whether good solution in C will occur,

It still provides us some selection guidelines of good solvent. Assume solutes A and B are given. Choosing solvent whose cohesion work lies in

between those of A & B will increase the likelihood of dissolution

The best choice is the solvent with cohesion work equal to the mid-value between those of A and B

contd

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4.3 Adsorption of Solute Molecules on Solid Surface

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C

CC

BB

BB

BBB

B

BB

BB

CB

BB B B B B BBBB

BBBB

BBBBB

C

CC

B B

BB

B

BB

B B B BB BBBBBBB B B B B B B B

BB B

BBB

BB

Scenario – Description A dilute solution of solute B in solvent C and a solid surface A

adsorption of B association of B

1

2 3

4

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Solution to BB Association Desorption to BB association (state 1 3)

A

B

AC C

BB

B

B

BBB

C C C

CC

desorption BB association

B

C

CBB

dC

dB

iC

iB

oC

oB

VDWBCdes

CCCCCC2

w2w

dC

iC

oC

dB

iB

oB

VDWC

VDWBBB

CCCCCC

www

2d,i,on

nC

nBdesBB13 CCwww

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Solution to Adsorption Desorption to adsorption (state 1 2)

A

B

AC C

BB

B

B

BBB

C C C

CC

desorption

A

C

AC B

BB

B

B

BBB

C C C

CC

adsorption

d

CdB

iC

iB

oC

oB

dC

dA

iC

iA

oC

oA

VDWBC

VDWACdes

CCCCCC

CCCCCC

www

d

CiC

oC

dB

dA

iB

iA

oB

oA

VDWC

VDWABads

CCC

CCCCCC

www

nC

nBd,i,on

nC

nAdesads CCCCwww

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Solution to Adsorption An interesting property of n

CnB

nC

nA CCCC

0CCC

CCCnA

nB

nC

nC

nB

nA

0CCC

CCCnA

nC

nB

nB

nC

nA

0CCC

CCCnB

nA

nC

nC

nA

nB

“solute in middle”

“solvent in middle”

“solid in middle”

favoring adsorption

favoring desorption

favoring adsorption BUT…!

contd

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Partial Wetting/Incomplete Adsorption

Another point of view using Young’s equation Before solutes form a well-organized solid, a

collection of solutes behave like a liquid Thus, Young’s equation is still valid

ACBCAB cos

vs.

d,i,on

2nB

nC

d,i,onnA

nB

nC

nB

nC 2

cos

Note ij is interfacial energy, not adhesion work

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Partial Wetting/Incomplete Adsorption contd

An interesting property of

2n

BnC

nA

nB

nC

nB

nC 2

1EnA

nB

nC

nC

nB

nA

-1EnA

nC

nB

nB

nC

nA

1E1nB

nA

nC

nC

nA

nB

“solute in middle”

“solvent in middle”

“solid in middle”

favoring wetting

favoring dewetting

favoring partial wetting

favoring film adsorption

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Discussion

C

CC

BB

BB

BBB

B

BB

BB

CB

BB B B B B BBBB

BBBB

BBBBB

contdC

CC

BB

BB

BBB

B

BB

BB

CB

BB B B B B BBBB

BBBB

BBBBB

C

CC

B B

BB

B

BB

B B B BB BBBBBBB B B B B B B B

BB B

BBB

BB

“solute in middle”adsorption of B

“solvent in middle”desorption of B

“solid in middle”partial wetting by B

In summary

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4.4 Limitations of Potential Energy Approach

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Limitations Entropy effect was not taken into account Thus, potential energy approach cannot give precise conclusion regarding solubility and adsorption Its prediction can only be used as a guideline but it turns out to be a quite useful one Since it adopts the geometric mean assumption for interaction between two unlike molecules

Potential energy approach can not be applied to interactions involving hydrogen or ionic bonding It also assumes pairwise additivity

It does not include replacement effect.