Transcript Slide 1

Membrane Osmometry
Alfredo Clemente
CH 392N
Prof. Grant Willson.
The University of Texas Austin
Membrane Osmometry
Molecular
Weight and polymer properties
Methods Used to determine Mn, Mw
Membrane Osmometry
Introduction
and Theory
Measuring Mn by osmotic pressure
Conclusions:
Advantages and disadvantages
Questions
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Relative fraction
Representative differential weight
distribution curves1
Molecular weight
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Relationship of polymer properties to
molecular weight.1
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Typical Molecular Weight Determination Methods1
Type of mol.
Method
wt. avg.
Light scattering (LS)
Mw
Mn
Membrane osmometry
Vapor phase osmometry
Mn
Electron and X-ray microscopy M n,w, z
Ebulliometry
Mn
Cryoscopy
Mn
Mn
End Group Analysis
Mn
Osmodialysis
M z ,w
Centrifugation
SEC, with c detector
SEC, with c and LS detectors
Viscometry
Range
Info.
To ∞
Shape
2x104 to 2x106
To 4x104
102 to ∞
Shape, dist
To 4x104
To 5x104
To 2x104
500-2500
To ∞
Relative
To ∞
Mol w Dist
M n,w
To ∞
Mol w Dist
Relative
To ∞
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Membrane Osmometry
Introduction and Theory
Osmosis and Osmotic Pressure
Osmosis and Chemical Potential
h
1

0
1
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Equilibrium of Chemical Potential2
 1 
  1   
dP

P0
 P T ,n1 ,n2
(I )
 G 

From i  
it followsthat
 ni  P ,T ,n j
( II )
0
1
P
  G 
 1 





 P T ,n1 ,n2 n1  P T ,n1 ,n2
 G 
Since
 V (i.e. the solutionvolum e) then

 P T ,n1 ,n2
( III)
 G 
 1 

 
 V1


 P T ,n1 ,n2  n1 T , P ,n2
( IV )
10  1  P  P0 V1
(V )
1  10  V1
(VI )
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Osmotic Pressure
Floury  Huggins expressionfor 1  10
1 2

1    RT2 / x  RT    2
2

1
 2
  RT2 / xV1  RT    2 / V1
2

V1  V1
0
1
(VII )
(VIII )
( IX )
xn2
xn2
2 

(n1  xn2 ) n1
(X )
V  n1V1
( XI )
2 / xV  n2 / V
( XII)
1
 2
2
  RT n2 / V   RT     x V1 n2 / V 
2

( XIII)
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Osmotic Pressure and
Mn
nM


n
i
i
i
m

n2
( XIV )
n2  m  n2 
c
    
V  V  m  M n
( XV )
2
RT  RT  1
 xV1 
   

 
c

c M n  V1  2
 M n 
x  V2 / V1

xV1 V2
1


M n M n 2
RT  RT  1



 


c
2 
c M n  V1  2  2


Mn
( XVI )
( XVII )
( XIX )
( XX )
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Osmotic Pressure and
RT
 
  
 c  M n
RT
 

 
 c  c 0 M n
 1

2
 RT 
 A2 c  A3c  ...
c
 Mn


Mn
( XXI)
( XXII)
( XXIII)
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Osmotic Pressure and
Mn
Typical plot of osmometry
2
experimental data
(п/c) / J kg-1
20
18
16
14
12
0
2
4
6
8
10
12
c/ g dm-3
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Measuring M nby osmotic pressure
Membrane osmometers used:
Static osmometer2
•Equilibrium by natural diffusion
•Large cell volumes
h 
•Long equilibrium times
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Measuring M nby osmotic pressure
Membrane osmometers used:
Dynamic osometer3
•Equilibrium by reducing
pressure on solution reservoir
•Small cell volumes
•Short equilibrium times
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Measuring M nby osmotic pressure
Membrane osmometers used:
Dynamic osometer3
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Osmotic Pressure and
0.06
Π, atm
0.05
0.04
0.03
0.02
20.0°C
Polystyrene in cyclohexane
34.5°C
0.01
0.010
0.020
0.030
c, g/mL
0.040
5.5E-05
5.0E-05
4.5E-05
20.0°C
34.5°C
50.0°C
0
0.000
5
6.0E-05
Polystyrene in cyclohexane
Π/ cRT, mol/g
0.07
Mn
0.050
50.0°C
4.0E-05
0.000
0.010
0.020
0.030
0.040
0.050
c, g/mL
20.0°C:Slope = A2 = -2.0x10-4 cm3 mol/g2
1/intercept = Mn = 1.97x104 g/mol
34.5°C:Slope = A2 = 1.7x10-5 cm3 mol/g2
1/intercept = Mn = 2.02x104 g/mol
50.0°C:Slope = A2 = 1.7x10-5 cm3 mol/g2
1/intercept = Mn = 2.00x104 g/mol
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Conclusion: Advantages and disadvantages
Disadvantages
Membrane problems: leakage, asymmetry and ballooning
Overestimation of molecular due low molecular weight
molecules
Not suitable for electrolytes
Advantages
Absolute value of Mn
No calibration with standards required
Independent of chemical heterogeneity
Applicable to polymers with broad range of molecular
weights
Measurement of Mn within 10,000 to 2x106
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Questions?
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References
1. Carraher, C. E., Jr Polymer Chemistry: An Introduction, 4th Ed., Marcel
Dekker, NY: 1996.
2. Young, R. J.; Lovell, P. A. Introduction to Polymers, 2nd Ed., Chapman &
Hall, New York: 1991.
3. Lipták B. G.; Brodgesell, A. Instrument Engineers' Handbook, Process
measurement and analysis. CRC Press, Florida: 1995
4. W. R. Krigbaum and L. H. Sperling, J. Phys. Chem., 64, 99 (1960)
5. Hiemenz, Paul C., Lodge, Timothy P.; Polymer Chemistry, 2nd Ed., CRC
Press, Boca Raton: 2007.
6. http://www.engga.uwo.ca/people/pcharpentier/3922004/MW%20Measurement.pdf
7. http://www.chem.ufl.edu/~polymer/instrumentation/vpo.html
8. http://www.chem.ufl.edu/~polymer/instrumentation/vpo.html
9.
http://www.eng.uq.edu.au/files/course/files/CHEE2006/CHEE2006%20Week%
2012_2.pdf
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References
10. http://www.humancorp.co.kr/catalog/272-277.pdf
11.
http://www.gonotec.com/content.OSMO_090.PRODUCTS_CHEM.OSMO_090
.USA.ENG.html
12. http://www.princeton.edu/~pccm/facilities-polymersynth-eq.htm
13 Chalmer, John M.; Meier, Robert J., Molecular Characterization and
Analysis of polymers, Elsevier Science, Burlington: 2008
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