Adsorption and Molecular Recognition in Templated Porous Materials: Theory and Computer Simulation

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Adsorption and Molecular Recognition in Templated
Porous MaterialsTheory and Computer Simulation
Lev Sarkisov and Paul Van Tassel
Department of Chemical Engineering, Yale
University
AICHE November 2005
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Templated Molecular Recognition (TMR) Materials

• Molecular recognition
• Strong and specific binding
• between a molecule and
• substrate
• Plays an important role in
• biological processes
• - Genetic information
• replication
• - Enzyme functions
• - Signal transduction

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Templated Molecular Recognition (TMR) Materials
Mixture of template and precursor monomers
Polymerization and template removal
Adsorption in templated porous material

• Potential applications
• - Bio-mimics
• - Protein immobilization
• - Sensors
• - Tissue engineering substrates
• - Separation and purification

• Recent progress
• - Molecularly imprinted polymers
• (Mosbach et al.)
• - Sol-gel materials
• (Davis et al., Brinker et al.)
• Limitations
• - No fundamental understanding
• of the elemental processes

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Quenched-Annealed Models of Adsorption Replica
Ornstein-Zernike Approach
Fluid (1) properties averaged over matrix (0)
degrees of freedom
Equilibrium distribution of particles
Fluid grand partition function
Quenching of the configuration (matrix)
Adsorption of fluid in matrix
Quenched-annealedsystem
Matrix canonical partition function
(Madden, Glandt 1988 Given, Stell 1992)
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Quenched-Annealed Models of Adsorption Replica
Ornstein-Zernike Approach
Fluid properties averaged over quenched degrees
of freedom
1
2
3
Replica system equilibrium mixture of matrix and
s identical copies of adsorbed fluid component,
not interacting with each other U(ij)0 i?j
i,j replica index
s
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Quenched-Annealed Models of Adsorption Replica
Ornstein-Zernike Approach
Relation between quenched-annealed and replica
systems
1
2
3
s
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Quenched-Annealed Models of Adsorption Replica
Ornstein-Zernike Approach for Templated Systems
Equilibrium distribution of particles
Equilibrium mixture of matrix and template
Quenching of the configuration (matrix)
Template removal matrixconfiguration quenched
Adsorption of fluid in matrix
Quenched-annealedsystem
Adsorption of fluid intemplated matrix
(Zhang, Van Tassel 2000)
(Madden, Glandt 1988 Given, Stell 1992)
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Quenched-Annealed Models of Adsorption Replica
Ornstein-Zernike Approach for Templated Systems
Equilibrium mixture of matrix and template
Template removal matrixconfiguration quenched
Adsorption of fluid intemplated matrix
(Zhang, Van Tassel 2000)
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Integral Equation Theory of Adsorption in
Templated Porous Materials Molecular Fluids
Real Systems
Complex Interactions
Molecular Species
(Zhang, Van Tassel 2000)
Fundamental Issues
Specific Applications

• What is the simplest system featuring elements
  of molecular
• recognition?
• How sensitive is molecular recognition effect to
  small changes
• in the structure?
• What is the structure of a binding site?

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Integral Equation Theory of Adsorption in
Templated Porous Materials Molecular Fluids
Real Systems
Complex Interactions
RISM
(Zhang, Van Tassel 2000)
Hard sphere systems
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Ornstein-Zernike Equations for Matrix (0),
Template(0) and Adsorbate (1) System of
Molecular Species
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Solution of Ornstein-Zernike Equations for
Matrix, Template and Adsorbate System of
Molecular Species
Hard Sphere Potential
Closure Relation
- Percus-Yevick
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Thermodynamic Properties from Correlation
Functions
Total chemical potential
Compressibility route
Integration of this leads to
continued
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Thermodynamic Properties from Correlation
Functions
Integration of this leads to (repeated from
previous slide)
where
is the excess chemical potential coming as a
result of matrix and template presence at the
fluid density
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Thermodynamic Properties from Correlation
Functions
Integration path for
Template density
is the excess chemical potential coming as a
result of matrix and template presence at
the fluid density
Matrix density
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Adsorption in TMR Materials Model Systems
Model porous materials
Adsorption of clusters
Adsorption of linear chains
Matrix without template
Templated Matrix
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TMR Materials Structural Characteristics
Porosity
M T A
X
X
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TMR Materials Adsorption
M T A
Theory
Simulation
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What have we learned?

• Templating always enhances porosity, adsorption
• Order of enhanced adsorption

T A
T A
T A
T A
gt
Simulation
gt
gt
Theory
gt
gt
gt

• For given adsorbate, is best template
• For given template, is best adsorbate
• Is templated molecular recognition predicted?

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Selectivity
Adsorption Isotherms
r1
bm1

• Template effect present if gt
  
• Define selectivity parameter as

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TMR Materials Selectivity
M T A
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Conclusions

• Present integral equation theory of adsorption /
  molecular recognition in a templated porous
  material
• Replica Ornstein-Zernike approach
• RISM formalism
• System clusters of hard spheres
• Percus-Yevick approximation
• Semi-quantitative agreement with simulation
• Adsorption and templating dominate over
  molecular recognition
• Molecular recognition apparent through careful
  analysis

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Future Work

• Better closure relations (e.g. accounting for
  bridge function)
• Alternatives to inefficient compressibility
  calculations
• Attractive interactions gt more pronounced
  molecular recognition?

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Acknowledgements
Funding NSF CTS-0337829