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gwnow@amu.edu.pl
theor@hermes.umcs.lublin.pl
Faculty of Chemistry, UAM, Grunwaldzka 6, 60-780 Poznań, Poland, Faculty of Chemistry, UMCS, M. Skłodowska-Curie Pl. 3, 20-031 Lublin,
Poland
Waldemar Nowicki, Grażyna Nowicka and Jolanta Narkiewicz-Michałek
Waldemar Nowicki, Grażyna Nowicka and Jolanta Narkiewicz-Michałek
Conformation of a SAW (112) chain grafted to a curved surface.
A single macromolecule in a cavity.
Conformation of a SAW (112) chain grafted to a curved surface.
A single macromolecule in a cavity.
System limitations:
• single linear polymer chain
• macromolecule attached to the surface at one point (terminally grafted chain)
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112
001
Model: the self-avoiding walk (SAW) on the cubic
lattice the 3D chess knight-like motion - (112) motion
(lattice coordination number equal to 24) periodic boundaries of the space
ISSHAC 2006
Model: the self-avoiding walk (SAW) on the cubic
lattice the 3D chess knight-like motion - (112) motion
(lattice coordination number equal to 24) periodic boundaries of the space
ISSHAC 2006
Model: the self-avoiding walk (SAW) on the cubic
lattice the 3D chess knight-like motion - (112) motion
(lattice coordination number equal to 24) periodic boundaries of the space the chain attached at one point to the obstacle
surface
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Model: the self-avoiding walk (SAW) on the cubic
lattice the 3D chess knight-like motion - (112) motion
(lattice coordination number equal to 24) periodic boundaries of the space the chain attached at one point to the obstacle
surface different curvature radii of the obstacle
Model: the self-avoiding walk (SAW) on the cubic
lattice the 3D chess knight-like motion - (112) motion
(lattice coordination number equal to 24) periodic boundaries of the space the chain attached at one point to the obstacle
surface different curvature radii of the obstacle the chain translocation through the hole
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Results:
Linear dimensions of the chain
Segment density distribution
Effective coordination number
Conformational entropy
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} SC method
} SAW method
Statistical counting method (SCM)
D. Zhao, Y. Huang, Z. He, R. Qian, J. Chem.
Phys. 104, 1672 (1996)
The effective coordination number of the lattice
The total number of chain conformations
The absolute conformational entropy
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Effective coordination number of the lattice. Unperturbed chain. The asymptote value equal to 22.220.01
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Entropy of an isolated free chain
The conformational entropy of free chain – results of SAW simulation
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Entropy of an isolated free chain
C F eff
A 1.16 – 22.22*
B 1.29 – 22.2151
C 0.57 1.3631 22.2021
D 1.23 1.1571 22.22*
1.17 1.17 4.6838
*) Sykes, M. F.; Guttman, J.; Watts, M. G.; Robberts,
P. D. J. Phys. A 1972, 5, 653
*)
The relative effective coordination number of the lattice
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Entropy of a chain terminally grafted to the plane
Cflat/Cfree eff/eff
0.00018 -3.00.1 1/1.0086*
D. Wu, P. D, J. Kang, Science in China B, 40, 1 (1997)
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Entropy of terminal attachment of the chain to the plane
Effect of the terminal attachement on the conformational entropy of the chain
Cflat/Cfree eff/eff
0.00018 -3.00.1 1/1.0086*
D. Wu, P. D, J. Kang, Science in China B, 40, 1 (1997)
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Effect of the terminal attachement on the conformational entropy of the chain
Entropy of terminal attachment of the chain to the plane
Effective coordination number of the lattice.
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Entropy of the chain terminally grafted to the curved surface. The concave obstacle.
The effect of the terminal attachment on the conformational entropy of the chain depends on the surface curvature radius.
There is the critical surface curvature radius at which the S vs. N dependence changes the sign of the second derivative.
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Entropy of the chain terminally grafted to the curved surface. The concave obstacle.
The entropy driven translocation of the chain
The entropy of chain translocation
through a hole in the plane
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the partition coefficient
The entropy driven translocation of the chain
The entropic force
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The entropy driven translocation of the chain
The entropic force
The entropic pressure
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1
1
1
10
32
B a
N
k
Tp
1
1
1
10
32
B a
N
k
Tp
A miniaturized pressure tool
The entropic pressure
Elastic surface
ISSHAC 2006
1
1
1
10
32
B a
N
k
Tp
1
1
1
10
32
B a
N
k
Tp
Ni
Nia
N
k
Tp
ii
1
1
1
10
3limlim
2B11
Ni
Nia
N
k
Tp
ii
1
1
1
10
3limlim
2B11
2B 10
3
a
N
k
Tp 2
B 10
3
a
N
k
Tp
The entropy driven translocation of the chain.The escape of the chain from the cored sphere
The change in the conformational entropy of the chain translocating
through a hole
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The entropic net force acting on the translocating chain
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The entropy driven translocation of the chain.The escape of the chain from the cored sphere
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The entropy driven translocation of the chain.The escape of the chain from the cavity.
The change in the conformational entropy of the chain translocating
through a hole
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The entropy driven translocation of the chain.The escape of the chain from the cavity.
The entropic net force acting on the translocating chain
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The change in the conformational entropy of the chain translocating
through a hole
The entropy driven translocation of the chain from one spherical cavity to another
The entropy driven translocation of the chain from one spherical cavity to another
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The entropic net force acting on the translocating chain
The entropy of the deformation of the coil
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W. Nowicki, Macromolecules, 35, 1424 (2002)
The entropy of the deformation of the coil
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The entropy driven translocation of the chain
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The entropy driven translocation of the chain
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The entropy driven translocation of the chain
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Visualisation of the SAW macromoleculeterminally attached to the surface
Model: a single linear polymer molecule in the athermal solution (SAW and SCM)
Results:• The conformational entropy of the chain
terminally attached to obstacles of different curvature• The entropy force and the entropy pressure
exerted by a macromolecule introduced to the confined environment• The entropy of translocation of the macromolecule through the hole
Model: a single linear polymer molecule in the athermal solution (SAW and SCM)
Results:• The conformational entropy of the chain
terminally attached to obstacles of different curvature• The entropy force and the entropy pressure
exerted by a macromolecule introduced to the confined environment• The entropy of translocation of the macromolecule through the hole
Model: a single linear polymer molecule in the athermal solution (SAW and SCM)
Results:• The conformational entropy of the chain
terminally attached to obstacles of different curvature• The entropy force and the entropy pressure
exerted by a macromolecule introduced to the confined environment• The entropy of translocation of the macromolecule through the hole
Model: a single linear polymer molecule in the athermal solution (SAW and SCM)
Results:• The conformational entropy of the chain
terminally attached to obstacles of different curvature• The entropy force and the entropy pressure
exerted by a macromolecule introduced to the confined environment• The entropy of translocation of the macromolecule through the hole
Thank youfor your attention
ISSHAC 2006
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