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![Page 1: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/1.jpg)
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.
![Page 2: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/2.jpg)
System limitations:
• single linear polymer chain
• macromolecule attached to the surface at one point (terminally grafted chain)
ISSHAC 2006
![Page 3: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/3.jpg)
ISSHAC 2006
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
![Page 4: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/4.jpg)
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
![Page 5: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/5.jpg)
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
![Page 6: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/6.jpg)
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 different curvature radii of the obstacle
![Page 7: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/7.jpg)
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
ISSHAC 2006
![Page 8: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/8.jpg)
Results:
Linear dimensions of the chain
Segment density distribution
Effective coordination number
Conformational entropy
ISSHAC 2006
} SC method
} SAW method
![Page 9: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/9.jpg)
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
ISSHAC 2006
![Page 10: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/10.jpg)
Effective coordination number of the lattice. Unperturbed chain. The asymptote value equal to 22.220.01
ISSHAC 2006
Entropy of an isolated free chain
![Page 11: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/11.jpg)
The conformational entropy of free chain – results of SAW simulation
ISSHAC 2006
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
*)
![Page 12: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/12.jpg)
The relative effective coordination number of the lattice
ISSHAC 2006
Entropy of a chain terminally grafted to the plane
![Page 13: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/13.jpg)
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)
ISSHAC 2006
Entropy of terminal attachment of the chain to the plane
Effect of the terminal attachement on the conformational entropy of the chain
![Page 14: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/14.jpg)
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)
ISSHAC 2006
Effect of the terminal attachement on the conformational entropy of the chain
Entropy of terminal attachment of the chain to the plane
![Page 15: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/15.jpg)
Effective coordination number of the lattice.
ISSHAC 2006
Entropy of the chain terminally grafted to the curved surface. The concave obstacle.
![Page 16: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/16.jpg)
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.
ISSHAC 2006
Entropy of the chain terminally grafted to the curved surface. The concave obstacle.
![Page 17: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/17.jpg)
The entropy driven translocation of the chain
The entropy of chain translocation
through a hole in the plane
ISSHAC 2006
the partition coefficient
![Page 18: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/18.jpg)
The entropy driven translocation of the chain
The entropic force
ISSHAC 2006
![Page 19: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/19.jpg)
The entropy driven translocation of the chain
The entropic force
The entropic pressure
ISSHAC 2006
1
1
1
10
32
B a
N
k
Tp
1
1
1
10
32
B a
N
k
Tp
![Page 20: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/20.jpg)
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
![Page 21: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/21.jpg)
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
ISSHAC 2006
![Page 22: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/22.jpg)
The entropic net force acting on the translocating chain
ISSHAC 2006
The entropy driven translocation of the chain.The escape of the chain from the cored sphere
![Page 23: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/23.jpg)
ISSHAC 2006
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
![Page 24: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/24.jpg)
ISSHAC 2006
The entropy driven translocation of the chain.The escape of the chain from the cavity.
The entropic net force acting on the translocating chain
![Page 25: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/25.jpg)
ISSHAC 2006
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
![Page 26: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/26.jpg)
The entropy driven translocation of the chain from one spherical cavity to another
ISSHAC 2006
The entropic net force acting on the translocating chain
![Page 27: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/27.jpg)
The entropy of the deformation of the coil
ISSHAC 2006
W. Nowicki, Macromolecules, 35, 1424 (2002)
![Page 28: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/28.jpg)
The entropy of the deformation of the coil
ISSHAC 2006
![Page 29: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/29.jpg)
The entropy driven translocation of the chain
ISSHAC 2006
![Page 30: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/30.jpg)
The entropy driven translocation of the chain
ISSHAC 2006
![Page 31: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/31.jpg)
The entropy driven translocation of the chain
ISSHAC 2006
![Page 32: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/32.jpg)
Visualisation of the SAW macromoleculeterminally attached to the surface
![Page 33: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/33.jpg)
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
![Page 34: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/34.jpg)
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
![Page 35: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/35.jpg)
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
![Page 36: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/36.jpg)
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
![Page 37: 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.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce65503460f949b3919/html5/thumbnails/37.jpg)
Thank youfor your attention
ISSHAC 2006