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)

ISSHAC 2006

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

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

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

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

Results:

Linear dimensions of the chain

Segment density distribution

Effective coordination number

Conformational entropy

ISSHAC 2006

} 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

ISSHAC 2006

Effective coordination number of the lattice. Unperturbed chain. The asymptote value equal to 22.220.01

ISSHAC 2006

Entropy of an isolated free chain

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

*)

The relative effective coordination number of the lattice

ISSHAC 2006

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)

ISSHAC 2006

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)

ISSHAC 2006

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.

ISSHAC 2006

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.

ISSHAC 2006

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

ISSHAC 2006

the partition coefficient

The entropy driven translocation of the chain

The entropic force

ISSHAC 2006

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

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

ISSHAC 2006

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

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

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

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

The entropy driven translocation of the chain from one spherical cavity to another

ISSHAC 2006

The entropic net force acting on the translocating chain

The entropy of the deformation of the coil

ISSHAC 2006

W. Nowicki, Macromolecules, 35, 1424 (2002)

The entropy of the deformation of the coil

ISSHAC 2006

The entropy driven translocation of the chain

ISSHAC 2006

The entropy driven translocation of the chain

ISSHAC 2006

The entropy driven translocation of the chain

ISSHAC 2006

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