Faculty of Chemistry, UAM, Grunwaldzka 6, Poznań, Poland, Faculty of Chemistry, UMCS, M. Skłodowska-Curie Pl. 3, Lublin, Poland 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.

System limitations: single linear polymer chain macromolecule attached to the surface at one point (terminally grafted chain) 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

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  0.01 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F  eff A1.16–22.22* B1.29– C D * *) 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

Cf lat /C free  eff /  eff  0.1 1/ * 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

Cf lat /C free  eff /  eff  0.1 1/ * 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

A miniaturized pressure tool The entropic pressure Elastic surface ISSHAC 2006

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

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 macromolecule terminally 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 you for your attention ISSHAC 2006