%0 Book Section %1 statphys23_0332 %A Hagita, K. %A Takano, H. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K confinement dynamics entangled polymer relaxation simulation statphys23 topic-7 %T Dynamics of a Entangled Polymer Chain in a Melt Confined into a Slit %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=332 %X Relaxation modes and rates of a single polymer chain in a melt confined into a slit by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model (BFM) 1, where only the excluded volume interaction is taken into account. Reduction of the glass transition temperatures $T_g$ of unentangled relatively short chains in thin polymer films as the films become thinner is examined by experiments2,3 and computer simulations 4-6. Here, the reduction of $T_g$ means a decrease of the longest relaxation time. In this study, the behaviors of the longest relaxation time of a polymer chain in a melt, which consists of polymer chains entangled each other, confined between two parallel walls are examined by Monte Carlo simulations of BFM. Polymer chains are located on an $L L W$ simple cubic lattice under periodic boundary conditions in the $x$- and $y$-directions. The relaxation modes and rates of a polymer chain of $N$ segments are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of positions of segments 7-10. We examine the $N$- and $W$-dependences of the longest relaxation time $\tau$, the mean square end-to-end distance $R_e^2 \rangle$ and the mean square radius of gyration $R_g^2 \rangle$ for N = 32 -- 512 and W = 8, 16, 32 and 64 at the volume fraction $= 0.5$. For each value of $W$, $R_e^2 \rangle$ behaves as $R_e^2 N$ and $R_e^2 \rangle/R_g^2 6$. These behavior are the same as those found in a melt of entagled polymers in three dimensions. For $N 128$, $\tau$ is almost the same as that in the bulk. For $N 128$, $\tau$ becomes systematically shoter as $W$ becomes smaller. The behavior of $\tau$ and $R_e^2 \rangle$ are analysed on the basis of the scaling relations, where $W$-dependences appear only through the number of segments between entanglement points $N_e$, the mean square distance of entanglement points $a^2$ and the microscopic friction constant $\zeta$. The consistency of the scaling analysis is discussed. 1) I. Carmesin and K. Kremer: Macromolecules 21 (1988) 2819.\\ 2) J. A. Forrest et. al.: Phys. Rev. E 56 (1997) 5705.\\ 3) J. Keddie, et. al.: Europhys. Lett. 27 (1994) 59.\\ 4) G. Xu and W. L. Mattice: J. Chem. Phys. 118 (2003) 5241.\\ 5) J. A. Torres, et. al.: Phys. Rev. Lett. 85 (2000) 3221.\\ 6) F. Varnik, et. al.: Phys. Rev. E 65 (2002) 021507.\\ 7) H. Takano and S. Miyashita: J. Phys. Soc. Jpn. 64 3688 (1995).\\ 8) S. Koseki, H. Hirao and H. Takano: J. Phys. Soc. Jpn. 66 (1997) 1631.\\ 9) K. Hagita and H. Takano: J. Phys. Soc. Jpn. 71 (2002) 673.\\ 10) K. Hagita and H. Takano: J. Phys. Soc. Jpn. 73 (2003) 1824.

@incollection{statphys23_0332, abstract = {Relaxation modes and rates of a single polymer chain in a melt confined into a slit by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model (BFM) [1], where only the excluded volume interaction is taken into account. Reduction of the glass transition temperatures $T_{\rm g}$ of unentangled relatively short chains in thin polymer films as the films become thinner is examined by experiments[2,3] and computer simulations [4-6]. Here, the reduction of $T_{\rm g}$ means a decrease of the longest relaxation time. In this study, the behaviors of the longest relaxation time of a polymer chain in a melt, which consists of polymer chains entangled each other, confined between two parallel walls are examined by Monte Carlo simulations of BFM. Polymer chains are located on an $L \times L \times W$ simple cubic lattice under periodic boundary conditions in the $x$- and $y$-directions. The relaxation modes and rates of a polymer chain of $N$ segments are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of positions of segments [7-10]. We examine the $N$- and $W$-dependences of the longest relaxation time $\tau$, the mean square end-to-end distance $\langle R_{\rm e}^2 \rangle$ and the mean square radius of gyration $\langle R_{\rm g}^2 \rangle$ for N = 32 -- 512 and W = 8, 16, 32 and 64 at the volume fraction $\phi = 0.5$. For each value of $W$, $\langle R_{\rm e}^2 \rangle$ behaves as $\langle R_{\rm e}^2 \rangle \propto N$ and $\langle R_{\rm e}^2 \rangle/\langle R_{\rm g}^2 \rangle \simeq 6$. These behavior are the same as those found in a melt of entagled polymers in three dimensions. For $N \leq 128$, $\tau$ is almost the same as that in the bulk. For $N \geq 128$, $\tau$ becomes systematically shoter as $W$ becomes smaller. The behavior of $\tau$ and $\langle R_{\rm e}^2 \rangle$ are analysed on the basis of the scaling relations, where $W$-dependences appear only through the number of segments between entanglement points $N_{\rm e}$, the mean square distance of entanglement points $a^2$ and the microscopic friction constant $\zeta$. The consistency of the scaling analysis is discussed. 1) I. Carmesin and K. Kremer: Macromolecules {\bf 21} (1988) 2819.\\ 2) J. A. Forrest et. al.: Phys. Rev. E {\bf 56} (1997) 5705.\\ 3) J. Keddie, et. al.: Europhys. Lett. {\bf 27} (1994) 59.\\ 4) G. Xu and W. L. Mattice: J. Chem. Phys. {\bf 118} (2003) 5241.\\ 5) J. A. Torres, et. al.: Phys. Rev. Lett. {\bf 85} (2000) 3221.\\ 6) F. Varnik, et. al.: Phys. Rev. E {\bf 65} (2002) 021507.\\ 7) H. Takano and S. Miyashita: J. Phys. Soc. Jpn. {\bf 64} 3688 (1995).\\ 8) S. Koseki, H. Hirao and H. Takano: J. Phys. Soc. Jpn. {\bf 66} (1997) 1631.\\ 9) K. Hagita and H. Takano: J. Phys. Soc. Jpn. {\bf 71} (2002) 673.\\ 10) K. Hagita and H. Takano: J. Phys. Soc. Jpn. {\bf 73} (2003) 1824.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Hagita, K. and Takano, H.}, biburl = {https://www.bibsonomy.org/bibtex/26c19f04a97df4d2327b79316bc09f0a6/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {4f0dfcd82f6b4b4d9d755a5fb31b7351}, intrahash = {6c19f04a97df4d2327b79316bc09f0a6}, keywords = {confinement dynamics entangled polymer relaxation simulation statphys23 topic-7}, month = {9-13 July}, timestamp = {2007-06-20T10:16:17.000+0200}, title = {Dynamics of a Entangled Polymer Chain in a Melt Confined into a Slit}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=332}, year = 2007 }