%0 Book Section %1 statphys23_0911 %A Binder, K. %A Buerzle, F. %A Nielaba, P. %A Sengupta, S. %A Ricci, A. %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 dimensional finite montecarlo phase scaling simulations size statphys23 systems topic-6 transitions two %T Ordering and phase transitions of 2D crystals confined in strips of finite widths and in presence of 1D periodic potentials %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=911 %X Monte Carlo simulations are used 1 to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential $r^-12$ in $d=2$ dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two walls providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase with n (characteristic for $d=1$). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made. 2D melting transitions for model colloids in presence of a 1D external periodic potential are investigated using Monte Carlo simulations 2, hereby extending former studies 3. We modeled the colloidal dispersion by hard disks in the canonical ensemble. In particular, we explore a hard disk system with commensurability ratio $p=3a/2d = 2$, where $a$ is the mean distance between the disks and $d$ the period of the external potential. In this system one expects from theoretical considerations 4 a novel `locked smectic' phase between the well known locked floating solid and the modulated liquid. This new phase, which was also observed in a recent experimental study 5, has been verified in our simulations 2. Furthermore, we used various statistical quantities like order parameters, their cumulants and response functions to obtain a phase diagram for the transitions between the three phases. 1) A. Ricci, P. Nielaba, S. Sengupta, K. Binder, Phys. Rev. E74, 010404(R) (2006); Phys. Rev. E75, 011405 (2007).\\ 2) F. Buerzle, Diploma thesis, University of Konstanz (2006).\\ 3) W. Strepp, S. Sengupta, P. Nielaba, Phys. Rev. E63, 046106 (2001).\\ 4) L. Radzihovsky, E. Frey, D.R. Nelson, Phys. Rev. E63, 031503 (2001).\\ 5) J. Baumgartl, M.Brunner, C.Bechinger, Phys.Rev.Lett.93, 168301 (2004).

@incollection{statphys23_0911, abstract = {Monte Carlo simulations are used [1] to study the effect of confinement on a crystal of point particles interacting with an inverse power law potential $\propto r^{-12}$ in $d=2$ dimensions. This system can describe colloidal particles at the air-water interface, a model system for experimental study of two-dimensional melting. It is shown that the state of the system (a strip of width D) depends very sensitively on the precise boundary conditions at the two walls providing the confinement. If one uses a corrugated boundary commensurate with the order of the bulk triangular crystalline structure, both orientational order and positional order is enhanced, and such surface-induced order persists near the boundaries also at temperatures where the system in the bulk is in its fluid state. However, using smooth repulsive boundaries as walls providing the confinement, only the orientational order is enhanced, but positional (quasi-) long range order is destroyed: The mean-square displacement of two particles n lattice parameters apart in the y-direction along the walls then crosses over from the logarithmic increase (characteristic for $d=2$) to a linear increase with n (characteristic for $d=1$). The strip then exhibits a vanishing shear modulus. These results are interpreted in terms of a phenomenological harmonic theory. Also the effect of incommensurability of the strip width D with the triangular lattice structure is discussed, and a comparison with surface effects on phase transitions in simple Ising- and XY-models is made. 2D melting transitions for model colloids in presence of a 1D external periodic potential are investigated using Monte Carlo simulations [2], hereby extending former studies [3]. We modeled the colloidal dispersion by hard disks in the canonical ensemble. In particular, we explore a hard disk system with commensurability ratio $p=\sqrt{3}a/2d = 2$, where $a$ is the mean distance between the disks and $d$ the period of the external potential. In this system one expects from theoretical considerations [4] a novel `locked smectic' phase between the well known locked floating solid and the modulated liquid. This new phase, which was also observed in a recent experimental study [5], has been verified in our simulations [2]. Furthermore, we used various statistical quantities like order parameters, their cumulants and response functions to obtain a phase diagram for the transitions between the three phases. 1) A. Ricci, P. Nielaba, S. Sengupta, K. Binder, Phys. Rev. {\bf E74}, 010404(R) (2006); Phys. Rev. {\bf E75}, 011405 (2007).\\ 2) F. Buerzle, Diploma thesis, University of Konstanz (2006).\\ 3) W. Strepp, S. Sengupta, P. Nielaba, Phys. Rev. {\bf E63}, 046106 (2001).\\ 4) L. Radzihovsky, E. Frey, D.R. Nelson, Phys. Rev. {\bf E63}, 031503 (2001).\\ 5) J. Baumgartl, M.Brunner, C.Bechinger, Phys.Rev.Lett.{\bf 93}, 168301 (2004).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Binder, K. and Buerzle, F. and Nielaba, P. and Sengupta, S. and Ricci, A.}, biburl = {https://www.bibsonomy.org/bibtex/2a22e5b20c6dab67b1301be0116a9355d/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {d46a4303a0286e4298e7c30c9ae5cc04}, intrahash = {a22e5b20c6dab67b1301be0116a9355d}, keywords = {dimensional finite montecarlo phase scaling simulations size statphys23 systems topic-6 transitions two}, month = {9-13 July}, timestamp = {2007-06-20T10:16:34.000+0200}, title = {Ordering and phase transitions of 2D crystals confined in strips of finite widths and in presence of 1D periodic potentials}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=911}, year = 2007 }