Zusammenfassung
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).
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