Résumé
Phil. Mag. B 82, 283 (2002) We present the results of molecular dynamics computer simulations of a simple
glass former close to an interface between the liquid and the frozen amorphous
phase of the same material. By investigating F_s(q,z,t), the incoherent
intermediate scattering function for particles that have a distance z from the
wall, we show that the relaxation dynamics of the particles close to the wall
is much slower than the one for particles far away from the wall. For small z
the typical relaxation time for F_s(q,z,t) increases like exp(Delta/(z-z_p)),
where Delta and z_p are constants. We use the location of the crossover from
this law to the bulk behavior to define a first length scale tilde{z}. A
different length scale is defined by considering the Ansatz F_s(q,z,t) =
F_s^{bulk}(q,t) +a(t) exp[-(z/xi(t))^{beta(t)}], where a(t), xi(t), and beta(t)
are fit parameters. We show that this Ansatz gives a very good description of
the data for all times and all values of z. The length xi(t) increases for
short and intermediate times and decreases again on the time scale of the
alpha-relaxation of the system. The maximum value of xi(t) can thus be defined
as a new length scale xi_max. We find that tilde{z} as well as xi_max increase
with decreasing temperature. The temperature dependence of this increase is
compatible with a divergence of the length scale at the Kauzmann temperature of
the bulk system.