VOLUME 82, NUMBER 11 PHYSICAL REVIEW LETTERS 15 MARCH 1999
Molecular Dynamics in Confining Space: From the Single Molecule to the Liquid State
A. Huwe and F. Kremer*
Department of Physics, University of Leipzig, D-04103 Leipzig, Germany
P. Behrens
Department of Chemistry, University of Hannover, D-30167 Hannover, Germany
W. Schwieger
Department of Chemistry, Martin-Luther-University Halle–Wittenberg, D-06108 Halle, Germany
(Received 15 September 1998)
The transition from the dynamics of isolated molecules to that of a bulk liquid is observed for
the first time by analyzing the dielectric relaxation 10
22
10
9
Hz of ethylene glycol (EG) guest
molecules confined to zeolitic host systems of different topology. Beyond a threshold channel size
the liquid character is lost, indicated by a dramatically increased relaxation rate and an Arrhenius-like
temperature dependence. Computer simulations of the molecular arrangement in a confining space
prove that an ensemble as small as six molecules is sufficient to exhibit the dynamics of a bulk liquid.
[S0031-9007(99)08701-3]
PACS numbers: 64.70.Pf, 77.22.Gm
The nature of glassy liquids is still not well understood
and is the focus of worldwide scientific discussion [1–6].
Central questions are the length scale on which the mo-
lecular fluctuations of a liquid take place, and under what
conditions the transition from a single molecule behav-
ior to that of a liquid occurs [7–17]. Guest molecules
[e.g., ethylene glycol (EG) HO-CH
2
-CH
2
-OH] being con-
fined to zeolitic host systems offer a unique possibility of
studying this: While in sodalite—because of steric rea-
sons—only one molecule of EG is present per zeolitic
cage, other zeolites (e.g., silicalite and zeolite beta) pos-
sess inner channel structures in which guest molecules can
interact with each other. In measuring the dynamics of the
(dielectrically active) guest molecules in (dielectrically in-
active) host systems over a frequency range from 10
22
to
10
9
Hz, broadband dielectric spectroscopy proves to be an
ideal experimental tool for these studies [14–19].
Silica sodalite is a clathrasil compound built from
identical, so-called b cages, with a free inner diameter of
0.6 nm. Ethylene glycol is one of the structure-directing
agents which controls the formation of silica sodalite
[20,21]. The EG molecules become occluded during
synthesis and cannot escape from the cages (unless they
are thermally decomposed) [21]. Besides silica sodalite,
silicalite-I and zeolite beta were used as zeolitic host
systems with three-dimensional pore systems. Silicalite
consists of pure silica and has two different types of
elliptical channels with cross sections of 0.56 nm 3
0.53 nm and 0.55 nm 3 0.51 nm [22]. In zeolite beta,
an aluminosilicate with a Si:Al ratio of 40, the channels in
[100] and [010] directions have a diameter of 0.76 nm 3
0.64 nm, whereas the channels in the [001] direction
have smaller pores 0.55 nm 3 0.55 nm [23]. Silicalite
and zeolite beta are filled with guest molecules after
synthesis and calcination. These nanoporous hosts are
heated to 330
±
C with a temperature increase of 20
±
Ch
and evacuated at 10
25
mbar for 36 h to remove water and
other volatile impurities. Afterwards they are filled with
EG from the vapor phase in a closed vacuum chamber
at 175
±
C. The samples are cooled to room temperature
and remain in the vacuum chamber for 24 h before the
dielectric measurements are carried out.
The dielectric measurements were performed using two
different systems based on different measurement prin-
ciples: Between 10
22
and 10
7
Hz, frequency response
analysis is carried out (Solatron–Schlumberger frequency
response analyzer FRA 1260 with a Novocontrol ac-
tive sample cell BDC–S). From 10
6
to 1.8 3 10
9
Hz
a Hewlett-Packard impedance analyzer (HP 4291A) is
employed. The sample temperatures are controlled by
means of a nitrogen gas jet having a stability better than
60.05 K. Details of the setup may be found in Ref. [24].
For the analysis of the dielectric measurements the imagi-
nary part e
00
of the dielectric function is fitted using a
superposition of a conductivity contribution and a gen-
eralized relaxation function according to Havriliak and
Negami [25],
e
00
s
0
e
0
a
v
s
2 Im
"
De
1 1 i vt
a
g
#
. (1)
In this notation, e
0
is the vacuum permittivity, s
0
is the
dc conductivity, and De is the dielectric strength. a and
g describe the symmetric and asymmetric broadening of
the relaxation time distribution function. From the fits
according to Eq. (1), the mean relaxation rate 1t
max
can
be deduced which is given at the frequency of maximum
dielectric loss e
00
for a certain temperature. It is shown
(Fig. 1) that the relaxation rates for EG in zeolite beta
and silicalite are separated by several orders of magnitude
and that the relaxation strength of EG in sodalite is
2338 0031-9007 99 82(11) 2338(4)$15.00 © 1999 The American Physical Society