Dynamics of glass-forming liquids. XV. Dynamical features of molecular liquids that
form ultra-stable glasses by vapor deposition
Zhen Chen and Ranko Richert
Citation: The Journal of Chemical Physics 135, 124515 (2011); doi: 10.1063/1.3643332
View online: http://dx.doi.org/10.1063/1.3643332
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THE JOURNAL OF CHEMICAL PHYSICS 135, 124515 (2011)
Dynamics of glass-forming liquids. XV. Dynamical features of molecular
liquids that form ultra-stable glasses by vapor deposition
Zhen Chen and Ranko Richert
Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona 85287-1604, USA
(Received 12 August 2011; accepted 6 September 2011; published online 30 September 2011)
The dielectric relaxation behavior of ethylbenzene (EBZ) in its viscous regime is measured, and the
glass transition temperature (Tg = 116 K) as well as fragility (m = 98) are determined. While the
Tg of EBZ from this work is consistent with earlier results, the fragility is found much higher than
what has been assumed previously. Literature data is supplemented by the present results on EBZ to
compile the dynamic behavior of those glass formers that are known to form ultra-stable glasses by
vapor deposition. These dynamics are contrasted with those of ethylcyclohexane, a glass former for
which a comparable vapor deposition failed to produce an equally stable glassy state. In a graph that
linearizes Vogel-Fulcher-Tammann behavior, i.e., the derivative of −logτ with respect to T/Tg raised
to the power of −1/2 versus T/Tg , all ultra-stable glass formers fall onto one master curve in a wide
temperature range, while ethylcyclohexane deviates for T Tg . This result suggests that ultra-stable
glass formers share common behavior regarding the dynamics of their supercooled liquid state if
scaled to their respective Tg values, and that fragility and related features are linked to the ability to
form ultra-stable materials. © 2011 American Institute of Physics. [doi:10.1063/1.3643332]
I. INTRODUCTION
Recently, molecular glasses have attracted significant interest due to the striking features of vapor-deposited films
which include higher stability, lower enthalpy, and higher
density than those of regular glasses that are prepared by
cooling the melt below the glass transition temperature Tg .1–3
Opposed to vapor deposition onto very cold substrates, such
ultra-stable glasses are obtained when the substrate temperature falls into the range of 0.8–0.9 Tg .4, 5 The term “ultrastable” is justified by the properties of such films, which
would require thousands to millions of years to produce via
standard physical aging.6 One of the commonly accepted explanations on this phenomenon is the enhancement of the
mobility on the glass/vacuum interface. The enhanced mobility allows the deposited molecules to have enough time
to rearrange and to find configurations as near as possible to
the equilibrium configurations before being buried by subsequent deposition. The temperature of maximal stability, often around 0.85 Tg , can be viewed as a compromise between
molecular mobility at the deposition interface and the driving
force towards deep states within the energy landscape.
To date, only several materials have been observed to
form ultra-stable glasses by vapor deposition. These include
ααβ-trisnaphthylbenzene (TNB),1 indomethacin (IMC),1
toluene (TOL),7 ethylbenzene (EBZ),8 n-propylbenzene
(NPB),9 iso-propylbenzene (IPB),9 nifedipine,10 felodipine,10
and phenobarbital.10 For simplicity, these materials will be
called ultra-stable glass formers in what follows. Ethylcyclohexane (ECH), if subject to the same vapor deposition technique, on the other hand, did not form a glass of equal stability according to Ishii.11 A fundamental question that naturally
arises is: what determines the capability to form ultra-stable
glasses by vapor deposition? We believe that investigations of
0021-9606/2011/135(12)/124515/6/$30.00
the glass transition behavior and relaxation dynamics of these
ultra-stable glass formers in their supercooled and standard
liquid states may shed light on the formation and nature of
ultra-stable glasses.
This study provides dielectric relaxation data of ethylbenzene in the temperature range near Tg , as no relaxation
time data had been available for this ultra-stable glass former. We then compile the activation behaviors of the above
ultra-stable glass formers (where available, i.e., with the exception of nifedipine, felodipine, and phenobarbital) and compare with that of the ethylcyclohexane, the case for which the
existence of an ultra-stable state remains to be observed. It
will be demonstrated that the activation behavior of all ultrastable glass formers exhibits a common behavior if scaled to
the respective Tg values, whereas the activation behavior of
ethylcyclohexane deviates from that of the ultra-stable glass
formers. The relevance of fragility regarding the ultra-stable
glass formation is discussed.
II. EXPERIMENTAL
Anhydrous ethylbenzene (EBZ, 99.8%) was purchased
from Aldrich and used without further purification. This simple aromatic molecular liquid has a melting point of 179 K
and a Tg of 115 K determined from a calorimetric study,12
and 111 K from a viscosity measurement.13
A homemade sample cell, schematically illustrated
previously,14 was used to prevent evaporation of EBZ during
the measurement. It consists of a 18 mm diameter plate held
by a sapphire disk with a uniform distance to a larger dish
like electrode. The electrode separation is determined to be
32 μm by a precision capacitance measurement. Due to the
Invar steel material, the sample cell geometry is invariant
to temperature changes. The sample cell was filled with the
135, 124515-1
© 2011 American Institute of Physics
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Z. Chen and R. Richert
J. Chem. Phys. 135, 124515 (2011)
liquid and then mounted in a sample holder. The following
procedure was employed to achieve a rapid cooling rate. The
sample holder was connected to the temperature controller
(Novocontrol Quatro) in order to be able to observe the cooling rate, but kept outside of the nitrogen-gas filled cryostat.
Then, the dewar pressurizing unit is turned on but with the gas
heater off, and the temperature set-point was set to −158 ◦ C
to obtain a high gas flow. Because the sample remained at
room temperature, the gas temperature in the nitrogen-gas
filled cryostat achieved values as low as about −163 ◦ C. The
sample holder was then directly inserted into liquid nitrogen
that is held by a thermo-flask. It was observed that the average
cooling rate exceeded 150 K/min. After the temperature of the
sample approached the destination temperature, the sample
holder was quickly placed into the cryostat and the temperature set point is adjusted towards the target temperature.
The frequency-dependent complex permittivity ε∗ (ω)
= ε (ω) − iε (ω), where ε and ε are dielectric permittivity and dielectric loss, respectively, was measured using a
Solartron 1260 gain-phase analyzer equipped with a Mestec
DM-1360 transimpedance amplifier. Data were acquired for
frequencies in the range from 0.03 Hz to 1 MHz, with
the frequencies being logarithmically spaced at a density of
8 per decade. The measurement temperature ranges from
116 K to 134 K in steps of 2 K with an accuracy better
than 0.05 K.
III. RESULTS AND DISCUSSION
Glass-forming materials are liquids for which crystallization can be avoided upon cooling through the melting temperature Tm . The supercooled regime between Tg and Tm is characterized by relaxation dynamics which are non-exponential
at a given temperature,15 and the temperature dependence
of some characteristic relaxation time constant τ 0 is usually
found to deviate from simple activated behavior.16 In the viscous regime, the empirical Vogel-Fulcher-Tammann (VFT)
expression is often found to account for the tendency of τ 0
to diverge at a finite temperature T0 ,17
log10 (τ0 /s) = A + B/(T − T0 ).
(1)
The above two features, extent of relaxation time dispersion and super-Arrhenius behavior, have been found to correlate in many systems.18 The deviation from Arrhenius type
dynamics is commonly gauged along the “strong” to “fragile”
scale, where a highly fragile case corresponds to pronounced
departure from simple activation.19 The most commonly used
metric for fragility is the so-called steepness index m, defined
as
d log10 τ m= .
(2)
d Tg /T T =Tg
A. Dielectric spectra and activation behavior
of ethylbenzene
Figure 1 shows the frequency dependence of the dielectric loss of EBZ in the temperature range of 116–134 K. The
ethylbenzene
0.15
T = 116 - 134 K (2 K)
0.10
''
124515-2
0.05
0.00
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
/ Hz
FIG. 1. Dielectric loss spectra of ethylbenzene in the temperature range of
116–134 K, recorded in steps of 2 K. The amplitude reduction seen for the
three highest temperatures is irreversible and due to crystallization.
obvious decrease in the magnitude of the dielectric loss peak
at the temperatures higher than 130 K is a result of partial
crystallization of the sample. Nevertheless, the loss peaks at
these temperatures are still well resolved and confinement effects on the dynamics of the remaining liquid are expected
only for much larger crystal fractions. Therefore, peak frequencies for these upper three temperatures are accurately
determined, but our conclusions would not change if these
points were disregarded. The dielectric loss curves are analyzed by using the empirical Havriliak-Negami (HN) function
that is given by20
ε
γ ,
ε∗ (ω) = ε∞ + 1 + (iωτH N )αH N H N
(3)
where α HN and γ HN quantify the symmetric and asymmetric broadening, respectively, ε = εs − ε∞ is the relaxation
strength with εs and ε∞ being the static dielectric constant
and dielectric constant in the high-frequency limit, respectively, and τ HN is the characteristic relaxation time. According to the fit results, α HN ranges from 0.87 to 0.93 and γ HN
ranges from 0.51 to 0.65, which are typical values for fragile
glass formers. Based upon the approximate translation provided by Alvarez,21 βKW W = (αH N γH N )1/1.23 , these parameters are equivalent to a stretching exponent β KWW = 0.55 at
Tg and approaching β KWW = 0.70 near T = 135 K.
The HN parameters α HN , γ HN , and τ HN are used to calculate the most probable relaxation time τ max , associated with
a loss peak positioned at ωmax = 1/τ max . The value is obtained
through the following relation:22
αH N γH N π
αH N π
sin−1/αH N
.
τmax = τH N ×sin1/αH N
2+2γH N
2+2γH N
(4)
Figure 2 shows the temperature dependence of the peak
relaxation time, τ max (T), derived from Eq. (4). This dielectric
relaxation data set of EBZ conforms to a VFT type behavior,
but a fit that also embraces the higher temperature viscosity
data of EBZ leads to different parameters. Like with many
other molecular glass formers, it turns out that the temperature
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Dynamics of ultra-stable glass formers
-1/2
log10(
0
6
-trisnaphthylbenzene
0
TB
4
indomethacin
iso-propylbenzene
-2
2
-2
-4
2
8
( dlog / dT)
max
/ s)
2
J. Chem. Phys. 135, 124515 (2011)
log10( / s )
124515-3
0
100
150
200
T/K
Tg = 115.7 K
m = 97.5
n-propylbenzene
-4
toluene
-6
-8
ethylbenzene
ethylbenzene
-6
115
-10
ethylcyclohexane
-12
120
125
130
135
140
T/K
dependence of the dynamics does not follow a single VFT law
over the entire accessible temperature range.23 In order to better characterize the temperature dependence, the derivative of
the experimental log10 (x) values with respect to temperature
was employed, where x = τ max in the case of the dielectric
measurement and using the Maxwell time x = η/G∞ , with
G∞ being the high frequency shear modulus in the case of viscosity data.24 More specifically, the plot of [−d log τ /dT ]−1/2
versus temperature T transforms a VFT type temperature dependence into a linear graph. The typical scenario derived
from such an analysis is the existence of a crossover temperature TB , which separates the distinct low and high temperature ranges in which different VFT laws are appropriate
for representing the temperature dependence.24 The inset of
Fig. 2 shows the plot of [−d log τ /dT ]−1/2 versus temperature
for EBZ, where the open triangles represent the viscosity data.
As can be clearly seen from the inset, the temperature dependences in the low and high temperature ranges, separated by
TB , follow different VFT laws. In the present context, the important aspect of this crossover is that a fit to T < TB provides
much more reliable glass transition and fragility values than a
VFT fit that targets the entire data range. The low temperature
range VFT behavior (A = −15.0, B = 344.4, and T0 = 95.5)
was used to determine the glass transition temperature Tg and
the fragility m of EBZ, using
m=
B
,
2−A
2−A
[B + T0 (2 − A)] .
B
3
4
5
6
7
8
9
10
1000 K / T
FIG. 2. Activation plot for the maximum relaxation time of the primary relaxation of EBZ. The filled circles are the dielectric measurement data in this
work, the solid line is the VFT fit. The inset shows the temperature dependence of the inverse square root of the derivative, [−dlogτ /dT]−1/2 , where the
open triangles represent the case derived from the viscosity data taken from
Barlow et al. (Ref. 23) and from Rossini (Ref. 39). The solid and dashed
lines in the inset are the VFT fits for the low and high temperature ranges,
respectively. The arrow indicates the crossover temperature.
Tg = T0 +
2
(5)
(6)
The value of Tg is consistent with those obtained from
a viscosity measurement,13 and more recently from a calorimetric study.12 The value of m has been thought to be around
FIG. 3. Activation plots for ααβ-trisnaphthylbenzene (TNB), indomethacin
(IMC), toluene (TOL), ethylbenzene (EBZ), n-propylbenzene (NPB), isopropylbenzene (IPB), and ethylcyclohexane (ECH). In the order of the
figure legends and decreasing Tg , the data sources are: TNB: dielectric
(Ref. 27), viscosity (Ref. 28); IMC: dielectric (Ref. 29); IPB: dielectric
(Refs. 30 and 31), viscosity (Ref. 23); NPB: dielectric (Refs. 30 and 32), viscosity (Refs. 23 and 33); TOL: dielectric (Ref. 34), viscosity (Ref. 23), spin
alignment (Refs. 35 and 36), deuteron-T1 (Ref. 36), microwave spectroscopy
(Ref. 37), nuclear magnetic resonance (Ref. 38); EBZ: dielectric (this work),
viscosity (Refs. 23 and 39); ECH: dielectric (Refs. 40 and 41), viscosity
(Refs. 13 and 33).
58,25 although this value relied on a long extrapolation of preliminary dielectric data within a very limited frequency range.
The result of this study indicates that EBZ has a fragility as
large as other alkylbenzenes such as toluene.26
B. Activation behavior of ultra-stable glass formers
and ethylcyclohexane
In what follows, the temperature dependences of the dynamics that were obtained from different techniques are compiled for those ultra-stable glass formers for which data is
available across a wide temperature range: TNB, IMC, IPB,
NPB, TOL, and EBZ. These will be compared against the dynamics of ECH, a compound which may form only slightly
more stable glasses by vapor deposition, or which becomes
ultra-stable only at conditions that have not been explored
to date.11 Figure 3 shows the activation plots for the above
glass formers, in which the different symbols represent relaxation times obtained from different techniques. The data are
collected from various sources as follows. TNB: dielectric27
and viscosity;28 IMC: dielectric;29 IPB: dielectric30, 31 and
viscosity;23 NPB: dielectric30, 32 and viscosity;23, 33 TOL:
dielectric,34 viscosity,23 spin alignment,35, 36 deuteron T1
(Ref. 36), microwave spectroscopy,37 and nuclear magnetic resonance;38 EBZ: dielectric and viscosity;23, 39 ECH:
dielectric40, 41 and viscosity.13, 33 The Maxwell relaxation time
τ = η/G∞ derived from viscosity data is adjusted via G∞ so
as to match the relaxation times from other techniques.
Common to the τ (T) traces in Fig. 3 is the feature demonstrated for EBZ above, namely that a single VFT law does not
capture the dynamics across the entire data ranges with high
fidelity. We employ the derivative method of Stickel et al.22, 24
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124515-4
Z. Chen and R. Richert
J. Chem. Phys. 135, 124515 (2011)
TABLE I. Compilation of parameters associated with the T ≤ TB dynamics of the glass-former of this study: glass
transition temperature Tg , fragility index m, VFT constants A, B, T0 , crossover temperature TB , and the value of G∞
used to match viscosity to relaxation times using η = τ /G∞ . VFT parameters are based upon data in the T < TB range,
both Tg and m are derived from the VFT fits.
Material
Abbr.
Tg
(K)
ααβ-Trisnaphthylbenzene
Indomethacin
Toluene
Ethylbenzene
n-Propylbenzene
Iso-propylbenzene
Ethylcyclohexane
TNBa
IMCb
TOL
EBZ
NPB
IPB
ECH
344.8
314.7
117.2
115.7
123.9
127.9
100.8
a
b
B
(K)
T0
(K)
−18.1
1620
264
414
0.18
−14.9
−15.0
−12.7
−15.0
−16.9
320.1
344.4
357.8
474.6
628.4
98.2
95.5
99.5
99.9
67.5
140.1
136.8
160.5
152.1
138.3
0.08
0.08
0.04
0.04
0.50
m
A
86.0
82.8
104.4
97.5
74.5
77.6
57.2
TB
(K)
G∞
(GPa)
The values are taken from Ref. 27.
VFT fit is not performed, the values of Tg and m are taken from Ref. 29.
to identify the crossover temperature TB (see inset of Fig. 2),
and then determine the VFT parameters on the basis of the T
< TB data only. This provides more accurate value for Tg and
m compared with overall VFT fits, and the results are compiled in Table I. The values of Tg of the ultra-stable glass
formers span a range of about a factor of 3, 116 K ≤ Tg
≤ 349 K, indicating that the glass transition temperature itself is not a factor relevant for the formation of the ultra-stable
state. An inspection of Fig. 3 suggests that the apparent activation energy near Tg , where log(τ /s) = +2, is a better indicator
of the ultra-stable glass forming ability at the typical vapor
deposition conditions. As demonstrated accordingly with an
Angell-plot in Fig. 4, ECH displays the smallest slope m at
Tg /T = 1, and is thus the least fragile of the systems included.
Note, however, that the fragility of n-propylbenzene is not
markedly larger than that of ethylcyclohexane, which would
imply that either there exists a critical fragility between 74.5
and 57.2 regarding ultra-stability or fragility is not the only
factor distinguishing ultra-stable glass formers.
In order to reveal possible general features of the dynamics of these known ultra-stable glass formers, we employ
the derivative of their relaxation time with respect to the Tg scaled temperature [−d log τ /d(T /Tg )]−1/2 . By plotting this
derivative as a function of the reduced temperature, T/Tg , we
obtain the graph shown in Fig. 5, where VFT behavior appears as a linear dependence with slope (Tg /B)1/2 that intersects the abscissa at the Vogel temperature T = T0 . For the
Tg ≤ T < TB segment, Eqs. (5) and (6) reveal the relation of
this slope to fragility as m1/2 /(2−A). Note that the derivative
used here implies that the choice of G∞ does not affect the
data in Fig. 5. It is interesting to find that all ultra-stable glass
formers fall into one master curve over a wide temperature
range, and that ethylcyclohexane obviously deviates from this
master curve, especially in the temperature range much higher
than Tg . It is important to realize that this master curve is obtained only when reducing the temperature scales to Tg , otherwise one would still get linear segments but with material
specific slopes and transition temperatures. Such a correlation between fragility and the change in slope in Fig. 5 at TB
had been noted before, with that kink quantified by the ratio
of VFT parameters Blo = B(T < TB ) and Bhi = B(T > TB ) using κ = Blo /Bhi .42 The effect of fragility on the appearance in
2
log10( / s )
0
-1
1.4
-1/2
ethylcyclohexane
iso-propylbenzene
n-propylbenzene
-trisnaphthylbenzene
ethylbenzene
indomethacin
toluene
[ dlog / d(T/Tg) ]
1
-2
-3
m = 57
-4
-5
-6
0.90
0.95
1.2
1.0
0.8
1.00
Tg / T
FIG. 4. Angell plot of the relaxation time of TNB, IMC, TOL, EBZ, NPB,
IPB, and ECH. The symbols identify different materials, but experimental
techniques are not discriminated. The dashed lines represent the VFT fits for
ethylcyclohexane (m = 57) and for ethylbenzene (m = 98).
TA
0.6
0.2
0.4
0.1
0.2
m = 98
0.85
TNB
IPB
NPB
TOL
EBZ
ECH
0.0
TB
1.0
1.5
0.0
0.8 0.9 1.0 1.1 1.2 1.3
2.0
2.5
3.0
T / Tg
FIG. 5. Plots of [−dlogτ /d(T/Tg )]−1/2 versus T/Tg for TNB, IPB, NPB, TOL,
EBZ, and ECH. The dashed lines are guides only, with linear behavior indicating VFT behavior with T0 given by the intersection with the abscissa. The
inset is an enlargement of scales near Tg .
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124515-5
Dynamics of ultra-stable glass formers
Fig. 5 can be substantiated by including other glass forming materials. For instance, based upon data compiled by
Stickel,43 ortho-terphenyl (m = 81) strictly follows the pattern of the fragile cases, whereas glycerol (m = 53) departs
from that pattern even more strongly than ECH.
The collapse of the activation behavior of the ultra-stable
glass formers onto one master curve irrespective of their
molecular structures and dynamic parameters seems to suggest also that these liquids have more in common than just
being fragile. All crossover temperatures are at TB ≈ 1.2
× Tg , and the τ (T) behavior for T < TB is approximated by a
VFT law that diverges near 0.8 × Tg (see inset of Fig. 5), i.e.,
near the substrate temperature for maximum stability for vapor deposited films. A crossover to Arrhenius behavior occurs
at a temperature TA ,32 with TA ≈ 2.0 × Tg being a common
estimate for this transition. While such changes in the temperature dependence are observed frequently, a uniform pattern
as seen in Fig. 5 is not the rule and results from comparing
data on the reduced scale, T/Tg . The temperature TA often coincides with relaxation time of 60 ps,32 while TB is associated
with dynamics in the 100 ns regime and coincides with the
merging temperature Tβ of a Johari-Goldstein (JG) (Ref. 44)
secondary relaxation with the primary or α-mode of structural
relaxation.45 The value of TB is also close to other definitions
of a dynamic crossover, such as the critical temperature of the
ideal mode-coupling theory.46
From the inset of Fig. 5, one can observe that the dynamics of ethylcyclohexane follows a VFT behavior similar
to those of the ultra-stable glass formers in the viscous regime
near Tg . However, according to Fig. 5, its dynamics deviates
substantially from those of the other materials for temperatures in excess of TB . This suggests that features related to
fast dynamics may play an important role regarding ultrastability, not just the behavior in the immediate vicinity of
Tg . A relevant factor could be the occurrence or strength of a
JG type β relaxation which indicates residual local mobility
as a glass is formed, as the secondary mode in ethylcyclohexane shows intra-molecular mode rather than JG character.40
Another factor may be the enhanced diffusivity or translationrotation decoupling of supercooled liquids that is significant
only for fragile materials.47 More generally, fragility indicates
a high sensitivity of the dynamics to changes in temperature,
which may be accompanied by a concomitant susceptibility
to other factors such as a free surface. A different explanation
(but also related to fragility) has been offered by Angell48 on
the basis of a first order liquid-liquid transition derived from
theoretical consideration by Matyushov and Angell.49 This
approach takes the view that the ultra-stable state is not just
a lower fictive temperature variant of the glassy state, but a
different structure. Consistent with this view is the growthfront type mechanism with which the ultra-stable state reverts
to the supercooled liquid.50 It has been pointed out that an
equivalent liquid-liquid transition is not expected in the case
of ethylcyclohexane.48
IV. CONCLUDING REMARKS
We measured the primary dielectric relaxation behavior
of ethylbenzene in the temperature range near Tg and de-
J. Chem. Phys. 135, 124515 (2011)
rived dynamic parameters such as the glass transition temperature Tg , stretching exponent β KWW , and fragility m. The
activation behaviors of known ultra-stable glass formers
(ααβ-trisnaphthylbenzene, indomethacin, toluene, ethylbenzene, n-propylbenzene, and iso-propylbenzene) are compared
with that of ethylcyclohexane, the latter possibly differing in
its capability of forming an ultra-stable glass by vapor deposition or requiring different conditions for achieving a similar state of kinetic and thermodynamic stability. From the
Tg -scaled derivative plots it is found that all known ultrastable glass formers fall onto a master curve, suggesting that
there exists some generality regarding their glass transition
behavior. The common features are the transition temperatures TB ≈ 1.2 × Tg and TA ≈ 2.0 × Tg , the Vogel temperatures T0 = 0.8 × Tg for the T < TB regime and T0 = 1.0
× Tg for the TB < T < TA range, as well as activation parameters B that scale with Tg in all three temperature segments.
These features could be not only common to the materials
capable of forming ultra-stable glasses, but to all glass formers of sufficient fragility. By contrast, less fragile systems
such as ethylcyclohexane and glycerol deviate from this common activation behavior of the ultra-stable glass formers, with
the departure being most obvious for temperatures above the
crossover temperature TB .
It should be pointed out that, to date, only several molecular glass formers have been investigated regarding their ability to form ultra-stable glasses by vapor deposition. For cases
such as ethylcyclobenzene, it remains to be clarified whether
their deposition conditions differ strongly from the typical
0.85 × Tg rule regarding the substrate temperature, or if
systems exist that are simply unable to enter such an ultrastable state. Therefore, more experimental data concerning
the dynamics and thermodynamics of the existing and future
ultra-stable glass formers are highly desirable for a deeper
understanding of the mechanism underlying this striking
phenomenon.
ACKNOWLEDGMENTS
Discussions with Mark Ediger and collaborators are
gratefully acknowledged. This material is based upon work
supported by the National Science Foundation (NSF) under
Grant No. CHE-1012124.
1 S.
F. Swallen, K. L. Kearns, M. K. Mapes, Y. S. Kim, R. J. McMahon,
M. D. Ediger, T. Wu, L. Yu, and S. Satija, Science 315, 353 (2007).
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