Molecular engineering of the glass transition: Glass-forming ability across a homologous series of cyclic stilbenes

Article abstract of DOI:10.1021/jp110975y

We report on the glass-forming abilities of the homologous series 1,2-diphenylcyclo-butene, pentene, hexene and heptene-a series that retains the cis-phenyl configuration characteristic of the well-studied glass former, o-terphenyl. We find that the glass

Full text of DOI:10.1021/jp110975y

ARTICLE
pubs.acs.org/JPCB
Molecular Engineering of the Glass Transition: Glass-Forming
Ability across a Homologous Series of Cyclic Stilbenes
Wen Ping
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China
Daniel Paraska, Robert Baker, and Peter Harrowell*
School of Chemistry, University of Sydney, NSW 2006, Sydney, Australia
C. Austen Angell
Department of Chemistry and Biochemistry, Arizona State University, Tempe, Arizona, United States
ABSTRACT: We report on the glass-forming abilities of the homologous series
1,2-diphenylcyclo-butene, pentene, hexene and hepteneꢀa series that retains
the cis-phenyl configuration characteristic of the well-studied glass former,
o-terphenyl. We find that the glass-forming ability shows a sharp maximum
for the six-membered ring and demonstrate that this trend in glass-forming ability is a consequence of a maximum, for the 1,
2-diphenylcyclohexene, of the reduced glass transition temperature Tg/Tm. Since the nonmonotonic trend in Tg/Tm is entirely due
to variations in Tm, we conclude that the design target for maximizing the glass-forming ability across an homologous series should
focus on the crystal stability and the factors that determine it.
size. In 1950, Fox and Flory7 proposed the following relation for
1. INTRODUCTION
polystyrene of molecular weight M,
o-Terphenyl (OTP) is an example of a small nonpolar mole-
cule that is a good glass former.1 This means that OTP exhibits a
6:9 ꢁ 104
Tg ¼ Tg,¥
ꢀ
ð1Þ
reversible transition between glass and liquid under moderate
rates of temperature change and, as a result, has been used
extensively in studies of the glass transition. Despite this attention,
we do not know why OTP is a good glass former. In general,
we know very little about what aspects of molecular structure
influence whether a pure molecular liquid will, on cooling, form
a crystal or a glass. The term “crystal engineering” was coined to
describe “the understanding of intermolecular interactions in
the context of crystal packing and the utilization of such under-
standing in the design of new solids with desired physical and
chemical properties”.2 There is a growing need for the develop-
ment of similar insights into the production of amorphous solids.
Since the production of the first metallic glass in 1960,3 the central
question of that field has been to understand how to chemically
manipulate the properties of amorphous alloys, with glass-form-
ing ability being the most crucial of these properties.4 More
recently, the increasing importance of obtaining amorphous
phases for small organic molecules in pharmaceuticals5 and
coatings in electronic applications6 has drawn attention to the
open question of the relationship between molecular structure
and glass-forming ability. The study of the variation of the glass-
forming ability across an homologous series of molecules is a
useful strategy for isolating the effect of specific structural features.
In this paper we examine the glass-forming ability of an homo-
logous series related to OTP, the cyclo-stilbenes.
M
a result that can be obtained by treating the polymer Tg as the linear
combination of the Tg from two species: bulk monomer and end
monomer. Equation 1 has been extended by Cowie8 who noted
that it failed to properly characterize the size dependence of Tg in
short oligomers. Hintermeyer et al.9 have argued that Tg saturates
with respect to molecular weight at the onset of entanglement, a
conclusion subsequently challenged by Agapov and Sokolov.10
Angell et al.11 noted that in small molecules the Tg tends to increase
linearly with molecular size across a homologous series. Wang and
Richert12 have also found a monotonic (although nonlinear)
increase in Tg with increasing molecular size for the n-alkanols.
(Reference 12 presents an extensive collection of Tg’s for a large
number of homologous series in the course of exploring the
relationship between Tg and the boiling point.)
The variation of Tg with molecular properties, while of
considerable interest, cannot be translated directly into informa-
tion about the variation of glass-forming ability. There are
relatively few studies of the glass-forming ability across homo-
logous series capable of identifying the role of specific structural
variations. Alba et al.13 exploited the superior glass-forming
ability of the low melting point m-xylene to study the glass
Received: November 17, 2010
There has been a considerable amount of work on the
dependence of the glass transition temperature Tg on molecular
Revised:
Published: April 05, 2011
February 14, 2011
r
2011 American Chemical Society
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2. METHODOLOGY
2.1. Synthesis of Cyclic Stillbenes. The C4, C5 and C6 1,
2-diphenylcycloalkenes are all known compounds, whereas the
C7 is new. All four compounds were prepared by McMurray
cyclization18 of dibenzoylalkanes, using the modification of Baum-
stark and co-workers19 where Ti(0) is obtained through the
reduction of TiCl3 with LiAlH4. A typical procedure, describing
the preparation of the C7 compound, is given in Appendix A.1.
While Baumstark and co-workers describe the synthesis of the C8
ring via this method, we only obtained a complex mixture of
hydrocarbons (13C NMR analysis) from which a pure compound
could not be obtained through either flash chromatography or
recrystallization.
Figure 1. The four cyclo-stilbenes used in this study: (from left to right)
1,2-diphenylcyclobutene, 1,2-diphenylcyclopentene, 1,2-diphenylcyclo-
hexene, and 1,2-diphenylcycloheptene, all in the cis configuration.
transition in mixtures of m-xylene and eithr o- or p-xylene.
Whitaker and McMahon14 reported on the glass-forming abilities
of the four isomers of tris-napthylbenzene: isomers 1ꢀ3 are good
glass formers, while isomer 4 is described as not forming a glass.
The reason for this difference lies in the striking difference in
the melting points. For isomers 1ꢀ3, Tm lies in the range
147ꢀ194 ꢀC as compared with a Tm for isomer 4 of 238 ꢀC.
Factors that influence the anomalous stability of isomer 4
presumably include molecular symmetry and the effect (and
likelihood) of rotations of the napthyl groups. Mandanici et al.15
looked at a series of alkylcyclohexanes. They report that propyl-
cyclohexane exhibits a significantly better glass-forming ability
than the ethyl- or the butyl-substituted compounds.
OTP was identified as a good glass former by Andrews and
Ubelhode16 in 1955, and its glass transition was studied in some
detail by Greet and Turnbull.1 As already mentioned, we do not
know why OTP is a good glass former. Andrews and
Ubbelohde16 suggested that the possibility of two different pair
packings (head-to-head and head-to-tail) may contribute to the
stability of the amorphous state. The ortho arrangement of the
phenyls is certainly important since p-terphenyl (the linear
conformation) is not a good glass former.16 We shall therefore
look at a homologous series of molecules that retains the cis
conformation of phenyl rings across a double bond but varies
the character of the central ring. The cyclo-stilbenes provide a
synthetically convenient series that meets these requirements. In
this study we have looked at four compounds: 1,2-diphenylcy-
clobutene, 1,2-diphenylcyclopentene, 1,2-diphenylcyclohexene,
and 1,2-diphenylcycloheptene. The structural feature of OTP
that has been retained (i.e, the cis arrangement of phenyl groups
across an unsaturated bond) corresponds to the cis-stilbene
structure (see Figure 1). The most stable isomer of stilbene is
the trans configuration. The trans configuration in the cyclo-
stilbenes requires the ring to twist and so is inaccessible for small
rings. Studies of the cycloalkenes17 have found that rings of size 8
or 9 represent the threshold above which the trans configuration
is again the stable configuration. It is interesting to note that the
cis to trans transition is, in the cyclo compounds, accompanied by
a transformation from an open achiral ring conformation to a
twisted chiral structure.
2.2. Differential Scanning Calorimetry. A Mettler Toledo
DSC823e was used to carry out the DSC. The samples (∼ 10 mg)
were sealed in aluminum pans.
2.3. Determination of the Crystal Structure of 1,2-Diphe-
nylcycloheptene. A colorless plate-like crystal of 1,2-diphenyl-
cycloheptene was mounted in a Bruker-Nonius FR591 Kappa
APEX II diffractometer employing graphite monochromated
MoKR radiation generated from a fine-focus rotating anode
and was used for the data collection. Cell constants were
obtained from a least-squares refinement against 3704 reflections
located between 5.45 and 54.53ꢀ 2θ. Data were collected at 150
K with φ and ω scans to 55.04ꢀ 2θ. The data integration and
reduction were undertaken with SAINT and XPREP,20 and
subsequent computations were carried out with the X-Seed21
graphical user interface. An empirical absorption correction
determined with SADABS22 was applied to the data.
The crystal structure belonged to the monoclinic space group
P21/c with lattice parameters a 12.0582(5) Å, b 5.6613(2) Å and c
20.5164(9) Å, lattice angle β 94.871(3)ꢀ and cell volume V
1395.5(1) Å3. The unit cell contains four molecules.
3. RESULTS
In Figure 2 we present the DSC scans on heating at 10 K/min
for the four cyclic stilbenes and for OTP. The melting and glass
transition temperatures, Tm and Tg, respectively, obtained from
the DSC data are provided in Table 1 and Figure 3. Tg is found to
increase monotonically with the increasing molecular weight.
While somewhat erratic, the variation of the melting point with
the size of the ring is characterized by a minimum value for 1,
2-diphenyl cyclohexene with a six-membered ring and an abrupt
increase in Tm for the 1,2-diphenylcycloheptene. We have
established that the 1,2-diphenylcycloheptene crystallizes into a
monoclinic P21/c crystal with four molecules per cell. Previous
determinations23 of the crystal structures of the cyclobutene and
cyclohexene analogues reveal similar monoclinic structures with
space groups P21 and P21/n, respectively, and both with four
molecules per cell. The OTP crystal is orthorhombic with four
molecules per unit cell. The crystal structures of the cyclic
stilbenes are monoclinic rather than orthorhombic only due to
small (5ꢀ10ꢀ) angular deviations from the orthrhombic.
This paper is organized as follows: In Section 2 we describe
the synthesis and characterization of the cyclo-stilbenes along
with the details of the differential scanning calorimetry (DSC),
large angle X-ray scattering measurements, and shear viscosity
measurements reported here. In Section 3 we report our
observations including the variation in glass-forming ability.
In Section 4 we feed our observed data into the classical
model of crystal nucleation and growth to predict the time
ꢀtemperature transformation (TTT) curves and obtain esti-
mates of the critical cooling rate in order to see what property of
the molecules is most responsible for the observed variation in
the glass-forming ability. Our conclusions are presented in the
final section.
In order to quantify the glass-forming ability, we have defined
the critical cooling rate Rc, i.e., the minimum cooling rate at
which any significant crystallization is avoided. The minimum
cooling rate is obtained by the following procedure: A liquid is
cooled at a rate R down to Tg and then heated at a fixed rate of 20
K/min. The enthalpy released upon heating is determined and
taken to be proportional to the amount of crystallization
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Table 1. Thermal Properties of the Four cyclo-Stilbenes (Where the ‘Ring’ Number Refers to the Number of Carbons in the Alkene
Ring)a
ΔHm (kJ/mol)
Tm (K)
ΔSm (kJ/molK)
ΔHc (kJ/mol)
Trg (= Tg/Tm)
Tg (K)
critical cooling rate Rc (K/min)
Ring4
Ring5
Ring6
Ring7
OTP
21.34
21.7
17.0
28.6
20.2
322.5
328.7
317.2
373.7
328
0.06618
0.06588
0.05356
0.07662
0.06159
19.5
21.0
16.5
10.4
20.1
0.668
0.676
0.726
0.623
0.75
216
222
230
233
246
35
1.05
, 0.1
.30
, 0.1
a The analogous values for OTP are included for comparison.
Figure 2. The DSC up scan curves of the five glassy materials prepared by a rapid liquid N2 quench into a glass state prior to up scanning: (a) glass
transition and (b) melting transition. (Crystallization occurred in the intervening temperature interval omitted from this figure.)
occurring during heating. The slower the cooling rate, the more
crystallization occurs during cooling and, therefore, the less
crystallization is observed during the subsequent heating stage.
Consider the quantity f, defined as the ratio of the heat released
upon crystallizing during the upscan divided by the heat absorbed
during melting (see Figure 4). If crystallization reached comple-
tion on cooling (a “slow” cooling rate), then there is nothing left
to crystallize upon heating, and f = 0. Likewise, after a very fast
quench, all of the crystallization occurs during heating, and f = 1.
(Here we have assumed that the crystallization processes occur-
ring during cooling and heating result in the same total amount of
crystal being formed.) The variation of f with the cooling rate is
plotted in Figure 5 for each of the four stilbenes. The critical
cooling rate Rc is the cooling rate at which some very small
threshold amount of crystallization occurs (i.e., where f drops
slightly below 1). We shall define Rc as the cooling rate at which
f = 0.95.
The range of accessible cooling rates in this experiment is 0.1
K/min < R < 30 K/min, roughly 2.5 orders of magnitude. If the
minimal cooling rate lies outside this range, then all we can do is
indicate whether it lies above or below the accessible range of
cooling rates. The observed critical cooling rates for the four
stilbenes and OTP have been recorded in Table 1. We find a large
nonmonotonic variation of Rc with the size of the alkane ring
with a striking minimum in the minimal cooling rate for the six-
membered ring. These results demonstrate the existence of an
optimal structure with regards to glass-forming ability as we
traverse the homologous series. It is worth noting that this
optimal molecule is the cyclic stilbene most similar to the
established glass former OTP.
The observation that Tg shows only a rather weak monotonic
variation along the series suggests that the explanation of the
dramatic nonmonotonic variation in the minimal cooling rate is
not due to variations in the relaxation kinetics of the supercooled
liquid but rather due to variation in the stability of the crystal.
This conclusion is supported by previous work on xylene
isomers. In the case of the isomer series o-, m-, and p-xylene, in
which all members have closely similar viscosities, boiling points,
and glass transition temperatures (and hence cohesive energies),
it is known24 from precise thermodynamic data that the differ-
ence in melting points that makes the m-isomer the best glass
former originates in a small (4 kJ/mol) difference in the crystal
lattice energies. While it is reasonable to ascribe differences in
lattice energy with differences in the efficiency of molecular
packing, there many open questions concerning the relationship
between molecular shape and lattice stability. Considering, then,
the thermodynamics of the freezing transitions of our cyclic
stilbene series, we find that the melting point Tm and the
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Figure 5. The ratio f (defined in the text) plotted against the cooling rate
R for the four stilbene molecules. Curves that remain fixed at f = 1 or 0 for
all cooling rates indicate a compound whose critical cooling rate lies below
or above, respectively, the accessible range of cooling temperatures.
Figure 3. The dependence of Tm (top curve), Tg (middle curve), and
Tg/Tm (bottom curve, right-hand axis) on the ring number of the cyclo-
stilbenes. The data for OTP is also included (at a ring number of 6) as
filled symbols.
Uhlmann.27 A sufficient condition for the formation of a glass
is that a liquid can be cooled fast enough to avoid the formation of
crystalline nuclei. This condition is more stringent than necessary
since the presence of nuclei is tolerable as long as their growth
rate is slow enough to result in negligible transformation.
Applying this less stringent condition and using the classical
expressions for the nucleation frequency and crystal growth rate,
we can (following Uhlmann27) derive an expression for the
minimum cooling rate necessary to avoid crystallization and
achieve a glass that depends only on a small number of material
quantities:
• Tm and Tg, the melting and glass transition temperatures
• ΔHf, the molar entropy change at melting
• η, the viscosity for Tg e T e Tm
• the liquid density and molecular diameter
Assuming that the rate of nucleation and the crystal growth
rate are, for a given temperature, both constant with time (i.e.,
transients and history dependence is ignored), then the volume
fraction, X, crystallized in time t can, for small X, be written27 as
Figure 4. A schematic of a DSC upscan. The enthalpies of crystal-
lization ΔHcryst and of melting ΔHmelt are indicated as the areas of the
respective peaks.
1
X ꢂ πIvu3t4
ð2Þ
3
where Iv is the nucleation frequency per unit volume and u is the
rate of advance of the crystal interface per unit area. If we choose
some small value of X, say 10ꢀ8, to define the point at which
crystallization has “occurred” then eq 2, when coupled to
expressions for Iv and u in terms of the temperature, provides
us with a relation between supercooling and crystallization time,
the so-called TTT curve.
enthalpy of fusion ΔHf exhibit a similar monotonic behavior with
minima for the 1,2-diphenylcyclohexene. In light of the similarity
of the crystal structures, it is tempting to ascribe this minimum in
ΔHf to a lower enthalpy of the liquid state at coexistence. (The
subsequent discussion, however, does not rely on this sug-
gestion.) We shall next examine whether the variations in Tm
and ΔHf across the series can account for the observed variation
in the minimum cooling rate.
Using Turnbull’s expression26 for the steady-state nucleation
rate per unit volume Iv, we have
c
2
Iv ¼ exp½ꢀbR3β=TrðΔTrÞ ꢃ
ð3Þ
4. WHAT PHYSICAL QUANTITIES DETERMINE THE
CRITICAL COOLING RATE?
η
where
In 1958, Turnbull and Cohen25 proposed that any liquid
could, in principle, form a glass. (There was scepticism at the time
as one prevailing view held that the short-range order of most
liquids was only trivially distorted from that of the crystal, and,
therefore, avoidance of crystallization would not generally be
possible.) The crucial role of the rate of cooling in glass forma-
tion was clearly formulated subsequently by Turnbull26 and
kT
c ¼
ð4Þ
ð5Þ
3πa3o
ðNV2Þ1=3σ
R ¼
ΔHf
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Figure 7. Calculated TTT curves for which the same enthalpy change
on fusion ΔHf (i.e., that for OTP) has been used for all compounds. The
only difference between the curves was the different values of Tg/
Figure 6. Calculated TTT curves for the four cyclo-stilbenes and OTP
as explained in the text.
T
m used.
ΔHf
ΔSf
conclude that the glass-forming ability across the cyclo-stilbene
series is determined by the value of the only other material
parameter remaining, i.e., To/Tm or, more generally, the reduced
glass transition temperature Tg/Tm. This conclusion is consistent
with Turnbull’s 1969 proposal26 that the reduced glass transition
temperature provides a good predictor of glass-forming ability.
The significance of Tg/Tm with regards the glass-forming
ability needs some qualification. Glass-forming ability is deter-
mined by the position of the “nose” of the TTT curve. Since this
nose occurs at temperatures well above Tg, it is clear that the
value of Tg really has no direct influence on glass-forming ability.
What actually matters is the growth in viscosity over super-
coolings down to T/Tm ∼ 0.9. The quantity Tg/Tm enters here
simply to the extent that the reduced glass transition temperature
provides a convenient parametrization of the viscosity increase
over these small supercoolings.
β ¼
¼
ð6Þ
RTm
R
and ao is the molecular diameter, b is a parameter dependent on
the shape of the nuclei (we shall assume the value 16π/3 for a
sphere), σ is the interfacial free energy per unit area, and η is the
shear viscosity. The reduced temperature is Tr = T/Tm and the
reduced supercooling is ΔTr = 1 ꢀ Tr. The crystal growth rate u is
given by the WilsonꢀFrenkel expression27
ꢂ
ꢀ
ꢁꢃ
c
ΔHf ΔTr
u ¼ 1 ꢀ exp ꢀ
ð7Þ
η
RT
For the interfacial tension σ, we shall use a phenomenological
expression recently proposed by Laird28
σ ¼ 0:5RTm=ðV2=3NAÞ
ð8Þ
Substituting eq 8 into eq 5 results in R = 1/(2β). We have very
little data on the temperature dependence of the shear viscosity
of the cyclo stilbenes and so shall assume that their viscosities
obey the same VolgerꢀFulcherꢀTamman expression as that for
OTP,1 i.e.,
5. DISCUSSION
In this paper we have shown that the glass-forming ability of
molecules related structurally to OTP changes nonmonotoni-
cally as one moves across the homologous series. In particular, we
found that 1,2-diphenylcyclohexene (the member of the series
most like OTP) has a considerably higher glass-forming ability (i.e.,
smaller minimum cooling rate) than molecules smaller and larger
than it in the series. Calculations of the TTT curves using
classical nucleation theory and the WilsonꢀFrenkel theory of
crystal growth rate were able to reproduce the observation that
1,2-diphenylcyclohexene was the optimal glass former in the
homologous series of cyclic stilbenes. Using these calculations,
we showed that the physical quantity responsible for this trend
was the ratio Tg/Tm. The good glass formers (OTP and 1,
2-diphenylcyclohexene) have a high reduced glass transition
temperature Tg/Tm (0.73 for 1,2-diphenylcyclohexene and
0.75 for OTP), while for the poorer glass formers this value is
below 0.68. While glass-forming ability is the specific focus of this
paper, we do note that the actual value of Tg is also an important
consideration. For OTP, Tg = 246 K, significantly higher than any
of the stillbenes studied here. In terms of this discussion, this high
Tg for OTP arises from the dual influences of a high melting point
and the high glass-forming ability shared with the cyclic stilbene
with a six membered ring.
ꢂ
ꢃ
689
η ¼ 4:65 ꢁ 10ꢀ5 exp
in units of Pas ð9Þ
T ꢀ 231
except that the characteristic temperature To is adjusted by
observed calorimetric Tg of each of the stilbenes. Specifically,
we find for OTP that To = Tg ꢀ 15K. We have used this same
expression to estimate the value of To for each of the stilbenes.
ꢀ
Finally, we have used ao = 10 Å for all the molecules.
Using eqs 3ꢀ9 we have calculated TTT curves for the four
cyclo stilbenes and for OTP. The results are plotted in Figure 6.
We find that the “noses” of the TTT curve occurs at Tr = 0.9 for
all the molecules, and that 1,2-diphenylcyclohexene does indeed
represent a minimum in the critical cooling rate from among the
homologous series. This means that our observations concerning
Rc are consistent with the predictions of the standard theory and,
therefore, we can use the theory to identify what physical
quantity or quantities determined the glass-forming behavior.
In Figure 7 we have recalculated the TTT curves but, this time,
replaced the actual values of ΔHf for each molecule with a single
value (that for OTP). Having removed the difference in heats of
fusion, we find little qualitative change in the TTT curves, with
1,2-diphenylcyclohexene, in particular, retaining its position as
the optimal glass former. On the basis of these results, we
Kauzman29 and Turnbull26 suggested that good glass forming
depended on Tg/Tm > 2/3. While our results concur with the
significance of the reduced glass transition temperature, the
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threshold vale of 2/3 appears to be lower bound on the threshold
for good glass-forming ability since we find examples of poor
glass formers with Tg/Tm ∼ 2/3. Alba-Simionesco et al.30
pointed out that the empirical 2/3 “rule” may simply reflect
the fact that Tm values become scarce when the material is too
good a glass former, hence reducing the number of examples of
large values of Tg/Tm in the literature.
that the molecular determination of glass-forming ability may be
best thought of as another branch of crystal engineering since the
clearest determinant of glass-forming ability is to be found in the
stability (relative to the glass transition) of the crystal. The cyclo-
stilbene results we have presented here underline the fact that
even a 5% variation in Tm can have a significant effect on the
glass-forming ability. This observation, along with the evidence
in the literature14 of minor changes in a molecule structure
resulting in large changes in Tm, emphasizes the subtlety of the
challenge of understanding the connection between molecular
structure and crystal stability to the level that allows prediction of
glass-forming ability.
In 1958, Turnbull and Cohen25 proposed that the ratio of
boilingpoint Tb overmelting point Tm provided a useful predictor
of glass-forming ability, with Tb/Tm > 2 being a mark of a good
glass former. This approach completely discards any information
about the temperature dependence of the relaxation kinetics
of the glass in favor of focusing on the stability of the crystal. As
is argued by Angell et al.,24 since Tb provides a measure of the
strength of the cohesive energy between molecules in the liquid, a
Tm that falls below the Tb/2 threshold is an indication of a poor
crystal whose packing does not allow the molecules to extract the
usual stability from the attractive interactions in the crystal.
The quest for a clear quantitative predictor of glass-forming
ability (i.e., the position of the “nose” on the TTT curve) has been
most seriously pursued in the metallic glass community. This
pursuit has produced a small crowd of measures4 in addition to
the reduced glass transition temperature Tg/Tm. Many of these
measures make use of the onset crystallization temperature Tx,
defined as the temperature at which crystallization is first observed
duringheating(atsomestandardrate) fromtheglass.31 Tx provides
information about the stability of the glass state with respect to
crystallization. While not directly connected to the cooling process
(there is a strong likelihood that a sample quenched to its glass
transition will have acquired a distribution of potential crystal nuclei
that will strongly influence the onset crystallization temperature on
heating), the idea4 is that the likelihood of forming a glass should be
related to the subsequent stability of that glass.
’ APPENDIX
A1. Further Details of the Synthesis of the cyclo-Stilbenes
1,3-Dibenzoylpropane and 1,4-dibenzoylbutane were obtained
from Aldrich and used as received. 1,2-Dibenzoylethane and 1,5-
dibenzoylpentane were prepared by the Friedel-Crafts acylation
of benzene with the corresponding diacid chlorides, using the
procedure described by Fuson and Walker.32 1,2-Dimethox-
yethane was obtained from Aldrich and dried statically over 4A
molecular sieves for several days prior to use. All other reagents
were obtained from Aldrich and used as received. Flash chroma-
tography was carried out using Scharlau GE 0048 Silica Gel 60,
0.04-0.06 mm (230-400 mesh ASTM).
The synthesis of 1,2-diphenylcycloheptene (see Figure A1)
proceeded as follows. LiAlH4 (0.68 g, 18 mmol) was added to
TiCl3 (6.5 g, 42 mmol) in dry 1,2-dimethoxyethane (250 mL)
under Ar. The mixture was heated under reflux for 15 min. Solid
1,5-dibenzoylpentane (2.3 g, 8.1 mmol) was then added in one
portion to the cool reaction mixture and then heating under reflux
resumed for 48 h. The cool reaction mixture was poured into
hexane followed by the addition of water. The organic phase was
separated, washed with water, dried over MgSO4, and the solvent
was then removed under reduce pressure. The residue was
then purified by flash chromatography, eluting with hexane
(product Rf = 0.5). Recrystallization from ethanol afforded the
pure cycloheptene as colourless plates (260 mg, 13% yield).
1H NMR (400 MHz, CDCl3) δ 1.72ꢀ1.75 (m, 4H),
1.92ꢀ1.94 (m, 2H), 2.70ꢀ2.73 (m, 4H), 6.96ꢀ7.11 (m, 10H).
Suryanarayana et al.4 compared a number of measures of glass-
forming ability against the maximum diameters at which fully
glass material can be obtained on quenching (related to the
critical cooling rate) for a large number of metallic glass formers.
Good correlations were found between some measures and
certain families of amorphous alloys. Most criteria worked well
for Nd- and Au-based alloys. The reduced glass temperature Tg/
Tm alone correlated well with the glass-forming ability of Co-
based alloys. Overall, however, none of the proposed measures
were found to provide a convincing prediction of glass-forming
ability. Remarkably, there were cases like the commercially
important Zr-based alloys, which exhibited little variation in their
(excellent) glass-forming ability despite exploring values for Tg/Tm
ranging from 0.5 to 0.7.
The survey presented in ref 4 raises an important issue. It is
quite possible that a number of different mechanisms are
responsible for glass stability, and that no single parameter can
capture all of these. For example, in concluding that Tg/Tm
determined glass-forming ability, we have used a simple correla-
tion between crystalꢀliquid interfacial free energy and the
melting temperature. Compounds for which this rule does not
hold can show strong deviations from this simple scaling. Such
considerations underlie the value of looking for predictors of
glass-forming ability just within homologous series so as to avoid
trying to compare what may be quite different stabilizing effects.
We began this paper pointing out the need for a level of
understanding in the molecular determination of glass-forming
ability analogous to that sought for crystals under the banner of
crystal engineering. We conclude this paper with the observation
Figure A1. ORTEP plot of 1,2-diphenylcycloheptene with crystallo-
graphic numbering. Non-hydrogen atoms are shown with thermal
ellipsoids at 50% probability.
4701
dx.doi.org/10.1021/jp110975y |J. Phys. Chem. B 2011, 115, 4696–4702

The Journal of Physical Chemistry B
ARTICLE
13C NMR (125 MHz, CDCl3) δ 26.7 (2CH2), 32.7 (CH2),
36.8 (2CH2), 125.4 (2CH), 127.5 (4CH), 128.9 (4CH), 141.0
(2C), 145.2 (2C).
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100, 1081.
A2. Further Details of the Structure Determination of the
1,2,-Diphenylcycloheptene Crystal. The colourless plate-like
crystal was attached with Exxon Paratone N, to a short length of
fibre supported on a thin piece of copper wire inserted in a
copper mounting pin. The crystal was quenched in a cold
nitrogen gas stream from an Oxford Cryosystems Cryostream.
A Bruker-Nonius FR591 Kappa APEX II diffractometer employ-
ing graphite monochromated MoKR radiation generated from a
fine-focus rotating anode was used for the data collection. Cell
constants were obtained from a least squares refinement against
3704 reflections located between 5.45 and 54.53ꢀ 2θ. Data were
collected at 150(2) Kelvin with φ and ω scans to 55.04ꢀ 2θ. The
data integration and reduction were undertaken with SAINT and
XPREP, and subsequent computations were carried out with the
X-Seed graphical user interface. An empirical absorption correc-
tion determined with SADABS was applied to the data.
The structure was solved in the space group P21/c(#14) by
direct methods with SHELXS-97, and extended and refined with
SHELXL-97. The non-hydrogen atoms in the asymmetric unit
were modelled with anisotropic displacement parameters. A
riding atom model with group displacement parameters was
used for the hydrogen atoms.
Formula C19H20, M = 248.35, Monoclinic, space group P21/
c(#14), a = 12.0582(5), b = 5.6613(2), c = 20.5164(9) Å, β =
94.871(3), V = 1395.5(1) Å3, Dc = 1.182 g cmꢀ3, Z = 4, crystal
size = 0.37 ꢁ 0.14 ꢁ 0.01 mm, colour = colorless, habit plate,
temperature = 150(2) K, λ(MoKR) = 0.71073 Å, μ(MoKR) =
0.066 mmꢀ1, T(SADABS)min,max = 0.933, 0.999, 2θmax = 55.04,
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Ramos, M. A. J. Chem. Phys. 2006, 125, 054514.
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hkl range = ꢀ15 15, ꢀ7 7, ꢀ24 26; N = 12282, Nind
=
3201(Rmerge = 0.0273), Nobs = 2398(I > 2σ(I)), Nvar = 172,
residuals [R1 = ∑ Fo| ꢀ |Fc /∑ Fo| for Fo > 2σ(Fo); wR2 =
2
2
(∑w(Fo ꢀ Fc2)2/∑(wFc2)2)1/2 all reflections w = 1/[σ2(Fo ) þ
(0/0368P)2 þ 0.4519P] where P = (Fo þ 2Fc2)/3] R1(F)
2
0.0394, wR2(F2) 0.0937, GoF(all) 1.007, ΔFmin,max ꢀ0.173,
0.230 eꢀ Åꢀ3
.
’ ACKNOWLEDGMENT
We gratefully acknowledge support from the Australian
Research Council.
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dx.doi.org/10.1021/jp110975y |J. Phys. Chem. B 2011, 115, 4696–4702