LIQUIDS, PLASTIC PHASES, AND GLASS TYRANSITIONS IN RELATION TO
CATION STRUCTURE IN C12 TETRAALKYLAMMONIUM BROMIDES
E. I. Cooper∗ and C. A. Angell**
Department of Chemistry
Purdue University
West Lafayette, IN 47907
ABSTRACT
With the initial objective of establishing a relation between crystal packing efficiency and
glassforming propensity of the fused state, all 15 straight chain isomers of the
tetraalkylammonium bromide C12H28N+Br- have been synthesized and characterized.
With most low-symmetry cations we achieve melting point (Tm) lowering of almost 200
K and, usually, glassforming capability on fast cooling. Even greater depressions of Tm
are frustrated by intervention of low density, disordered cubic phases as crystallization
products. This circumstance (which precludes detailed correlation of phase transition
behavior to cation symmetry) has permitted a comparative study of a rich variety of
liquidglass transitions and plastic crystalglass transitions in systems of constant
composition, which has become the focus of the paper. Correlation of phase stability
domains with crystal and liquid densities is made. Liquid-formed glasses prove to have
much smaller normalized heat capacity changes (∆Cp/Cp (glass)) at Tg than normal,
evidently due to large residual configurational heat capacities in the glass. This contrasts
with the relatively large ∆Cp of the plastic crystal glass transition. In one case we observe
a glass transition in a solid mesophase, possibly created by freezing of "melted" sidechains.
∗
Present address: IBM T.J. Watson Research Center, Yorktown Heights, New York 10598
Present address: Department of Chemistry, Arizona State University, Tempe, AZ 85287-1604
**
1
INTRODUCTION
In the study of supercooling of liquids and the glass transition, an essential requirement is
that nucleation of crystals be suppressed. Although a high liquid/crystal surface tension
will sometimes lead to large nucleation barriers, it is more common that nucleation is
suppressed because of the depression of the thermodynamic freezing point Tm to
temperatures where high liquid viscosities cause low nucleation rates.(1,2) An effective
study of glass formation must therefore involve a study of factors affecting freezing
points. Gaining a better understanding of these factors is also of considerable inportance
in several areas of chemistry and materials science.
An earlier study(1) pointed to the possible importance of molecular symmetry and its role
in determining the efficiency of ordered packing hence of crystal stability, but the study
was limited by the small number of isomers in the systems for which data were available
(disubstituted benzenes). In an attempt to provide a better empirical base for this type of
investigation, we have synthesized, and studied in certain basic respects, all 15 straightchain isomers of the organic salt tetrapropylammonium bromide) by changing the length
of the alkyl groups about the central nitrogen. However, the variety of phase transition
behavior observed within this family has resulted in a major broadening of the original
scope of the work.
We have observed both a broad set of liquid-glass transitions and plastic crystal to centerof-mass ordered glass transitions,(2) both of which exemplify the ergodicity-breaking
(disorder-freezing) type of transition to which so much theoretical attention is currently
being given.(3,4) We also observe other continuous transitions in which ergodicitybreaking evidently plays no role. We have been able to correlate the occurrence of these
different types of transitions with certain thermodynamic and volumetric characteristics
of these substances which reflect on the subtleties of packing of the variably symmetric
cations within the crystal lattice. Thus this has become a study of phase stability and
phase transitions with special emphasis on metastable states, in a system in which variety
is introduced at constant composition.
2
The phase transition phenomenology of organic crystals and salts can be very
complicated and a large literature is devoted to it.(5,6) The phenomenology is dominated
by the entropy of disorder of different elements of the crystal structure. Most disordereed
are the so-called "plastic crystals" which, by the Timmeran's criterion, (7) melt to isotropic
liquids with entropies of melting ∆Sm of less than 21 J/K·mol, in our description of the
highly disordered phases found in the present work as "plastic crystals." Their low ∆Sm
requires that much of the rotational entropy of the molten state be present in the
crystalline phase, hence the terms "rotator phase" or "rotational crystalline state" (the
term preferred by Kitaigorodsky(5)) may be used. The term ODIC phases, for
"orientationally disordered crystal" has recently been widely adopted for their
description. In some cases the crystal disorder originates in the conformational disorder
and packing of the longer alkyl chains in the cations so the less specific term "condis
crystal" proposed by Wunderlich et al.(8) may often be appropriate. Our study, however,
is not aimed at discovering the molecular origin of the phase transitions we observe since
this cannot be achieved with the thermodynamic tools we have employed. Rather we are
concerned with exploiting the chemical simplicity of our isocompositional system to
simplify the problem of relating the different types of ergodicity-breaking phenomena
which may be observed, to the cation structure. Thus our purpose will be best served by
continuing the use of the term "plastic crystal," in order to avoid the implication of any
single ordering mechanism in discussion of the orgodicity-breaking phenomena (glass
transitions) we observe in these crystalline media.
In most, but not all, cases, it is necessary to exploit the sluggish kinetics of first order
transitions from liquid to crystal, and from disordered-crystal to ordered-crystal, in order
to observe the "freezing-in" of disorder, or "loss of ergodicity" involved in the glass
transition. This happens at a temperature, Tg, at which temperature-dependent relaxation
time for the order parameter (whether defect population, orientational distribution, or
other) becomes long with respect to the time scale on which temperature in the sample is
equilibrated by thermal diffusion.(9) The degree of disorder frozen in at Tg therefore must
depend on the cooling rate. However, on reheating, the internal order parameter is re-
3
established at its equilibrium value as soon as the glass transition temperature is passed.
It follows that the entropy change in any reversible phase transition that occurs above the
glass transition temperature occurs within a (metastably) equilibrated phase and hence
must be independent of the initial quenching rate (unless, of course, the cooling process
was too slow, and allowed partial formation of a second phase).
In cases in which the heat capacity associated with the ordering is large, the continuous
ordering process can have a very temperature-dependent (and usually non-Arrhenius)
relaxation time and the ergodicity-breaking process then has a sharply-defined
calorimetric signature. This is the familiar liquidglass transition heat capacity jump,
∆Cp. In other cases, the disordering can be thermodynamically weaker, i.e. the change in
heat capacity is small relative to the vibrational heat capacity, so the ergodicity-breaking
transition may pass unnoticed. In liquidglass cases of the latter type where this has
been studied carefully,(10,11) the transition is also spread out over a wide temperature range
because of a smaller relaxation time temperature dependence, and careful quantitative
measurements, or high heating rates are necessary to detect it. Because the relaxation
temperature dependence in these cases is usually closer to Arrhenius form, they have
been described as "strong" in the now widely used "strong/fragile" liquid classification.(12)
The term implies that the structure is little affected by change of temperature. It
appears(13,14) that there are many examples of such "strong" behavior among
orientationally disordering crystals, and that the "strength" may be related to how small is
the disturbance caused to the lattice by the reorientation. The smaller the disturbance the
smaller the ∆Cp, the more Arrhenius the behavior, hence the greater the "strength."
Examples are thiophene(15) and pentachloro benzene(14) in which the heat capacity jump at
the ODIC glass transition is very small. We will see examples of large and small glass
transitions in this work. (The determination of the relaxation time characteristics to
correlate with these will be a matter for future work using different techniques.) There
are also evidently cases in which the glass transition is smeared out by the presence of
several contributing processes (as happens in the case of proteins) or by an intrinsically
broad distribution of relaxation times in a single process. Such a situation renders proper
characterization very difficult.
4
Because of the large number of compounds involved in this study, it is desirable to have a
simplifying nomenclature. Thus we will abbreviate the names of the members of this
family of compounds by a notation keyed to the lengths of the four alkyl chains in each
case; thus tetrapropylammonium bromide becomes 3333, which
dipentyldimethylammonium bromide is designated 5511, etc. Since these compounds
existin many possible stable and metastable crystal modifications, and since the different
crystals can exhibit ergodic-to-nonergodic (i.e. glass-like) transitions, it is necessary to
develop a systematic notation which allows the phase undergoing a given transition to be
quickly related to parent phases in its line. A nomenclature adopted by Andre et al.(16) has
many of the needed features, but needs some modification to satisfy our needs because
we have generated, by fast melt cooling, metastable phases which are distinct from the
line of phases produced by the equilibrium route. We propose the scheme illustrated in
Fig. 1 which we believe covers most possibilities for this and other systems.
Figure 1 can be regarded as an enthalpy level diagram with temperature as the X axis, so
that steps represent first-order phase changes of slope represent second-order phase
changes or glass transitions. We use Roman numerals to indicate, in order of descent
from the liquid, the stable crystalline phases. If a given phase supercools through a phase
transition it acquires a prime to indicate metastability. If the metastable phase, e.g. I',
generates a new phase on cooling, then that phase will be designated a II-phase since it is
the second phase generated along that line, but it must be qualified, II", to distinguish it
from the metastable continuation of the II phase on the stable (lowest) descent path.
Likewise, the product of metastable freezing of the liquid must be a type-I phase since it
is the first to appear from the liquid in its line, but it must be a I' to distinguish it from the
supercooled state of the stable I phase. In this scheme it is simple to modify the
designation in the unlikely even t that a sluggish but stable transition to a lower enthalpy
phase should later be found to occur, e.g. from II, and before III in the present sequence
is reached. This would require the new phase to be designated III and the present III
phase to become III". (Obviously, the same phase may occasionally form by different
thermal routes, e.g. by cooling two different metastable phases. Depending on the
5
Fig. 1
Nomenclature tree for the phases observable in complex systems. Phases I always derive from the
liquid state. The unprimed I is a thermodynamically stable phase. II phases always derive from I phases by
crystallization. II phases obtained by crystallization of metastable I' or I" phases. The number of primes
will indicate the relative degree of metastability. Any crystalline phase carrying rotational or other
configurational degrees of freedom can become a glassy state with respect to configurational degrees of
freedom if quenched fast enough. The glasses and glass transition temperatures are therefore distinguished
from one another by being given the designation of the phase in which the freezing of the degree of
freedom occurred. They are unlikely to be found in the lower enthalpy phases. Transitions which are
thermodynamically reversible are shown with double arrows. Transitions from metastable states direct to
lower enthalpy stable phases are possible (see dashed line in Fig. 1 and rationale in Fig. 7, curve 1).
thermal analysis data, other methods -- e.g. X-ray diffraction may then be needed to
remove ambiguity).
An ergodicnonergodic transition occurring in a phase along one of the descent lines is
designated as Tg( ) with the parenthesis containing the designation of the phase which
was the ergodic phase. The liquid-to-glass transition, which in our experience so far will
be the highest temperature ergodic-nonergodic transition in the whole tree, will be
designated Tg(L) since the prime seems superfluous in this case.
6
To alleviate the complexity of the system, we will analyze our findings in four stages.
An initial section will be given to discussion of the original problem we set out to study,
viz. The relation between structure, melting point, and glass formation. In a second
stage, we analyze the liquid-to-glass transition phenomenology of those isomers which
could be vitrified. A third section is then given to the phenomenology of the plastic
crystal phases of the various isomers, and the range of glass transition behavior that they
display. The comparison of plastic crystal glass transitions with liquidglass transition
in the same isomer proves of special interest. Finally, a short section is given to observed
transitions which are continuous but not kinetically controlled.
EXPERIMENTAL SECTION
Synthesis
Two members of the family, 3333 and 9111, are commercial products and were used as
received (from Fischer Scientific and Eastman Kodak, respectively). Most other
compounds were sythesized in one step by the Menschutkin reaction between tertiary
amine and alkyl bromide in acetonitrile, from reagent-grade chemicals which were
purified to a colorless state whenever necessary. Typical conditions: <50°C (chosen over
the commonly used reflux conditions so as to minimize side reactions), e.g. 3-4 weeks at
22° or 2-6 days at 45°; slight excess of the more volatile of the two reactants; ~40 vol. %
acetonitrile; protection against air and light.
In the cases of 6321, 5421, 5331, 4422, 5511, and 5322, the tertiary amine (for which we
use the same notation as for the quaternary products), not being readily available, was
prepared in an additional step. The amine 321 (b.p. 88-89°) was made by reductive
methylation of N-ethylpropylamine with CH2O + HCO2H(17); the amine 421 (b.p. 112114°) -- by reductive alkylation of N-methylbutylamine with NaBH4+CH3CO2H(18); 533
(b.p. 90°/22 torr), 442 (b.p. 172.5-175.5), 511 (b.p. 119-120°), 522 were made by
alkylation of the symmetrical secondary amine in excess with the corresponding alkyl
7
bromide, with excess K2CO3 in methanol or Na2CO3 in glycerol.(19) In the cases of 5421
and 6321, the final product was a racemic mixture which we made no attempt to resolve.
The reaction mixtures were evaporated to dryness under vacuum. The crude crystalline
products were recrystallized from anhydrous solvents: CH2Cl2, CHCl3 or tetrahydrofuran
(THF) by addition of, respectively, THF, ether, or ether + pentane. This order of the
three combinations of solvents parallels an order of increasing solubility (decreasing
melting enthalpy) of the compounds. Dissolution is clearly exothermic for many of the
quaternary bromides in CHCl3 and, for some, in CH2Cl2.
Recrystallization of the lower melting members of this family was difficult. Because of
their low lattice energy, cooling tends to yield two liquid phases rather than nucleation of
the crystalline phase. Easily filtrable particle size was obtained by warming to nearly
complete dissolution and slow cooling. Filtration, washing with anhydrous solvents
(THF, ether, pentane), and drying in vacuo at 50-70° were done under N2 in Kintes'
Airless-wareR. The purity of the products -- as judged by elemental analysis or
volumetric analysis of Br- was satisfactory, and further recrystallization was in general
not required; when recrystallizations were carried out (as for 7311 and 4332) they did not
lead to significant increases in either the sharpness, or the temperature, of melting
according to differential scanning calorimetry (DSC) and hot-stage microscopy. The
soundness of our synthetic procedures is illustrated by the fact that 6222 -- the only
previously reported low-melting compound in the series -- was found to melt at 115°C,
no less than 7K higher than the highest of several prior references.(20) The recrystallized
salts are hygroscopic (the lower the melting point, the more so). They were kept in
desiccators and did not deteriorate noticeably in more than two years.
Several mixtures of pairs of lower-melting compounds were prepared, in ratios
corresponding to expected eutectic compositions in the binary systems calculated by
assuming ideal-solution behavior of the melting-point depression. The mixtures (Table
2) were briefly melted in a dry glove box, allowed to cool to room temperature and aged
for >50 days before measurements to allow for completion of a sluggish phase transition.
8
Characterization
All compounds were characterized by DSC with respect to temperatures and enthalpies of
melting and/or of other phase transitions. The room temperature density of all
compounds was measured by the flotation method.(21) The lower melting compounds
were also examined by x-ray powder diffraction (XRPD) and, in a preliminary manner,
by a dilatometric technique. An account of their transport properties in the liquid state
will be published elsewhere.(22)
DSC runs were performed on 3-10 mg samples, sealed inside Al pans in a dry glove box,
using a Perkin-Elmer DSC 4. Weights (averages of three weighings) were accurate to
<0.02 mg. Temperature and enthalpy of transition were calibrated by the melting
transition of indium for high temperatures and by the solid-to-plastic, and melting,
transitions of 99.95% pure cyclohexane (BDH) for low temperatures, with linear
interpolation of the corrections. At least two samples were examined of each compound,
at different times; they were "aged" at room temperature for over a year, increasing the
likelihood that the thermodynamically stable phase was investigated. A series of cooling
and heating runs was performed on each sample; these usually included: (i) repeated
melting or transition to a plastic phase (I in our notation) and comparison of moderate
cooling and fast quenching through the same transition; (ii) heating through glass
transition, if present, usually starting at -100°C; (iii) heating and cooling through other
transitions of interest, if present. Melting point were double-checked by hot-stage
microscopy under N2. Melting always yielded clear liquids, however no special attempt
was made to identify or classify liquid crystals. In order to facilitate diagnosis of
metastability in the solvent-precipitated phases, one sample of each compound except for
the four highest melting ones was subjected to slow cooling (0.1-0.3°/min), from slightly
below the melting point (but not >130°) to room temperature, before going through the
regular series of runs. Most runs were performed at +10°/min; data derived from runs
performed at different rates were corrected accordingly.
9
For investigation of glass formation in the lower-melting compounds, samples were
repeatedly melted briefly (for 1-3 min), and then quenched. Repeated melting at <140°C
did not lead to significant decomposition (as expressed in Tm and ∆Hm), in accordance
with Gordon's observations on the decomposition rate of tetraalkylammonium
bromides.(24) Quenching was either at the capability limit rate (<320°/min) of the DSC4
or by pouring N2 over the sample (~2x103°K/min). By using an internal calibration, the
Perkin-Elmer TADS DSC software allows the change of heat capacity at the glass
transition to be obtained on demand. This estimate was obtained for most samples that
gave reproducible glass transition behavior. In one case -- 5511 -- for which the glassy
phase was relatively stable, the Perkin-Elmer heat capacity program (which subtracts a
baseline run) was used to measure with +15% accuracy the heat capacity of the glassy
and the crystalline materials over a range (-60° to 10°C) encompassing the glass
transition.
Densities at 25.5 + 0.5°C were measured by flotation of a few mg of solid in a mixture of
2,2,4-trimethylpentane and hexadecafluoro-1,3-dimethylcyclohexane, in a ratio adjusted
so that most of the material stays off the flask's bottom. This "end-point" was
reproducible to within +0.005, and in most cases +0.002 g/cm3. (The above "optimized
flotation medium" OFM was chosen for the bulkiness, branching, and low polarizability
of the components' molecules, after an unreasonably high density was obtained for 5511
in a standard cyclohexane-CCl4 mixture; The high value is believed to be due to small,
polarizable CCl4 molecules dissolving in the disordered solid, since replacing CCl4 with
the slightly bulkier CCl2FCClF2 in the mixture with cyclohexane was enough to yield a
density only 0.005 g/cm3 higher than the one measured using our OFM). For
confirmation, the solution was filtered and the filtrate density was measured and shown to
be unchanged from the intitial OFM value. AgNO3 tests on water extracts of the filtrates
were negative, proving that the salts were insoluble in the OFM.
X-ray powder diffraction patterns were obtained for all the lower-melting (m.p. <140°C)
compounds. Debye-Scherrer capillaries (dia. 0.5 mm) were filled and wax-stoppered
inside a dry glove-box. The film was protected by Al foil against the Br-derived strong
10
background scattering. A 114.6 mm-diameter camera with a rotating sample-holder was
used. Attempts to determine the complete structure of two of the higher-melting
compounds (4422, 4431) by single-crystal x-ray diffraction failed because of the high
degree of disorder in the structure even near liquid nitrogen temperature.
Density changes with temperature were estimated for a few compounds, especially
around phase transitions. Samples of 3-4 g salt were immersed in decalin in a volumetric
apparatus that was then ultrasonically degassed, resealed, and immersed in a heating bath.
Due to some possible solubility of decalin in the higher entropy phases and to the slow
equilibration (leading to slight decomposition above 100°C), these results should be
considered preliminary.
RESULTS
We present in Table 1 (adapted with changed from ref. 2) the principal transition
temperatures of the compounds which are of interest in this study; viz., melting points Tm,
glass transition temperatures Tg of liquid (Tg(L)) and plastic crystal (Tg(I)) etc. states, and
their respective crystallization (devitrification) temperatures Tc, where applicable. A
more detailed description of phase transitions and their thermodynamic characteristics is
reserved for later tables following explanatory material given in discussion of Figures 26.
Fig. 2 illustrates the behavior of compounds which could be quenched in to glasses from
the melt (usually by immersion of the sealed DSC pan in liquid N2). As Table 1 records,
the Tg values are very similar. On heating, the glasses have a narrow stability range,
crystallizing sharply about 15-30K above their Tgs, sometimes forming a metastable
phase which at a higher temperature converts into a more stable one (Ostwald's step rule).
Approximate changes of heat capacity at the glass transition are given in Table 2. The
quality of these data is confirmed by precise (1%) measurements obtained with a
different calorimeter which are being published elsewhere.(23)
11
Table 1 (a) compound satisfies Timmeran's criterion for plastic crystal (∆SF < 21 Jmol-1K-1)
(b) almost satisfies Timmerans' criterion for plastic crystal (21 <∆SF < 26 Jmol-1K-1)
(c) lowest crystalline state density at RT; most stable glass.
Fig. 2 Two examples of liquidglass transitions. 6411 evidently devitrifies to the stable I phase, which
is uncommon. Temperatures marked on graphs include corrections from calibration runs where
needed.
12
Fig. 3 Three examples of the glass transition in plastic crystals. (i) In 4322, (Tg, I' = -51°), the plastic phase
(I) is the only solid phase ever observed. (ii) Phase I' of 5322, Tg,I' = -74° is also stable but can be
crystallized to II. It has a larger ∆Cp at Tg,I' than any of the glassliquid transitions of Fig. 2. (iii) Phase I'
of 4422, Tg,I', = -74°, is kinetically unstable, requires quenching of I to form, and crystallizes immediately
to a new phase II", just above Tg,I'. II" then transforms back to I' at 10°C. The excess heat capacity of I' is
easily seen by comparison of upscans 1 and 2. Phases and transitions are marked on scan sections.
Temperatures marked on graphs include corrections when needed. The parentheses beside the scan
numbers give the cooling rate to produce the sample (upper number in deg/min) and the heating rate of the
scan (lower number in deg/min).
Fig. 3 shows the typical behavior of the higher-melting, globular-cation compounds. On
cooling from below the melting point, the first crystalline phase formed (the designated
crystal I) undergoes a glass-like transition if the cooling rate is high enough. Unlike the
"liquid-formed" glasses, the Tg values (and the stabilities against crystallization to a nonplastic phase) of these plastic-crystal glasses are very variable, as seen by comparing the
traces of 4422 and 4332 in Fig. 3. It is notable that the 4332 compound is very stable as a
plastic crystal and could not be crystallized into an ordered phase. Approximate changes
of heat capacity at the glass transition of the plastic crystal are given in Table 2.
13
Fig. 4 Example of the generation by fast cooling of the liquid, of a metastable crystal phase of high
enthalpy (and probably low density) which shows a smeared-out glass transition Tg,I' on heating before
recrystallization to stable phase I. Figures in parentheses beside scan numbers are cooling and heating rates
respectively as in Fig. 3. 100°C/min heating was needed to highlight the glass transition. Notes: (a) The
small III transition appears to be symmetric only because of the fast heating; it appears as a sharp
transition at a lower temperature (i.e. shows hysteresis) on cooling, and is therefore different from the "type
H" transitions in Fig. 5. (b) Phase II has an anomalously high density for a low melting isomer, though the
transparent, unstable I" (changes to II in < 1h at room temperature) is presumably a low density phase. (c)
The plastic phase is named I" since it formed from the liquid by freezing below TIII (run not shown),
which makes it "double metastable." I' (supercooled I) could have formed under the same conditions, but
the large exothermic transition of the plastic phase at 70°C on heating, when compared with the small
∆HIII' rules that out.
Fig. 4 shows a more complex case, that of 6222 -- the only low-melting salt in the series
which, after quenching in liquid N2, does not exhibit a glass transition. In this case a
metastable phase, I", is formed instead; this is also found on 320°/min cooling. The highdensity room-temperature II phase is not recovered on heating, exothermic conversion
proceeding instead directly into the crystal I phase. A very fast scan (100°/min) of the I"
as compared to the II phase magnifies thermal effects enough to show that the I" phase
14
does show a very smeared-out relaxation process (between -80 and -20°C) reminiscent of
a glass transition (see Fig. 3, curve (i)). Similar processes may operate in the I phases of
the other low-melting compounds, but the absence of an underlying ordered phase
prevents us from identifying them because of the lack of a direct basis (the II phase) for
comparison of the heating curves as in the 6222 case.
In most cases the solid-state phase transitions in this series are sluggish. Cooling at
moderate rates (-1°…-10°/min) generally leads to hysteresis and often to incomplete
recovery of the original phase on reheating. Sometimes it leads to the formation of
different, more disordered phases which may be identified by their different patterns of
phase transitions on heating, and by their lower total entropies of transition, ∑∆Str.
In sharp contrast, Fig. 5 shows two cases (9111 and 5421) in which the fast cooling of a
Fig. 5 McCullough Type H transitions in 5421 and 9111 metastable phases. II" of 9111 is a disordered
phase obtained by >40°/min cooling through the III (90°) transition. On reheating, II"I also occurs at
90° but with only 87% of ∆HIII'·II" also does not exhibit the 1st order IIIII transition (-58°) on cooling.
Note near absence of hysteresis effects, suggesting these are continuous, probably displacive, transitions,
though the enthalpy change can be quite high (see Table 2).
15
high-temperature phase (I-9111, I-5421) replaces a first-order transition to an ordered
phase II by a transition with higher-order character a less ordered phase. In 9111 (see
Fig. 1), phase II" -- obtained by fast cooling through III -- exhibits a weak transition of
this type, II"III"', which replaces the IIIII (-58°) transition (II" returns to I on
heating, with a smaller ∆Str than III). These transitions show nearly symmetrical cuspshaped peaks, with almost no hysteresis effects in spite of a broad temperature range of
~20°C. In McCullough's classification(25) these are H-type transitions, which are
discussed later.
Table 2 contains the detailed thermodynamic data on the glass and crystal phase
transitions observed when starting with the solvent-precipitated, room-temperature aged
salts. Samples slowly cooled (at -0.1…-0.3°/min) from near Tm (when low) or from 100130° to room temperature were usually either similar or slightly more disordered (as
judged from ∆Str). For the survey of lower temperature behavior, the sample was first
cooled to <-100°C events may thus have been missed. Transition temperatures observed
on reheating at 10°/min are estimated to be accurate to +1° and enthalpies to +3%. For
transitions occurring at >140°C, however, the accuracy diminishes because of thermal
decomposition.
The conditions of formation and crystallization of glassy (liquid and plastic) phases are
reported in Table 3. Also in this table are the ratios Tg/Tm (or Tg/Ttr) -- which at least for
liquid-formed glasses is considered to be a predictor of glass stability(26) -- and the
dimensionless quantity (Tc-Tg)/Tg, which we have preferred as a parameter for the
comparison of actual stability of different glasses.(27) The uncertainty in Tg is +2L (unless
noted otherwise), because of some arbitrariness in defining the "straight" baseline below
the transition.
The DSC heat capacity values for glassy and crystalline 5511 at several temperatures are
given below. At -60, -50, -40,, -35 (Tg), and -19°C (just before crystallization), Cp for
glass [crystals] was, respectively: 283 [270]; 297 [280]; 313 [288]; 332 [292]; and 401
[305] J/K·mol. The accuracy is probably better than +5%.
16
Table 3 Thermodynamic data on C12H28N+Br- isomers*.
Notes: (a) decomposition too fast; (b) transition to an ordered state could not be obtained; (c) 12.0 for
slow-cooled sample; (d) samples with different history; (e) crystallization too close to Tg; (f) slow
cooled: (g) solvent-precipitated; (h) the magnitude and temperature of this transition depends strongly on
sample history; (I) shoulder at 124°; (j) after quenching from > 100°: 90°, 25.8 kJ/mol, 71.2 Jmol-1K-1;
(k) full vitrification on quenching could not be achieved; (l) mixtures obtained by melting and long
annealing at room temperature; (m) with pre-melting transition(s) at 140-142°; (n) some pre-melting
apparent, could not be reduced by recrystallization.
*
Data usually on solvent-precipitated materials; many transitions are affected by sample history to within
3°(T) and 5% (∆H, ∆S). Larger or more unusual effects are noted.
17
X-ray powder diffraction patterns of as-recrystallized 6321, 6411, 7311, 7221, 5511,
5421 and 6222 are available upon request. The first four were indexed as cubic
structures, with no systematic (hkl) extinctions. The first three exhibit practically
identical patterns, with only minor intensity differences in a few lines. The unit cell
parameter, ao, was calculated to be 16.96 Å with Z = 12 molecules/unit cell and dx (calc.)
= 1.088 g/cm3, in good agreement with the 1.085, 1.070, 1.095 g/cm3 measured densities
for 6321, 6411, 7311 respectively. The fourth cubic compound -- 7221 -- yields a
somewhat more diffuse pattern, with ao = 23.35 Å, Z = 32, dx = 1.111 g/cm3, in good
agreement with the measured value of 1.104 g/cm3. In both cases, a few very weak lines
yield forbidden (h2 + k2 + l2) values, though, so a superstructure of the above unit cells
may be present.
Of the other three compound X-rayed, only 5511 could be indexed. It is tetragonal with
ao + 31.7(5) Å, c = 12.6(2) Å, with Z = 32, dx = 1.11(2) g/cm3. Due to the small number
of useful lines in the pattern, this determination is tentative. The compounds 6222 and
5421 could not be indexed as tetragonal, hexagonal or rhombohedral, which is
unfortunate in view of the interesting characteristics of the isomers in question (see
below).
The room temperature densities are collected in Table 2, as well as in Fig. 6(a) where
they are plotted against melting points. The plot and its relation to Fig. 6(b) will be
discussed later. Table 4 shows the approximate volume changes which accompany major
phase transitions in several compounds. Note the negligible volume changes on melting
for the low-density cubic structures (7221, 6321) and the considerable volume increase
upon formation of plastic phases from lower temperature ordered phases (4422, 5322).
Liquid densities for 6222, 6321, 7221 and 5511 at 125° are listed in Table 4 and also
included in Fig. 6(a). The high density of 6222 is discussed below.
18
Fig. 6 Densities at room temperature of C12H28N+Br- isomers displayed: (a) against their melting points,
with densities of some liquids at 125°C displayed for comparison, (b) against the sum of the entropies of
phase transitions observed between room temperature and the liquid state. The points m1-m3 represent
binary mixtures (last 3 items in Table 2). For ∑∆S of 9111, which decomposes on melting, ∆Str(90°) was
added to ∆Sm of 8211, which is probably close to the unavailable ∆Sm of 9111. The plot suggests that
compounds with low melting points but high densities at room temperature have undergone ordering
transitions before room temperature is reached, while the remainder have not.
DISCUSSION
When this work was started only three compounds of the 15-member family were known:
(i) the symmetric and high-melting (295°C(27b) with decomposition) isomer 3333 which
crystallizes in a ZnS (sphalerite) structure(28), (ii) the 9111 compound which melts with
19
decomposition at 230°(29) after a side-chain melting transition at 90°C, and (iii) a much
lower melting (108°C)(20) isomer 6222. With the extension of the series to lowersymmetry cations three related trends were expected:
1.
Isomers with less symmetric cations would experience greater difficulty finding
satisfactory ordered packing schemes, hence would have lower densities.(30)
2.
Consequent on the lower densities, the lattice energies of the low-symmetry
cation crystals would be lower, hence as demonstrated in refs 1 and 2, their
melting points would be lower, possibly reaching ambient temperature.
3.
The liquid states would all be of similar viscosity at equal temperatures, hence the
isomers containing low-symmetry cations would be more viscous at the expected
lower melting points, hence would be more sluggish to crystallize on cooling, and
therefore would pass more easily into the glassy state.
As is seen immediately from Table 1 these expectations are not well borne out. While
there is indeed a wide range of melting points, the relatively symmetrical 6222 compound
has almost the lowest among them despite its relatively high density. Furthermore,
despite its position as the isomer with the third lowest melting point, it cannot be vitrified
by the fastest cooling applied in our study, whereas five of the other low melting isomers
can be. Finally the lowest melting of all the isomers, 5511 (Tm=100°C), is one of the
more symmetrical. As usual, the failure of expectations leads to new understanding.
The discrepancies are at least partly to be understood in terms of the alternatives to
closest packing which are available in the crystalline state, i.e. the postponement of
melting by intercession of high entropy crystalline phases. For instance, the isomer 5421
would melt far below the observed Tm of 114°C if it were not for the intervention during
heating of the solid state transition at 41°C which introduces an entropy increase
amounting to 43% of the accumulated entropy at fusion. The same could be said for the
higher melting 5322 and 4431. The way in which the intervention of such transitions can
raise the melting point is discussed in the next section. The low melting point of the
20
otherwise anomalous 6222 isomer would, on the other hand, not be much altered if the
corresponding solid state phase-transition at 59°C were suppressed, since the latter
transition only introduces 14% of the accumulated entropy at fusion.
The intercession of these higher entropy crystalline phases, however, makes possible the
observation of a wealth of alternative glass transition phenomena, such as glass
transitions within orientationally disordered phases, and within molten side-chain
crystalline phases, as well as interesting and imperfectly understood McCullough type-H
phase transitions within orientationally disordered phases, and within molten side-chain
crystalline phases, as well as interesting and imperfectly understood McCullough type-H
phase transitions. An in-depth study of such a family of compounds could do much to
enhance our understanding of the relation between the various ergodic and non-ergodic
phase transitions observable in condensed matter. In the following sections we enter into
detail on the various types of transitions observed and their relationship to certain other
measurable properties, as well their relation to the primary objectives of this study.
(1) Melting Points, Thermodynamic Relations, and Glassforming Properties
It is useful to develop an argument for melting point lowering in terms of easily measured
thermodynamic quantities in order to see why, in the terms of the same quantities, the
expectations outlined above were only partly borne out.
Suppose that symmetry factors affect packing of molecular ions to an important extent
only in the crystalline state, and that the randomness of the liquid makes it possible for all
isomers to achieve comparable densities (as seen in Table 4 and Fig. 6). Then it would
be correct to expect smaller changes of volume on fusion for the less symmetrical
isomers (however, see ref. 30), hence smaller changes of enthalpy(31). So long as the
entropy of melting consists only of the entropy of disordering of centers of mass and of
that associated with freeing group rotation modes for a similar number of carbon atoms
(the ones not attached to N+, eight in our case), a relatively constant value of ∆Sm would
apply and the melting point Tm = ∆Hm/∆Sm would be lower for the less symmetrical
21
compounds. Indeed, the tendency of lower symmetry compounds to melt at lower
temperatures than their higher symmetry "relatives" has been noted before for tetra-alkyl
ammonium salts(32), as well as for disubstituted benzenes.(1,2) In particular, the work of
Gordon and SubbaRao(33) on straight-chain isomers of tetrapentylammonium salts seems
to be consistent with this expectation. A kinetic argument, based on the need for a
specific orientation of asymmetric molecules or molecular ions as they attempt to join the
protonucleus near critical nucleation size on undercooling, would also lead to the
expectation of slower nucleation kinetics, hence increased probability of glass formation
on cooling even when compared to compounds with similar Tm but higher symmetry.
Examination of the density data in Table 2 shows that the densities of most of the new
compounds are indeed lower than the previous low of 1.158 g/cm3 (for 6222). However,
as seen in Fig. 6(a), the corollary of lower melting points does not actually follow. Only
two isomers have lower melting points than that of 6222 and in neither case is the
decrease large.
The weak points of both the thermodynamic and the kinetcic arguments are revealed
when one considers the thermochemical data in Table 2, especially the entropies of
transition and melting. It can be seen that the lower density compounds also tend to have
much lower entropies of melting and lower overall entropies of transition (including
melting) above 25° (∑∆Str), evidently due to a high configurational disorder in the solid
state. Thus, with ∆Sm and ∆Hm both getting smaller, there is no simple reason for Tm to
exhibit a clear trend. Furthermore, configurational constraints should have only a minor
effect on the nucleation rate of highly disordered solids; therefore, it is not surprising that
-- as data in Table 3 show -- there is no correlation between cation symmetry and the
stability of glasses of compounds with similar melting points (5421, 6411, 6321, 7311).
The fact that three isomers, of two different cation symmetries (6321 vs. 6411/7311),
have identical crystal structure and cell parameter, is compelling evidence for the
dominance of solid state disorder over symmetry considerations, at least for the longerchain isomers.
22
As Fig. 6(b) makes clear, there is in fact a fairly good correlation between density at 25°C
and ∑∆Str as defined above. In other words, the free volume created because of poor
packing makes possible the activation of various disordering modes involving parts of the
cation itself (side-chain modes) or possibly reorientation of the cation as a whole. As a
result, the entropy of the solid approaches that of the liquid. Intuitively it may seem
obvious that the lower-density isomers should have higher room temperature solid-state
entropy, as found. However, it is not necessarily so: Bridgman found amongst inorganic
compounds, e.g. KI, that the lower density phase is quite often also the lower entropy
one.(34) The fact that the intuitive rule works quite well in our series may be largely due
to the catenated, low rigidity nature of the organic ions; this makes small increments of
free volume available for creating small scale, local disorder and for exploring a variety
of energetically close but structurally distinct states. In any case, Fig. 7 illustrates the
way in which a transition to a more disordered solid phase with a higher entropy, hence
large dG/dT, can push the final melting points to higher values. The molecules in the
higher entropy phase may be configurationally disordered (between several energetically
similar configurations), and may also experience greatly increased mobility, either
rotational (as in plastic crystals) or combined translational and rotational (as in liquid
crystals). We consider the properties of the plastic crystal phases in a separate section, 3,
below.
Mixtures
An attempt to produce more easily glassforming systems retaining the same C12H28N+Brcomposition by use of the common thermodynamic device of melting-point lowering by
mixing, fails in the present case. We consider the three mixtures with 5511, summarized
in Table II (bottom). Interestingly enough, ~1:1 mixtures show positive deviation from
additivity of both room-temperature densities and melting points, so are not ideal solid
solutions of either the I phases (plastic crystals) or the II phases, see Table 2 (bottom).
The temperature domain of the plastic crystal state, which is very narrow in pure 5511, is
broadened, and the supercooled plastic crystal, I', is greatly stabilized kinetically in its
mixtures with other isomers, presumably because the transition temperature lowering
23
principle, which failed to materialize for the melting transition because of solid solubility,
works very well for the ordered crystal phases/plastic crystal transitions. This
ovservation is being exploited in separate studies of the solid solution physical chemistry.
2.
Glassy Phases
Considering the glassforming isomers which can be vitrified, we recall firstly (Table 1)
that the five isomers which could be vitrified without difficulty viz. 5421, 5511, 6321,
6411, and 7311, all have glass transition temperatures Tg within 4°C of one another.
Compared with the spread of values found for the freezing of orientational order in the
plastic crystals phase (see next section), this is remarkable, and supports the initial
supposition that in the liquid state, the differences in cation shape are of minor
importance. One case which may be exceptional is that of 6222 which exhibited neither
vitrification nor glassy plastic crystal behavior. Liquid 6222 is also significantly denser
than other low-melting isomers (see Table 4). This is interesting and is to be correlated
with the behavior of the structurally equivalent pure C13 hydrocarbon (3,3-diethylnonane)
which is the densest of the C13 family R4C with ∑C(R) = 12(35) The 6222 isomer is, also,
somewhat unexpectedly, the best liquid state electrical conductor among our lowestmelting isomers,(22) presumably due to a more compact cation structure leading to a
smaller degree of ion pairing (highest Walden product). There is some suggestion, from
conductivity studies and observations on a C16-compound of similar shape, that the glassy
state of 6222, if formed by sufficiently rapid quenching, could have a higher Tg, but this
matter will be discussed in a subsequent paper.
While the glass transiton temperatures are similar, the stability of the glasses and
supercooled liquids against crystallization varies significantly, as can be seen from note
(d) to Table 3. Moreover, it is apparent that the Tg/Tm parameter(26) (column 6 in Table 3)
is not a good predictor of the stability of the glasses formed by these. Thought the range
of values is small (0.575-0.637), the most stable glass and supercooled melt are formed
by 6411, the least likely candidate (the one with the lowest Tg/Tm). It is noteworthy that
6411 also has the lowest experimental crystal density in the family (1.070 g/cm3),
24
Table 3
† Teq is the temperature of the equilibrium state transition which is suppressed in the quenching.
* apparently works only on impure material (premelted), quenched from above 100°. For a similar case see
Ref. 51
(a) no underlying ordered phase could be identified
(b) metastable phase quenched, no known Ttr.
(c) freezing or tranition point when cooling at 10°/min.
(d) the stability against crystallization of the cooled liquids on cooling correlated well with the stability of
the glasses on heating: Tf is the crystallization temperature on cooling; Tc is the devitrification
temperature on heating.
significantly lower than its x-ray density (1.088). Thus crystalline 6411 must have a high
concentration of defects (e.g. of the Schottky type), which may have a destabilizing effect
on crystallization protonuclei; the same is not true of denser isomorphic 6321 and 7311.
25
In the absence of more extensive data, this explanation is tentative, but the 6411 case
serves to indicate the potential relevance of crystal structure subtleties to glass stability.
Detailed treatment of the physical properties of the liquid state (viscosity, conductivity,
glass transition dynamics, and kinetics) is reserved for a following paper, but we report
here the outstanding phase-transition related results, viz. The change in heat capacity as
the liquid passes into the glassy state. The results are most unusual and need discussion
in the context of plastic crystal behavior.
In the first place the ∆Cp values (see Table 2) are much smaller than expected from
previous studies of non-network ionic liquids. The values, which average ~58 J/K·mol,
may be compared to those of other liquids by converting to J/K·(mole of beads) where
"beads"(36) are the reorientable/rearrangeable units of the molecular ionic system, e.g. 2
for NH4Br, 4 for CN-CH2-CH2-CN, and either 13 or 14 for C12H28NBr depending on
whether the central N is considered an independent site (which is probably not
appropriate in our case though perhaps is for (CH3)4NBr). Using the notation "mb" for
Table 4 (a) results are probably accurate to + 0.5% unless stated otherwise.
(b) the 6222 compound is also the densest of the 15 quarternary C13 hydrocarbons (which had a variation
of only 0.03 b/cc(35)).
(c) by extrapolation from 116°C to 125°C to compare with others.
(d) by analogy with other n111 compounds with n = 14, 1(52) and, less directly, with n = 10, 12, 18, 22(45).
(e) this low value probably reflects the melting of a plastic phase formed a few deg below Tm on slow
heating
26
"mole of beads", we obtain ∆Cp = ~4 J/K·mb which is to be compared with the value of
11.2 J/K·mb given by Wunderlich(36) for the general case of glassforming liquids, 15.1
J/K·mb given by Alba and Angell(37) for simple molecular (fragile) liquids, and 16 J/K·gatom found by Bruce and Moynihan(38) and Torell et al.(39) for ionic fluoride and chloride
glasses respectively. The explanation probably lies in the presence of a large (and
therefore interesting) residual configurational heat capacity in the glassy state since we
find that the measured specific heat of the glass, in the one case we have studied
quantitatively, 5511, is unusually high for an organic compound. We deduce this as
follows.
Whereas inorganic compounds of simple ions usually(40) reach the classical Dulong-Petit
heat capacity, 25 J/K·g-atom, just below Tg, organic compounds typically have exhibited
only 60-80% of the Dulon-Petit value, 15-20 J/K·mb when the latter is considered on a
"per-mole-of-beads" basis (e.g. 2-methylpentane, 6 beads, 14 J/K·mb at Tg = 80K;
glycerol, 6 beads, 15, J/K·mb at Tg = 184K; and sorbitol, 12 beads, 20 J/K·mb even if we
adopt the maximum 14 beds per mole. The implication is than an excess configurational
heat capacity associated with local "looseness" or "rearrangeability" in the glass remains
to be lost between Tg and absolute zero. Although no secondary relaxations with large
∆Cp were observed in this study, they would not have been evident unless specifically
sought. This is because we did not quantitatively study the sub-Tg behavior, and because
the secondary relaxation would probably be smeared out over a wide range of
temperature (as in the case of the 6222 metastable plastic crystal discussed below) and
therefore not obvious to the qualitative study. That these conjectures are basically correct
is demonstrated in a separate quantitative heat capacity study of two of the isomers, in
which the behavior of these moderately complex systems is related to that of the more
complex protein system.(23)
If the glass-like Cp is, on the above basis, revised downward to e.g. 24-8 = 16 J/K·mb, a
more normal value, and one consistent with the less-than-"fragile"(13)
viscosity/temperature relation for these compounds (to be discussed in a separate
27
paper(22)). These conjectures will be substantiated in a separate detailed study to be
published elsewhere. It is sufficient for our present purposes to recognize that all
vitrifications observed in this study are very similar in character. Taken in conjunction
with the equally similar viscosity behavior to be reported elsewhere(22), we can affirm
here the essential commonality of the liquid behavior, hence of the liquid free energy
surface for the C12H28NBr family as assumed at the beginning of the discussion in section
(1) above.
3.
Orientationally Disordered (Plastic) Crystals
Most materials in the study, while possessing different patterns of phase transitions, show
characteristics of plastic crystals in their I phases (the ones stable immediately below the
melting point). With the exception of 6222, all compounds with reliably measured ∆Sm
(Tm < 200°C) either comply with Timmerman's criterion for plastic crystals (∆Sm < 2.5 R,
4 cases) or deviate from it by at most 20% (2.5R < ∆Sm < 3R, 6 cases), see Table 2.
Seven of the compounds can be quenched from their solid I phases to a glassy crystal
state(41) since, when reheated, they undergo a heat capacity increase that is clearly a glass
transition of a plastic (orientationally disordered(42)) crystal. In at least one case (7221),
this I phase has a cubic structure, which is typical of plastic crystals.(5)
Unlike the liquid-derived glasses described in the previous section, we find that the
plastic crystals show a range of glass transition temperatures, supercooling tendencies
(through the III transitions), and stabilities against phase transformation above the
glass transition. In one extreme case (4422), quenching in liquid N2 from >52°C is
needed to obtain the glass [Tg(I') = -74°], which on heating converts immediately into an
ordered solid (Tc = -61°). At the other extreme, notwithstanding its similarity in cation
structure, is the compound 4332 (Tg = -51°). In spite of prolonged annealing at 25°, 5°
and -15°, 4332 could never be obtained in anything but the plastic phase. The same
seems true of 6411 and 7311 which remain plastic crystals after 7 years annealing at
ambient.(23) Such a variety of behavior is to be expected if the disordering process at the
glass transition involves only parts of the ion, e.g. restricted rotation processes as opposed
28
to free isotropic rotation of the whole cation. Also, one would expect the structural
differences between the cations of the different compounds to express themselves by
different degrees of mutual interference, leading to different kinetics into, and out of, the
plastic phase.
The plastic crystal glass transition is exhibited by most of the higher melting compounds,
and its form usually is similar to that of the glass-to-liquid transition, as illustrated by the
heating traces in Fig. 3 for 5322 after slow (0.3°/min) cooling and after quenching
(320°/min). The I phases of the lower melting compounds (6411, 6321 and 7311) gave
ambiguous glassy crystal states in Perkin-Elmer DSC scans despite the evidence from Xray data that three at least are high symmetry rotator phases. These have now been wellcharacterized using the more stable Setaram DSC III instrument and are reported on
elsewhere.(23) In the 6222 and 6321 cases, fast quenching of the I" phase and I phase,
respectively, produced phases with less definite (more smeared-out) versions of the glass
transition (see Fig. 4), and these could be enhanced by suitable annealing (6321, not
shown). It is possible that even broader transitions exist in other cases, which would also
be revealed by comparative studies using DSCs with more stable baselines.
An interesting and unexpected feature of the glassy crystal glass transitions is the
magnitude of the ∆Cp relative to those observed for the glass-to-liquid transition.
Normally the latter would be expected to be the larger,(43,44) but here we observe the
reverse. Table 2 shows that, within the rather large uncertainty of the TADS-calculated
∆Cp, the plastic crystal phenomenon is at least twice as large as for the liquid. This is
presumably to be correlated with the unusually large heat capacities of the liquid-derived
glassy phases, which we described above and which we held responsible for the
unexpectedly small values of the glass-to-liquid ∆Cp. No quantitative study of the glassy
crystal state heat capacity was undertaken in this study, but a subsequent study(23) using a
more precise calorimeter has confirmed the expectation that, below the plastic crystal
glass transition, a normal glassy state heat capacity is to be found. The total heat capacity
change found by combining glass"plastic glass" with "plastic glass"supercooled
liquid components, then assumes normal values for a glass-to-liquid transition.(23) the
29
interpretation of the relative ∆Cp values for the two glass states would then attribute the
larger value for glassy crystalplastic crystal transition to the absence of residual
configurational heat capacity in the glassy crystal.
4.
Other Transitions
The glass transition seen in 9111 (I' phase) after a liquid nitrogen quench from above the
high-∆S transition at 90°C, can probably ve ascribed to a glass transition Tg(I) within the
long hydrocarbon chains. Following Iwamoto et al.(45) (into whose sequential study on
long-side-chain alkyltrimethyl ammonium bromides our 9111 results fit neatly), the 90°C
transition can be ascribed to a side-chain melting phenomenon rather than to
transformation to a rotator phase. It is this phenomenon which is held responsible for the
liquid-like appearance of the high temperature phase of long chain tetraalkylammonium
salts and which leads to their description as analogues of smectic "mesophases"(45,46) (the
melting point being analogous to the "clear point" i.e. the smectic-isotropic phase
transition). If this is a correct description then it would appear that we have prepared
what might be called a "side-chain glass". This glass (GI), in our case, is very unstable
and crystallizes so close to Tg that no assessment of its ∆Cp could be made for inclusion
in Table 2. The stability problem could presumably be solved by branching of the C9
chain, and the study of such a compound would make an interesting sequel to this work.
McCollough Type-H Transitions
Another transition, which is of interest because of its apparent lack of hysteresis
character, can be seen in 9111 by study of crystallization products of the side-chain glass
(GI just described), i.e. in the II" or II"' phase produced from GI, see Figs 1 and 7. On
rescanning this sample from -120°, a small transition is found, centered around -14°C, to
a phase whose designation is not clear in our scheme (since the transition occurs above
the temperature of original crystallization). Unlike most of the other transitions we have
30
Fig. 7 Free energy vs. temperature relations for liquids, high entropy (rotator phase) crystals, and lower
entropy phases, showing (in part (b)) how the presence of rotator phases of high entropy (i.e. liquid like
slopes of the G curves) and moderate lattice energy EL (EL = G at 0K) can cause postponement of melting
(see phase 1 in Fig. 7). Rotator phases of low lattice energy can only be observed by first supercooling the
liquid (see LI" in part (a)). Note, from part (b), that there is a possibility of mistakenly identifying low
temperature stable phases like II as a new metastable phase I" if it forms from the supercooled liquid. The
"real" I" can only be formed at greater supercoolings.
observed, this one is exactly reversed on cooling, see Fig. 5. The small displacement in
temperature is believed due to instrument lag and a consequent uncertainty in temperature
calibration for cooling runs. The enthalpy change observed in this transition is ~2.0
kJ/mole, and apparently it is somewhat dependent on sample history.
A very similar transition is seen in the simpler case of 5421. In this case the symmetrical
transition, centered around 24°C, emerges every time the as-crystallized sample is heated
through the III transition 41°C (Table 2) and cooled down again below 30°. The
enthalpy change in this case can be reliably determined and proves to be 3.5 kJ/mole,
31
much larger than for phase transitions in liquid crystal mesophases in which a
comparable reversibility is seen.
Phase transitions with this character have been described, and designated type-H
transitions, by McCullough(25). Their origin and physics is obscure. Since they are quite
energetic but also reversible they presumably either are displacive in origin, requiring no
nucleation d growth process, or are cooperative type higher-order transitions. A
theoretical model which gives transitions of this form in compounds containing alkyl
chains has been described by Baur,(47) according to calculations reported by Wunderlich
et al.(8) The model is based on a cooperative chain excitation scheme which can be
treated in the Bragg-Williams approximation and which yields transitions like those in
Fig. 5 near the high cooperation limit, just before collapse to a first-order transition.
The 5421 transition occurs in a convenient temperature range for further study of this
interesting phenomenon, which may be rather common. Additional examples we have
found,(48) in apparently stable phases, are the tetrafluoroborates
CH3(CH2)3N+(CH3)2C2H5BF4- (-68°, 0.7 kJ/mole) and CH3O(CH3)3BF4-·LiBF4 (-110°, 0.7
kJ/mole).
CONCLUDING REMARKS
While the present study has revealed a rich variety of phenomena within a relatively
simple system of constant composition, many aspects of high interest content remain to
be fully explored. The unusually large residual configurational heat capacity in the
glassy phases formed from the liquid is a new finding which has been followed up
elsewhere.(23) The extreme case of a separate quasi-liquid-to-glass transition in the sidechain component of the 9111 high temperature phase (I) suggests the possibility of
successive glass transitions in the same amorphous phase, now verified(23) and raises the
interesting question of what characteristics the second glass transition could have to
distinguish it from the usual β relaxation. This in turn raises questions about possible
32
modifications or enhancement of the "two-level systems" which now appear to be the tail
end of the usual β relaxations.(49-50)
The already observed uncrystallizable nature of the plastic crystal state of e.g. 4332 may
be amenable to enhancement by further stabilizing the plastic state through mixing. This
probably implies the existence of non-ergodic states which are the ground state of the
molecular ionic system; if true, this presents a challenge to theory. These and other
questions will be taken up in future studies of these and related systems, with the overall
aim of establishing some hierarchical scheme for ergodic and non-ergodic cooperative
phase transitions in condensed phases.
ACKNOWLEDGMENTS
This work has been supported by the NSF-DMR under Solid State Chemistry Grant No.
DMR9108028-002.
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34
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Of course very high density packing of some low symmetry objects is possible.
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objects; it also implicitily attests to their rarity.
31.
A major component of ∆Hm should be expansion work done against electrostatic
and van der Walls attractive forces.
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35
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36