1

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

liquid��glass transitions and plastic crystal��glass 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" side-

chains.

∗ 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

2

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 straight-

chain 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 center-

of-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 ergodicity-

breaking 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.

3

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-

4

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 liquid��glass 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 liquid��glass 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.

5

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

6

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 ergodic�nonergodic 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.

7

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 liquid�glass 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. 112-

114°) -- 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

8

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.

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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.

10

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

11

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 2-

6.

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)

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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 liquid��glass transitions. 6411 evidently devitrifies to the stable I phase, which

is uncommon. Temperatures marked on graphs include corrections from calibration runs where

needed.

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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 glass�liquid 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 non-

plastic 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.

14

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 II�I 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 TII�I (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

∆HII�I' 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 high-

density 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

15

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 I�II (90°) transition. On reheating, II"�I also occurs at

90° but with only 87% of ∆HII�I'·II" also does not exhibit the 1st order II�III 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).

16

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 I�II -- exhibits a weak transition of

this type, II"��III"', which replaces the II��III (-58°) transition (II" returns to I on

heating, with a smaller ∆Str than II�I). These transitions show nearly symmetrical cusp-

shaped 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 100-

130° 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%.

17

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 within3°(T) and 5% (∆H, ∆S). Larger or more unusual effects are noted.

18

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.

19

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

20

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 lower-

symmetry 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

21

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

22

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 longer-

chain isomers.

23

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+Br-

composition 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

24

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 lowest-

melting 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),

25

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.

26

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

27

"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·g-

atom 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

28

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 I�II 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

29

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 X-

ray data that three at least are high symmetry rotator phases. These have now been well-

characterized 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

30

interpretation of the relative ∆Cp values for the two glass states would then attribute the

larger value for glassy crystal�plastic 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

31

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 L�I" 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 II�I 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,

32

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 side-

chain 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

33

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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Physique, 1985, 82, 773.

14. Williams, G. Private communication.

15. Fuchs, A. H., Virlet, J., Andre, D., and Szwarc, H., J. Chim. Phys., 1985, 82, 293.

16. Andre, D.; Dworkin, A.; Figuiere, P.; Fuchs, A. H.; Szwarc, H. J. Phys. Chem.

Solids, 1985, 46, 505.

17. Ickle, R. N.; Wisegarver, B. B., Organic Syntheses, Coll Vol. III, Wiley, New

York, (1955) p. 723.

18. Marchini, P.; Liso, G.; Reho, A. J. Org. Chem., 1975, 40, 3453.

19. Smith, P. A.; Frank, S. J. Am. Chem. Soc., 1952, 74, 509.

20. Ford, W. T.; Hauri, R. J.; Hart, D. J. J. Org. Chem., 1973, 38, 3916, report the

highest m.p. on record (108°).

21. MacGillavry, C. H.; Henry, N. F. M., in International Tables for X-ray

Crystallography, The Kynoch Press, Birmingham, 1962, III, 18.

35

22. Cooper, E. I.: Angell, C. A. (to be published).

23. Fan, J., Cooper, E. I., and Angell, C. A., J. Phys. Chem., 1994, 98, 9345.

24. Gordon, J. E. J. Org. Chem., 1965, 30, 2760.

25. McCullough, J. P. Pure Appl. Chem. 1961, 2, 221.

26. Sakka, S.; Mackenzie, J. D., J. Non-Cryst. Sol., 1971, 6, 145.

27. (a) Cooper, E. I.; Angell, C. A. J. Non-Cryst. Sol., 1983, 56, 75.

(b) Nakayama, H., Bull. Chem. Soc. Jpn., 1981, 54, 3717.

28. Zalkin, A. Acta Crystallogr., 1957, 10, 557.

29. Kellet, J. C. Jr.; Doggett, W. C. J. Pharm. Sci., 1966, 55, 414.

30. Of course very high density packing of some low symmetry objects is possible.

"The Graphic Work of M. C. Escher," (Ballantine Books, New York, 1960, pp. 6-

10) supplies convincing two-dimensional evidence for the existence of such

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.

32. Gordon, J. E., in "Techniques and Methods of Organic and Organometallic

Chemistry", D. B. Denney, Ed., Marcel Dekker, New York, NY, 1969, Chapter 3.

33. Gordon, J. E.; SubbaRao, G. N. J. Am. Chem. Soc., 1978, 100, 7445.

34. Bridgman, P. W. Proc. Am. Acad. Arts Sci., 1937, 72, 42, quoted in D. M. Newns

& L. A. K. Staveley, Chem. Rev., 1966, 66, 267. "…it is worth noting that the

data for KI show that the denser phase need not necessarily have the smaller

entropy. Bridgman (11) found that in fact this was the case in no less than 43% of

all the transitions he studied." (emphasis added).

35. Mann, G.; Muhlstadt, M.; Braband, J.; Doring, E. Tetrahedron, 1967, 23, 3393.

36. Wunderlich, B. J. Phys. Chem., 1960, 64, 1052.

37. (a) Alba, C.; Busse, L. E.; Angell, C. A.

(b) Alba, C.; Fan, J.; Angell, C. A. (to be published).

38. Gavin, D. L.; Chung, K. H.; Bruce, A. J.; Moynihan, C. T.; Drexhage, M. G.; El

Bay-oumi, O. H. J. Am. Ceram. Soc., 1982, 65, C182.

39. Torell, L. M.; Ziegler, D. C.; Angell, C. A.; J. Chem. Phys., 1984, 81, 5053.

36

40. (a) Hagerty, J. S.; Cooper, A. R.; Heasley, J. H. Phys. Chem. Glasses, 1968, 9(2),

47; 1968, 9(4), 132.

(b) Angell, C. A. J. Am. Ceram. Soc., 1968, 51, 117.

41. Adachi, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Japan, 1968, 41, 1073.

42. Smith, G. W. Comments on Solid State Phys., 1978, 9(1), 21-35.

43. Haida, O.; Suga, H.; Seki, S. J. Chem. Thermod., 1977, 9, 1133.

44. Adachi, K.; Suga, H.; Seki, S. Bull. Chem. Soc. Japan, 1971, 44, 78.

45. Iwamoto, K.; Ohnuki, Y.; Sawada, K.; Seno, M. Mol. Cryst. Liq. Cryst., 1981, 73,

95.

46. Margomenou-Leonidopoulou, G.; Malliaris, A.; Paleos, C. M. Thermochimica

Acta, 1985, 85, 147.

47. Baur, H. Colloid and Polymer Sci., 1974, 252, 641.

48. Cooper, E. I.; Angell, C. A. (unpublished work). See also, Cooper, E. I., and

Angell, C. A., Solid State Ionics, 1986, 18 & 19, 570.

49. Johari, G. S. Lectures Notes in Physics, 1987, 277, 89.

50. Setthna, J. Ann. Y. Acad. Sci., 1986, 484, 130.

51. Fung, B. M.; Gangoda, M. J. Am. Chem. Soc., 1985, 107, 3995.

52. Norbert, A.; Brun, B.; Chan-Dara; I. Bull. Soc. Fr. Mineral. Cristalogr., 1975, 98,

111.