Phase transition has long been a central issue in the science of matter [1
]. This statement also applies to the case of the science of crystals, i.e., crystallography, because the symmetry plays an essential role in discussing phase transitions [3
]. Molecular crystals have offered essential examples where molecular dynamics bring about intrinsic phase transitions from nominally perfect crystals into partially disordered states such as plastic crystals and liquid crystals [4
]. In contrast to the understanding of phase transitions as the way of acquiring disorder (entropy) in the previous sentence, there exists a counter view, the emergence of order. In the latter context, the concept of “spontaneous symmetry-breaking” was one of the essentials reached in the past [5
]. The situation is expressed in microscopic terms as follows: In a high symmetry phase (usually at high temperature), some disorder contributes to establishing the higher symmetry, and the ordering contradicts some part of the symmetries, resulting in the formation of the low symmetry phase (at lower temperatures). An example of the high symmetry state is the paramagnetic state with random orientations of Ising spins, which are allowed only two (up and down) states. The equivalence of two states brings a macroscopic symmetry (between the upper and lower sides) of the ensemble. Upon cooling, the ensemble undergoes the so-called order-disorder transition into an ordered phase, in which the number of one orientation, say “up”, is larger than that of the other. The symmetry is lower than the high temperature phase due to the loss of the macroscopic up/down symmetry. If the equivalence of two orientations of each spin is violated (even at high temperatures), the random orientations are impossible, and the macroscopic symmetry does not exist. Indeed, ferromagnets do not undergo phase transitions under a field [6
]. This example leads us to a naive recognition of the relevance of two equivalent states, over which the disorder occurs. The question treated in this paper is: Is a transition of the order-disorder type when the disorder is over non-equivalent configurations?
The compound we chose in this study is sorbose, the molecular structure of which is shown for the d
-form in Figure 1
. Sorbose is the hexose that was identified in the l
-form for the first time in nature. The existing report of heat capacity on crystalline l
] indicates the presence of a phase transition around 200 K. The structural studies at room temperature reported for l
-sorbose crystals [8
] suggested possible involvement of the structural disorder in the transition mechanism. However, the reported disorder is over non-equivalent configurations if we consider only a single molecule. The perfect order to the major configuration (with not O1B, but O1A in this case) does not contradict the symmetry (space group) of the room temperature phase. The relationship between the structural disorder and the nature of the phase transition remains unclear, accordingly.
The present study of our project was to establish the thermodynamic properties of sugars in an extended temperature range. The project started while considering the situation that a reliable heat capacity at room temperature has been reported for only four hexoses [7
]. Partial results of the project were already published [11
]. Since complete coverage over monosaccharides necessitates the inclusion of the so-called rare sugars, we dared to use the rare counterpart (d
-sorbose) of the naturally abundant l
-form in the present study. Excellent coincidence with the existing data on the l
] strengthens the common belief that ensembles of two enantiomers are equivalent in the isolated state.
This paper is organized as follows. After the description of the experiments (Section 2
), we describe the experimental results of the calorimetry (Section 3.1
and Section 3.2
) and crystallographic experiments of the high (Section 3.3
) and low temperature (Section 3.4
) phases in this order. The description of the calorimetry includes not only those related to phase transitions and standard thermodynamic functions (Section 3.1
), but also the newly found glass transition (Section 3.2
). Section 3.5
discusses the main subject, which is represented in the title and summarized in the last sentence of the first paragraph. Section 4
concludes the paper by summarizing findings with a comment about the meaning of this paper from a broader perspective.
Triggered by the fact that the structural disorder, previously reported for crystalline l
], did not seem to contribute to establishing any symmetry, we started the present study.
The precise heat capacity calorimetry established thermodynamic information for a wide temperature range and the occurrence of two additional phase transitions above and a glass transition below the main transition, which was known. Since thermal anomalies associated with newly found transitions are tiny, the main transition at 199.5 K was responsible for the significant parts of excess thermodynamic quantities (enthalpy and entropy). The combined magnitude of excess entropy for three successive phase transitions was 5.23 J K mol, which was close to, but smaller than the expected entropy () for an idealized order-disorder transition having two states (Ising model). Freezing of the residual disorder occurred with the glass transition around 120 K. The crystallographic experiments at several temperatures failed to detect the symptoms of the newly found transitions, but gave the structural change at the main transition. The structure of the low temperature phase was a regular spatial arrangement of two conformers, over which the disorder happened in the high temperature phase. This finding indicated that the symmetry broken in the successive transitions was not the symmetry on a single site, but the symmetry involving a translation. The structural disorder was involved in the latter, as in the antiferromagnetic Ising model under the field.
The authors demonstrated that molecular systems are a sound stage, even if not the best, for studies of structural phase transitions. The previous examples included testing a unified model for displacive and order-disorder transitions [27
] in a clean (neat) system [28
], systematic studies of the effects of well-defined impurities on such well-characterized systems [30
], and the identification of a dipolar Ising system with an easily accessible transition temperature [32
]. A new subject of the phase transition to exotic superstructures was also presented recently [33
]. The present study is another example in the same spirit: molecular crystals offer typical systems for condensed matter physics because of the richness of their variety.