Classification and Definition of “Soft Crystals”

Abstract

“Soft crystals” typically undergo structural transformations in response to weak stimuli while maintaining the crystalline structural order. These transformations are often manifested as visible phenomena, such as changes in optical properties (color and/or luminescence color). In this chapter, the structural order, activation energy, and softness of “soft crystals” are compared with those of conventional hard crystals and soft materials, including liquid crystals and gels. Based on the results of this comparison, “soft crystals” are defined more precisely.

1 What Are “Soft Crystals”?

How are “soft crystals” characterized and defined? When the main features of “soft crystals”, such as vapochromism, mechanochromism, and superelasticity/ferroelasticity, were discussed, their key characteristics were typically extracted as follows: “many crystal polymorphs can be formed”; “phase transition and/or structural transformation can occur even under gentle stimuli at room temperature”; “because of the various intermolecular electronic interactions, such as d–π, d–d, or π–π ones, intermolecular rearrangements are accompanied by color and/or luminescence color changes”; “there are large voids in crystals”; “crystals with flexible molecular structures and substituents tend to exhibit mechanochromism”; and “energy changes during phase transitions and/or structural transformations should be gradual”. Furthermore, “adsorption/desorption of large molecules”, “chemical conversion”, and “chemical reaction-based chemiluminescence” can be also observed for such crystals.

Considering these key characteristics from various points of view, we will attempt to define “soft crystals” in this chapter.

2 Crystal Polymorphisms

In crystals of molecules composed of various atoms, many kinds of intermolecular interactions can lead to the formation of several crystal structures with different molecular arrangements. This phenomenon is called crystal polymorphisms. “Soft crystals” mainly consisting of organic molecules and metal complexes are characterized by the (1) existence of various crystal polymorphs and (2) occurrence of phase transitions between these polymorphs under gentle stimuli. In this section, a historical background of polymorphism in molecular crystals is briefly described.

Controlling crystal polymorphism is an important task, especially in the research and development of drugs (Note 1) because their stability, solubility, and dissolution rate depend on the crystalline form, which can strongly influence drug efficacy. The second example is crystal polymorphs of phthalocyanine pigments in relation to photo- and electronic properties. Phthalocyanine crystals are practically used as near-infrared light-active photoconductors in photocopiers and laser beam printers, and their photoconductivity is considerably influenced by the crystal structures (Note 2). In spite of these social demands, the engineering of molecular crystals, which aims to achieve a desired molecular arrangement, has long been dependent on serendipity and screening. In recent decades, international blind tests for predicting molecular crystal structures have been performed, and various prediction methods based on theoretical calculations of crystal structures are rapidly developing [1].

Note 1: Crystal polymorphism is a widely observed phenomenon, which has been investigated by crystal scientists for a long time. In this book, vapochromic molecular crystals are also discussed as important structures, and pseudo-polymorphs, such as solvated crystals and hydrated crystals, are considered crystal polymorphs in a broad sense. First, crystal polymorphism is utilized in the field of pharmaceutical manufacturing. Pharmaceuticals in commercial formulations and/or at the development stage are mainly produced in the crystalline form, and 70–80% of all pharmaceuticals have crystal polymorphs owing to their complex and/or flexible molecular structures. The physicochemical properties of polymorphic pharmaceuticals are dependent on their crystal forms, which affect the pharmacokinetics of solid dosages, such as solubility and biocompatibility. Because of the necessity to control the quality and stability of products at their manufacturing stage, the solubility, dissolution kinetics, and storage stability of various crystal polymorphs are investigated in pharmaceutical industries.

Note 2: Phthalocyanine pigments have been used in GaAsAl laser printers or copiers as near-infrared light-active photoconductors; however, they produced different crystal polymorphs whose photoconductivity strongly depended on the crystal structure. Therefore, it is important to elucidate the relationship between crystal polymorphs and their photoconductivity and control their crystal structures when manufacturing printers and copiers. This aspect is briefly discussed in Chap. 3.

3 Comparison of “Soft Crystals” with Conventional “Hard Crystals” and “Soft Materials”

According to the principles of basic chemistry, the hardness and softness of materials depend on the type of their atomic bonds. In contrast to conventional hard crystals consisting of covalent and/or ionic bonds, the characteristic feature of “soft crystals” is the coexistence of “strong intramolecular atomic bonds” and “weak but non-negligible intermolecular atomic interactions”, which are summarized as follows.

Diamond crystals composed solely of carbon–carbon covalent bonds (357 kJ mol⁻¹) are known as the kings of stable hard crystals. However, diamond is a metastable state at room temperature and atmospheric pressure, and its conversion to graphite is thermodynamically spontaneous (the Gibbs free energy difference between these two states is ΔG° =  − 2.9 kJ mol⁻¹). Fortunately, diamond exhibits its eternal brilliance due to the very large activation Gibbs free energy of ΔG^‡ ~ 1.0 × 10³ kJ mol⁻¹ under ambient pressure. Intermolecular hydrogen bonds (10–20 kJ mol⁻¹) and van der Waals interactions (10–30 kJ mol⁻¹) in molecular crystals are much weaker than the covalent and ionic bonds (e.g., NaCl: 785 kJ mol⁻¹) in hard crystals; therefore, the lattice enthalpies (<100 kJ mol⁻¹) of molecular crystals formed by van der Waals interactions and hydrogen bonds are much smaller than those of typical ionic crystals (≥several 100 kJ mol⁻¹) [2]. Thus, the state of atomic bonding strongly contributes to the enthalpy terms of ΔG^‡ values for solid-state structural transformations, such as phase transitions. Meanwhile, the existence of large voids and/or flexible substituents is also characteristic of “soft crystals”, which facilitates solid-state structural transformations and may decrease their ΔG^‡ values by increasing the entropy terms.

In contrast to soft materials, “soft crystals” produce discrete X-ray diffraction patterns, indicating a long-range structural order. Figure 2.1a displays the relationship between the activation energy of a structural change (ΔG^‡) and the structural order of different forms of condensed matter, such as “Crystals”, “Liquid Crystals”, “Gel”, “Glass”, and “Liquid” [3]. As the degree of structural order increases in the series “Liquid” < “Gel” < “Liquid Crystals” < “Crystals”, the ΔG^‡ value tends to increase, which impedes structural transformations. In this figure, amorphous solid materials, such as “Glass”, are stiff but less ordered; therefore, they should be located in the lower right part of Fig. 2.1a. “Soft crystals”, which contain highly ordered structures but undergo structural transformations at low ΔG^‡ values (Fig. 2.1b), are classified as unexplored and placed in the upper left part (opposite to “Glass”) in Fig. 2.1a.

Fig. 2.1

Schematic drawings showing the a structural order in condensed matter and activation energy of structural transformation (ΔG^‡) and b energetic characteristics of soft crystals and conventional hard crystals. Reprinted with permission from reference [3]

Therefore, “soft crystals” can undergo structural transformations accompanied by changes in electronic properties at room temperature upon gentle stimuli. Thus, they may be potentially used as next-generation materials because their structural transformations cause visible changes in morphology and/or optical properties, such as color and luminescence. Meanwhile, as compared with soft materials or polymers, “soft crystals” exhibit smaller structural fluctuations, and their solid-state structures are ordered in the long range, making them suitable for the transport/delocalization of electrons or excitons.

4 Comparison of “Soft Crystals” with “Liquid Crystals” and “Plastic Crystals”

Molecular crystals generally possess optically anisotropic properties (anisotropic crystals) because of the ordered centers of gravity and orientations of their constituent molecules. When molecular crystals are melted by heating, they become an optically isotropic liquid. However, in the case of pseudo-spherical molecules, a solid-state phase transition occurs before melting owing to the molecular reorientational motion around the molecular centers of gravity. This state is called “isotropic crystals” or “plastic crystals” (Note 3). In the case of rod-like or disk-like molecules, even when the order of the molecular center of gravity is destroyed, the crystals sometimes remain anisotropic because of the partial restriction of the molecular reorientational motion. This state is called “liquid crystals” (Note 4). Figure 2.2 classifies different states of condensed matter, such as “Crystals including soft crystals”, “Amorphous”, “Liquid”, “Liquid crystals”, and “Plastic crystals” in terms of their orientational order and positional order (center of gravity). In Fig. 2.2, the structural order presented in Fig. 2.1 is divided into two parts (the orientational order and positional order), and “soft crystals” are clearly classified into “crystals” with respect to the existing liquid and plastic crystals.

Fig. 2.2

Positional/orientational order-based relationship between the amorphous state, liquid state, liquid crystals, plastic crystals, and crystals including soft crystals

Note 3: Phase transitions due to the restricted rotation or reorientation of molecules in their crystalline states have been known for a long time. Simon and von Simpson discussed their possibility and reported a phase transition caused by the reorientation of tetrahedral NH₄⁺ ions in NH₄Cl crystals (ref. [4]).

Note 4: Because liquid crystals exhibit optically anisotropic properties, such as dielectric constant and refractive index, owing to the difference between their molecular long and short axes, they have been applied in displays with electrically modulated optical characteristics.

5 Mechanical Softness of Molecular Crystals

As mentioned in Chap. 1, molecular crystals sometimes exhibit superelasticity or ferroelasticity. How can the mechanical softness of molecular crystals be characterized? Naumov et al. performed global analyses of the mechanical properties of organic molecular crystals, such as strength and toughness, and compared them with those of various engineering materials, including polymers, ceramics, and metals [5]. In their work, Young's modulus (E), a proportionality constant between strain and stress widely utilized for elastic materials, and hardness (H), served as a measure of resistance to deformation and scratching, were focused on. By plotting these parameters versus material density, the softness of organic molecular crystals was compared with those of other materials (Fig. 2.3).

Fig. 2.3

Young’s modulus (E)–density (top) and hardness (H)–density (bottom) plots constructed for organic crystals and other classes of materials. The opaque bubbles represent ranges of performance indices determined for particular materials, while the larger translucent envelopes enclose points obtained for a given class of materials. Reprinted with permission from ref. [5]

Because the red areas in Fig. 2.3 representing molecular crystals contain only organic compounds, they should be expanded towards higher densities by adding metal complexes. Although it may be possible to discover softer molecular crystals in the future, we can determine the positions of molecular crystals in a wide range of materials. Even at this stage, organic molecular crystals with high mechanical properties have been reported, and their softness enables the utilization of these materials in devices requiring high flexibility and mechanical compliance. Because the horizontal axis denotes the density of materials, the red area corresponding to organic molecular crystals partially overlaps with the region representing polymers. This means that molecular crystals are much lighter than ceramics and metals, which has an important advantage in the functionalization of organic materials. Meanwhile, in contrast to polymers, the long-range structural order and anisotropy in molecular crystals are their distinct advantages that outweigh disadvantages, such as the difficulty of mass production.

The combination of multiple strong hydrogen bonds oriented along a particular direction can provide guidance for the design of flexible molecular crystals. Naumov et al. reported the rough relationship between hydrogen bonding and softness in organic crystals (Fig. 2.4), which was derived from the detailed analysis of hydrogen bonds in well-characterized crystal structures, i.e., the properties of “soft crystals”. This relationship may be potentially used for designing not only molecular crystals but also various types of soft molecular materials, such as gels and polymers whose structures cannot be determined precisely. This analysis focused on strong and designable hydrogen bonds; however, similar analyses may be performed for other intermolecular interactions.

Fig. 2.4

Correlation of the number and strength of hydrogen bonds with the mechanical properties of organic crystals. Dependence of the combined measure of softness, (EH)^1/2, on the hydrogen bond density. Reprinted with permission from ref. [5]

Gong proposed the intrinsic correlation between the elastic moduli of crystals and their lattice constants (Fig. 2.5). The elastic modulus G, which represents the energy density for causing material deformation, is expressed by the formula U/b³, where b and U denote the lattice constant and the deformation energy of the lattice, respectively. According to this equation, the energy density decreases with increasing the lattice constant, which in turn increases the crystal softness. This is consistent with the fact that “soft crystals” whose crystal lattices are composed of ~1 nm-sized molecules or supramolecules, can exhibit softness in contrast to the extremely hard diamond crystal lattice composed of ~0.1 nm-sized atoms. By increasing the lattice constant, flexible molecular structures and/or large voids can be introduced, and thus, the crystals can be softened. Gong et al. successfully prepared macroscopically oriented lipid molecular films with a period of approximately 100 nm by polymerizing and fixing lipids in a hydrogel [6]. The gels can be easily deformed by applying a very weak pressure, and their structural color is varied by changing the periodic distance. Although the formation of crystal structures becomes difficult with increasing the lattice constant, the gels exhibiting discrete diffraction patterns of ultrasmall-angle X-rays are regarded as one-dimensional crystals with a lattice constant of 100 nm. Thus, this proposal illustrates how to not only extend the concept of “soft crystals” but also increase crystal softness.

Fig. 2.5

Conceptual image of the correlation between the elastic moduli of crystals and their lattice constants

6 Definition of “Soft Crystals”

Various phenomena related to “soft crystals”, such as vapochromism and mechanochromism, have been extensively studied in recent years. Mechanochromism corresponding to the single crystal → amorphous structural transformation is induced by gently grinding crystals. Meanwhile, the organic vapor-induced crystallization of amorphous solids, which accompanies vapochromism, has been reported as well. Therefore, to accurately characterize the properties of “soft crystals”, this book describes not only representative “soft crystals” with discrete X-ray diffraction patters but also various related processes.

In Sect. 2.3, “soft crystals” are compared with conventional hard crystals and soft materials in terms of their activation energy and structural order. In Sect. 2.4, “crystals including soft crystals” are compared with liquid crystals and plastic crystals from the viewpoint of the orientational order and positional order. Thus, “soft crystals” are clearly distinguishable from liquid crystals in terms of their positional order and from conventional hard crystals in terms of their activation energy. However, “soft crystals” can be stably prepared and isolated despite their ability to undergo structural transformations at room temperature after applying weak but specific stimuli. In Fig. 2.6, the qualitative activation energy ΔG^‡ is plotted along the vertical axis against the positional order (the horizontal axis) and orientational order (the third axis), which are displayed in Fig. 2.2. Importantly, “soft crystals” are stable at room temperature in the absence of specific stimuli (similar to conventional crystals) because the ΔG^‡ value is significantly larger than the thermal energy. However, in contrast to conventional hard crystals, the structural transformations of “soft crystals” are caused by weak but specific stimuli because of the decrease in ΔG^‡. In other words, “soft crystals” can be defined in a narrow sense as crystals that are normally stable but undergo structural transformations in the presence of specific stimuli, which decrease the ΔG^‡ value.

Fig. 2.6

Schematic diagrams illustrating the positional/orientational orders in condensed matter and the activation energies of structural transformations (ΔG^‡) before (left) and after (right) applying a gentle stimulus