Crystals molecular rotation

The entropy of fusion of a normal crystal can be considered as the sum of the increase in disorder due to the breakup of the crystal lattice, the configurational contribution, and that due to greater fieedom for internal motions. The configurational contributions predominate. They can be considered as the sum of the translational disorder and the effect of onset of molecular rotation. In this light a transition from a normal crystal to a plastic crystal introduces some of the disorder normally associated with melting. The sum of the entropy of transition to a plastic crystal and the subsequent entropy of fusion is within the range of the entropy of fusion of normal crystals. Molecular rotation in plastic crystals are not usually free. Thus the entropy of transition is somewhat less than what would be observed for a transition to free rotation. 

E. Posnjak, F.C. Kracek, Molecular Rotation in the Solid State. The Variation of Crystal 1 Structure of Ammonium Nitrate with Temperature , JACS 54, 2766-86 (July 1932) 4) D.P. 

As the density of a gas increases, free rotation of the molecules is gradually transformed into rotational diffusion of the molecular orientation. After unfreezing , rotational motion in molecular crystals also transforms into rotational diffusion. Although a phenomenological description of rotational diffusion with the Debye theory [1] is universal, the gas-like and solid-like mechanisms are different in essence. In a dense gas the change of molecular orientation results from a sequence of short free rotations interrupted by collisions [2], In contrast, reorientation in solids results from jumps between various directions defined by a crystal structure, and in these orientational sites libration occurs during intervals between jumps. We consider these mechanisms to be competing models of molecular rotation in liquids. The only way to discriminate between them is to compare the theory with experiment, which is mainly spectroscopic. 

Chapter 9, on entropy and molecular rotation in crystals and liquids, is concerned mostly with statistical mechanics rather than quantum mechanics, but the two appear together in SP 74. Chapter 9 contains one of Pauling s most celebrated papers, SP 73, in which he explains the experimentally measured zero-point entropy of ice as due to water-molecule orientation disorder in the tetrahedrally H-bonded ice structure with asymmetric hydrogen bonds (in which the bonding proton is not at the center of the bond). This concept has proven fully valid, and the disorder phenomenon is now known to affect greatly the physical properties of ice via the... 

Chapter 9. Entropy and Molecular Rotation in Crystals and Liquids 773... 

In the crystal, the total number of vibrations is determined by the number of atoms per molecule, N, and the nmnber of molecules per primitive cell, Z, multiplied by the degrees of freedom of each atom 3ZN. In the case of a-Sg (Z =4, N =8) this gives a total of 96 vibrations ( ) which can be separated in (3N-6)—Z = 72 intramolecular or "internal" vibrations and 6Z = 24 intermo-lecular vibrations or lattice phonons ("external" vibrations). The total of the external vibrations consists of 3Z = 12 librational modes due to the molecular rotations, 3Z-3 = 9 translational modes, and 3 acoustic phonons, respectively. 

Smectic phases are more highly ordered than nematic phases, and with an ordering of the molecules into layers. There are a number of different smectic phases which reflect differing degree of ordering. Crystal smectic phases are characterised by the appearance of inter-layer structural correlations and may in some cases be accompanied by a loss of molecular rotational freedom. 

The lattice energy of a crystal of known structure (atomic positions) is thus calculated by compiling all possible distances between pairs of atoms in different molecules. The method of atom-atom potentials has been employed to investigate phenomena pertaining to static as well as dynamic lattices and the subject has been reviewed by Kitaigorodsky (1973) as well as by Ramdas Thomas (1980). Typical of the problems that have been investigated by this method are defects and planar faults, phase transitions and molecular rotation in crystals. 

Because of the orientational freedom, plastic crystals usually crystallize in cubic structures (Table 4.2). It is significant that cubic structures are adopted even when the molecular symmetry is incompatible with the cubic crystal symmetry. For example, t-butyl chloride in the plastic crystalline state has a fee structure even though the isolated molecule has a three-fold rotation axis which is incompatible with the cubic structure. Such apparent discrepancies between the lattice symmetry and molecular symmetry provide clear indications of the rotational disorder in the plastic crystalline state. It should, however, be remarked that molecular rotation in plastic crystals is rarely free rather it appears that there is more than one minimum potential energy configuration which allows the molecules to tumble rapidly from one orientation to another, the different orientations being random in the plastic crystal. 

Existence of a high degree of orientational freedom is the most characteristic feature of the plastic crystalline state. We can visualize three types of rotational motions in crystals free rotation, rotational diffusion and jump reorientation. Free rotation is possible when interactions are weak, and this situation would not be applicable to plastic crystals. In classical rotational diffusion (proposed by Debye to explain dielectric relaxation in liquids), orientational motion of molecules is expected to follow a diffusion equation described by an Einstein-type relation. This type of diffusion is not known to be applicable to plastic crystals. What would be more appropriate to consider in the case of plastic crystals is collision-interrupted molecular rotation. 

The 1-dichloro-d-bromo-camphor sulphonie salts are the least soluble. The colour of these optically active derivatives is the same as that of the racemic salts. 1-Dichloro-diethylenediamino-chromie d-a-bromo-camphor sulphonate, [Cren2Cl2]SO3C10H14OBr, forms small, shining violet crystals, and has specific rotation [molecular rotation of [M]D + 176-9°. Solutions of both isomers are rapidly raeemised. 

Careful stepwise crystallization of cobalt acetylacetonate from solutions of the partially resolved chelate produced surprising results (14). A typical experiment is summarized in Table VI. The molecular rotation of the filtrates steadily increased as each crystal crop was removed until no solute remained in solution— at this time all optical activity had, of course, been lost. All crystal crops were racemic It seems that the racemate is being preferentially crystallized from solution and at the same time a surface racemization is taking place to make up the deficient enantiomorph as the d, l crystals are formed. 

Turning to the low temperature transition of the homopolymer of PHBA at 350 °C, it is generally accepted that the phase below this temperature is orthorhombic and converts to an approximate pseudohexagonal phase with a packing closely related to the orthorhombic phase (see Fig. 6) [27-29]. The fact that a number of the diffraction maxima retain the sharp definition at room temperature pattern combined with the streaking of the 006 line suggests both vertical and horizontal displacements of the chains [29]. As mentioned earlier, Yoon et al. has opted to describe the new phase as a smectic E whereas we prefer to interpret this new phase as a one dimensional plastic crystal where rotational freedom is permitted around the chain axis. This particular question is really a matter of semantics since both interpretations are correct. Perhaps the more important issue is which of these terminologies provides a more descriptive picture as to the nature of the molecular motions of the polymer above the 350 °C transition. As will be seen shortly in the case of the aromatic copolyesters, similar motions can be identified well below the crystal-nematic transition. 

Molecular rotation In a normal crystal every atom occupies a precise mean position, about which it vibrates to a degree depending on the temperature molecules or polyatomic ions have precisely defined orientations as well as precise mean positions. When such a crystal is heated, the amplitude of the thermal vibrations of the atoms increases with the temperature until a point is reached at which the regular structure breaks down, that is, the crystal melts. But in a few types of crystal it appears that notation of molecules or polyatomic... 

Since molecular rotation does occur in certain crystals, it is necessary, when attempting to determine the structure of any crystal, to com sider this possibility. If there appears to be a conflict between the symmetry of a molecule in the crystal and the expectation based on stereochemical principles, or if it is found impossible to obtain correct calculated intensities on the assumption that the molecules are fixed, it should be considered whether the hypothesis of molecular rotation provides an explanation. 

There are a few exceptions to the statements of the previous paragraph. The vibrational Raman spectrum of liquid H2 shows rotational fine structure for H2, the rotational levels are widely spaced and intermolecular forces are reasonably small. Certain solids when heated undergo a transition to a solid state in which molecular rotation in the crystal is possible. Solid H2 undergoes such a transition, as shown by the heat-capacity curve see Davidsoriy Section 16-9. 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

However, the NMR properties of solid-phase methane are very complex, due to subtle effects associated with the permutation symmetry of the nuclear spin set and molecular rotational tunnelling.55 Nuclear spin states ltotai = 0 (irred. repr. E), 1 (T) and 2 (A) are observed. The situation is made more complicated since, as the solids are cooled and the individual molecules go from rotation to oscillation, several crystal phases become available, and slow transitions between them take place. Much work has been done in the last century on this problem, including use of deuterated versions of methane for example see Refs. 56-59. Much detail has emerged from NMR lineshape analysis and relaxation time measurements, and kinetic studies. For example, the second moment of the 13C resonance is found to be caused by intermolecular proton-carbon spin-spin interaction.60 Thus proton inequivalence within the methane molecules is created. 

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