The influence of correlation of molecular orientations and of molecular flexibility on excess volumes of mixtures of branched and linear alkanes

It is shown that the excess volumes of mixtures of alkanes are not only influenced by equation-of-state effects, but also by differences in orientational order and, probably, in flexibility of the component molecules.     

The oblique chiral nematic phase in calamitic bimesogens

ABSTRACT

The discovery of the oblique chiral (or, the twist-bend, N_TB) nematic phase predicted for bent-core mesogens has engendered much interest due to its unique structure and physical properties, and the possibility of use in the next generation of fast electro-optic technology. Bimesogenic calamitic as well as bent-core mesogens are found to form the N_TB phase. Here, we report direct measurements of the temperature dependence of the conical tilt and the evidence of volcano-like orientational distribution of molecules in the N_TB phase. Optical and x-ray scattering investigations of two single-component calamitic bimesogens and their mixtures show that, while the Maier–Saupe orientational distribution function (ODF) is valid for the higher temperature nematic phase, a generalised expansion in terms of even Legendre functions is needed for the N_TB phase. Temperature dependence of the ODFs and the order parameters 〈P₂(cosβ)〉, 〈P₄(cosβ)〉, and 〈P₆(cosβ)〉 has been measured in both phases. The parameters 〈P₂(cosβ)〉 and 〈P₄(cosβ)〉 increase/decrease in the N/N_TB phase with decreasing temperature, while 〈P₆(cosβ)〉 remains vanishingly small for all samples. The value of 〈P₄(cosβ)〉 becomes negative in the N_TB phase confirming a conical distribution of molecules as they follow a helical trajectory keeping the local director tilted at an angle α wrt the macroscopic director. The heliconical tilt calculated from ODFs, exhibits a power law behaviour with temperature, vanishing at the transition to the N phase.     

Rotor-synchronized two-dimensional 13C CP/MAS NMR studies of the orientational order of polymers. I. High-performance ultrahigh molecular weight polyethylene fibers

The orientational order of three morphological components, identified previously as two crystalline components, C₁ and C₂, and an amorphous component, A of four polyethylene fibers, including two gelspun ultrahigh molecular weight (PE-I and PE-II) and two meltspun moderate molecular weight (PE-D and PE) polyethylene fibers are further analyzed by rotor-synchronized two-dimensional ¹³C CP/MAS (ROSMAS) nuclear magnetic resonance (NMR) techniques. Our results indicate that the orientational order of these components differ substantially among themselves in a given fiber and among different fibers of the same component. Values of β_1/2, the polar angle at which the orientational distribution function (ODF) P 〈β〉 decays to half its maximum, are determined to be: 18° (C2 of PE-II), 21° (C2 of PE-I), 29° (C2 of PE-D), 31° (C1 of PE-I) and 50° (C2 of PE). No orientational sideband can be detected for component A, suggesting that the A component is due to the amorphous domain. The implication of this results and the technical limit of this technique are analyzed. © 1993 John Wiley & Sons, Inc.     

Considerations in the determination of orientational order parameters from X-ray scattering experiments

An assessment of the data processing and analysis methods used to obtain the second- and fourth-rank orientational order parameters of liquid crystals from X-ray scattering experiments has been carried out, using experimental data from four extensively studied alkyl-cyanobiphenyls and calculated data generated from two general types of theoretical orientational distribution function. The application of a background subtraction and two different baseline correction methods to the scattering profiles is assessed, along with three different methods to analyse the processed data. The choice of baseline correction method is shown to have a significant effect: an offset to zero overestimates the order parameters from the experimental and calculated data sets, particularly for lower order parameters arising from broad distributions, whereas an offset to a value estimated from regions of low scattering intensity provides experimental values close to those reported from other experimental techniques. By contrast, the three different analysis methods are shown generally to result in relatively small absolute differences between the order parameters. We outline a straightforward general approach to experimental X-ray scattering data processing and analysis for uniaxial phases that results in order parameters that match well with those reported using other experimental techniques.     

Rotor-synchronized two-dimensional 13C CP/MAS NMR studies of the orientational order of polymers 2. Melt-extruded poly(ethylene terephthalate) fibers

Determination of the orientational order of morphological components in polyethylene terephthalate (PET) is sought through quantitative application of two-dimensional rotor synchronized magic angle spinning (ROSMAS) ¹³C NMR technique. Previous study in our laboratories had established a procedure for resolution of the carbonyl carbon (CA) and glycol ethylene carbon (GE) resonances into those corresponding to four morphological components.¹ Due to paucity of sidebands in the GE resonances, the focus has been on the CA resonances in this attempt to obtain orientation distributions. A set of PET fibers possessing a broad range of crystalline and orientational order has been used to infer the meaning of NMR-based orientation measurements vis-a-vis other techniques. A surprising finding of this study is the observation that the orientational orders of the broad component in the ¹³C CP/MAS spectrum and the narrow component are very similar in these fibers. ©1995 John Wiley & Sons, Inc.     

Dynamics of the acousto‐optic effect in a nematic liquid crystal

In a nematic liquid crystal cell, the application of an ultrasonic wave induces a rotation of the director, leading to a change in the optical transmission through the cell. In this study, we investigate the dynamic response of the optical intensity after the ultrasonic wave is switched on or off. Our experiments show that the optical intensity follows a double‐exponential function of time, indicating that the system has two relaxation modes with widely different time scales. The fast mode has an amplitude and time scale qualitatively consistent with the dynamics of the Fréedericksz transition, but the slow mode shows novel behaviour associated with the acousto‐optic effect.     

The behavior of benzene confined in a single wall carbon nanotube

We present the molecular dynamics study of benzene molecules confined into the single wall carbon nanotube. The local structure and orientational ordering of benzene molecules are investigated. It is found that the molecules mostly group in the middle distance from the axis of the tube to the wall. The molecules located in the vicinity of the wall demonstrate some deviation from planar shape. There is a tilted orientational ordering of the molecules which depends on the location of the molecule. It is shown that the diffusion coefficient of the benzene molecules is very small at the conditions we report here. © 2015 Wiley Periodicals, Inc.     

Terms representing the reorganization of bonding within charge‐bond order matrices of reacting molecules

The usual way of obtaining charge‐bond order (CBO) matrices of molecules by summing up the MO LCAO coefficients over occupied molecular orbitals (MOs) is extended to derive terms representing the reorganization of bonding in reacting systems. The CBO matrix of a certain molecule (reactant) under influence of another one (reagent) is expressed in the form of power series with respect to intermolecular interaction. Terms of this series responsible for the internal reorganization of bonding in the reactant are also shown to be representable by sums of MO LCAO coefficients of the relevant isolated compound. As opposed to the case of a single molecule, the new sums embrace all MOs of the reactant and their pairs. This result is conditioned by the fact that the actual occupation numbers of MOs differ from either two or zero in the bimolecular system because of the intermolecular charge transfer, and bond orders arise between pairs of MOs in addition. Partial increments to the final reorganization of bonding related to individual MOs and to their pairs are then studied separately. These increments may be classified on the basis of criteria applied to MOs they originate from. In particular, symmetric and antisymmetric increments are distinguished with respect to any symmetry operation of the isolated reactant lost under influence of an approaching reagent. Increments of the same symmetry are subsequently collected into separate groups representable by specific graphical schemes. Consequently, the final pattern of charge and bond order redistribution in the reactant under influence of an approaching reagent follows from superposition of a few principal schemes. The results are illustrated by consideration of specific examples, in particular of addition of electrophile to the butadiene molecule. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Optical properties and photonic density of states in one-dimensional and three-dimensional liquid-crystalline photonic crystals

ABSTRACT

Complex optical investigations were performed in one-dimensional (cholesteric) and three-dimensional (Blue Phase II) liquid-crystalline photonic crystals. Spectra of optical transmission and luminescence in the range of the photonic stop band contain information about the local anisotropy, characteristics of the photonic stop band, photonic density of states. We determine the photonic density of states in one-dimensional and three-dimensional liquid-crystalline photonic crystals employing measurements of polarised luminescence. The width of the photonic band gap, density of states and the optical characteristics related to the density of states essentially change with temperature in one-dimensional cholesteric photonic crystal. Drastic transformation of the density of states was found at the transition from one-dimensional to three-dimensional (Blue Phase II) photonic crystal. The results of our investigations demonstrate the possibility to employ the applied method for various types of photonic structures.     

Fast computation,rotation, and comparison of low resolution spherical harmonic molecular surfaces

A procedure that rapidly generates an approximate parametric representation of macromolecular surface shapes is described. The parametrization is expressed as an expansion of real spherical harmonic basis functions. The advantage of using a parametric representation is that a pair of surfaces can be matched by using a quasi-Newton algorithm to minimize a suitably chosen objective function. Spherical harmonics are a natural and convenient choice of basis function when the task is one of search in a rotational search space. In particular, rotations of a molecular surface can be simulated by rotating only the harmonic expansion coefficients. This rotational property is applied for the first time to the 3-dimensional molecular similarity problem in which a pair of similar macromolecular surfaces are to be maximally superposed. The method is demonstrated with the superposition of antibody heavy chain variable domains. Special attention is given to computational efficiency. The spherical harmonic expansion coefficients are determined using fast surface sampling and integration schemes based on the tessellation of a regular icosahedron. Low resolution surfaces can be generated and displayed in under 10 s and a pair of surfaces can be maximally superposed in under 3 s on a contemporary workstation. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 383–395, 1999     

Tuning the mesogenic properties of 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals: the effect of a phenoxy end-group in two sterically equivalent series

Two sterically equivalent series of phenoxy-terminated 5-alkoxy-2-(4-alkoxyphenyl)pyrimidine liquid crystals were synthesised, and their mesogenic properties were characterised by polarised optical microscopy and differential scanning calorimetry (DSC). The phenoxy end-group causes a significant increase in melting point and inhibits – at least partially – the mesomorphism of these materials relative to the parent isomers; in most cases, the broad enantiotropic SmC phase formed by the parent isomers is suppressed by the addition of the phenoxy end-group. However, detailed analyses by small-angle X-ray scattering and monodomain 2D X-ray scattering suggest that these compounds form a SmA phase with a partially intercalated bilayer structure in which the phenoxy end-groups are nanosegregated. Such an intercalated bilayer structure might enable the tuning of smectogenic properties by appropriate substitution of the phenoxy end-groups.     

The rotation and the phase transition in solid C60

The interaction between C60's in solid C60 has been calculated by (exp-6-1) potential, and the cause and the controlled factor of the high rapid rotations of C60 's were discussed. In order to describe the disordered degree of C60 rotation, an equivalent M is introduced. The phase transitions at the ~260 K and at the ~90 K are studied from the viewpoint of C60 rotation. The potential barriers of the ordered rotation below the ~260 K and the disordered rotation above the ~260 K have been given, and the effect of the external pressure on the temperature of phase transition has also been given.     

Hindered internal rotation in molecular systems: quantum statistics of equilibrium and rate constants in the Wigner function formalism

Summary The quantum statistics of a symmetric hindered internal rotator in a molecule or molecular complex is developed within the Wigner function formalism. Different shapes of the rotational barrier are considered. The partition function and the thermodynamic functions are given as Wigner-Kirkwood series expansions in terms of powers of Planck's constant squared. One gets simple closed expressions containing the modified Bessel functionsJ ₀ andJ ₁ of the argumentiV ₀/2kT whereV ₀ is the barrier height. Some problems concerning the evaluation of equilibrium and rate constants of chemical reactions are discussed.Supported by the Alexander von Humboldt-Stiftung     

Using operators to expand the block matrices forming the Hessian of a molecular potential

We derive compact expressions of the second‐order derivatives of bond length, bond angle, and proper and improper torsion angle potentials, in terms of operators represented in two orthonormal bases. Hereby, simple rules to generate the Hessian of an internal coordinate or a molecular potential can be formulated. The algorithms we provide can be implemented efficiently in high‐level programming languages using vectorization. Finally, the method leads to compact expressions for a second‐order expansion of an internal coordinate or a molecular potential. © 2014 Wiley Periodicals, Inc.     

Theoretical analysis of the internal rotation and determination of molecular structures of HSSH,HSSF and FSSF

Summary A detailed investigation of the internal rotation of hydrogen persulfide and fluoro-derivatives is presented. High quality potential functions containing only three and four parameters were determined through a very simple interpolation method. Reduced torsional potentials are defined and used to assess the quality of the interpolated functions. Equilibrium structures and barriers to internal rotation reported here are in close agreement with the available experimental data. High barrier heights and the comparative analysis of structural parameters of all three molecules indicate significant bonding through the mechanism of hyperconjugation.     

On the role of localized molecular orbitals in the formation of bond dipoles

The hypothesis of the classical chemistry about bond dipoles resulting from shifts of separate pairs of electrons is proved using the non-canonical method of molecular orbitals (MOs). To this end, a relation is sought between the total charge distribution inside an individual chemical bond of a polyatomic molecule and the square of the respective single localized MO (LMO). General expressions for these MOs are obtained directly on the basis of the Brillouin theorem without invoking additional localization criteria. The two characteristics under comparison are presented in an explicit algebraic form in terms of meaningful components. Reshaping of square of the ‘own’ LMO of the given bond is shown to play the decisive role in the formation of secondary dipoles of initially homopolar bonds (e.g. of C–C and C–H bonds in substituted alkanes), as well as of bonds of relatively low initial polarity. Thus, representability of these dipoles by shifts of the ‘own’ pairs of electrons of respective bonds is supported. For bonds of a high initial polarity, the secondary dipoles are shown to originate mainly from contributions of LMOs of other bonds extending over the antibonding basis orbital of the given bond. Moreover, the actual secondary bond dipole takes an opposite direction vs. that predicted by the shift of the respective ‘own’ pair of electrons in this case. The latter result serves to account for the known low nucleofugality of highly electronegative heteroatoms in the S_N2 reactions.     

The Wigner function of the rotating Kratzer oscillator mapped onto the Morse oscillator

In this article, the rotating Kratzer oscillator in quantum phase space is studied. The Langer transformation is used to map the Kratzer oscillator with centrifugal term onto a one‐dimensional Morse oscillator. As a result, the Wigner distribution functions for the Morse oscillator are obtained. The quantum states of the system are visualized in the phase space for a few vibrational and rotational quantum numbers. The results obtained in the phase space correspond to those derived in the standard quantum theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010