Molecular organization in liquid crystals: A comparative computational analysis

A comparative computational analysis of molecular organization in four-nematogenic acids (nOCAC) having two, four, six, and eight carbon atoms in the alkyl chain is carried out with respect to translatory and orientational motions. The evaluation of the atomic charge and dipole moment at each atomic center is performed through the complete neglect differential overlap (CNDO/2) method. The Rayleigh-Schrödinger perturbation theory, along with the multicentered-multipole expansion method, is employed to evaluate the long-range interactions, while the “6-exp” potential function is assumed for short-range interactions. The total interaction-energy values obtained through these computations are used to calculate the probability of each configuration at the phase transition temperature via the Maxwell-Boltzmann formula. Further, the flexibility of various configurations is studied in terms of variation of probability due to small departures from the most probable configuration. A comparative picture of molecular parameters, such as the total energy, binding energy, and total dipole moment, is given. An attempt is made to explain the nematogenic behavior of these liquid crystals in terms of their relative order and, thereby, to develop a molecular model for the liquid crystallinity.     

Order–Disorder Phenomenon of Nematogens at Molecular Level—A Computational Approach

The phase behavior of nematogenic p-n-Alkoxy cinamic acids (nOCAC) with alkyl chain carbon atoms (n = 2,4) has been reported with respect to the translational and orientational motions. The atomic net charge and dipole moment components at each atomic center have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh-Schrodinger Perturbation theory with the multicentered-multipole expansion method has been employed to evaluate the long-range interactions, and a “6-exp.” potential function has been assumed for the short-range interactions. The minimum energy configurations obtained during the different modes of interactions have been taken as input to calculate the configurational probability using the Maxwell–Boltzmann formula in nonpolar organic solvents, i.e., carbon tetrachloride (CCl₄), and chloroform (CHCl₃) at room temperature 300 K. Further, entropy of each configuration has been computed. It has been observed that the molecules show the remarkable behavior in the solvents. An attempt has been made to develop new and interesting computational model for nematogens in the solvents and order–disorder phenomenon at molecular level.     

Computational analysis of ordering in higher homologous series of nBAC: The effect of a dielectric medium

A computational analysis of ordering in higher homologous series of p-n-alkylbenzoic acids (nBAC) that have 7 (7BAC) and 9 (9BAC) carbon atoms in the alkyl chain has been carried out on the basis of quantum mechanics and intermolecular forces. The molecular geometry of 7BAC and 9BAC has been constructed on the basis of published crystallographic data with the standard values of bond lengths and bond angles. The evaluation of atomic charge and dipole moment at each atomic center has been carried out through the complete neglect differential overlap (CNDO/2) method. The configurational energy has been computed via the Rayleigh-Schrödinger perturbation method. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium at the nematic-isotropic-transition temperature through the use of the Maxwell-Boltzmann formula. It has been observed that there is a considerable rise in the probability of interactions, although the order of preference remains the same. The present article offers theoretical support to the experimental observations. In addition, this provides a new way of looking at the liquid-crystalline molecules in a dielectric medium.     

Molecular structure,vibrational spectroscopic and chemical reactivity of nematogenic p-n-alkylbenzoic acids: A comparative computational analysis

Molecular structure and vibrational spectroscopic studies of higher homologous series nematogenic p-n-alkylbenzoic acids (nBAC) that have 6 (6BAC) and 7 (7BAC) carbon atoms in the alkyl chain have been investigated using the Density Functional Becke3-Lee-Yang-Parr (B3LYP) level with the basis set 6-31++G (d.p) and Hartree Fock (HF) with the same basis set. The observed vibrational spectra has been resolved and assigned in detail for comparision with both the molecules. These results indicate that DFT and HF values are slightly different at both the levels. A comparision of chemical reactivity such as HOMO (E_H), LUMO (E_L) energies, energy gap (E_g), ionization energy (I), electron affinity (A), electro negativity (χ), chemical hardness (η), electronic chemical potential (μ), electrophilicity index (ω), and softness (S) has been made. It has been observed that the decrement has occurred in the energy band gap value of isolated molecule with increment in alkyl chain length. This provides valuable information regarding enhancing the stability of liquid crystal materials by maintaining the conductivity.     

Vibrational spectra,electronic properties and effect of alkyl chain length on chemical stability of nematogens – A comparision using DFT and HF methods

The vibrational spectra of lower homologous series of nematogenic p-n-alkylbenzoic acids (nBAC) with 4 (4BAC) and 5 (5BAC) carbon atoms in the alkyl chain have been investigated using the Density Functional Becke3-Lee-Yang-Parr (B3LYP) level with the basis set 6–31++G(d.p) and Hartree Fock (HF) with the same basis set. The observed vibrational spectra has been resolved and assigned in detail for comparision with both the molecules. These results indicate that DFT and HF values are slightly different at both the level. A comparision of electronic properties such as HOMO (E_HOMO), LUMO (E_LUMO) energies, energy gap (E_g), ionization potential (I), electron affinity (A), electro negativity (χ), chemical hardness (η), electronic chemical potential (μ), electrophilicity index (ω), and softness (S) has been made. It has been observed that decrement occurred in the energy band gap value of isolated molecule with increment in alkyl chain length. This provides valuable information regarding the stability of liquid crystal materials.     

Probabilistic and thermodynamic approach on phase behavior of nematic liquid crystals: A comparative study

The systems chosen for the present investigation, p-n-alkylbenzoic acid (nBAC; n = 6, 7) exhibits nematic-isotropic transition. A comparative study based on quantum probabilistic and statistical thermodynamics has been carried out with respect to translational and orientational motions. The evaluation of net atomic charges and dipole moment at each atomic centre has been carried out through the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh-Schrodinger perturbation theory along with multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while the ‘6-exp’ potential function has been assumed for short-range interactions. The total interaction energy values obtained through these computations have been used as input to calculate the probability of occurrence of a particular configuration using the Maxwell-Boltzmann formula. Further, thermodynamic parameters such as Helmholtz free energy, and entropy at room temperature (300 K), and nematic-isotropic transition temperatures have been computed. An attempt has been made to understand the structure-phase behaviour relationship at molecular level.     

Structural,electrochemical and optical properties of 4′-n-alkyl-4-cyanobiphenyl (nCB) – A computational approach

The structures of nCB (n = 6 & 7 where n is the number of carbon atoms in the alkyl chain) have been optimized using the Becke3-Lee-Yang-Parr (B3LYP) hybrid functional with 6–31G+(d) basis set using the crystallographic geometry as input. The electronic structures of the dimer molecules have been computed using the optimized geometries. The spectra of the dimer molecules have been calculated by employing the DFT method. The features of electronic transitions and excited states have been calculated via configuration interaction singles (CIS) with the semiempirical Hamiltonian Zerner intermediate neglect of differential overlap (ZINDO). The photo sensitivity of liquid crystalline alkyl cyanobiphenyl has been presented on ultraviolet (UV) absorption based approach through Density functional theory (DFT) calculations. The structural and electrochemical properties such as HOMO (H), LUMO (L), and energy gap (Eg = E_L – E_H) have been investigated. A comparison of dimers during the different modes of interactions suggests an absorption maxima at longer wavelength for 7CB, indicating the high photo sensitivity. Further, the 6CB dimers exhibit a lower band gap; hence its conductivity is high in comparison with the 7CB dimers.     

Role of dielectric medium on benzylidene aniline: A computational analysis

A computational analysis of ordering in N-(p-n-ethoxy benzylidene)-p-n-butyl aniline (2O.4) was performed based on quantum mechanics and intermolecular forces. The atomic charge and dipole moment at atomic centre were evaluated using the all valance electron CNDO/2 method. The modified Rayleigh-Schrodinger perturbation theory and multicentre—multipole expansion method were employed to evaluate long-range intermolecular interaction, while a 6-exp potential function was assumed for short-range interactions. The total interaction energy values obtained in these computations were used as input for calculating the probability of each configuration in a noninteracting and nonmesogenic solvent (i.e., benzene) at room temperature (300 K) using the Maxwell-Boltzmann formula. The molecular parameter of 2O.4, including the total energy, binding energy, and total dipole moment were compared with N (p-n-butoxy benzylidene)-p-n-ethyl aniline (4O.2). The present article offer theoretical support to the experimental “observations, as well as a new and interesting way of looking at liquid crystalline molecule in a dielectric medium.     

7-Hexyloxy-3-[4’-(3-methylbutyloxy) phenyl]-4H-1-benzopyran-4-one: Study of Smectic behaviour and UV absorption profile

The intermolecular interaction energies between a pair of 7-Hexyloxy-3-[4’-(3-methylbutyloxy) phenyl]-4H-1-benzopyran-4-one (HMBPB) molecules have been estimated with respect to translational and orientational motions. The complete neglect differential overlap (CNDO/S) method has been employed to calculate the net atomic charge and atomic dipole moment components at each atomic center. The modified Rayleigh-Schrodinger perturbation theory along with multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for short-range interactions. The total interaction energy values obtained through these computations have been used to calculate the probability of each configuration at room temperature (300K), and isotropic-smectic transition temperature (412.6K). Molecular arrangements inside a bulk of materials and smectic behavior of the compound in terms of their relative order have been discussed. Translational and rotational rigidity of the molecule has been analyzed to understand the smectic behaviour. The UV absorption profile has been estimated using CNDO/S, and INDO/S methods.     

Conformational Behavior and Influence of Organic Solvents on a Strong Polar Group Nematogen at Room Temperature—A Computational Model

The conformational behavior and influence of organic solvents on a nematogen, 4’-n-alkyl-4-cyanobiphenyl, with strong polar group propyl (3CB) that is of commercial and application interest has been studied with respect to the translational and orientational motions. The atomic net charge and dipole moment components at each atomic center have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh-Schrodinger Perturbation theory with the multicentered-multipole expansion method has been employed to evaluate the long-range interactions, and a “6-exp.” potential function has been assumed for the short-range interactions. The minimum energy configurations obtained during the different modes of interactions have been taken as input to calculate the configurational probability using the Maxwell–Boltzmann formula in nonpolar organic solvents, i.e., carbon tetrachloride (CCl₄), and chloroform (CHCl₃) at room temperature 300 K. It has been observed that the molecules show the interesting property in the organic solvents. The interaction energies of dimer complexes have been taken into consideration in order to investigate the most energetically stable configuration. An attempt has been made to develop an interesting computational model for nematogen at molecular level.     

An X – Ray Study of the p-n-Alkoxycinnamic Acids. Part III.1

The effect upon molecular packing of increasing chain length in a homologous series of mesogens has been examined in the case of the p-n-alkoxycinnamic acids by determination of the crystal structures of the four nematogenic acids having two, four, six, and eight carbon atoms in the alkyl chain. The chains have the all-trans extended conformation, and the molecules exist in the crystal as planar hydrogen-bonded dimers. The dimers are arranged in end-to end fashion in parallel rows. Similar side-to-side packing of pairs of dimmers is found in each crystal structure giving a good fit between adjacent aromatic cores, but the amplitudes of thermal vibration of the chain carbon atoms increase markedly with increasing chain length, indicating a low packing efficiency for these moieties.     

Nematic Behavior of 5OCB in a Dielectric Medium at Phase Transition Temperature ‐A Statistical Analysis

A statistical analysis has been carried out to determine the configurationally preference of a pair of 5OCB (4′‐n‐pentyloxy‐4‐biphenylcarbonitrile) molecules with respect to translatory and orientational motions. The CNDO/2 method has been employed to evaluate the net atomic charge and atomic dipole components at each atomic centre of the molecule. Modified Rayleigh‐Schrodinger perturbation theory along with multicentered‐multipole expansion method has been employed to evaluate long‐range intermolecular interactions, while a ‘6‐exp’ potential function has been assumed for short‐range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in vacuum and in a dielectric medium at phase transition temperature using Maxwell‐Boltzmann formula. It has been observed that the probabilities are redistributed in dielectric medium and there is considerable rise in the probabilities of interactions, although the order of preference remains the same. On the basis of stacking, in‐plane and terminal interaction energy calculations, all possible geometrical arrangements of the molecular pairs have been considered. The results are discussed in the light of experimental as well as other theoretical observations.     

Thermotropic liquid crystalline compounds with lateral long-chain substituents (II).: Synthesis and liquid crystalline properties of 1,4-Bis [4-substituted-benzoyloxy]-2-n-alkylbenzenes

We synthesized 102 new 1,4-bis-[4-subst.-benzoyloxy]-2-n-alkylbenzenes of the general formula with R = alkyl, alkyloxy, alkanoyloxy, alkyloxycarbonyloxy and n = 0 to 16. Surprisingly all of the new compounds are liquid crystalline nematic. Thus it is proved that lateral long chain substituents are compatible with liquid crystalline properties.     

Calorimetric investigations in liquid crystalline terephthalylidene-bis-[4-n-alkylanilines] (TBAA)

By means of the calorimeter DSC-2 the temperatures and enthalpies of phase transitions were measured in the homologues of TBAA with the alkyl chain length n from 2 up to 10, in order to confirm the existence of nine types of liquid crystalline mesophases and of the polymorphism in the solid state within this series. Pre-and posttransitional phenomena, hysteresis effects in low temperature smectics and relations between enthalpies and chain lenght resp. kind of concerning phases could be observed.     

Role of dielectric medium on mesogenic compounds (BCHs) at phase transition temperature: A comparative computational analysis

A comparative computational analysis on two liquid crystalline disubstituted biphenylcyclohexanes (BCHs) of general formula R‐C₆H₁₀‐C₆H₄‐X with R: C₃H₇; X: H (BCH30) and R: C₅H₁₁; X: CN (BCH5CN) has been carried out on the basis of quantum mechanics and intermolecular forces. The evaluation of atomic charge and dipole moment at each atomic centre has been carried out through an all‐valence electron (CNDO/2) method. The configurational energy has been computed using the Rayleigh‐Schrodinger perturbation method. The total interaction energy values obtained were used to calculate the probability of each configuration in dielectric medium (i.e. non‐interacting and non‐mesogenic solvent, benzene) at room temperature, transition temperature and above transition temperature using the Maxwell‐Boltzmann's formula. The flexibility of various interacting configurations has been studied in terms of variation of probability due to small departures from the most probable configurations. Further, the various possible geometrical arrangements between a molecular pair during the different modes of interactions have been considered. An attempt has been made to develop a new and interesting model for mesogenic compounds in a dielectric medium. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Theoretical study of closo-decaborate novel nematogen: Thermodynamic behavior and phase stability

The present article deals with the thermodynamic behavior and phase stability of closo-decaborate nematogen viz. dinitrogen-10-(4-pentyl-1-thiacyclohexyl)-closo-decaborate (DPTD) at a molecular level. The atomic net charge and dipole moment at each atomic center have been evaluated using the complete neglect differential overlap (CNDO) method. The modified Rayleigh–Schrodinger perturbation method along with multicentered–multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for the short-range interactions. The total interaction energy values obtained through these computations have been used to calculate the probability of each configuration at room temperature (300 K), nematic–isotropic transition temperature (435 K), and above transition temperature (500 K) using the Maxwell–Boltazman formula. Further, the entropy of each configuration has been computed during the different modes of interactions. The adopted framework provides valuable information on thermodynamic behavior, and phase stability of novel nematogen based on parameters, i.e., molecular and thermodynamic, introduced in this article.     

Anisotropic Dispersion Interactions In Liquid Crystals

The polarizability and shape anisotropics of a new class of aliphatic liquid crystals, 4,4′-di-n-alkyl-bibicyclo[2.2.2]octanes (n, n-BBCO) have been calculated as a function of the alkyl chain length and its degree of flexibility to inquire about the relative importance of attractive and repulsive interactions in stabilizing the liquid crystalline phase. The calculated polarizability anisotropics are found to be much smaller than that of conventional mesogens. In the context of the Maier-Saupe theory, this indicates that anisotropic dispersion interactions make only a minor contribution to the stability of this class of liquid crystals. The cylindrical symmetry exhibited by the n, n-BBCO homologues and their rigid molecular structure suggest that they might be ideally suited for critical testing of existing theories of the nematic-isotropic phase transition.     

Molecular ordering of 4O.2 compound in a dielectric medium at room temperature‐A theoretical approach

The molecular ordering of N‐(4‐n‐butoxybenzylidene)‐4′‐ethyaniline [4O.2] in a dielectric medium (benzene) has been carried out on the basis of statistical mechanics and intermolecular forces. The atomic net charge and atomic dipole moment at each atomic centre has been evaluated using the CNDO/2 method. The modified Rayleigh‐Schrodinger perturbation theory with multicentered‐multipole expansion method has been employed to evaluate the long‐range intermolecular interactions, while ‘6‐exp’ potential function has been assumed for the short‐range interactions. The total interaction energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium at room temperature (300K) using the MB‐formula. The flexibility of various interacting configuration has been studied in terms of variation of probability due to departure from the most probable configuration. A comparative picture of the molecular parameters like total energy, binding energy and total dipole moment has been given. An attempt has been made to analyse the characteristic features of nematogenic 4O.2 compound in terms of its relative order. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The role of a dielectric medium in a smectogenic Schiff base compound: A computational analysis

A computational analysis of ordering in a smectogenic Schiff base compound, N-(4-n-heptyloxybenzylidine)-4-hexylaniline, has been carried out with the help of quantum mechanics and computer simulation. The complete neglect differential overlap (CNDO/2) method has been employed to compute the net atomic-charge and atomic dipole moment at each atomic center. The modified Rayleigh-Schrödinger perturbation theory with the multicentered-multipole expansion method has been employed to evaluate long-range intermolecular interactions, while a “6-exp” potential function has been assumed for short-range interactions. The interaction-energy values obtained through these computations were used to calculate the probability of each configuration in a dielectric medium at the phase-transition temperature (353 K). An attempt has been made to develop a new model of a smectogen in a dielectric medium. The present investigation provides theoretical support to the experimental observations.     

Dielectric properties of gadolinium-based liquid crystalline complex

The permittivity components of the liquid crystalline gadolinium complex with Lewis bases and β-diketonates as ligands are measured in the frequency range from 100 Hz to 5 MHz. The magnitude and sign of the dielectric anisotropy of the complex are determined. Two dispersion regions of the permittivities are found in the liquid crystalline phase. The mechanisms responsible for the relaxation phenomena occurring in the sample are established. The dielectric relaxation times, activation energies, and dipole moment of the complex are obtained. The results of the study are compared with the dielectric properties of ytterbium and terbium complexes having the same ligand environment.