Browsing by Author "Jokhan Ram"

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A study of isotropic-nematic transition of quadrupolar Gay-Berne fluid using density-functional theory approach
(2011) Ram Chandra Singh; Jokhan Ram
The effects of quadrupole moments on the isotropic-nematic (IN) phase transitions are studied using the density-functional theory (DFT) for a Gay-Berne (GB) fluid for a range of length-to-breadth parameters in the reduced temperature range. The pair-correlation functions of the isotropic phase, which enter into the DFT as input parameters are found by solving the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 are considered. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent function. As the length-to-breadth ratio of quadrupolar GB molecules is increased, the IN transition is seen to move to lower density (and pressure) at a given temperature. It has been observed that the DFT is good to study the IN transitions in such fluids. The theoretical results have also been compared with the computer simulation results wherever they are available. © 2011 Copyright Taylor and Francis Group, LLC.
Anisotropic screening in polar fluids and the extent of its accommodation by molecular perturbation theories that use sphericalized reference states
(1984) Shri Singh; Jokhan Ram; Saul Goldman
We developed a function that is sensitive to many-body screening of the anisotropy in dense molecular fluids and applied it to dipolar fluids and to ST2 water. For these fluids, the function was found to be oscillatory with distance and to become damped, for dipolar fluids, with increasing strength of the dipole moment. We then compared this function to the screening implied by the Gray-Gubbins and RAM reference state potentials. For ST2 water these comparisons suggested that a composite potential made up of equal proportions of the RAM and the Gray-Gubbins potential might be better than either the RAM or the Gray-Gubbins potentials alone. © 1984 American Institute of Physics.
Density functional theory of freezing of a system of conjugated oligomers parameterised via Gay–Berne potential
(Taylor and Francis Ltd., 2016) Shikha Dwivedi; Pankaj Mishra; Jokhan Ram
Density functional theory (DFT) of freezing is used to study the isotropic–nematic, isotropic–smectic A and nematic–smectic A phase transitions in a system of large, semi-flexible conjugated oligomers parameterised within Gay–Berne (GB) potential. The pair correlation functions of the isotropic fluid, used as structural inputs in the DFT, are calculated by solving the Percus–Yevick integral equation theory. Large number of spherical harmonic coefficients of each orientation-dependent functions has been considered to ensure the numerical accuracy at different densities and temperatures for the system of these model GB ellipsoids having large aspect ratio (length-to-breadth ratio). We found that the system of GB ellipsoids parameterised for conjugated oligomers shows stable isotropic, nematic and smectic A phases. At low temperatures, on increasing the density, isotropic fluid makes a direct transition to smectic A phase. Nematic phase get stabilised in between the isotropic and smectic A phases on increasing the temperature. Using the transition parameter obtained through the DFT, we have plotted the temperature–density and pressure–temperature phase diagrams which are found to be qualitatively similar to the one obtained in simulations for the systems with low aspect ratio GB particles. © 2016 Taylor & Francis.
Density-functional theory of liquid crystal surfaces
(Taylor and Francis Inc., 1996) Yashwant Singh; Jokhan Ram
We develop a density-functional theory based on weighted density formalism to describe the surfaces of liquid crystals. The expression for the surface free energy is written in terms of order parameters characterizing the nature and amount of ordering in the interface and the structural parameters which involve the spherical harmonic coefficients of the direct pair correlation function of an effective isotropic fluid the density of which is determined using a criterion of the weighted density-functional formalism. We report preliminory results of our calculations for nematic/vapour and nematic/isotropic liquid interfaces.
Density-functional theory of the nematic phase: Results for a system of hard ellipsoids of revolution
(1991) Jokhan Ram; Yashwant Singh
A second-order density-functional theory is used to study the isotropic-nematic transition in a system of hard ellipsoids of revolution. The direct pair-correlation functions of the coexisting isotropic liquid that enter in the theory as input information are obtained from solving the Ornstein-Zernike equation using the Percus-Yevick closure relation. The spherical harmonic expansion coefficients of the correlation functions obtained from this solution are in good agreement with those found from computer simulations. We find that a system spontaneously transforms to a nematic phase when the structural parameter denoted by c^22(0) attains a value close to 4.40. This value of c^22(0) depends, although very weakly, on the value of the length-to-width ratio of the molecules. The transition parameters we found are in very good agreement with the results generated by computer simulations. By using the harmonic coefficients of the direct pair-correlation functions, we have calculated the Frank elastic constants of the nematic phase. © 1991 The American Physical Society.
Effect of shape anisotropy on the phase diagram of the Gay-Berne fluid
(2005) Pankaj Mishra; Jokhan Ram
We have used the density functional theory to study the effect of molecular elongation on the isotropic-nematic, isotropic-smectic A and nematic-smectic A phase transitions of a fluid of molecules interacting via the Gay-Berne intermolecular potential. We have considered a range of length-to-width parameter 3.0 ≤ x0 ≤ 4.0 in steps of 0.2 at different densities and temperatures. Pair correlation functions needed as input information in density functional theory are calculated using the Percus-Yevick integral equation theory. Within the small range of elongation, the phase diagram shows significant changes. The fluid at low temperature is found to freeze directly from isotropic to smectic A phase for all the values of x0 considered by us on increasing the density while the nematic phase stabilizes in between isotropic and smectic A phases only at high temperatures and densities. Both isotropic-nematic and nematic-smectic A transition density and pressure are found to decrease as we increase x0. The phase diagram obtained is compared with computer simulation result of the same model potential and is found to be in good qualitative agreement. © EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2005.
Effects of molecular elongation on liquid crystalline phase behaviour: Isotropic-nematic transition
(2003) Ram Chandra Singh; Jokhan Ram
We present the density-functional approach to study the isotropic-nematic transitions and calculate the values of freezing parameters of the Gay-Berne liquid crystal model, concentrating on the effects of varying the molecular elongation, x0. For this, we have solved the Percus-Yevick integral equation theory to calculate the pair-correlation functions of a fluid the molecules of which interact via a Gay-Berne pair potential. These results have been used in the density-functional theory as an input to locate the isotropic-nematic transition and calculate freezing parameters for a range of length-to-width parameters 3.0 ≤ x0 ≤ 4.0 at reduced temperatures 0.95 and 1.25. We observed that as x0 is increased, the isotropic-nematic transition is seen to move to lower density at a given temperature. We find that the density-functional theory is good to study the freezing transitions in such fluids. We have also compared our results with computer simulation results wherever they are available. © 2003 Elsevier B.V. All rights reserved.
Equilibrium theory of molecular fluids: Structure and freezing transitions
(Elsevier, 2014) Jokhan Ram
In this article we review equilibrium theory of molecular fluids which includes structure and freezing transitions. The application of the theory to evaluate the pair correlation functions using Integral Equation methods and Computer Simulations have been discussed. Freezing of classical complex fluids based on the density functional approach is also discussed and compare a variety of its versions. Transitions discussed are sensitive to the value of direct correlation functions of the effective liquid which is required as an input information in the theory. Accurate evaluation of pair correlation functions is emphasized. Calculation of these correlation functions which pose problems in the case of ordered phases is discussed. The pair correlation functions of the ordered phase, which are supposed to be made up of two contributions, one that preserves the symmetry of the isotropic phase and a second that breaks it, are discussed. A new free-energy functional developed for an inhomogeneous system that contains both symmetry conserved and symmetry broken parts of the direct pair correlation function is discussed. The most useful three dimensional reference interaction site model (3D-RISM) and its extension done recently by many workers is discussed. Application of this theory to a large variety of complex systems in combination with the density functional theory method implemented in the Amsterdam density functional software package is discussed. Coupling of the 3D-RISM salvation theory with molecular dynamics in the Amber molecular dynamics package is also given.The importance of the density functional theory for the study of the structure and phase behaviour of hard polyhedral is also discussed. The dynamical density functional and its generalized form applied for many important class of problems such as binary mixture, anisotropic particles dynamics of freezing and wetting, colloidal samples, particle self diffusion in complex environment, colloidal sedimentation and active self-propelled particles is discussed. © 2014 Elsevier B.V.
Integral equation theory for molecular fluids: Effect of quadrupolar interactions
(Elsevier Science Publishers B.V., 2000) Sushma Gupta; Jokhan Ram; Ram Chandra Singh
The Percus-Yevick (PY) and the hypernetted chain (HNC) integral equations have been solved for fluids of hard ellipsoids of a revolution represented by a hard Gaussian overlap model and for fluids of quadrupolar hard Gaussian overlap model. The structural and thermodynamic properties of the isotropic phase are discussed in detail. Ellipsoids with length-to-width ratios of 1.792, 3.0, 4.0 and 5.0 are considered and results are reported for different densities and quadrupole moments. It is shown that both the HNC and PY theories are in reasonable agreement with the computer simulation results.
Molecular theory of elastic constants of liquid crystals. III. Application to smectic phases with tilted orientational order
(2001) Yashwant Singh; Jokhan Ram
Using the density-functional formalism we derive an expression for the distortion free energy of systems with continuous broken symmetry and use it to derive an expression for the elastic constants of smectic phases in which the director is tilted with respect to the smectic layer normal. As in the previous papers of this series [Y. Singh, S. Singh, and K. Rajesh, Phys. Rev. A 45, 974 (1992); Y. Singh, K. Rajesh, V. J. Menon, and S. Singh, Phys. Rev. E 49, 501 (1994)], the expressions for the elastic constants are written in terms of order and structural parameters. The structural parameters involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. The density of this effective isotropic liquid depends on the nature and amount of ordering present in the system and is evaluated self-consistently. We estimate the value of elastic constants using reasonable guesses for the order and structural parameters. © 2001 The American Physical Society.
Pair correlation functions and a free energy functional for the nematic phase
(American Institute of Physics Inc., 2007) Pankaj Mishra; Swarn Lata Singh; Jokhan Ram; Yashwant Singh
In this paper we have presented the calculation of pair correlation functions in a nematic phase for a model of spherical particles with the long-range anisotropic interaction from the mean spherical approximation (MSA) and the Percus-Yevick (PY) integral equation theories. The results found from the MSA theory have been compared with those found analytically by Holovko and Sokolovska [J. Mol. Liq. 82, 161 (1999)]. A free energy functional which involves both the symmetry conserving and symmetry broken parts of the direct pair correlation function has been used to study the properties of the nematic phase. We have also examined the possibility of constructing a free energy functional with the direct pair correlation function which includes only the principal order parameter of the ordered phase and found that the resulting functional gives results that are in good agreement with the original functional. The isotropic-nematic transition has been located using the grand thermodynamic potential. The PY theory has been found to give a nematic phase with pair correlation function harmonic coefficients having all the desired features. In a nematic phase the harmonic coefficient of the total pair correlation function h (x1, x2) connected with the correlations of the director transverse fluctuations should develop a long-range tail. This feature has been found in both the MSA and PY theories. © 2007 American Institute of Physics.
Solution of the Percus-Yevick equation for pair-correlation functions of molecular fluids
(1994) Jokhan Ram; Ram Chandra Singh; Yashwant Singh
The Percus-Yevick (PY) integral equation has been solved for two model fluids: (i) a fluid of hard ellipsoids of a revolution represented by a Gaussian overlap model, and (ii) a fluid the molecules of which interact via a Gay-Berne [J. Chem. Phys. 74, 3316 (1981)] model potential. The method used involves an expansion of angle dependent functions appearing in the integral equation in terms of spherical harmonics. The dependence of the accuracy of the results on the number of terms taken in the basis set is explored for both fluids at different densities, temperatures, and lengths to width ratios of the molecules. We have compared our results with those of computer simulations wherever they are available. We find that the PY theory gives reasonable values of the harmonic coefficients for both fluids at all fluid densities when all terms involving the index l up to six in the expansion are considered. For the Gay-Berne fluid we have developed a perturbation expansion for a calculation of the structure and thermodynamic properties of the isotropic phase. © 1994 The American Physical Society.
Structure and freezing of a fluid of long elongated molecules
(2004) Pankaj Mishra; Jokhan Ram; Yashwant Singh
The pair correlation functions of a fluid of long elongated molecules interacting via the Gay-Berne pair potential are calculated using the Percus-Yevick integral equation theory. Numerical accuracy has been examined by considering a large number of spherical harmonic coefficients for each orientation-dependent functions for a system of molecules having a length-to-breadth ratio equal to 4.4 at different densities and temperatures. The pair correlation functions of the isotropic fluid found from the Percus-Yevick theory have been used in the density-functional theory to locate the isotropic-nematic, isotropic-smectic A and nematic-smectic A transitions. It is found that at low temperatures the fluid freezes directly into the smectic A phase on increasing the density. The nematic phase is found to stabilize in between the isotropic and smectic A phases only at high temperatures and high densities. The calculated phase diagram is in good qualitative agreement with computer simulation results.
Structure and freezing of fluids interacting via the Gay-Berne (n - 6) potentials
(2002) Ram C. Singh; Jokhan Ram; Yashwant Singh
We have calculated the pair-correlation functions of a fluid interacting via the Gay-Berne (n -6) pair potentials using the Percus-Yevick integral equation theory and have shown how these correlations depend on the value of n that measures the sharpness of the repulsive core of the pair potential. These results have been used in the density-functional theory to locate the freezing transitions of these fluids. We have used two different versions of the theory known as the second order and the modified weighted-density-functional theory and examined the freezing of these fluids for 8 ≤ n ≤ 30 and in the reduced temperature range lying between 0.65 and 1.25 into the nematic and the smectic A phases. For none of these cases smectic A phase was found to be stabilized though in some range of temperature for a given n it appeared as a metastable state. We have examined the variation of freezing parameters for the isotropic-nematic transition with temperature and n. We have also compared our results with simulation results wherever they are available. While we find that the density-functional theory is good to study the freezing transitions in such fluids the structural parameters found from the Percus-Yevick theory need to be improved particularly at high temperatures and lower values of n. © 2002 The American Physical Society.
Structure and freezing of fluids interacting via the Gay-Berne [formula presented] potentials
(2002) Ram C. Singh; Jokhan Ram; Yashwant Singh
We have calculated the pair-correlation functions of a fluid interacting via the Gay-Berne [formula presented] pair potentials using the Percus-Yevick integral equation theory and have shown how these correlations depend on the value of n that measures the sharpness of the repulsive core of the pair potential. These results have been used in the density-functional theory to locate the freezing transitions of these fluids. We have used two different versions of the theory known as the second order and the modified weighted-density-functional theory and examined the freezing of these fluids for [formula presented] and in the reduced temperature range lying between 0.65 and 1.25 into the nematic and the smectic A phases. For none of these cases smectic A phase was found to be stabilized though in some range of temperature for a given n it appeared as a metastable state. We have examined the variation of freezing parameters for the isotropic-nematic transition with temperature and [formula presented] We have also compared our results with simulation results wherever they are available. While we find that the density-functional theory is good to study the freezing transitions in such fluids the structural parameters found from the Percus-Yevick theory need to be improved particularly at high temperatures and lower values of [formula presented]. © 2002 The American Physical Society.
Structures and phase transition in a two-dimensional system of Gay-Berne molecules
(Elsevier B.V., 2019) Pallabi Kundu; Pankaj Mishra; Anubha Jaiswal; Jokhan Ram
We have used Percus-Yevick liquid integral equation theory and classical density functional theory of freezing to study the structure and isotropic-nematic phase transitions in a two-dimensional system of soft ellipses interacting via full Gay-Berne interaction potential. The accuracy of the pair-correlation functions given by integral equation theory has been tested by those obtained by NVT Monte-Carlo simulation. The theory is found to overestimate the structure as we move to either higher density or to the case of a longer aspect ratio. Isotropic-nematic transition parameters have been calculated for three different systems of ellipses characterized by their major to minor axis ratio κ=3.0,3.5 and 4.0 at temperature T*=2.0. The same has been calculated at T*=1.0 for the system with κ=3.0. Nematic phase is found to stabilize for all the 2D systems of GB ellipses. Isotropic-nematic transition is found to be weakly first order. © 2019 Elsevier B.V.
The Percus-Yevick approximation for quadrupolar molecular fluids
(2009) Ram Chandra Singh; Braj Mohan Singh; Jokhan Ram
The Percus-Yevick integral equation theory has been solved to study the equilibrium and structural properties of quadrupolar Gay-Berne fluids. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 have been considered. Molecules with length-to-breadth ratios 3.0 and 4.0 have been considered and results are reported for different densities, temperatures, and quadrupole moments. The values of pair correlation functions have been compared with the available computer simulation results. © 2009 IOP Publishing Ltd.
Thermodynamically self-consistent integral equation theory for pair-correlation functions of molecular fluids-II
(2006) Ram Chandra Singh; Jokhan Ram
A closure for the pair-correlation functions of molecular fluids is described in which the hypernetted-chain and the Percus-Yevick approximations are "mixed" as a function of interparticle separation. An adjustable parameter α in the mixing function is used to enforce thermodynamic consistency, by which it is meant that identical results are obtained when the equations of state are calculated via the virial and compressibility routes, respectively. The mixed integral equation for the pair-correlation functions has been solved for two model fluids: (i) a fluid of the hard Gaussian overlap model, and (ii) a fluid the molecules of which interact via a modified Gay-Berne model potential. For the modified Gay-Berne fluid we have slightly modified the original Gay-Berne potential to study the effect of attraction on hard core systems. The pair-correlation functions of the isotropic phase which enter in the density-functional theory as input informations have been calculated from the integral equation theories for these model fluids. We have used two different versions of the density-functional theory known as the second order and modified weighted-density-functional theory to locate the isotropic-nematic (I-N) transitions and calculate the values of transition parameters for the hard Gaussian overlap and modified Gay-Berne model fluids. We have compared our results with those of computer simulations wherever they are available. We find that the density-functional theory is good to study the I-N transition in molecular fluids if the values of the pair-correlation functions in the isotropic phase are accurately known. © 2006.
Thermodynamically self-consistent integral-equation theory for pair-correlation functions of a molecular fluid
(1996) Ram Chandra Singh; Jokhan Ram; Yashwant Singh
We propose a “mixed” integral equation for the pair correlation function of molecular fluids which interpolates between the hypernetted-chain and Percus-Yevick approximations. Thermodynamic consistency between the virial and compressibility equation of state is achieved by varying a single parameter in a suitably chosen mixing function. The integral equation proposed here generalizes the suggestion by Rogers and Young [Phys. Rev. A 30, 999 (1984)] to an angle-dependent pair potential. When compared to available computer simulation data, the equation is found to yield excellent results for both the thermodynamic properties and the pair-correlation functions. © 1996 The American Physical Society.
Tunable attractive interaction and the phase diagram of a system of Gay-Berne ellipsoids: A density functional approach
(Elsevier B.V., 2016) Shikha Dwivedi; Pankaj Mishra; Ram Chandra Singh; Jokhan Ram
Density functional theory has been used to investigate the effect of the variation of attractive interaction on phase diagram of a system of axially symmetric liquid crystalline molecules interacting via Gay-Berne intermolecular potential. The pair correlation functions of the isotropic fluid, used as structural input in the density functional theory have been calculated by using Percus-Yevick integral equation theory. Considering the isotropic, nematic and smectic A phases as the candidate structures, we observe that the transition parameters and the topology of the phase diagram changes significantly with the variation in the strength of attractive interaction between the molecules. The dominance of the attractive interaction over repulsive one, is found to cause an enhanced tendency of the system to freeze into smectic A phase. Both isotropic-nematic and nematic-smectic A transition densities and pressure are found to decrease as we increase the strength of the attraction among the particles. The pair correlation functions and phase transition parameters are compared with the available computer simulation results of the similar model potential and are found to be in good qualitative agreement. © 2016 Elsevier B.V.