Sign Of The Order Parameter In Oriented Systems And Its Utility In The Study Of The Dynamic Properties Of Molecules

Novel one and two dimensional NMR techniques are proposed and utilized for the determination of the signs of the order parameters used for the study of the mobility of the fatty acid chains. The experiments designed to extract this information involve the use of the intensities of the side bands in the spectra of oriented systems spinning at the magic angle. Advantages of the two dimensional technique over the one dimensional method are discussed. The utility of the method in the study of the dynamic properties of membranes and model systems is pointed out.

Determination of the sign of the order parameter from MAS spectra of oriented molecules

The use of the intensities of the spinning sidebands in the magic-angle spinning spectra of oriented molecules is proposed for the determination of the signs of the order parameters. The method is demonstrated for benzene and chloroform oriented in nematic phases of liquid crystals. On the basis of the theoretical expressions derived for the various order sidebands, the applicability of the method for different experimental conditions is discussed.

Dynamo onset as a first-order transition: Lessons from a shell model for magnetohydrodynamics

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydro-dynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number Pr-M and the magnetic Reynolds number Re-M. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (Pr-M(-1), Re-M) plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

GINZBURG-LANDAU LIKE THEORY OF HIGH TEMPERATURE SUPERCONDUCTIVITY IN THE CUPRATES: EMERGENT d-WAVE ORDER

High temperature superconductivity in the cuprates remains one of the most widely investigated, constantly surprising and poorly understood phenomena in physics. Here, we describe briefly a new phenomenological theory inspired by the celebrated description of superconductivity due to Ginzburg and Landau and believed to describe its essence. This posits a free energy functional for the superconductor in terms of a complex order parameter characterizing it. We propose that there is, for superconducting cuprates, a similar functional of the complex, in plane, nearest neighbor spin singlet bond (or Cooper) pair amplitude psi(ij). Further, we suggest that a crucial part of it is a (short range) positive interaction between nearest neighbor bond pairs, of strength J'. Such an interaction leads to nonzero long wavelength phase stiffness or superconductive long range order, with the observed d-wave symmetry, below a temperature T-c similar to zJ' where z is the number of nearest neighbors; d-wave superconductivity is thus an emergent, collective consequence. Using the functional, we calculate a large range of properties, e. g., the pseudogap transition temperature T* as a function of hole doping x, the transition curve T-c(x), the superfluid stiffness rho(s)(x, T), the specific heat (without and with a magnetic field) due to the fluctuating pair degrees of freedom and the zero temperature vortex structure. We find remarkable agreement with experiment. We also calculate the self-energy of electrons hopping on the square cuprate lattice and coupled to electrons of nearly opposite momenta via inevitable long wavelength Cooper pair fluctuations formed of these electrons. The ensuing results for electron spectral density are successfully compared with recent experimental results for angle resolved photo emission spectroscopy (ARPES), and comprehensively explain strange features such as temperature dependent Fermi arcs above T-c and the ``bending'' of the superconducting gap below T-c.

Structural characterization and molecular order of rodlike mesogens with three- and four-ring core by XRD and C-13 NMR spectroscopy

Structural characterizations using XRD and C-13 NMR spectroscopy of two rodlike mesogens consisting of (i) three phenyl ring core with a polar cyano terminal and (ii) four phenyl ring core with flexible dodecyl terminal chain are presented. The three-ring-core mesogen with cyano terminal exhibits enantiotropic smectic A phase while the four-ring mesogen reveals polymesomorphism and shows enantiotropic nematic, smectic C, and tilted hexatic phases. The molecular organization in the three-ring mesogen is found to be partial bilayer smectic Ad type, and the interdigitation of the molecules in the neighboring layers is attributed to the presence of the polar terminal group. For the four-ring mesogen, the XRD results confirm the existence of the smectic C and the tilted hexatic mesophases. A thermal variation of the layer spacing across the smectic C phase followed by a discrete jump at the transition to the tilted hexatic phase is also observed. The tilt angles have been estimated to be about 45 degrees in the smectic C phase and about 40 degrees in tilted hexatic phase. C-13 NMR results indicate that in the mesophase the molecules are aligned parallel to the magnetic field. From the C-13-H-1 dipolar couplings determined from the 2D experiments, the overall order parameter for the three-ring mesogen in its smectic A phase has been estimated to be 0.72 while values ranging from 0.88 to 0.44 have been obtained for the four-ring mesogen as it passes from the tilted hexatic to the nematic phase. The orientations of the different rings of the core unit with respect to each other and also with respect to the long axis of the molecule have also been obtained.

Orientational order as the origin of the long-range hydrophobic effect

The long range attractive force between two hydrophobic surfaces immersed in water is observed to decrease exponentially with their separation-this distance-dependence of effective force is known as the hydrophobic force law (HFL). We explore the microscopic origin of HFL by studying distance-dependent attraction between two parallel rods immersed in 2D Mercedes Benz model of water. This model is found to exhibit a well-defined HFL. Although the phenomenon is conventionally explained by density-dependent theories, we identify orientation, rather than density, as the relevant order parameter. The range of density variation is noticeably shorter than that of orientational heterogeneity. The latter is comparable to the observed distances of hydrophobic force. At large separation, attraction between the rods arises primarily from a destructive interference among the inwardly propagating oppositely oriented heterogeneity generated in water by the two rods. As the rods are brought closer, the interference increases leading to a decrease in heterogeneity and concomitant decrease in free energy of the system, giving rise to the effective attraction. We notice formation of hexagonal ice-like structures at the onset of attractive region which suggests that metastable free energy minimum may play a role in the origin of HFL. (C) 2015 AIP Publishing LLC.

Use of polydispersity index as control parameter to study melting/freezing of Lennard-Jones system: Comparison among predictions of bifurcation theory with Lindemann criterion, inherent structure analysis and Hansen-Verlet rule

Using polydispersity index as an additional order parameter we investigate freezing/melting transition of Lennard-Jones polydisperse systems (with Gaussian polydispersity in size), especially to gain insight into the origin of the terminal polydispersity. The average inherent structure (IS) energy and root mean square displacement (RMSD) of the solid before melting both exhibit quite similar polydispersity dependence including a discontinuity at solid-liquid transition point. Lindemann ratio, obtained from RMSD, is found to be dependent on temperature. At a given number density, there exists a value of polydispersity index (delta (P)) above which no crystalline solid is stable. This transition value of polydispersity(termed as transition polydispersity, delta (P) ) is found to depend strongly on temperature, a feature missed in hard sphere model systems. Additionally, for a particular temperature when number density is increased, delta (P) shifts to higher values. This temperature and number density dependent value of delta (P) saturates surprisingly to a value which is found to be nearly the same for all temperatures, known as terminal polydispersity (delta (TP)). This value (delta (TP) similar to 0.11) is in excellent agreement with the experimental value of 0.12, but differs from hard sphere transition where this limiting value is only 0.048. Terminal polydispersity (delta (TP)) thus has a quasiuniversal character. Interestingly, the bifurcation diagram obtained from non-linear integral equation theories of freezing seems to provide an explanation of the existence of unique terminal polydispersity in polydisperse systems. Global bond orientational order parameter is calculated to obtain further insights into mechanism for melting.

Solute induced liquid crystalline behaviour of a quaternary ammonium salt and its application to structure determination

A new liquid crystalline phase, induced by the addition of small amounts of a non-mesogenic solute (such as dimethyl sulphoxide or methyl iodide) to a quaternary ammonium salt, N-methyl-N,N,N-trioctadecylammonium iodide (MTAI), has been detected by NMR and optical microscopic studies. In some cases, there is a coexistence of nematic and smectic phases. Information on the ordering of the phases in the magnetic field of the spectrometer has been derived from NMR spectra of a dissolved molecule, C-13-enriched methyl iodide. The low order parameter of the pure thermotropic nematic phase of the salt provides first-order spectra of the dissolved oriented molecules. Analyses of spectra of cis,cis-mucononitrile exemplifies the utility of the MTAI nematic phase in the determination of structural parameters of the solute.

Cluster model of the glass transition

A cluster model of the glass transition has been developed, treating the relative size of the cluster as an order parameter. The model accounts for some of the features of the glass transition.

NMR Investigations on Di- and Tri-Azanaphthalenes Oriented in Liquid Crystals

Proton NMR spectra of 1,3-diazanaphthalene and 1,2,4-triazanaphthalene have been investigated in the nematic phase of three liquid crystals. The spectral analysis provided direct dipole-dipole couplings which have been used to derive the molecular structure. Geometry of the phenyl ring in both the molecules deviates from the regular hexagonal structure. Signs of the order parameter of the largest magnitude are opposite in liquid crystals with positive diamagetic anisotropies.

Mean-field results of a lattice-gas model of multilayer adsorption

A lattice-gas model of multilayer adsorption has been solved in the mean-field approximation by a different numerical method. Earlier workers obtained a single solution for all values of temperature and pressure. In the present work, multiple solutions have been obtained in certain regions of temperature and pressure which give rise to bysteresis in the adsorption isotherm. In addition, we have obtained a parameter which behaves like an order parameter for the transition. The potential-energy function shows a double minimum in the region of bysteresis and a single maximum elsewhere.

Esr study of (SO4)2- dynamics in relation to the ferroelectric phase transition in ammonium sulfate

Ferroelectric phase transition in ammonium sulfate has been studied by ESR of CrO43- radical substituting for SO42- ion in (NH4)2SO4. In addition to discontinuous changes at Tc, certain continuous changes are observed in ESR parameters of this probe below Tc, which reflect the role of the sulfate ion in the phase transition. A microscopic mechanism of the phase transition is proposed and discussed in terms of the change of orientation of the sulfate tetrahedron through a finite angle. The degree of the change of orientation below Tc is thought to be the possible order parameter of the phase transition.

Structure and dynamics of two-dimensional sheared granular flows

The structure and dynamics of the two-dimensional linear shear flow of inelastic disks at high area fractions are analyzed. The event-driven simulation technique is used in the hard-particle limit, where the particles interact through instantaneous collisions. The structure (relative arrangement of particles) is analyzed using the bond-orientational order parameter. It is found that the shear flow reduces the order in the system, and the order parameter in a shear flow is lower than that in a collection of elastic hard disks at equilibrium. The distribution of relative velocities between colliding particles is analyzed. The relative velocity distribution undergoes a transition from a Gaussian distribution for nearly elastic particles, to an exponential distribution at low coefficients of restitution. However, the single-particle distribution function is close to a Gaussian in the dense limit, indicating that correlations between colliding particles have a strong influence on the relative velocity distribution. This results in a much lower dissipation rate than that predicted using the molecular chaos assumption, where the velocities of colliding particles are considered to be uncorrelated.

Coexistence curve of acetonitrile and cyclohexane liquid system

The paper reports a detailed determination of the coexistence curve for the binary liquid system acetonitrile+cyclohexane, which have very closely matched densities and the data points get affected by gravity only for t=(Tc−T)/ Tc[approximately-equal-to]10−6. About 100 samples were measured over the range 10−6