High-Resolution Solid State C-13 NMR Studies of Bent-Core Mesogens of Benzene and Thiophene

Bent-core mesogens are an important class of thermotropic liquid crystals as they exhibit unusual properties as well as morphologies distinctly different from rodlike mesogens. Two bent-core mesogens with differing center rings namely benzene and thiophene are considered and investigated using high-resolution oriented solid state C-13 NMR method in their liquid crystalline phases. The mesogens exhibit different phase sequences with the benzene-based mesogen showing a B-1 phase, while the one based on thiophene showing nematic and smectic C phases. The 2-dimensional separated local field (2D-SLF) NMR method was used to obtain the C-13-H-1 dipolar couplings of carbons in the center ring as well as in the side-wing phenyl rings. Couplings, characteristic of the type of the center ring, that also provide orientational information on the molecule in the magnetic field were observed. Together with the dipolar couplings of the side-wing phenyl ring carbons from which the local order parameters of the different subunits of the core could be extracted, the bent angle of the mesogenic molecule could be obtained. Accordingly, for the benzene mesogen in its B-1 phase at 145 degrees C, the center ring methine C-13-H-1 dipolar couplings were found to be significantly larger (9.5-10.2 kHz) compared to those of the side-wing rings (1.6-2.1 kHz). From the local order parameter values of the center (0.68) as well as the side-wing rings (0.50), a bent-angle of 130.3 degrees for this mesogen was obtained. Interestingly, for the thiophene mesogen in its smectic C phase at 210 degrees C, the C-13-H-1 dipolar coupling of the center ring methine carbon (2.11 kHz) is smaller than those of the side-wing phenyl ring carbons (2.75-3.00 kHz) which is a consequence of the different structures of the thiophene and the benzene rings. These values correspond to local order parameters of 0.85 for the center thiophene ring and 0.76 for the first side-wing phenyl ring and a bent-angle of 149.2 degrees. Thus, the significant differences in the dipolar couplings and the order parameter values between different parts in the rigid core of the mesogens are a direct consequence of the nature of the center ring and the bent structure of the molecule. The present investigation thus highlights the ability of the C-13 2D-SLF technique to provide the geometry of the bent-core mesogens in a straightforward manner through the measurement of the C-13-H-1 dipolar couplings.

Molecular topology of three ring nematogens from C-13-H-1 dipolar couplings

Molecules in their liquid crystalline phase undergo rotational motion about the long axis of the molecule and the shape adopted by the rotating molecule plays an important role in influencing the mesophase morphology. In this context, obtaining the topology and the relative orientation of the different sub-units are important steps. For studying the liquid crystalline phase, C-13 NMR spectroscopy is a convenient method and for certain specifically designed nematogens, 2-dimensional separated local field (2D-SLF) NMR spectroscopy provides a particularly simple and straightforward means of arriving at the molecular topology. We demonstrate this approach on two three ring based nematogens designed with a phenyl or a thiophene ring at one of the termini. From the C-13-H-1 dipolar couplings of the terminal carbon obtained using the 2D-SLF NMR technique, the order parameter of the local symmetry axis of the terminal phenyl ring as well as of the long molecular axis could be easily estimated. For the thiophene nematogen, the lack of symmetry of the thiophene moiety necessitates some additional computational steps. The results indicate that the thiophene unit has its local ordering axis oriented away from the long molecular axis by a small angle, consistent with a bent structure expected in view of the thiophene geometry. The experiment also demonstrates the ability of 2D-SLF NMR to provide high resolution spectra by separation of several overlapped resonances in terms of their C-13-H-1 dipolar couplings. The results are consistent with a rod-like topology of the core of the investigated mesogens. The investigation demonstrates the potential of 2D-SLF NMR C-13 spectroscopy for obtaining atomistic level information and its utility for topological studies of different mesogens.

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.

Sensitivity of polarization fluctuations to the nature of protein-water interactions: Study of biological water in four different protein-water systems

Since the time of Kirkwood, observed deviations in magnitude of the dielectric constant of aqueous protein solution from that of neat water (similar to 80) and slower decay of polarization have been subjects of enormous interest, controversy, and debate. Most of the common proteins have large permanent dipole moments (often more than 100 D) that can influence structure and dynamics of even distant water molecules, thereby affecting collective polarization fluctuation of the solution, which in turn can significantly alter solution's dielectric constant. Therefore, distance dependence of polarization fluctuation can provide important insight into the nature of biological water. We explore these aspects by studying aqueous solutions of four different proteins of different characteristics and varying sizes, chicken villin headpiece subdomain (HP-36), immunoglobulin binding domain protein G (GB1), hen-egg white lysozyme (LYS), and Myoglobin (MYO). We simulate fairly large systems consisting of single protein molecule and 20000-30000 water molecules (varied according to the protein size), providing a concentration in the range of similar to 2-3 mM. We find that the calculated dielectric constant of the system shows a noticeable increment in all the cases compared to that of neat water. Total dipole moment auto time correlation function of water < dM(W) (0)delta M-W (t) > is found to be sensitive to the nature of the protein. Surprisingly, dipole moment of the protein and total dipole moment of the water molecules are found to be only weakly coupled. Shellwise decomposition of water molecules around protein reveals higher density of first layer compared to the succeeding ones. We also calculate heuristic effective dielectric constant of successive layers and find that the layer adjacent to protein has much lower value (similar to 50). However, progressive layers exhibit successive increment of dielectric constant, finally reaching a value close to that of bulk 4-5 layers away. We also calculate shellwise orientational correlation function and tetrahedral order parameter to understand the local dynamics and structural re-arrangement of water. Theoretical analysis providing simple method for calculation of shellwise local dielectric constant and implication of these findings are elaborately discussed in the present work. (C) 2014 AIP Publishing LLC.

Acoustic phonon behavior of PbWO4 and BaWO4 probed by low temperature Brillouin spectroscopy

Temperature dependent acoustic phonon behavior of PbWO4 and BaWO4 using Brillouin spectroscopy has been explained for the first time. Low temperature Brillouin studies on PbWO4 and BaWO4 have been carried out from 320-20 K. In PbWO4, we observe a change in acoustic phonon mode behavior around 180 K. But in the case of BaWO4, we have observed two types of change in acoustic phonon mode behavior at 240 K and 130 K. The change in Brillouin shift omega and the slope d omega/dT are the order parameter for all kinds of phase transitions. Since we do not see hysteresis on acoustic phonon mode behavior in the reverse temperature experiments, these second order phase transitions are no related to structural phase change and could be related to acoustic phonon coupled electronic transitions. In PbWO4 he temperature driven phase transition at 180 K could be due to changes in he environment around he lead vacancy (V-pb(2-)) changes the electronic states. In the case of BaWO4, the phase transition at 240 K shows he decrease in penetration depth of WO3 impurity. So it becomes more metallic. The transition at 130 K could be he same electronic transitions as that of PbWO4 as function of temperature. The sound velocity and elastic moduli of BaWO4 shows that it could be the prominent material for acousto-optic device applications. (C) 2014 Elsevier Ltd. All rights reserved.

Structural investigation of resorcinol based symmetrical banana mesogens by XRD, NMR and polarization measurements

Synthesis and structural characterization of two novel symmetrical banana mesogens built from resorcinol with seven phenyl rings linked by ester and imine with a terminal dodecyl/dodecyloxy chain has been carried out. Density functional theory (DFT) has been employed for obtaining the geometry optimized structures, the dipole moments and C-13 NMR chemical shifts. The HOPM and DSC studies revealed enantiotropic B-2 and B-7 phases for the dodecyl and dodecyloxy homologs respectively. The powder X-ray studies of both the mesogens indicate the presence of layer ordering. The polarization measurements reveal an anti-ferroelectric switching for the B-2 phase of the dodecyl homolog whose structure has been identified as SmCSPA. The B-7 phase of the dodecyloxy homolog was found to be non-switchable. High resolution C-13 NMR study of the dodecyl homolog in its mesophase has been carried out. C-13-H-1 dipolar couplings obtained from the 2-dimensional separated local field spectroscopy experiment were used to obtain the orientational order parameters of the different segments of the mesogen. Very large C-13-H-1 dipolar couplings observed for the carbons of the central phenyl ring (9.7-12.3 kHz) in comparison to the dipolar couplings of those of the side arm phenyl rings (less than 3 kHz) are a direct consequence of the ordering in the banana phase and the shape of the molecule. From the ratio of the local order parameter values, the bent-angle of the mesogen could be determined in a straight forward manner to be 120.5 degrees.

Tuning the metal-insulator transition in NdNiO3 heterostructures via Fermi surface instability and spin fluctuations

We employed in situ pulsed laser deposition (PLD) and angle-resolved photoemission spectroscopy (ARPES) to investigate the mechanism of the metal-insulator transition (MIT) in NdNiO3 (NNO) thin films, grown on NdGaO3(110) and LaAlO3(100) substrates. In the metallic phase, we observe three-dimensional hole and electron Fermi surface (FS) pockets formed from strongly renormalized bands with well-defined quasiparticles. Upon cooling across the MIT in NNO/NGO sample, the quasiparticles lose coherence via a spectral weight transfer from near the Fermi level to localized states forming at higher binding energies. In the case of NNO/LAO, the bands are apparently shifted upward with an additional holelike pocket forming at the corner of the Brillouin zone. We find that the renormalization effects are strongly anisotropic and are stronger in NNO/NGO than NNO/LAO. Our study reveals that substrate-induced strain tunes the crystal field splitting, which changes the FS properties, nesting conditions, and spin-fluctuation strength, and thereby controls the MIT via the formation of an electronic order parameter with QAF similar to (1/4,1/4,1/4 +/- delta).

Composition dependent multiple structural transformations of myoglobin in aqueous ethanol solution: A combined experimental and theoretical study

Experimental studies (circular dichroism and ultra-violet (UV) absorption spectra) and large scale atomistic molecular dynamics simulations (accompanied by order parameter analyses) are combined to establish a number of remarkable (and unforeseen) structural transformations of protein myoglobin in aqueous ethanol mixture at various ethanol concentrations. The following results are particularly striking. (1) Two well-defined structural regimes, one at x(EtOH) similar to 0.05 and the other at x(EtOH) similar to 0.25, characterized by formation of distinct partially folded conformations and separated by a unique partially unfolded intermediate state at x(EtOH) similar to 0.15, are identified. (2) Existence of non-monotonic composition dependence of (i) radius of gyration, (ii) long range contact order, (iii) residue specific solvent accessible surface area of tryptophan, and (iv) circular dichroism spectra and UV-absorption peaks are observed. Interestingly at x(EtOH) similar to 0.15, time averaged value of the contact order parameter of the protein reaches a minimum, implying that this conformational state can be identified as a molten globule state. Multiple structural transformations well known in water-ethanol binary mixture appear to have considerably stronger effects on conformation and dynamics of the protein. We compare the present results with studies in water-dimethyl sulfoxide mixture where also distinct structural transformations are observed along with variation of co-solvent composition. (C) 2015 AIP Publishing LLC.

Structure and Dynamics of Octamethylcyclotetrasiloxane Confined between Mica Surfaces

Using a molecular model for octamethylcydotetrasiloxane (OMCTS), molecular dynamics simulations are carried out to probe the phase state of OMCTS confined between two mica surfaces in equilibrium With a reservoir. Molecular dynamics simulations are carried out for elevations ranging from 5 to 35 K above the melting point for the OMCTS model used in this study. The Helmholtz free energy is, computed for a specific confinement using the :two-phase thermodynamic (2PT) method. Analysis of the in-plane pair correlation functions did not reveal signatures of freezing even under an extreme confinement of two layers. OMCTS is found to orient with a wide distribution of orientations with respect to the mica surface, with a distinct preference for the surface parallel configuration in the contact layers. The self-intermediate scattering function is found to decay with increasing relaxation times as the surface separation is decreased, and the two-step relaxation in the scattering function, a signature of glassy dynamics, distinctly evolves as the temperature is lowered. However, even at 5 K above the melting point, we did not observe a freezing transition and the self-intermediate scattering functions relax within 200 ps for the seven-layered confined system. The self diffusivity and relaxation times obtained from the Kohlrausch-Williams-Watts stretched exponential fits to the late alpha-relaxation exhibit power law scalings with the packing fraction as predicted by mode coupling theory. A distinct discontinuity in the Helmholtz free energy, potential energy, and a sharp change in the local bond order parameter, Q(4), was observed at 230 K for a five-layered system upon cooling, indicative of a first-order transition. A freezing point depression of about 30 K was observed for this five-layered confined system, and at the lower temperatures, contact layers were found to be disordered with long-range order present only in the inner layers. These dynamical signatures indicate that confined OMCTS undergoes a slowdown akin to a fluid approaching a glass transition upon increasing confinement, and freezing under confinement would require substantial subcooling below the bulk melting point of OMCTS.

Optimal management of beaver population using a reduced-order distributed parameter model and single network adaptive critics

Beavers are often found to be in conflict with human interests by creating nuisances like building dams on flowing water (leading to flooding), blocking irrigation canals, cutting down timbers, etc. At the same time they contribute to raising water tables, increased vegetation, etc. Consequently, maintaining an optimal beaver population is beneficial. Because of their diffusion externality (due to migratory nature), strategies based on lumped parameter models are often ineffective. Using a distributed parameter model for beaver population that accounts for their spatial and temporal behavior, an optimal control (trapping) strategy is presented in this paper that leads to a desired distribution of the animal density in a region in the long run. The optimal control solution presented, imbeds the solution for a large number of initial conditions (i.e., it has a feedback form), which is otherwise nontrivial to obtain. The solution obtained can be used in real-time by a nonexpert in control theory since it involves only using the neural networks trained offline. Proper orthogonal decomposition-based basis function design followed by their use in a Galerkin projection has been incorporated in the solution process as a model reduction technique. Optimal solutions are obtained through a "single network adaptive critic" (SNAC) neural-network architecture.

Reduced Order Suboptimal Control Design for a Class of Nonlinear Distributed Parameter Systems Using POD and /spl thetas/-D Techniques

A new computational tool is presented in this paper for suboptimal control design of a class of nonlinear distributed parameter systems. First proper orthogonal decomposition based problem-oriented basis functions are designed, which are then used in a Galerkin projection to come up with a low-order lumped parameter approximation. Next, a suboptimal controller is designed using the emerging /spl thetas/-D technique for lumped parameter systems. This time domain sub-optimal control solution is then mapped back to the distributed domain using the same basis functions, which essentially leads to a closed form solution for the controller in a state feedback form. Numerical results for a real-life nonlinear temperature control problem indicate that the proposed method holds promise as a good suboptimal control design technique for distributed parameter systems.

Unsteady laminar incompressible second-order boundary-layer flow at a three-dimensional stagnation point

The unsteadely laminar incompressible second-order boundary-layer flow at the stagnation point of a three-dimensional body has been studied for both nodal and saddle point regions. The effects of mass transfer and Prandtl number have been taken into account. The equations governing the flow have been solved numerically using an implicit finite-difference scheme. It has been found that the parameter characterizing the unsteadiness in the velocity of the free stream, the nature of the stagnation point, the mass transfer and Prandtl number strongly affect the second-order skin friction and heat transfer. The overall skin friction becomes less due to second-order effects but the heat transfer has the opposite behaviour. For large injection, the second-order skin-friction and heat-transfer results prevail over the first-order boundary layer results whereas for the case of large suction the behaviour is just the opposite.

An account of chronological developments in control of distributed parameter systems

Control systems arising in many engineering fields are often of distributed parameter type, which are modeled by partial differential equations. Decades of research have lead to a great deal of literature on distributed parameter systems scattered in a wide spectrum.Extensions of popular finite-dimensional techniques to infinite-dimensional systems as well as innovative infinite-dimensional specific control design approaches have been proposed. A comprehensive account of all the developments would probably require several volumes and is perhaps a very difficult task. In this paper, however, an attempt has been made to give a brief yet reasonably representative account of many of these developments in a chronological order. To make it accessible to a wide audience, mathematical descriptions have been completely avoided with the assumption that an interested reader can always find the mathematical details in the relevant references.

Dissipativeness and Stability of a Class of Distributed Parameter Systems

Input-output stability of linear-distributed parameter systems of arbitrary order and type in the presence of a distributed controller is analyzed by extending the concept of dissipativeness, with certain modifications, to such systems. The approach is applicable to systems with homogeneous or homogenizable boundary conditions. It also helps in generating a Liapunov functional to assess asymptotic stability of the system.