Orientational Order Transition Research Articles

Effect of graphene nanoparticles on the isotropic to nematic phase transition

ABSTRACT A model combining with Flory-Huggins theory of isotropic mixing and Landau theory is developed to describe the effect of graphene nanoparticles on the isotropic to nematic phase transition. The temperature and concentration of graphene nanoparticles dependence on the orientational order parameter, transition temperature and thermodynamic quantities near the isotropic to nematic phase transition are discussed. The orientational order parameter, transition temperature and enthalpy near the isotropic to nematic phase transition increase with the increase of graphene nanoparticles.

Orientational order and phase transitions in deuterated methane: a neutron total scattering and reverse Monte Carlo study

We report a study of the orientational order and phase transitions in crystalline deuterated methane, carried out using neutron total scattering and the reverse Monte Carlo method. The resultant atomic configurations are consistent with the average structures obtained from Rietveld refinement of the powder diffraction data, but additionally enable us to determine the C–D bond orientational distribution functions (ODF) for the disordered molecules in the high-temperature phase, and for both ordered and disordered molecules in the intermediate-temperature phase. We show that this approach gives more accurate information than can been obtained from fitting a bond ODF to diffraction data. Given the resurgence of interest in orientationally-disordered crystals, we argue that the approach of total scattering with the RMC method provides a unique quantification of orientational order and disorder.

An orientational order transition in a sheared suspension of anisotropic particles

Under Stokesian conditions, a neutrally buoyant non-Brownian spheroid in simple shear flow rotates indefinitely in any of a one-parameter family of closed (Jeffery) orbits characterized by an orbit constant $C$. The limiting values, $C=0$ and $C=\infty$, correspond to spinning and tumbling modes respectively. Hydrodynamics alone does not determine the distribution of spheroid orientations across Jeffery orbits in the absence of interactions, and the rheology of a dilute suspension of spheroids remains indeterminate. A combination of inertia and stochastic orientation fluctuations eliminates the indeterminacy. The steady-state Jeffery-orbit distribution arising from a balance of inertia and thermal fluctuations is shown to be of the Boltzmann equilibrium form, with a potential that depends on $C$, the particle aspect ratio ($\unicode[STIX]{x1D705}$), and a dimensionless shear rate ($Re\,Pe_{r}$, $Re$ and $Pe_{r}$ being the Reynolds and rotary Péclet numbers), and therefore lends itself to a novel thermodynamic interpretation in $C{-}\unicode[STIX]{x1D705}{-}Re\,Pe_{r}$ space. In particular, the transition of the potential from a single to a double-well structure, below a critical $\unicode[STIX]{x1D705}$, has similarities to a thermodynamic phase transition, and the small-$C$ and large-$C$ minima are therefore identified with spinning and tumbling phases. The hysteretic dynamics within the two-phase tumbling–spinning envelope renders the rheology sensitively dependent on the precise shear rate history, the signature in simple shear flow being a multivalued viscosity at a given shear rate. The tumbling–spinning transition identified here is analogous to the coil–stretch transition in the polymer physics literature. It should persist under more general circumstances, and has implications for the suspension stress response in inhomogeneous shearing flows.

Motility-Induced Phase Separation of Active Particles in the Presence of Velocity Alignment

Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and with the medium acting as a momentum sink, even momentum is not conserved. In this scenario, a mapping into an equilibrium system seems unlikely. Here, we show that an entropy functional can be derived for SPPs with velocity alignment and density-dependent speed, at least in the (orientationally) disordered phase. This non-trivial result has important physical consequences. The study of the entropy functional reveals that the system can undergo phase separation before the orientational-order phase transition known to occur in SPP systems with velocity alignment. Moreover, we indicate that the spinodal line is a function of the alignment sensitivity and show that density fluctuations as well as the critical spatial diffusion, that leads to phase separation, dramatically increase as the orientational-order transition is approached.

Monte Carlo simulation of the effects of higher-order anisotropy on the spin reorientation transition in the two-dimensional Heisenberg model with long-range interactions

The strength of perpendicular anisotropy is known to drive the spin reorientation in thin magnetic films. Here we consider the effect different order anisotropies have on two phase transitions; the spin reorientation transition and the orientational order transition. We find that the relative magnitude of different order anisotropies can significantly enhance or suppress the degree to which the system reorients. Specifically Monte Carlo simulations reveal significant changes in the cone angle and planar magnetization. In order to facilitate rapid computation we have developed a stream processing technique, suitable for use on GPU systems, for computing the transition probabilities in two dimensional systems with dipole interactions.

Phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls are investigated by using a cell dynamics simulation of the time-dependent Ginzburg—Landau theory. The morphological dependence of the wall-block interaction and the distance between walls (confinement degree) has been systematically studied, and the effect of repulsive interactions between different monomers is also discussed. It is interesting that multiple novel morphological transitions are observed by changing these factors, and various multilayered sandwich structures are formed in the mixture. Furthermore, the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed. From the simulation, we find that much richer morphologies can form in a binary mixture of diblock copolymers than those in a pure diblock copolymer. Our results provide an insight into the phase behaviors under parallel wall confinement and may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition in soft materials through confinement.

Domain patterns in a diblock copolymer-diblock copolymer mixture with oscillatory particles

We investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-diblock copolymer mixtures in the presence of periodic oscillatory particles. Under certain conditions, although the macrophase separation of a system is almost isotropic, microphase separation of one diblock copolymer takes place and becomes anisotropic gradually. By changing the oscillatory frequency and amplitude, the orientational order transition of a striped microphase structure from the state parallel to the oscillatory direction to the state perpendicular to the oscillatory direction is observed. We also find that the order transition occurs when we change the initial composition ratio. Furthermore, we examine the domain size and the orientational order parameter of microstructure in the process of orientational order transition. The results may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition of soft materials by changing the oscillatory field.

Orientational order transition of the striped microphase structure of a copolymer-homopolymer mixture under oscillatory particles

Based on the three-order-parameter model, we investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-homopolymer mixtures in the presence of periodic oscillatory particles. Under suitable conditions, although the macrophase separation of a system is almost isotropic, the microphase separation of the system will be significantly perturbed by the oscillatory field, and composition fluctuations are suppressed anisotropically. The isotropy of the microphase will be broken up. By changing the oscillatory amplitude and frequency, we observe the orientational order transition of a striped microphase structure from the isotropic state to a state parallel to the oscillatory direction, and from the parallel state to a state perpendicular to the oscillatory direction. We examine, in detail, the microstructure and orientational order parameter as well as the domain size in the process of orientational order transition under the oscillatory field. We study also how the microphase structure changes with the composition ratio of homopolymers and copolymers in mixtures. The results suggest that our model system may provide a simple way to realize orientational order transition of soft materials.

Surface ordering transitions at a liquid crystal-solid interface above the isotropic smectic-A transition.

The degree of orientational order induced by confining cylindrical surfaces is monitored via deuteron nuclear magnetic resonance linesplitting and linewidth above the smectic-A to isotropic phase transition. The orientational order strongly depends on the length of the surfactant coupling molecule, on the surface coverage, and on the liquid crystal. Continuous and stepwise growth of orientational order and surface-induced orientational order transitions found in the isotropic phase are explained in terms of a simplified model of surface-induced layering and molecular self-diffusion.

2H NMR spectroscopy of liquid crystals: Structure and orientational order of a chiral smectogen as a model compound of side-group LC polymers

2H NMR spectroscopy is employed to investigate the orientational order, molecular structure and phase transitions of the chiral smectic liquid crystal (S)-[4-(2-methylbutyl)phenyl]-4′-octylbiphenyl carboxylate (8BEF5), partially deuterated in both the chiral chain and the phenyl moiety. 8BEF5 shows a rich polymorphism; the following phases have been observed: Blue phase, N*, SmA, SmC*, SmI*, SmF*, SmJ* and SmG* phases. The tilt angle and the orientational order of the phenyl fragment has been investigated throughout the mesophasic range; the additive potential method has been applied in the SmA phase in order to obtain the order parameter of the “average” conformer of the whole molecule. Molecular structure of (S)-[4-(2-methylbutyl)phenyl]-4′-n-octylbiphenyl carboxylate.

2H-NMR and SAXS of a ferroelectric liquid crystal: unwinding of the ferroelectric chiral helix by high magnetic fields

2H-NMR in three different magnetic fields and small angle X-ray scattering (SAXS) are employed to investigate the orientational order, molecular organisation and phase transitions of the chiral smectic liquid crystal (−)-(S)-[4-(2-methylbutyloxycarbonyl)phenyl] 4- n-heptyl-biphenyl-carboxylate (MBHB) suitably deuterated for 2H-NMR measurements. Unwinding of the ferroelectric chiral helix by high magnetic fields is observed and discussed. Tilt angle values are obtained with the two different techniques and compared. The results show the importance of molecular conformation for the structural properties of this mesogen.

2H NMR spectroscopy of liquid crystals: structure and orientational order of a chiral smectogen in its A, C* and J* phases

2H NMR spectroscopy is employed to investigate the orientational order, molecular structure and phase transitions of the chiral smectic liquid crystal 1-methylheptyl 4'-(4-n-decyloxybenzoyloxy)biphenyl-4-carboxylate (10B1M7), showing smectic A, C* and J phases, as well as several sub-smectic C* phases. Two optically pure, differently deuteriated isotopomers have been purposely synthesized and studied.

Epitropic liquid crystals — a new liquid phase

Abstract We review modern research for liquids forming epitropic liquid crystals (ELC) adjacent to walls. We consider the structure and various properties which differ from those of traditional nematic liquid crystals, such as the structural order parameter, the limited space, and the formation mechanism. The special methods and the results of these investigations are discussed in detail. An analysis of ELC layers is given (structure and influence of various affecting factors). It is shown that epitropic liquid crystals are formed by various polar organic liquids with molecules containing substituted benzene rings. It is established that in the epitropic liquid crystal layers, that is in the epitropic mesophases, there exists a secondary orientational order transition. The width of this layer and the molecular orientation depend on the dipole-dipole forces, the specific interaction with the solid substrate, and the dispersion forces of the liquid. We discuss the status and the outlook of recent experimental and theoretical work and conclude with a few remarks concerning the application of ELC layers in electronics, lubrication, tribology, and the biology of human organs.

The orientational-ordering transition in single crystals of selected C 60 complexes with organic donors followed by infrared spectroscopy

Investigations of infrared spectra of single crystals of the complex of fullerene C 60 with dianthracene (DAN) and C 60 grown from CS 2 solution (clathrate) versus temperature, between 4 and ca. 430 K, have been performed. A phase transition for the complex and the clathrate accompanied by a splitting of the F 1u(4) band into at least two components was detected at temperatures higher than 260 K. The line splitting was attributed to C 60 symmetry lowering as a result of suppression of its rotation. Phase transitions at 80, 160 and 305 K have been observed for DAN C 60 (C 6H 6) 3; the nature of the transitions has been suggested.

Effect of isotopic disorder on the Fu modes in crystalline C60.

The reflectance of undoped single crystals of natural ${\mathrm{C}}_{60}$ and isotopically pure $^{12}\mathrm{C}_{60}$ and $^{13}\mathrm{C}_{60}$ has been measured from 400 to 1600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at high resolution (0.2 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) above and below the orientational-ordering transition. In natural ${\mathrm{C}}_{60}$, the ${\mathit{F}}_{\mathit{u}}$(1) mode shows evidence for isotopic splitting at 295 K; all the other modes are singlets. Below the orientational-ordering transition, the ${\mathit{F}}_{\mathit{u}}$(1) mode splits into five resolvable components, the ${\mathit{F}}_{\mathit{u}}$(3) and ${\mathit{F}}_{\mathit{u}}$(4) modes split into quartets, and the ${\mathit{F}}_{\mathit{u}}$(2) mode appears to remain a singlet. In the isotopically pure materials all the modes are singlets at 295 K; below the orientational-ordering transition, the ${\mathit{F}}_{\mathit{u}}$(1) mode splits into only four components; the ${\mathit{F}}_{\mathit{u}}$(3) and ${\mathit{F}}_{\mathit{u}}$(4) modes split into triplets; the ${\mathit{F}}_{\mathit{u}}$(2) mode shows only weak evidence for splitting. In those modes which display crystal-field splitting, isotopic disorder generates only a weak side band. The ${\mathit{F}}_{\mathit{u}}$(1) mode displays fine structure which may be related to the intrinsic merohedral disorder in the ground state. It is proposed that the anomalous increase in the oscillator strength of the ${\mathit{F}}_{\mathit{u}}$(4) mode is due to a modulation of the charge density along the 〈110〉 intermolecular bonding directions.

Computer simulation of domain formation in the order-disorder phase transition of the KSCN model.

The tetragonal-orthorhombic improper ferroelastic phase transition and domain formation of the order-disorder KSCN model is studied by molecular-dynamics simulation. A two-dimensional model of either 105\ifmmode\times\else\texttimes\fi{}105 or 49\ifmmode\times\else\texttimes\fi{}49 unit cells represents a layer of this crystal. The simulation determines the orientational and strain order parameters and transition temperature. The mean-field theory gives excellent qualitative agreement of the calculated and simulated phase transition temperature. On quenching from the disorder phase and subsequent annealing, a tweed texture is obtained, which later evolves to a stripe phase with well oriented ferroelastic domain walls and arbitrarily oriented antiphase boundaries.

Magnetic Susceptibility of Molecular Carbon: Nanotubes and Fullerite

Elemental carbon can be synthesized in a variety of geometrical forms, from three-dimensional extended structures (diamond) to finite molecules (C(60) fullerite). Results are presented here on the magnetic susceptibility of the least well-understood members of this family, nanotubes and C(60) fullerite. (i) Nanotubes represent the cylindrical form of carbon, intermediate between graphite and fullerite. They are found to have significantly larger orientation-averaged susceptibility, on a per carbon basis, than any other form of elemental carbon. This susceptibility implies an average band structure among nanotubes similar to that of graphite. (ii) High-resolution magnetic susceptibility data on C(60) fullerite near the molecular orientational-ordering transition at 259 K show a sharp jump corresponding to 2.5 centimeter-gram-second parts per million per mole of C(60). This jump directly demonstrates the effect of an intermolecular cooperative transition on an intramolecular electronic property, where the susceptibility jump may be ascribed to a change in the shape of the molecule due to lattice forces.

Orientational order in dense molecular hydrogen: A first-principles path-integral Monte Carlo calculation.

A quantum-mechanical simulation of orientational order in solid molecular hydrogen is presented, based on path-integral Monte Carlo calculations. The effective potential between nearest-neighbor hydrogen molecules is derived from first-principles total energy calculations, taking full account of the symmetries of the Hamiltonian within a hexagonal close-packed arrangement of the molecule centers. A first-order orientational order transition is found by studying short- and long-range angular correlations and the behavior of the corresponding order parameters. A pressure-temperature phase diagram is constructed and compared to relevant experimental and theoretical results.

Anomalous splitting of the F1u(-->3Fu) vibrations in single-crystal C60 below the orientational-ordering transition.

The reflectance of undoped single-crystal ${\mathrm{C}}_{60}$ has been measured from 100 to 1600 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at high resolution above and below the orientational-ordering transition. All of the ${\mathit{F}}_{1\mathit{u}}$ modes allowed in the free molecule are observed in the solid at \ensuremath{\approxeq}526, 576, 1183, and 1430 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Below the orientational-ordering transition, all the lines split into quartets, with the exception of the 576 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ line, which narrows and remains unsplit. The appearance of quartets is attributed to the possibility of triplet splitting of the ${\mathit{F}}_{1\mathit{u}}$(->3${\mathit{F}}_{\mathit{u}}$) modes due to the local crystal field in the low-temperature phase, as well as the perturbation of the local crystal field due to the merohedral disorder, that may lead to further line splitting.

Glass transition in single-crystal C60 studied by high-resolution dilatometry.

The thermal expansion of single-crystalline ${\mathrm{C}}_{6}$ is studied using high-resolution capacitance dilatometry. In addition to the orientational-ordering transition at 261 K, we observe a transition at ${\mathit{T}}_{\mathit{g}}$\ensuremath{\approxeq}90 K due to the freezing in of orientational disorder, which has the character of a glass transition. The relaxation near ${\mathit{T}}_{\mathit{g}}$ is studied by varying the heating (cooling) rate over more than two decades. It is found to obey an Arrhenius behavior with ${\mathit{E}}_{\mathit{a}}$=288\ifmmode\pm\else\textpm\fi{}5 meV within a simple glass-transition model.