Slow dynamics of isotropic-nematic phase transition in silica gels

Impact of random-field-type disorder on nematic liquid crystalline structures

We study bicomponent systems where one component represents a liquid crystalline (LC) phase, and the other component randomly perturbs the LC order. Such systems can serve as a testbed to systematically analyse the impact of qualitatively different types of random-type sources of perturbation on the orientational and/or translational order. This mini-review presents typical representatives of such systems, where orientational and translational order is probed in nematic and smectic A LCs, respectively. As a source of perturbation, we consider either different porous matrices (control-pore glass, aerogels) or aerosil nanoparticles, which can form in LCs' different fractal-like network organizations. In such complex systems, LC ordering fingerprints the interplay among LC elastic forces, interfacial forces, and randomness. The resulting LC behaviour could be characterised by either long-range, quasi long-range, or short-range order. We demonstrate under which conditions random-field-like phenomena or interfacial effects dominate. However, these effects are relatively strongly entangled in most experimental systems, and individual impacts cannot be precisely identified.

Nematic and Smectic Phases: Dynamics and Phase Transition

We study in this paper the dynamics of molecules leading to the formation of nematic and smectic phases using a mobile 6-state Potts spin model with Monte Carlo simulation. Each Potts state represents a molecular orientation. We show that, with the choice of an appropriate microscopic Hamiltonian describing the interaction between individual molecules modeled by 6-state Potts spins, we obtain the structure of the smectic phase by cooling the molecules from the isotropic phase to low temperatures: molecules are ordered in independent equidistant layers. The isotropic-smectic phase transition is found to have a first-order character. The nematic phase is also obtained with the choice of another microscopic Hamiltonian. The isotropic-nematic phase transition is a second-order one. The real-time dynamics of the molecules leading to the liquid-crystal ordering in each case is shown by a video.

Computational studies of history dependence in nematic liquid crystals in random environments

Glassy liquid crystalline systems are expected to show significant history-dependent effects. Two model glassy systems are the RAN and SSS (sprinkled silica spin) lattice models. The RAN model is a Lebwohl-Lasher lattice model with locally coupled nematic spins, together with uncorrelated random anisotropy fields at each site, while the SSS model has a finite concentration of impurity spins frozen in random directions. Here Brownian simulation is used to study the effect of different sample histories in the low temperature regime in a three-dimensional (d = 3) model intermediate between SSS and RAN, in which a finite concentration p < p(c) (p(c) the percolation threshold) of frozen spins interacts with neighboring nematic spins with coupling W. Simulations were performed at temperature T ∼ T(NI)/2 (T(NI) the bulk nematic-isotropic transition temperature) for temperature-quenched and field-quenched histories (TQH and FQH, respectively), as well as for temperature-annealed histories (AH). The first two of these limits represent extreme histories encountered in typical experimental studies. Using long-time averages for equilibrated systems, we calculate orientational order parameters and two-point correlation functions. Finite-size scaling was used to determine the range of the orientational ordering, as a function of coupling strength W,p and sample history. Sample history plays a significant role; for given concentration p, as disorder strength W is increased, TQH systems sustain quasi-long-range order (QLRO) and short-range order (SRO). The data are also consistent with a long-range order (LRO) phase at very low disorder strength. By contrast, for FQH and p ≤ 0.1, only LRO and QLRO occur within the range of parameters investigated. The crossover between regimes depends on history, but in general, the FQH phase is more ordered than the AH phase, which is more ordered than the TQH phase. However, at temperatures close to the isotropic-nematic phase transition of pure samples we observe SRO for p = 0.1 even for FQH. We detect also in the QLRO phase a domain-type structural pattern, consistent with ideas introduced by Giamarchi and Doussal [Phys. Rev. B 52, 1242 (1995)] on superconducting flux lattices. In the weak-disorder limit the orientational correlation length obeys the Larkin-Imry-Ma scaling ξ ∼ D(-2/(4-d)).

Dynamic coupling between a multistable defect pattern and flow in nematic liquid crystals confined in a porous medium

When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are large enough, the system shows multistability. Our lattice Boltzmann simulations demonstrate dynamic couplings between the multistable defect pattern and the flow in a regular porous matrix. At sufficiently low flow speed, the topological defects are pinned at the quiescent positions. As the flow speed is increased, the defects show cyclic motions and nonlinear rheological properties, which depend on whether or not they are topologically constrained in the porous networks. In addition, we discover that the defect pattern can be controlled by controlling the flow. Thus, the flow path is recorded in the porous channels owing to the multistability of the defect patterns.

Memory and topological frustration in nematic liquid crystals confined in porous materials

Orientational ordering is key to functional materials with switching capability, such as nematic liquid crystals and ferromagnetic and ferroelectric materials. We explored the confinement of nematic liquid crystals in bicontinuous porous structures with smooth surfaces that locally impose normal orientational order on the liquid crystal. We find that frustration leads to a high density of topological defect lines permeating the porous structures, and that most defect lines are made stable by looping around solid portions of the confining material. Because many defect trajectories are possible, these systems are highly metastable and efficient in memorizing the alignment forced by external fields. Such memory effects have their origin in the topology of the confining surface and are maximized in a simple periodic bicontinuous cubic structure. We also show that nematic liquid crystals in random porous networks exhibit a disorder-induced slowing-down typical of glasses that originates from activated collisions and rearrangements of defect lines. Our findings offer the possibility to functionalize orientationally ordered materials through topological confinement.

Nematics with quenched disorder: violation of self-averaging

We consider the isotropic-to-nematic transition in liquid crystals confined to aerogel hosts, and assume that the aerogel acts as a random field. We generally find that self-averaging is violated. For a bulk transition that is weakly first order, the violation of self-averaging is so severe that even the correlation length becomes non-self-averaging: no phase transition remains in this case. For a bulk transition that is more strongly first order, the violation of self-averaging is milder, and a phase transition is observed.

High-resolution calorimetric study of the nematic to smectic-A transition in aligned liquid crystal-aerosil gels

High-resolution ac calorimetry has been used to study the nematic to smectic- A (N-SmA) phase transition in the liquid crystal octylcyanobiphenyl (8CB) confined in aligned colloidal aerosil gels. A stable and robust nematic alignment was achieved by repeated thermal cycling of the samples in the presence of a strong uniform magnetic field. In some ways (such as transition temperature and integrated enthalpy), the dependence of the specific heat peak associated with the N-SmA transition on the aerosil density for aligned gels is consistent with that observed in unaligned (random) gel samples. However, a power-law analysis reveals that the behavior of the critical exponent alpha is quite different. For random gels, alpha varies gradually with aerosil density, whereas we find that alpha for aligned gels shifts abruptly to an XY -like value for the lowest aerosil density studied and remains essentially constant as the sil density increases. This aerosil density independence of alpha is consistent with the critical behavior of the smectic correlation lengths obtained from an x-ray scattering study of 8CB in aligned aerosil gels. The combined calorimetric and x-ray results indicate that the role of quenched randomness in aligned gels of 8CB+sils differs significantly from that in random gels.

Phase behavior and molecular mobility of n-octylcyanobiphenyl confined to molecular sieves: dependence on the pore size

The molecular dynamics of 4-n-octyl-4'-cyanobiphenyl (8CB) confined inside the pores of a series of AlMCM-41 samples with the same structure, constant composition (SiAl=14.7) but different pore sizes (diameter between 2.3 and 4.6 nm) was investigated by broadband dielectric spectroscopy (10(-2)-10(9) Hz) in a large temperature interval. Two relaxation processes are observed: one has a bulklike behavior and is assigned to the 8CB in the pore center. The relaxation time of the second relaxation process is essentially slower than that of the former one and this process is related to the dynamics of molecules in a surface layer with a paranematic order. Both relaxation processes are specifically influenced by the interaction of the molecules with the surface and by the confinement. Above the clearing temperature the temperature dependence of the relaxation rate of the bulklike process obeys the Vogel-Fulcher-Tammann (VFT) law. The Vogel temperature increases with decreasing pore size. This is explained by increasing influence of paranematic potential of the surface layer with decreasing pore size. The temperature dependence of the relaxation rate of the surface layer follows also the VFT formula and the Vogel temperature decreases with decreasing pore size. This temperature dependence is controlled by both the interaction of the 8CB molecules with the surface via hydrogen bonding and by spatial confinement effects. To discriminate between both effects the data for the surface layer of 8CB confined to the molecular sieves are compared with results concerning 8CB adsorbed as a quasimonolayer on the surface of silica spheres of aerosil. On this basis a confinement parameter is defined and discussed.

Liquid crystal 8CB in random porous glass: NMR relaxometry study of molecular diffusion and director fluctuations

We present the measurements of the proton spin-lattice relaxation time T1 of liquid crystal 4-n-octyl-4'-cyanobiphenyl (8CB) confined into randomly oriented approximately 15 nm pores of untreated porous glass. In the low kilohertz range the spin-lattice relaxation rate in the nanoconfined 8CB is about ten times larger than in the bulk. We show that the increase is mainly due to molecular reorientations mediated by translational displacements (RMTD). In the paranematic phase the power law describing the RMTD dispersion, (T1(-1))RMTD proportional, omega(-p), is well characterized by the exponent p=0.5+/-0.06 and suggests an equipartition of diffusion modes with different wavelengths. The largest distance related to the decay of the orientational correlation function is about twice the diameter of the cavity. The situation is different in the nematic phase, where the orientational correlation is eventually lost at approximately 60 nm in the direction along the pore, a distance corresponding roughly to the length of a pore segment in the glassy matrix. The exponent p is between 0.65 and 0.9, depending on the temperature, which implies that in the nematic phase long wavelength modes are relatively more important--a consequence of the uniform director field along the pore. These observations are in agreement with the model of mutually independent pores with nematic director parallel to the pore axis in each segment. We point out that in strongly confined liquid crystals the proton NMR relaxometry does not provide the evidence of director fluctuations correlated over micrometer distances as was suggested earlier. The local translational diffusion of molecules within the cavities is found about as fast as in bulk.

Molecular dynamics of a short-range ordered smectic phase nanoconfined in porous silicon

4-n-octyl-4-cyanobiphenyl has been recently shown to display an unusual sequence of phases when confined into porous silicon (PSi). The gradual increase of oriented short-range smectic (SRS) correlations in place of a phase transition has been interpreted as a consequence of the anisotropic quenched disorder induced by confinement in PSi. Combining two quasielastic neutron scattering experiments with complementary energy resolutions, the authors present the first investigation of the individual molecular dynamics of this system. A large reduction of the molecular dynamics is observed in the confined liquid phase, as a direct consequence of the boundary conditions imposed by the confinement. Temperature fixed window scans reveal a continuous glasslike reduction of the molecular dynamics of the confined liquid and SRS phases on cooling down to 250 K, where a solidlike behavior is finally reached by a two-step crystallization process.

Memory effects in nematics with quenched disorder

We present a combined experimental and Monte Carlo study of a nematic phase in the presence of quenched disorder. The turbidity of a nematic liquid crystal embedded in a porous polymer membrane is measured under different applied field conditions for field-cooled and zero-field-cooled samples. We find that a significant permanent alignment of the nematic can be induced by fields as low as 0.1 V/microm applied during the isotropic to nematic transition. An analogous effect and dependence on sample history is found by studying the order parameter of a sprinkled disorder Lebwohl-Lasher spin model, indicating that dilute quenched randomness is sufficient to produce memory effects in nematics. The large memory induced by field cooling appears to be written in the system during the transition as a result of the field action on freely oriented nematic nuclei. At lower temperature the nuclei consolidate into permanent nematic textures developed from the interaction with quenched disorder.

Dielectric spectroscopy of aerosil-dispersed liquid crystal embedded in Anopore membranes

The complex dielectric permittivity epsilon* values are presented for aerosil-dispersed 4-pentyl-4-cyanobiphenyl (5CB) confined in Anopore membranes. The dielectric permittivities are measured in the frequency range from 10(-2) Hz to 1 GHz at temperatures ranging from 50 degrees C down to -20 degrees C. In bulk 5CB, which has only a nematic phase, there exist two main relaxation processes: one due to the rotation of molecules around their short axes for parallel orientation of the director to the probing field and another fast relaxation process due to the librational motion of molecules for perpendicular orientation. Inside Anopore membranes both these main relaxation processes can be observed, but with subtle differences. The relaxation process due to the rotation of molecules around the short axis is faster in Anopores at all temperatures in comparison with the bulk process. Hydrophilic aerosil particles, when dispersed in the liquid-crystal (LC) phase, attach to each other via hydrogen bonds and form a three-dimensional interconnecting aerosil network, thus dividing the LC phase into small domains. Dispersing 5CB with different concentrations of hydrophilic aerosils leads to a decrease in relaxation time with aerosil concentration. In these dispersed systems a slow additional relaxation process emerges. This slow process becomes stronger with higher concentrations of aerosil. From our experiments we conclude that this process is the relaxation of 5CB molecules homeotropically aligned to the surface of the aerosil particles. In the case of 5CB-aerosil dispersions enclosed in Anopore membranes this slow process still exists and increases also with aerosil concentration. The relaxation time of the rotation of the 5CB molecules around their short axis systematically increases in these 5CB-aerosil samples in Anopore membranes with aerosil concentration from the 5CB-Anopore behavior towards the behavior observed for 5CB-aerosil dispersions. We explain the evolution as resulting from opposing tendencies from size effects (in the Anopore membranes) and disorder effects (in the aerosil dispersions).

Influence of nanosized confinements on 4-n-decyl-4'-cyanobiphenyl (10CB): a broadband dielectric study

Real (epsilon') and imaginary (epsilon") parts of the complex dielectric permittivity (epsilon*) of the liquid crystal (LC) 4-n-decyl-4'-cyanobiphenyl (10CB) embedded in Anopore membranes and Vycor porous glass, as well as dispersed with hydrophilic aerosils, have been studied by means of broadband dielectric spectroscopy in the frequency range from 10(-2) Hz to 1 GHz . In bulk 10CB, which has a direct transition from an isotropic to a smectic- A phase, there exists one main relaxation process for the parallel orientation of the director with respect to the probing field and a faster one for the perpendicular orientation. All molecular relaxation processes in 10CB are of Debye type and have Arrhenius like temperature dependence. For 10CB embedded in untreated and surface treated cylindrical pores of Anopore membranes the dielectric spectra are similar to the bulk with the exception that both the rotation around the short axis and the libration motion are faster in the pores. In the case of 10CB dispersed with two different concentrations of hydrophilic aerosils an emergence of a slow relaxation process, which is stronger for the higher concentration, is additionally observed along with the bulklike processes. The slow process in the LC-hydrophilic aerosil system is attributed to the relaxation of the molecules that are homeotropically aligned close to the surfaces of the aerosil particles. This process also has an Arrhenius type of temperature dependence. For 10CB embedded in narrow channels of Vycor porous glass three relaxation processes are observed. Two of these processes are bulklike and are due to the librational motion of molecules and the rotation of molecules around their short axes. The slowest process seems to be a surface process, similar in origin to that observed for 10CB dispersed with hydrophilic aerosils, and is prominent amongst all. The material in the Vycor porous glass could be supercooled by at least 185 degrees below bulk crystallization temperature. The slow process has a Vogel-Fulcher-Tamman (VFT) type of temperature dependence typical for glass formers in this wide temperature range. In addition, the bulklike processes are found to be strongly modified and also have a VFT like temperature dependence from measurements done in a wide temperature range. This behavior is in contrast to other reports of glassy behavior in confined LC, where the glassy behavior as concluded from a slow relaxation process observed in a narrow temperature range.

Slow dynamics of thin nematic films in the presence of adsorbed nanoparticles

Recent experiments indicate that liquid crystals can be used to optically report the presence of biomolecules adsorbed at solid surfaces. In this work, numerical simulations are used to investigate the effects of biological molecules, modeled as spherical particles, on the structure and dynamics of nematic ordering. In the absence of adsorbed particles, a nematic in contact with a substrate adopts a uniform orientational order, imposed by the boundary conditions at this surface. It is found that the relaxation to this uniform state is slowed down by the presence of a small number of adsorbed particles. However, beyond a critical concentration of adsorbed particles, the liquid crystal ceases to exhibit uniform orientational order at long times. At this concentration, the domain growth is characterized by a first regime where the average nematic domain size LD obeys the scaling law LDt approximately t1/2; at long times, a slow dynamics regime is attained for which LD tends to a finite value corresponding to a metastable state with a disordered texture. The results of simulations are consistent with experimental observations.

Liquid crystals in random porous media: disorder is stronger in low-density aerosils

The nature of glass phases of liquid crystals in random porous media depends on the effective disorder strength. We study how the disorder strength depends on the density of the porous media and demonstrate that it can increase as the density decreases. We also show that the interaction of the liquid crystal with random porous media can destroy long-range order inside the pores.

Universal nuclear spin relaxation and long-range order in nematics strongly confined in mass fractal silica gels

We show how the low-frequency dependence of the proton spin-lattice relaxation time T1(nu) of octylcyanobiphenyl liquid crystals confined in high-density silica gels evidences a long-range order nematic phase in spite of the strong confinement and random disorder of the gels. The universal value and frequency dependence observed, T1(nu) proportional, variant nu(2/3), is interpreted within a relaxation model due to director fluctuations in nematic liquid crystals confined to mass fractal porous media. The model provides a relation T1(nu) proportional, variant nu(2-d/2), giving a reliable value of the structural fractal dimension d(f)=2.67 for all the host silica gels.

Broadband dielectric spectroscopy study of molecular dynamics in the glass-forming liquid crystal isopentylcyanobiphenyl dispersed with aerosils

The glass-forming liquid crystal isopentylcyanobiphenyl (CB15) filled with different concentrations of hydrophilic and hydrophobic aerosils has been investigated by broadband dielectric spectroscopy in the frequency range from 10(-2) Hz to 10(7) Hz over a temperature range of 173 K-300 K. CB15 that consists of chiral molecules has a monotropic system of phases nematic (N*) and smectic-A upon supercooling and forms a glass further on. In the isotropic phase a single Davidson-Cole process exists in the substance, which is due to the rotation of the molecules around their short axes. In the supercooled N* phase a Cole-Cole process that is an order of magnitude faster is additionally present and is due to the rotation in a cone around the local director. The relaxation times of the process due to rotation around short axes obey the empirical Vogel-Fulcher-Tamman behavior typical for glass-forming systems. Filling of the liquid crystal (LC) with different concentrations of hydrophilic aerosils leads to the emergence of a slow relaxation process that grows with the increasing concentration of the aerosils. The aerosil particles, which form a three-dimensional network dividing the LC phase into domains, have little effect on the relaxation times of the bulk processes. As a consequence the glass transition temperature is merely affected. On the other hand, in LCs dispersed with hydrophobic aerosils the slow process is quite weak. The slow process is attributed to the relaxation of the molecules that are homeotropically attached at the surfaces of the aerosil particles. The LC-aerosil surface interaction leads to a considerable slowing down of the molecular rotation around their short axis. The process has an Arrhenius-like temperature dependence of the relaxation times with an activated type of dynamics, which can be explained by considering a nonincreasing rearranging region of cooperativity in surface layers.

Complex dielectric relaxation in supercooling and superpressing liquid-crystalline chiral isopentylcyanobiphenyl

Results of broadband dielectric studies in glass-forming liquid crystalline chiral isopentylcyanobiphenyl (5(*)CB) are presented. Tests conducted as a function of temperature and pressure revealed the coexistence of glassy and critical properties. The latter are associated with the isotropic-cholesteric phase transition at T(I-Ch) approximately 250 K under atmospheric pressure. Dielectric loss curves in the isotropic liquid and in the cholesteric phase are clearly broadened on cooling and pressuring towards the glass transition. Although in the isotropic phase there is a single stretched loss curve, in the mesophase an additional relaxation process can be distinguished. The evolution of relaxation times is non-Arrhenius and can be portrayed by the Vogel-Fulcher-Tamman relation or its pressure counterpart. The glassy dynamics coexists with the critical-like behavior for the static dielectric permittivity and for the maxima of the dielectric loss curves. Their temperature and pressure dependences are associated with the critical exponent phi=1-alpha approximately 1/2, where alpha approximately 1/2 is the specific heat critical exponent. This behavior is associated with the continuous phase transition placed at DeltaT approximately 1.5 K below the clearing temperature for P=0.1 MPa. It has been found that 5(*)CB shows a unique pressure-temperature phase diagram. Pressure and temperature changes which begin in the isotropic liquid below at ca. T approximately 265 K always result in the transition to the cholesteric phase which can be supercooled or superpressed. For T>265 K the phase transition to another phase, presumably a solid one, always occurs. However, a cholesteric-solid phase border seems to exist only in isothermal pressure tests. It does not appear in the temperature studies.

Nematics with quenched disorder: how long will it take to heal?

Nematics with quenched disorder have been repeatedly predicted to form glass phases. Here we present turbidity experiments and computer simulations aimed at studying glass key features such as dynamics and history dependence in randomly perturbed nematics. Electric field-cooling alignment has been employed to prepare samples in suitably oriented starting states. Remarkable remnant order and slow dynamics are found both by experiment and simulations, indicating that random disorder can, by itself, induce a nematic glass state even without perturber restructuring.

Softening of first-order transition in three-dimensions by quenched disorder

We study by extensive Monte Carlo simulations the effect of random bond dilution on the phase transition of the three-dimensional four-state Potts model that is known to exhibit a strong first-order transition in the pure case. The phase diagram in the dilution-temperature plane is determined from the peaks of the susceptibility for sufficiently large system sizes. In the strongly disordered regime, numerical evidence for softening to a second-order transition induced by randomness is given. Here a large-scale finite-size scaling analysis, made difficult due to strong crossover effects presumably caused by the percolation fixed point, is performed.

Nematics with quenched disorder: what is left when long range order Is disrupted?

It is now generally accepted that even low amounts of quenched disorder disrupt long-range order in anisotropic systems with continuous symmetry. However, very little is known on the key item of the nature of the residual order, if any, and particularly if this has quasi-long-range or truly-short-range character. Here we address this problem both experimentally for the nematic 6CB in dilute aerosils and with computer simulations. We find that the residual order is short ranged and scales with disorder density in agreement with the Imry-Ma argument.

Quasi-long-range order in nematics confined in random porous media

We study the effect of random porous matrices on the ordering in nematic liquid crystals. The randomness destroys orientational long-range order and drives the liquid crystal into a glass state. We predict two glass phases, one of which possesses quasi-long-range order. In this state the correlation length is infinite and the correlation function of the order parameter obeys a power dependence on the distance. The small-angle light-scattering amplitude diverges but slower than in the bulk nematic. In the uniaxially strained porous matrices two new phases emerge. One type of strain induces an anisotropic quasi-long-range-ordered state while the other stabilizes nematic long-range order.

Effects of quenched disorder on the orientational order of the octylcyanobiphenyl liquid crystal

Deuteron NMR (DNMR) measurements were performed with high-temperature and spectral resolution on the octylcyanobiphenyl (8CB) liquid crystal confined to the randomly interconnected pores of silica aerogel as a function of temperature and silica density. The aerogel density was varied by one order of magnitude and the temperature spanned the isotropic (I), nematic (N), and smectic-A (SmA) phases of 8CB. For all samples, the liquid crystal was confined to pores smaller than the micron-sized magnetic coherence length. Thus the observed line shapes reflect the director pattern, n(r-->), and the orientational order, Q, as dictated by the porous host. The DNMR spectral patterns are consistent with powder line shapes representative of a randomized n(r-->) characterized by a single Q. The nematic domains formed are of finite dimension that likely exceeds the confining size. The weakly first-order nematic-to-isotropic phase transition becomes less discontinuous with decreasing pore size, eventually becoming continuous at an aerogel density between 0.36 and 0.5 g/cm(3). In the most severe confinement, no phase transitions are observed with only a continuous evolution of Q present. The orientational order is suppressed from the bulk's with no enhancement upon the onset of the SmA phase. This indicates a decoupling of nematic and smectic order parameters and a severe suppression of the SmA phase by this porous media.

Equilibrium structures and pretransitional fluctuations in a very thin hybrid nematic film

The stability of different structures of a nematic liquid crystal in a planar hybrid film is examined within the framework of a Gaussian description of order fluctuations. In a very thin film the director field is not bent smoothly but exhibits a steplike change if the anchorings at the confining substrates are strong (G approximately > or =10(-3) J/m(2)) and comparable in magnitude. A (dis)continuous structural transition to the bent-director state which occurs with increasing film thickness or decreasing temperature is governed by the lowest bending director fluctuation mode. Its relaxation rate exhibits a critical slowdown when the film thickness approaches the "supercooling" limit or transition point, respectively. The (dis)continuity of the structural transition depends on the temperature and film thickness. The upper limit for the corresponding tricritical point is determined. The lowest order parameter mode, which corresponds to fluctuations of the position of the central exchange region, is characterized by a nearly critical behavior of the relaxation rate. The spectra of the two noncritical biaxial fluctuation modes are degenerate, whereas the fluctuation profiles are just mirror images with respect to the middle plane of the film.

Kinetics of phase ordering of nematic liquid crystals confined in porous media

Employing a time-dependent Ginzburg-Landau model, we investigate the influence of a random field on the phase ordering kinetics of nematic liquid crystals. We find that in the scaling regime the effect of random field (slowing down the growth of nematic) dominates over initial conditions for spatial dimensionality d< or =2, whereas for d>2 the random field has all its effect in the "initial-growth" regime. In this last case the mere confinement of liquid crystals is insufficient to produce slow growth of the nematic order.

Effects of quenched disorder in the two-dimensional Potts model: a Monte Carlo study

Motivated by recent experiments on phase behavior of systems confined in porous media, we have studied the effect of randomness on the nature of the phase transition in the two-dimensional Potts model. To model the effects of the porous matrix we introduce a random distribution of couplings P(J(ij))=pdelta(J(ij)-J1)+(1-p)delta(J(ij)-J2) in the q state Potts Hamiltonian. An extensive Monte Carlo study is made on this system for q=5. We studied two different cases of disorder (a) J(1)/J(2)-->infinity and p=0.8 and (b) J(1)/J(2)=10 and p=0.5. We observed, in both cases, that the weak first order transition that appears in the pure case, changes to a second-order transition. A finite size scaling analysis shows that the correlation length exponent nu is close to 1 and the best fit to the dependence of the specific heat on system size is logarithmic. This suggests that both cases belong to the universality class of the Ising model. In contrast, the magnetic exponents point to a different universality class.