Structure and dynamics of ferroelectric liquid crystals under random geometrical restrictions

The dynamics of ferroelectric liquid crystals confined in porous nitro-cellulose membrane (Synpor) are investigated by broadband dielectric spectroscopy, and a characterization of the mesomorphism is achieved by DSC and X-ray scattering. The complex inner membrane structure of random interconnected voids can be treated as a frozen random defect disorder in the mesophases. Its influence on the molecular dynamics of the confined mesogens is negligible. However, Goldstone and soft modes of DOBAMBC (2-methylbutyl 4-(4-decyloxybenzylideneamino)cinnamate) are suppressed by the confinement and not detected dielectrically. In the short pitch and high spontaneous polarization material C7, 4-(3-methyl-2-chloropentanoyloxy)-4'-heptyloxybiphenyl, confinement has a minor influence on the soft mode, and the Goldstone mode is clearly present, although with reduced strength, broadened with respect to the bulk, and shifted to higher frequencies by more than one decade. The results are interpreted as effects of random confinement on the length scale of the helical pitch.     

Collective dynamic modes in ferroelectric liquid crystal-aerosil dispersions

The influence of the concentration of hydrophilic aerosil particles on the collective dynamic modes of the ferroelectric liquid crystal S-(-)-2-methylbutyl 4-n-nonanoyloxybiphenyl-4'-carboxylate near the SmA-SmC* phase transition is investigated by means of dielectric spectroscopy in the frequency range 10^-2-10⁷ Hz. For aerosil densities ρ_s = 0.025, 0.05, 0.08 and 0.15 g cm^-3 considerable changes in the dielectric intensities of Goldstone and soft modes are observed. The characteristic frequency of the Goldstone mode slightly increases with increasing concentration of aerosil. The frequency degeneracy occurring in the SmA-SmC* phase transition is lifted in the presence of aerosil and an increase in the frequency gap is observed. Complete disappearance of the Goldstone mode at ρ_s = 0.20 g cm^-3 occurs, along with significant broadening of the soft mode. The results are interpreted as an effect of structure, surface interactions and length scale of the helix in disordered confinement.     

Dynamics of the Goldstone mode near the point of polarization sign reversal in ferroelectric liquid crystal–aerosil mixtures

Dielectric spectroscopy was used to study the influence of random disorder in aerosil–ferroelectric liquid crystal dispersions on the dynamics of the Goldstone mode near the point of polarization sign reversal and the relaxation rate and dielectric strength of the collective modes. In general, the dielectric strength and the relaxation frequency of the Goldstone mode decrease, in comparison with the bulk, with increasing aerosil density near a point of polarization sign reversal. However, the characteristic frequency of the Goldstone mode varies with silica density in an opposite manner on each side of this point. This can be explained as a different sensitivity on the spatial confinement of different molecular conformers above and below the point of polarization sign reversal. The experimental results of temperature and frequency dependence of the complex dielectric constant are compared with predictions of the generalized Landau model for ferroelectric liquid crystals.     

Dynamics of the Goldstone mode near the point of polarization sign reversal in ferroelectric liquid crystal-aerosil mixtures

Dielectric spectroscopy was used to study the influence of random disorder in aerosil-ferroelectric liquid crystal dispersions on the dynamics of the Goldstone mode near the point of polarization sign reversal and the relaxation rate and dielectric strength of the collective modes. In general, the dielectric strength and the relaxation frequency of the Goldstone mode decrease, in comparison with the bulk, with increasing aerosil density near a point of polarization sign reversal. However, the characteristic frequency of the Goldstone mode varies with silica density in an opposite manner on each side of this point. This can be explained as a different sensitivity on the spatial confinement of different molecular conformers above and below the point of polarization sign reversal. The experimental results of temperature and frequency dependence of the complex dielectric constant are compared with predictions of the generalized Landau model for ferroelectric liquid crystals.     

Collective dynamics of a ferroelectric smectogen in geometrical confinement

We investigate the influence of geometric confinement on the dynamics in a ferroelectric smectic C* material. Molecular and collective relaxation processes are studied by means of broadband dielectric spectroscopy. In microporous material (pore size 200nm) the Goldstone mode (GM) is still observed, but it is shifted to lower frequencies compared with bulk samples. In nanoporous material (pore size 7.5 nm), the collective reorientation modes are completely suppressed. In all samples, the molecular processes seem to be uninfluenced by the confinement.     

The dielectric relaxation processes in an antiferroelectric liquid crystal under cylindrical confinement

In the cylindrical pore geometry of inorganic Anopore membranes the collective relaxation processes observed in a bulk antiferroelectric liquid crystal change considerably under confinement. The frequency degeneration of the soft and Goldstone modes present at the smectic A* (SmA*)-chiral smectic C (SmC*) phase transition in the bulk phase is removed under geometrical restrictions. The relaxation rate of the soft mode is strongly modified due to the deformation of the smectic layers in the curved geometry of the pores and is superimposed by the molecular relaxation process in the SmA* and SmC* phases. The soft mode in confinement splits into two relaxation processes, which are present through all other mesophases (SmC* and SmC_a*). One of them is nearly temperature independent and slightly decreases in frequency in the SmC_a* phase. This Goldstone-like process can be assigned to the highly deformed helical structure fluctuations. The second one exhibits the characteristic features for the molecular and soft mode relaxation processes depending on the temperature range. The biquadratic and the piezoelectric coupling between the tilt angle and spontaneous polarization are revealed in their temperature dependence.     

The characteristic dielectric behaviour in ferroelectric liquid crystals at a phase transition and the contribution of the soft mode

The characteristic dielectric behaviour of ferroelectric liquid crystals with a large spontaneous polarization has been studied as functions of the D.C. bias field, frequency, cell thickness and applied pressure. Under the condition in which the contribution of the Goldstone mode is suppressed, a sharp peak in the temperature dependence of the dielectric constant is clearly observed at the transition between S_A and S*_C phases T_SC*sA. The relaxation of the soft mode is observed both in the S_A and S*_C phases by eliminating the contribution of the Goldstone mode under a D.C. bias field. Another relaxation is also observed in the S*_C phase around several kHz in addition to that of the soft mode and the Goldstone mode. The pressure effect on the soft mode was also studied.     

Dielectric and electro-optic properties of two biphenylyl benzoate-based ferroelectric mesogens with tilted hexagonal phases

ABSTRACT

Two partially fluorinated ferroelectric liquid crystals (2F3R, 3F3R) with biphenylyl benzoate core have been investigated by frequency domain dielectric spectroscopy and electro-optic method. Both the compounds exhibit SmC* phase over a wide range of temperature along with tilted hexatic phase SmF* and soft crystal phases SmJ* (in 2F3R) and SmG* (in 3F3R) and one coexistence phase of (SmF*+SmC*). Both BOO phason and tilt phason relaxations are observed in SmF* phase and cooperative relaxation behaviour is also observed in crystal-like smectic phases. Goldstone mode relaxation is observed in SmC* phase and Maxwell Wagner mode is observed in all the phases. In 2F3R soft mode is detected in both SmC* and SmA* phases but not in 3F3R which melts directly to isotropic phase from SmC* phase. Compounds possess moderate values of spontaneous polarisation and exhibit quite sharp electrical response especially in 2F3R. Rotational viscosities, pitch and elastic constant are also measured. Effect of chain length and fluorination on various physical parameters has been discussed.     

Collective and non-collective excitations in antiferroelectric and ferrielectric liquid crystals studied by dielectric relaxation spectroscopy and electro-optic measurements

The dynamics of different molecular modes in four antiferroelectric liquid crystal substances have been studied by a combination of spectroscopic methods.The fastest motion is the reorientation around the molecular long axis, here found in the low GHz range by time domain spectroscopy. The reorientation around the short axis has a characteristic frequency of about 10kHz and is detected by frequency domain spectroscopy in the homeotropic configuration. As for the collective excitations, the Goldstone and soft modes, characteristic of the ferroelectric phase, have counterparts in the antiferroelectric phase which appear very different. There are two characteristic peaks in the spectrum, one at high frequency, about 100kHz, the other at low frequency, about 10 kHz. The latter has often been mistaken for short axis reorientation and both have been attributed to soft modes. By combining different experimental techniques and different geometries it can be shown that neither is a soft mode, but both are collective modes of different character: the high frequency mode corresponds to fluctuations where molecules in neighbouring layers are moving in opposite phase, the low frequency mode to phase fluctuations in the helicoidal superstructure. In materials exhibiting a C* phase in addition to the C*a or C* gamma phases, an additional strong peak appears in at least one lower-lying phase adjacent to the C* phase. We show that this peak, which we call a hereditary peak, has nothing to do with the antiferroelectric or ferrielectric order, but is just the Goldstone peak from a coexisting C* phase. In the same way, a Goldstone mode peak from the C* gamma phase may appear in the underlying C* a phase. In a general way, narrow phases like C* gamma, being bounded by first order transitions on both sides (C* a -C* gamma -C*) are likely to show non-characteristic (hereditary) peaks from both adjacent phases.     

Dielectric response of ferroelectric*C liquid crystals in a bias electric field

The dielectric response of the ferroelectric chiral smectic C phase in a bias electric field is studied theoretically within the Landau model using the constant amplitude approximation. It is argued that the response consists of two modes, one of which is related to the unwinding of the helix (the unwinding mode), whereas the other mode is associated with the distortion of the polarization distribution at constant pitch of the helix (the Goldstone mode). The relaxation frequency of the unwinding mode (fu), which is inversely proportional to the square of the sample dimension along the helical axis, is estimated to be of the order of 10^-4Hz for a sample of length l≈ 1 mm along the helical axis. Consequently, in dielectric experiments performed usually at frequencies higher than fu, only the Goldstone mode contribution is detected. In this way, we can explain the behaviour of the measured static dielectric susceptibility which goes to zero as the critical field is approached from below, although the model predicts that the total static dielectric susceptibility, being a sum of the Goldstone mode and the unwinding mode contribution, diverges at the critical field.     

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.     

From random sphere packings to regular pillar arrays: effect of the macroscopic confinement on hydrodynamic dispersion

Flow and mass transport in bulk and confined chromatographic supports comprising random packings of solid, spherical particles and hexagonal arrays of solid cylinders (regular pillar arrays) are studied over a wide flow velocity range by a numerical analysis scheme, which includes packing generation by a modified Jodrey-Tory algorithm, three-dimensional flow field calculations by the lattice-Boltzmann method, and modeling of advective-diffusive mass transport by a random-walk particle-tracking technique. We demonstrate the impact of the confinement and its cross-sectional geometry (circular, quadratic, semicircular) on transient and asymptotic transverse and longitudinal dispersion in random sphere packings, and also address the influence of protocol-dependent packing disorder and the particle-aspect ratio. Plate height curves are analyzed with the Giddings equation to quantify the transcolumn contribution to eddy dispersion. Confined packings are compared with confined arrays under the condition of identical bed porosity, conduit cross-sectional area, and laterally fully equilibrated geometrical wall and corner effects on dispersion. Fluid dispersion in a regular pillar array is stronger affected by the macroscopic confinement and does not resemble eddy dispersion in random sphere packings, because the regular microstructure cannot function as a mechanical mixer like the random morphology. Giddings' coupling theory fails to preserve the nature of transverse dispersion behind the arrays' plate height curves, which approach a linear velocity-dependence as transverse dispersion becomes velocity-independent. Upon confinement this pseudo-diffusive behavior can outweigh the performance advantage of the regular over the random morphology.     

Dynamic behavior of water within a polymer electrolyte fuel cell membrane at low hydration levels

Protonic conduction across the membrane of a polymer electrolyte fuel cell is intimately related to the dynamic behavior of water present within the membrane. To further the understanding of water dynamics in these materials, quasielastic neutron scattering (QENS) has been used to investigate the picosecond dynamic behavior of water within a perfluorosulfonated ionomer (PFSI) membrane under increasing hydration levels from dry to saturation. Evaluation of the elastic incoherent structure factor (EISF) reveals an increase in the characteristic length-scale of confinement as the number of water molecules in the membrane increases, tending to an asymptotic value at saturation. The fraction of elastic incoherent scattering observed at high Q over all hydration levels is well fit by a simple model that assumes a single, nondiffusing hydronium ion per membrane sulfonic acid site. The quasielastic component of the fitted data indicates confined dynamic behavior for scattering vectors less than 0.7 A(-1). As such, the dynamic behavior was interpreted using continuous diffusion confined within a sphere at Q < 0.7 A(-1) and random unconstrained jump diffusion at Q > 0.7 A(-1). As the number of water molecules in the membrane increases, the characteristic residence times obtained from both models is reduced. The increased dynamical frequency is further reflected in the diffusion coefficients predicted by both models. Between low hydration (2 H2O/SO3H) and saturation (16 H2O/SO3H), the continuous spherical diffusion coefficient changes from 0.46 +/- 0.12 to 1.04 +/- 0.12 (10(-5) cm2/s) and jump diffusion indicates an increase from 1.21 +/- 0.03 to 2.14 +/- 0.08 (10(-5) cm2/s). Overall, the dynamic behavior of water has been quantified over different length scale regimes, the results of which may be rationalized on the basis of the formation of water clusters in the hydrophilic domain that expand toward an asymptotic upper limit with increased hydration.     

Investigation of the helix unwinding process in thick freely suspended smectic films

Optical and electro-optical measurements have been performed on free-standing chiral smectic films sufficiently thick (10 000 layers) to preserve the natural smectic helix. The Goldstone mode appears at about 200Hz, showing that these films are a much better approximation of the 'ideal' smectic bulk state than a thick planar sample between glass plates (where the Goldstone mode is found at about 3 kHz). In these films the unwinding of the helix is studied, as a function of applied electric field, by monitoring Bragg reflections and their Fourier components. When the helix deforms, a reflection appears which at first sight might be taken for a subharmonic, but must be interpreted as the main 'full pitch mode' reflection relative to the 'half pitch' reflection from the undeformed helix. Our measurements further confirm that in anticlinic materials no helix unwinding takes place prior to the antiferroelectric-ferroelectric transition.     

The semi-phenomenological model of antiferroelectricity in chiral smectic liquid crystals III. Dielectric spectroscopy

In the framework of the model of short pitch modes (SPM) developed for antiferroelectric liquid crystals, the sets of various relaxation modes related to ferro-, antiferro- and ferrielectric phases are explained. The 'soft-like' modes describe the amplitude perturbations of short pitch modes, while the Goldstone modes describe the azimuthal perturbations of the molecular packings related to short pitch modes. The frequencies of the Goldstone modes are mainly determined by the chirality parameter, depending on the number of short pitch modes. The relaxation modes described correspond to the observed phase diagrams in liquid crystal materials for which the measurements of dielectric spectra are presented.     

Relaxation dynamics of a polymer in a 2D confinement

The molecular dynamics of oligomeric poly(propylene glycol) (PPG) liquids (MW=1000, 2000, and 4000 g/mol) confined in a two-dimensional layer-structured Na-vermiculite clay has been studied by broadband dielectric spectroscopy. The alpha-relaxation and the normal mode relaxation processes were studied for all samples in bulk and confinement. The most prominent experimental observation was that for the normal mode process: the relaxation rate in the clay is drastically shifted to lower frequencies compared to that of the bulk material. This slowing down is probably caused by the strongly reduced number of accessible chain conformations in two dimensions. Also the temperature dependence of the relaxation time for the normal mode process is strongly affected by the confinement. In contrast, for the alpha-relaxation of the confined polymers we observed only a slight increase of the relaxation rate at high temperatures compared to the corresponding bulk samples, and a decrease of its relaxation strength relative to the beta relaxation. Thus, the glass transition is unaffected by the 2D confinement, suggesting that the underlying phenomena responsible for the glass transition is the same as in bulk. Moreover, in the clay the intensity of the normal mode is stronger than that of the alpha-process, in contrast to the bulk samples where the opposite behavior is observed.     

The characteristic dielectric behaviour in ferroelectric liquid crystals at a phase transition and the contribution of the soft mode

The characteristic dielectric behaviour of ferroelectric liquid crystals with a large spontaneous polarization has been studied as functions of the D.C. bias field, frequency, cell thickness and applied pressure. Under the condition in which the contribution of the Goldstone mode is suppressed, a sharp peak in the temperature dependence of the dielectric constant is clearly observed at the transition between S_A and S*_C phases T _{S C *s A}. The relaxation of the soft mode is observed both in the S_A and S*_C phases by eliminating the contribution of the Goldstone mode under a D.C. bias field. Another relaxation is also observed in the S*_C phase around several kHz in addition to that of the soft mode and the Goldstone mode. The pressure effect on the soft mode was also studied.     

Molecular and collective modes in ferroelectric liquid crystals studied by dielectric spectroscopy

The complex dielectric permittivity has been measured for a ferroelectric liquid crystal in the range 102-109Hz. Six different relaxations have been obtained and characterized: soft mode (SmA* and SmC* phases), Goldstone mode (SmC* phase), rotation around molecular long axis, rotation around molecular short axis, ferroelectric domain mode (SmC* phase) and an internal motion associated with a polar group. Strengths and frequencies of these modes have been obtained for the different phases for different bias fields. Using these results together with spontaneous polarization and molecular tilt measurements we have also obtained the rotational viscosities associated with the soft mode and the Goldstone mode. We explain the results in the light of the so-called Landau extended model, concluding that the biquadratic coupling between polarization and tilt is quite important with regard to the bilinear coupling. This fact has been used to explain the noticeable increase of the activation energy of the frequency of the mode related to the rotation around the molecular long axis at the SmA*-SmC* phase transition.     

Reorientation dynamics of nanoconfined water: power-law decay, hydrogen-bond jumps, and test of a two-state model

The reorientation dynamics of water confined within nanoscale, hydrophilic silica pores are investigated using molecular dynamics simulations. The effect of surface hydrogen-bonding and electrostatic interactions are examined by comparing with both a silica pore with no charges (representing hydrophobic confinement) and bulk water. The OH reorientation in water is found to slow significantly in hydrophilic confinement compared to bulk water, and is well-described by a power-law decay extending beyond one nanosecond. In contrast, the dynamics of water in the hydrophobic pore are more modestly affected. A two-state model, commonly used to interpret confined liquid properties, is tested by analysis of the position-dependence of the water dynamics. While the two-state model provides a good fit of the orientational decay, our molecular-level analysis evidences that it relies on an over-simplified picture of water dynamics. In contrast with the two-state model assumptions, the interface dynamics is markedly heterogeneous, especially in the hydrophilic pore and there is no single interfacial state with a common dynamics.     

The existence of four dielectric modes in the planar oriented S*c phase of a fluorinated substance

Abstract

Soft mode and Goldstone mode properties have been studied for a fluorinated substance. The dielectric spectra have been measured on the planar oriented samples, in the frequency range from 10 Hz to 10 MHz. The thickness of the sample was 10 μm and two kinds of capacitors were used: (i) a low resistance EHC cell and (ii) gold coated electrodes. A bias field up to 10kV cm^?1 has been applied to show the existence of both the soft mode and domain mode in the S*_c phase below T _c. In the S*_c phase a strong Goldstone mode has been observed with a low critical frequency (v ^G _C = 15 Hz). The high frequency side at the Goldstone mode spectrum is accompanied by a shoulder which consists of the soft mode and domain mode as well. In the vicinity of the S*_A-S*_C transition the dielectric parameters of the soft mode obey a Curie-Weiss law. The slope ratio is equal to ?1·62 for the inverse of dielectric increments (Δ∈^?1) and ?1·73 for the critical frequencies (v _c) obtained by using gold electrodes. The respective values received for the EHC cell are ?4·14 and ?2·1. The dielectric parameters of the domain mode have been obtained versus temperature and bias field. We can qualitatively show that a high frequency molecular relaxation is present in the S*_A and S*_C phases as the high frequency limit of dielectric permittivity is distinctly higher than the refractive index squared.