Layer Compression Modulus Research Articles

Layer Compression Modulus in Smectic Liquid Crystals

We have studied the layer compression modulus B for smectic liquid crystals near the SmA–SmC * , SmA–SmC A * , SmA–ferrielectric phase transitions. B shows a significant pretransitional softening due to the order parameter fluctuations above the phase transitions, suggesting that these phase transitions are not of the Landau mean-field type. We also measured B near the nematic-SmA and SmA–CryB phase transitions. In the vicinity of the nematic-SmA phase transition, critical exponent of B is in very good agreement with that determined by light scattering. At the SmA–CryB phase transition, B suddenly increases without pretransitional behavior.

Critical fluctuations near the smectic-hexatic phase transition with anticlinic structure.

Layer compression modulus B measurements have been conducted near the transitions between smectic and hexatic phases with synclinic and anticlinic structures. In the synclinic structure, B shows no pretransitional softening near the phase transition. However, in the anticlinic structure, we observed evident critical softening of B near the smectic-hexatic phase transition. These results clearly reveal that the introduction of the in-plane hexatic order in the anticlinic structure is different from the usual smectic-hexatic phase transition.

Layer Compression Modulus of Chiral Smectic Liquid Crystals Showing V-shaped Switching

Measurements of layer compression modulus B have been performed on the chiral smectic liquid crystals showing V-shaped switching to study elastic properties. The temperature dependence of B in binary mixtures shows the usual cusp-like behavior at the untilted-tilted smectic phase transition in contrast to that in a three-component mixture showing V-shaped switching [Shibahara et al.: Phys. Rev. E 63 (2001) 051707]. Moreover, we observed the abrupt softening of B in the close vicinity of the tilted-tilted smectic phase transition (ferrielectric-antiferroelectric phase transition) for the first time.

Observation of a pretransitional effect near a virtual smectic-A--smectic-C* transition.

Unusual softening of the layer compression modulus B has been observed near the phase boundary where the smectic-C* phase vanishes in a naphtalene-based liquid crystal mixture. From the systematic study of x-ray and layer compression measurements, this unusual effect is attributed to the pretransitional softening near a virtual smectic-A-smectic-C* phase transition in the smectic-A phase, which no longer appears on the thermoequilibrium phase diagram. This phenomenon is similar but not equivalent to supercritical behavior.

Observation of a soft smectic liquid-crystal phase in a mixture showing V-shaped switching.

We present the experimental observation of a soft smectic liquid crystal phase in a three-component liquid crystal mixture reported to exhibit V-shaped switching. Unlike the layer compression modulus B of the usual smectic phase, B of the soft smectic phase has a peculiar temperature and frequency dependence. It was found that this characteristic feature is one of the main driving force to realize an ideal V-shaped switching.

Critical fluctuations at the untilted-tilted phase transition in chiral smectic liquid crystals

The layer compression modulus B was measured near the Sm-A-Sm-C* and Sm-A-Sm-C(*)(A) transitions of chiral smectic liquid crystals. B shows a marked pretransitional softening due to the order parameter fluctuations above the phase transition. The width of the critical region of the Sm-A-Sm-C* and Sm-A-Sm-C(*)(A) transitions is smaller than that of the Sm-A-Sm-C(*)(alpha) transition. The critical exponents of B are in agreement with the theoretical description based on renormalization-group method. These results reveal that these transitions are not of the Landau mean-field type.

Critical Behavior of Layer Compression Modulus near the Smectic-A–Smectic-Cα*Transition

The layer compression modulus was measured near the smectic- A-smectic- C(*)(alpha) phase transition in a chiral smectic liquid crystal. The layer compression modulus B shows marked pretransitional effects above the phase transition. The critical softening of B can be fit to a simple power law. It is described by the theoretical description based on the renormalization-group method and seems to suggest a crossover behavior. These effects clearly show that the transition is not of the Landau mean-field type.

Layer compression modulus of the antiferroelectric liquid crystal MHPBC

The layer compression modulus B was determined near the smectic-A-smectic-Cα* phase transition in an antiferroelectric liquid crystal 4-(l-methylheptyloxycarbonyl)-phenyl 4′-octylbiphenyl-4-carboxylate (MHPBC). The temperature dependence of B clearly defined the smectic-A-smectic-Cα* phase transition temperature and supplied a new and clear evidence that the smectic-Cα* phase is a tilted phase. The pretransitional softening of B can be represented by a simple power law and explained well by the theoretical description based on renormalization-group method. These results clearly show that the transition is not of the Landau mean-field type.

Softening of the interactions between surfactant bilayers in a lamellar phase due to the presence of a polymer

The compressibility modulus of a lamellar phase containing a neutral polymer guest molecule was measured directly using a surface force apparatus. The system studied consisted of sodium dodecyl sulphate (SDS), pentanol, water and polyethylene glycol (PEG) . The lamellar phase was induced from a micellar phase in situ via a confinement induced isotropic to lamellar phase transition. This avoided problems resulting from the viscosity and turbidity normally characteristic of these lamellar phase samples. Increasing the amount of PEG resulted in a marked decrease in the layer compressibility modulus indicating a decrease in the repulsive forces between the lamellae. The origin of such a phenomenon is discussed in terms of different mechanisms including depletion interactions, bridging interactions and modification of the electrostatic interaction between the lamellae by the polymer.

Hydrodynamic and Nonhydrodynamic Behavior of Layer-Compression ModulusBat the Nematic–Smectic-APhase Transition in 8OCB

We present dynamic compression experiments which show that layer-compression modulus $B$ does not exhibit dispersion in the 100 Hz--1 kHz domain and varies with temperature according to a simple power law over four decades. These results indicate that the saturation effect predicted by Nelson and Toner does not exist for this compound, and that the thermal variation of $B$ determined at higher frequencies by a second-sound technique is not hydrodynamic, contrary to what is claimed. We show that it is affected by two relaxation mechanisms.

Layer Compression Modulus of Electrostatically Stabilized Lyotropic Lamellar Phases Revisited: Application to the Quantitative Analysis of a Polymer Induced Critical SmA–SmA Phase Separation

We present a calculation of the smectic compression modulus B of a lyotropic lamellar phase stabilized by electrostatic interactions. This calculation, based on a numerical solution of the Poisson-Boltzmann equation, shows that the classical analytical expressions of B given in the literature in the two asymptotic limits (absence of added salt, or large added salt concentration) are valid under very restrictive conditions only. The motivation of this study lies in the understanding of the physical behavior of a doped amphiphilic lamellar phase formed from a mixture of non ionic surfactants (Triton X100/Triton X35), cationic surfactant (cetylpyridinium chloride), water, decane and water-soluble polymer (polyvynilpyrolidone). A critical lamellar/lamellar phase separation observed in our system is quantitatively well-explained by using both the present calculations and a recent model proposed by Ligoure et al. which predicts the polymer-mediated intermembrane interaction contribution to the smectic compression modulus.

Measurement of the Layer Compressibility Modulus of a Lamellar Mesophase with a Surface Forces Apparatus

A l'aide d'un appareil de mesures de force, nous avons contraint une phase lamellaire. Le profil de force mesure entre les deux surfaces de l'appareil immergees dans la mesophase est periodique, oscillant, amorti et discontinu. Nous avons developpe un modele qui considere la geometrie specifique des surfaces du montage. Un reseau de boucles de dislocation concentriques est retenu afin de remplir l'espacement d'epaisseur variable tout en maintenant un alignement homeotrope des couches. La reponse elastique de ce reseau rend compte qualitativement des differentes caracteristiques du profil de force mesure et permet de preciser la forme parabolique des oscillations. L'analyse des donnees produit alors une evaluation du module de compressibilite de couche avec une bonne precision. Cependant cette analyse elastique n'explique pas pourquoi les oscillations se superposent a une attraction aux faibles separations. Nous discutons deux origines possibles pour cette attraction. Une comparaison quantitative ne permet pas de conclure sur leur pertinence.

Experimental Study of a Lyotropic Lamellar Phase Swollen with Polymer Solutions

We report on the effect of a hydrosoluble neutral polymer on the stability of a lamellar phase made of charged surfactant bilayers. In the system investigated, the smectic structure exists for a wide range of dilutions, with smectic periods continuously varying between 30 and 300 A. Our results show that the lamellar structure still exists when pure water is replaced with aqueous solutions of polyethyleneglycol (PEG: radius of gyration R g = 29 A, molecular weight M w = 22600 g /mol). Large amounts of PEG can be solubilized in the mesophaae: up to 50% of the water can be replaced by the polymer. However, the added polymer causes a reduction in the swelling of the phase and most remarkably produces at intermediate polymer and bilayer concentrations a phase separation between two lamellar phases of different periods. We have studied the system with static (X-ray or neutron) and dynamic (light) scattering techniques. The polymer gets partially aasociated to the surfactant bilayer, as revealed by the small decrease of the smectic spacing as a function of PEG concentration at constant surfactantcosurfactant volume fractions. Besides, the interactions between bilayers are less repulsive in the presence of PEG than the weakly-screened electrostatic repulsion expected with our ionic surfactant. Interactions may even become attractive, which leads to a phase separation between two lamellar phases. The decrease in the layer compression modulus B is studied through its consequences on Bragg peak linewidth, small angle scattering and baroclinic mode relaxation frequency. The eventual presence of critical points on the border of the closed-loop smecticsmectic miscibility gap is investigated

New interpretation of second-sound measurements at the nematic-smectic-A transition: Nonhydrodynamic behavior of the layer-compression elastic constant.

We show that second-sound measurements taken in the vicinity of the nematic-smectic-$A$ transition are not in the hydrodynamic regime as is presently thought. A dynamic effect associated with relaxation of critical fluctuations explains why the layer-compression modulus $B$ deduced from these experiments deviates from a simple power law and levels off as $T\ensuremath{\rightarrow}{T}_{\mathrm{AN}}$.

Statistical Theory of Smectic A and Columnar Phases in Hard Rod Fluids

Abstract The free energy of smectic A and columnar phases in parallel hard cylinders with length L and width D are calculated as functions of the order parameters. In the third vial approximation we find the second order nematic to smectic A (N-SA) lyotropic phase transition at a packing fraction η = ηNA = 0.355 where the smectic layer spacing d is dc = 1.35L. These values agree with results by computer simulation: ηNA = 0.35 and dc = 1.27L. Incorporating an attractive potential, we show the system exhibits the second order N-SA phase transition at a temperature TNA, and find for T < TNA the relation (d/dc - 1)/(1 - T/TNA) ∼ 10−1 and the layer compression modulus B - 15(kT/vmol) (1 - T/TNA), where vmol is the molecular volume. The stability of the columnar phase due to the hard core repulsion cannot be proved in the second virial approximation.

Anomalous Hydrodynamic Behaviors of Smectic Liquid Crystals at Low Frequencies

We report the details of the measurements of the layer compression modulus B and the longitudinal viscosity \ ildeη of several thermotropic smectic phases in the frequency range from 10 Hz to 1 kHz. We confirmed for smectic phases having liquidlike layers (including smectic-A, smectic-C and chiral smectic-C phases) that \ ildeη has an anomalous frequency (ω) dependence of the type \ ildeκ/ω predicted theoretically by Mazenko, Ramaswamy and Toner, and also by Katz and Lebedev. The temperature dependence of B and the strength of the anomalous viscosity \ ildeκ were measured in detail, which revealed, in particular, that a close correlation exists between \ ildeκ and B. We also found that, under an applied magnetic field, which tends to suppress the thermal fluctuations of smectic layers, \ ildeκ decreases whereas B increases, a result which is consistent with the premise of the advocated theories.

Statistical Theory of Smectic A Phase in Hard Rod Fluids

The free energy of smectic A liquid crystalline phase in perfectly aligned hard cylinders with length L and diameter D is calculated using the third virial approximation as a function of the order parameter. The second order phase transition from low density nematic phase to high density smectic A phase is found at a packing fraction η=0.355 (=η c ), where the layer spacing d is d c =1.35 L . Due to attractive interactions, the system can form the smectic phase at a temperature T c by a second order thermotropic transition even for cases η<η c . For such thermotropic smectic A phase, temperature dependences of the layer spacing: ( d / d c -1)/(1- T / T c )∼10 -1 and the layer compression modulus: B ∼15 ( k T /ν mol )(1- T / T c ) are predicted, where ν mol is the molecular volume.

Mechanical Transfer Function of Thin Smectic A Slab having Homeotropic Structure

We derive a formula which expresses the low frequency longitudinal mechanical transfer function of thin smectic A slab having homeotropic structure in terms of the layer compression modulus and the viscosity coefficients. A corresponqing formula for thin homeotropic nematic slab is also given.

Dynamic light scattering study of dilute lamellar phases.

Dynamic light scattering measurements on oriented samples of lyotropic smectics have been performed. The layer compressibility modulus $B$ is extracted from the anisotropic dispersion relation of the so-called slip mode, which arises from the coupling between concentration and layer displacement fluctuations. The samples are diluted with three different solvents (repeat distances 50 to 800 \AA{}): The behavior of $B$ suggests either undulation or electrostatic repulsions between membranes, depending on the swelling solvent.