Copolymers as amphiphiles in ternary mixtures: An analysis employing disorder, equimaxima, and Lifshitz lines

R. Holyst and M. Schick

J. Chem. Phys. 1992, 96, 7728

We study the phase diagram and scattering functions of a ternary mixture of A and B homopolymers, in equal concentrations, and AB diblock copolymer. We locate the disorder line, which marks the appearance of damped oscillatory decaying correlation functions in the system, and also the Lifshitz and equimaxima lines of the structure functions. At these lines, the oscillatory component becomes dominant in a given correlation so that the peak in scattering intensity is no longer at the zero wave vector. We find that while the Lifshitz line of the structure function of all A monomers is quite close to the disorder line, that of A monomers in the homopolymer only is far from it. This shows that the copolymer orders the homopolymers inefficiently, a behavior which is also reflected in the copolymer’s weak ability to solubilize them, and which contrasts with the amphiphilic solubilizers of oil and water. The disorder line and all Lifshitz lines meet at a Lifshitz tricritical point. As these ternary mixtures provide a rare opportunity to study this unusual point, we discuss its effects on the structure functions and surface tensions.

Nonmonotonic behavior of a contact angle on approaching critical end points

J. Putz, R. Hołyst and M. Schick

Phys. Rev. A 1992, 46, 3369

We study the behavior of the contact angle of a middle-phase pendant drop at an oil-water interface in an amphiphilic system. A Landau theory with a one-component order parameter is employed. We find that as a weak amphiphilic system departs from its balanced state, the contact angle decreases monotonically to zero at a wetting transition as a critical end point is approached. In a stronger system, the angle initially increases with this departure before ultimately falling to zero. For a very strong system, the angle can increase to 180° before falling to zero. In such a case, three wetting transitions would be encountered

Mechanical vibrations of freely suspended smectic liquid-crystal films

R. Hołyst

Phys. Rev. A 1992, 46, 6748

The low-frequency vibrations of freely suspended smectic liquid-crystal films are analyzed. The characteristic frequencies for very thin films can be used for the determination of the smectic-liquid-crystal–vapor surface tension. In thick films one can also determine from the vibrational frequencies the compressional elastic constant B for smectic liquid crystals.

Ordering of smectic liquid crystals at surfaces

R. Hołyst

Phys. Rev. B 1992, 46, 15542

It is argued that an enhancement of the surface hexatic in-plane ordering is due to the quench of the out-of-plane surface-layer fluctuations. It is shown that the layer-by-layer freezing (liquid-hexatic phase transition) in freely suspended liquid-crystal films can be induced by the layer fluctuation profile. The obtained results relating transition temperatures to the bend elasticity and the surface tension can be also applied to monolayers undergoing liquid-hexatic phase transition on liquid or liquid-crystal surfaces.

Interfacial properties of amphiphilic systems: The approach to Lifshitz points

G. Gompper, R. Hołyst, and M. Schick

Phys. Rev. A 1991, 43, 3157

Recent experiments on oil, water, and surfactant mixtures indicate that these systems can be brought close to a Lifshitz tricritical point. We investigate the interfacial properties of a system in the vicinity of such a point, based on a single-order-parameter Ginzburg-Landau model. We find that the microemulsion does not wet the oil-water interface all the way to the Lifshitz tricritical point. In addition, the scattering intensity shows a characteristic scaling form. The interfacial behavior near Lifshitz critical end points is also examined.

Landau-Peierls instability, x-ray-diffraction patterns, and surface freezing in thin smectic films

R. Hołyst

Phys. Rev. A 1991, 44, 3692

A model of x-ray diffraction for thin smectic-A liquid-crystal films is presented. The effect of the smectic-layer displacement fluctuations and correlations and the molecular form factor on the interlayer structure and the x-ray-diffraction pattern is discussed. In thin films the influence of the displacement-displacement correlation function on the x-ray-diffraction pattern is very small and can be neglected in the analysis of experimental data. On the other hand, both the displacement-fluctuation term (Debye-Waller factor) and molecular form factor produce strong measurable effects and so can be determined. We discuss the dependence of displacement fluctuations, calculated in the framework of the Landau–de Gennes model, on the smectic elastic constants and the smectic-vapor surface tension and show that these constants can be determined from the x-ray-diffraction pattern. The analysis of the hydrodynamic (collective) layer fluctuations and the individual molecular-motion fluctuations shows that the latter can be neglected in comparison to the former. The fluctuation amplitudes predicted by the model agree within 5% with the recent experimental measurements performed on smectic-I on –C films.

In thin smectic films the fluctuation amplitudes σ(r)=[〈u2(r)〉]1/2 are only ∼4 Å compared with ∼8 Å in a macroscopic sample. The fluctuations are suppressed at the two free surfaces by the large surface tension, grow away from each surface, and have a parabolic profile near the center of the film. We argue that one of the reasons for surface freeezing in smectic liquid crystals is the quench of the layer fluctuations by the large surface tension. However, we also show that in systems with small surface tension the fluctuations at the surface are in fact larger than the ones in the interior of the system. The growth of the diffuse scattering, due to the displacement-displacement correlations, with the thickness of the smectic film is discussed and shown to evolve towards the structure predicted for large samples by Gunther, Imry, and Lajzerowicz [Phys. Rev. A 20, 1733 (1980)]. The model for the displacement layer fluctuations including the director as an independent variable is presented. Furthermore, the coupling between the layer fluctuations and the nematic order parameter in smectic liquid crystals is qualitatively discussed. It is argued that the compressional modes induce the nematic order-parameter fluctuations and that a large fluctuation profile may induce the smectic-A–smectic-C phase transition in thin films. Eventually in tilted smectic liquid crystals the layer fluctuation profile may induce a tilt profile. Finally, it is shown that the presented model can be applied to smectic systems other than smectic-A; we give explicit formulas for the x-ray-scattering intensity from the smectic-Ad films and also calculate the fluctuations amplitudes for the stratified smectic-I on –C system.

Study of the Landau bicritical point in dense systems of hard biaxial molecules

R. Hołyst and A. Poniewierski

Molecular Physics 1990, 69, 193-197

We study two systems of hard biaxial molecules: hard spheroplatelets and hard ellipsoids, using the liquid-crystalline version of the smoothed density approximation (SDA). The first system is studied for all elongations of the spheroplatelet c, whereas the second only for c ⩽ 7. For both systems, we locate the line of Landau bicritical points at which a direct transition from the isotropic phase to the biaxial phase occurs. We find that the density of the isotropic phase at the Landau bicritical point is always higher than that at the isotropic-nematic transition in the limit of uniaxial molecules and the difference ranges from 10 to 30 per cent. For hard ellipsoids, we obtain a similar scaling behaviour at the Landau bicritical point as for spheroplatelets, i.e. b ∼c 1/2, where b denotes the breadth of the ellipsoid.

Orientation of Liquid-Crystal Molecules at the Nematic-Isotropic Interface and the Nematic Free Surface

R. Hołyst and A. Poniewierski

MOLECULAR CRYSTALS AND LIQUID CRYSTALS, 1990, 92, 65-67

Using the generalized Kirkwood-Buff formula for a surface tension we study the interfacial properties of liquid crystals. Surface tension, δ, is calculated for the dilute hard rod system in the sharp interface approximation as a function of a tilt angle, θt, measured from the normal to the flat interface. This function has a minimum at θeqt corresponding to the preferred orientation of liquid crystal molecule at the nematic-isotropic interface and in our case θeqt = 60°. We also argue that hard-core repulsion favours perpendicular alignment at the nematic free surface i.e θt=0°.

Density-functional theory for systems of hard rods

A. Poniewierski and R. Hołyst

Phys. Rev. A 1990, 41, 6871

We present a density-functional theory, based on the smoothed density approximation, to study systems of hard rods with full translational and orientational freedom. For hard spherocylinders, we find both the nematic-isotropic and the nematic–smectic-A transition in a wide range of length-to-width ratios (L+D)/D. We locate the tricritical point for the nematic–smectic-A transition and also make some predictions about the nematic–smectic-A–smectic-B point. Finally, we calculate the nematic elastic constants. The predictions of our theory are compared with the results of computer simulations and other theories. We also make some comments about application of the theory to systems of hard ellipsoids of revolution and hard cylinders.

Nematic–smectic- A d phase transition at zero packing fraction

R. Hołyst

Phys. Rev. A, 1990, 42, 3438

We analyze a system of hard parallel molecules that are composed of hard cylindrical cores and infinitely long and infinitely thin tails. We show that this system exhibits a continuous nematic–smectic-Ad phase transition at zero packing fraction. The transition is studied in the framework of the virial expansion of the free energy. Keeping only the second virial coefficient in the expansion we find the transition at B2ρ=1.80 and d1/L=1.56, where the density ρ is measured in units of the second virial coefficient B2, and the basic smectic period d1 in units of the total length L of a molecule.

Smectic-A, crystalline and columnar ordering in the system of hard parallel cylinders

R. Hołyst and A. Poniewierski

Molecular Physics 1990, 71, 561-566

We study a system of hard parallel cylinders in the framework of the smoothed-density approximation (SDA). Using a bifurcation analysis, we argue that, apart from the nematic phase, smectic-A, solid (or crystalline smectic-B) and columnar phases should also occur in this system. We predict the following sequence of phase transitions: nematic-smectic-A at η* = η/ηcp = 0·31, smectic-A-solid (or smectic-B) at η* ≈ 0·59 and solid (or smectic-B)-columnar at η* ≈ 0·84, where ηcp = 0·9069 is the close-packing density. In our approach we cannot distinguish between a solid phase and a crystalline smectic-B phase.

X-ray determination of the molecular tilt and layer fluctuation profiles of freely suspended liquid-crystal films

D. J. Tweet, R. Hołyst, B. D. Swanson, H. Stragier, and L. B. Sorensen

Phys. Rev. Lett. 1990, 65, 2157

X-ray diffraction has been used to study the interlayer structure of fluid freely suspended liquid-crystal films versus film thickness. The observed scattering is described extremely well by a simple interlayer density model based on predicted layer fluctuation σi and tilt angle φi profiles. The diffraction data determine the individual σi’s to about ±0.1 Å, and the layer-fluctuation profiles calculated for the hydrodynamic fluctuations agree to this precision. The tilt profiles calculated using a simple elastic theory are also in excellent agreement with the data.

Fluctuations in thin smectic-A films

R. Hołyst, D. J. Tweet, and L. B. Sorensen

Phys. Rev. Lett. 1990, 65, 2153

The smectic layer displacement fluctuation profile, σ(r)=〈u2(r)1/2, has been calculated for thin smectic-A films. In thin smectic-A films the calculated fluctuation amplitudes are only σ≊4 Å, compared to σ≊8 Å in a macroscopic sample. The fluctuations are suppressed at the two free surfaces by the surface tension, grow rapidly away from each surface, and have a parabolic profile near the center of the film. These results are in quantitative agreement (±0.1 Å) with recent x-ray measurements.

Interlayer structure of thin smectic films from their x-ray diffraction patterns

R. Hołyst

Phys. Rev. A 1990, 42, 7511(R)

The theory of x-ray diffraction for smectic-A films is presented. The effect of the smectic layer fluctuations and correlations and the molecular form factor on the interlayer structure and the x-ray diffraction pattern is discussed. The application of the presented theory to smectic-C, smectic-I, smectic-Ad, and smectic-A2 films is suggested.

Nematic–smectic-A transition for perfectly aligned hard spherocylinders: Application of the smoothed-density approximation

R. Hołyst and A. Poniewierski

Phys. Rev. A 1989, 39, 2742

We apply the smoothed-density approximation to study the nematicsmectic-A transition for the system of perfectly aligned hard spherocylinders. We find that the transition occurs for all length-to-width ratios L/D of a spherocylinder and is always continuous. The bifurcation analysis is applied to locate the transition. Our results are in reasonable agreement with those obtained in computer simulations

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