Order and strain in main-chain smectic liquid-crystalline polymers and elastomers

The layer correlations in main-chain smectic liquid-crystal polymer and elastomer systems have been studied using high-resolution X-ray scattering. In contrast to side-chain smectic polymers, in main-chain systems the polymer chains are oriented parallel to the layer normal. As a result they couple directly to the lamellar structure and any polymer defect is translated into layer distortions. For the homopolymers the resulting X-ray lineshapes are well described by Lorentzians. This is interpreted as an average of algebraically decaying order in domains with dimensions of hundreds of nm and a wide dispersion of sizes. The elastomers show much broader peaks than the correponding polymers. This is attributed to strong non-uniform strain within the finite-size domains due to defects of the layer structure. An erratum to this article is available at .     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

A biaxial nematic gel phase in aqueous vanadium pentoxide suspensions

Aqueous suspensions of V₂O₅ ribbons are one of the very few examples of mineral liquid crystals. In the concentrated regime, we show that these ribbons organize in a biaxial nematic gel phase. A Couette shear cell was used to produce a well oriented sample for in situ synchrotron X-ray scattering studies. We observed two perpendicular anisotropic sections of reciprocal space, which proves the biaxial symmetry of the nematic order. The thermodynamic and flow properties of the biaxial nematic are well described by hard-core theories. We suggest the use of a shear geometry to produce and investigate single domains of other biaxial nematics, reported but still questioned in the literature. Received 26 May 1999     

Self-assembly of rod-coil block copolymers from weakly to moderately segregated regimes

We report on the self-assembly behaviour of two homologue series of rod-coil block copolymers in which, the rod, a π -conjugated polymer, is maintained fixed in size and chemical structure, while the coil is allowed to vary both in molecular weight and chemical nature. This allows maintaining constant the liquid crystalline interactions, expressed by Maier-Saupe interactions, ω , while varying the tendency towards microphase separation, expressed by the product between the Flory-Huggins parameter and the total polymerization degree, χN . Therefore, the systems presented here allow testing directly some of the theoretical predictions for the self-assembly of rod-coil block copolymers in a weakly segregated regime. The two rod-coil block copolymer systems investigated were poly(DEH-p-phenylenevinylene-b-styrene), whose self-assembly takes place in the very weakly segregated regime, and poly(DEH-p-phenylenevinylene-b-4vinylpyridine), for which the self-assembly behaviour occurs under increased tendency towards microphase separation, hereby referred to as moderately segregated regime. Experimental results for both systems are compared with predictions based on Landau expansion theories.     

Phase behavior of binary blends of symmetric polystyrene-polybutadiene diblock copolymers studied using SANS

Binary blends of compositionally symmetric diblock copolymers are investigated using small-angle neutron scattering. The study focuses on the miscibility of blends of polystyrene-polybutadiene diblock copolymers as a function of chain length ratio and blend composition, and the results are related to the theoretical phase diagram put forward by M.W. Matsen (J. Chem. Phys. 103, 3268 (1995)). Three different low molar mass copolymers were blended with a high molar mass copolymer. We find very good coincidence with the theoretical phase diagram obtained. Only for blends having a chain length ratio of 0.06, theory predicts that a larger amount of short copolymers can be dissolved in the matrix of long copolymers, and vice versa. With the latter blends and volume fractions of short chains between 0.11 and 0.70, the second-order Bragg-peaks do not vanish, which indicates that the lamellae are asymmetric. Received: 9 February 1998 / Revised: 20 April 1998 / Accepted: 24 April 1998     

Chord length distributions and small-angle scattering

Chord length distributions describe size, shape and spatial arrangement of geometrical objects (particles). The chord length distribution is in principle proportional to the second derivative of the correlation function of small-angle scattering. It is calculable from a relative measurement of the scattering intensity I(h). In structure research, the characterization of numerous particle systems can be achieved by comparing experimental chord distributions with theoretical ones, provided the latter are available with sufficiently high precision for a lot of fundamental, universal shapes. Both sides of this concept are exemplified: – the step from a relative measurement of the scattering intensity of an isotropic two-phase sample to the chord length distribution (errors in and in , limited h-interval, corresponding to the region (1-2) nm < r in real space, must be observed); as well as the geometric matter of calculation of chord distributions as fingerprints for basic geometric figures, including the non-convex case. Received 15 March 1999 and Received in final form 26 April 2000     

Analytical solution of 1D Ising-like systems modified by weak long range interaction

It is well-known that 1D systems with only nearest neighbour interaction exhibit no phase transition. It is shown that the presence of a small long range interaction treated by the mean field approximation in addition to strong nearest neighbour interaction gives rise to hysteresis curves of large width. This situation is believed to exist in spin crossover systems where by the deformation of the spin changing molecules, an elastic coupling leads to a long range interaction, and strong bonding between the molecules in a chain compound leads to large values for nearest neighbour interaction constants. For this interaction scheme an analytical solution has been derived and the interplay between these two types of interaction is discussed on the basis of experimental data of the chain compound which exhibits a very large hysteresis of 50 K above RT at 370 K. The width and shape of the hysteresis loop depend on the balance between long and short range interaction. For short range interaction energies much larger than the transition temperature the hysteresis width is determined by the long range interaction alone. Received 26 November 1998     

A molecular theory of smectic C liquid crystals made of rod-like molecules

Organic compounds exhibiting the smectic C phase are made of rod-like molecules that have dipolar groups with lateral components. We argue that the off-axis character of the lateral dipolar groups can account for tilt in layered smectics (SmC, SmC*, SmI etc.). We develop a mean-field theory of the smectic C phase based on a single-particle potential of the form U _C ∝ sin(2θ)cosφ, consistent with the biaxial nature of the phase, where θ and φ are the polar and azimuthal angles, respectively. The hard-rod interactions that favour the smectic A phase with zero tilt angle are also included. The theoretical phase diagrams compare favourably with experimental trends. Our theory also leads to the following results: i) a first-order smectic C to smectic A transition above some value of the McMillan parameter α, leading to a tricritical point on the smectic C to smectic A transition line and ii) a first-order smectic C to smectic C transition over a very small range of values of the model parameters. We have also extended the theory to include the next higher-order term in the tilting potential and to include the effect of different tilt angles for the molecular core and the chain in the SmC phase. Received 3 August 2002 RID="a" ID="a"Present address: Department of Physics, Vijaya College, R. V. Road, Bangalore - 560 004, India. RID="b" ID="b"e-mail: nvmadhu@rri.res.in     

Influence of the nematic order on the rheology and conformation of stretched comb-like liquid crystalline polymers

We have studied the rheology and the conformation of stretched comb-like liquid-crystalline polymers. Both the influence of the comb-like structure and the specific effect of the nematic interaction on the dynamics are investigated. For this purpose, two isomers of a comb-like polymetacrylate polymer, of well-defined molecular weights, were synthesized: one displays a nematic phase over a wide range of temperature, the other one has only an isotropic phase. Even with high degrees of polymerization N, between 40 and 1000, the polymer chains studied were not entangled. The stress-strain curves during the stretching and relaxation processes show differences between the isotropic and nematic comb-like polymers. They suggest that, in the nematic phase, the chain dynamics is more cooperative than for a usual linear polymer. Small-angle neutron scattering has been used in order to determine the evolution of the chain conformation after stretching, as a function of the duration of relaxation t _r. The conformation can be described with two parameters only: , the global deformation of the polymer chain, and p, the number of statistical units of locally relaxed sub-chains. For the comb-like polymer, the chain deformation is pseudo-affine: is always smaller than (the deformation ratio of the whole sample). In the isotropic phase, has a constant value, while pincreases as tr. This latter behavior is not that expected for non-entangled chains, in which p varies as t _r ^1/2 (Rouse model). In the nematic phase, decreases as a stretched exponential function of t _r, while p remains constant. The dynamics of the comb-like polymers is discussed in terms of living clusters from which junctions are produced by interactions between side chains. The nematic interaction increases the lifetime of these junctions and, strikingly, the relaxation is the same at all scales of the whole polymer chain. Received 5 May 1999 and Received in final form 18 October 1999     

Shear- and vibration-induced order-disorder transitions in granular media

By molecular dynamics simulations we investigate the order-disorder transitions induced in granular media by an applied drive combining vibrations and shear. As the steady state is attained, the pack is found in disordered configurations for comparatively high intensities of the drive; conversely, ordering and packing fractions exceeding the random close packing are found when vibrations and shear are weak. As forcing amplitudes get smaller, we find diverging time scales in the dynamics, as the system enters a jamming region. Under this perspective, our picture supports the intuition that externally applied forcing has, in driven granular media, a role similar to temperature in thermal systems.     

Symplectic integration approach for metastable systems

Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schr?dinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity breaking, reassure the H-theorem of global stability [M. Shiino, Phys. Rev. A 36, 2393 (1987)], and reproduce spatially extended response under alternate source fields.     

Antiferromagnetic Ising spin glass competing with BCS pairing interaction in a transverse field

The competition among spin glass (SG), antiferromagnetism (AF) and local pairing superconductivity (PAIR) is studied in a two-sublattice fermionic Ising spin glass model with a local BCS pairing interaction in the presence of an applied magnetic transverse field Γ. In the present approach, spins in different sublattices interact with a Gaussian random coupling with an antiferromagnetic mean J₀ and standard deviation J. The problem is formulated in the path integral formalism in which spin operators are represented by bilinear combinations of Grassmann variables. The saddle-point Grand Canonical potential is obtained within the static approximation and the replica symmetric ansatz. The results are analysed in phase diagrams in which the AF and the SG phases can occur for small g (g is the strength of the local superconductor coupling written in units of J), while the PAIR phase appears as unique solution for large g. However, there is a complex line transition separating the PAIR phase from the others. It is second order at high temperature that ends in a tricritical point. The quantum fluctuations affect deeply the transition lines and the tricritical point due to the presence of Γ.     

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. Received 8 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: demartino@hmi.de     

Tracer diffusion and correlations in ordered adsorption systems with defect-controlled transport mechanisms

In this study we develop a theory of tracer diffusion in 2D lattice-gas systems with strongly repulsive nearest neighbor interactions. The study is performed for a square lattice in the vicinity of half monolayer coverage. In this case the lattice gas forms a highly-ordered c phase. The adatom kinetics is reduced to the problem of random walks of long-living structural defects. The correlated motion of tracer-defect pairs is considered. Equations for correlation functions of tracer-vacancy, tracer-excessive adatoms and tracer-dimer pairs are derived and solved in terms of microscopic jump probabilities of defects. The solutions are exact in the case of dominant single defect transport mechanisms. In the case of dimer transport we applied the approximation of short-range correlation length. The values obtained for the correlation factor are in good agreement with the results of computer simulations in the over-stoichiometric range, while for sub-stoichiometric coverages the agreement is not very good. Received 20 September 1999 and Received in final form 14 April 2000     

Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

We test the influence of the Coulomb interaction on the thermodynamic and cluster generation properties of a system of classical particles described by different lattice models. Numerical simulations show that the Coulomb interaction produces essentially a shift in temperature of quantities like the specific heat but not qualitative changes. We also consider a cellular model. The thermodynamic properties of the system are qualitatively unaltered. Received: 7 November 2000 / Accepted: 17 May 2001     

Solid-state structure of polypeptide-based rod-coil block copolymers: Folding of helices

This work compares the solid-state structures of films made from a polystyrene-poly(Z-L-lysine) (1) and a polystyrene-poly(-benzyl-L-glutamate) (2) block copolymer, both having virtually the same numbers of repeating units and block length ratios. Small-angle X-ray scattering (SAXS) revealed a hexagonal-in-undulated lamellar morphology for both films. The long-period and the thickness of layers obtained for 2 were by a factor of three smaller as compared to 1, indicating that PBLGlu helices were folded twice, whereas PZLLys helices were fully stretched. Another difference shows up in the packing of helices, the level of ordering being considerably lower in 2. This might be due to spatial restrictions in the proper alignment of back-folded helical segments.     

Twist free energy in a spin glass

The field theory of a short range spin glass with Gaussian random interactions, is considered near the upper critical dimension six. In the glassy phase, replica symmetry breaking is accompanied with massless Goldstone modes, generated by the breaking of reparametrization invariance of a Parisi type solution. Twisted boundary conditions are thus imposed at two opposite ends of the system in order to study the size dependence of the twist free energy. A loop-expansion is performed to first order around a twisted background. It is found, as expected but it is non trivial, that the theory does renormalize around such backgrounds, as well as for the bulk. However two main differences appear, in comparison with simple ferromagnetic transitions: (i) the loop expansion yields a (negative) anomaly in the size dependence of the free energy, thereby lifting the lower critical dimension to a value greater than two (ii) the free energy is lowered by twisting the boundary conditions. This situation is common in spin glasses, reflecting the non-positivity of mode multiplicity in replica symmetry breaking, but its physical meaning is still unclear. Received 12 April 2002 / Received in final form 30 July 2002 Published online 19 November 2002     

Lyotropic bicontinuous cubic phase single crystals investigated using high-resolved X-ray scattering

Single crystals of an Ia d bicontinuous direct cubic phase formed by a non-ionic surfactant in water are investigated using high-resolved X-ray diffraction. The shape of the Bragg peaks confirms the existence of a 3D long-range order inside the cubic phase. A weak diffuse scattered intensity signal is measured very near the Bragg peaks. We attribute this signal to thermal diffuse scattering (TDS) and we give an estimation of the contribution of elastic waves to this TDS. Received 4 May 2000     

Evidence of the hexagonal columnar liquid-crystal phase of hard colloidal platelets by high-resolution SAXS

A vast majority of compounds with bent core or banana shaped molecules exhibit the phase sequence B₆-B₁-B₂ as the chain length is increased in a homologous series. The B₆ phase has an intercalated fluid lamellar structure with a layer spacing of half the molecular length. The B₁ phase has a two dimensionally periodic rectangular columnar structure. The B₂ phase has a monolayer fluid lamellar structure with molecules tilted with respect to the layer normal. Neglecting the tilt order of the molecules in the B₂ phase, we have developed a frustrated packing model to describe this phase sequence qualitatively. The model has some analogy with that of the frustrated smectics exhibited by highly polar rod like molecules.