Phases hexagonales colonnaires thermotrope et lyotrope : défauts observés par cryofracture et caractère anomal du thermotrope

Electron microscopy observations of replicas of freeze-fractured samples of two columnar hexagonal phases of different nature (a lyotropic one, the inverse AOT in water; a thermotropic one, ) yield very different results: most defects at microscopic scales are screw dislocations in the lyotropic phase, longitudinal edge dislocations in the thermotropic phase. A possible way to interpret these differences is as follows: in the lyotropic the Lamé coefficients and μ and the bend modulus K₃ would not display any anomaly compared to expected values; in the thermotropic the shear modulus μ would be ten times smaller than the compressibility modulus , while K₃ would still be comparable to (but larger than) the bend modulus of a small molecules liquid crystal. We present an elementary theoretical model of the latter case which could explain the anomalous measurements of K₃ and of the longitudinal compressibility (Ref. [#!ref10!#]) without contradicting more recent measurements of (Refs. [#!ref17!#,#!ref22!#]). Essentially, the hexagonal phase would be a phase with defects (longitudinal dislocations) akin to an hexatic phase but with some differences. Re?u : 26 mai 1997 / Révisé : 20 Janvier 1998 / Accepté : 27 avril 1998     

Stability of fluid flow past a membrane

The stability of the flow of a fluid past a solid membrane of infinitesimal thickness is investigated using a linear stability analysis. The system consists of two fluids of thicknesses R and H R and bounded by rigid walls moving with velocities and , and separated by a membrane of infinitesimal thickness which is flat in the unperturbed state. The fluids are described by the Navier-Stokes equations, while the constitutive equation for the membrane incorporates the surface tension, and the effect of curvature elasticity is also examined for a membrane with no surface tension. The stability of the system depends on the dimensionless strain rates and in the two fluids, which are defined as and for a membrane with surface tension , and and for a membrane with zero surface tension and curvature elasticity K. In the absence of fluid inertia, the perturbations are always stable. In the limit , the decay rate of the perturbations is O(k ³ ) smaller than the frequency of the fluctuations. The effect of fluid inertia in this limit is incorporated using a small wave number asymptotic analysis, and it is found that there is a correction of smaller than the leading order frequency due to inertial effects. This correction causes long wave fluctuations to be unstable for certain values of the ratio of strain rates and ratio of thicknesses H. The stability of the system at finite Reynolds number was calculated using numerical techniques for the case where the strain rate in one of the fluids is zero. The stability depends on the Reynolds number for the fluid with the non-zero strain rate, and the parameter , where is the surface tension of the membrane. It is found that the Reynolds number for the transition from stable to unstable modes, , first increases with , undergoes a turning point and a further increase in the results in a decrease in . This indicates that there are unstable perturbations only in a finite domain in the plane, and perturbations are always stable outside this domain. Received: 29 May 1997 / Revised: 9 October 1997 / Accepted: 26 November 1997     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice

We study the exact low energy spectra of the spin 1/2 Heisenberg antiferromagnet on small samples of the kagomé lattice of up to N=36 sites. In agreement with the conclusions of previous authors, we find that these low energy spectra contradict the hypothesis of Néel type long range order. Certainly, the ground state of this system is a spin liquid, but its properties are rather unusual. The magnetic () excitations are separated from the ground state by a gap. However, this gap is filled with nonmagnetic () excitations. In the thermodynamic limit the spectrum of these nonmagnetic excitations will presumably develop into a gapless continuum adjacent to the ground state. Surprisingly, the eigenstates of samples with an odd number of sites, i.e. samples with an unsaturated spin, exhibit symmetries which could support long range chiral order. We do not know if these states will be true thermodynamic states or only metastable ones. In any case, the low energy properties of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice clearly distinguish this system from either a short range RVB spin liquid or a standard chiral spin liquid. Presumably they are facets of a generically new state of frustrated two-dimensional quantum antiferromagnets. Received: 27 November 1997 / Accepted: 29 January 1998     

Structure and rheology of concentrated wormlike micelles [4]at the shear-induced isotropic-to-nematic transition

We have investigated the simple shear flow behavior of wormlike micelles using small-angle neutron scattering and mechanical measurements. Ternary surfactant solutions made of cetylpyridinium chloride, hexanol and brine (0.2 M NaCl) and hereafter abbreviated as CPCl-Hex were studied in the concentrated regime, . In a preliminary report (Berret et al. [#!ref16!#]), the discontinuity of slope observed in the shear stress versus shear rate curve was interpreted in terms of first-order phase transition between an isotropic state and a shear-induced nematic state ( transition). At the transition rate, , the solution exhibits a macroscopic phase separation into viscous and fluid layers (inhomogeneous shear flow). Above a second characteristic shear rate, the flow becomes homogeneous again, the sheared solution being nematic only. The neutron patterns obtained in the two-state inhomogeneous region have been re-examined. Based on a consistent analysis of both orientational and translational degrees of freedom related to the wormlike micelles, we emphasize new features for the transition. In the present paper, the shear rate variations of the relative proportions of each phase in the two-state region, as well as the viscosity ratio between isotropic and nematic phases are derived. We demonstrate in addition that slightly above the transition rate, the shear induced nematic phase is already strongly oriented, with an order parameter P ₂ = 0.65. The orientational state is that of a nematic flow-oriented monodomain. Finally, from the locations of the neutron scattering maxima for each isotropic and nematic contributions, we evaluate the concentrations for each phase and and derived a dynamical phase diagram of CPCl-Hex, in terms of the stress versus and . According to the classification by Schmitt et al. [#!ref22!#], the transition observed in CPCl-Hex micellar solutions could result from a positive flow-concentration coupling, in agreement with the observed monotonically increasing shear stress in the two-phase region. Received: 16 February 1998 / Revised: 18 February 1998 / Accepted: 24 May 1998     

Steps and facets at the surface of soft crystals

We consider the shape of crystals which are soft in the sense that their elastic modulus μ is small compared to their surface tension γ, more precisely μa < γ where a is the lattice spacing. We show that their surface steps penetrate inside the crystal as edge dislocations. As a consequence, these steps are broad with a small energy which we calculate. We also calculate the elastic interaction between steps a distance d apart, which is a 1/d ² repulsion. We finally calculate the roughening temperatures of successive facets in order to compare with the remarkable shapes of lyotropic crystals recently observed by Pieranski et al. [#!Pieranski!#,#!EPJ!#]. Good agreement is found. Received 25 June 2001     

AC field induced two-dimensional aggregation of multilamellar vesicles

The aggregation of 2D colloidal crystals can be performed by applying an AC field to a colloidal dispersion. This technique is used in this work for assembling multilamellar vesicles in suspension. The dynamics of the aggregation is followed by real-time recording of the pictures of the microsphere assembly through a phase contrast microscope. The influence of both the frequency and the amplitude of the alternating field on the dynamical evolution of the concentration of layered particles is discussed with respect to their size. A phenomenological model of double layer induced trapping of the particles is proposed and an electroconvective instability of the fluid surrounding the particles is suggested from the observation of the local dynamics of the particles, in accordance with a very recent argument of Yeh et al. [#!Yeh:97!#]. Received: 4 December 1997 / Revised: 24 March 1998 / Accepted: 4 May 1998     

Director field configurations around a spherical particle in a nematic liquid crystal

We study the director field around a spherical particle immersed in a uniformly aligned nematic liquid crystal and assume that the molecules prefer a homeotropic orientation at the surface of the particle. Three structures are possible: a dipole, a Saturn-ring, and a surface-ring configuration, which we investigate by numerically minimizing the Frank free energy supplemented by a magnetic-field and a surface term. In the dipole configuration, which is the absolutely stable structure for micron-size particles and sufficiently strong surface anchoring, a twist transition is found and analyzed. We show that a transition from the dipole to the Saturn ring configuration is induced by either decreasing the particle size or by applying a magnetic field. The effect of metastability and the occurrence of hysteresis in connection with a magnetic field are discussed. The surface-ring configuration appears when the surface-anchoring strength W is reduced. It is also favored by a large saddle-splay constant K₂₄. A comparison with recent experiments [#!itapdb:Poulin1997!#,#!itapdb:Poulin1998!#] gives a lower bound for W, i.e., for the interface of water and pentylcyanobiphenyl (5CB) in the presence of the surfactant sodium dodecyl sulfate. Received 2 November 1998     

Atomic beam deflection by coherent momentum transfer and the dependence on weak magnetic fields

The deflection of Ne atoms in the metastable state ³ P ₂ by coherent transfer of the momenta of 4 or 8 photons is demonstrated, based on the technique developed for coherent population transfer with delayed pulses (STIRAP). After deflection the intensity profile of the isotope of mass 20 is fully seperated from that for the undeflected atoms of mass 22. It is furthermore shown, how the interplay of Larmor precession of the electronic magnetic moment and the sequential deflection in two spatially separated zones can be used to measure the magnetic field, integrated over the flight-path between the transfer zones. Received: 1 October 1997 / Revised: 22 December 1997 / Accepted: 11 March 1998     

Magnetization dynamics below of EuO and EuS

Between 4.2 K and the Curie temperatures of the cubic Heisenberg ferromagnets EuS and EuO, their homogeneous dynamic susceptibilities have been investigated by means of a broad-band reflectometer operating from 0.1 GHz to 40 GHz. For internal magnetic fields larger than the anisotropy fields H A ( T ) of both materials, their static susceptibilities exhibit a -divergence, which reveals quantitatively the dominance of dipolar-anisotropic spin-wave fluctuations. displays a Lorentzian shape the damping frequency of which obeys scaling in terms of .The scaling function agrees quantitatively with work by Frey and Schwabl [#!FS88!#] for dipolar Heisenberg ferromagnets at temperatures above T_c. Building upon their approach, the resonance frequency of the Lorentzian can be related to a memory effect in the damping determined by the large value of the relaxation rate of the longitudinal magnetization fluctuations . For EuS, this relation is substantiated directly by inelastic neutron scattering. All these features reveal the hitherto uncovered importance of the dipolar anisotropic fluctuations below T_c of ferromagnets. Received: 4 March 1998 / Accepted: 12 May 1998     

Magnetic tunneling told to ignorants by two ignorants

Magnetic tunneling of a large spin subject to the Hamiltonian is investigated by elementary methods for weak fields H. In zero field (H=0) the tunnel frequency in the ground state is found to be equal to [0pt] multiplied by a quantity whose variation with s is slower than exponential. This result coincides with that of path integral methods [#!schi!#]. For the values of the longitudinal field which allow tunneling, the tunnel frequency is shown to vanish when H _y =0 for certain “diabolic" values of [0pt] , in qualitative agreement with experiments by Wernsdorfer and Sessoli. The particular case H _z =0 was already obtained by Garg by means of path integrals. The diabolic values of are in agreement with numerical results but, as already noticed by Wernsdorfer and Sessoli, they disagree with the experimental ones. This may be an effect of higher order anisotropy terms, which is briefly addressed in the conclusion. Received 17 May 2000     

A model for ripple instabilities in granular media

We extend the model of surface granular flow proposed in [#!bcre!#] to account for the effect of an external `wind', which acts as to dislodge particles from the static bed, such that a stationary state of flowing grains is reached. We discuss in detail how this mechanism can be described in a phenomenological way, and show that a flat bed is linearly unstable against ripple formation in a certain region of parameter space. We focus in particular on the (realistic) case where the migration velocity of the instability is much smaller than the grains' velocity. In this limit, the full dispersion relation can be established. We relate the critical wave vector to the mean hopping length and to the ratio of the flight time to the `stick' time. We provide an intuitive interpretation of the instability. Received: 30 January 1998 / Revised: 12 May 1998 / Accepted: 8 June 1998     

Elastic property of bilayer membrane in copolymer-homopolymer mixtures

We study the domain morphology in a phase separated state of diblock copolymer-homopolymer mixtures. In the situation that one of the blocks of copolymers is incompatible with homopolymers, formation of a bilayer membrane of block copolymers is shown to be possible in the matrix of homopolymers. Starting with the free energy functional in terms of the local volume fractions of each monomer, we derive the bending and curvature rigidities in the Helfrich free energy for a membrane. It is found that the curvature modulus is negative only in a limited region of the parameters, where a closed shape of a membrane like a vesicle is possibly formed. We establish a method to calculate the rigidities without a molecular picture in a consistent way with the field theoretic model free energy. Stability of a bilayer membrane compared with micelles is also investigated. Received: 22 July 1997 / Received in final form: 1 December 1997 / Accepted: 22 January 1998     

Comment on “Growth of Molecular Superlattice in Fully Hydrated Dipalmitoylphosphatidylcholine during Subgel Phase Formation Process” by H. Takahashi, K. Hatta and I. Hatta

This comment shows that data recently reported [#!ref1!#] as being seemingly in conflict with earlier data [#!ref2!#] are, in fact, in excellent agreement. Together, both studies confirm that the kinetics of the subgel phase transformation in dipalmitoylphosphatidylcholine (DPPC) lipid bilayers obeys Kolmogorov-Avrami (K-A) theory [#!ref3!#,#!ref4!#] with an anomalously low effective dimensionality. Received: 11 December 1997 / Accepted: 28 January 1998     

Geometrical derivation of a new ground state formula for the n-electron Friedel resonance model

The n-electron ground state of the Friedel resonance model can be written as a single Slater determinant of n s-electrons plus d-electron-s-hole companion. This new formula is derived geometrically in the Hilbert space. The derivation uses the fact that a n-electron Slater determinant, built from N band states, corresponds to a n-dimensional subspace in the N-dimensional Hilbert space. Received: 4 November 1997 / Accepted: 19 November 1997     

Lifetime of metastable fluorine atoms

For laser collimation of neutral F atoms, a resonance transition cycle between the metastable and the upper excited states (3s⁴ P _5/2?3p⁴ D ⁰ _7/2) can be used as a two-level closed system. We have determined the lifetime of the metastable state (3s⁴ P _5/2) in F atoms by measuring the decay curve of the fluorescence intensity as a function of distance from the plasma source. Combining the measured velocity of F radicals from the Doppler shift of the fluorescence peak, we have obtained the lifetime of the F metastable state as 3.7±0.5 μs. With this short metastable lifetime of F radicals, the simple Doppler cooling method using spontaneous light force is not practical for laser collimation of F radicals. Use of stimulated light force may be necessary to collimate F radical beams in a short distance. Received: 4 July 2000 / Published online: 13 September 2000     

Metastable states in two-lane traffic flow models with slow-to-start rule

Using computer simulations, we show that metastable states still occur in two-lane traffic models with slow to start rules. However, these metastable states no longer exist in systems where aggressive drivers (which do not look back before changing lanes) are present. Indeed, the presence of only one aggressive driver in the circuit, triggers the breakdown of the high flow states. In these systems, the steady state is unique and its relaxation dynamics should depend on the lane changing probability p_ch and the number of aggressive drivers present in the circuit. It is found also that the relaxation time τ diverges as the form of a power-law: τ∝p_ch ^-β, β=1. 89.40.+k     

Metastable states of spin glasses on random thin graphs

In this paper we calculate the mean number of metastable states for spin glasses on so called random thin graphs with couplings taken from a symmetric binary distribution . Thin graphs are graphs where the local connectivity of each site is fixed to some value c. As in totally connected mean field models we find that the number of metastable states increases exponentially with the system size. Furthermore we find that the average number of metastable states decreases as c in agreement with previous studies showing that finite connectivity corrections of order 1/c increase the number of metastable states with respect to the totally connected mean field limit. We also prove that the average number of metastable states in the limit is finite and converges to the average number of metastable states in the Sherrington-Kirkpatrick model. An annealed calculation for the number of metastable states of energy E is also carried out giving a lower bound on the ground state energy of these spin glasses. For small c one may obtain analytic expressions for . Received 14 October 1999 and Received in final form 14 December 1999     

A phenomenology of boundary lubrication: the lumped junction model

We propose a phenomenological model of boundary lubricated junctions consisting of a few layers of small molecules which describes the rheological properties of these sytems both in the static, frozen, and sliding, molten, states as well as the dynamical transition between them. Two dynamical regimes can be distinguished, according to the level of internal damping of the junction, which depends on its thickness and on the normal load. In the overdamped regime, under driving at constant velocity v through an external spring, the motion evolves continuously from “atomic stick-slip” to modulated sliding. Underdamped systems exhibit, under given external stress, a range of dynamic bistability where the sheared static state coexists with a steadily sliding one. The frictional dynamics under shear driving is analyzed in detail, it provides a complete account of the qualitative dynamical scenarios observed by Israelashvili et al., and yields semiquantitative agreement with experimental data. A few complementary experimental tests of the model are suggested. Received: 18 December 1997 / Received in final form and accepted: 26 March 1998