Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

A DMRG study of the -symmetric Heisenberg chain

The spin one-half Heisenberg chain with U q [ SU (2)] symmetry is studied via density-matrix renormalization. Ground-state energy and q-symmetric correlation functions are calculated for the non-Hermitian case with integer r. This gives bulk and surface exponents for (para)fermionic correlations in the related Ising and Potts models. The case of real q corresponding to a diffusion problem is treated analytically. Received: 18 February 1998 / Accepted: 17 March 1998     

Monolayers of diblock copolymer at the air-water interface: the attractive monomer-surface case

We have studied both experimentally and theoretically the surface pressure isotherms of copolymers of polystyrene-polyethyleneoxide (PS-PEO) at the air-water interface. The SCMF (single chain mean-field) theory provides a very good agreement with the experiments for the entire range of surface densities and is consistent with the experiments if an adsorption energy per PEO monomer at the air-water interface of about one k_{B T} is taken. In addition, the chain density profile has been calculated for a variety of surface densities, from the dilute to the very dense ones. The SCMF approach has been complemented by a mean-field approach in the low density regime, where the PEO chains act as a two-dimensional layer. Both theoretical calculations agree with the experiments in this region. Received: 19 June 1997 / Revised: 2 February 1998 / Accepted: 11 February 1998     

Epitaxial growth of CeO2 on (100) InP using reactive r.f. magnetron sputtering

The epitaxial growth of CeO₂ thin films has been realized on (100) InP substrates using reactive r.f. magnetron sputtering. Oxide films were nucleated in the presence of molecular hydrogen (4% H₂/Ar sputtering gas) in order to reduce the native oxide formation on the InP surface, which interferes with CeO₂ epitaxy. A metal cerium target was used as the cation source, with water vapor serving as the oxidizing species. Epitaxial films were sputter-deposited at a substrate temperature of 550 °C in a H₂O vapor pressure of approximately 10^-3 Torr. Crystallinity of the oxide films was examined using θ–2θ X-ray diffraction, ω-rocking curves, and in-plane φ-scans. The best results were obtained when the initial nucleation layer was deposited with P(H₂O)<10^-5 Torr, followed by deposition at P(H₂O)=10^-3 Torr. The epitaxial growth of CeO₂ on InP could prove enabling in efforts to integrate functional oxides with InP-based optoelectronic and microwave technologies. Received: 20 February 20002 / Accepted: 21 February 2002 / Published online: 19 July 2002     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

Spin correlations in the two-dimensional spin-5/2 Heisenberg antiferromagnet

We report a neutron scattering study of the instantaneous spin correlations in the two-dimensional spin S =5/2 square-lattice Heisenberg antiferromagnet Rb₂MnF₄. The measured correlation lengths are quantitatively described, with no adjustable parameters, by high-temperature series expansion results and by a theory based on the quantum self-consistent harmonic approximation. Conversely, we find that the data, which cover the range from about 1 to 50 lattice constants, are outside of the regime corresponding to renormalized classical behavior of the quantum non-linear model. In addition, we observe a crossover from Heisenberg to Ising critical behavior near the Néel temperature; this crossover is well described by a mean-field model with no adjustable parameters. Received: 3 March 1998 / Received in final form: 4 May 1998 / Accepted: 19 May 1998     

Collective electronic excitations in a semiconductor superlattice in the Landau and Wannier-Stark ladder regime

Using a mean-field approximation, we have developed a systematic treatment of collective electronic modes in a semiconductor superlattice (SL) in the presence of strong electric and magnetic fields parallel to the SL axis. The spectrum of collective modes with zero wavevector along the SL axis is shown to consist of a principle magnetoplasmon mode and an infinite set of Bernstein-like modes. For non-zero wavevector along the SL axis, in addition to the cyclotron modes, extra collective modes are found at the frequencies |Nω _c±Mω _s|, which we call cyclotron-Stark modes (ω _c and ω _s are respectively the cyclotron and Stark frequencies, N and M are integer numbers). The frequencies of the modes propagating in “oblique” direction with respect to the SL axis show oscillatory behavior as a function of electric field strength. All the modes considered have very weak spatial dispersion and they are not Landau damped. The specific predictions made for the dispersion relations of the collective excitations should be observable in resonant Raman scattering experiments. Received 29 August 2002 / Received in final form 25 February 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: 612033@inbox.ru     

Singularity of the specific heat of two-dimensional random Ising models

The singularity of the specific heat is studied for the dilution (J>J'>0) type and Gaussian type random Ising models using the Pfaffian method numerically. The type of singularity at the paramagnetic-ferromagnetic phase boundary is studied using the standard regression method using data up to system size. It is shown that the logarithmic type singularity is more reliable than the double-logarithmic type and cusp type singularities. The critical temperatures are estimated accurately for both the dilution type and Gaussian type random Ising models. A phase diagram relating strength of the randomness and temperature is also presented. Received: 26 February 1998 / Revised: 15 May 1998 / Accepted: 25 June 1998     

Ferroelectric SrxBa1-xNb2O6 optical waveguiding thin films on SiO2-coated Si(100) substrates

x Ba_1-xNb₂O₆ (x=0.5) films (abbreviated as SBN:0.5) on SiO₂-coated Si substrates are potential components for the application of integrated electro-optics devices. SBN:0.5 optical waveguiding thin films on SiO₂-coated Si substrates with a very thin MgO diffusion buffer have been successfully prepared by pulsed laser deposition. The as-grown films have a refractive index of 2.28, which is close to that of bulk SBN. X-ray analysis showed that the as-grown films have a single-phase tetragonal tungsten bronze structure. The SBN:0.5 thin films prepared by PLD exhibit favorable ferroelectric and optical waveguiding properties. The composition and the morphology of the films were also examined by XPS and by SEM, respectively. Ferroelectric SBN:0.5 optical waveguiding thin films on SiO₂-coated Si substrates are expected to be used in integrated electro-optic devices. Received: 27 February 1997/Accepted: 17 October 1997     

Dynamical mean-field study of the Mott transition in thin films

The correlation-driven transition from a paramagnetic metal to a paramagnetic Mott-Hubbard insulator is studied within the half-filled Hubbard model for a thin-film geometry. We consider simple-cubic films with different low-index surfaces and film thickness d ranging from d=1 (two-dimensional) up to d=8. Using the dynamical mean-field theory, the lattice (film) problem is self-consistently mapped onto a set of d single-impurity Anderson models which are indirectly coupled via the respective baths of conduction electrons. The impurity models are solved at zero temperature using the exact-diagonalization algorithm. We investigate the layer and thickness dependence of the electronic structure in the low-energy regime. Effects due to the finite film thickness are found to be the more pronounced the lower is the film-surface coordination number. For the comparatively open sc(111) geometry we find a strong layer dependence of the quasi-particle weight while it is much less pronounced for the sc(110) and the sc(100) film geometries. For a given geometry and thickness d there is a unique critical interaction strength U _c2 (d) at which all effective masses diverge and there is a unique strength U _c1 (d) where the insulating solution disappears. U _c2 (d) and U _c1 (d) gradually increase with increasing thickness eventually approaching their bulk values. A simple analytical argument explains the complete geometry and thickness dependence of U_c2. U_c1 is found to scale linearly with U_c2. Received 19 August 1998     

Real-time observation of the diffusive motion of 2×2 adlayer formed on Ag(100) nanoparticle facet by nitric acid adsorption

1-x-y Ge_xC_y have been grown on Si(100) substrates by rapid thermal chemical vapor deposition (RTCVD) using C₂H₄ as C source. The composition and microstructure of Si_1-x-yGe_xC_y films were characterized by Auger electron spectroscopy, Raman spectra and Fourier-transform infrared spectroscopy. The results show that lower temperature and higher SiH₄/C₂H₄ flow ratio are helpful in forming the substitutional C and improving the crystal quality. A possible mechanism for C incorporation in Si_1-x-yGe_xC_y layers grown by RTCVD using C₂H₄ is proposed. Received: 26 April 1998 / Accepted: 28 September 1998 / Published online: 24 February 1999     

Coupled Hamiltonians and three-dimensional short-range wetting transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate

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(y) representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d = 3 at critical and complete wetting, respectively, which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. Building on earlier work by Parry and Boulter we investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates X_i(y) we show that arbitrary two-field models H[X₁,X₂] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set

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of Hamiltonians based on proper collective coordinates s(y) near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,

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]

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, in which the degree of coupling is controlled by an angle like variable δ^*, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility χ₁ is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalised critical amplitude θ in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.     

Laser deposition of amorphous diamond films from liquid aromatic hydrocarbons

6 H₅CH₃, C₆H₆, and C₆H₅CH(CH₃)₂) to pulsed visible laser radiation of a copper vapor laser (λ=510.6 nm). The X-ray Auger electron spectroscopy (XAES), reflection high energy electron diffraction (RHEED), and Raman analysis are employed to characterize the deposited films. The sp³ fraction in deposited films amounts to 60–70% and depends on the precursor. The average film thickness on a glass substrate is about 100 nm. The films show excellent adherence, are transparent in the visible and have microhardness of 50–70 GPa, as measured by nanoindentor. Received: 28 September 1998 / Accepted: 13 January 1999     

Stability and vibrations of catenoid-shaped smectic films

Catenoid-shaped smectic films are spanned between two coaxial circular frames separated by a distance H. It is shown that there exists a critical height H^* such that below it two shapes of the catenoid are possible. The stability of these two shapes is analysed in terms of their vibrations. The spectrum of eigenfrequencies is calculated as a function of the catenoid height. It is shown that the frequency of the fundamental mode is real for the stable shape and imaginary for the other shape. Experimental study of vibrational eigenmodes performed on stable SCE4 films confirms this theoretical prediction. Received: 25 November 1997 / Received in final form: 30 January 1998 / Accepted: 9 March 1998     

Ground-state landscape of J Ising spin glasses

Large numbers of ground states of two-dimensional Ising spin glasses with periodic boundary conditions in both directions are calculated for sizes up to 40². A combination of a genetic algorithm and Cluster-Exact Approximation is used. For each quenched realization of the bonds up to 40 independent ground states are obtained. For the infinite system a ground-state energy of e =-1.4015(3) is extrapolated. The ground-state landscape is investigated using a finite-size scaling analysis of the distribution of overlaps. The mean-field picture assuming a complex landscape describes the situation better than the droplet-scaling model, where for the infinite system mainly two ground states exist. Strong evidence is found that the ground states are not organized in an ultrametric fashion in contrast to previous results for three-dimensional spin glasses. Received 12 October 1998     

CO2 laser-induced plasma CVD synthesis of diamond

2 laser maintenance of a stationary optical discharge in a gas stream, exhausting over a substrate into the air (laser plasmatron). Nano- and polycrystalline-diamond films were deposited on tungsten substrates from atmospheric-pressure Xe(Ar):H₂:CH₄ gas mixtures at flow rates of 2 ?/min. A 2.5-kW CO₂ laser focused beam produced plasma. The deposition area was about 1 cm² and growth rates were up to 30–50 μm/h. Peculiarities and advantages of laser plasmatrons are discussed. Received: 15 January 1998/Accepted: 16 January 1998     

Flow birefringence and stress optical law of viscoelastic solutions of cationic surfactants and sodium salicylate

The optical and rheological properties of different viscoelastic solutions of surfactant are studied in order to gather experimental data used to calculate the value of the stress optical coefficient C. Three surfactants of the same family (CTAB) have been chosen; they differ by the length of the hydrocarbon chain; it concerns the dodecyltrimethylammonium bromide (C₁₅H₃₄BrN or DoTAB), the myristyltrimethylammonium bromide (C₁₇H₃₈BrN or MyTAB), and the hexadecyltrimethylammonium bromide (C₁₉H₄₂BrN or CTAB). Different parameters like the temperature of the solution and the salinity of the solvent have been made to vary. Flow birefringence experiments and rheological measurements are performed on these solutions in order to study the dependence of the extinction angle , of the birefringence intensity and of the shear stress with the shear rate . These data are used to check the stress optical law which turns out to be valid in a wide range of shear rates. The stress optical coefficient C is then computed: it is found to vary with the salinity of the solvent and the temperature of the solution for a given surfactant. Then, for all solutions of this work the variations of C are related to the variations of the polarizability anisotropy and the persistence length. Received: 18 February 1998 / Revised: 23 June 1998 / Accepted: 22 July 1998