Characterization of the structure and the size distribution of branched polymers formed by co-polymerization of MMA and EGDMA

Free radical co-polymerization of methyl methacrylate (MMA) and ethyl glycol dimethyl methacrylate (EGDMA) in solution leads to the formation of polydisperse branched PMMA which grows in size until the system gels. The structure and the size distribution of the PMMA aggregates were characterized at infinite dilution using static and dynamic light scattering and size exclusion chromatography (SEC). The reaction extent was measured using SEC and Raman spectroscopy. The results show that the structure and size distribution of PMMA aggregates formed close to the gel point are compatible with those of percolating clusters. The structure factor of semi-dilute solutions of PMMA aggregates is the same as that of dilute solutions at distance scales much smaller than the correlation length of the concentration fluctuations (). However, the cut-off function of the pair correlation function at for semi-dilute solutions is more gradual than the cut-off function at for dilute solutions. Received 11 May 1998 and Received in final form 22 October 1998     

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     

Numerical study of local and global persistence in directed percolation

The local persistence probability P _l (t) that a site never becomes active up to time t, and the global persistence probability P _g (t) that the deviation of the global density from its mean value does not change its sign up to time t are studied in a (1+1)-dimensional directed percolation process by Monte-Carlo simulations. At criticality, starting from random initial conditions, P _l (t) decays algebraically with the exponent . The value is found to be independent of the initial density and the microscopic details of the dynamics, suggesting is an universal exponent. The global persistence exponent is found to be equal or larger than . This contrasts with previously known cases where . It is shown that in the special case of directed-bond percolation, P _l (t) can be related to a certain return probability of a directed percolation process with an active source (wet wall). Received: 15 December 1997 / Revised: 6 April 1998 / Accepted: 29 May 1998     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

Critical exponents in a percolation picture of the fluorescence quenching during the sol-gel transition

Herewith we report on the measurements of the time evolution of the fluorescence yield and the Rayleigh scattering, performed during the gelation process in the following solutions: gelatin in water, gelatin in a heavy water and agarose in water. Our results provide the experimental evidence of the universal power law, resulting from the percolation theory, which expresses the dependence of the fluorescence yield on the number of intermolecular bonds created during the sol-gel transition. The values of universal critical exponents present in this law are found to have the same values for all investigated materials. Received 4 May 2000     

Optical extinction of an assembly of spherical particles in an absorbing medium: Application to silver clusters in absorbing organic materials

The theory presented by Gerardy and Ausloos for the calculation of the linear optical response of aggregates of spherical particles is analytically continued for absorbing embedding media. The method is based on the calculation of the extinction rate by a single particle embedded in an absorbing matrix. Explicit expressions for the extinction and scattering cross-sections are given. The method is applied to calculate the energy losses in several organic matrices with embedded silver clusters. Comparison with experimental data shows a very good agreement. Received: 21 December 1998     

Topology invariance in percolation thresholds

An universal invariant for site and bond percolation thresholds ( and respectively) is proposed. The invariant writes where and are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d. The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6. Received: 7 July 1997 / Accepted: 5 November 1997     

A Raman and dielectric study of ferroelectric ceramics

Dielectric and Raman scattering experiments were performed on various ceramics with composition Ba(Ti_1-xZr_x)O₃. Such lead-free, environmental-friendly materials were shown, from dielectric measurements, to exhibit behaviours extending from conventional to relaxor ferroelectrics on increasing the zirconium concentration. The evolution of the Raman spectra was studied as a function of temperature for various compositions, and the spectroscopic signature of the corresponding phases was determined. In the relaxor state, the variation of the integrated intensity of the Raman lines with temperature showed a plateau at low temperature. This anomaly was also detected as a peak in depolarization current measurements, and attributed to ergodicity breaking which characterizes usual relaxor systems. Raman results hint at locally rhombohedral polar nanoregions resulting from the random fields associated with Zr ions. Received 25 September 1998     

Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

The scattering of ultrasound from bubbles of m radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and “active” emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross-sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross-sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross-sections exceed the scattering cross-sections. Received: 26 February 1998 / Revised: 13 March 1998 / Accepted: 15 March 1998     

On some natural and model 2D bimodal random cellular structures

The topological and metric properties of a few natural 2D random cellular structures, namely an armadillo shell structure and young soap froths, which are formed from two classes of cells, large and small, have been characterized. The topological properties of a model generated from a Kagome tiling, which mimics such random binary structures, have also been exactly calculated. The distribution of the number of cell sides is bimodal for the structures investigated. In contrast to the classical Aboav-Weaire law for homogeneous 2D random cellular structures, nm(n), the mean total number of edges of neighbouring cells of cells with n sides does not vary linearly with n. Only the nm(i, n) (i=1,2) determined separately for every class of cells are linear in n for all investigated structures. Topological properties and correlations between metric and topological properties are finally compared with the predictions of various literature models. Received: 24 December 1997 / Revised: 7 April 1998 / Accepted: 20 April 1998     

Ageing of random porous media following fluid deterministic displacement, freezing, thawing

This paper introduces and investigates a simple model of random porous media degradation via several fluid displacing, freezing, and thawing cycles. The fluid transport is based on the deterministic method. The result shows that the topology and the geometry of porous media have a strong effect on displacement processes. The cluster size of the viscous fingering (VF) pattern in the percolation cluster increases with the increase of iteration parameter n. When iteration parameter , the VF pattern does not change with n. When and , the peak value of the distribution increases as n increases; is the normalized distribution of throat sizes after different displacement-damage but before the freezing. The distribution of throat size N(r) after displacement but before freezing damage, shows that the major change, after successive cycles, happens at r>0.9. The peak value of the distribution reaches a maximum when and r=1, where is the normalized distribution of the size of invaded throats for different iterations. This result is different from invasion percolation. The distribution of velocities normal to the interface of VF in the percolation cluster is also studied. When , the scaling function distribution is very sharp. The sweep efficiency E increases along with the increasing of iteration parameter n and decreases with the network size L. And E has a minimum as L increases to the maximum size of the lattice. The VF pattern in the percolation cluster has one frozen zone and one active zone. Received 30 March 1999 and Received in final form 8 August 1999     

Some remarks on Yang-Baxter algebras

We point out the existence of an alternative algebraic structure in Yang-Baxter algebra with trigonometric R-matrix, which appears to be the generalization of the Yangian in Yang-Baxter algebras with rational R-matrix and which is described most naturally by q-commutators. Some properties are presented, in particular in the case of the well-known symmetric six-vertex model. Received: 13 February 1998 / Revised: 16 March 1998 / Accepted: 17 April 1998     

Super strong effect of surface impurities on the resistance and Hall effect of quench condensed Cs films

Thin films of Cs, quench condensed onto a He cold quartz plate, possess electronic mean free paths which considerably exceed the film thicknesses. When theses films are covered in situ with sub monolayers of Au, Ag, In, Rh and Pb in the range between 0.01 and 1 monolayers the film resistance and the Hall constant increase dramatically. This corresponds to a scattering cross section of the surface impurities which is larger than 1 in units of Various models are explored to explain these unusual behavior. None yields a satisfactory explanation for this extremely strong effect of surface impurities on the resistance and the Hall effect. Received: 8 January 1998 / Accepted: 17 March 1998     

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission. Received: 17 November 1997 / Revised: 28 May 1998 / Accepted: 20 July 1998     

An universal relation between fractal and Euclidean (topological) dimensions of random systems

It is shown that a dimension-invariant form for fractal dimension D of random systems (where d is Euclidean dimension of the embedding space) is in good agreement with results of numerical simulations performed by different authors for critical (p=p _c ) and subcritical (p<p _c ) percolation, for lattice animals, and for different aggregation processes. Received: 9 July 1998 / Revised and Accepted: 12 July 1998     

Reaction dynamics of Cl O ClO O

Applying the two photon laser induced fluorescence technique for nascent state resolved ClO() detection, the reaction dynamics of Cl+O ClO+O₂ is investigated. The ClO product is formed in its electronic ground state ClO(). A complete product state analysis in terms of vibration, rotation, spin-orbit and -states indicates that nascent ClO radicals are formed in v =0-6 vibrational states peaking at v =3. The ClO fragment shows a moderate rotational excitation, described by a Boltzmann distribution with a temperature parameter of 1300 K 200 K. The spin orbit ratio of :. Most of the excess energy is released as translational energy or as internal energy of the O₂ product. By comparing our results with the trajectory studies of Farantos and Murrell, we favour a reaction mechanism, where the transition complex is planar containing an essentially linear OOCl group. In order to determine the possible influence of vibrationally excited ClO on other trace components of the atmosphere, especially the reaction ClO(v >0)+ O₃, a rough estimate of the vibrational relaxation rate of ClO with the major atmospheric collision partner, N₂, has been performed. A measurement of the vibrational distribution of ClO at different N₂ pressures indicates a mean vibrational relaxation rate of . Received: 27 February 1998 / Revised: 1st April 1998 / Accepted: 15 April 1998     

Universal conductance in quantum wires in the presence of Umklapp scattering

The effects of Umklapp scattering on the zero-temperature conductance in one-dimensional quantum wires are reexamined by taking into account both the screening of external potential and the non-uniform chemical potential shift due to electron-electron interaction. It is shown that in the case away from half-filling the conductance is given by the universal value, 2e ² /h, even in the presence of Umklapp scattering, owing to these renormalization effects of external potential. The conclusion is in accordance with the recent claim obtained for the system with non-interacting leads being attached to a quantum wire. Received: 5 February 1998 / Received in final form: 16 March 1998 / Accepted: 17 April 1998     

Influence of hydrodynamics on the dynamics of a homopolymer

We present an analytical approach of the dynamics of a polymer when it is quenched from a solvent into a good or bad solvent. The dynamics is studied by means of a Langevin equation, first in the absence of hydrodynamic effect, then taking into account the hydrodynamic interactions with the solvent. The variation of the radius of gyration is studied as a function of time. In both cases, for the first stage of collapse or swelling, the evolution is described by a power law with a characteristic time proportional to N ^4/3 (N), where N is the number of monomers, without (with) hydrodynamic interactions. At larger times, scaling laws are derived for the diffusive relaxation time. Received: 10 March 1998 / Received in final form: 15 September 1998 / Accepted: 25 September 1998     

Light scattering from mesoscopic objects in diffusive media

No direct imaging is possible in turbid media, where light propagates diffusively over length scales larger than the mean free path .The diffuse intensity is, however, sensitive to the presence of any kind of object embedded in the medium, e.g. obstacles or defects. The long-ranged effects of isolated objects in an otherwise homogeneous, non-absorbing medium can be described by a stationary diffusion equation. In analogy with electrostatics, the influence of a single embedded object on the intensity field is parametrized in terms of a multipole expansion. An absorbing object is chiefly characterized by a negative charge, while the leading effect of a non-absorbing object is due to its dipole moment. The associated intrinsic characteristics of the object are its capacitance Q or its effective radius ,and its polarizability P. These quantities can be evaluated within the diffusion approximation for large enough objects. The situation of mesoscopic objects, with a size comparable to the mean free path, requires a more careful treatment, for which the appropriate framework is provided by radiative transfer theory. This formalism is worked out in detail, in the case of spherical and cylindrical objects of radius R, of the following kinds: (i) totally absorbing (black), (ii) transparent, (iii) totally reflecting. The capacitance, effective radius, and polarizability of these objects differ from the predictions of the diffusion approximation by a size factor, which only depends on the ratio .The analytic form of the size factors is derived for small and large objects, while accurate numerical results are obtained for objects of intermediate size .For cases (i) and (ii) the size factor is smaller than one and monotonically increasing with ,while for case (iii) it is larger than one and decreasing with . Received: 7 August 1998 / Accepted: 3 September 1998