The crossover from 2D to 3D percolation: Theory and numerical simulations

We describe here the crossover between 2D and 3D percolation, which we do on cubic and square lattices. As in all problems of critical phenomena, the quantities of interest can be expressed as power laws of , where and h are the percolation threshold and the thickness of the film, respectively. When these quantities are considered on the scale of the thickness h of the films, the corresponding numerical prefactors are of order one. However, for many problems, the scale of interest is the elementary one. The corresponding expressions contain then prefactors in power of h which we calculate. For instance, we show that the mass distribution n(m) of the clusters is given by a master function of , where h is the thickness of the film and are tabulated 2D and 3D critical exponents. We consider also the size R ²(m) of the clusters as a function of their mass m, for which we provide both scaling laws and numerical data. Therefore, any property corresponding to a given moment of mass and size can be obtained from our results. These results might be useful for describing transport properties, such as electric conductivity, or the mechanical properties of thin films made of disordered materials.Received: 24 October 2002, Published online: 26 August 2003PACS: 68.60.-p Physical properties of thin films, nonelectronic - 73.50.-h Electronic transport phenomena in thin films - 05.50. + q Lattice theory and statistics (Ising, Potts, etc.)     

Influence of hydrodynamics on many-particle diffusion in 2D colloidal suspensions

We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective-diffusion coefficients and , respectively, where D₀ is the single-particle diffusion coefficient, as a function of the density of the colloids . At low Schmidt numbers , we find that hydrodynamics has essentially no effect on the behaviour of . At larger Sc, seems to be enhanced at all densities, although the differences compared to the case without hydrodynamics are rather minor. The collective-diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case without hydrodynamic interactions.Received: 20 October 2003, Published online: 23 March 2004PACS: 68.35.Fx Diffusion; interface formation - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 82.20.Wt Physical chemistry and chemical physics: Computational modeling; simulation     

Blobs,channels and “cigars”: Morphologies of liquids at a step

We have studied the equilibria of liquid droplets wetting a step edge with an opening angle by a combination of analytical and numerical methods. Depending on the wetting properties of the substrate walls and on the liquid volume, different locally or globally stable liquid morphologies are found. Complete spreading of the liquid along the bottom edge of the step is observed at equilibrium contact angles satisfying . If the contact angle exceeds a threshold value the liquid exists in a blob-like configuration. Surprisingly, we find an intermediate regime at a sufficiently high liquid volume and in a range of contact angles , in which cigar-shaped configurations arise in addition to the blob. We close the paper by a detailed discussion of the stability of this novel liquid morphology.PACS: 47.55.Dz Drops and bubbles - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 68.08.Bc Wetting     

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, , of a single, infinitely long-charged polymer in the presence of screening. A Gaussian variational method is employed, taking as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, , as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.PACS: 36.20.-r Macromolecules and polymer molecules - 82.70.-y Disperse systems; complex fluids - 87.15.-v Biomolecules: structure and physical properties     

Conducting polymers as driving electrodes for Polymer-Dispersed Liquid-Crystals display devices: On the electro-optical efficiency

Intrinsically conducting polymer (ICP) thin films are used as driving electrodes for Polymer-Dispersed Liquid-Crystals (PDLC) display devices. In order to investigate the electro-optical efficiency of these organic electrodes, three different kinds of conducting polymers, i.e. polyaniline doped with 10-camphorsulfonic acid (PANI(HCSA)), polypyrrole doped with dodecylbenzenesulfonic acid (PPY(DBSA)), and polyethylenedioxythiophene doped with polystyrenesulfonate (PEDOT(PSS)), were prepared or purchased, and coated either on glass or plastic substrates. Optical absorption studies in the UV-Vis range of the conducting polymer-coated substrates were first performed showing the presence of conducting species for the three types of polymers. The electrical characteristics of the resulting films were measured with the four-probes technique. PANI(HCSA) exhibits a higher conductivity ( ) compared to PPY(DBSA) ( ), and PEDOT(PSS) ( ). It is also shown that for a given conducting polymer, its electrical conductivity decreases when a plastic substrate is used. These observations have been related to significant morphological changes observed by scanning electron microscopy (SEM). A mixture of Norland Optical Adhesive 65 and nematic liquid-crystal E7 in the weight ratio (35:65) was used as precursor of the PDLC material. Better electro-optical responses (transmission properties, drive voltages and switching times) of PDLC films were obtained for devices prepared with (PPY(DBSA))-based electrodes. The electro-optical performances of the PDLC display devices also depend on the nature of the ICP substrate used.Received: 25 September 2002, Published online: 29 July 2003PACS: 73.61.Ph Polymers; organic compounds - 42.79.Kr Display devices, liquid-crystal devices - 82.35.Cd Conducting polymers - 42.70.Df Liquid crystals F. Roussel: rfred@purple.univ-littoral.fr     

Deformation of adhering elastic tubes

Deformation of an elastic tube adhering onto a substrate due to van der Waals attractive force is investigated by means of numerical minimization and scaling theory. The onset of the deformation is determined by the critical value of , where is the bending constant, is the depth of the van der Waals potential, and N is the size of the tube. For a significantly deformed tube, we found a scaling behavior of the bending energy, which is explained within the shell theory.Received: 11 September 2003, Published online: 2 March 2004PACS: 68.35.-p Solid surfaces and solid-solid interfaces: Structure and energetics - 68.55.-a Thin film structure and morphology - 81.07.De Nanotubes     

Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor

Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction ( ) and time. At volume fractions below , the gel structure is fractal on small length scales with . g(r) shows a weak minimum at the correlation length ( ), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given , where is the gel time, it is a universal function of . At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity.Received: 27 April 2004, Published online: 26 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 02.70.Uu Applications of Monte Carlo methods     

The effect of thermal fluctuations on Schulman area elasticity

We study the elastic properties of a two-dimensional fluctuating surface whose area density is allowed to deviate from its optimal (Schulman) value. The behavior of such a surface is determined by an interplay between the area-dependent elastic energy, the curvature elasticity, and the entropy. We identify three different elastic regimes depending on the ratio between the projected (frame) and the saturated areas. We show that thermal fluctuations modify the elastic energy of stretched surfaces ( ), and dominate the elastic energy of compressed surfaces ( ). When the elastic energy is not much affected by the fluctuations; the frame area at which the surface tension vanishes becomes smaller than and the area elasticity modulus increases.Received: 14 July 2002, Published online: 19 August 2003PACS: 87.16.Dg Membranes, bilayers, and vesicles - 68.03.Cd Surface tension and related phenomena - 05.70.Np Interface and surface thermodynamicsP. Pincus: Also at Physics and Materials Departments and Program in Biomolecular Science and Engineering, UCSB.     

Diffusion of gelation clusters in the Zimm model

Starting from a Zimm model, we study self-diffusion in a solution of crosslinked monomers. We focus on the effects of the hydrodynamic interaction on the dynamics and the critical behaviour at the sol-gel point. Hydrodynamic interactions cause the clusters diffusion constant to depend not only on the clusters size but also on the clusters shape --in contrast to the Rouse model. This gives rise to a non-trivial scaling of the Kirkwood diffusion constant averaged over all clusters of fixed size n, with given in terms of the spectral dimension of critical percolation clusters. The long-time decay of the incoherent scattering function is determined by the diffusive motion of the largest clusters. This implies the critical vanishing of the cluster-averaged effective diffusion constant at the gel point with exponent .Received: 24 July 2003, Published online: 21 November 2003PACS: 64.60.Ht Dynamic critical phenomena - 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling     

Dynamics of propylene glycol and its oligomers confined in clay

The dynamics of propylene glycol (PG) and its oligomers 7-PG and PPG, with (about 70 monomers), confined in a Na-vermiculite clay have been investigated by quasi-elastic neutron scattering and dielectric spectroscopy. The liquids are confined to a single molecular layer between the clay platelets, thus giving a true 2D liquid. The results show that the average relaxation time , deduced from neutron scattering at a momentum transfer Q of about , is in perfect agreement with the dielectric -relaxation time, although neutron scattering does not only probe the main ( -) relaxation, but all motions of hydrogens on the experimental time scale. At room temperature is proportional to Q ², indicating that the relaxations are mainly due to ordinary translational diffusion. The most unexpected finding is that (or the dielectric -relaxation time) is almost unaffected by the 2D confinement, in contrast to the dielectrically active normal mode of PPG which is substantially slower in the confinement. Only the 7-mer has a significantly slower segmental translational diffusion in the clay. The results suggest that the interactions to the clay surfaces are weak and that the present 2D confinement has a very small influence on the time scale of all our observed relaxation processes, except the normal-mode relaxation.Received: 1 January 2003, Published online: 8 October 2003PACS: 61.25.Em Molecular liquids - 68.35.Ja Surface and interface dynamics and vibrations - 61.12.-q Neutron diffraction and scattering     

Exact effective force between star-polymers in a $\Theta$-solvent

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f₁ and f₂, immersed in a common -solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, , decreases with the center-to-center distance r as , with the exact universal amplitude . Second, in dimension d = 2, we find that the force decays more slowly as , with the exact universal amplitude . For high distances compared to the gyration radius, , of a single polymer chain at the -point, an exponential decay of the force is expected.Received: 3 February 2004, Published online: 24 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.20.-y Classical statistical mechanics     

Can the glass transition in bulk polymers be modeled by percolation picture?

Recent observations (Eur. Phys. J. E 9, 135 (2002)) showed that the vitrification process, which sets in during the linear bulk methyl methacrylate (MMA) polymerization carried out below glass transition temperatures, can be modelled by static percolation picture. To generalize this observation for different kind of bulk linear or crosslinked polymers not enough data are present in the literature. To cover partly this deficit we studied the glass transition of MMA and styrene (Sty) crosslinking copolymerization in varying ratios of MMA and Sty. Both the fluorescence intensity I and the lifetime of pyrene (Py) used as a nanosecond in situ fluoroprobe were monitored during the gelation time. Both I and increase dramatically as a result of the reduced mobility of the probes trapped in the glassy regions, appearing near the glass transition point. The average size of the glassy regions just below, and the strength of the infinite network formed upon the connection of the glassy regions above the glass transition point obey power law relations. The data around were interpreted on the basis of the percolation theory and we observed that the corresponding exponents and give static percolation values independent of the polymer composition.Received: 9 July 2004, Published online: 1 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 64.70.Pf Glass transitions - 82.35.Jk Copolymers, phase transitions, structure     

Mechanical properties of mono-domain side chain nematic elastomers

We investigate the behavior of the shear rigidity modulus G = G + iG of three mono-domain side chain liquid-crystalline elastomers composed of side chain polysiloxanes cross-linked by either flexible or rigid cross-linkers. The measurements were taken in a frequency domain ranging form Hz to Hz applying the shear in a plane perpendicular to or containing the director. The measurements as a function of temperature show an anisotropy of G which appears around , when decreasing the temperature, and which is due to the expected lowering of coming from the coupling between the shear and the director. The measurements as a function of frequency show that G has two components for both geometries, in both the isotropic phase and in the nematic phase around the phase transition. One reflects the network behavior in its hydrodynamic regime (G is constant and , where f is the frequency), the other which appears at higher frequencies is characterized by a scaling law behavior ( ) of the Rouse type. We discuss the results in the framework of available theories and show that the three elastomers present a non-soft behavior, even for the elastomer for which the contrary was claimed, and that there is no separation of time scales between the director and the network. We also present data on a poly-domain sample and a non-mesomorphic one which complement these results.Received: 19 February 2004, Published online: 24 August 2004PACS: 83.80.Va Elastomeric polymers - 61.30.-v Liquid crystals - 83.60.Bc Linear viscoelasticityPresented at the First World Congress on Biomimetics and Artificial Muscles, 9-11 December 2002, Albuquerque, New Mexico, USA. Some aspects of this work have been published as an abridged version in the Proceedings of the Conference.     

Spin-dependent transport in films composed of Co clusters and C $_{\mathsf{60}}$ fullerenes

Granular films of Co-cluster/C₆₀ mixtures have been prepared by the co-deposition of well defined Co clusters (mean diameter 4.5 nm) and C₆₀ fullerenes onto a cold ( 35 K) substrate. Films having a Co cluster volume fraction show a resistivity , typical for tunneling with a Coulomb barrier. The tunneling magnetoresistance (TMR) has a value of TMR ( % for and is decreasing by almost one order of magnitude going to . We explain this unusual decrease of the TMR with increasing as caused by electron-doping of the C₆₀ fullerenes due to the known charge transfer process occurring between transition metal surface and C₆₀. Increasing electron doping may lead to an increasing probability for spin-flip processes within the tunneling barrier, resulting in a decrease of the TMR.Received: 17 March 2004, Published online: 3 August 2004PACS: 75.47.-m Magnetotransport phenomena; materials for magnetotransport - 73.40.Gk Tunneling - 73.40.Rw Metal-insulator-metal structures     

Enhancement of the orientational order parameter of nematic liquid crystals in thin cells

We report measurements of birefringence of several nematic liquid crystals having transverse as well as longitudinal dipole moments in thin (1.4 to ) and thick (7 to cells. Rubbed polyimide-coated glass plates are used to get planar alignment of the nematic director in these cells. We find significant enhancement (6 to ) of ( , where S is the orientational order parameter) in thin cells in all compounds with aromatic cores even at temperatures far ( C) below the nematic-isotropic transition point. The enhancement is larger in compounds having several phenyl rings and lower if the number of phenyl rings is reduced. In a compound that does not have an aromatic core no significant enhancement is observed, implying that the strength of the surface potential depends on the aromaticity of the cores. Assuming a perfect orientational order at the surface, calculations based on the Landau-de Gennes theory show that the thickness averaged enhancement of S is sharply reduced as the temperature is lowered in the nematic phase. The measured order parameter S is further enhanced in thin cells because of the stiffening of the elastic constant which reduces the thermal fluctuations of the nematic director. The combined effect is however too small at low temperatures to account for the experimental data.Received: 22 February 2004, Published online: 24 May 2004PACS: 61.30.-v Liquid crystals - 61.30.Pq Microconfined liquid crystals: droplets, cylinders, randomly confined liquid crystals, polymer dispersed liquid crystals, and porous systems - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitionsSurajit Dhara: Present address: Department of Physics, Birla Institute of Technology and Science, Pilani 333 031, India.     

Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean . After a small perturbation of relative amplitude , e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time , the MWDs first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after . The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after . By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ( ) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbations linearity, the response is non-linear until the late episode (3). For very small perturbations, , response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, -methylstyrene.Received: 23 September 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization     

Ionic diffusion and space charge polarization in structural characterization of biological tissues

In this study, a new approach to the analysis of the low-frequency (1-10⁷ Hz) dielectric spectra of biological tissue, has been described. The experimental results are interpreted in terms of ionic diffusion and space charge polarization according to Sawadas theory. The new presentation of dielectric spectra, i.e. ( has been used. This method results in peaks which are narrower and better resolved than both the measured loss peaks and an alternative loss quantity . The presented method and Sawadas expression have been applied to the analysis of changes in the spatial molecular structure of a collagen fibril network in pericardium tissue exposed to glutaraldehyde (GA), with respect to the native tissue. The diffusion coefficient of ions was estimated on the basis of a dielectric dispersion measurement for an aqueous NaCl solution with a well-calibrated distance between the electrodes. The fitting procedure of a theoretical function to the experimental data allowed us to determine three diffusive relaxation regions with three structural distance parameters , describing the spatial arrangement of collagen fibrils in pericardium tissue. It has been found that a significant decrease in the structural distance from 87 nm to 45 nm may correspond to a reduction in the interfibrillar distance within GA cross-linked tissue.Received: 3 November 2003, Published online: 22 June 2004PACS: 77.22.-d Dielectric properties of solids and liquids - 87.14.-g Biomolecules: types     

The pion nucleon coupling constant

The latest elastic scattering data are re-analysed to determine the coupling constant g_c of the charged pion, using the dispersion relation for the invariant amplitude B^{(+ )}. Depending on the choice of data-base, values to 13.65 are obtained with errors of . The mass difference between charge states of is MeV, close to twice the mass difference between neutron and proton. The difference in widths on resonance is MeV. One may account for a width difference of 4.5 MeV from phase space for decays and the extra channel .Received: 21 January 2004, Published online: 3 March 2004     

First observation of excited states in the <Superscript>110</Superscript>Mo nucleus

The ground-state band in ¹¹⁰Mo has been observed for the first time. The band, comprising six levels, has been populated in the spontaneous fission of ²⁴⁸Cm and studied by means of prompt -ray spectroscopy using the EUROGAM2 array. The ratio suggests that the deformation of ¹¹⁰Mo is smaller than that in ¹⁰⁸Mo but may stabilize at higher neutron number, where an oblate shape is expected. The new data suggests that the deformation of Sr and Zr isotopes decreases above neutron number N = 64.Received: 23 February 2004, Published online: 2 June 2004PACS: 23.20.Lv transitions and level energies - 21.60.Cs Shell model - 25.85.Ca Spontaneous fission - 27.60. + j