Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

The dispersion state of sodium-sulphonated polystyrene ( NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c^* is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c^* and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c ^*), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c ^*), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c ^*, NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. Received 14 May 1999 and Received in final form 15 March 2000     

Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a simple one-dimensional model for the swelling or the collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a Θ-solvent that is rapidly changed into a good solvent (swelling) or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands in space as t ^1/3, as predicted by a Flory-like continuum theory. The dynamics slows down after a time ∝N ² when the chain becomes stretched, and the polymer gets stuck in metastable “zig-zag” configurations, from which it escapes through thermal activation. The size of the polymer in the final stages is found to grow as . In the case of collapse, the chain very quickly (after a time of order unity) breaks up into clusters of monomers (“pearls”). The evolution of the chain then proceeds through a slow growth of the size of these metastable clusters, again evolving as the logarithm of time. We enumerate the total number of metastable states as a function of the extension of the chain, and deduce from this computation that the radius of the chain should decrease as 1/ln(ln t). We compute the total number of metastable states with a given value of the energy, and find that the complexity is non-zero for arbitrary low energies. We also obtain the distribution of cluster sizes, that we compare to simple “cut-in-two” coalescence models. Finally, we determine the aging properties of the dynamical structure. The subaging behaviour that we find is attributed to the tail of the distribution at small cluster sizes, corresponding to anomalously “fast” clusters (as compared to the average). We argue that this mechanism for subaging might hold in other slowly coarsening systems. Received 23 October 2000     

Change in the chemical potential of niobium at transition to the superconducting state

A temperature-modulation technique was applied to investigate change in the chemical potential of niobium film at transition to the superconducting state. The first derivative of the chemical potential is continuous at T _c whereas the second derivative shows a jump. Received 10 April 2000     

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length N. We find R≃N ^ν(log N)^γ, where ν = and λ is the exponent which characterizes the long-range interaction U∝ 1/r ^λ. The exponent γ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings by a direct numerical minimization of the variational energy for chains of increasing size 2⁴ < N < 2¹⁵. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length 2⁴ < N < 2¹⁰. The non-universal behavior of the exponent γ previously derived within the variational method is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in d = 3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are present. Received 8 August 2000 and Received in final form 19 December 2000     

Static and dynamic properties of supercooled thin polymer films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. An analysis of the temperature dependence of the α-relaxation time suggests that the critical temperature, T _c, of MCT decreases with D. If the confinement is not too strong ( D≥10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T _c(D), to the critical temperature. This suggests that T - T _c(D) is an important temperature scale of our model both in the bulk and in the films. Received 12 September 2001     

Velocity measurement of a settling sphere

We study experimentally the motion of a solid sphere settling under gravity in a fluid at rest. The particle velocity is measured with a new acoustic method. Variations of the sphere size and density allow measurements at Reynolds numbers, based on limit velocity, between 40 and 7 000. At all Reynolds numbers, our observations are consistent with the presence of a memory-dependent force acting on the particle. At short times it has a t ^-1/2 behaviour as predicted by the unsteady Stokes equations and as observed in numerical simulations. At long times, the decay of the memory (Basset) force is better fitted by an exponential behaviour. Comparison of the dynamics of spheres of different densities for the same Reynolds number show that the density is an important control parameter. Light spheres show transitory oscillations at Re∼ 400, but reach a constant limit speed. Received 12 April 2000 and Received in final form 13 July 2000     

Morphology and electrical properties of pulsed-laser deposited Bi2Sr2CaCu2O8+δ films on vicinal substrates

Thin films of Bi₂Sr₂CaCu₂O_8+δ have been grown on vicinal (001) SrTiO₃ substrates by pulsed-laser deposition. Transmission electron microscopy (TEM) and X-ray diffraction reveal well ordered films with the c axis of the film parallel with the c axis of the substrate for miscut angles up to θ_S≈15°. TEM also reveals the step-like film morphology due to step-flow growth. The in-plane and out-of-plane resistivities are independent of film thickness within the range 20–300 nm and agree quite well with Bi₂Sr₂CaCu₂O_8+δ single-crystal data. Received:15 May 2000 / Accepted:17 May 2000 / Published online: 9 August 2000     

Interaction force between incompatible star-polymers in dilute solution

We consider a low-density assembly of spherical colloids, such that each is clothed by L end-grafted chemically incompatible polymer chains either of types A or B. These are assumed to be dissolved in a good common solvent. We assume that colloids are of small size to be considered as star-polymers. Two adjacent star-polymers A and B interact through a force F originating from both excluded-volume effects and chemical mismatch between unlike monomers. Using a method developed by Witten and Pincus (Macromolecules 19, 2509 (1986)) in the context of star-polymers of the same chemical nature, we determine exactly the force F as a function of the center-to-center distance h. We find that this force is the sum of two contributions F _e and F _s. The former, that results from the excluded volume, decays as F _e∼A _L h ^-1, with the L -dependent universal amplitude A _L∼L ^3/2. While the second, which comes from the chemical mismatch, decays more slowly as F _s∼χB _L h ^{-1 - τ}, where τ is a critical exponent whose value is found to be τ 0.40, and χ is the standard Flory interaction parameter. We find that the corresponding L-dependent universal amplitude is B _L∼L ^{3 + τ /2}. Theses forces are comparable near the cores of two adjacent star-polymers, i.e. for h∼h _c∼a (a is the monomer size). Finally, for two star-polymers of the same chemical nature (A or B), the force F that simply results from excluded-volume effects coincides exactly with F _e, and then the known result is recovered. Received 2 October 2000 and Received in final form 24 January 2001     

Gels at interfaces

We discuss the adsorption of polymer gels on flat surfaces. Even in cases of complete wetting where the spreading power S is positive and where an equivalent liquid would spread, the elastic stresses due to the gel deformation upon adsorption oppose the spreading. The competition between elasticity characterized by the bulk shear modulus G and capillarity characterized by the spreading power S defines a typical length scale ℓ = S/G for the deformation in the gel. For loose gels ℓ can be of the order of 1 μm. Macroscopic gels larger than ℓ deform only at their edges over a region of size ℓ. Microscopic gels smaller than ℓ show a finite deformation despite the elastic stresses. The elastic stresses limit the spreading of the polymer, but solvent can be sucked out of a swollen gel by wetting the surface. The thin solvent film can extend rather far from the gel edge and carry solvent. We calculate the kinetics of the solvent film formation and of the solvent transfer from a more swollen gel to a less swollen gel. Received 16 July 2001     

Spinodal dewetting of thin liquid films at soft interfaces

We study theoretically the behavior of nanoscopic liquid films L (thickness e) intercalated between a solid S and a rubber R (elastic modulus μ). Thickness modulations involve a healing length , which results from a competition between elastic and disjoining pressure. With van der Waals interactions, , where a is a molecular size and h₀ the rubber capillary length ( , interfacial tension). If the Hamaker constant of the intercalated liquid is negative, the film dewets by amplification of peristaltic fluctuations (“spinodal dewetting”). The typical size of the contacts is predicted to scale like for films of thicknesses . The rise time of the fastest mode, predicted to scale like , should be very sensitive to the film thickness. Received 11 February 2000 and Received in final form 22 May 2000     

The origin of the redshift in Brillouin spectra of silica films containing tin nanoparticles

The abrupt change of velocity in surface acoustic waves in thin films of amorphous SiO_x containing nanometre scale -Sn crystals is shown to be directly associated with the size-dependent melting of the nanoparticles, confirming preliminary experiments. High resolution thin film powder diffraction using synchrotron radiation shows that the abrupt redshift in the Brillouin spectra satellites occurs at the same temperature as the melting of the nanoparticles, evident for the loss of the Bragg peaks. Effective medium theory is used to explain the origin of the anomaly. A central peak in the Brillouin spectrum, the intensity of which shows a maximum at the melting temperature, can be interpreted in terms of overdamped fluctuations in the dielectric function. The melting temperature as a function of particle size is in agreement with theoretical predictions. No evidence for strain could be found on the X-ray diffraction profiles; the a- and c-axis thermal expansion coefficients are the same as those in bulk tin. Received 30 March 2000 and Received in final form 24 July 2000     

A cluster Monte Carlo algorithm for 2-dimensional spin glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100² down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e ^2βJ) and not as a power law as T↦T _c = 0. Received 10 January 2001 and Received in final form 29 May 2001     

Drift of a polymer chain in a porous medium --A Monte Carlo study

We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B _c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B _c itself is found to decrease linearly with C. Received 20 August 2001 and Received in final form 19 November 2001     

Mobility in thin polymer films ranging from local segmental motion, Rouse modes to whole chain motion: A coupling model consideration

Large increases of mobility of local segmental relaxation observed in polymer films as the film thickness is decreased, as evidenced by decreases of the glass temperature, are not found for relaxation mechanisms that have longer length scales including the Rouse relaxation modes and the diffusion of entire polymer chains. We show that the coupling model predictions, when extended to consider polymer thin films, are consistent with a large increase of the mobility of the local segmental motions and the lack of such a change for the Rouse modes and the diffusion of entire polymer chains. There are two effects that can reduce the coupling parameter of the local segmental relaxation in thin films. One is the chain orientation that is induced parallel to the surface when the film thickness h becomes smaller than the end-to-end distance of the chains and the other is a finite-size effect when h is no longer large compared to the cooperative length scale. Extremely thin ( ≈ 1.5 nm) films obtained by intercalating a polymer into layered silicates have thickness significantly less than the cooperative length scale near the bulk polymer glass transition temperature. As a result, the coupling parameter of the local segmental relaxation in such thin films is reduced almost to zero. With this plausible assumption, we show the coupling model can explain quantitatively the large decrease of the local segmental relaxation time found experimentally. Received 1 August 2001 and Received in final form 1 December 2001     

Collapse of sodium polyacrylate chains in calcium salt solutions

The sodium salt of polyacrylic acid (NaPA) precipitates in the presence of Ca²⁺-ions. This phase behaviour can be represented by a phase diagram where the critical NaPA concentration is plotted versus the critical Ca²⁺ concentration resulting in a straight line as a phase boundary. The location of this phase boundary is influenced by the presence of an inert monovalent salt like NaCl. The present contribution focuses on the coil dimensions of NaPA chains in dilute aqueous solution corresponding to the one phase region of such a phase diagram. A variety of parameters with which the size and shape of the polyelectrolyte chains can be modulated are revealed. Approaching the phase boundary by decreasing the NaPA concentration at a constant Ca²⁺ content leads to a collapse of the NaPA chains. Combined static and dynamic light scattering suggests a compact spherical shape as the final state of this transition, both in 0.1 M NaCl and in 0.01 M NaCl. In the lower NaCl concentration, indication is presented for the existence of a cigar or pearl necklace like intermediate. Most strikingly, the collapsed chains can be reexpanded by increasing the concentration of inert NaCl at constant content of NaPA and Ca²⁺. Clearly, excessive Na⁺-ions displace the Ca²⁺-ions from the NaPA chains. Received 18 July 2000 and Received in final form 24 August 2000     

Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

Ionic distribution and polymer conformation, near phase separation, in sodium polyacrylate/divalent cations mixtures: small angle X-ray and neutron scattering

Anomalous small angle X-ray scattering experiments show that before demixion in sodium polyacrylate/cobalt and sodium polyacrylate/calcium mixtures all the divalent counterions are in the close vicinity of the polyacrylate chain. The present results are consistent with previous UV/VIS spectroscopy, which have shown that all cobalt ions are chemically associated with acrylate groups. The chemical association dehydrates the acrylate monomers. However, the hydrophobicity of the complexed monomers is not strong enough to induce a collapse of the polymer chain at small spatial scale before the demixion. Indeed, the scattered intensity (X-ray and neutron scattering) decreases with the scattering vector q as q^-x with for q > 0.1 nm ^-1 which indicates that the local conformation of the chain is Gaussian. Received 21 January 1999     

Hall effect plateaus and giant Shubnikov-de Haas oscillations in (BiSb)Telayered single crystals near the quantum limit

On bulk layered single crystals (Bi_0.25Sb_0.75)₂Te₃ with a hole concentration cm^-3 and a mobility cm²/Vs magnetoresistance and Hall effect investigations were performed in the temperature range T = 1.4 K ... 20 K in magnetic fields up to 18 T. For the magnetic field perpendicular to the layered structure giant Shubnikov-de Haas oscillations are measured; the positions of the maxima are triplets in the reciprocally scaled magnetic field. From the damping of the amplitudes with increasing temperature the cyclotron mass m _c = 0.12m ₀ is evaluated. Correlated with the SdH oscillations doublets of Hall effect plateaus (or kinks in low fields) are found. The weak well known Shubnikov-de Haas oscillations from the generally accepted multivallied highest valence band can be detected as a modulation on the giant oscillation. The high anisotropy of the SdH oscillations and their triplet structure in connection with the layered crystal structure lead us to suggest that the effects are caused by hole carrier pairing (mediated by the bipolaron mechanism) in quasi 2D sheets parallel to the crystal layer stacks. The measured Hall plateau resistances coincide with the quantum Hall effect values considering the number of layer stacks and the valley degeneracy of the 3D hole carrier reservoir. The ratio of spin splitting to Landau (cyclotron) splitting is observed to be . Received: 12 September 1997 / Revised: 8 January 1998 / Accepted: 22 January 1998     

Phase behavior of a suspension of hard spherocylinders plus ideal polymer chains

We study isotropic-isotropic and isotropic-nematic phase transitions of fluid mixtures containing hard spherocylinders (HSC) and added non-adsorbing ideal polymer chains using scaled particle theory (SPT). First, we investigate isotropic-nematic (I -N phase coexistence using SPT in the absence of polymer. We compare the results obtained using a Gaussian form of the orientational distribution function (ODF) to minimize the free energy versus minimizing numerically. We find that formal numerical minimization gives results that are much closer to computer simulation results. In order to describe mixtures of HSC plus ideal chains we studied the depletion of ideal chains around a HSC. We analyze the density profiles of ideal chains near a hard cylinder and find the depletion thickness δ is a function of the ratio of the polymer's radius of gyration R_g and the cylinder radius R_c. Our results are compared with a common approximation in which the depletion thickness is taken equal to the radius of gyration of the polymer chain. We incorporate the correct depletion thickness into SPT and find that for R _g/R _c < 1.56 using ideal chains gives phase transitions at smaller polymer concentrations, whereas for R _g/R _c > 1.56 , which is a common experimental situation, the phase transitions are found at larger polymer concentrations with respect to δ = R _g . The differences are significant, especially for R _g ≫ R _c , so we can conclude it is essential to take into account the properties of ideal polymer chains and the resulting depletion near a cylinder. Finally, we present phase diagrams for rod-polymer mixtures which could be realized under experimental conditions.