Kinetics of microphase separation in interpenetrated polymer networks in solution

We present here a theoretical study of the early kinetics of the microphase separation in crosslinked polymer blends, made of two incompatible polymers A and B, dissolved in a common good solvent. Use is made of an extended blob model used previously for the investigation of the static properties of such a transition. We are interested in the variation of the relaxation rate, , versus the wave number q, in the vicinity of the spinodal temperature. We first show that kinetics is entirely dominated by local motions, which are of Rouse type. Slow motions are absent, because of the permanent presence of crosslinks. Second, we find that the characteristic frequency, (q ) = , increases with increasing wave number q according to a sixth power law, that is (q ) q^6{-9/4}, where is the overall monomer volume fraction. Therefore, the swelling of strands due to the excluded-volume forces leads to a renormalization of the characteristic frequency by a multiplicative factor scaling as ^{-9/4}. The main conclusion is that the presence of a good solvent necessitates relaxation rates less important than those relative to crosslinked mixtures in the molten state.     

Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed. Received: 21 November 1997 / Received in final form: 21 April 1998 / Accepted: 24 April 1998     

3d Monte Carlo simulation of site-bond continuum percolation of spheres

We present off-lattice Monte Carlo simulations of site-bond percolation of semi-penetrable spheres or, equivalently, of hard spheres with a finite bond range. We will show that the crucial parameter is the effective volume fraction ( φ_e), i.e. the volume that is occupied or within the bond range of at least one particle. For the equivalent system of semi-penetrable spheres 1 - φ_e is the porosity. The bond percolation threshold (p _b) can be described in terms of φ_e by a simple analytical expression: log(φ_e)/log(φ_ec) + log(p _b)/log(p _bc) = 1, with p _bc = 0.12 independent of the bond range and φ_ec a constant that decreases with increasing bond range. Received: 10 March 2003 / Accepted: 23 April 2003 / Published online: 21 May 2003 RID="a" ID="a"e-mail: jean-christophe.gimel@univ-lemans.fr     

Flocculation and percolation in reversible cluster-cluster aggregation

Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (t_e). t_e is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is d_f=2.0 and the size distribution has a power law decay with exponent τ=1.5. At larger values of t_e transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension d_f=2.7 and the power law exponent of the size distribution is τ=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction.     

Density-correlator signatures of the vulcanization transition

Certain density correlators, measurable via various experimental techniques, are studied in the context of the vulcanization transition. It is shown that these correlators contain essential information about both the vulcanization transition and the emergent amorphous solid state. Contact is made with various physical ingredients that have featured in experimental studies of amorphous colloidal and gel systems and in theoretical studies of the glassy state. Received 30 September 2000     

Multifractal properties of aperiodic Ising model on hierarchical lattices: role of the geometric fluctuations

The role of the geometric fluctuations on the multifractal properties of the local magnetization of aperiodic ferromagnetic Ising models on hierarchical lattices is investigated. The geometric fluctuations are introduced by generalized Fibonacci sequences. The local magnetization is evaluated via an exact recurrent procedure encompassing real space renormalization group decimation. The symmetries of the local magnetization patterns induced by the aperiodic couplings is found to be strongly (weakly) different, with respect to the ones of the corresponding homogeneous systems, when the geometric fluctuations are relevant (irrelevant) to change the critical properties of the system. At the criticality, the measure defined by the local magnetization is found to exhibit a non-trivial F(α) spectra being shifted to higher values of α when relevant geometric fluctuations are considered. The critical exponents are found to be related with some special points of the F(α) function and agree with previous results obtained by the quite distinct transfer matrix approach. Received 2 April 2001 and Received in final form 14 August 2001     

Complex dynamics in gelling systems

We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical-mechanics model. The model is based on percolation and bond fluctuation dynamics. The values for the critical exponents of the viscosity and elasticity agree with a part of the experimental observations and of the theoretical predictions. The obtained relaxation patterns well reproduce the behaviour observed in different gelling systems. Received 10 March 2002 and Received in final form 30 April 2002     

DMRG studies on interchain coupling model for quasi-one-dimensional organic magnet

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦. Received 14 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de     

Adsorption from pure and mixed vapours of n-hexane and n-perfluorohexane

We have used a modified surface force apparatus (SFA) to study adsorption onto mica surfaces from near-saturated vapours of n-hexane and n-perfluorohexane, and mixtures thereof. For relative vapour pressures in the range 0.9-0.998 the films adsorbed from vapours of the pure liquids range in thickness from 1 to 4 nm, in crude agreement with the predictions of non-retarded van der Waals-Lifshitz theory. The observed deviations from theory show a qualitative difference between the two liquids, which may reflect differences in the significance of structural contributions to the disjoining pressure. Under the same experimental conditions, adsorption from vapours of (one-phase) liquid mixtures gives rise to films which are significantly thicker, over a broad range of intermediate compositions, than those adsorbed from the pure vapours, with a broad maximum in thickness observed near the critical composition of the bulk liquid mixture. Received 30 July 2001     

Non-equilibrium behavior at a liquid-gas critical point

Second-order phase transitions in a non-equilibrium liquid-gas model with reversible mode couplings, i.e., model H for binary-fluid critical dynamics, are studied using dynamic field theory and the renormalization group. The system is driven out of equilibrium either by considering different values for the noise strengths in the Langevin equations describing the evolution of the dynamic variables (effectively placing these at different temperatures), or more generally by allowing for anisotropic noise strengths, i.e., by constraining the dynamics to be at different temperatures in d _|| - and d _⊥-dimensional subspaces, respectively. In the first, isotropic case, we find one infrared-stable and one unstable renormalization group fixed point. At the stable fixed point, detailed balance is dynamically restored, with the two noise strengths becoming asymptotically equal. The ensuing critical behavior is that of the standard equilibrium model H. At the novel unstable fixed point, the temperature ratio for the dynamic variables is renormalized to infinity, resulting in an effective decoupling between the two modes. We compute the critical exponents at this new fixed point to one-loop order. For model H with spatially anisotropic noise, we observe a critical softening only in the d _⊥-dimensional sector in wave vector space with lower noise temperature. The ensuing effective two-temperature model H does not have any stable fixed point in any physical dimension, at least to one-loop order. We obtain formal expressions for the novel critical exponents in a double expansion about the upper critical dimension d _c = 4 - d _|| and with respect to d _|| , i.e., about the equilibrium theory. Received 4 April 2002 Published online 13 August 2002     

Early stages of phase separation from polydisperse polymer mixtures

We study the early stages of phase separation in a mixture of a polydisperse and a monodisperse polymer within the Cahn-Hilliard framework. We model the polydisperse component using a finite, but arbitrarily large, number of components, and show that the number of components required for convergent behaviour to be achieved is computationally undemanding. We study the growth rate of fluctuations following a quench into the two-phase region of the phase diagram. The q-dependence of the growth rate is shown to be commensurate with the behaviour of a monodisperse-monodisperse mixture, with the major difference being an effective mobility that is dependent on the quench depth. We also study the deviation of the time dependence of the scattering function from single exponential behaviour. Received 29 June 2000 and Received in final form 20 November 2000     

Jump of the minimal site and a new correlation function in the Bak-Sneppen model

A new type of spatio-temporal correlation function for the process approaching the self-organized criticality is investigated within the Bak-Sneppen model for biological evolution. In terms of the “directional shorter distance” between the two sites with minimum fitness at two successive updates, the correlation function is defined and studied numerically for the nearest- and random-neighbor versions of the model. Qualitatively different behaviors of the jump of the minimal site in the two models are presented, and the behaviors of the correlation functions are shown also different. Received 14 April 2001 and Received in final form 28 June 2001     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

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     

Time of avalanche mixing of granular materials in a half filled drum

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference δ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time τ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when δ is an integer part of π. Introduction of fluctuations of δ suppresses the singularities of τ(δ) and smoothes the dependence τ(δ). Received 27 October 2000 and Received in final form 13 March 2001     

Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation

The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter.     

Finite-size scaling in systems with long-range interaction

The finite-size critical properties of the (n) vector ϕ⁴ model, with long-range interaction decaying algebraically with the interparticle distance r like r ^{-d - σ}, are investigated. The system is confined to a finite geometry subject to periodic boundary condition. Special attention is paid to the finite-size correction to the bulk susceptibility above the critical temperature T _c. We show that this correction has a power-law nature in the case of pure long-range interaction i.e. 0 < σ < 2 and it turns out to be exponential in case of short-range interaction i.e.σ = 2. The results are valid for arbitrary dimension d, between the lower ( d _< = σ) and the upper ( d _> = 2σ) critical dimensions. Received 2 July 2001 and Received in final form 4 Septembre 2001     

Aggregation of non-bonding molecules in a rapidly growing gel

The aggregation of non-bonding molecules in a rapidly growing gel is studied under three different conditions by means of Molecular Dynamics simulations. The aggregation takes place even under the unfavorable condition when the non-bonding molecules constitute only a small fraction of the total. The results also show that the morphology of the growing domains is different depending on the concentration of the non-bonding molecules. Received 30 November 1999     

Hydrodynamic-flow-driven phase evolution in a polymer blend film modified by diblock copolymers

We have studied surface-directed phase separation in thin films of deuterated polystyrene and poly(bromostyrene) (with 22.7% of monomers brominated) using ³He nuclear reaction analysis, dynamic secondary ion mass spectroscopy and atomic force microscopy combined with preferential dissolution. The crossover from competing to neutral surfaces of the critical blend film (cast onto Au) was commenced: polyisoprene-polystyrene diblock copolymers were added and segregated to both surfaces reducing in a tuneable manner the effective interactions. Two main stages of phase evolution are characterised by i) the growth of two surface layers and by ii) the transition from the four-layer to the final bilayer morphology. For increasing copolymer content the kinetics of the first stage is hardly affected but the amplitude of composition oscillations is reduced indicating more fragmented inner layers. As a result, a faster mass flow to the surfaces and an earlier completion of the second stage were observed. The hydrodynamic flow mechanism, driving both stages, is evidenced by nearly linear growth of the surface layer and by mass flow channels extending from the surface layer into the bulk. The final bilayer structure, formed even for the surfaces covered by strongly overlapped copolymers, is indicative of long-range (antisymmetric) surface forces. Received 15 March 2000 and Received in final form 9 February 2001