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     

Asymmetric landscapes of early spinodal decomposition

We address the effect of an asymmetric concentration-dependent mobility on the early stages of spinodal decomposition in polymer blends and solutions, and characterise it quantitatively. This is particularly important when one of the components has a slower dynamics than the other, e.g., because it is closer to its glass transition, or is weakly cross-linked. Composition mode coupling is proposed as the underlying physical mechanism, and then investigated by means of numerical simulations of the Cahn-Hilliard equation in one (1d) and two (2d) dimensions. In general, this coupling broadens the peak in the structure factor: in 1d an asymmetric concentration profile is obtained, with sharpened interfaces, whereas in 2d the formation is favoured of sharp peaks of the phase rich in the more mobile component. It is shown how the changing morphology of this phase-separating system can be described with the aid of Minkowski functionals. Received 28 August 2000 and Received in final form 18 July 2001     

Thermophysical properties of fluorinated acrylate homopolymers: Mixing and phase separation

The thermophysical properties of fluorinated acrylate homopolymers are investigated by differential scanning calorimetry (DSC) and optical microscopy and discussed in terms of relative lengths of the fluorinated chain and the hydrocarbon spacer between the acrylate moiety and the fluorinated chain. These compounds exhibit an intrinsic microphase-separation (Isotropic+Isotropic morphology) occurring between the fluorinated chains and the acrylate polymer backbone. It is shown that the enthalpy of mixing is a function of the length of the lateral fluorocarbon chains. The thermophysical behaviour of these materials may be regarded as demixed systems exhibiting an Upper Critical Solution Temperature. The photopolymerization process of one of the monomer is studied by isothermal photocalorimetry. High acrylate double-bond conversion and fast curing rates were obtained thus demonstrating the promising use of these materials for coating and film processing applications using UV-curing techniques. Received 30 January 2002     

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     

Solid-like friction of a polymer chain

We propose a simple friction model for isolated polymer chains on a solid substrate. The chains are pulled at constant velocity by one end, the other end can be trapped on the solid substrate on localised sites. We focus on the energy dissipation due to the traps. This simple model leads to nontrivial friction laws, depending on the velocity and the distance between traps. Some refinements of the model such as the effect of thermal fluctuations are also reported. Received 20 March 2000     

What can polymer crystal structure tell about polymer crystallization processes?

Contrary to most or all other materials, crystallization of chiral but racemic polymers such as isotactic polypropylene is accompanied by a conformational rearrangement which leads to helical geometries: the building units of the crystal are helical stems, -20nm long, which can be either right-handed or left-handed. Helical hand cannot be reversed within the crystal structure: it is therefore a permanent marker and an indicator of molecular processes (in particular segregation/selection of helical hands) which take place during crystal growth, and more precisely during the crucial step of “efficient” helical stem deposition. The issue of proper helical hand selection during polymer crystal growth is mainly illustrated with isotactic polypropylene. Its various crystalline polymorphs (, , and smectic) display virtually all possible combinations of helical hands, azimuthal settings and even non-parallel orientation of helix axes in space. Furthermore, a specific homoepitaxy which generates a lamellar branching in the phase “quadrites” and composite structures makes it possible a) to determine the helical hand and associated azimuthal setting of every stem in the crystalline entities and b) to determine the impact on the crystal structure and morphology of “mistakes” in helical hand of the depositing stem. Analysis of these morphologies demonstrates that the crystallization of isotactic polypropylene (and by implication of other achiral, helical polymers) is a highly sequential and “substrate-determined” process, i.e. that the depositing stem probes the topography of the growth face prior to attachment. These observations appear difficult to reconcile with crystallization schemes in which molecules (helical segments) are prearranged in a kind of pseudo-crystalline bundle (and as such, are not subjected to the high constraints of crystal symmetry) before deposition as a preassembled entity on the substrate. Received: 5 May 2000     

Kinetics of phase separation in ramified polymer blends of arbitrary topology

We present here a theoretical study of kinetics of phase separation within a mixture made of two chemically incompatible ramified polymers. For simplicity, we assume that they have the same topology. We are interested in the variation of the relaxation rate, _q, versus the wave number q, in the vicinity of the spinodal temperature. The kinetics is governed by local (Rouse) and reptation motions (faster and slower modes). For qR_G 1 (R_G being the gyration radius), kinetics is entirely controlled by local motions where each chain moves inside its own tube, and we show that the corresponding characteristic frequency, ^{-1}_q, scales as ^{-1}_{q G}q⁶, where _G is a known topological factor. For qR_G 1, however, kinetics is rather dominated by long-wavelength (reptation) motions where unlike ramified polymers creep inside a long tube. For this case, we find that ^{-1}_q ( 0 )q² (_c - ), where ( 0 ) is another known topological factor that represents the total mobility of free monomers belonging to connected chains and reticulation points, and _c accounts for the critical value of the segregation parameter. Finally, the derived relaxation rate must be compared to that relative to a linear polymer mixture.     

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     

Density functional theory for nonuniform polymer melts: Based on the universality of the free energy density functional

A density functional theory is proposed for nonuniform freely jointed tangential hard sphere polymer melts in which the bonding interaction is treated on the basis of the properties of the Dirac δ-function, thus avoiding the use of the single chain simulation in the theory. The excess free energy is treated by making use of the universality of the free energy density functional and the Verlet-modified (VM) bridge function. To proceed numerically, one of the input parameters, the second-order direct correlation function of a uniform polymer melt is obtained by solving numerically the Polymer-RISM integral equation with the Percus-Yevick (PY) closure. The predictions of the present theory for the site density distribution, the partition coefficient and the adsorption isotherm, near a hard wall or between two hard walls are compared with computer simulation results and with those of previous theories. Comparison indicates that the present approach is more accurate than the previous integral equation theory and the most accurate Monte Carlo density functional theories. The predicted oscillations of the medium-induced force between two hard walls immersed in polymer melts are consistent with the experimental results available in the literature. Received 18 April 2000     

Cellular solid behaviour of liquid crystal colloids 1. Phase separation and morphology

We study the phase ordering colloids suspended in a thermotropic nematic liquid crystal below the clearing point and the resulting aggregated structure. Small () PMMA particles are dispersed in a classical liquid crystal matrix, 5CB or MBBA. With the help of confocal microscopy we show that small colloid particles densely aggregate on thin interfaces surrounding large volumes of clean nematic liquid, thus forming an open cellular structure, with the characteristic size of inversely proportional to the colloid concentration. A simple theoretical model, based on the Landau mean-field treatment, is developed to describe the continuous phase separation and the mechanism of cellular structure formation. Received 13 March 2000 and Received in final form 6 June 2000     

Kinetics of reversible surface crystallization and melting in poly(ethylene oxide): Effect of crystal thickness observed in the dynamic heat capacity

Poly(ethylene oxide) (PEO) in the semi-crystalline state shows a reversible surface crystallization and melting; a temperature decrease leads to a certain crystal thickening, a temperature increase reversely to an expansion of the amorphous intercrystallite layers. Dynamic calorimetry provides a means to investigate the kinetics of the process. The structural rearrangement in the region of the crystalline-amorphous interface can only be accomplished if the chains can slide through the crystallites. One therefore expects the associated time to change with the crystallite thickness. Variations of the crystal thickness of PEO can be achieved by choosing different crystallization temperatures. We studied the effect of the crystal thickness employing temperature-modulated differential scanning calorimetry and heat wave spectroscopy, and by carrying out small-angle X-ray scattering experiments for the structural characterization. The effect of the crystal thickness is clearly observed. Results indicate that the sliding diffusion through the crystallites takes place by helical jumps of whole stems. Data yield the activation energy per unit length of the stems. Received 20 April 2001 and Received in final form 13 August 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     

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     

Stability of thin polymer films on a corrugated substrate

We study the wetting behaviour of thin polystyrene (PS) films on regularly corrugated silicon substrates. Below a critical film thickness the PS films are unstable and dewet the substrates. The dewetting process leads to the formation of nanoscopic PS channels filling the grooves of the corrugated substrates. Films thicker than the critical thickness appear stable and follow the underlying corrugation pattern. The critical thickness is found to scale with the radius of gyration of the unperturbed polymer chains. Received 6 April 2000 and Received in final form 24 August 2000     

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.     

Elastic rod model of a supercoiled DNA molecule

We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod-like chain, involving two elastic constants, the bending and the twist rigidities. Writing this model in terms of Euler angles, we show that the corresponding Hamiltonian is singular and needs a small distance cut-off, which is a natural length scale giving the limit of validity of the model, of the order of the double-helix pitch. The rod-like chain in the presence of the cut-off is able to reproduce quantitatively the experimentally observed effects of supercoiling on the elongation-force characteristics, in the small supercoiling regime. An exact solution of the model, using both transfer matrix techniques and its mapping to a quantum mechanics problem, allows to extract, from the experimental data, the value of the twist rigidity. We also analyse the variation of the torque and the writhe-to-twist ratio versus supercoiling, showing analytically the existence of a rather sharp crossover regime which can be related to the excitation of plectoneme-like structures. Finally we study the extension fluctuations of a stretched and supercoiled DNA molecule, both at fixed torque and at fixed supercoiling angle, and we compare the theoretical predictions to some preliminary experimental data. Received 1 April 1999 and Received in final form 4 January 2000     

Linear hydrodynamics and viscoelasticity of nematic elastomers

We develop a continuum theory of linear viscoelastic response in oriented monodomain nematic elastomers. The expression for the dissipation function is analogous to the Leslie-Ericksen version of anisotropic nematic viscosity; we propose the relations between the anisotropic rubber moduli and new viscous coefficients. A new dimensionless number is introduced, which describes the relative magnitude of viscous and rubber-elastic torques. In an elastic medium with an independently mobile internal degree of freedom, the nematic director with its own relaxation dynamics, the model shows a dramatic decrease in the dynamic modulus in certain deformation geometries. The degree to which the storage modulus does not altogether drop to zero is shown to be both dependent on frequency and to be proportional to the semi-softness, the non-ideality of a nematic network. We consider the most interesting geometry for the implementation of the theory, calculating the dynamic response to an imposed simple shear and making predictions for effective moduli and (exceptionally high) loss factors. Received 16 October 2000 and Received in final form 10 December 2000     

Swollen-collapsed transition in random hetero-polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic charges interacting with the solvent is introduced, whose continuum counterpart has been proposed by Garel, Leibler and Orland [#!GLO!#]. The transfer matrix technique is used to study various constrained annealed systems which approximate at various degrees of accuracy the original quenched model. For highly hydrophobic chains an ordinary -point transition is found from a high temperature swollen phase to a low temperature compact phase. Depending on the type of constrained averages, at very low temperatures a swollen phase or a coexistence between compact and swollen phases are found. The results are carefully compared with the corresponding ones obtained in the continuum limit, and various improvements in the original calculations are discussed. Received: 10 April 1998 / Revised: 4 June 1998 / Accepted: 1st July 1998