Polyelectrolyte multilayer formation: Electrostatics and short-range interactions

We investigate the phenomenon of multilayer formation via layer-by-layer deposition of alternating charged polyelectrolytes. Using mean-field theory, we find that a strong short-range attraction between the two types of polymer chains is essential for the formation of multilayers. For strong enough short-range attraction, the adsorbed amount per layer increases (after an initial decrease), and finally it stabilizes in the form of a polyelectrolyte multilayer that can be repeated hundreds of times. For weak short-range attraction between any two adjacent layers, the adsorbed amount (per added layer) decays as the distance from the surface increases, until the chains stop adsorbing altogether. The dependence of the threshold value of the short-range attraction as function of the polymer charge fraction and salt concentration is calculated.     

Influence of polydispersity on the phase behavior of statistical multiblock copolymers with Schultz-Zimm block molecular weight distributions

In this paper we investigate in a systematic way the influence of polydispersity in the block lengths on the phase behavior of AB-multiblock copolymer melts. As model system we take a polydisperse multiblock copolymer for which both the A-blocks and the B-blocks satisfy a Schultz-Zimm distribution. In the limit of low polydispersity the expressions for the vertex functions are clarified by using simple physical arguments. For various values of the polydispersity the phase diagram is presented, which shows that the region of stability of the bcc phase increases considerably with increasing polydispersity. The strong dependence of the periodicity of the microstructure on the polydispersity and on the interaction strength is presented. Received 2 July 1998     

Heterogeneous dynamics at the glass transition in van der Waals liquids: Determination of the characteristic scale

Recent experiments have demonstrated that the dynamics in liquids close to the glass transition temperature is strongly heterogeneous. The characteristic size of these heterogeneities has been measured to be a few nanometers at T _g. We extend here a recent model for describing the heterogeneous nature of the dynamics which allows both to derive this length scale and the right orders of magnitude of the heterogeneities of the dynamics close to the glass transition. Our model allows then to interpret quantitatively small probes diffusion experiments. Received 29 March 2002 and Received in final form 11 November 2002 RID="a" ID="a"e-mail: long@lps.u-psud.fr     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

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     

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     

Detachment of stretched viscoelastic fibrils

New experimental results are presented about the final stage of failure of soft viscoelastic adhesives. A microscopic view of the detachment of the adhesive shows that after cavity growth and expansion, well adhered soft adhesives form a network of fibrils connected to expanded contacting feet which fail via a sliding mechanism, sensitive to interfacial shear stresses rather than by a fracture mechanism as sometimes suggested in earlier work. A mechanical model of this stretching and sliding failure phenomenon is presented which treats the fibril as a nonlinear elastic or viscoelastic rod and the foot as an elastic layer subject to a friction force proportional to the local displacement rate. The force on the stretched rod drives the sliding of the foot against the substrate. The main experimental parameter controlling the failure strain and stress during the sliding process is identified by the model as the normalized probe pull speed, which also depends on the magnitude of the friction and PSA modulus. In addition, the material properties, viscoelasticity and finite extensibility of the polymer chains, are shown to have an important effect on both the details of the sliding process and the ultimate failure strain and stress. Electronic supplementary material Appendix B is only available in electronic form at and are accessible for authorised users.     

Adsorption of a random heteropolymer with random self-interactions onto an interface

We consider the adsorption of a random heteropolymer onto an interface within the model of Garel et al. [#!gareletal89!#] by taking into account random self-interactions and ternary repulsive interactions between the monomers. Within the replica trick and by using a self-consistent preaveraging procedure we map the adsorption problem onto the problem of binding state of a quantum mechanical Hamiltonian. The analysis of the latter is treated within the variational method based on the 2nd Legendre transform. Our study reveals a complex behaviour of the localization of the heteropolymer. In particular, we predict a reentrant localization transition for moderate values of the asymmetry of the distribution function of the monomer sequences along the heteropolymer. Received 9 October 2001 and Received in final form 27 February 2002 Published online 6 June 2002     

Solvable lattice gas models of random hetero-polymers at finite density: I. Statics

We introduce -dimensional lattice gas versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the problems related to the (quenched) average over the randomness in statistical mechanical models of proteins, without having to deal with the hard geometrical constraints occurring in finite-dimensional models. Our exact solution, which is specific to the -dimensional case, is compared to the results obtained by a saddle-point analysis and by the grand ensemble approach, both of which can also be applied to models of finite dimension. We find, somewhat surprisingly, that the saddle-point analysis can lead to qualitatively incorrect results. Received 15 June 1999 and Received in final form 14 October 1999     

Polymers grafted to a fluid and flexible membrane: Extreme sensitivity to the grafting density

Equilibrium phase coexistence between two chemical species implies the equality of the chemical potentials and of the osmotic pressures. We study this problem on a deformable membrane when one type of the molecules serves as anchor for polymeric chains immersed in the surrounding medium (considered as a good solvent). We derive the general conditions for phase coexistence when both the curvature of the membrane and the density field of the anchor molecule are free to adjust themselves. We show that curvature favors phase segregation. Our model predicts that membranes decorated with polymeric chains exhibit new shape bifurcations without equivalent in fixed density systems. Received: 26 November 2002 / Accepted: 2 April 2003 / Published online: 12 May 2003 RID="a" ID="a"e-mail: nicolas@drfmc.ceng.cea.fr RID="b" ID="b"e-mail: bfourcade@cea.fr     

Spontaneous condensation in DNA-polystyrene- b-poly(l-lysine) polyelectrolyte block copolymer mixtures

We investigated the condensation of calf thymus DNA by amphiphilic polystyrene_m-b-poly(l-lysine)_n block copolymers ( PS_m-b- PLys_n, m, n = degree of polymerization), using small-angle X-ray scattering, polarized optical microscopy and laser scanning confocal microscopy. Microscopy studies showed that the DNA condenses in the form of fibrillar precipitates, with an irregular structure, due to electrostatic interactions between PLys and DNA. This is not modified by the presence of hydrophobic PS block. Scattering experiments show that the structure of the polyplexes corresponds to a local order of DNA rods which becomes more compact upon increasing n. It can be concluded that for DNA/ PS_m-b- PLys_n polyplexes, the balance between the PLys block length and the excess charge in the system plays an essential role in the formation of a liquid crystalline phase.     

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     

Confinement of columnar diblock copolymers: Simulations, theory and applications

The inherent nanoscale morphologies of self-organizing diblock copolymer melts are now being investigated for a variety of technological applications. To obtain global, well-oriented, regular patterns requires suitably confining and aligning the melt between two flat plates. Here we consider such confinement for an asymmetrical diblock melt, which forms columns of the minority phase in a matrix of the majority phase. We investigate this system with a combination of numerical simulations and strong segregation theory and make suggestions as to when perpendicular orientation should prevail over parallel orientation of the columns. Received 22 May 2001 and Received in final form 14 February 2002     

Morphologies of diblock copolymer thin films before and after crystallization

Spin-coated thin films of about 100nm of low-molecular-weight hydrogenated poly(butadiene-b- ethyleneoxide) (PB_h-PEO) diblock copolymers have been crystallized at various constant temperatures. Crystallization has been observed in real time by light microscopy. Detailed structural information was obtained by atomic force microscopy, mainly enabled by the large viscoelastic contrast between amorphous and crystalline regions. The behavior in thin films is compared to the bulk properties of the polymer. Crystallization started from an annealed microphase separated melt where optical microscopy indicated a lamellar orientation parallel to the substrate. A small difference in the length of the crystallizable block produced significantly different crystallization behavior, both in the bulk and in thin films. For thin films of the shortest diblock copolymer (45% PEO content) and for an undercooling larger than about 10 degrees, crystallization created vertically oriented lamellae. These vertical lamellae could be preferentially aligned over several micrometers when crystallization occurred close to a three-phase contact line. Annealing at temperatures closer to the melting point or keeping the sample at room temperature for several months allowed the formation of a lamellar structure parallel to the substrate. A tentative interpretation based on kinetically caused chain folding and relaxation within the crystalline state, with implications on general aspects of polymer crystallization, is presented. Received 19 March 1999 and Received in final form 14 December 1999     

Height and density correlations at liquid surfaces; application to X-ray scattering

We calculate height-height correlation functions, near-surface density-density correlation functions and the corresponding frequency integrated spectra for a heat conducting viscous fluid. We calculate scattering cross-sections for the static and dynamic X-ray scattering experiments recently developed to investigate the nanometer-scale structure and fluctuations of liquid interfaces. We show that the density-density correlations make an important contribution to the scattering, even using evanescent waves, and that they are strongly affected by the surface. We also discuss the implications for X-ray photon correlation spectroscopy and X-ray inelastic scattering. Received 12 October 2001 Published online 6 June 2002     

The osmotic coefficient of rod-like polyelectrolytes: Computer simulation, analytical theory, and experiment

The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and dilute, salt-free solutions. The classical Poisson-Boltzmann solution of the cell model correctly predicts a strong decrease in the osmotic coefficient, but upon closer look systematically overestimates its value. The contribution of ion-ion-correlations are quantitatively studied by MD simulations and the recently proposed DHHC theory. However, our comparison with experimental data obtained on synthetic, stiff-chain polyelectrolytes shows that correlation effects can only partly explain the discrepancy. A quantitative understanding thus requires theoretical efforts beyond the restricted primitive model of electrolytes. Received 25 July 2000 and Received in final form 4 December 2000     

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     

Film thickness effects on the distribution of high-molecular-weight heterotelechelic polymers

High-molecular-weight heterotelechelic deuteriopolystyrene, NDPSF, possessing an amine functional group at one end of the chain and a fluorocarbon group at the other was tethered to a silicon substrate by its amine functional group. These layers were coated with an unfunctionalised polystyrene matrix, HPS, such that the total film thickness covered a range from 2.2 to 9 times the radius of gyration of NDPSF. The detailed distribution of the polymers after annealing for times much greater than the reptation period of either of the components, was obtained using neutron reflectometry. No evidence for bridging of the two interfaces was found for the thicker films, but the finite concentration of the NDPSF polymer observed for the thinnest films may be due to bridging since the energy gain of the fluorocarbon end is just greater than the loss due to configurational entropy losses. A linear increase in the ellipsometric thickness of the excess of NDPSF at the substrate was discovered and we attribute this to the NDPSF slowly being leached out of the layer initially at the substrate followed by diffusion into the bulk of the film. The concentration profiles obtained are consistent with hindered relaxation of the large NDPSF molecules, when they are tethered at the substrate or at the vacuum surface. Received 21 August 2001 and Received in final form 7 January 2002     

Surface glass transition in bimodal polystyrene mixtures

Using the cluster-embedding method of V. Zaporojchenko et al. (Macromolecules 34, 1125 (2000)), we measured the glass transition temperature T _g at the polystyrene/vacuum interface of bimodal mixtures of monodisperse polystyrenes of 3.5k and 1000k. Embedding of ≈ 1 nm Au clusters was monitored in situ by X-ray photoelectron spectroscopy (XPS). The clusters were formed by evaporation of Au onto the polymer surface. Only one glass transition was observed in the mixtures. The surface glass transition temperatures are correlated to but are below the bulk values of the mixtures and obey the Gordon-Taylor equation. The results suggest that the earlier reported molecular-weight dependence of the surface glass transition is not due to segregation of short chains to the surface.