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     

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     

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     

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     

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     

Anomalous adhesion in adsorbed polymer layers

Anomalous adhesion behaviour observed in the polydimethylsiloxane/heptane/silica system is reported. This behaviour is characterised by the infrequent appearance of one or more elastic minima which occur in addition to the ever-present primary adhesion. The resulting elastic force is attributed to loops connecting the tip to the substrate and can be described by two models; a worm-like chain, and a freely jointed chain. Both models give similar values for the characteristic segment length of around 0.24 nm and indicate that the chains have been extended by between 90 to 95% of their chain contour length before desorption. In some cases multiple adhesions were observed between tip and substrate and have been used to suggest a method for determining the distribution of adsorbed polymer loops. Received: 12 November 1997 / Accepted: 6 March 1998     

Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte-Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge , and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i,j), proportional to . In this article, we take (resp. ()) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the along the chain, with periodicity 2p. The simulations are done for various chain lengths N, in d=2 (square lattice) and d=3 (cubic lattice). There is a critical value p _c (d,N) of the periodicity, which distinguishes between different low temperature structures. For p >p _c , the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p <p _c (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, and to illustrate the physics of the various phase transitions. A tentative variational approach is also presented. Received: 10 March 1998 / Received in final form: 25 June 1998 / Accepted: 1st July 1998     

Phase separation of polymer blends in solution near adsorbing surface

In this paper, we consider a mixture of two polymers A and B of different chemical nature, dissolved in a common good solvent, in contact with an interacting surface. We start from a mixture of two incompatible homopolymers A and B in the molten state, and assume that the surface adsorbs strongly one or both polymer species at high temperature. It is assumed that this is a strong adsorption, so that chains cannot desorb once they are linked to the surface. This constrains the system to a quenched composition on the surface. Once the adsorption process is finished, a quantity of a good solvent is added to get a semi-dilute solution. We assume that demixing transition in the presence of solvent occurs at lower temperature. The purpose is to discuss the influence of the quenched surface fluctuations on the critical properties of the mixture. Within the framework of the so-called blob model, we determine the exact shape of the composition profile as a function of the distance z to the surface, for any value of the relevant parameters, namely, the temperature T, the molecular weight M, the monomer concentration c and the surface composition x₀. Our analysis reveals a universal character of the composition profile for , where the characteristic size D is some known length depending on the relevant parameters of the problem, and not on temperature, and is the thermal correlation length. Near surface, for (a is the monomer size), the profile is no longer universal, and in particular, it is sensitive to the boundary condition. Far from the surface, that is , the profile tends exponentially to its bulk value. We show that the length Dapproaches its lowest value as the surface composition reaches its saturated value l. In this limit, we find that the profile shape is a characteristic of critical adsorption in simple binary fluid mixtures. Finally, this work must be regarded as a natural extension of a previous one, which was concerned with the same problem, but in the absence of solvent. Received 24 June 1999 and Received in final form 5 November 1999     

Overlap properties and adsorption transition of two Hamiltonian paths

We consider a model of two (fully) compact polymer chains, coupled through an attractive interaction. These compact chains are represented by Hamiltonian paths (HP), and the coupling favors the existence of common bonds between the chains. We use a (n=0 component) spin representation for these paths, and we evaluate the resulting partition function within a homogeneous saddle point approximation. For strong coupling (i.e. at low temperature), one finds a phase transition towards a “frozen” phase where one chain is completely adsorbed onto the other. By performing a Legendre transform, we obtain the probability distribution of overlaps. The fraction of common bonds between two HP, i.e. their overlap q, has both lower () and upper () bounds. This means in particular that two HP with overlap greater than coincide. These results may be of interest in (bio)polymers and in optimization problems. Received 4 December 1998 and Received in final form 10 March 1999     

Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents

We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions on either side of the wedge. We report on a comprehensive study of a linear chain by exact enumeration, with various attachments of the walk's ends to the surface, in wedges of angles and , with general mixed boundary conditions. Received: 20 October 1997 / Accepted: 13 May 1998     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998     

Encapsulation of filaments of a self-assembling bicopper complex in polymer nanowires

We report on the preparation conditions and the characterization by calorimetry and small-angle neutron scattering of a molecular composite material obtained via the heterogeneous nucleation of the fibrils of a thermoreversible gel. This physical process allows encapsulation of monomolecular filaments of a self-assembling bicopper complex into nanosized polymer fibrils. Due to the existence of 1-D arrangements of copper atoms, this material may possess unusual magnetic properties (spin ladders). Received 20 January 1999 and Received in final form 14 May 1999     

Dielectric properties of side chain liquid crystalline elastomers: influence of crosslinking on side chain dynamics

Dielectric response, from 1 Hz to 10 MHz, of liquid crystalline side chain elastomers has been compared to the one of analogous uncrosslinked materials. Results are discussed in terms of mobility of the mesogens. Two different systems have been investigated: smectic A elastomers allow to determine the influence of crosslinking on the relaxation (i.e. the reorientation of the whole mesogen around the chain), a S _C ^* elastomer shows the drastic influence of the polymer network on the Goldstone mode. Received 12 October 1998     

Piezoelectricity of chiral nematic elastomers

A molecular model of freely jointed chains of chiral monomers is developed to describe the piezoelectric effect in chiral nematic elastomers. The model, an extension of the neo-classical theory of nematic polymer networks, takes into account a chiral biasing of molecular alignment under shear which leads to induced polarisation if the monomers contain a transverse dipole moment. The resulting theory is fully non-linear in elastic deformations, in the spirit of ordinary rubber elasticity. The expansion to the highest order in small strains gives the three linear piezoelectric coefficients predicted by phenomenological models. Received 7 September 1998 and Received in final form 19 October 1998     

Copolymer at a selective interface and two-dimensional wetting: a grand canonical approach

We consider two different problems involving the localization of a single polymer chain: (i) a periodic AB copolymer at a selective fluid-fluid interface, with the upper (resp. lower) fluid attracting A (resp. B) monomers (ii) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization transition in a grand canonical approach. We recover the results obtained in previous studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some finite size effects are also determined and tested numerically. Received 13 April 2000     

Calculation of scattering from stretched copolymers using the tube model: a generalisation of the RPA

There are many experimental situations in which polymer chains are constrained or localised into a small region of space (e.g. melt chains confined to a “tube”, network chains pinned by crosslinks). We show that detailed consideration of the quenched variables is vital in these experiments. This paper provides a crucial link between microscopic models with localising constraints and scattering patterns by a generalisation of the Random Phase Approximation (RPA) which allows for quenched translational variables. A method is developed which deals with correlations between the quenched variables brought about by incompressiblity (for example, in a polymer melt there are correlations between tubes because of the interaction between chains). As an example, the generalised RPA is applied to models based on the Warner-Edwards picture of the tube. Theoretical results for a melt of H-shaped copolymers are compared with experimental scattering. Early results suggest that to fit the scattering we may be forced to relax one of the central assumptions of the tube model; that the tube deforms affinely, that all chains retract by the same amount or that the tube diameter does not couple to the strain. Received 26 October 1998 and Received in final form 19 March 1999     

Rheology of nanosized hairy grain suspensions

Suspensions of nanosized hairy grains have been prepared by grafting long polydimethylsiloxane chains (molecular weight ) onto silica particles (radius ), dispersed into a good solvent of PDMS. Depending on the particle volume fraction, different rheological behaviors are observed. In the very dilute regime, the suspensions are perfectly stable and the particles behave almost as hard spheres: flow penetration inside the corona is then very weak. When the particle volume fraction goes to the close packing volume fraction, the suspension viscosity does not diverge as for hard spheres due to the increase of flow penetration inside the corona and to corona entanglements. The particles have then the same behavior as polymer stars having an intermediate number of arms (). Finally, in the concentrated regime (), the suspensions form irreversible gels. We shown that this unexpected gelation phenomenon is related to the presence of the silica cores: grafted PDMS chains can adsorb onto different particles and form irreversible bonds between the cores. The viscosity and elastic modulus evolutions during gelation are well described by the scalar percolation model of sol-gel transition. Received 23 March 1998     

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