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     

The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films

We present a detailed study of free polymer surfaces and their effects on the measured glass transition temperature (T_g) of thin polystyrene (PS) films. Direct measurements of the near-surface properties of PS films are made by monitoring the embedding of 10 and 20 nm diameter gold spheres into the surface of spin-cast PS films. At a temperature T = 378K( > T_g), the embedding of the spheres is driven by geometrical considerations arising from the wetting of the gold spheres by the PS. At temperatures below T_g ( 363K < T < 370K), both sets of spheres embed 3-4 nm into the PS films and stop. These studies suggest that a liquid-like surface layer exists in glassy PS films and also provide an estimate for the lower bound of the thickness of this layer of 3-4 nm. This qualitative idea is supported by a series of calculations based upon a previously developed theoretical model for the indentation of nanoscale spheres into linear viscoelastic materials. Comparing data with simulations shows that this surface layer has properties similar to those of a bulk sample of PS having a temperature of 374 K. Ellipsometric measurements of the T_g are also performed on thin spin-cast PS films with thicknesses in the range 8nm < h < 290nm. Measurements are performed on thin PS films that have been capped by thermally evaporating 5 nm thick metal (Au and Al) capping layers on top of the polymer. The measured T_g values (as well as polymer metal interface structure) in such samples depend on the metal used as the capping layer, and cast doubt on the general validity of using evaporative deposition to cover the free surface. We also prepared films that were capped by a new non-evaporative procedure. These films were shown to have a T_g that is the same as that of bulk PS (370±1 K) for all film thicknesses measured (> 7 nm). The subsequent removal of the metal layer from these films was shown to restore a thickness-dependent T_g in these samples that was essentially the same as that observed for uncapped PS films. An estimate of the thickness of the liquid-like surface layer was also extracted from the ellipsometry measurements and was found to be 5±1 nm. The combined ellipsometry and embedding studies provide strong evidence for the existence of a liquid-like surface layer in thin glassy PS films. They show that the presence of the free surface is an important parameter in determining the existence of T_g reductions in thin PS films.     

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     

Very fast relaxation in polycarbonate glass

Relaxations in amorphous bis-phenol A polycarbonate are studied by neutron scattering, as a function of temperature below the glass transition. Two different processes are observed. One is very fast, with a characteristic time (∼ 0.3 ps), that is independent of temperature and momentum transfer. Conversely the other is slower, with a time which is dependent on temperature and momentum transfer. The very fast localized anharmonic motion is interpreted by the overdamping of low-frequency vibrational modes, by nearby dynamic holes. The slower relaxation is thermally activated and momentum transfer dependent. It corresponds to molecular group motions and possibly to the short-time regime of the segmental relaxation. Received 29 February 2000 and Received in final form 13 June 2000     

Molecular dynamics of hyperbranched polyesters in the confinement of thin films

Broadband Dielectric Spectroscopy is employed to investigate the molecular dynamics in thin films of hyperbranched polyesters (type AB₁B₂, with -OH and -OCOCH₃ as terminal groups). Three relaxation processes are detected: alpha, beta and gamma. While the latter two are not influenced by the confinement, a pronounced effect is observed on the alpha relaxation: with decreasing film thickness the slower relaxation modes of the dynamic glass transition are gradually suppressed, resulting in an increase of the average relaxation rate and in a linear decrease of the dielectric strength. This is attributed to an immobilization in confinement of the polymeric segments located at the periphery of the hyperbranched macromolecular structures.     

Dramatic stiffening of ultrathin polymer films in the rubbery regime

Recently, we (P.A. O'Connell, G.B. McKenna, Science 307, 1760 (2005)) introduced a novel nano-bubble inflation method to measure the absolute creep compliance of nanometer thick polymer films. In that work it was shown that even at film thicknesses as small as 27.5nm the glass temperature was unchanged for poly(vinyl acetate) (PVAc). Perhaps more importantly, and the subject of the present work, was the observation that these ultrathin films show a dramatic stiffening in the rubbery plateau regime, i.e., the compliance was reduced by over two orders of magnitude compared to the bulk material. In the present work we substantiate the previous results in a study of the thickness dependence of the rubbery compliance of PVAc and polystyrene (PS) films for thicknesses from 13nm to 276nm. We show the substantial stiffening of the plateau region for both materials. Furthermore, the rubbery compliance (inverse of stiffness) scales with approximately the second power ( 1.8±0.2) in the film thickness for both materials.     

Some relevant parameters affecting the glass transition of supported ultra-thin polymer films

We have measured, the thickness dependence of the glass transition temperature T(g)( h), using ellipsometry at variable temperature, for poly(methyl-methacrylate) (PMMA) of various tacticity in confined geometry. We report that several factors significantly affect T(g)( h): i) polymer microstructure (stereoregularity of PMMA) related to local dynamics; ii) interfacial interactions; iii) conformation of the polymer chains. These results raise many fundamental questions on the origin of the thickness-dependent glass transition. Why and how do the interactions with the substrate significantly affect T(g)( h)? Does T(g)( h) depend on the modifications of conformational parameters of the chains (their entropy)? What is the correlation between local dynamics and T(g)( h) in thin films? The aim of this paper is to summarise these open questions, which should stimulate further investigations in the thin polymer film scientific community.     

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     

The mechanisms of recrystallization after melting in syndiotactic polypropylene and isotactic polystyrene

Several semicrystalline polymers show a recrystallization after melting during a heating scan. We have studied the mechanisms of such recrystallization processes for two different polymers, namely syndiotactic polypropylene (sPP) and isotactic polystyrene (iPS). This was done by monitoring the structure evolution during the recrystallization process and its changes during a subsequent heating scan via time- and temperature-dependent SAXS measurements, respectively. The results of this study showed that the sPP samples exhibited a recrystallization mechanism similar to the multi-stage route found upon initial crystallization of semicrystalline polymers from an entangled melt. Meanwhile, a different recrystallization mechanism was shown by the iPS samples. In this case, the recrystallization process proceeded as a direct growth into the melt in a one-step process. This is the first time we have observed such a mechanism which resembles the picture presented by the classical models for crystallization from an entangled polymer melt. The reason for such different mechanisms may be related to the initial melt state prior to crystallization. It seems as though, when crystallization sets in an entangled polymer melt, it follows the multi-stage route, whereas if the melt is locally disentangled, it proceeds by a direct growth mechanism. Received 23 July 2001 and Received in final form 4 October 2001     

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     

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     

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     

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.     

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.     

A non-Gaussian model in polymeric network

We investigate a finite chain approximation, the non-Gaussian Tsallis distribution, to the polymeric network, which gives an improvement to the Gaussian model. This distribution presents some necessary characteristics, like a cutoff to the maximum chain length and a continuous limit to the Gaussian one for a large number of monomers. It also presents a simple quadratic structure that allows to generalize the Gaussian properties such as exact-moments calculation and Wick theorem. We obtain the free-energy density in its full tensorial structure.     

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     

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     

The mobility of the amorphous phase in polyethylene as a determining factor for slow crack growth

Polyethylene (PE) pipes generally exhibit a limited lifetime, which is considerably shorter than their chemical degradation period. Slow crack growth failure occurs when pipes are used in long-distance water or gas distribution though being exposed to a pressure lower than the corresponding yield stress. This slow crack growth failure is characterized by localized craze growth and craze fibril rupture. In the literature, the lifetime of PE pipes is often considered as being determined by the density of tie chains connecting adjacent crystalline lamellae. But this consideration cannot explain the excellent durability of the recent bimodal grade PE for pipe application. We show in this paper the importance of the craze fibril length as the determining factor for the pipe lifetime. The conclusions are drawn from stress analysis. It is found that longer craze fibrils sustain lower stress and are deformed to a lesser degree. The mobility of the amorphous phase is found to control the amount of material that can be sucked in by the craze fibrils and thus the length of the craze fibrils. The mobility of the amorphous phase can be monitored by dynamic mechanical analysis measurements. Excellent agreement between the mobility thus derived and lifetimes of PE materials as derived from FNCT (full notch creep test) is given, thus providing an effective means to estimate the lifetime of PE pipes by considering well-defined physical properties.     

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