Dynamics of strongly entangled polymer systems: activated reptation

The effect of excluded-volume interactions on the reptation dynamics of long polymer chains is considered theoretically. It is shown that interactions give rise to an exponential increase of the reptation time, , if polymer chains are long enough: , where is the number of monomers per entanglement. We propose a novel dynamical mechanism of activated reptation implying that neighboring chains exchange conformations of their terminal fragments. It is shown that the exchange mechanism is compatible with the equilibrium polymer chain statistics and that it provides a bridge between the previous theories. Received: 25 July 1997 / Accepted: 8 October 1997     

Equilibrium statistical distributions for subchains in an entangled polymer melt

In de Gennes-Doi-Edwards theory for entangled polymeric melts, a length scale r₀ is introduced, giving the equilibrium mesh size of the physical network of chains. Each polymer molecule is then represented as a random walk, with a step size r₀ (a “subchain”, made up of n₀ Kuhn segments) dictated by the existence of entanglements. Progressing from this simple picture, an issue that has been constantly overlooked so far, despite its potential relevance, is that of finite-size effects at the de Gennes-Doi-Edwards characteristic length scale. Actually, since a subchain in a melt is a “small”, nonmacroscopic system, fluctuations of both its length and its number of Kuhn segments are certainly nonnegligible. An ad hoc theoretical treatment from nonstandard (nano) statistical mechanics and thermodynamics seems then required, to find the anticipated equilibrium statistical distributions of the subchain population. In this contribution, we carefully discuss this topic. Some predictions from the nonstandard fluctuation-inclusive approach on the statistics of subchains are here obtained, and compared with existing simulations, even down to the atomistic level.     

Charge relaxation in polyampholytes of various statistics

We discuss theoretically the relaxation of charge fluctuations in polyampholyte solutions. It has been shown previously by some of us (J. Wittmer et al. Europhys. Lett. 24, 263 (1993)) that the charge distribution along the polyampholyte backbone has a dramatic influence on the polarization energy and hence on the solubility. Here it is demonstrated that a similar effect exists for the charge relaxation. The charge relaxation mechanism qualitatively depends on the statistics: for alternating polyampholytes the relaxation is mainly due to local dipole inversion and is not primarily driven by electrostatic interactions, whereas for random polyampholytes it is driven by electrostatic interactions. Intermediate statistics (with short-ranged (exponential) correlations) appear as a combination of these two limiting cases: short-wavelength modes are insensitive to the loss of correlations along the backbone, whereas long-wavelength modes correspond to a random statistics with renormalized charges. The relaxation of the dielectric constant is also calculated. Received: 20 December 2002 / Accepted: 13 March 2003 / Published online: 24 April 2003 RID="a" ID="a"e-mail: johner@ics.u-strasbg.fr     

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation. Received: 9 January 1998 / Revised: 24 April 1998 / Accepted: 2 July 1998     

Globules of annealed amphiphilic copolymers: Surface structure and interactions

A mean-field theory of globules of random amphiphilic copolymers in selective solvents is developed for the case of an annealed copolymer sequence: each unit can be in one of two states, H (insoluble) or P (soluble or less insoluble). The study is focussed on the regime when H and P units tend to form long blocks, and when P units dominate in the dilute phase, but are rare in the globule core. A first-order coil-to-globule transition is predicted at some T = T _cg. The globule core density at the transition point increases as the affinity of P units to the solvent, ˜, is increased. Two collapse transitions, coil → “loose” globule and “loose” globule → “dense” globule, are predicted if ˜ is high enough and P units are marginally soluble or weakly insoluble. H and P concentration profiles near the globule surface are obtained and analyzed in detail. It is shown that the surface excess of P units rises as ˜ is increased. The surface tension decreases in parallel. Considering the interaction between close enough surfaces of two globules, we show that they always attract each other at a complete equilibrium. It is pointed out, however, that such equilibrium may be difficult to reach, so that partially equilibrium structures (defined by the condition that a chain forming one globule does not penetrate into the core of the other globule) are relevant. It is shown that at such partial equilibrium the interaction is repulsive, so the globules may be stabilized from aggregation. The strongest repulsion is predicted at the coil-to-globule transition point T _cg: the repulsion force decreases with the distance between the surfaces according to a power law. In the general case (apart from T _cg) the force vs. distance decay becomes exponential; the decay length ξ diverges as T → T _cg. The developed theory explains certain anomalous properties observed for globules of amphiphilic homopolymers.     

Excluded-volume polymer-induced depletion interaction between parallel flat plates

The interaction between two parallel plates due to non-adsorbing polymer chains with excluded volume is calculated using the adsorption method. The adsorption is calculated from the profile of the polymer segment concentration between the plates, which is obtained from the product function of the concentration profile near a single wall, involving the correlation length. The renormalization group theory provides expressions for the osmotic pressure and consequently for the osmotic compressibility, chemical potential and correlation length of a polymer solution. Both the local polymer concentration profiles as well as the minimum of the interaction potential between the plates agree with recently published self-avoiding random walk computer simulations. Received 9 August 2001     

Scaling concepts for polymer brushes and their test with computer simulation

After a brief review of the scaling concepts for static and dynamic properties of polymer brushes in good solvents and Theta solvents, the Monte Carlo evidence is discussed. It is shown that under typical conditions the diameter of the last blob is of the order of 10-20% of the brush height, and therefore pronounced deviations from the self-consistent field predictions occur. In bad solvents, lateral microphase separation occurs leading to an irregular pattern of “dimples”. Particularly interesting is the response of brushes to shear deformation, and the interaction between two interpenetrating brushes. Recent attempts to understand the resulting shear forces via molecular-dynamics simulations are briefly described, and an outlook on related experiments is given. Dedicated to Prof. H.E. Stanley on the occasion of his 60th birthday Received 11 March 2002 and Received in final form 3 June 2002     

Shape transformations of protein-like copolymer globules

Shapes of globules formed by amphiphilic multi-block-copolymers in a selective solvent are considered theoretically. We focus on copolymers consisting mostly of insoluble H-units forming large core surrounded by a shell of soluble P-blocks. It is shown that the globule becomes non-spherical when the effective shell tension is low enough. The resultant shape depends on the shell bending energy: it is prolate if this energy is larger than the elastic energy of the core, and oblate in the opposite case. The central result is the prediction of the formation of a surface pattern of fingers accompanying or even preempting the shape transition mentioned above. We elucidate and discuss the following finger morphologies: 1) nearly spherical knob; 2) a necklace of spherical beads extending away from the surface; 3) mostly cylindrical fingers; 4) large thorn-like fingers. The first 3 morphologies develop at equilibrium as the shell area increases (or, equivalently, the shell tension decreases). Considering the relevant kinetical aspects we show that formation of fingers is a nucleation and growth process, and that the energy of their equilibrium nucleation is likely to be high. Therefore, the finger formation may be delayed, and may actually occur in the regime where the plain spherical surface is metastable. It is the last morphology (thorn-like fingers) that characterizes the metastable regimes when the finger formation is controlled by a high activation energy. The universal features of the above predictions inviting experimental tests are discussed.     

Scattering properties of salt-free wormlike micellar solutions

Static and dynamic light scattering and conductivity experiments were carried out on salt-free aqueous micellar solutions of cetyltrimethylammonium n-hexane sulfonate (CTAC_6SO_3) and cetyltrimethylammonium n-heptane sulfonate (CTAC_7SO_3) as a function of surfactant concentration. This study confirms the analogy between the behavior in the semi-dilute regime of elongated micellar systems and “classical” polyelectrolyte solutions. Time-resolved scattering experiments performed after a variation of concentration from about twice the overlap volume fraction to less than half of it revealed the existence of a structural relaxation with a characteristic time of several hours. Received 21 December 1999     

Stratification of foam films made from polyelectrolyte solutions

Studies of thin liquid films, made from semidilute polyelectrolyte solutions, are presented. The disjoining pressure variation with film thickness exhibits oscillations, corresponding to film stratification. The oscillations become sharper as the polymer concentration c increases, and disappear when salt is added. The period of the oscillations scales as c ^-1/2. The observed stratification is related to the polymer network and the size of the steps to the mesh size ξ. Received 25 April 2000 and Received in final form 3 October 2000     

Confinement-induced differences between dielectric normal modes and segmental modes of an ion-conducting polymer

Dielectric measurement in the range 0.1 Hz to 1 MHz were used to study the motions of polymers and ions in an ion-conducting polymer, polypropylene oxide containing small quantities (on the order of 1%) of lithium ions (LiClO₄), confined as a sandwich of uniform thickness between parallel insulating mica surfaces. In the dielectric loss spectrum, we observed three peaks; they originated from the normal mode of the polymer, segmental mode of the polymer, and ion motions. With decreasing film thickness, the peak frequencies corresponding to the normal mode and ion motion shifted to lower frequencies, indicating retardation due to confinement above 30 nm. This was accompanied by diminished intensity of the dielectric normal-mode relaxation, suggesting that confinement diminished the fluctuations of the end-to-end vector of the chain dipole in the direction between the confining surfaces. On the contrary, the segmental mode was not affected at that thickness. Finally, significant retardation of the segmental mode was observed only for the thinnest film (14 nm). The different dynamical modes of the polymer (segmental and slowest normal modes) respond with different thickness and temperature dependence to confinement. Received 31 August 2001 and Received in final form 30 October 2001     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Persistence length for a model semirigid polyelectrolyte as seen by small angle neutron scattering: a relevant variation of the lower bound with ionic strength

In a SANS experiment, we have directly determined for the first time the conformation of hyaluronan, a model semirigid polyelectrolyte. At high ionic strength, this is completely possible, where the scattered intensity crosses over (when decreasing q) from a q(-1) rod variation to a q(-2) and, where fitting to the "wormlike" chain model gives the backbone, intrinsic, persistence length: L0 = 86.5 A. At low ionic strength, we can safely check that the measured persistence length appears increased by at least the amount predicted by Odijk for the electrostatic contribution, L(e) (approximately kappa(-2), square of the Debye screening length). However, the intensity at the lowest q is not only due to the single chain, since it crosses over from a q(-1) to a q(-4) variation, characteristic of polymer associations.     

Nematic ordering in anisotropic elastomers: Effect of frozen anisotropy

Nematic ordering in anisotropic non-Gaussian elastomers is considered theoretically using mean field approximation. We focus on the effect of anisotropy during network cross-linking on the system elasticity and, in particular, on the so-called soft deformation mode. As the main result, we calculate the dependence of the elastomer free energy on the angle between the axis of “frozen” anisotropy and the nematic director. The dependence of the isotropic-nematic transition point on the orientational field acting on the monomers during the cross-linking process is also calculated. Received: 5 November 1997 / Revised and Accepted: 29 June 1998     

Static and dynamic properties of supercooled thin polymer films

The dynamic and static properties of a supercooled (non-entangled) polymer melt are investigated via molecular-dynamics (MD) simulations. The system is confined between two completely smooth and purely repulsive walls. The wall-to-wall separation (film thickness), D, is varied from about 3 to about 14 times the bulk radius of gyration. Despite the geometric confinement, the supercooled films exhibit many qualitative features which were also observed in the bulk and could be analyzed in terms of mode-coupling theory (MCT). Examples are the two-step relaxation of the incoherent intermediate scattering function, the time-temperature superposition property of the late time α-process and the space-time factorization of the scattering function on the intermediate time scale of the MCT β-process. An analysis of the temperature dependence of the α-relaxation time suggests that the critical temperature, T _c, of MCT decreases with D. If the confinement is not too strong ( D≥10monomer diameter), the static structure factor of the film coincides with that of the bulk when compared for the same distance, T - T _c(D), to the critical temperature. This suggests that T - T _c(D) is an important temperature scale of our model both in the bulk and in the films. Received 12 September 2001     

Glassy effects in the swelling/collapse dynamics of homogeneous polymers

We investigate, using numerical simulations and analytical arguments, a simple one-dimensional model for the swelling or the collapse of a closed polymer chain of size N, representing the dynamical evolution of a polymer in a Θ-solvent that is rapidly changed into a good solvent (swelling) or a bad solvent (collapse). In the case of swelling, the density profile for intermediate times is parabolic and expands in space as t ^1/3, as predicted by a Flory-like continuum theory. The dynamics slows down after a time ∝N ² when the chain becomes stretched, and the polymer gets stuck in metastable “zig-zag” configurations, from which it escapes through thermal activation. The size of the polymer in the final stages is found to grow as . In the case of collapse, the chain very quickly (after a time of order unity) breaks up into clusters of monomers (“pearls”). The evolution of the chain then proceeds through a slow growth of the size of these metastable clusters, again evolving as the logarithm of time. We enumerate the total number of metastable states as a function of the extension of the chain, and deduce from this computation that the radius of the chain should decrease as 1/ln(ln t). We compute the total number of metastable states with a given value of the energy, and find that the complexity is non-zero for arbitrary low energies. We also obtain the distribution of cluster sizes, that we compare to simple “cut-in-two” coalescence models. Finally, we determine the aging properties of the dynamical structure. The subaging behaviour that we find is attributed to the tail of the distribution at small cluster sizes, corresponding to anomalously “fast” clusters (as compared to the average). We argue that this mechanism for subaging might hold in other slowly coarsening systems. Received 23 October 2000     

Gels at interfaces

We discuss the adsorption of polymer gels on flat surfaces. Even in cases of complete wetting where the spreading power S is positive and where an equivalent liquid would spread, the elastic stresses due to the gel deformation upon adsorption oppose the spreading. The competition between elasticity characterized by the bulk shear modulus G and capillarity characterized by the spreading power S defines a typical length scale ℓ = S/G for the deformation in the gel. For loose gels ℓ can be of the order of 1 μm. Macroscopic gels larger than ℓ deform only at their edges over a region of size ℓ. Microscopic gels smaller than ℓ show a finite deformation despite the elastic stresses. The elastic stresses limit the spreading of the polymer, but solvent can be sucked out of a swollen gel by wetting the surface. The thin solvent film can extend rather far from the gel edge and carry solvent. We calculate the kinetics of the solvent film formation and of the solvent transfer from a more swollen gel to a less swollen gel. Received 16 July 2001     

Spherical polyelectrolyte block copolymer micelles: Structural change in presence of monovalent salt

Spherical polyelectrolyte block copolymer micelles were investigated as a function of added NaCl salt concentration using Small-Angle Neutron Scattering (SANS) and Light Scattering (LS). The micelles are formed by the self-association of charged-neutral copolymers made of a long deuterated polyelectrolyte moiety (NaPSS_d)₂₅₁ and a short hydrophobic moiety (PEP)₅₂. In presence of salt, the core shape and the aggregation number of the micelles are not affected. The hydrodynamic radius of the micelle is found to be identical to the radius of the whole micelle deduced from neutron scattering and thus the hydrodynamic radius is a valid measure of the corona thickness. At the lowest salt concentrations investigated the thickness of the corona, R_s, remains essentially constant and a contraction is observed above an added-salt concentration c_s of 2×10^-2 M where this crossover concentration corresponds to the average ionic strength of the free counterions in the corona. The contraction takes place while maintaining a rod-like behavior of the chains at short scale and obeys to: R_s c_s^-0.18. The exponent 0.18 suggests an electrostatic persistence length proportional to the Debye screening length.     

The timescale of spinodal dewetting at a polymer/polymer interface

We investigate the dynamics of spinodal dewetting in liquid-liquid polymer systems. Dewetting of poly(methyl-methacrylate) (PMMA) thin films on polystyrene (PS) “substrates” is followed in situ using neutron reflectivity. By following the development of roughness at the PS/PMMA interface and the PMMA surface we extract characteristic growth times for the dewetting process. These characteristic growth times are measured as a function of the molecular weight of the two polymers. By also carrying out experiments in the regime where the dynamics are independent of the PS molecular weight, we are able to use dewetting to probe the scaling of the PMMA thin film viscosity with temperature and molecular weight. We find that this scaling reflects bulk behaviour. However, absolute values are low compared to bulk viscosities, which we suggest may be due in part to slippage at the polymer/polymer interface. Received 25 June 2001 and Received in final form 5 December 2001