The segregation of poly(styrene-b-isoprene) diblock copolymers to the surface of a polystyrene melt: the effect of the ratio of block lengths

The effect of the ratio of block lengths on the interfacial partitioning of poly(styrene-block-1,4 isoprene) diblock copolymers from their mixtures with polystyrene homopolymer melt is investigated utilizing a series of copolymers with almost constant molecular weight but different compositions. The concentration profile of the copolymer is measured directly using the nuclear reaction analysis technique; a segregation of the diblock is found at both the air/polymer surface, due to the lower surface energy of polyisoprene, and at the substrate/polymer interface. No significant effect of the block length ratio on the free-surface excess was observed. The block molecular weights have apparently led to dangling chain conformations in the non-overlapping mushroom and in the overlapping mushroom regimes whereas the brush regime was not accessible; no indications of a real border between the two former regimes was found. Received: 20 July 1998 / Received in final form and Accepted: 11 September 1998     

The lamellar-disorder interface: one-dimensional modulated profiles

We study interfacial behavior of a lamellar (stripe) phase coexisting with a disordered phase. Systematic analytical expansions are obtained for the interfacial profile in the vicinity of a tricritical point. They are characterized by a wide interfacial region involving a large number of lamellae. Our analytical results apply to systems with one dimensional symmetry in true thermodynamical equilibrium and are of relevance to metastable interfaces between lamellar and disordered phases in two and three dimensions. In addition, good agreement is found with numerical minimization schemes of the full free energy functional having the same one dimensional symmetry. The interfacial energy for the lamellar to disordered transition is obtained in accord with mean field scaling laws of tricritical points. Received: 28 March 1997 / Revised: 6 February 1998 / Accepted: 16 February 1998     

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     

Effects of finite thickness on interfacial widths in confined thin films of coexisting phases

The capillary broadening of a 2-phase interface is investigated both experimentally and theoretically. When a binary mixture in a thin film with thickness D segregates into two coexisting phases the interface between the two phases may form parallel to the substrate due to preferential surface attraction of one of the components. We show that the interfacial profile (of intrinsic width w₀) is broadened due to capillary waves, which lead to fluctuations, of correlation length of the local interface positions in the directions parallel to the confining walls. We postulate that acts as an upper cutoff for the spectrum of capillary waves on the interface, so that the effective mean square interfacial width w varies as . In the limit of large D this yields or respectively for the case of short- or long-range forces between walls and the interface. We used the Nuclear Reaction Analysis depth profiling technique, to investigate this broadening effect directly in two binary polymer mixtures. Our results reveal that the interfacial width indeed increases with film thickness D, though the observed interfacial width is lower than the predicted w. This is probably due to surface tension effects imposed by the confining surfaces which are not taken into account in our model. Received: 19 February 1998 / Received in final form: 2 September 1998 / Accepted: 8 September 1998     

Interfacial roughness and angle dependence of giant magnetoresistance in magnetic superlattices

Using the two-point conductivity formula, we numerically evaluate the giant magnetoresistance (GMR) in magnetic superlattices with currents in the plane of the layers (CIP), from which the effect of the interfacial roughness and magnetization configuration on the GMR is studied. With increasing interfacial roughness, the maximal GMR ratio is found to first increase and then decrease, exhibiting a peak at an optimum strength of interfacial roughness. For systems composed of relatively thick layers, the GMR is approximately proportional to ,where is the angle between the magnetizations in two successive ferromagnetic layers, but noticeable departures from this dependence are found when the layers become sufficiently thin. Received 21 September 1998 and Received in final form 22 December 1998     

A neutron reflectometry study of polystyrene network interfaces

We have used neutron reflectometry to measure interfacial widths between two polystyrene films, where either one or both films are crosslinked. The observed interfacial width between two networks is larger than the size expected for “dangling ends”, which suggests motion of heterogeneous regions of the networks. In the case when one of the networks is replaced by a linear polymer, the interfacial profile can be asymmetric with a diffusion “front” of linear polymer penetrating the network to a length scale of up to 200 ?. In the case of a more densely crosslinked network and a high molecular weight linear polymer the interface is symmetric implying negligible penetration. Received: 4 December 1996 / Revised: 13 October 1997 / Accepted: 23 December 1997     

Apparent slip at a polymer-polymer interface

We consider a planar interface between strongly-segregated homopolymers subjected to steady shear in the plane of the interface. We develop a constitutive equation for stress relaxation in an inhomogeneous system for chains obeying Rouse dynamics. Using this equation, the interfacial viscosity for a symmetric blend is found to be in agreement with a scaling prediction due to de Gennes, where is the bead friction coefficient, b is the segment length, is the segment volume and is the Flory-Huggins interaction parameter driving the phase separation. We generalize our results to asymmetric blends and describe a phenomenological extension to entangled melts. Received: 18 August 1997 / Received in final form: 1 December 1997 / Accepted: 2 December 1997     

Structural origin of magnetic anisotropy in Co-Pt alloy films probed by polarized XAFS

Polarized X-ray absorption fine structure (XAFS) measurements at the Co K and Pt L₃ edges show that the perpendicular magnetic anisotropy found in epitaxial fcc CoPt₃ (111) films stems from the existence of anisotropic local ordering. Such ordering, induced during the codeposition process and dependent on the growth temperature, is characterized by preferential CoCo pairs in the film plane, balanced by preferential CoPt pairs out of the plane, resulting from some Co 2D-segregation. Polarized XAFS at the Pt edge reveals similar anisotropic local ordering in epitaxial hcp Co₃Pt (0001) films exhibiting a larger magnetocrystalline anisotropy compared to that of bulk hcp Co. Besides, a polarization dependence of the Co XANES profile is observed only for the Co₃Pt films exhibiting hcp symmetry. Received: 29 April 1998 / Revised: 27 July 1998 / Accepted: 31 August 1998     

Flow equations for band-matrices

Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a new generator for the continuous unitary transformation proposed in this paper one can avoid some of the problems of former applications. General properties of the new generator are derived. It turns out that the new generator is especially useful for Hamiltonians with a banded structure. Two examples, the Lipkin model, and the spin-boson model are discussed in detail. Received: 2 February 1998 / Accepted: 17 March 1998     

Shear banding instability in wormlike micellar solutions

Using NMR velocimetry and mechanical measurements we study the flow dynamics, within a cone-and-plate rheometer, of the wormlike micelle system, cetylpyridinium chloride/sodium salicylate (CPyCl/NaSal) at 100 mM/60 mM concentration in distilled water. Depending on precise conditions within the system, two classes of behaviour are observed, one in which the boundary between different shear rate phases fluctuates rapidly (on the order of tens of milliseconds) and one in which it migrates slowly with a time constant of many seconds. These modes of behaviour may depend on minor solution impurities, which presumably affect the detailed constitutive properties, but also on the externally applied shear rate within a given system. We argue that the slow migrations are governed by stress relaxation effects while the rapid migrations are flow driven and arise from interfacial instability. Received: 2 June 1998 / Received in final form and Accepted: 27 July 1998     

Bending of charged flexible membranes due to the presence of macroions

We investigate the bending of flexible charged membranes due to the presence of rigid rodlike macroions in the framework of the Debye-Hückel approximation. When the macroions are fixed in space at some distance from the bilayer the membrane bends towards them; we calculate the exact deformation profile. On the other hand a macroion which is adsorbed on the membrane causes a deflection of the bilayer. Finally, we consider swollen lamellar polyanion/charged-lipid complexes where the macroions are intercalated between charged lipid bilayers. We predict the occurrence of a double adsorption (pinching effect) of the macroion for sufficiently flexible membranes. Received: 9 February 1998 / Revised: 9 June 1998 / Accepted: 2 July 1998     

Dynamics of polymeric manifolds in melts: the Hartree approximation

The Martin-Siggia-Rose functional technique and the selfconsistent Hartree approximation is applied to the dynamics of a D-dimensional manifold in a melt of similar manifolds. The generalized Rouse equation is derived and its static and dynamic properties are studied. The static upper critical dimension, d _uc =2D/(2-D), discriminates between Gaussian (or screened) and non-Gaussian regimes, whereas its dynamical counterpart, , discriminates between Rouse- and renormalized-Rouse behavior. The Rouse modes correlation function in a stretched exponential form and the dynamical exponents are calculated explicitly. The special case of linear chains D=1 shows agreement with Monte-Carlo simulations. Received: 22 May 1998 / Received in final form: 31 August 1998 / Accepted: 8 September 1998     

Rayleigh-Schrödinger perturbation theory for electron-phonon interaction in two dimensional quantum dots with asymmetric parabolic potential

Within the framework of the second-order Rayleigh-Schr?dinger perturbation theory, we investigate the effects of the interaction of the electron and longitudinal-optical phonons in two-dimensional semiconductive quantum dots with respect to a general potential. We propose a simple expression for the ground state energy, and compare it with those obtained by Landau-Pekar strong coupling theory. It is shown both analytically and numerically that the results obtained from the second-order Rayleigh-Schr?dinger perturbation theory could be better than those from Landau-Pekar strong coupling theory when the coupling constant is sufficiently small. Moreover, some interesting problems, such as polarons in quasi-one-dimensional quantum wires, and quasi-zero-dimensional asymmetric or symmetric quantum dots can be easily discussed only by taking different limits. After the numerical calculations, we find that there exists a simple dimensional scaling and symmetry relation for the ground state polaron energy. Furthermore, we apply our results to some weak-coupling polar semiconductors such as GaAs, CdS. It is shown that the polaronic effects are found to be quiet appreciable if the confinement lengths and smaller than a few nanometers. Received: 3 December 1997 / Revised: 6 July 1998 / Accepted: 17 September 1998     

Energy dissipation in solid friction

Dissipation in solid friction is studied as a function of the elastic properties of the two sliding surfaces. The two surfaces have been constructed by embedding macroscopic asperities in an elastic layer. It is shown that when the surfaces are rigid the energy dissipation is smaller than in the elastic case. The scaling of the friction force as a function of the asperity number is also studied. Received 9 November 1998     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

Charge transfers in complex transition metal alloys ()

We introduce a new Non-Orthogonal Tight-Binding model, for complex alloys, in which electronic structure is characterized by charge transfers. We give the analytic calculation of a charge transfer, in which overlapping two-center terms are rigorously taken into account. Then, we apply numerically this result to an approximant phase of a quasicrystal of alloy. This model is more particularly adapted to transition metals, and gives realistic densities of states. Received: 7 July 1997 / Revised: 10 March 1998 / Accepted: 3 April 1998     

Singularity of the specific heat of two-dimensional random Ising models

The singularity of the specific heat is studied for the dilution (J>J'>0) type and Gaussian type random Ising models using the Pfaffian method numerically. The type of singularity at the paramagnetic-ferromagnetic phase boundary is studied using the standard regression method using data up to system size. It is shown that the logarithmic type singularity is more reliable than the double-logarithmic type and cusp type singularities. The critical temperatures are estimated accurately for both the dilution type and Gaussian type random Ising models. A phase diagram relating strength of the randomness and temperature is also presented. Received: 26 February 1998 / Revised: 15 May 1998 / Accepted: 25 June 1998     

Effectiveness of Maleic Anhydride Grafted EPDM Rubber (EPDM-g-MAH) as Compatibilizer in NR/Organoclay Nanocomposites Prepared by Melt Compounding

The effectiveness of maleic anhydride grafted ethylene propylene diene monomer rubber (EPDM-g-MAH) as an interfacial compatibilizer in enhancing the extent of interaction between natural rubber (NR) matrix and organoclay (OC) nanolayers, and also the eventually developed microstructure during a melt mixing process, has been evaluated as an alternative material to be used in place of commonly used epoxidized NR with 50 mol % epoxidation (ENR50). The latter usually weakens the processability of the final compound. The curing behavior, rheological, and dynamic mechanical properties of the prepared nanocomposites have been evaluated. Microstructural characterizations revealed better interfacial compatibilization by EPDM-g-MAH than ENR50, which is attributed to the lower polarity of the EPDM-g-MAH and hence more affinity for the NR matrix to be diffused onto the galleries of OC. This was confirmed with transmission electron microscopy (TEM) examination and higher elasticity exhibited by the unvulcanized NR/OC/EPDM-g-MAH nanocomposites in melt rheological measurements. Also, lower damping behavior was observed for the vulcanized NR/OC/EPDM-g-MAH samples. These imply intensified polymer–filler interfacial interaction and hence restricted viscous motions by the NR segments. Vulcanized NR/OC nanocomposites compatibilized with EPDM-g-MAH showed greater enhancements in tensile properties than the sample compatibilized with ENR50.