Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed. Received: 21 November 1997 / Received in final form: 21 April 1998 / Accepted: 24 April 1998     

Thermophysical properties of fluorinated acrylate homopolymers: Mixing and phase separation

The thermophysical properties of fluorinated acrylate homopolymers are investigated by differential scanning calorimetry (DSC) and optical microscopy and discussed in terms of relative lengths of the fluorinated chain and the hydrocarbon spacer between the acrylate moiety and the fluorinated chain. These compounds exhibit an intrinsic microphase-separation (Isotropic+Isotropic morphology) occurring between the fluorinated chains and the acrylate polymer backbone. It is shown that the enthalpy of mixing is a function of the length of the lateral fluorocarbon chains. The thermophysical behaviour of these materials may be regarded as demixed systems exhibiting an Upper Critical Solution Temperature. The photopolymerization process of one of the monomer is studied by isothermal photocalorimetry. High acrylate double-bond conversion and fast curing rates were obtained thus demonstrating the promising use of these materials for coating and film processing applications using UV-curing techniques. Received 30 January 2002     

Size effect on alloying ability and phase stability of immiscible bimetallic nanoparticles

In the present paper, the surface and size effects on the alloying ability and phase stability of immiscible alloy nanoparticles have been studied with calculating the heats of formation of Au-Pt alloy nanoparticles from the single element nanoparticles of their constituents (Au and Pt) with a simple thermodynamic model and an analytic embedded atom method. The results indicated that, besides the similar compositional dependence of heat of formation as in bulk alloys, the heat of formation of alloy nanoparticles exhibits notable size-dependence, and there exists a competition between size effect and compositional effect on the heat of formation of immiscible system. Contrary to the positive heat of formation for bulk-immiscible alloys, a negative heat of formation may be obtained for the alloy nanoparticles with a small size or dilute solute component, which implies a promotion of the alloying ability and phase stability of immiscible system on a nanoscale. The surface segregation results in an extension of the size range of particles with a negative heat of formation. The molecular dynamics simulations have indicated that the structurally and compositionally homogeneous AuPt nanoparticles tend to form a core-shell structure with temperature increasing.     

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     

Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions

We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together (ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement with our previous work (Europhys. Lett. 73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k _ring(t) ∝ t ^-δ and k _eq(t) ∝ t ^1-δ for times less than the longest polymer relaxation time. Here δ is an effective exponent which approaches δ = 5/4 for very long Rouse chains. Our present analysis also suggests a “sub-leading” term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics, our RG analysis indicates that the leading time dependence for the reaction rate is k(t) ∼ 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial conditions. We also find a logarithmic correction term which we “exponentiate” to a logarithmic form with a Landau pole. The presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction rate.     

Interface formation by low energy deposition of core-shell Ag-Co nanoclusters on Ag(100)

Molecular Dynamics is used to study the formation of an interface between a single crystalline Ag matrix and core-shell AgCo nanoclusters deposited with energies ranging from 0.25 eV to 1.5 eV per atom. As a consequence of the slowing down, clusters deform, may become epitaxial with the substrate and keep their core-shell structure. The consequences of the cluster-surface interaction are studied in detail for a realistic size and energy range and the accumulation of clusters is modelled. It is found that the interface formed is no more than a few atomic layers thick and that both the cobalt cluster cores and the silver shells display limited epitaxy with the substrate. The effect is not much energy dependent and is larger for the Ag shells that for the Co cores.     

Phenomenology and theory of horizontally oscillated granular mixtures

We overview the physics of a granular mixture subject to horizontal oscillations, recently investigated via experiments and molecular dynamics simulations. First we discuss the rich phenomenology exhibited by this system, which encompasses both segregation and dynamical instabilities. Then we show that the phenomenology can be explained via an effective interaction approach, by which the driven, non-thermal, granular mixture in mapped into a monodispersed thermal system of particles interacting via an effective potential. After determining the effective interaction we discuss its microscopic origin and investigate how it induces the observed phenomenology. Finally, as much as in thermal fluids, from the effective interaction we derive a Cahn-Hilliard dynamics equation, which appears to capture the essential characteristics of the dynamics of the granular mixture.     

Kinetics of phase separation in ramified polymer blends of arbitrary topology

We present here a theoretical study of kinetics of phase separation within a mixture made of two chemically incompatible ramified polymers. For simplicity, we assume that they have the same topology. We are interested in the variation of the relaxation rate, _q, versus the wave number q, in the vicinity of the spinodal temperature. The kinetics is governed by local (Rouse) and reptation motions (faster and slower modes). For qR_G 1 (R_G being the gyration radius), kinetics is entirely controlled by local motions where each chain moves inside its own tube, and we show that the corresponding characteristic frequency, ^{-1}_q, scales as ^{-1}_{q G}q⁶, where _G is a known topological factor. For qR_G 1, however, kinetics is rather dominated by long-wavelength (reptation) motions where unlike ramified polymers creep inside a long tube. For this case, we find that ^{-1}_q ( 0 )q² (_c - ), where ( 0 ) is another known topological factor that represents the total mobility of free monomers belonging to connected chains and reticulation points, and _c accounts for the critical value of the segregation parameter. Finally, the derived relaxation rate must be compared to that relative to a linear polymer mixture.     

Time of avalanche mixing of granular materials in a half filled drum

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference δ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time τ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when δ is an integer part of π. Introduction of fluctuations of δ suppresses the singularities of τ(δ) and smoothes the dependence τ(δ). Received 27 October 2000 and Received in final form 13 March 2001     

Hydrodynamic-flow-driven phase evolution in a polymer blend film modified by diblock copolymers

We have studied surface-directed phase separation in thin films of deuterated polystyrene and poly(bromostyrene) (with 22.7% of monomers brominated) using ³He nuclear reaction analysis, dynamic secondary ion mass spectroscopy and atomic force microscopy combined with preferential dissolution. The crossover from competing to neutral surfaces of the critical blend film (cast onto Au) was commenced: polyisoprene-polystyrene diblock copolymers were added and segregated to both surfaces reducing in a tuneable manner the effective interactions. Two main stages of phase evolution are characterised by i) the growth of two surface layers and by ii) the transition from the four-layer to the final bilayer morphology. For increasing copolymer content the kinetics of the first stage is hardly affected but the amplitude of composition oscillations is reduced indicating more fragmented inner layers. As a result, a faster mass flow to the surfaces and an earlier completion of the second stage were observed. The hydrodynamic flow mechanism, driving both stages, is evidenced by nearly linear growth of the surface layer and by mass flow channels extending from the surface layer into the bulk. The final bilayer structure, formed even for the surfaces covered by strongly overlapped copolymers, is indicative of long-range (antisymmetric) surface forces. Received 15 March 2000 and Received in final form 9 February 2001     

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     

Kinetics of microphase separation in interpenetrated polymer networks in solution

We present here a theoretical study of the early kinetics of the microphase separation in crosslinked polymer blends, made of two incompatible polymers A and B, dissolved in a common good solvent. Use is made of an extended blob model used previously for the investigation of the static properties of such a transition. We are interested in the variation of the relaxation rate, , versus the wave number q, in the vicinity of the spinodal temperature. We first show that kinetics is entirely dominated by local motions, which are of Rouse type. Slow motions are absent, because of the permanent presence of crosslinks. Second, we find that the characteristic frequency, (q ) = , increases with increasing wave number q according to a sixth power law, that is (q ) q^6{-9/4}, where is the overall monomer volume fraction. Therefore, the swelling of strands due to the excluded-volume forces leads to a renormalization of the characteristic frequency by a multiplicative factor scaling as ^{-9/4}. The main conclusion is that the presence of a good solvent necessitates relaxation rates less important than those relative to crosslinked mixtures in the molten state.     

Swollen-collapsed transition in random hetero-polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic charges interacting with the solvent is introduced, whose continuum counterpart has been proposed by Garel, Leibler and Orland [#!GLO!#]. The transfer matrix technique is used to study various constrained annealed systems which approximate at various degrees of accuracy the original quenched model. For highly hydrophobic chains an ordinary -point transition is found from a high temperature swollen phase to a low temperature compact phase. Depending on the type of constrained averages, at very low temperatures a swollen phase or a coexistence between compact and swollen phases are found. The results are carefully compared with the corresponding ones obtained in the continuum limit, and various improvements in the original calculations are discussed. Received: 10 April 1998 / Revised: 4 June 1998 / Accepted: 1st July 1998     

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.     

Aggregation of non-bonding molecules in a rapidly growing gel

The aggregation of non-bonding molecules in a rapidly growing gel is studied under three different conditions by means of Molecular Dynamics simulations. The aggregation takes place even under the unfavorable condition when the non-bonding molecules constitute only a small fraction of the total. The results also show that the morphology of the growing domains is different depending on the concentration of the non-bonding molecules. Received 30 November 1999     

Phase separation between phospholipids and grafted polymer chains onto a fluctuating membrane

We re-examine here the theoretical study of the phase separation between phospholipids and grafted long polymer chains onto a fluid membrane. The polymer chains are assumed to be anchored to the membrane by one extremity (anchor). The anchors are big amphiphile lipid molecules. The anchors and phospholipids forming the bilayer phase separate under the variation of a suitable parameter (temperature, pressure, membrane environment, ...). To investigate the demixtion transition, we elaborate a new approach that takes into account the membrane undulations. We show that these undulations have the tendency to induce additional attractive forces between anchors, and consequently, the separation transition is accentuated and occurs at high temperature. Quantitatively, we show that the membrane undulations contribute with an extra positive segregation parameter χ_m > 0 , which scales as χ_m κ^-2 , where κ is the bending rigidity constant. Therefore, the attraction phenomenon between species of the same kind is significant only for those membranes of small bending rigidity constant. Finally, the study is extended to the case where the lengths of the anchored polymer chains are randomly distributed. To achieve calculations, we choose a length distribution of fractal form. The essential conclusion is that the polydispersity increases the size of domains alternatively rich in phospholipids and anchors.     

Influence of a random field on particle fractionation and solidification in liquid-crystal colloid mixtures

The influence of a random-anisotropy (RA) type disorder on the phase separation of nematogen-colloid mixtures is studied theoretically by combining the phenomenological Landau-de Gennes, Carnahan-Starling, and hard-sphere crystal theories. We assume that the colloids enforce the RA disorder on the surrounding thermotropic liquid-crystal (LC) molecules. We adopt the Imry-Ma argument according to which the lower-temperature phase exhibits a domain-type pattern. The colloids impose a finite degree of orientational ordering even in the isotropic (paranematic) phase. In the ordered phase they give rise to a domain-type structure, resulting in the distorted nematic (speronematic) phase. The RA field opposes the phase separation tendency. With increasing disorder the difference between the paranematic and speronematic ordering decreases. Consequently there is a critical disorder, above which both phases become identical from the orientation point of view, but have different concentrations of colloids. We have also estimated another characteristic value of disorder above which the isotropic phase can exist only in a liquid state, the crystal phase being suppressed completely.     

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.     

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