Softcomp is a Project
of the European Commission
developed under the
6th Framework Programme.
© 2005 SoftComp
Scientific highlights 2010

Influence of topology on effective potentials: coarse-graining ring polymers

A. Narros, A. J. Moreno, and C. N. Likos
SoftComp partner: Univ. Vienna, Austria
Soft Matter 6 (2010) 2435

Ring-shaped polymers result by means of a simple (mathematical or chemical) operation: take a linear chain and glue its two ends together. However, this innocent-looking modification, opens up a new array of challenges for theorists and experimentalists alike. The reason lies in the fact that transforming a chain into a ring changes a fundamental mathematical property of the object, namely its topology. The latter can assume arbitrarily complicated variations if one takes into account that the process of gluing the ends together can entrap a number of knots, whose complexity can grow uncontrollably as the degree of polymerization increases. To make things even harder, the topological constraints cannot be written down as a term in the Hamiltonian of the system, so that analytical or perturbative approaches do not come into question.

In a collaboration between the SOFTCOMP nodes at the University of Düsseldorf and at the University of the Basque country, suitable microscopic models of ring polymers have been developed, which guarantee the conservation of the topological invariants in concentrated ring-polymer solutions and allow for efficient simulation of the systems. By systematically increasing the knot complexity from the trivial (knot-free) ring polymer up to fivefold knots, it was found that topology has a dramatic impact on the effective interactions between polymers, bringing about novel physical aspects in the behavior of the system.

The very fruitful collaboration that has profited from SOFTCOMP through exchanges and visits of the partners, is being supported by the Marie-Curie IEF Fellowship “RINGEFF”, 2009 – 2011, and its continuation for the further future is already under way.

The effective interaction between the centers of mass of linear chains (green), kont-free rings (black), trefoil-knotted (red) and fivefold-knotted rings, showing the nontrivial effects of topology.

Unusual features of depletion interactions in soft polymer-based colloids mixed with linear homopolymers

M. Camargo and C. N. Likos
SoftComp partner: Univ. Vienna, Austria
Physical Review Letters 104 (2010) 078301

Conventional wisdom has it that when non-adsorbing linear polymer chains are added to a suspension of big, colloidal particles, they bring about a so-called depletion attraction between the colloids, whose characteristics can be tuned by the size and concentration of the additives. In particular, the range of the attraction is set by the depletants' size, while its depth is controlled by their concentration. Whereas these features are certainly true for hard colloidal particles, Camargo and Likos demonstrated in the article above that this is not the case when the colloids are soft, polymer-based particles such as star polymers of microgels. In this case, which is very common in soft matter composites, the penetrability of the soft colloids leads to a novel and unusual form of depletion, whose range is essentially independent of the size of the depletants and it is rather determined by the properties of the depleted soft colloids. Further, it has been shown that these effects can all be captured in the framework of a previously suggested, ad-hoc model that describes the attractions by means of a Fermi-like distribution model, and the parameters of the latter have been mapped to physical characteristics of the soft mixtures.

The work has profited from the rich scientific environment and the presence of discussion partners within SOFTCOMP. One of the authors (M.C.) has also spent a two-month SOFTCOMP-financed exchange visit at the partner University of the Basque Country, working on a different but related problem together with Dr. A. J. Moreno.

A simulation snapshot of two star polymers (dark blue and red), swimming in an ocean of homopolymer chains (light blue).

Microemulsion nanocomposites

N.Puech, S.Mora, T.Phou, G.Porte, J.Jestin and J.Oberdisse
SoftComp partner: CNRS-Montepellier, France
Soft Matter, accepted for publication

What are the effects of incorporation of hard nanoparticles in transient networks? How are mechanical properties affected, and how can we physically understand these changes? These questions are of fundamental and practical interest in material science, especially in polymer science where reinforcement phenomena by nanoparticles are still poorly understood.

Silica nanoparticles have been added to a model transient network made of oil-in-water microemulsion droplets bridged by telechelic copolymers [1]. The phase diagram of the transient network and in particular the percolation threshold characterized by rheology was found to be shifted, suggesting participation of the hydrophilic particles in the network made of hydrophobic droplets. The shift in percolation towards lower droplet or polymer concentration lead to a peculiar reinforcement behaviour of such microemulsion nanocomposites, modifying both the modulus and the relaxation time. The reinforcement has been modelled based on nanoparticles connected to the network via droplet adsorption. This implied that fewer microemulsion droplets were needed to reach percolation through finite-sized clusters. Contrast-variation Small Angle Neutron Scattering coupled to a reverse Monte Carlo approach was used to analyse the microstructure, cf. Figure 1. The rather surprising double-peak intensity curves were shown to be in good agreement with the adsorption of droplets on the nanoparticles. This gave additional credit to the idea that silica connected to the network via bound micelles played the role of anchors to the droplet-copolymer clusters.

Scattered intensity of silica-matched microemulsion nanocomposites compared to two models.

Dynamics of entangled polymers in the presence of nanoparticles

K.Nusser, G.J.Schneider, L.Willner, P.Falus and D. Richter
SoftComp partner: Forschungszentrum Juelich (Group Prof. Richter), Germany
Submitted for publication

The dynamics in an entangled polymer melt has been very successfully described by the reptation model suggested by de Gennes. In this model, the confinement imposed on one chain by all surrounding chains is perceived as a virtual tube with diameter dtube.

If nanoparticles are added to the polymer melt, an additional confinement on the polymer motion is introduced. Very recently we have studied the influence of this geometrical confinement on the chain dynamics. By using poly(ethylene-alt-propylene) as the polymer component and silica nanoparticles with a hydrophobized surface as fillers, a largely repulsive model system was realized, where energetic interactions and adsorption only play a minor role for the polymer motion.

Figure shows the results of a Neutron Spin Echo study on this system for increasing filler fraction Φ. An increase of the plateau level at long times t hints to an increase of the overall confinement on the polymer motion. We were able to describe this increasing confinement by an apparent confinement length dapp in the mathematical frame of the reptation model. This apparent confinement consists of two independent contributions dtube and dgeo, where the former is the well-known entanglement contribution and the latter is dictated by the particle structure (see inset of the figure). With increasing filler fraction Φ the geometric confinement becomes dominant, whereas entanglements are less and less important - the chains disentangle.

Scattered intensity of silica-matched microemulsion nanocomposites compared to two models.

Large Domain fluctuations enable catalytic activity in phosphoglycerate kinase

R.Inoue, R.Biehl, T.Rosenkranz, J.Fitter, M.Monkenbusch, M.-S.Appavou, B. Farago and D.Richter
SoftComp partner: Forschungszentrum Juelich (Group Prof. Richter), Germany
Biophysical Journal, 99 (2010) 2309

Large-scale domain motions of enzymes are often essential for their biological function. Phosphoglycerate kinase has a widely open domain structure with a hinge near to the active center between the two domains. Structural analysis by small angle neutron scattering revealed that the structure in solution is more compact as compared to the crystal structure, but would not allow the functionally important phosphoryl transfer between the substrates, if the protein would be static. Brownian large scale domain fluctuations on a timescale of 50 ns was revealed by neutron spin echo spectroscopy. The found dynamics was compared to the displacement patterns of low frequency normal modes (see figure). In particular the lowest normal mode facilitates a close encounter of the key residues in the active center to build the active configuration. The observed dynamics enables the function of the protein. Moreover, the presence of the substrates has only a small influence on the dynamics.

The ternary 3PG-MgATP complex of yeast PGK. Q dependence of the internal dynamics contribution A(Q) to the NSE signal from 5% PGK and 5% PGKsub compared to the calculation based on a normal mode model.

Thermoresponsive hybrid microgel particles with intrinsic optical and magnetic anisotropy

C.Dagallier, H.Dietsch, P.Schurtenberger and F.Scheffold
SoftComp partner: Univ. Fribourg, Switzerland
Soft Matter, 6 (2010) 2174

We currently investigate dynamical arrest, i.e. glass or gel formation, where we use thermoresponsive microgels as ideal model systems. As we are interested in the arrest of rotational motion we decided to design novel hybrid microgel particles. These particles, containing a magnetic spindle-shaped hematite core, allow now to investigate several aspects of dense microgel suspensions. We can study in detail the arrest of the rotational dynamics as the system is driven into a glassy state taking advantage of the anisotropic magnetic cores adding a switchable anisotropy. In a recent article published in Soft Matter we described a simple synthetic route of these tunable particles and demonstrated their use in a fundamental study on their rotational motion close to dynamical arrest. We believe that these particles may have a considerable impact on fundamental investigations of the phase behaviour of soft particles, and as novel building blocks for responsive and switchable materials.

Scheme illustrating the thermal and magnetic response of the hybrid particles visible on the transmission electron microscopy image. Cover of Soft Matter, 2010, 6(10) with a representation of the hematite core enclosed in a microgel.

Growth and Branching of Charged Wormlike Micelles

M.In, B.Bendjeriou, L.Noirez and I.Grillo
SoftComp partner: CNRS-Montpellier, France
Langmuir Letter 26/13 (2010) 10411

Beside the main cylindrical curvature, wormlike micelles present heterogeneities in curvature because their ends are necessarily spherical and they can present junctions that are locally flat. The concentrations of these defects determine the rheological properties and the phase behavior of surfactant solutions. They have been measured in aqueous solutions of Gemini type surfactants.
Due to electrostatic interactions the micelles are not randomly distributed but rather adopt a preferred first neighbour distance. This translates into a pronounced correlation peak in the scattering patterns. The volume fraction dependence of the peak position q* directly reveals all the transitions of shape from spherical to branched cylindrical micelle and has been quantitatively interpreted in terms of growth and branching. Both of these condensation phenomena result from the work of effective attractive forces, but observing them through the correlation peak points out the fact that they are also boosted by repulsive interactions.

(a): Position of the correlation peak as a function of the volume fraction Φ. ▼ : DTAB ; ▲ : 12-6-12-6-12; ●: 12-3-12; ■ : 12-2-12; • : 12-3-12-3-12. The equations of the continuous lines from the thinnest to the thickest one are: 0.227∙ Φ1/3; 0.207∙ Φ1/2; 0.254 Φ1.
(b) Aggregation number vs. Φ, same symbols legend as in figure a.
(c): junction density in trimeric surfactant 12-3-12-3-12 solutions.
All data are for solutions in D2O at 25°C.

Efficiently suppressing coalescence in polymer blends using nanoparticles: role of interfacial rheology

S.Vandebril, J.Vermant and P.Moldenaers
SoftComp partner: K.Univ. Leuven, Belgium
Soft Matter 6 (2010) 3353

Blending of two or more immiscible polymers is an attractive route to generate new materials. However, during processing in the liquid state, the flow-induced microstructure changes continuously due to the complex interplay between break-up and coalescence, typically resulting in a coarse morphology with poor properties. Hence the need to generate and stabilize a fine morphology is obvious and block copolymers are typically used as compatibilizers. In this work the use of nanoparticles as an alternative to compatibilize immiscible polymer blends is investigated. It is demonstrated that nanoparticles that are located at the interface can indeed efficiently suppress coalescence in polymer blends. A combination of optical microscopy and interfacial rheometry using planar interfaces has been used to demonstrate that the nanoparticles mainly affect the surface rheological properties, whereas classical compatibilizers also strongly affect the interfacial tension.

a) Cryo-SEM image of 70/30 vol% PDMS/PIB blend with 1wt % anisotropic particles (hematite core-silica shell) with DCDMS coating;
b) Evolution of the morphology as a function of shearing time in a 70/30 vol% PDMS/PIB blend, unfilled and with 1% of spherical or anisotropic particles (particle concentration in vol%).

Polymer chain stiffness versus excluded volume: A Monte Carlo study of the crossover towards the wormlike chain model

H.-P.Hsu, W.Paul and K.Binder
SoftComp partner: Univ. Mainz and Univ. Halle, Germany
Europhys. Lett. 92 (2010) 28003

As the intrinsic stiffness of a linear polymer chain under good solvent conditions varies over a wide range, one can observe both a crossover from a rod-like regime to a Gaussian random coil regime and a further crossover towards self-avoiding walk (SAW) regime. Using a simple coarse-grained model, the SAW on the simple cubic lattice, and introducing a bond-bending potential to control the flexibility of a polymer chain, our Monte Carlo results for chain lengths up to Nb= 50000 provide sufficient accuracy for testing the applicability of the Kratky-Porod worm-like chain model, and verifying the multiple crossover behavior predicted by theory (Fig. 1a). For bottle-brush polymers containing a long flexible macromolecule as a backbone to which flexible side chains are densely grafted, our results obtained using the bond fluctuation model on a simple cubic lattice show that no pre-asymptotic Gaussian regime appears (Fig. 1b). The reason for the difference to the SAW is that here stiffening goes together with thickening of the chain which can therefore always be described as a flexible chain of spherical blobs. Analysis of experimental data for bottle-brush polymers using concepts of the Porot-Kratky worm-like chain model therefore is not possible, and conflicting experimental results in the literature can be traced to the inapplicability of this model for this type of polymer. The extremely good statistics for large macromolecules needed for this analysis was obtainable by a combination of advanced simulation algorithms and the stable and performant computer installation provided by the SoftComp cluster at the Jülich Supercomputing Centre.

a) Log-log plot of the rescaled mean square end-to-end distance for the semi-flexible SAW model versus chain length Nb. Various values of the stiffness parameter qb are indicated.
b) Same as a) but for bottle-brush polymers using a grafting density and several choices of the side chain length N.

Curvature Dependence of Surface Free Energy of Liquid Drops and Bubbles

B.J.Block, S.K.Das, M.Oettel, P.Virnau and K.Binder
SoftComp partner: Univ. Mainz, Germany
J. Chem. Phys. 133 (2010) 154702

The surface tension γ of nanodroplets or -bubbles of a minority phase is of crucial importance for the nucleation of that phase since it directly influences the free energy barrier in the nucleation process. However, previous simulation work experienced difficulties in precisely pinpointing this surface tension. Using a novel Monte-Carlo method aimed at studying two-phase configurations in nanoscopically confined systems, it was possible to extract the surface tension of spherical and cylindrical droplets in one- and two-component Lennard-Jones fluids. Thereby it was found that for a range of droplet radii R relevant for nucleation theory, γ(R) deviates strongly from γ(∞) which can be accounted for by a term of order γ(∞)/γ(R)-1 ~ R-2. The leading order (Tolman) deviation ~1/R is quantitatively less important for the one-component system and absent in the symmetric two-component case. Furthermore, for the one-component system this analysis is stroongly supported by complementary density functional calculations.
This article was choosen as a Research Highlight in October 2010 by the Editorial Board of The Journal of Chemical Physics.

Depending on the oversaturation in a finite box, spherical (left) or cylindrical (right) droplets of a minority phase (shown with blue balls) can be stabilized. The surface tension of these droplets is then determined via the statistical weight of such a configuration.

Last modified: 27/12/2011