Self Assembly in Soft- and Biomatter<br>program leader: Paul van der Schoot

Although most people have never heard of soft matter, we handle it every day! Think of mayonnaise, paint, toothpaste, yoghurt and hair gel but also of LCD displays and the material that biological cells are made up of. Common denominator in this bewilderingly wide class of materials is the existence of structure on length scales from a few nanometers to a few micrometers. The existence of structure on the scale in between that of atoms and everyday life is what sets soft matter apart from both hard and wet matter, i.e., common solids and liquids. It bestows upon it properties that are unique and in a sense in between that of liquids and solids.

This supramolecular structure so typical of soft matter is self-organised, i.e., it appears by itself in this form of matter that usually is made up of very many, often chemically very complex components, one of which is typically a host fluid where the others are dispersed in. Because of this propensity to self-organise, and because the energy scales involved are on the order of the thermal energy, soft matter is an ideal playground for the application of statistical mechanics. This is exactly what we do: we apply statistical mechanics to soft and biomaterials, relying mostly on paper-and-pencil theory, sometimes invoking numerical calculations, and off late also computer simulations.

What we are interested in is finding out what the physical principles are of self assembly in these materials, how the molecular structure of the dispersed molecules and particles and interactions between, them dictate the kind supramolecular structure that emerges. We are also interested in finding out in what way that the supramolecular structure itself dictates the behaviour of soft materials on macroscopic scales. Topics that we work on include liquid crystals, supramolecular polymers, colloidal suspensions, protein solutions and, last but not least, viruses. All the work we do is in close collaboration with experimental, theoretical and simulation groups all around the world.

Research Highlights

1. Hierarchical Self-Assembly

Hierarchical self-assembly provides a powerful strategy for producing molecular nanostructures. Although widely applied, the mechanistic details of self-assembly processes are poorly understood. By combining spectroscopic studies with statistical mechanical theory that deals explicitly with nucleation-type processes, we analysed the self-assembly of p-conjugated molecules into helical supra-molecular fibrillar structures. The data support a nucleation-growth pathway that gives rise to a very high degree of cooperativity and hence to very long fibers. The self-assembly turns out to depend strongly on the molecular structure of the solvent, even for innocuous compounds such as homologous series of alkanes, suggesting that an organized shell of solvent molecules plays an explicit role in rigidifying the aggregates and guiding them toward further assembly into bundles and/or gels. [Probing the nucleation event in chemical self-assembly, P. Jonkheijm, P. van der Schoot, A. Schenning, E. Meijer, Science 313 (2006), 80-83.]

2. Nanocomposites

Nanocomposites of conducting nanoparticles in an insulating polymeric matrix are good candidates for transparent electrodes and EM shielding. We formulated a generalized connectedness percolation theory that can be made tractable for particle mixtures even if they consist of infinitely many different components. Applying our methodology to composites containing carbon nanotubes, we were able to explain huge variations found experimentally in the onset of electrical conduction. It turns out that the percolation threshold is extremely sensitive to any degree of variation in particle length and/or diameter. The theory also allows us to model the influence of the presence of poorly conductive species in the mixture, such as is the case for single-walled nanotubes, and the impact of non-trivial interactions between the particles. We found that weakly attractive interactions strongly favour percolation. [Continuum percolation of polydisperse nanofillers, R. Otten and P. van der Schoot, Physical Review Letters, 103 (2009), 225704, 1-4.]

3. Wetting Phenomena

Wetting phenomena involving liquid crystals are important in device applications and in industrial processes involving, e.g., the spinning of super-strong fibers from liquid-crystalline dispersions. We studied theoretically and experimentally the capillary rise of the interface between coexisting isotropic and uniaxial nematic phases in dispersions of platelets in contact with a wall. Because of a weak surface anchoring, the director field in the capillary rise region is uniform, allowing us to predict the capillary rise from the surface tension and anchoring strength. From the measured rise of the meniscus at the wall we determine the exceedingly low isotropic-nematic surface tension of 3 nN/m and anchoring strength of 2 nN/m. We find that the capillary rise profile is not monotonic, resulting from the interaction between the preferred direction of the particles and the surface anchoring. [Isotropic-nematic interface and wetting in suspensions of colloidal platelets, D. van der Beek, H. Reich, P. van der Schoot, M. Dijkstra, T. Schilling, R. Vink, M. Schmidt, R. van Roij, and H. Lekkerkerker, Phys. Rev. Lett. 97 (2006), 087801, 1-4.]

4. Self-diffusion in complex fluids

Self-diffusion in complex fluids is dominated by the crowding. To understand how this two affects particle motion we propose a novel dynamical density-functional theory, involving the coupling of a test particle to the fluctuating background of identical particles. Applying the formalism to nematic and lamellar smectic liquid crystals, we find that temporary cages formed by neighboring particles compete with permanent free energy barriers in particular in spatially non-uniform phases, resulting in non-Gaussian diffusive motion that become correlated in orthogonal spatial directions. Qualitative agreement with experiments demonstrates the importance of explicitly dealing with time-dependent self-consistent molecular fields. [Self diffusion of particles in complex fuids: temporary cages and permanent barriers, M. Bier, R. van Roij, M. Dijkstra and P. van der Schoot, Phys. Rev. Lett. 101 (2008), 215901, 1-4.]

5. Spherical viruses

Spherical viruses tend to have a fixed size that depends on the kind of virus. By applying statistical theories of polymers and colloids, we investigated the physical mechanisms underlying size selection, and in particular the effect of genome length and structure, electrostatics and the relative genome and protein concentrations. We find that the coat proteins may well adjust the size of the shell to the size of their genome, which in turn depends on the number of charges on it. Furthermore, we find that different stoichiometric ratios of proteins and genome produce virus particles of various sizes, consistent with in vitro experiments, an effect, whilst observed, has so far been ignored in the field. [Size regulation in ss-RNA viruses, R. Zandi and P. van der Schoot, Biophys. J., 96 (2009), 9-20.]