Jan Groenewold

Surface roughness directed self-assembly of patchy particles into colloidal micelles

Colloidal particles with site-specific directional interactions, so called “patchy particles”, are promising candidates for bottom-up assembly routes towards complex structures with rationally designed properties. Here we present an experimental realization of patchy colloidal particles based on material independent depletion interaction and surface roughness. Curved, smooth patches on rough colloids are shown to be exclusively attractive due to their different overlap volumes. We discuss in detail the case of colloids with one patch that serves as a model for molecular surfactants both with respect to their geometry and their interactions. These one-patch particles assemble into clusters that resemble surfactant micelles with the smooth and attractive sides of the colloids located at the interior. We term these clusters “colloidal micelles”. Direct Monte Carlo simulations starting from a homogeneous state give rise to cluster size distributions that are in good agreement with those found in experiments. Important differences with surfactant micelles originate from the colloidal character of our model system and are investigated by simulations and addressed theoretically. Our new “patchy” model system opens up the possibility for self-assembly studies into finite-sized superstructures as well as crystals with as of yet inaccessible structures.

Wrinkling of plates coupled with soft elastic media

If a rigid plate is subjected to stress and attached to a soft elastic medium, it is very likely that this stress is relieved by wrinkling: The plate buckles into a large number of waves. First the basic equation for wrinkling is rederived. Then the more complicated case of isotropic wrinkling is discussed, i.e., wrinkling resulting from isotropic compression of the plate. Wrinkles with different directions coexist while creating defects. A simple model describing the order in the direction of the wrinkles is presented in this paper. Near an edge the order is anomalously large. The measurements done by Bowden and coworkers (Appl. Phys. Lett. 75 (1999) 2558) on order near an edge are explained quantitatively by this model.

Colloidal molecules with well-controlled bond angles

We present a straightforward technique for the synthesis of asymmetric colloidal molecules with uniform and well-controlled bond angles. The new method makes use of coalescence of liquid protrusions on polystyrene spheres. The bond angle between the seed particles and central sphere can be chosen as desired by adjusting the size of the liquid protrusion. The surprising uniformity of the colloidal molecules comprised of small numbers of seed particles is proven by comparison with 3D models. Considering different origins for this uniformity we conclude that the asymmetric and unique shape is induced by aggregation inside the liquid droplets upon polymerization. This technique offers a new and simple way to make a wide variety of asymmetric colloidal molecules in a reproducible and controlled fashion.

Non-equilibrium cluster states in colloids with competing interactions

Cluster formation and gelation are studied in a colloidal model system with competing short-range attractions and long-range repulsions. In contrast to predictions by equilibrium theory, the size of clusters spontaneously formed at low colloidal volume fractions decreases with increasing strength of the short-range attraction. Moreover, the microstructure and shape of the clusters sensitively depend on the strength of the short-range attraction: from compact and crystalline clusters at relatively weak attractions to disordered and quasi-linear clusters at strong attractions. By systematically varying attraction strength and colloidal volume fraction, we observe gelation at relatively high volume fraction. The structure of the gel depends on attraction strength: in systems with the lowest attraction strength, crowding of crystalline clusters leads to microcrystalline gels. In contrast, in systems with relatively strong attraction strength, percolation of quasi-linear clusters leads to low-density gels. In analyzing the results we show that nucleation and rearrangement processes play a key role in determining the properties of clusters and the mechanism of gelation. This study implies that by tuning the strength of short-range attractions, the growth mechanism as well as the structure of clusters can be controlled, and thereby the route to a gel state.

Colloidal cluster phases, gelation and nuclear matter

The combination of short-range attractions and long-range repulsions can lead to interesting clustering phenomena. In particular there are strong indications that the colloidal cluster phase is in fact a manifestation of such a competition. Here we compute the stability boundary of the cluster phase by invoking counter-ion condensation. It is found that a condensation catastrophe leading to an infinite cluster sets in if the level of charge on the colloid is too low. The same ingredients leading to the cluster phase are found in nuclear physics: strong short-range attractions due to nuclear force and weak long-range Coulomb repulsions. We will show explicitly here the equivalence of a semi-empirical mass formula for the binding energy of the nucleus and the free energy of a cluster in a colloidal cluster phase. This identification enables an exploitation of theoretical results from nuclear physics to the colloidal domain and, perhaps, the construction of a colloidal system mimicking various aspects of nuclear matter.

Integrating information from novel risk factors with calculated risks the critical impact of risk factor prevalence

Case vignette: a 60-year-old man visits his physician for assessment of his 10-year cardiovascular risk. On the basis of his systolic blood pressure, lipid profile, smoking status, and the fact that he is nondiabetic, the Framingham risk score estimates his risk to be 8%. The physician wonders if he could further specify the patients risk by performing an additional test like coronary calcium score or microalbuminuria (MA). For matters of convenience and costs he decides to test MA, which turns out positive. Assuming that MA has an invariable and exact relative risk (RR), independent from the aforementioned classical risk factors, of 2.0, what would this mans estimated risk become? Prediction of absolute disease risk is an essential component of cost-effective disease prevention strategies. In cardiovascular disease (CVD) prevention, for example, antiplatelet and statin therapy is applied if absolute risk of CVD is considered sufficiently high. Various prediction models are available for the purpose of risk calculation. These models are derived from large population-based cohorts in which conventional CVD risk factors and prospective event registrations are available. Well known examples include the Framingham risk score and the risk model of the European SCORE consortium.1,2 Obviously, with regard to individual risk estimation, risk models have inherent shortcomings in terms of precision and reliability. In an attempt to improve risk prediction, much focus has been on the potential benefit of adding information relating to novel risk factors. Various statistical methods have been developed to assess the ability of novel risk factors to improve risk stratification. These methods include assessment of discrimination and calibration of the conventional versus the updated risk model.3,4 The ultimate goal of adding novel risk factors is to improve a patients health by correctly reclassifying him or her into high, intermediate, and low risk …

Pattern formation in thin polymer films by spatially modulated electric fields

We present a theoretical model and experimental data describing the response of a thin liquid polymer film to a heterogeneous electric field. The theory predicts two different regimes separated by a distinct boundary: in one regime the film is characterized by steady-state low amplitude surface modulations following the periodicity of the electric field, in the other regime the film breaks up into pillars centered around the region of highest field strength. The theoretical analysis describes the film destabilization in terms of two dimensionless variables, which fully describe the low amplitude limit. The corresponding experimental system was realized with a photo-structured epoxy resin covering the top electrode and thin polystyrene films that were destabilized by the applied electric field and characterized by AFM after quenching. Theoretical and experimental results allow us to determine the destabilization conditions and to identify the experimental variables that characterize film destabilization. The theoretical framework provides a tool for the experimentalist to predict in detail the structures generated by film destabilization, thereby enabling a new way of ‘soft-lithography’.

Nanoscale structuring of semiconducting molecular blend films in the presence of mobile counterions

The controlled fabrication of submicrometer phase-separated morphologies of semiconducting organic materials is attracting considerable interest, for example, in emerging thin-film optoelectronic device applications. For thin films of spin-coated blends of PCBM ([6,6]-phenyl-C 61-butyric acid methyl ester) and cationic cyanine dyes, we used atomic force microscopy scans to infer the structure formation mechanism: The solutions separate into transient bilayers, which further spinodally destabilize because of long-range molecular interactions. A thin layer ruptures earlier than a thick layer, and the earlier instability determines the morphology. Consequently, the resulting morphology type mainly depends on the ratio of the layer thicknesses, whereas the periodicity of structures is determined by the absolute film thickness. These findings allow control of the feature sizes, and nodular domains with diameters well below 50 nm were produced. Films prepared with dyes possessing a mobile counterion were always unstable. To rationalize the findings, we developed a thermodynamic model showing that electrostatic forces induced by the mobile counterions act as destabilizing pressure.

Sheet-like assemblies of spherical particles with point-symmetrical patches

We report a computational study on the spontaneous self-assembly of spherical particles into two-dimensional crystals. The experimental observation of such structures stabilized by spherical objects appeared paradoxical so far. We implement patchy interactions with the patches point-symmetrically (icosahedral and cubic) arranged on the surface of the particle. In these conditions, preference for self-assembly into sheet-like structures is observed. We explain our findings in terms of the inherent symmetry of the patches and the competition between binding energy and vibrational entropy. The simulation results explain why hollow spherical shells observed in some Keplerate-type polyoxometalates (POM) appear. Our results also provide an explanation for the experimentally observed layer-by-layer growth of apoferritin--a quasi-spherical protein.

Rotational diffusion affects the dynamical self-assembly pathways of patchy particles

Significance Recent experiments show that the rotational diffusion of proteins and patchy colloids does not always follow the Stokes–Einstein relation, especially in crowded environments or with the use of external fields. Because cellular cytoplasm is very crowded, this finding can have consequences for protein complex formation such as viruses. We study the kinetic network of simple models for proteins and patchy colloids and find that their dynamical self-assembly pathways change with varying the rotational diffusion constant. In particular, lowering the rotational diffusion avoids frustrated intermediate states. Such control of kinetic networks would also benefit the design of new self-assembled functional materials. Predicting the self-assembly kinetics of particles with anisotropic interactions, such as colloidal patchy particles or proteins with multiple binding sites, is important for the design of novel high-tech materials, as well as for understanding biological systems, e.g., viruses or regulatory networks. Often stochastic in nature, such self-assembly processes are fundamentally governed by rotational and translational diffusion. Whereas the rotational diffusion constant of particles is usually considered to be coupled to the translational diffusion via the Stokes–Einstein relation, in the past decade it has become clear that they can be independently altered by molecular crowding agents or via external fields. Because virus capsids naturally assemble in crowded environments such as the cell cytoplasm but also in aqueous solution in vitro, it is important to investigate how varying the rotational diffusion with respect to transitional diffusion alters the kinetic pathways of self-assembly. Kinetic trapping in malformed or intermediate structures often impedes a direct simulation approach of a kinetic network by dramatically slowing down the relaxation to the designed ground state. However, using recently developed path-sampling techniques, we can sample and analyze the entire self-assembly kinetic network of simple patchy particle systems. For assembly of a designed cluster of patchy particles we find that changing the rotational diffusion does not change the equilibrium constants, but significantly affects the dynamical pathways, and enhances (suppresses) the overall relaxation process and the yield of the target structure, by avoiding (encountering) frustrated states. Besides insight, this finding provides a design principle for improved control of nanoparticle self-assembly.