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## New Trends in Simulating Colloids: from Models to Applications

#### CECAM-HQ-EPFL, Lausanne, Switzerland

#### Organisers

In the last decades, the field of colloidal science has attracted a growing attention, both for its scientific merits, as well as for technological applications. One of its most interesting aspects is represented by the wide arena of disciplines that it involves, ranging from physics to chemistry, from food science to photonic crystals, from biophysics to biomedical research. In addition, the nature of the problem promotes synergies between theoretical, simulation, and experimental approaches alike. This fundamental interplay can be explained with a historical example. The existence of a freezing transition in hard-spheres was predicted for the first time by Kirkwood in the fifties based on a theoretical approach [3]. The numerical proof of the existence of such transition came from the pioneering work of Alder and Wainwright in 1957 [4]. It was only in 1968 that Hoover and Ree calculated the phase boundary of this transition by numerical simulations [5]. At that time, the hard sphere system was regarded as a pure toy model, since 'real' interactions at the atomic and molecular level were deemed to be much more complicated. These results, nevertheless, demonstrated that it is possible to obtain phase transitions driven solely by entropy [6]. The advent of modern colloid science has shed new light on this observation, and the possibility to synthesize particles that interact via effective hard-sphere potentials allowed the experimental observation of the liquid-solid phase transition predicted by these early simulation [7]. Nowadays, hard sphere colloids are extremely well characterized, and they have become one of the standard models of glass formers in theory [8, 9], simulations [10] and experiments [11, 12]. In other words, what started-off as a toy model in 1968, has nowadays become one of the most widely studied experimental systems in colloid science. The usual starting point for theoretical colloid research is to reduce the complexity of the problem by means of coarse graining certain degrees of freedom. In this way, extremely complicated interactions, due to charges, dispersion forces, ions/counter-ions effects, depletion agents etc., can be integrated out, leading to a set of system specific) effective potentials [13]. Once the effective potentials are known, one can readily use the full arsenal of Statistical Mechanics to predict the phase behavior. The success of this approach has been demonstrated in several different systems. For short-ranged attractive colloidal systems, for example, both the anomalous phase diagram, characterized by metastable fluid-fluid phase separation [14, 15], and the glass properties [16], have been studied using simple two-body effective potentials. Experiments have confirmed that the phase behavior obtained using these effective potentials indeed shows up in real colloidal solutions as well [17]. In addition, also phase separation in colloid-polymer mixtures is well described using effective interactions [18, 19]. It is clear that in colloid science there is a continuous feedback between experiments on the one hand, and simulations and theory on the other. Experiments can uncover new phenomena, for which better understanding may subsequently be provided via simulation and theory. The reverse is, of course, also possible, namely of simulations and theory inspiring new experiments. This is precisely what we envision with the present CECAM workshop. There is an urgent need for the theoretical and computational colloid community to discuss and identify new trends in the field of colloid experiments. As is well known, there has been a revolution in the resolution at which colloid experiments can be performed: individual colloidal particles can now be visualized directly in real time using confocal microscopy [20, 21]. This also means that a tremendous amount of new detailed information is available, previously unheard of compared to, say, atomic systems. It has already become obvious that theoretical and simulation concepts need to be 'tuned' accordingly. A striking example are the recent real- space investigations of the colloid-polymer interface [22]. In atomic systems, interface information is typically gathered in scattering experiments. This yields rather coarse-grained information, involving large distances over many particles. In contrast, by the colloid experiments of Aarts et. al. [22], it has become necessary to consider the interface all the way down to the single particle level. This has already led to numerous theoretical and simulation efforts attempting to explain what precisely an interface means on such short length scales [23-26]. Similarly, the recent real-space investigations of colloid-polymer mixtures close to criticality [27] may inspire similar theoretical work and simulations in this field also. For nearly two decades, much computational modeling in colloidal systems has been based on the assumption of a spherically symmetric interaction potential [9, 10] and this approach is still producing many important results today. The phenomenology that can be described is extremely rich, and much progress has been made: the description of critical phenomena [28], identifications of exotic ordered phases [29, 30], the field of gelation and glass transitions [31, 32], as well as protein solutions [33-35], to name a few. When binary mixtures are considered, the increase in complexity opens-up new incredible possibilities. In the beautiful experimental work of the group of van Blaaderen, for example, the fine tuning of colloidal charges brought along the discovery a new arena of exotic crystal structures [36], some of which are promising candidates for the creation of photonic crystals with a band gap in the visible region [37]. Far from being restricted to the experimental arena, these systems have been widely investigated numerically and detailed free energy calculations have enabled the construction of the phase diagram [36]. The importance of modeling binary mixtures is not just relevant for colloidal systems, but has implications for medical applications also. For example, binary mixtures of eye-lens proteins can be described quite well using a simple spherical potential, and it was shown that a delicate balance of the interspecies interaction controls thermodynamic stability, a fact of importance to cataract formation [1]. Crucial to the success of computer modeling binary mixtures are efficient algorithms. One problem is the size-asymmetry between the species, which usually makes standard Metropolis type algorithms inefficient. Regarding size-asymmetric Lennard-Jones mixtures, impressive results have been obtained using geometric cluster moves [38, 39]. A different cluster move has been designed to analyze in detail the demixing transition in colloid-polymer solutions [38] algorithms have also been developed to study nucleation [40], which plays a key role in crystal formation, or algorithms to overcome free energy barriers [41]. Nowadays, thanks to recent advances in synthesis techniques [42, 43], colloidal particles can be made of different (non-spherical) shapes [44, 45]. The surfaces of these particles can be functionalized in many ways, such that the particle interactions become, for instance, directional or 'patchy'. The ultimate scientific and technological goal is to construct new devices, using these functionalized particles as elementary building blocks. Theoreticians are eagerly following this development, and several groups have already initiated research into this direction. The effect of 'patchy' interactions on the location of the liquid-liquid critical point and the coexistence curve, for instance, has been studied by Bianchi et. al. [46]. Also the phase behavior of rod-like colloidal suspensions and colloidal platelets is presently under intense investigation [47, 48]. Interestingly, an important parallel can be drawn between 'functionalized' colloids and so-called 'primitive models'. The latter are widely used to describe molecular systems [49, 50]. Experiments in-silico have been used to investigate self-assembly of non-spherical particles, as well as the dynamical properties of ellipsoidal [51] and patchy particles [52]. Besides colloidal systems, nature offers another system in which non-spherical and patchy particles play a crucial role: proteins! The techniques used to probe colloidal systems have always been extremely fruitful for proteins also. In fact, protein phase diagrams are often 'analogous' to those of colloids. Think, for instance, of the metastable liquid-liquid critical point present in both systems. The investigation of non-spherical colloidal particles and their interactions should therefore prove rewarding for protein science also. Indeed, some numerical investigations are already exploiting this analogy [53, 54]. Another exciting new direction that we envision is represented by colloidal particles functionalized with DNA. In this case, the interactions are not only patchy and directional, but exhibit an even greater level of complexity. One goal is to design specific DNA sequences to promote self-assembly. The first experimental results in this direction look promising [54-56], and so do computer simulations [57, 58].

## References

**Austria**

Gerhard Kahl (Institut für Theoretische Physik, TU Wien) - Organiser

**France**

Giuseppe Foffi Foffi (Laboratoire de Physique des Solides) - Organiser

**Germany**

Richard Vink (University of Goettingen) - Organiser