Daan Frenkel ontvangt de Bakhuis Roozeboom Medaille 2015 voor de grote bijdrage die hij met zijn creatieve computersimulaties heeft geleverd aan de ontwikkeling van de fasenleer – de wetenschap die het gedrag van materie onder veranderende omstandigheden bestudeert.

Ter gelegenheid van de uitreiking op maandag 25 januari 2016 organiseert de KNAW die dag een symposium over het onderzoek van Daan Frenkel.

### Interfacial Tension of Nanodroplets

**George Jackson, Professor of Chemical Physics at Imperial College London**

The physical description of small fluid drops covers two centuries from the first mechanical treatment of Young and Laplace, through the formal thermodynamics of Gibbs and Tolman, to modern statistical mechanics. In spite of this, there is still controversy with respect to the effect that curvature has on surface properties. We investigate the interfacial tension of Lennard-Jones and water droplets with diameters in the nanometer range using molecular dynamics simulations. A thermodynamic route, namely the test-area (TA) method [1,2], is employed to determine the surface tension. The TA method involves extracting an ensemble average of the Boltzmann factor of the perturbative changes in configurational energy within the canonical ensemble upon the application of isochoric deformations in the surface area. A finite difference method is then used to directly estimate the derivative of the Helmholtz free energy with respect to the interfacial area and relate it to the surface tension. This method is preferred over the more common mechanical (virial pressure tensor) calculation, which can be shown to accounts for only the leading-order contribution to the surface tension. One can show that the TA method includes second- and higher-order contributions to the changes in free energy which can be associated with fluctuations in the configurational energy [2,3]. The curvature (size) dependence of the vapour-liquid interfacial tension for drops of Lennard-Jones [2] and TIP4P/2005 water [3] particles are investigated. In contrast to the LJ case, one is able to stabilise ultra-small clusters of water (down to 16 molecules) due to the relatively large intermolecular interactions, allowing us to determine ‘tensions’ for the smallest of drops. It is seen that the interfacial free energy essentially vanishes monotonically in the limit of these small clusters, driven mainly by an increase in the entropic contribution to the tension, further leading to enhanced departures from the spherical shapes of these clusters. The findings are markedly different from those obtained from a classical mechanical description.

**References**[1] G. J. Gloor, G. Jackson, F. J. Blas, and E. de Miguel, J. Chem. Phys.

**123**, 134703, (2005)

[2] J. G. Sampayo, A. Malijevský, E. A. Müller, E. de Miguel, and G. Jackson, J. Chem. Phys.

**132**, 141101, (2010)

[3] G. V. Lau, I. J. Ford, P. A. Hunt, E. A. Müller, and G. Jackson, J. Chem. Phys.

**142**, 114701, (2015); G. V. Lau, P. A. Hunt, E. A. Müller, G. Jackson, and I. J. Ford, J. Chem. Phys. http://dx.doi.org/10.163/1.4935198

### Entropy strikes back again

**Marjolein Dijkstra, Professor of Computer Simulations of Soft Condensed Matter at Utrecht University**

In this talk, I will discuss the role of entropy in the self-assembly of colloidal hard particles. In the 1940s, Onsager showed that a fluid of hard rods exhibits a spontaneous ordering transition upon increasing the density. In addition, computer simulations showed a spontaneous disorder-order transition of hard spheres. These developments showed that entropy alone can drive disorder– order transitions, and hence one can obtain ‘Order through Disorder: Entropy strikes back’ as stated by Daan Frenkel. Here I will summarize several of these entropy-driven phase transitions that have been investigated over the past decades. Very recently, many examples have also been found that entropy can also lead to DISORDER in the self-assembled ordered structures, and hence the system can settle for a compromise by introducing ‘disorder’ in the ordered structures. A remarkable example is that in the case of large and small hard spheres with a diameter ratio of about 0.3 a so-called interstitial solid solution is formed. Instead of ordering both species on a crystal lattice, only the larger species are nicely ordered, whereas the sublattice of the smaller species is very disordered as it exhibits a high number of vacancies. The system prefers a truly ‘interstitial’ solution to the problem of maximizing entropy by favouring ‘disorder’ in ‘order.’ Another intriguing example of disorder in an ordered crystal structure is a system of hard cubes, where the crystal phase also contains a surprisingly high number of vacancies. These vacancies are delocalized, resulting in fluid-like behaviour over the delocalization length of the defect, and give rise to pronounced diffusion. Again the total entropy of the system is maximized by ‘disorder’ in an ordered crystalline structure. Finally, in the case of hard (asymmetric) dumbbell particles and snowman-shaped particles, the system can freeze into an aperiodic crystal, in which not only the orientations but also the centres of mass of the particles are disordered, whereas the constituent spheres of the particles are positioned on a periodic crystal lattice. The disordered aperiodic crystal is stabilized by the huge number of ways that the spheres can be connected to form a dimer particle. In conclusion, one can obtain ‘Disorder in Order through Disorder,’ and ‘Entropy strikes back once more.’

### A soft spot for hard particles

**Bela Mulder, Leader of Theory of Biomolecular Matter Group at AMOLF**

Many biologists implicitly believe that the laws of physics are suspended when one enters the living cell. The fact that this is a fallacy, especially where entropy is concerned, also explains why my attempts to move away from my thesis work with Daan Frenkel have on the whole miserably failed: ‘It’s hard particles all the way down!’ In this talk I will touch upon two relevant examples. The first regards what can be rightly seen as entropy’s ‘fifth column’ in the cell, the long DNA polymers that form chromosomes. Although real chromosomes are not simply bare DNA, and have an as yet poorly understood structure at intermediate scales, their sheer length, ranging from 1.5mm in the lowly E. coli bacterium to several cm’s in humans, means that at some length scale they start behaving as simple volume excluding polymers. This point of view has lead to novel insights into chromosome segregation in bacteria, and the architecture of the cell nucleus in plants and mammals. Recent in vitro experiments on DNA ‘squeezed’ into micro-volumes, have also inspired us to revisit the theory of strongly confined polymers. The second example concerns the effect of spatial confinement on the structure of cytoskeletal polymers. These filamentous biopolymers, of which actin and microtubules are the most prominent examples, readily reach lengths in excess of 10μm, i.e. the dimensions of a typical cell. Inspired by in vitro experiments in micro-chambers we have studied using Monte Carlo simulations the behaviour of strongly confined actin, simply modelled as rigid hard rods, in a variety of strongly confining geometries. We have found striking patterns of orientational organisation that are defined by novel types of defect structures. Exploring the difference between a disk-like and an annular (‘donut’) confinement, we can show that both that geometry and topology play a role in determining the organization. Finally, we in a lens-like confinement mimicking the structure of the mitotic spindle, we touch on the interesting dynamical pathways involving the motion of defects, by which these systems relax to their stable state.

### The Puzzle of Self Assembly and the Self Assembly of Puzzles

A holy grail of nano-technology is to create truly complex, multi-component structures by self assembly. Most self-assembly has focused on the creation of ‘structural complexity’. In my talk, I will discuss ‘Addressable Complexity’: the creation of structures that contain hundreds or thousands of distinct building blocks that all have to find their place in a 3D structure. Recent experiments have demonstrated the feasibility of making such structures. Simulation and theory yield surprising insights that can inform the design of novel structures and materials.