Ordered structures in dipolar and ferrofluidic systems

Systems with electric or magnetic dipolar interactions play a highly relevant role in a wide variety of applications, ranging from technology to biophysics. Thus a deeper understanding of their structural and thermodynamic properties is not only of purely academic interest, but can also be of importance in more applied and/or technologically relevant problems. The most natural model that captures the main features of these systems are, of course, dipolar particles. Their pair potentials are given by a spherically symmetric short range contribution and a long range interaction term between the freely rotating dipolar moments. Over many decades, this system has attracted a remarkable amount of interest in the liquid state community, revealing thereby a large variety of unexpected features: among those are the formation of ramified chains (or even sheets) at low densities or the occurrence of a ferroelectric phase at high densities. Excellent agreement between the theoretical predictions and experimental results, obtained for instance for Fe3 O4 , provide justification that dipolar particles represent indeed a reliable model for realistic dipolar systems. Despite all the efforts realized during the past years, many questions related to dipolar systems still remain open. This applies in particular for the ordered structures of this system which have been studied only marginally, so far. The aim of the present project is to fill this gap: our efforts will focus on a comprehensive investigation of the emerging ordered structures of dipolar systems and their thermodynamic properties. Particular emphasis will be put on the influence of the spherically symmetric short range interaction (exchange interactions, repulsion vs. attraction) and on the spatial confinement of the system: to this end we will consider various geometries ranging from dipolar monolayers over multilayers to bulk systems. Another aspect we want to address for this class of systems is chirality. From the methodological point of view our requirements can be clearly specified: we need a reliable and highly accurate method to evaluate the thermodynamic potential (i.e., essentially the lattice sum) for systems with long range interactions and an efficient and reliable optimization tool which helps us to identify the ordered equilibrium structures under given macroscopic parameters. Here our competences are complemented in an ideal manner by the expertise of our French cooperation partners: during past years, our group has contributed significantly to the implementation of efficient and reliable optimization tools based on ideas of genetic algorithms; on the other side, our French cooperation partners have accumulated over many years a remarkable expertise in treating long range interactions in theoretical and simulation approaches, Thus, we can count on a high degree of synergy in our project as we tackle the ambitious problems addressed in this proposal. With our investigations we will contribute to a deeper insight into the ordered phases that dipolar systems are able to form in different geometries. Based on this knowledge, we will investigate the thermal stability of these structures and study different mechanisms that are responsible for the melting process. By investigating dipolar systems in geometries between two and three dimensions we will be able to investigate in detail the complex process how a three dimensional crystal grows out of a two dimensional lattice. Despite the fact that the planned scientific activities have a rather fundamental character, we expect that our results will be of relevance in scientific cooperations with experimental and industrial research group which we envisage for the near future.

Systems with long-range interactions are ubiquituous in our daily life: viruses, DNA, proteins, or molecules of typical soft matter systems are only a few examples. One of their common, characteristic features is that these macromolecules are able to self-assemble into larger, complex units which by virtue of natures highly sophisticated strategies - are characterized by well-designed functionalities. This particular ability rests to a significant extent on one common feature of all these molecules: all these particles carry charges and/or higher polar moments; thus these particles interact via a highly selective, long-range interaction. It was the specific aim of this proposal to provide a profound understanding how these long-range interactions influence the self-assembly capacities of such mesoscopic molecules. This deeper insight is indispensable when it comes to interpret and to understand the emerging self-assembly scenarios. This deeper insight is indispensable when it comes to interpret and to understand the emerging self-assembly scenarios. This knowledge is also crucial when one wants to try to use the capacity of these particles in a constructive manner: following a bottom-up strategy in the realm of materials design one can then even design particles in such a way that they self-assemble into units on a larger length-scale with desired, targeted properties. Our investigations were based on concepts of theoretical physics: on the one hand we have used computer simulations, which essentially mimic the movement of the particles on the computer; on the other hand we have used highly specialized optimization techniques, that are able to identify in a reliable and efficient manner the minimum of the thermodynamic properties, leading thus to the (ordered) equilibrium configurations of the system at hand; in our case, this optimization tool was based on ideas of evolutionary algorithm. The scientific conclusions that we can draw from our investigations can be summarized as follows: the long-range interactions stemming from multi-polar interactions represent an essential ingredient that makes particles capable to form very strong, highly directional and selective interactions; in this way they are able to form highly complex, functional units which otherwise are difficult to assemble with conventional macromolecules. Moreover we could demonstrate that suitably designed interactions of these particles (e.g. via suitable surface decorations) can lead to desired target structures in the spirit of computational materials design. From the numerical/conceptual point of view we were able to establish new, reliable and robust numerical tools which are thus ready to be used in future investigations within the community.