Multiscale modelling approaches can provide valuable insight to researchers across a broad range of fields. At the same time, the interdisciplinary applicability of these approaches means that both new learners and experienced researchers may not have a clear understanding of the theoretical and computational fundamentals underpinning these methods. Theoretical Foundations of Multiscale Modelling aims to address this knowledge gap, providing a clear insight to the thermodynamical and statistical mechanical foundations of methods commonly employed, and highlighting the potential and limitations of each approach.
Starting with an overview of the basics of statistical mechanics, the first chapters of the book illustrate the general theory of molecular modelling, the concepts and methods for the study of complex molecular systems, then progressing to cover key strategies employed to perform computational calculations and simulations. The second part of the book reviews how the most recent, cutting-edge tools of the trade are used in practice through a selection of case studies highlighting multiscale modelling, multiple resolution simulation methods, and machine-learning applications. This is also achieved by presenting case studies from recent scientific literature, highlighting the advantages of a multiscale treatment for the understanding of complex molecular phenomena.
Drawing on the experience of its authors, Theoretical Foundations of Multiscale Modelling is an insightful guide for all those learning, applying, or interested in exploring multiscale modelling methods for their work.
Michele Cascella is professor at the Department of Chemistry, University of Oslo
Raffaello Potestio is professor at the Department of Physics, University of Trento
From Chapter 1: introduction to soft matters (pagg. 1-5)
1.1 Invitation: fantastic matter and where to find it
The object of this book is the theoretical scaffold of the analytical and computational methods that, in the course of several decades, have been developed to investigate soft matter systems. Before addressing our core topic, then, we need to build ourselves a sufficiently clear picture of the context in which these methods are developed, and necessarily, of the systems on which they are applied. More specifically, we need to define soft matter. What is soft matter? How is it defined? How does it distinguish itself from, say, condensed matter or nuclear matter? As we will see in the course of this brief introduction, defining soft matter with neat and unambiguous boundaries is rather difficult, if not outright impossible. At the same time, having the clearest possible idea of what soft matter is, and what it is not, is useful and important in order to comprehend the range of applicability, and the limitations, of the methods we employ to study it. As a starting point, we can attempt at identifying soft matter systems (objects, materials...) and discuss if and up to what degree they can be included in the list.
Hence, where should we look for such items? Not very far, actually. In Fig. 1.1 we report a picture of the desk of one of the authors at the time of writing. This image contains various examples of soft matter systems, that are listed and discussed hereafter.
Plastics Several objects or object parts, such as the telephone, the pen, or the USB key, are made of artificial plastic. These are materials made of polymers, long chains of repeating molecular units whose individual and collective properties are among the most studied and better understood. The reason why polymers are widely investigated since their discovery is easy to grasp: being the molecular constituents of plastic, they lie at the foundations of modern economy and society – for the good and for the bad; additionally, a number of molecules of biological origin (proteins, DNA...) are polymers. The attention researchers put on polymers is thus fuelled by scientific as well as industrial, economic, and environmental reasons; however, it is not sufficient to justify the impressive degree of understanding that the scientific community has gained about these peculiar molecules. The key fact that has largely contributed to the comprehension of polymers is, in fact, the universal character of their behaviour in appropriate conditions – the physical and mechanical properties of sufficiently long polymers do not depend in detail by their chemical composition, rather, on more general features that can be shared even by apparently very diverse molecular species, and can even help the understanding of phenomena not at all involving chemistry.
Liquids The water contained in the (alas, plastic) bottle is a liquid. Simple, one-component liquids as well as mixtures of more or less complex molecules are relevant examples of soft matter; their importance for the comprehension of a broad spectrum of systems (be they either natural or artificial) is self-evident, and several powerful theoretical and computational tools have been developed to study them. In particular, water is a majorly important liquid because of its ubiquitous presence, its surprisingly rich and uncommon phase diagram, and its central role in biochemical and biological processes.
Gases Gaseous systems, such as the atmosphere present in the room, are just as important as liquids. When the density is sufficiently low, they offer themselves to some major simplification in their theoretical treatment, which allows the development of exact or approximated models, the comprehension of phase transitions, and the validation of methods for the study of more complex systems. When the density becomes larger, and the motion of the gas particles is not only due to diffusion in equilibrium conditions, other interesting phenomena kick in, such as flow and turbulence. The comprehension of how gaseous systems behave is of paramount importance for the comprehension of climate as well as for the study and/or the design of machines of size ranging from the micrometre (microswimmers, airborne viruses) to the tens of metres (airplanes).
Colloids Many of the objects lying on the desk – as well as the desk itself – are coated with paint. Paint is a colloidal suspension, composed by small molecules in the liquid phase in which nonsoluble, much larger nanoparticles are dispersed. A number of different colloidal systems exists, depending on the relative size of the solvent and solute particles and the interactions among them, giving rise to a broad range of physical properties of the overall system. Closely related to colloids are creams, gels, and emulsions, that is, mixtures of immiscible liquids such as oil and water.
Liquid crystals Both the laptop monitor and the external screen contain liquid crystals, which are composed by molecules having nonspherical shapes. Due to this broken rotational symmetry, the molecules in the liquid tend to align along a preferred direction, thereby blocking light whose polarisation is orthogonal to the system’s axis. The overall orientation of the molecules can be tuned through the application of an external electric field, hence their effectiveness in the realisation of screens. Liquid crystals thus entail this dual nature of a liquid, in that molecules diffuse and do not maintain a permanent position in space, and of a crystal, due to the long-range positional and orientational order of the molecules’ symmetry axes. Furthermore, they can contain topological defects, points or lines of singularity in the orientation field that cannot be resolved (eliminated, created) by means of a continuous deformation of the liquid. These defects are so “real” that they physically interplay with the colloidal particles suspended in the liquid crystal, and can be employed to control their position and move them around.
Biological matter The most diverse, studied, fascinating soft matter systems are those of biological origin. About four billion years of evolution have generated an impressive variety of molecules, macromolecules, systems, and materials whose properties and processes are at the centre of a fibrillating research work. On the humble desk here depicted, several biological systems can be seen. We could start from the cellulose that constitutes the paper of books and notebooks. Cellulose is a semicrystalline fibre that makes up the skeleton of plants, and finds useful application in our lives since the dawn of humankind. Cellulose can be further found in a much more rigid arrangement in the wood of the desk. The water contained in the bottle is most likely contaminated with germs, bacteria, and viruses; the air in the room is as well. However, the most compelling biological object on display is clearly the apple, as it contains water, ions, vitamins, lipids, proteins, sugars, nucleic acids, all combined in a colourful circus of structures and molecular machines. Far from being a static object – a still life – in its seeds this apple contains living cells, carrying out all those complex tasks required to perpetrate the still largely mysterious process of life. Putting our trust in the fundamental laws of Physics, and their validity in all realms of the Universe, we look at this process as one that is not inherently different from all other mechanical, chemical, nuclear, radiative, thermodynamical phenomena that populate physics and chemistry books; we are thus motivated to investigate living systems to achieve a deep comprehension of their function in terms of the same rules that govern the atoms of rocks and stars. It is one of the aims of this book to collect and illustrate some of the instruments that are nowadays employed to this end.
Not all items present on the desk are made of soft matter, and not all soft matter systems are represented among those on the desk. Many other systems can in fact be ascribed to the broad category of soft matter, such as granular materials or active matter; the latter comprises both chemically active particles (usually of artificial origin) and living systems such as bacteria, fishes, and human crowds. In recent years a large amount of effort has been put in the investigation of such systems, the main difficulty being that they are strongly out of equilibrium, and most of the well-established machinery of statistical mechanics cannot be applied.
Conversely, items are there that have fallen outside of the soft matter list rattled off above: we can mention, for example, the graphite of the pencil. Graphite is a crystalline solid: should it be considered a soft matter material or not? Indeed a large amount of work has been carried out to investigate the properties of graphite and its close cousin, graphene, which is at the peak of its popularity among scientists as well as the general public. Usually, those researchers focussing on graphene and other carbon-based molecules and materials (e.g. fullerenes) belong to the cohorts of condensed matter physicists or materials scientists; recently, though, soft matter physicists have acquired steadily growing interest in the properties of graphene, e.g. its thermal or charge transport efficiency, its lubricating capacity, and many other interesting features which become even more fascinating when this material is combined with others, especially biological ones.
And what about metals? Sure metals and liquids have little in common, at least at room temperature (a notable exception is mercury). However, under the appropriate conditions, also metals become extremely interesting for soft matter researchers, for example when polymers or proteins interact with a metallic surface, or single metal atoms coalesce in solution to form nanoparticles of a few nanometres in diameter.
Coming back to the original question: what is soft matter? We now have an idea of the systems encompassed by this term, but what do they have in common? This one is another tricky question, because, as it happens for most interesting things in life, any attempt at a general definition typically leaves out some of the items that intuitively should be there, and includes something that might look misplaced. In order to make some order among our ideas, let us now look for a set of criteria to stick to.
Courtesy by Elsevier