Ebook: Complex Materials in Physics and Biology

Recent years have seen surprising connections develop between physics and such re search fields as mathematics, chemistry, biology, medicine, and even economics. These connections now constitute the fascinating research area known as complex materials and systems. Statistical physics is key in exploring this new expanding field because it is able to show how phenomena and processes long thought to be unrelated can, by means of few unifying concepts, be given a common description. By generalizing methods previously used to order phenomena in simple systems, statistical physics enables us to understand real-world phenomena comprised of complex materials—e.g., biomolecules, polymers, granular substances, glasses, water, membranes, and interfaces—or exhibiting complex processes—e.g., dynamical arrest, chaos, turbulence, network propagation, epidemic spreading, biological functioning, and economic fluctuations. At its current stage of development, this generalizing approach is supported by two conceptual pillars: scaling and universality. For this reason scaling and universality was the conceptual frame for the CLXXVI Course of the International School of Physics “Enrico Fermi”, held from 29 June to 9 July 2010 in Varenna, Italy. The Course was organized and focused so that these topics would be discussed, and a special emphasis was placed on “complex materials in physics and biology”.

This volume includes most of the lectures that were presented at the School. Their focus is on recent advances and developing perspectives in the study of complex materials and processes as they relate to physics and biology. The topics are discussed in terms of both fundamental science and technological applications, and the volume organizes the contributions to give both an overview of the field and a detailed examination of the new ideas and unsolved problems currently attracting the attention of researchers. Although all of the lecturers are leading researchers in the field who have made significant contributions to the field, this collection is organized pedagogically so that a wider audience will find it coherent and accessible. We hope that having the lectures in published form will allow them to be more educationally useful—with the caveat that, because the study of complex materials and processes is rapidly expanding, with many important experimental and theoretical discoveries in recent years, no single volume can be truly comprehensive.

The organization of topics in this volume reflects the actual organization of the Course and provides a kind of conceptual “backbone” sequence that includes: Scaling and Universality, Supra-molecular System and Solutions, Polymer systems, Static and Dynamics of Liquid Water, Arrested Dynamics and Jamming, Dynamic of out-of-Equilibrium Systems, Physics of Confined Liquids, Granular Matter, Physics of Biological and Medical Systems, Networks in Physical and Social Sciences, Turbulence in Physics, Biology and Economics, and Switching Phenomena in Biology and Economics.

Because this volume provides up-to-date reviews of cutting-edge topics by leading authorities, it should be a reference work useful to both advanced research professionals and beginning graduate students. For each topic it provides both an introduction and a complete presentation of recent theoretical and experimental developments, and it is designed to both broaden the readers' competence within their own field and encourage exploration of new problems in related fields.

To facilitate the free interchange of ideas, the lecturers and seminar leaders also made themselves available as course participants. This active presence on their part made possible a constant updating of the topics discussed and kept the focus clearly on a “state-of-the-art” level. The Course scheduled extra time for informal discussion, and student participants were encouraged to participate in the poster sessions. Both the seminar contributions and the posters are included in this volume. Finally, an important goal of this open school approach was fully achieved: every lecturer that proposed and wrote a contribution did so in collaboration with a student.

The opening lectures by Ben Widom (proposed in collaboration with Sahand Hormoz) concerns the nature of effective attractive forces between hydrophobic solute molecules in a polar solvent. Sow-Hsin Chen reports recent developments on the dynamics of biopolymers and their hydration water studied by neutron scattering. A detailed examination of the wetting transitions in fluid interfaces is proposed in a second contribution of Ben Widom (with Alessio Squarcini). A deeper review on the geometrical characterization of dynamical heterogeneities in chemical gels, colloidal gels and colloidal glasses, is reported in the contribution of Antonio Coniglio.

Developments in physical modeling and physical techniques as applied to the study of water (and other anomalous liquids) are discussed in the lectures of David Chandler, Giancarlo Franzese, Sow-Hsin Chen, Maria Antonietta Ricci, and Lars Pettersson. An important research topic is introduced by David Chandler (collaborating with Patrick Varilly): molecular- and nano-scale fluctuations in water. Results of research on water and anomalous liquids are presented by Giancarlo Franzese (with Valentino Bianco and Romina Ruberto). Presentations on the properties of confined water are given by Sow-Hsin Chen (“The Dynamic Crossover Phenomenon in Confined Water and its Relation to the Liquid-Liquid Critical Point: Experiments and MD Simulations”) and Maria Antonietta Ricci (“Uno, Nessuno e Centomila: The intricate structure of confined water”). Finally, the findings of an experimental study are presented in the Lars Pettersson contribution (“Liquid Water Structure from X-ray Spectroscopy and Simulations”).

The interaction of moving fluids with particles is the subject of the Hainz Herrmann lecture. The use of the precise tools of statistical physics to understand economic fluctuations is discussed by Luciano Pietronero (“Critical Overview of Agent-Based Models for Economics”).

Aspects of complex systems are treated in detail in complementary lectures. A discussion of long-term memory in climate records and the detection problem is provided by Armin Bunde. David Campbell (with Yasmine Meroz) discusses how a “little discovery” led to an entirely new field with a series of novel approaches to a range of phenomena in the natural world in his lecture entitled “The Fermi Pasta Ulam (FPU) Problem: A Path to Complexity.” Finally, Shlomo Havlin presents, using a new application of modern statistical physics to social network structure and dynamics, a description of the “Catastrophic Cascade of failures in interdependent networks.”

The Course faculty included 12 lecturers and 10 invited seminar speakers. The participants were an extremely gifted group of young students and practitioners who actively contributed to the School not only through questions and discussions, but also through the presentation of short, highly articulate, and original seminars and posters—some of which are published here.

The aim of the Course was not only to present reviews of all the various phenomena, but also to stimulate the search for a unified approach to the area by gathering together participants from a variety of specialized backgrounds. We all worked very hard, attending nearly 50 hours of lectures, seminars and discussions within a period of only two weeks. We hope this effort was rewarding for everyone attending.

Three “ground rules” were adopted: i) each session was to consider coherent arguments, ii) lecturers could be interrupted at any time during the talks for questions, and iii) speakers, young researchers, and students were encouraged to mix in the dining rooms, the coffee breaks, and the long after-lunch recess. The outcome was as we had hoped: numerous spontaneous discussions and lively debates took place in an honest, friendly atmosphere of work. Many of these discussions occurred in the beautiful gardens of Villa Monastero and Villa Cipressi. Judging from the positive and often enthusiastic reactions of the lecturers and participants during and after the Course, the event was extraordinarily successful in achieving its intended objectives.

It is fortunate that we are able to present in this volume the final versions of nearly all the lectures and seminars presented at the Course. So much important and high quality material was presented that it defies condensation or hierarchical ordering: the participants—experienced scientists, postdocs, and graduate students—have contributed with skill and enthusiasm.

On behalf of all the participants of the course we would like to express our gratitude to the Italian Physical Society for the opportunity to expand our knowledge by means of the School, and for providing hospitality in the exquisite Villa Monastero setting. Special thanks go to Professor Luisa Cifarelli, President of both the Italian and European Physical Societies and fair lady of our community, for the encouragement and advice she offered during the preparation period and during the School itself. We also thank the Istituto Nazionale di Fisica Nucleare (Italy), the Consorzio Nazionale Interuniversitario per la Struttura della Materia (CNISM-Italy), the Italian Research Project of National Interest (MIUR-PRIN08 project AFW2JS), and the Fondazione Bonino-Pulejo (Messina-Italy) for their generous financial support. We are grateful for the invaluable contributions and suggestions by G. Maino, scientific secretary for the School.

Last, but certainly not least, we offer our heartfelt appreciation to Barbara Alzani and Monica Bonetti of the SIF for their valuable, excellent cooperation before, during, and after the School period, and for their heroic work in producing the present volume.

Before concluding, some personal remarks. First, we wish to thank the Ente Villa Monastero for making available to us invaders such beautiful buildings and gardens. And, lastly, we thank the citizens of Varenna for their warmth and hospitality.

We offer this volume to the reader in the hope that it will provide something of the enjoyment and reward that we and the other participants in the School experienced.

F. Mallamace and H. E. Stanley

The nature of effective attractive forces between hydrophobic solute molecules in a polar solvent is described. We discuss the properties of the pair distribution functions, characterizing the correlations between the solvents molecules and those between the solute molecules in the limit of infinite dilution. Analytical expressions in one-dimension show that under appropriate thermodynamic conditions, the solute-solute correlations remain discernible at much greater distances compared to that of the solvent molecules. We also present an attempt at going beyond one dimension.

In this paper, both the dynamics of a protein and its hydration water are investigated by quasi-elastic neutron scattering (QENS) experiments. In addition, molecular dynamics (MD) simulations of a realistic hydrated protein powder model are also introduced to reproduce the experimental results. We start from the introduction of the incoherent neutron scattering method for studying dynamics of a protein and its hydration water. Then we discuss in details the coupling of the dynamics of a protein and its hydration water, including the following topics: the elastic scan and the reduction from it the mean squared displacement (MSD) of hydrogen atoms in protein and its hydration water; evidence of the dynamic crossover from pressure dependence of the measured relaxation time of hydration water in biopolymers by QENS; synchronization of the dynamic crossover phenomena in other biopolymers and their hydration water; an alternative method for detecting the dynamic crossover temperature. We also show our observation of a logarithmic-like beta-relaxation in the study of intermediate time protein dynamics at the end of this paper.

With this paper we present an overview of mean-field density-functional models for the study of the line tension and boundary tension at wetting. The system under consideration is the three-phase equilibrium with two components. The investigation of the critical behavior of the line tension can be implemented by mean-field models, derived as extensions of the van der Waals theory. First-order and second-order wetting transitions are described by suitable choices of the free-energy density functional. Recently a new model was proposed and its wetting phase diagram has been explored. Within the same framework wetting transitions of first order, higher than first order and infinite order are described. The order of the wetting transition depends sensitively on the parameters of the model. A criterion for the characterization of the transition is given.

One of the challenges in soft and condensed matter over the last years is understanding the phenomena of the glass and jamming transitions. A recent advance in the field is the idea that the dynamical heterogeneities play here the same role as the critical fluctuations in ordinary critical phenomena. This is due to the fact that the decay of density fluctuations in glasses and jammed systems takes place thanks to the dynamically correlated motions of groups of particles. In this paper, after a brief review of the properties of the dynamical heterogeneities, we describe their geometrical interpretation in chemical gels, colloidal gels and colloidal glasses, respectively, characterized by bonds with an infinite lifetime, with a finite lifetime, and by the absence of physical bonds.

This paper is the written form of three lectures delivered by one of us (DC) at the International School of Physics “Enrico Fermi”, Course CLXXVI, “Complex Materials in Physics and Biology”, held in Varenna, Italy in July 2010. It describes the physical properties of water from a molecular perspective and how these properties are reflected in the behaviors of water as a solvent. Theory of hydrophobicity and solvation of ions are topics included in the discussion.

Water is an anomalous liquid because its properties are different from those of the majority of liquids. However, the category of anomalous liquids could be greater than what so far supposed. Here, we review what is anomalous about water, which are the other liquids that are as well anomalous, and which are those that could be anomalous. We ask questions such as: Why is water anomalous? Are other liquids anomalous for the same reason as water? How can we define models that capture the complexity of water and other anomalous liquids, but are tractable for theory and simulations? Can we make predictions with these models that can be tested in experiments? We discuss here possible answers to these questions.

In this lecture results are presented about the experimental evidence of the existence of a dynamic crossover and of a liquid-liquid (L-L) critical point in supercooled confined water. In particular the topics covered are: the discovery of the density minimum and of the peaking of the thermal expansion coefficient performed by an extensive study of the equation of state (EOS) of 1-D confined water; the finding of a dynamic crossover in the alpha-relaxation times of 1-D and 3-D confined water by quasi-elastic neutron scattering (QENS) studies; supporting evidence for the dynamic crossover derived from molecular dynamics (MD) simulations on bulk and confined water and from an extended mode-coupling theory (eMCT) of a Lennard-Jones (L-J) system; evidence of the dynamic crossover phenomenon in other glass-forming liquids.

The possibility of avoiding ice formation when water is confined in small enough volumes has opened up many new investigations into the properties of this still poorly understood liquid. Here we report the results of a neutron diffraction experiment on confined water, showing that its density and microscopic structure change with the distance from the substrate and upon supercooling. Common properties of the bulk liquid (that is “Uno” - one, because it is homogeneous by definition), such as density and molar volume, become ill-defined and inappropriate for a rigorous description of the multitude of situations (“Centomila” - one hundred thousand) found in the confined state: such average quantities are inadequate (“Nessuno” - no one) for describing the highly confined system. To stress these conclusions, we have titled this article after a novel by Nobel laureate L. Pirandello.

This paper deals with insights into the structure of liquid water obtained from X-ray spectroscopies, diffraction, small-angle scattering and molecular dynamics simulations. From a large collaborative effort by experimentalists and theoreticians to understand liquid water, a picture consistent with thermodynamic models proposing a transition between high-density and low-density liquid states in the supercooled region has evolved. Through the observation of two coexisting structural motifs in the X-ray spectroscopies even in ambient water, a connection is established between the anomalous properties in the supercooled regime to the behavior of water at higher temperatures. Diffraction data are shown to be inconclusive regarding the local structures found in the liquid, but experimental extended X-ray absorption fine structure data are shown to contain new information regarding the hydrogen bonding network. Lastly, small-angle X-ray scattering data showing an increasing correlation length upon supercooling suggest, combined with simulations, that a liquid-liquid critical point is present in the deeply supercooled regime.

For finite Reynolds numbers the interaction of moving fluids with particles is still only understood phenomenologically. We will present various numerical studies. First we will introduce a numerical technique to simulate granular motion in a fluid. Particle trajectories are calculated by Newton's law and collisions are described by soft-sphere potentials. The fluid flow is calculated solving the Navier-Stokes equation. The momentum transfer is directly calculated from the stress tensor around particles. This scheme is validated calculating the drag coefficient, finding the limitations on the Reynolds number in mesh size and computer time. Then we discuss sedimentation of two particles and reproduce the “Draft, Kiss and Tumbled” effect showing that we can reproduce hydrodynamic interactions on the scale of the particle. The terminal velocity of particles is in good agreement with experiments and we recover the Richardson and Zaki law. We also will use the Lattice Boltzmann Method and the solver “Fluent” which elucidates this issue from different points of view. We show that the distribution of particle velocities inside a sheared fluid can be obtained over many orders of magnitude. We also consider the case of fixed particles, i.e. a porous medium and present the distribution of channel openings and fluxes. These distributions show a scaling law in the density of particles and for the fluxes follow an unexpected stretched exponential behaviour. The next issue will be filtering, i.e. the release of massive tracer particles within this fluid. Interestingly a critical Stokes number below which no particles are captured and which is characterized by a critical exponent of 1/2. Finally we will also show data on saltation, i.e. the fact that the motion of particles on a surface which are dragged by the fluid performs jumps. This is the classical aeolian transport mechanism responsible for dune formation. The empirical relations between flux and wind velocity are reproduced. Finally we also briefly discuss quicksand and its collapse.

We present an overview of some representative Agent-Based Models in Economics. We discuss why and how Agent-Based Models represent an important step in order to explain the dynamics and the statistical properties of financial markets beyond the Classical Theory of Economics. We perform a schematic analysis of several models with respect to some specific key categories such as agents' strategies, price evolution, number of agents, etc. In the conclusive part of this review we address some open questions and future perspectives and highlight the conceptual importance of some usually neglected topics, such as non-stationarity and the self-organization of financial markets.

In recent years, there is growing evidence that long-term correlations play an important role in climate, physiology, and computer science as well as in financial markets; the examples range from river floods, temperatures, and wind fields to market volatilities, heart-beat intervals and internet traffic. Here, we review several methods to detect long-term correlations, also in the presence of external trends, and give examples for long-term correlations in climate. Finally, we show how external trends can be detected in data with long-term memory, and apply the results to estimate the anthropogeneous part of the recent warming of the athmosphere and the oceans.

The central theme of this lecture provides an interesting lesson in scientific discovery —how a “little discovery” led to an entire new field and a series of novel approaches to a range of phenomena in the natural world. In a sense that hopefully will be clear in the end, it is about “sensitivity to initial conditions,” which is singularly appropriate for a subject that involves “chaos”. An attempt has been made to follow the guidance of a master, the mathematician Mark Kac, who said that in lecturing it is important to tell the truth and nothing but the truth, but not the whole truth.

Modern network-like systems are usually coupled in such a way that failures in one network can affect the entire system. In infrastructures, biology, sociology, and economy, systems are interconnected and events taking place in one system can propagate to any other coupled system. Recent studies on such coupled systems show that the coupling increases their vulnerability to random failure. Properties for interdependent networks differ significantly from those of single-network systems. In this paper, these results are reviewed and the main properties discussed.

Protein hydration water is responsible for the biological activity of the protein itself. This is true for all proteins that in fact become active with at least a hydration level h=0.2 (g of water/g of dry protein). For lysozyme at low temperature, below 220 K the strong rigidity of the low-density hydrogen bond network extended on the protein surface inhibits protein side-chains motion. At high temperature, above 346 K, the very short lifetime of hydrogen bonds lets the protein unfold irreversibly. Below this temperature a reversible folding/unfolding process exists, in which lysozyme folds and unfolds rapidly as a function of temperature and permanence time. In this work, we present a proton Nuclear Magnetic Resonance study at very high resolution of the kinetic equilibrium that characterizes the folding/unfolding process of hydrated lysozyme.

In analogy to metal nanocomposites, the investigated hybrid organic-inorganic aggregates induce an enhancement of the scattered light. To explain the observed broadening of the absorption band and the wavelength dependence of the scattering, the systems can be considered as a nanoparticle composite. The scattering enhancement obeys the scaling law with the same optical spectral dimension d₀=0.3 as that obtained through numerical simulations on cluster-cluster aggregates of purely metal nanoparticle composites.

Plants, algae, and their derivatives paper, textiles, etc. are complex systems that are chiefly composed of a web of cellulose fibers. The arrangement of solvents within the polymeric structure is of great importance since cellulose degradation is strongly influenced by water accessibility. Here we show a model based on small angle neutron scattering (SANS) data able to deconvolve the scattering contributions of both polymeric structures and solvent clusters trapped along the polymeric fibers. The relevance of our model resides in the exploitation of a large number of biopolymer networks that are known to share structures similar to that of cellulose.

A light scattering approach on a micellar solution formed by a PS-PEO diblock copolymer was used to investigate the charge fluctuations of the solvent, a room temperature ionic liquid. The results suggest a pairwise potential model for the intermicellar interactions consisting of a hard sphere core and a repulsive Yukawa tail. The screening length is consistent with the nanometric scale of the charge fluctuations of the solvent, as estimated by recent theoretical works on the fluid structure of a molten salt in proximity of a charged surface.

Structural, dynamical and optical properties of self-assembled uncharged porphyrin-based macromolecules were studied by Light Scattering and UV-vis Spectroscopy. The results show that size, rigidity of the formed aggregates, and the local arrangement of the macromolecules inside the aggregate strongly depend on the molecular architecture and on the position of the peripheral polyethylene oxide arms in the porphyrin structures.

We have investigated DMPC:butanol and DPPC:hexanol systems with a high alcohol concentration (two molecules per phospholipid) by means of X-ray diffraction, differential scanning calorimetry and density measurements. A lowering of the main transition temperature for the membrane/alcohol systems has been observed. The phospholipid bilayer/alcohol systems are characterized by a higher density value than the pure membrane as determined by volumetric measurements. The analysis of diffraction patterns has shown the existence of a more packed structure in both systems due to the presence of alcohol. The area of polar head has also been estimated for both samples.

The anomalous properties of water have attracted great attention from the scientific community for a long time and they are still a topic of intense research. These remarkable properties, most pronounced in the supercooled metastable state, can be ascribed to water unique structure, consisting of a random and fluctuating three-dimensional network of hydrogen bonds. Although it is clear that the hydrogen bond network, its fluctuations, rearrangements and dynamics determine the properties of water, these are far from being completely understood. These issues have received great interest in recent years thanks to possibilities opened by novel experimental techniques, detailed theoretical predictions, and computer simulation methods. In particular, Deep Inelasting Scattering (DINS) technique has been recently shown to be particularly suited to study the interactions between a single proton and its neighboring oxygens in terms of proton mean kinetic energy and momentum distribution. In this report we present a preliminary study, using DINS technique, of two samples: supercooled water under pressure, and heavy water in both stable and supercooled phase. Although those studies need further investigation, we can identify some important and still unclear aspects.

Using the membrane stress tensor, we study the fluctuations of the membrane-mediated Casimir-like force. This method enables us to recover the Casimir force between two inclusions and to calculate its variance. We show that the Casimir force fluctuates very strongly. We also study the distance dependence of the variance of the Casimir force. This distance dependence has the same physical origin as the Casimir force itself.

We study the thermodynamics of mixtures of Jagla ramp potential (JRP) particles and hard spheres (HS), with HS mole fractions 0.10, 0.15, 0.20 and 0.50. The bulk JRP system exhibits both water-like anomalies and a liquid-liquid critical point (LLCP). In the mixtures, the presence of a LLCP is preserved up to the highest HS mole fraction. The results indicate that the temperature of occurrence of the LLCP increases in solutions of hydrophobic solutes in water.