EMERGENT PHENOMENA IN CONDENSED MATTER, SOFT MATTER AND COMPLEX SYSTEMS

Physical systems composed of a large number of reciprocally interacting constituents provide the natural context for the rise of emergent phenomena. Despite the intrinsic difficulty in providing a mathematical definition of what is meant for ‘emergence’ (see [Baas, in Langton, Alife III, Santa Fe Studies in the Sciences of Complexity, Proc. Volume XVII, Addison-Wesley, (1994)]), the intuitive notion of emergent property is that of a collection of interact- ing objects showing a novel collective behavior, qualitatively different from and not immediately attributable to the behaviors of the individual components. Non-linear interactions among elements of the system, or interactions between the system and the environment, or merely the large number of constituents are usually the motivations addressed to be responsible for emergent behavior. It is important to remark that emergent properties can only be inferred from a comprehension of the collective properties of the microscopic constituents [Kivelson et al, npj Quant. Mater. 1, 16024 (2016)]. In this regard, computer simulations provide a unique tool to support experimental observation, develop abstract models and investigate systems’ properties at a microscopic level. In general, condensed matter, particularly soft matter but also the complex systems studied in Physics, are necessarily described via simplified models, which include the key features of the corresponding real systems. On the one hand, this certainly represents a powerful approach when it finds its roots in the concept of universality, connected with critical phenomena, but this also turns into a limiting factor for the realistic description of the considered phenomena. On the other hand, it makes the properties of such abstract simulated systems calculable and investigable via computer simulations. As a consequence, the simulations assume a key role in complementing the comparison between experiments and theory [Frenkel and Smit, Understanding Molecular Simulations, Academic Press (2002); Allen and Tildesley, Computer simulation of liquids, Oxford University Press (2017)]. In this sense, simulations are often regarded as being computer experiments, in which materials properties and novel phases of matter can be investigated. The present PhD thesis is a collection of the main results coming from four different research lines which I have been involved into in the last 3 years. The topics could appear to be rather diverse but they are all connected by the presence of emergent phenomena which were studied via computer simulations (Molecular Dynamics and Monte Carlo methods, mainly). Three of these four research lines are related to collaborations with as many experimental groups. The first group I started collaborating with is led by dr. R. Grisenti, at the University of Frankfurt (https://www.atom. uni-frankfurt.de/hhng-grisenti/index.html). As reported in Chapter 1 and in a recent paper which I contributed to as first co-author [Schottelius, Mambretti et al., Nat. Mat. (2020)], we studied the crystal growth of supercooled Ar–Kr liquid mixtures by means of a micro–jet experiment, Molecular Dynamics simulation and thermodynamic analysis. The second ongoing collaboration is with the group of prof. P. Milani, which is the leader of the CIMaINa laboratories (http://cimaina.unimi.it/) at the Università degli Studi di Milano. We developed an abstract stochastic model of resistive switching devices that they are characterizing for neuromorphic applications (see Chapter 3). More recently, I started a collaboration with the group led by prof. T. Bellini at the Università degli Studi di Milano (https://sites.google.com/site/unimisoft/), in order to investigate the spinodal decomposition of mixtures of DNA nanostars via light scattering experiments and Monte Carlo simulations, as described in Chapter 4. I will now provide a brief overview of the contents of each Chapter, where each Chapter corresponds to a different research line. Crystal growth from a supercooled melt is of fundamental theoretical and practical importance in many fields, ranging from materials science to the production of phase–change memories. To date, the temperature dependence of the growth rates of many materials, including pure metals, metallic alloys, colloids and many others are still under intense scrutiny (see e.g. Tang et al., Nat. Mat. (2013) and Sun et al., Nat. Mat. (2018)). The majority of systems display a maximum growth rate at a temperature located between the melting point and the glass transition [Orava et al., J. Chem. Phys. (2014)]. Several materials are characterized by a range of many orders of magnitude between this maximum value and the crystal growth rates measured in other regimes. We still lack a deep comprehension of the mechanism underlying this phenomenology, which emerges from experiments and simulations both. Classical models of crystal growth from a melt hypothesize either a diffusion-limited process, or a collision–limited one, but for a lot of materials them both fail to fit the available data. This situation claims for further investigation about the key elements that tune the crystal growth rates from supercooled liquids, extending the current theoretical framework. Jointly with the experimental group of dr. Grisenti (which performed measurements at the EU-XFEL facility https://www.xfel.eu/), we studied the crystallization of supercooled mixtures of argon and krypton via Molecular Dynamics. Our results showed that their crystal growth rates (obtained from the analysis of simulated configurations exploiting Steinhardt angular order parameters) can be reconciled with existing crystal growth models only by explicitly accounting for the non–ideality of the mixtures. Our theoretical and computational contribution aided in highlighting the importance of thermodynamic aspects in describing the crystal growth kinetics, yielding a substantial step towards a more sophisticated theory of crystal growth. A second project concerns the study of soft matter systems in one dimension (1D), detailed in Chapter 2. Soft matter systems are made of particles which can overlap by paying a finite energy cost and they are renowned for being able to display complex emerging phenomena. Some of them, for example, are characterized by the presence of clustering phases [Prestipino, Phys. Rev. E (2014)]. Recently, a surprising quantum phase transition has been revealed in a 1D system composed of bosons interacting via a pairwise soft potential in the continuum. It was shown that the spatial coordinates undergoing two-particle clustering could be mapped into quantum spin variables of a 1D transverse Ising model [Rossotti et al., Phys. Rev. Lett. (2017)]. Extending the description and the results provided in a very recent paper I contributed to as first author [Mambretti et al., Phys. Rev. E (2020)], in the second Chapter we investigate the manifestation of an analogous critical phenomenon in 1D classical fluids of soft particles in the continuum. In particular, we studied the low–temperature behavior of three different classical models of 1D soft matter, whose inter–particle interactions allow for cluster- ing. The two–particle cluster phase is largely explored, by simulating the systems at the commensurate density via Monte Carlo and Simulated Annealing methods. The same string variables exploited in the aforementioned quantum case highlight that, at the right commensurate density, the peculiar pairing of neighboring soft particles can be nontrivially mapped onto a 1D discrete classical Ising model. We also observe a related phenomenon, i.e. the presence of an anomalous peak in the low–temperature specific heat, thus indicating the emergence of Schottky phenomenology in a non–magnetic fluid. The third Chapter presents the case of an electrical resistor network featuring novel emergent properties, such as memristivity and the possibility to be used as a self–assembled logic gate; an article on this topic is currently in preparation. The growing difficulties arising in the improvement of the performance of standard computing architectures encouraged the quest for different approaches aiming at reproducing the computational capability and energy efficiency of the human brain, by mimicking neurons and synapses as probabilistic computing units [Markovic et al., Nat. Rev. Phys. 2, 499–510 (2020)]. Networks based on the bottom–up assembling of nanoscale building blocks and characterized by resistive switching (RS) activities are becoming increasingly popular as possible solutions for a straightforward fabrication of complex architectures with neuromorphic features [Wang et al., Nat. Rev. Mat. 5, 173-195 (2020)]. Specifically, it has recently been demonstrated that metallic nanostructured Au films, under certain conditions show a non–ohmic electrical behavior and complex and reproducible resistive switching, which can be exploited for the innovative realization of logic gates. In these devices, the nonlinear dynamic switching behavior resulting from an applied input voltage can be exploited for developing hardware for reservoir computing applications. In Chapter 3, I show how it is possible to simulate a complex model (Stochastic Resistor Network Model, SRNM) able to imi- tate the phenomenology and give hints for the development of experiments ongoing at the CIMaINa research laboratories, regarding the electrical current passage through nanostructured cluster gold films [Mirigliano et al., Nanotechnology, 31, 23, (2020)]. To this purpose, I personally contributed to develop from scratch a C++ code, parallelized via the Armadillo library (http://arma.sourceforge.net/). To study the electrical transport properties of this system, we modeled the experimental sample as a network of interconnected resistors whose effective resistance under a given voltage can be determined using spectral graph theory. The network state evolves stochastically via random physically–inspired update moves, and its effective total resistance (and the related Power Spectral Density) has been analyzed. The structure and the topology of the network were studied via the investigation of the shortest path connecting the source and the sink of the system, thus exploring the possible paths in which the current could flow. Moreover, we also applied Information Theory entropy–based tools to investigate the time evolution of network resistance at a local, coarse–grained, scale. We observed that specific input signals corresponding to 2 logical ‘bits’ pro- duce rich outputs associable to a logical NAND gate, which posses functional completeness. Given that relevant differences could be detected between the behavior of the network at low voltage before and after the so called ‘writing’ step (where the system is under a high applied voltage), memristive effects naturally emerge in the study of network properties. These results encourage further investigations, both experimental and via the innovative SRNM approach we developed, in order to exploit these RS devices in hardware computing applications as self–assembled logic gates. Last, in Chapter 4 I focus on another soft matter system, that I have started to investigate during my PhD research activity, regarding Monte Carlo simulations of low valence DNA–based colloidal particles. This last Chapter is mainly devoted to the description of the simulation method I have been developing during my more recent PhD research activities, while the preliminary results presented obviously need to be confirmed and extended by further studies. Particles with a limited number of attractive spots (patches) on their surface are generally characterized by non–crystalline low energy states; they rather generate a disordered 3D network in which all the sticky sites are engaged in (mutually exclusive) patch–patch bonds [Bianchi et al., Phys. Rev. Lett. (2006)]. One of the most promising experimental realizations of such peculiar colloids is extremely recent: laboratory synthesized DNA nanostars (NS) with fixed valence [Bi et al., PNAS (2013)]. In this field the landmark is represented by our collaborators from the group led by prof. T. Bellini. Recently, they started to investigate the behavior of mixtures of nanostars with leftwise or rightwise chirality of the DNA strands, characterized by a merely repulsive interspecies interaction. To date, our contribution mainly consisted in the development of an abstract model of these DNA nanostars, schematized as limited valence soft patchy particles, whose equilibrium configurations are sampled via a canonical Monte Carlo program. Their different chirality is represented by a mixed interaction which only comprises excluded volume terms. Our goal in this project is twofold: on the one hand, we aim to reconstruct the temperature–density phase diagram of such mixtures, also depending on the mixing ratio. Experiments revealed a critical behavior and a phase separation processes for dilute mono–component DNA solutions; the properties of a mixture of two components, each found in critical conditions, are studied in this work. In this Chapter, after a detailed overview of the experimental, computational and theoretical studies regarding low valence particles, the simulation code is described and it is presented a comparison between the simulation results and the experimental measurements at equilibrium. The peculiar structures found in the patchy particles network claim for further analysis, as well as the interesting behavior near the critical point for mono–component and bi–component systems both. The second perspective of this research regards the unexplored aggregation and cluster growth process of such particles. In this concern, part of the future research effort will be devoted to the transformation of our custom code into a Brownian Monte Carlo in order to unveil the mechanisms underlying the dynamics of such particles during their aggregation stages. The conclusions and further perspectives concerning each of the four topics addressed in this work can be retrieved at the end of each Chapter.