Session W01: Soft Materials and Statistical Physics

Programming Soft Materials by Inverse Design

Soft Materials are ubiquitous in everyday life and are crucial in many different forms of revolutionary technologies. One property of Soft Materials is their ability to self-assemble into intricate structures from a finite set of building blocks with continuously tunable parameters. This giant design space of building blocks is a double-sided sword: on one side it provides researchers infinite possibilities to design building blocks for targeted functions, while on the other side it might take forever to search the design space. Here, we propose a new inverse design method that captures both interaction and geometry of building blocks. By enabling rigid body functionalities in JAX-MD, an end-to-end differentiable molecular dynamics engine, we can create soft materials model with components that are simple enough to design yet powerful enough to capture complex materials properties. In this talk, I will discuss the implementation of the methods alongside examples to showcase its potential applications.   

Deflection of hoops placed on two separate cylindrical rods

We study the deformation of a thin elastic cylindrical shell longitudinally placed on two parallel rods due to self-weight. The position of two contact lines, self-weight, and friction between the shell and rods affect the configuration of the shell. We first experimentally investigate the deflection of short cylindrical shells (hoops) for two cases. In the first case, we fabricate rings with various thicknesses and diameters and place them on identical supports. When the thickness to diameter of hoops is uniform, the size of the hoop governs the normalized deflection. When the thickness-to-diameter ratio increases while the diameter is fixed, the deflection of the hoop is reduced. Next, we vary the distance between the two rods to change the contact position of the hoop. Moreover, we conduct the finite element simulations and find good agreement with the experiment results. Furthermore, we develop the theoretical model to determine the deflection of soft hoops. Our results can be applied to develop strategies to handle nanorings, carbon nanotubes, and huge steel pipes.   

Effects of aspect ratio and axial tensile load on the long balloon inflation

Although the localized bulging of long cylindrical tubes has been extensively studied experimentally and analytically, there is a lack of investigation on the deformation of short and moderate-length tubes. Here we study the snap-through instability of a hyper-elastic cylindrical tube under inflation, focusing on how the aspect ratio of the tube and additional axial tensile loads affect the bulging shape profile and initiation pressure. First, we conduct bulging experiments using latex rubber tubes by varying the length-to-diameter aspect ratio and additional tensile load. Additionally, we perform finite element simulations with various geometries and loading and theoretical analyses of an infinite-length tube. Through the simulations, we investigate the critical aspect ratio of the tube that divides the bulging mode into two modes: whole bulging of short tubes and localized bulging of long tubes. The experimental and simulation results show that the initiation pressure decreases and converges as the aspect ratio and axial tensile load increase. Furthermore, we find that axial tension greater than the shear modulus prevents snap-through in short tubes and negates the effects of aspect ratio on the initiation pressure. We believe that the results of this study can provide insights into controlling the bulging mode and initiation pressure in tube-like soft devices, such as soft pneumatic actuators and energy harvesters.   

A Zoo of Chiral Structures: Electrostatic Directed Assembly of Charged, Chiral Amphiphiles

In self-assembled systems, molecular chirality is manifested in fascinating membrane shapes at nano- to meso-scale. The most common shapes are helical membranes, helical scrolls (cochleates) and twisted membranes. These shapes have been observed in natural and synthetic systems. Despite the prevalence, an understanding of the interconversion mechanisms between different chiral morphologies is lacking. In this study, we were able to generate all the common chiral structures in perhaps the simplest chiral molecular series Cn-K, where one amino acid [lysine (K)] is coupled to alkyl tails of n (= 8-18) carbons. This was accomplished by tuning the solution ionic conditions. Scroll-like assemblies were observed when the molecular degree of ionization was high, and the electrostatic interactions were short-ranged. By contrast, helical and twisted membranes are observed for long (n = 10-18) and short (n = 8-10) molecular tails, respectively, when the molecular degree of ionization was low and the electrostatic interactions were long-ranged. These results were derived by combining X-ray scattering and electron/atomic force microscopy. Overall, our study reveals that electrostatic interactions can be used to guide chiral shape selection and nano-scale structure in molecular self-assemblies.   

Introducing cluster tomography for complex systems

In nature, many phenomena lead to cluster formation, including magnetic domains, bacteria swarming, cell migration and the collective motion of animal groups, as well as distinct regions of the brain or cities. Here we propose a quantitative approach to assess the geometric complexity of such clustered systems, called cluster tomography. Cluster tomography asks how many clusters are crossed by a probe that is shot through a complex system of clusters. To answer this question, we consider lines that cross the entirety of finite 2d and 3d percolation systems. The number of clusters N crossed by these lines scales linearly with the size of the system L as aL where a is non-universal and therefore depends on microscopic details of the system. However, at criticality we find an additional singularity of the form b_γ log(L) where the universal prefactor b_γ depends only on the angle γ at which the line intersects the system’s surface. Our numerical results are verified by analytical arguments found by extending known results for line segments that cross only a part of the system (i.e., partial tomography). With the universal singularities only being observed at criticality, cluster tomography can be used in a wide variety of applications including detecting phase transitions and identifying universality classes in complex systems.   

Dissipation and thermalization in 1D systems with nonlinear bath coupling

One of the big outstanding challenges for this technology is understanding the fundamental mechanisms of ion transport. There are two main pathways to studying this problem. On one hand, microscopic Molecular Dynamics (MD) simulations make it possible to explore the system behavior on very short time scales, tracking individual atoms to analyze the details of their motion. Unfortunately, extending the time of these highly realistic simulations comes at a very high computational cost. On the other hand, using the Langevin equation gives insight to the long-time limit, but at the cost of disconnecting microscopic details from macroscopic parameters like drag. The work proposes a simplified framework where the link between microscopic motion and the emergence of macroscopic quantities is clearer. 

A key feature that sets ionic drag in crystals apart from dissipative motion in fluids is the long-range order in crystalline systems. This order, along with the comparable masses of the mobile and medium particles is expected to introduce additional correlations, both spatial and temporal, in the particle-medium interactions. The simplicity of the system allows us to treat it in a non-Markovian way, making it possible to explore the phenomena that depend on long-time correlations. 

We study a simple system, where a mobile particle, constrained to move in one dimension, interacts with an infinitely long chain of masses connected by identical springs. When the particle is launched along the chain, it dissipates energy and, eventually, becomes trapped in one of the energy minima, as expected. Our analytic and numerical results demonstrate that the drag experienced by the particle due to its interaction with the chain exhibits a non-monotonic dependence on the particle speed, vanishing at high speeds. Analytics predict that including bias in the system to compensate for the energy loss due to drag can give rise to several distinct steady-state drift velocities, a fact confirmed by simulations. Due to our model’s simplicity, we can show how the system parameters impact the dissipation rate.   

Non-linear Diffusion processes and hydrodynamic cascades in lattice gas models.

We define and explore lattice models of classical nonlinear diffusion. We find evidence for stretched exponential relaxation of finite momentum modes as predicted analytically by Delacretaz and collaborators. We compute the time-momentum scaling function for the structure factor and also define and study numerically infrared cascades in Fourier space.   

Phase transitions beyond criticality: normal form and analytic corrections for the 2D Ising Model

The renormalization group predicts universal scaling laws near critical phase transitions. But can we extend this understanding of the critical point to accurately capture the behavior throughout the surrounding phases? To this end, normal form theory provides a useful framework: analytic variable changes (in temperature or field, for example) extend the universal scaling function to the entire phase. We apply this idea to the 2D Ising model, where Onsager's exact solution enables quantitative tests of the accuracy of analytic corrections. By working in a special coordinate frame, in which the Fisher zeros lie on a straight line, we produce expansions of the free energy that converge for all temperatures. Even with minimal knowledge of the critical point, fitting the expansion to data (low- and high-temperature cluster expansions) deep within the phases produces similar results, accurately capturing both the phases and phase transition. Our approach may prove useful for mapping out phases in unsolvable statistical physics models or in experimental systems exhibiting critical transitions.   

An asymptotic approach for the statistical thermodynamics of certain model systems

In classical statistical thermodynamics, calculating the configuration integral is both vital and elusive. Analytic relations for configuration integrals are desirable for modeling purposes, but it is typically impossible to obtain them. Certain systems become analytically tractable after replacing steep potential energies with harmonic potentials or athermal rigid constraints, but these approximations are often inadequate, especially when modeling the stretching of molecules. It is therefore necessary to develop a systematic approach to improve upon the approximations provided by these reference systems. Here, a general asymptotic approach is introduced, where the configuration integral for the full system is obtained in terms of that of the reference system and several corrections. This asymptotic approach is first demonstrated using the simple example of a classical three-dimensional oscillator. Next, the approach is applied to modeling the stretching of single polymer chains and to modeling thermally assisted crack growth, where results are verified with respect to numerical calculations. Overall, this asymptotic approach is a valid and effective tool for statistical thermodynamics in general.   

Complexity, typicality, and eigenstate thermalization in fermion systems

The discovery of quantum many-body scar (QMBS) states has revealed the possibility of having states with low entanglement entropy (EE) that violate the eigenstate thermalization hypothesis (ETH) in nonintegrable systems. Such states with low EE are rare but naturally exist in the integrable system of free fermions. By representing the occupation pattern of each free fermion eigenstate as a classical binary string, we find that the Kolmogorov complexity of the string correctly captures the scaling behavior of EE for the eigenstate. This allows us to distinguish typical and atypical eigenstates directly by their intrinsic complexity. We further reveal that the fraction of atypical eigenstates which do not thermalize in the one-dimensional free fermion system vanishes exponentially in the thermodynamic limit. By introducing an arbitrarily weak two-body interaction between the fermions, we demonstrate analytically that those atypical states would be always eliminated. Specifically, we show that the probability of having a state with EE satisfying a sub-volume scaling law decreases double exponentially as the system size. Thus, our results provide a quantitative argument for the ETH and disappearance of QMBS states in weakly interacting fermion systems.   

Multilayer Graphene as an Endoreversible Otto Engine

Graphene is perhaps the most prominent "Dirac material," a class of systems whose electronic structure gives rise to charge carriers that behave as relativistic massless fermions. This emergence of relativistic behavior at laboratory scale energies makes graphene an ideal environment for probing the thermodynamics of relativistic quantum systems. For multilayer graphene structures, subject to an external magnetic field, the energy spectrum strongly depends on the number of layers, and we examine the performance of a finite-time endoreversible Otto cycle with multilayer graphene systems as working mediums. We show that there exists a simple relationship between the engine efficiency and the number of layers, and that the efficiency at maximum power can exceed that of a classical working medium.