Rigidity Transition Research Articles

Physical properties of third generation multicomponent Ge10-xSe60Te30Inx (x = 0, 2, 4, 6) chalcogenide glasses

Abstract Selenium-based chalcogenide glasses are best suitable materials for optical data storage due to their amorphous-to-crystalline phase transformation. Average coordination number and number of constraints for Ge10-xSe60Te30Inx (x = 0, 2, 4, 6) system have been discussed with two topological effects, floppy and rigid transition. Mean bond energy and glass transition temperature have been investigated using chemical bond approach to understand structural features of glasses. Heat of atomization, mean bond energy and glass transition temperature have been studied theoretically.

Dynamic and static analyses of glass-like properties of three-dimensional tissues.

The mechanical properties of tissues are influenced by those of constituent cells in various ways. For instance, it has been theoretically demonstrated that two-dimensional confluent tissues comprising mechanically uniform cells can undergo density-independent rigidity transitions, and analysis of the dynamical behavior of tissues near the critical point revealed that the transitions are geometrically controlled by the so-called cell shape parameter. To investigate whether three-dimensional tissues behave similarly to two-dimensional ones, we herein extend the previously developed model to three dimensions both dynamically and statically, demonstrating that two mechanical states similar to those of glassy materials exist in the three-dimensional case. Scaling analysis is applied to the static model focused from the rearrangement viewpoint. The obtained results suggest that the upper critical dimension of tissues equals two and is therefore the same as that of the jamming transition.

Lifetime-shortened acoustic phonons and static order at the Brillouin zone boundary in the organic-inorganic perovskite CH3NH3PbCl3.

Lead halide hybrid perovskites consist of an inorganic framework hosting a molecular cation located in the interstitial space. These compounds have been extensively studied as they have been identified as promising materials for photovoltaic applications with the interaction between the molecular cation and the inorganic framework implicated as influential for the electronic properties. CH3NH3PbCl3 undergoes two structural transitions from a high temperature cubic unit cell to a tetragonal phase at 177 K and then a subsequent orthorhombic transition at 170 K. We have measured the low-frequency lattice dynamics using neutron spectroscopy and observe an energy broadening in the acoustic phonon linewidth towards the high-symmetry point when approaching the transitions. Concomitant with these zone boundary anomalies is a hardening of the entire acoustic phonon branch measured in the limit near the (2, 0, 0) Bragg position with decreasing temperature. Measurements of the elastic scattering at the Brillouin zone edges , and show Bragg peaks appearing below these structural transitions. Based on selection rules of neutron scattering, we suggest that the higher 177 K transition is displacive with a distortion of the local octahedral environment and the lower transition is a rigid tilt transition of the octahedra. We do not observe any critical broadening in energy or momentum, beyond resolution, of these peaks near the transitions. We compare these results to the critical properties reported near the structural transitions in other perovskites and particularly CsPbCl3 [Y. Fujii, S. Hoshino, Y. Yamada, and G. Shirane, Phys. Rev. B 9, 4549 (1974)]. We suggest that the simultaneous onset of static resolution-limited Bragg peaks at the zone boundaries and the changes in acoustic phonon energies near the zone center is evidence of a coupling between the inorganic framework and the molecular cation. The results also highlight the importance of displacive transitions in organic-inorganic hybrid perovskites.

Characterizing the nature of the rigidity transition

Particulate matter, such as foams, emulsions, and granular materials, attain rigidity in a dense regime: the rigid phase can yield when a threshold force is applied. The rigidity transition in particulate matter exhibits {\it bona fide} scaling behavior near the transition point. However, a precise determination of exponents describing the rigidity transition has raised much controversy. Here, we pinpoint the causes of the controversies. We then establish a conceptual framework to quantify the critical nature of the yielding transition. Our results demonstrate that there is a spectrum of possible values for the critical exponents for which, without a robust framework, one cannot distinguish the genuine values of the exponents. Our approach is two-fold: ({\it i}) a precise determination of the transition density using rheological measurements and ({\it ii}) a matching rule that selects the critical exponents and rules out all other possibilities from the spectrum. This enables us to determine exponents with unprecedented accuracy and resolve the long-standing controversy over exponents of jamming. The generality of the approach paves the way to quantify the critical nature of many other types of rheological phase transitions such as those in oscillatory shearing.

“Biowheel-Axle” Assembly of β-Cyclodextrin Fitted onto Bile Acid Units Linked by PEG Spacers through Inclusion Polymerization

A “biowheel-axle” assembly of polyrotaxanes of β-cyclodextrin (β-CD) threaded onto bile acid moieties linked by a poly(ethylene glycol) (PEG) spacer of tunable length was prepared through an “inclusion polymerization” approach. The bile acid-diamine derivatives were allowed to first form inclusion complexes with β-CD and then polymerized with PEG-dicarbonate, followed by end-capping with a stopper of monoamino-β-CD, resulting in “biowheels” of β-CD with PEGylated bile acids as the axle in tandem. All steps were performed without the use of catalysts. The complexation between β-CD and bile acid units of the polymer chain was confirmed by the 2D NOESY NMR technique and powder X-ray diffraction, showing 85% of bile acid units entered the cavity of β-CD. The change of PEG spacer length from 45 to 6 ethylene glycol units led to a flexible–rigid conformation transition of the polyrotaxanes, supported by the random and straight orientation of the “biowheels” shown by scanning tunneling microscopy images. The con...

Dynamical rigidity transition in the viscoelastic properties of chalcogenide glass-forming liquids

The viscoelastic properties of supercooled AsxSe100-x (0 ≤ x ≤ 30) and AsxSe100-x-yIy (x = 20, 30 and y = 10, 20) liquids are studied using oscillatory parallel plate rheometry. In addition to the α-relaxation process, the shear relaxation of liquids with selenium chains longer than ~ 3 atoms is also characterized by a low-frequency polymeric mode. The temporal decoupling of this low-frequency soft/floppy relaxation mode from that of the α-relaxation mode is a unique function of the average selenium chain length. The floppy mode abruptly vanishes for liquids with average chain lengths shorter than ~ 3 Se atoms, thus implying a dynamical rigidity transition. When taken together, these results indicate that, contrary to the conventional wisdom, the pertinent structural variable associated with such transition in the viscoelastic behavior is not the average coordination number but instead the intermediate-range structural elements such as the average selenium chain length.

About impedance spectra and dynamics of charge carriers in neat poly(ethylene oxide) structures

Impedance spectra of linear and cross-linked poly(ethylene oxide) (PEO) are analyzed in a wide range of temperature. Dielectric responses differ at low and high temperature due to tendency of PEO to crystallization below melting temperature. Extent of crystallization depends on cross-linking density. The network in PEO with high cross-linking density is rigid and morphology transition shifts to very low temperature. Debye-like relaxation appears at low temperature similar as in ionic liquids. Onset of polarization relaxation shifts to higher temperature with increasing mesh size that is coupling of electric and structural relaxation appears. This is also nicely reflected by scaled conductivity. It demonstrates that the structure in cross-linked systems is a superposition of chemical and physical networks. They relax separately at low temperature and frequency under condition of sufficient rigidity.

A geometrically controlled rigidity transition in a model for confluent 3D tissues

The origin of rigidity in disordered materials is an outstanding open problem in statistical physics. Previously, a class of 2D cellular models has been shown to undergo a rigidity transition controlled by a mechanical parameter that specifies cell shapes. Here, we generalize this model to 3D and find a rigidity transition that is similarly controlled by the preferred surface area S0: the model is solid-like below a dimensionless surface area of with being the average cell volume, and fluid-like above this value. We demonstrate that, unlike jamming in soft spheres, residual stresses are necessary to create rigidity. These stresses occur precisely when cells are unable to obtain their desired geometry, and we conjecture that there is a well-defined minimal surface area possible for disordered cellular structures. We show that the behavior of this minimal surface induces a linear scaling of the shear modulus with the control parameter at the transition point, which is different from the scaling observed in particulate matter. The existence of such a minimal surface may be relevant for biological tissues and foams, and helps explain why cell shapes are a good structural order parameter for rigidity transitions in biological tissues.

Anomalous glassy dynamics in simple models of dense biological tissue

In order to understand the mechanisms for glassy dynamics in biological tissues and shed light on those in non-biological materials, we study the low-temperature disordered phase of 2D vertex-like models. Recently it has been noted that vertex models have quite unusual behavior in the zero-temperature limit, with rigidity transitions that are controlled by residual stresses and therefore exhibit very different scaling and phenomenology compared to particulate systems. Here we investigate the finite-temperature phase of two-dimensional Voronoi and Vertex models, and show that they have highly unusual, sub-Arrhenius scaling of dynamics with temperature. We connect the anomalous glassy dynamics to features of the potential energy landscape associated with zero-temperature inherent states.

No unjamming transition in a Voronoi model of biological tissue.

Vertex models are a popular approach to simulating the mechanical and dynamical properties of dense biological tissues, describing the tissue as a network of polygons. Recently a class of two-dimensional vertex models was shown to exhibit a disordered rigidity transition controlled by the preferred cellular geometry, which was subsequently echoed by experimental findings. An attractive variant of these models uses a Voronoi tessellation to describe the cells, which reduces the number of degrees of freedom as compared the original vertex model. The Voronoi model was also endowed with a non-equilibrium model of cellular motility, leading to rich, glassy behavior. This glassy behavior was suggested to be inextricably linked to an underlying jamming transition. We test this conjecture, exploring the low-effective-temperature limit of the 2D Voronoi model by studying cell trajectories from detailed dynamical simulations in combination with rigidity measurements of energy-minimized disordered cell configurations. We find that the zero-temperature limit of this model has no unjamming transition. We show that this absence of an unjamming transition is intimately linked to the marginality of the model, i.e. the fact that the constraints imposed on cell areas and perimeters precisely balance the number of degrees of freedom in the model. Our work suggests that constraint counting arguments are useful to understand rigidity in a broad class of models of dense biological tissues.

Hydrodynamics of shape-driven rigidity transitions in motile tissues.

In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell polarization and motility might be governed by the internal shear stiffness of nearby tissue, deemed "plithotaxis". Meanwhile, other work has demonstrated that there is a direct relationship between cell shapes and tissue shear modulus in confluent tissues. Joining these two ideas, we develop a hydrodynamic model that couples cell shape, and therefore tissue stiffness, to cell motility and polarization. Using linear stability analysis and numerical simulations, we find that tissue behavior can be tuned between largely homogeneous states and patterned states such as asters, controlled by a composite "morphotaxis" parameter that encapsulates the nature of the coupling between shape and polarization. The control parameter is in principle experimentally accessible, and depends both on whether a cell tends to move in the direction of lower or higher shear modulus, and whether sinks or sources of polarization tend to fluidize the system.

Ground improvement using SPVD and RPE

Excessive total and differential settlement at the intersection of a surcharged prefabricated vertical drain (SPVD) and a rigid piled embankment on soft ground during the post-construction period leads to considerable time and costs being spent on repetitive remedial works in the future. This paper presents a sustainable design approach for high and long embankment filling on soft clay at the approach to the structure by introducing the intersection of an SPVD at the transition to a rigid piled embankment in order to regulate the differential settlement between the two conventional ground treatment approaches. This paper also presents a full-scale field study to validate the performance of the intersection of the SPVD at the transition to the rigid piled embankment. By introducing the intersection ground treatment, post-construction settlement and differential settlement are minimised significantly, while the post-construction total settlement at the rigid transition piled embankment (TPE) zone is reduced significantly by about 80 to 95% of the total settlement, as compared to a conventional TPE.

Geometry and the onset of rigidity in a disordered network.

Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture, the number of nodes and the number of bonds between them, this rigidity transition must have a geometric origin. Naive, degree-of-freedom-based mechanical analyses such as the Maxwell-Calladine count or the pebble game algorithm overlook such geometric rigidity transitions and offer no means of predicting or characterizing them. We apply tools that were developed for the topological analysis of zero modes and states of self-stress on regular lattices to two-dimensional random spring networks and demonstrate that the onset of rigidity, at a finite simple shear strain γ^{★}, coincides with the appearance of a single state of self-stress, accompanied by a single floppy mode. The process conserves the topologically invariant difference between the number of zero modes and the number of states of self-stress but imparts a finite shear modulus to the spring network. Beyond the critical shear, the network acquires a highly anisotropic elastic modulus, resisting further deformation most strongly in the direction of the rigidifying shear. We confirm previously reported critical scaling of the corresponding differential shear modulus. In the subcritical regime, a singular value decomposition of the network's compatibility matrix foreshadows the onset of rigidity by way of a continuously vanishing singular value corresponding to the nascent state of self-stress.

Structural properties of Ge-S amorphous networks in relationship with rigidity transitions: Anab initiomolecular dynamics study

We investigate the amorphous ${\mathrm{Ge}}_{x}{\mathrm{S}}_{100\ensuremath{-}x}$ (with $10\ensuremath{\le}x\ensuremath{\le}40)$ system from ab initio simulations. Results show a very good agreement with experimental findings from diffraction and the topology of the obtained structural models is further analyzed and compared with the selenide analog. Differences emerge, however, from a detailed molecular dynamics analysis showing that the ring statistics and the homopolar defects do not evolve similarly. The findings are also connected to rigidity theory, which provides a topological approach to decoding the physics of network glasses, and the effects of composition and temperature are analyzed.

Characterizing rare fluctuations in soft particulate flows

Soft particulate media include a wide range of systems involving athermal dissipative particles both in non-living and biological materials. Characterization of flows of particulate media is of great practical and theoretical importance. A fascinating feature of these systems is the existence of a critical rigidity transition in the dense regime dominated by highly intermittent fluctuations that severely affects the flow properties. Here, we unveil the underlying mechanisms of rare fluctuations in soft particulate flows. We find that rare fluctuations have different origins above and below the critical jamming density and become suppressed near the jamming transition. We then conjecture a time-independent local fluctuation relation, which we verify numerically, and that gives rise to an effective temperature. We discuss similarities and differences between our proposed effective temperature with the conventional kinetic temperature in the system by means of a universal scaling collapse.

Effects of Catalyst Content, Anhydride Blending, and Nanofiller Addition on Anhydride-Cured Epoxidized Linseed Oil-Based Thermosets

A series of formulations based on epoxidized linseed oil, ELO cured with various anhydride hardeners, were investigated to assess the potential for enhanced elastic properties and thermal transitions through variations in catalyst concentration (1,8-diazabicyclo[5.4.0]undec-7-ene, DBU), hardener type (nadic methyl anhydride, NMA, methyltetrahydrophthalic anhydride, MTHPA, and their blends with phthalic anhydride, PA), and nanofiller (organically modified hydrotalcite, Perkalite F100S) content. To facilitate rapid screening, Shore D hardness was used as a proxy for Young’s modulus, and the limits of this approach were tested via comparisons with modulus measurements made via dynamic mechanical analysis (DMA). ELO cured with MTHPA at a 1:1 epoxy/anhydride molar ratio with 4.5 phr DBU gave a particularly attractive combination of rigidity, homogeneity, and alpha transition temperature rarely seen in thermosets composed of a 100% biobased epoxy component. Nanocomposite formation provided a modest increase in ...

Irradiation-induced topological transition in SiO2: Structural signature of networks' rigidity

By affecting the connectivity of atomic networks, composition, temperature, or pressure can induce topological transitions between the three atomic states of rigidity — flexible, isostatic, and stressed-rigid. However, no clear structural signature of such transitions has been elucidated thus far. Here, based on realistic molecular dynamics simulations of irradiation-induced damage in quartz, we report the first evidence of a rigid-to-flexible rigidity transition controlled by structural variations only. This topological transition is shown to arise from the simultaneous loss of atomic Eigenstress and onset of network flexibility, and features a well-defined structural signature in the medium-range order of the atomic network.

Endocytic reawakening of motility in jammed epithelia.

Dynamics of epithelial monolayers has recently been interpreted in terms of a jamming or rigidity transition. How cells control such phase transitions is, however, unknown. Here we show that RAB5A, a key endocytic protein, is sufficient to induce large-scale, coordinated motility over tens of cells and ballistic motion in otherwise kinetically-arrested monolayers. This is linked to increased traction forces and to the extension of cell protrusions, which align with local velocity. Molecularly, impairing endocytosis, macropinocytosis or increasing fluid efflux abrogates RAB5A-induced collective motility. A simple model based on mechanical junctional tension and an active cell reorientation mechanism for the velocity of self-propelled cells identifies regimes of monolayer dynamics that explain endocytic reawakening of locomotion in terms of a combination of large-scale directed migration and local unjamming. These changes in multicellular dynamics enable collectives to migrate under physical constraints and may be exploited by tumors for interstitial dissemination.

Glassy materials with enhanced thermal stability

Abstract

The relation between stretched-exponential relaxation and the vibrational density of states in glassy disordered systems

Amorphous solids or glasses are known to exhibit stretched-exponential decay over broad time intervals in several of their macroscopic observables: intermediate scattering function, dielectric relaxation modulus, time-dependent elastic modulus, etc. This behaviour is prominent especially near the glass transition. In this Letter we show, on the example of dielectric relaxation, that stretched-exponential relaxation is intimately related to the peculiar lattice dynamics of glasses. By reformulating the Lorentz model of dielectric matter in a more general form, we express the dielectric response as a function of the vibrational density of states (DOS) for a random assembly of spherical particles interacting harmonically with their nearest-neighbours. Surprisingly we find that near the glass transition for this system (which coincides with the Maxwell rigidity transition in this model), the dielectric relaxation is perfectly consistent with stretched-exponential behaviour with Kohlrausch exponents 0.56<β<0.65, which is the range where exponents are measured in most experimental systems. Crucially, the root cause of stretched-exponential relaxation can be traced back to soft modes (boson-peak) in the DOS.