# One-day workshop on the Physics of Liquids and Glasses, 16 March 2020

**A satellite meeting of GVSLMP: One-day workshop on the Physics of Liquids and Glasses**

Date: 16th March 2020

Venue: Science Seminar House, Kyoto University

Map: Building #9 on the campus map (www.sci.kyoto-u.ac.jp/en/map.html)

Organizer: Ryoichi Yamamoto, Kyoto University

**Program:**

- 10:00-11:30
**Peter Harrowell (Sydney)**: “Normal Modes and Slow Relaxation: What is the Connection Between Structure and Dynamics in Supercooled Liquids?” - 11:30-12:15
**Hideyuki Mizuno (Tokyo)**: “Anharmonic properties of vibrational modes in amorphous solids”

Lunch Break

- 13:30-15:00
**Walter Kob (Montpelier)**: “On the structure of liquids: More order than expected”

Coffee Break

- 15:30-16:15
**Norihiro Oyama (AIST)**: “Stress drop events in amorphous solids under finite rate shear essentially differ from those under athermal quasistatic shear” - 16:15-17:00
**Simon Schnyder (Kyoto)**: “Crowding in Heterogeneous Media: Breakdown of Universality for Soft Interactions”

**Abstracts:**

**Peter Harrowell (School of Chemistry, University of Sydney)**

“Normal Modes and Slow Relaxation: What is the Connection Between Structure and Dynamics in Supercooled Liquids?”

In 2008, a close correlation was demonstrated between the spatial distribution of localised soft modes of the inherent structure of a supercooled liquid and the dynamic heterogeneities evident as the iso-configurational propensity of motion in the liquid [1,2]. Since this work, the connection between soft modes of the inherent structure and dynamic heterogeneities have been confirmed in a range of materials [3]. This correlation is still one of the clearest demonstrations of structurally determined dynamics but the actual mechanism by which this correlation is imposed remains a mystery. In this talk we will present recent results on efforts to establish an explicit connection between structure and dynamics along with a critique of the intrinsic limitations of such a program.

- A. Widmer-Cooper, H. Perry, P. Harrowell and D. Reichman, Nature Phys. 4, 711 (2008).
- A. Widmer-Cooper, H. Perry, P. Harrowell and D. Reichman, J. Chem. Phys. 131, 194508 (2009).
- X. Ma et al, Phys. Rev. Lett. 122, 028001 (2019); Y. Zong et al, Phys. Rev. Lett. 121, 228003 (201); M. Habibi, S. Plotkin and J. Rottler, Biophys. J. 114, 562 (2018); A. Smesset and J. Rottler, Phys. Rev. E 92, 052308 (2015); R. Jack, A. Dunleavy and C. P. Royall, Phys. Rev. Lett. 113, 095703 (2014); M. Mosayabi et al, Phys. Rev. Lett. 112, 105503 (2014).

**Hideyuki Mizuno (Department of Basic Science, The University of Tokyo)**

“Anharmonic properties of vibrational modes in amorphous solids”

Recent works have made a significant step forward in understanding harmonic vibrational states in amorphous solids. In particular, it has been established that quasi-localized vibrational modes emerge in addition to phonon-like vibrational modes. In this work, we study anharmonic properties of these vibrational modes. We reveal that vibrational modes exhibit anharmonicities that induce particle rearrangements and cause transitions to different states. These anharmonicities are distinct from those in (perfect) crystals, where particle rearrangements never occur.

**Walter Kob (Laboratoire Charles Coulomb, University of Montpellier)**

“On the structure of liquids: More order than expected”

The structure of liquids and glasses is usually characterized by means of the radial distribution function or the static structure factor. Computer simulations or confocal microscopy experiments on colloidal systems allow also to access the bond angle distributions or the local connectivity of the atoms. However, all these quantities are basically one-dimensional in nature and hence it is hard to infer from them the real three dimensional structure of amorphous systems. As a consequence the structure of liquids and glasses is usually considered to be boring for distances beyond the

second/third nearest neighbor. In this talk I will show that this is not the case at all and that by considering simple three dimensional correlation functions one finds a surprisingly ordered arrangement of

the particles even at significantly larger distances. This order grows quite quickly if the temperature is lowered, showing that amorphous systems are way more ordered than expected from the study of the usual two-point correlation functions.

**Norihiro Oyama (MathAM-OIL , AIST)**

“Stress drop events in amorphous solids under finite rate shear essentially differ from those under athermal quasistatic shear”

Despite its ubiquity, the understanding of amorphous systems remains a big challenge of statistical physics and material science. One established knowledge about such systems is the universally observed yielding transition under a sufficiently large external field (in most cases, shearing deformation). After experiencing the yielding transition, an amorphous system starts to flow in accordance with the external shear, with the macroscopic stress being roughly constant. The closer look at the stress under very slow rate shear as a function of strain, however, provides complicated behavior: the stress-strain curve is composed of elastic-like linearly rising regimes which are cut into pieces by intermittent sudden drops due to plastic deformations[2]. Many efforts have been dedicated to the study of those plastic events and especially the athermal quasistatic (AQS) protocol, or imposing external field with zero temperature and zero rate, has played a central role.

Utilizing AQS shear, a single plastic event can be isolated in a well-defined way and e.g., the cause of plastic instability was revealed theoretically and then further confirmed numerically[2]. Although AQS protocol is a sort of idealized numerical model, its validity has been proposed at least qualitatively and therefore is believed to be realistic in a certain limiting situation. In this work, we conducted numerical simulations of amorphous systems under both finite rate and AQS shear and compared the statistics of stress drop events of those two systems. As a result, we revealed that although the nature of the plastic events under a finite but slow shear shares the same origin as the case under AQS shear as reported previously[3], the stress drop events (which correspond to plastic events in AQS systems) have qualitatively different statistical features, however slow the shear rate is.

Furthermore, the qualitative behavior varies depending not only on the shear rate but also on the system size and the strength of dissipation. In this presentation, the speaker will discuss the origin of such changes in the qualitative behaviors in terms of real space dynamics, focusing on the low shear rate and thermodynamic limit.

[1] N.Oyama, S. Takahata and K. Saitoh, in preparation

[2] C. Maloney and A. Lema\hat{i}tre, Phys. Rev. Lett., 93, 195501 (2004)

[3] A. Lema\hat{i}tre and C. Caroli, Phys. Rev. Lett. 103, 065501 (2009), M. Tsamados, Euro. Phys. J. E, 32, 165

**Simon Schnyder (FIFC, Kyoto University)**

“Crowding in Heterogeneous Media: Breakdown of Universality for Soft Interactions”

In heterogeneous materials, such as in biological cells, porous media or ionic conductors, anomalous diffusion is observed, i. e. the mean-squared displacement (MSD) of a tracer particle grows sub-diffusively over long periods of time. A paradigm for modeling of transport in heterogenous media is the Lorentz Model, in which a single mobile particle moves in a static matrix built of overlapping hard disk obstacles. There, anomalous diffusion is the signature of a universal localization transition caused by the percolation of the matrix. In experiments and simulations a wide range of exponents have been reported, and it remains unclear if those exponents represent transient behavior, or whether they can be connected to a universal behavior. We generalized the Lorentz Model in molecular dynamics simulations by introducing interacting tracer particles and soft interactions and performed experiments of a colloidal Lorentz Model. We showed that due to the soft interactions the localization transition becomes rounded and that the universality of the dynamics breaks down.1) T.O.E. Skinner et al, PRL 111, 128301 (2013).

2) S.K. Schnyder et al, Soft Matter 11, 701 (2015).

3) S.K. Schnyder et al, PRE 95, 032602 (2017).

4) S.K. Schnyder & J. Horbach, PRL 120, 78001 (2018).