# Research

The overall themes of my research are supercooled liquids and the glass transition. A brief introduction to these topics is given below. After the introduction, I will explain additional research topics and provide a few relevant papers dealing with the specific topic. The articles can be accessed by clicking on the associated links. Comments are always welcome.

• ## Supercooled liquids and glasses

A liquid cooled below the melting line without crystallizing is called a supercooled liquid. Most liquids can be supercooled and eventually form a glass when sufficiently supercooled. Upon approaching this glass transition, supercooled liquids display dramatic changes in, e.g., their viscosity as is illustrated in Fig. 1. This observation remains an unresolved mystery of the glass transition, also called the non-Arrhenius problem, and is a field of intensive research.

• ## Excess-entropy scaling

The excess entropy $$S_{\rm ex} = S - S_{\rm id}$$ is the entropy minus the ideal gas contribution at the same density and temperature. Physically, it quantifies the number of available states of the liquid relative to that of an ideal gas. The excess entropy was proposed by Rosenfeld in 1977 to correlate to dimensionless transport coefficients, i.e., $$\widetilde{X} = f(S_{\rm ex})$$. Rosenfeld found for single-component atomic liquids a quasiuniversal relation which enables prediction of unknown transport coefficients if the excess entropy is known. Since then excess-entropy scaling has been the subject of intensive research. An example of a quasiuniversal relation is illustrated in Fig. 2 for binary mixtures (Ref. 1) where the excess entropy collapses the data to an almost universal curve. A similar universality even works in nanoconfinement which has very different behavior from bulk liquids (Ref. 2).

### Relevant papers:

1. Excess-entropy scaling in supercooled binary mixtures
I. H. Bell, J. C. Dyre, and T. S. Ingebrigtsen, Nat. Commun. 11, 4300 (2020)

2. Predicting how nanoconfinement changes the relaxation time of a supercooled liquid
T. S. Ingebrigtsen, J. R. Errington, T. M. Truskett, and J. C. Dyre, Phys. Rev. Lett. 111, 235901 (2013)

• ## Shear thinning

Shear thinning is a phenomenon which occurs when you force a liquid to flow. Initially, the viscosity remains constant but when the driving force becomes large enough the viscosity starts to decrease. This property is used when you paint a house, or when you apply toothpaste in the morning. Nevertheless, the microscopic origin behind shear thinning remains to date unclear. Ref. 1 details that the structural changes in the extentional direction under Couette shear flow (π/4 radians), captured in the form of the orientation-dependent two-body entropy $$s_{2}^{\theta}$$, correlates very well to shear thinning. This can be seen in Fig. 3D where the sheared dynamics maps onto the equilibrium dynamics even in the highly nonlinear region using this new definition of $$s_{2}$$ when $$\theta = \pi/4$$.

### Relevant papers:

1. Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids
T. S. Ingebrigtsen, and H. Tanaka, Proc. Natl. Acad. Sci. U.S.A. 115, 87 (2018)

• ## Crystallization

Crystallization is the process where a small solid nucleus is formed inside a liquid. This nucleus then grows and turns the liquid into a crystal. Everyday crystallization occurs when water turns into ice below zero degrees. Sometimes one would like to avoid crystallization to obtain, e.g., the glass state (see introduction) which can have desirable properties distinct from the crystal. Ref. 1 studied crystallization in supercooled binary mixtures. A basic mechanism to crystallization was always found to be present in mixtures where spontaneous concentration fluctuations initiate crystallization. These fluctuations make the full utilization of, e.g., metallic glasses rather difficult.

### Relevant papers:

1. Crystallization instability in glass-forming mixtures
T. S. Ingebrigtsen, J. C. Dyre, T. B. Schrøder, and C. P. Royall, Phys. Rev. X 9, 031016 (2019)

• ## Roskilde-simple liquids

Roskilde-simple (RS) liquids are liquids with strong correlations between the virial-potential energy fluctuations in the constant volume ensemble. This class of liquids was discovered in the ''Glass and Time'' group at Roskilde University in 2007. Van the Waals and metallic liquids are RS liquids but, e.g., hydrogen-bonding liquids are not RS. The strong UW correlation is illustrated in Fig. 5 (Ref. 2). Roskilde-simple liquids are characterized by having isomorphs in their thermodynamic phase diagram which are invariance curves of structure and dynamics in appropriate dimensionless units. This fact makes these liquids simpler than other types of liquids (Ref. 3). RS liquids are relevant in many different situations, e.g., molecular liquids (Ref. 2), polydisperse systems (Ref. 1), and more.

### Relevant papers:

1. Effect of size polydispersity on the nature of Lennard-Jones liquids
T. S. Ingebrigtsen, and H. Tanaka, J. Phys. Chem. B 119, 11052 (2015)

2. Isomorphs in model molecular liquids
T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, J. Phys. Chem. B 116, 1018 (2012)

3. What is a simple liquid?
T. S. Ingebrigtsen, T. B. Schrøder, and J. C. Dyre, Phys. Rev. X 2, 011011 (2012)

• ## NVU dynamics

In molecular dynamics (MD) computer simulations Newton's second law is solved numerically. This keeps the energy E, the number of particles N, and the volume V constant. The dynamics is therefore called NVE dynamics. Over the years many different numerical algorithms for MD have been developed such as constant temperature NVT dynamics. In three papers (Refs. 1-3) we developed a new MD algorithm keeping not the energy E but the potential energy U constant, i.e., NVU dynamics. NVU dynamics is equivalent to Newton's first law on a many dimensional hypersurface. It turns out that NVU dynamics gives almost identical results to Newtonian NVE dynamics (Fig. 6).

### Relevant papers:

1. NVU dynamics. III. Simulating molecules at constant potential energy
T. S. Ingebrigtsen, and J. C. Dyre, J. Chem. Phys. 137, 244101 (2012)

2. NVU dynamics. II. Comparing to four other dynamics
T. S. Ingebrigtsen, S. Toxvaerd, T. B. Schrøder, and J. C. Dyre, J. Chem. Phys. 135, 104102 (2011)

3. NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface
T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, J. Chem. Phys. 135, 104101 (2011)