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Supercooled liquids

Zhigang Suo

Harvard University

Prager Medal Symposium in honor of Bob McMeekingSES Conference, Purdue University, 1 October 2014

Mechanics of supercooled liquids

Journal of Applied Mechanics 81, 111007 (2014)

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Jianguo Li Qihan Liu Laurence Brassart

Supercooled liquid

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liquid

supercooled liquid

crystal

Temperature

Volu

me

mel

ting

poin

t

A simple picture of liquid

• A single rate-limiting step: molecules change neighbors• Two types of experiments: viscous flow and self-diffusion

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Stokes-Einstein relation

Stokes (1851)

Einstein (1905)

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liquid

particle

Success and failure of Stokes-Einstein relation

TNB

OTP

IMC

6Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014). Based on experimental data in the literature

A supercooled liquid forms a dynamic structure

Ediger, Annual Review of Physical Chemistry 51, 99 (2000).

The dynamic structure jams viscous flow, but not self-diffusion.

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Given that the Stokes-Einstein relation fails, we regard viscous flow and self-diffusion as independent processes,and formulate a “new” fluid mechanics.

Our paper

Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Homogeneous state

Incompressible molecules

Helmholtz free energyof a composite system

Liquid force reservoir

9Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Thermodynamic equilibrium

10m

embr

ane

reservoir

liquid

osmosisLi, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Linear, isotropic, viscous, “porous” liquid

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Alternative way to write the model

• Analogous to Biot’s poroelasticity. (Poroviscosity?)• Different from Newton’s law of viscosity

change shape change volume

Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Inhomogeneous field

Diffusionflux

Netflux

Convectionflux

ii kTD

J ,

12Suo. Journal of Applied Mechanics 71, 77 (2004)

0, ijij b

4 partial differential equations

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4 boundary conditions

Boundary-value problem

Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Length scale

14Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Time scale

Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

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A cavity in a supercooled liquid

• A small object evolves by self-diffusion. • A large object evolves by viscous flow.

Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)

Summary1. A supercooled liquid is partially jammed. A drop in

temperature jams viscous flow, but does not retard self-diffusion as much.

2. We regard viscous flow and self-diffusion as independent processes, and formulate a “new” fluid mechanics.

3. A characteristic length exists. A small object evolves by self-diffusion, and a large object evolves by viscous flow.

4. Other partially jammed systems: cells, gels, glasses, batteries.

17Li, Liu, Brassart, Suo. Journal of Applied Mechanics 81, 111007 (2014)