Supercooled liquids

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Supercooled liquids
Zhigang Suo Harvard University
Prager Medal Symposium in honor of Bob
McMeeking SES Conference, Purdue University, 1
October 2014
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Mechanics of supercooled liquids
Jianguo Li
Qihan Liu Laurence
Brassart

• Journal of Applied Mechanics 81, 111007 (2014)

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Supercooled liquid
liquid
Volume
supercooled liquid
melting point
crystal
Temperature
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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)
particle
Einstein (1905)
liquid
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Success and failure of Stokes-Einstein relation
TNB
IMC
OTP
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014). Based on
experimental data in the literature
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A supercooled liquid forms a dynamic structure
The dynamic structure jams viscous flow, but not
self-diffusion.
Ediger, Annual Review of Physical Chemistry 51,
99 (2000).
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Our paper
Given that the Stokes-Einstein relation fails,
we regard viscous flow and self-diffusion as
independent processes, and formulate a new
fluid mechanics.
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014)
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Homogeneous state
Helmholtz free energy of a composite system
Liquid force reservoir
Incompressible molecules
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014)
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Thermodynamic equilibrium
reservoir
liquid
membrane
osmosis
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014)
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Linear, isotropic, viscous, porous liquid

• Analogous to Biots poroelasticity.
  (Poroviscosity?)
• Different from Newtons law of viscosity

Alternative way to write the model
change shape change volume
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014)
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Inhomogeneous field
Diffusion flux
Net flux
Convection flux
Suo. Journal of Applied Mechanics 71, 77 (2004)
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Boundary-value problem
4 partial differential equations
4 boundary conditions
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014)
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Length scale
Li, Liu, Brassart, Suo. Journal of Applied
Mechanics 81, 111007 (2014)
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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)
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Summary

1. 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.

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