Anisimov/Sengers Research Group - 2012

HOW PURE WATER CAN UNMIXMikhail Anisimov

Institute for Physical Science &Technology and Department of Chemical & Biomolecular Engineering, University of Maryland, College Park

108th StatMech , Rutgers University December 16, 2012

ONE SUBSTANCE – TWO DIFFERENT LIQUIDS

A JOURNEY FROM HOT TO COLD WATER

Discovery of supercooled water

The air temperature in the thermometer was marked at fifteen degrees [–9 °C ]. After one hour, I found the water was still fluid in the ball.

Supercooled water was first described in 1721 by Fahrenheit.

[D. G. Fahrenheit, Phil. Trans. 33, 78 (1724)]

Supercooled water exists in nature

• In clouds, water droplets can be liquid down to about –38 °C (–36 °F)

• When an airplane flies through a supercooled water cloud, the droplets will freeze on impact: icing

180 200 220 240 260 2800

100

200

300

400

TH

Pre

ssur

e (M

Pa)

Temperature (K)

no man's land

TM

-80 -60 -40 -20 0°C

stableliquidwater

supercooled water(metastable)

Metastable liquid water at –90 °C

Homogeneous ice nucleation

240 260 280 300

980

990

1000

D

en

sity

(kg

/m3 )

Temperature (K)

Despretz (1837)

Hare and Sorensen (1987)

Stable liquidSupercooled liquid

WATER: ONE SUBSTANCE – TWO DIFFERENT LIQUIDS

High-temperature water: highly compressible, low dielectric constant, no (or little) hydrogen bonds, good solvent for organics

Low-temperature water: almost incompressible, very high dielectric constant, strong hydrogen-bond network, good solvent for electrolytes

Dielectric constant of water (IAPWS)

0 100 200 300 4000

20

40

60

80

100 Hodge and Angell 1978

Temperature (°C)

Liquid

Vapor

ONE SUBSTANCE – TWO DIFFERENT LIQUIDS: ISOBARIC HEAT CAPACITY OF LIQUID WATER

0 100 200 300 400

4

6

8

10

Supercooled liquid water at 1 bar Saturated liquid water Liquid water at 1 bar Angell et al. 1982

Cp

(kJ

kg-1

K-1

)

Temperature (°C)

-50

Tc

Red is the prediction by our model

TH TM

240 260 280 300 320 340 3604.0

4.5

5.0

5.5

6.0

He

at c

ap

aci

ty C

P (

kJ k

g-1

K-1

)

Temperature (K)

Stable liquidSupercooled liquid

Anisimov and Voronel (1972)

Angell et al. (1982)

Archer and Carter (2000)

HEAT CAPACITY OF WATER UPON SUPERCOOLING

WATER’S POLYAMORPHISM:

Second (liquid-liquid) critical point in water (Poole et al. 1992)

2

2

Fluctuations of volume:

Fluctuations of entropy:

T

P

dP S

dT V

V

S C

At the liquid-liquid critical point C the P/T slope is 30 times greater than at the vapor-liquid critical point of water and negativeC the location of LLCP as recently suggested by Holten and Anisimov, 2012

Brown curve: liquid-liquid coexistenceContinuation is Widom line, the line of stability minima

180 200 220 240 260 2800

100

200

300

400

Pre

ssur

e (M

Pa)

Temperature (K)

-80 -60 -40 -20 0°C

supercooledwater

stablewater

LDL

HDL

C

180 200 220 240 260 2800

100

200

300

400

TH

Pre

ssur

e (M

Pa)

Temperature (K)

TM

-80 -60 -40 -20 0°C

Mishima’s experiment (2000)

stablewater

Ice III

Ice V

Ice I

C

O. Mishima, PRL 85, 334 (2000)

How can pure liquid unmix?

1. Energy driven: a second minimum or a special shape of the molecular interaction energy (vapor-liquid is energy driven: lattice gas, van der Waals)

2. Entropy driven: a “mixture” of two “states” with negative entropy of mixing (some polymer solutions, networks)

3. A combination of both

dP S H

dT V T V

Clapeyron's equation itself does not answer whether the liquid-liquid separation is energy-driven or entropy driven

[Mishima and Stanley, Nature, 396, 329 (1998)]

TWO-STATE MODEL

• Assumption: water is a nonideal “mixture” of two configurations of hydrogen bonds: high-density/high-entropy state and a low-density/low-entropy state

• The fraction of each state is controlled by thermodynamic equilibrium• Liquid-liquid phase separation occurs when the non-ideality becomes

strong enough

A B,

Suggested equation of state: athermal two-state model

A B A( )G G x G G

[ ln (1 )ln(1 )]kT x x x x

( ) (1 )kT P x x

pure A and B states Gibbs energies

ideal mixing entropy contribution

non-ideal contribution

x molecular fraction of low-density structure B. Equilibrium fraction is found from = 0

B A

lnG G

KkT

K is chemical equilibrium constant of “reaction”

thus x is the extent of the reaction

A B

This liquid-liquid phase separation is driven by non-ideal entropy

Regular-solution unmixing (energy driven) versusathermal-solution (entropy driven) unmixing

A B A( ) ln (1 )ln(1 ) ( ) (1 )[ ]G G x G G kT x x x x P x x

A B A( ) ln (1 )ln(1 ) ( ) ([ 1 )]G G x G G kT x x x x P x x

Regular solution (equivalent to lattice gas/Ising model)

Athermal solution

ω determines the critical temperature

ω determines the critical pressure

The critical temperature is determined by the reaction equilibrium constant:

B A

ln ( , ) 0G G

K T PkT

Interaction parameter

The critical pressure is determined by the reaction equilibrium constant:

B A

ln ( , ) 0G G

K T PkT

Energy-driven phase separation

Entropy-driven phase separation

A B,

A B,

Fraction of low-density structure

mW model simulations: Moore and Molinero, J. Chem. Phys. 130, 244505 (2009).

x

[1]

Liquid-liquid transition is zero ordering field h1. The order parameter is entropy change.For liquid-gas transition the order parameter is the density change.

h1= ln K = 0

The scaling field h2 determines whether the transition is energy- or entropy-driven. If h2 = ΔT, the transition is energy driven. If h2 = -ΔP, the transition is entropy driven.

Liquid

Gas

102

100

10–2

10–4

Pres

sure

(MPa

)

200 400 600 800Temperature (K)

C2 C1

h1

h2

Relations between scaling and physical fields for liquid–liquid and liquid–vapor critical points of water

h1

h2 1

2

1

2 ( )

h

h T

V

S

1

2

1

2

h T a P

h P

S

V

h1 and h2 are Ising scaling fields

1 2and are scaling densities

1 is the order parameter

Heat capacity

230 240 250 260 270 280 290

75

80

85

90

95

100

Angell et al. (1982) Bertolini et al. (1985) Tombari et al. (1999) Archer and Carter (2000) Our model

CP (

J K

-1 m

ol-1

)

Temperature (K)

Compressibility

220 240 260 280 300

3

4

5

6

7

190

Kanno and Angell (1979) Mishima (2010) our model

TM

Com

pres

sibi

lity

(10-4

MP

a-1)

Temperature (K)

0.110

50

100

150

P/MPa

H2O(melting temperatures)

Density

0.1 MPa

100

200380

Temp. of max. densityx = 0.12

Density of cold and supercooled water.Black curves are the predictions of thecrossover two-state model.TH is the homogeneous nucleationtemperature. The red line is the line ofmaximum density, the green line is aconstant LDL fraction of about 0.12.

Best description of all available experimental data achieved to date!

Conclusions• We accurately describe all property data on supercooled water with a

two-state model based on an athermal mixing of two states. This model assumes that the liquid-liquid transition in water is entropy driven.

• Heavy water (D2O) shows similar anomalies and can be described by our model equally well.

• A regular-solution model (purely energy-driven liquid-liquid phase separation) does not work well (the description quality is an order of magnitude worse).

Current Activity• Application to atomistic models of water and to supercooled aqueous

solutions.• Adding a solute to supercooled water may move the critical point into

the experimentally accessible region.