Liquid-Liquid Phase Transitions and Water-Like Anomalies in Liquids Erik Lascaris Final oral...

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Liquid-Liquid Phase Transitions and Water-Like Anomalies in Liquids

Erik Lascaris

Final oral examination9 July 2014

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Outline

• Anomalies in water and simple models

• Liquid-liquid phase transition in water

• Liquid-liquid phase transition in silica

• Conclusions

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Outline




• Conclusions

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Water has many anomalies(compared to other liquids)

• Famous website by Martin Chaplin http://www1.lsbu.ac.uk/water/anmlies.html now lists 70 anomalies!(on 9 July 2014)

• Today we focuson 3 of them

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1. Density anomaly

At 1 atm Temperature of Maximum Density (TMD) is 4 °C

As we increase T, density increases!

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2. Diffusion anomaly

In water, self-diffusion increasesas density and pressure increase (at low T)

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3. Melting line with negative slope

Applying pressure can melt ice!

Most liquids:

details

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Water has many anomalies(compared to other liquids)

• Where do these come from?

• What is their origin?

Let’s try a simple model!

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Hard core + linear ramp potential

• Monatomic particles (spheres)

• Pairwise interaction:

• Particles can partially overlap

Hard coreLinear ramp

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PT diagram

Melting linewith negative slope

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PT diagramDensity anomaly

increase T increase density

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PT diagramDiffusion anomaly

increase P increase diffusivity

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PT diagram

How can weexplain theseanomalies?

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Two length scales• Particles have (1) no overlap or (2) partial overlap

Low density state

(low T, low P)

High density state

(high T, high P)

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Two length scales• Particles have (1) no overlap or (2) partial overlap• Increase T more overlap density increase

High TLow T

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Two length scales• Particles have (1) no overlap or (2) partial overlap• Increase T more overlap density increase• Increase P more overlap diffusion increase

High pressureLow pressure

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Low pressure High pressure

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High pressureLow pressure

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When T or P too high:Normal liquid again!

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Melting line• Clapeyron relation for slope melting line dP/dT:

• Change in entropy always positive: S > 0• Usually crystal more dense than liquid: V > 0• However, two length scales leads to V < 0

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Changing the modelTo obtain a better understanding: try different potentials

Hard Core + Linear Ramp Linear Ramp

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PT diagram

Hard Core + Linear Ramp Linear Ramp

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Changing the modelTo obtain a better understanding: try different models

Cut Ramp

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PT diagrams of Cut Ramp potential

Several anomalies:• Density anomaly• Melting line with negative

slope• Diffusion anomaly

All within same pressure range!

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PT diagrams of Cut Ramp potential

How can we explain this?

Look at Radial Distribution Function!

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Radial Distribution Function (RDF)RDF = probability for atom to find a neighbor a distance r away (normalized to ideal gas)

ideal gas crystal

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RDF of Linear Ramp (0% cut)

Low pressure(no anomalies)

RDF at T = 0.040

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RDF at T = 0.040

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RDF at T = 0.040

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Medium pressure(inside anomaly region)

RDF at T = 0.040

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High pressure(no anomalies)

RDF at T = 0.040

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RDF of 50% Cut Ramp


RDF at T = 0.040

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RDF of 50% Cut Ramp

Medium pressure(no anomalies)

RDF at T = 0.040

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RDF of 50% Cut Ramp

High pressure(no anomalies)

RDF at T = 0.040

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Two “competing” length scales

Particles are either near r=0 orr=1 but rarely on the ramp!

Within anomaly region, someparticles are on the ramp

0% cut: anomalies 50% cut: no anomalies

HCLR

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Anomalies: conclusions

For anomalies to occur, we require:

• Need two length scales in potential– Liquid has two preferred liquid states

• Length scales need to be “competing”– Anomalies occur when liquid is in between states

Water has anomalies does it have two length scales?

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Two length scales in water!

High-DensityAmorphous

ice (HDA)

Katrin Amann-Winkel (2013)Loerting Group, Universität Innsbruck

Low-DensityAmorphous

ice (LDA)

When cooled super fast,it’s possible to create

two types of “glassy” water!

Spontaneous crystallization

Liquid-liquid phase transition in water

• Two liquids belownucleation temperature:– Low density liquid (LDL)– High density liquid (HDL)

• Separated by liquid-liquidphase transition (LLPT) line

• Line ends in a liquid-liquidcritical point (LLCP)

Hypothesis(Poole/Sciortino/Essmann/Stanley, Nat. 1992)

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Outline


• Liquid-liquid phase transition in water(using ST2 model)


• Conclusions

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ST2 water model

+

+–

–Stillinger & Rahman, J. Chem. Phys. 60, 1545 (1974)

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Isochores in NVT ensemble

Adapted from: Poole et al., JPCM 17, L431 (2005)

0.80 g/cm3

NVT: Simulations with constant Number of molecules, constant Volume, and constant Temperature

Isochores are found by connecting data points of the same density

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0.80 g/cm30.81 g/cm3



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0.80 g/cm30.81 g/cm3

0.82 g/cm3




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Isochores in NVT ensembleHDL

LDL




0.80 g/cm3 Isochores cross at the Liquid-Liquid Critical Point (LLCP)

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Measuring location (T, P) of the LLCP

• It’s hard to locate LLCP accurately using only crossing isochores…

• Alternative method:Fitting order parameter to 3D Ising model!

• Requires NPT (constant Pressure) simulations

Will be explained on next few slides!

“Phase flipping” in NPT ensemble46

LDL HDL

LLCP

Density as a function of time:

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Density distribution

Phase flipping histogram of density

LDL

HDL

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Energy distribution

Phase flipping histogram of energy

LDL

HDL

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Order parameter distribution

2D histogram of energy & density

LDL

HDL

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2D histogram of energy & density

Order parameter:M = r + 27.6 ELDL

HDL

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Order parameter M can befit to 3D Ising model

Order parameter:M = r + 27.6 ELDL

HDL LDL HDL

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Outline



• Liquid-liquid phase transition in silica(using WAC model and BKS model)

• Conclusions

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Two models of silica (SiO2)

WAC model• Woodcock, Angell, and

Cheeseman• Introduced 1976• Ions: Si+4 and O–2

• Simple 1:2 mixture of Si and O ions

• Each ion has a charge + electrostatics

• Repulsive potential between ionsto prevent Si-O fusion

BKS model• van Beest, Kramer, and

van Santen• Introduced 1990• Ions: Si+2.4 and O–1.2

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PT diagram of BKS

Saika-Voivod, Sciortino, and PoolePhys. Rev. E 63, 011202 (2000)

Lascaris, Hematti, Buldyrev, Stanley, and AngellJ. Chem. Phys. 140, 224502 (2014)

LLCP? Crossing isochores? No LLCP at low T

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PT diagram of WAC

Lascaris, Hematti, Buldyrev, Stanley, and AngellJ. Chem. Phys. 140, 224502 (2014)

LLCP? Crossing isochores? Maybe LLCP at low T!

Saika-Voivod, Sciortino, and PoolePhys. Rev. E 63, 011202 (2000)

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Response functions WACAt critical point: all response functions should diverge!

Maxima are at different (T,P) no LLCP!

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Why is WAC closer to LLCP than BKS?Studies by Molinero et al. suggest that

“tetrahedrality” of the liquid plays a role

Liquids like water and SiO2

form tetrahedral bondsRigid bonds lead to fast

crystallization intohexagonal crystal

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Rigid bonds lead to fast crystallization intohexagonal crystal

High-Density Liquid • Compact• Liquid with

high diffusivity

Floppy bonds lead to high-density liquid

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Rigid bonds lead to fast crystallization intohexagonal crystal

High-Density Liquid • Compact• Liquid with

high diffusivity

Liquid-liquid phase transition requires existence of two liquids: LDL and HDL

Low-Density Liquid • Expanded• Local structure

closer to crystal

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Conclusion:bond stiffness needs to be just right• Too stiff crystallization• Too flexible only HDL• Just right LDL + HDL

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Si-O-Si bond angle distributionDistribution WAC is sharper: stiff Distribution BKS more broad: floppy

Hard to compare: bond angle depends on temperature!

details

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Bond angle as spring systemPretend Si-O-Si bond angle is controlled by a spring:

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Pretend Si-O-Si bond angle is controlled by a spring:

Imaginary spring(spring constant k2) WAC more stiff closer to LLCP

details

Bond angle as spring system

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Outline




• Conclusions

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Conclusions (1)

• Simple models explain origin of anomalies:

– Two length scales• Low density structure (expanded)• High density structure (collapsed)

– Region with anomalies is where these structures energetically compete

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Conclusions (2)

• Best way to locate liquid-liquid critical point (LLCP)is by fitting order parameter to 3D Ising

• We did not find LLCP in silica models WAC, BKS

• Liquid-liquid phase transitions might berelated to bond angle stiffness– Modeling liquid as network of springs might help

predicting if liquid has a LLCP

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Also a big THANKS to my collaborators:– Gene Stanley (advisor)– Sergey Buldyrev– Austen Angell– Mahin Hemmati– Giancarlo Franzese– Tobias Kesselring– Hans Herrmann– Gianpietro Malescio

THANK YOU!

Liquid-Liquid Phase Transitions and Water-Like Anomalies in Liquids

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