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
• Anomalies in water and simple models
• Liquid-liquid phase transition in water
• Liquid-liquid phase transition in silica
• 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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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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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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Two length scales• Particles have (1) no overlap or (2) partial overlap• Increase T more overlap density increase• Increase P more overlap diffusion increase
Low pressure High pressure
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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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Two length scales• Particles have (1) no overlap or (2) partial overlap• Increase T more overlap density increase• Increase P more overlap diffusion increase
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 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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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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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
• Anomalies in water and simple models
• Liquid-liquid phase transition in water(using ST2 model)
• Liquid-liquid phase transition in silica
• Conclusions
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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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Isochores in NVT ensemble
Adapted from: Poole et al., JPCM 17, L431 (2005)
0.80 g/cm30.81 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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Isochores in NVT ensemble
0.80 g/cm30.81 g/cm3
0.82 g/cm3
Adapted from: Poole et al., JPCM 17, L431 (2005)
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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Isochores in NVT ensembleHDL
LDL
NVT: Simulations with constant Number of molecules, constant Volume, and constant Temperature
Isochores are found by connecting data points of the same density
Adapted from: Poole et al., JPCM 17, L431 (2005)
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!
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Order parameter distribution
2D histogram of energy & density
Order parameter:M = r + 27.6 ELDL
HDL
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Order parameter distribution
Order parameter M can befit to 3D Ising model
Order parameter:M = r + 27.6 ELDL
HDL LDL HDL
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Outline
• Anomalies in water and simple models
• Liquid-liquid phase transition in water
• 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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Why is WAC closer to LLCP than BKS?Studies by Molinero et al. suggest that
“tetrahedrality” of the liquid plays a role
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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Why is WAC closer to LLCP than BKS?Studies by Molinero et al. suggest that
“tetrahedrality” of the liquid plays a role
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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Why is WAC closer to LLCP than BKS?Studies by Molinero et al. suggest that
“tetrahedrality” of the liquid plays a role
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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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
• Anomalies in water and simple models
• Liquid-liquid phase transition in water
• Liquid-liquid phase transition in silica
• 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