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

Liquid-Liquid Phase Transitions and Water-Like Anomalies in Liquids. Erik Lascaris Final oral examination 9 July 2014. Anomalies in water and simple models Liquid-liquid phase transition in water Liquid -liquid phase transition in silica Conclusions. Outline.

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

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  1. Liquid-Liquid Phase Transitions and Water-Like Anomalies in Liquids Erik Lascaris Final oral examination 9 July 2014

  2. Anomalies in water and simple models Liquid-liquid phase transition in water Liquid-liquid phase transition in silica Conclusions Outline

  3. Anomalies in water and simple models Liquid-liquid phase transition in water Liquid-liquid phase transition in silica Conclusions Outline

  4. Famous website by Martin Chaplinhttp://www1.lsbu.ac.uk/water/anmlies.html now lists 70 anomalies!(on 9 July 2014) Today we focuson3 of them Water has many anomalies(compared to other liquids)

  5. 1. Density anomaly As we increase T, density increases! At 1 atmTemperature of Maximum Density (TMD) is 4 °C

  6. 2. Diffusion anomaly In water, self-diffusion increasesas density and pressure increase (at low T)

  7. Most liquids: 3. Melting line with negative slope Applying pressure can melt ice! details

  8. Where do these come from? What is their origin? Water has many anomalies(compared to other liquids) Let’s try a simple model!

  9. Monatomic particles (spheres) Pairwise interaction: Particles can partially overlap Hard core + linear ramp potential Hard core Linear ramp

  10. PT diagram Melting linewith negative slope

  11. PT diagram Density anomalyincrease T increase density

  12. PT diagram Diffusion anomalyincrease P  increase diffusivity

  13. PT diagram How can we explain these anomalies?

  14. Particles have (1) no overlap or (2) partial overlap Two length scales Low density state (low T, low P) High density state (high T, high P)

  15. Particles have (1) no overlap or (2) partial overlap Increase T  more overlap density increase Two length scales Low T High T

  16. Particles have (1) no overlap or (2) partial overlap Increase T  more overlap density increase Increase P  more overlap diffusion increase Two length scales Low pressure High pressure

  17. Particles have (1) no overlap or (2) partial overlap Increase T  more overlap density increase Increase P  more overlap diffusion increase Two length scales Low pressure High pressure

  18. Particles have (1) no overlap or (2) partial overlap Increase T  more overlap density increase Increase P  more overlap diffusion increase Two length scales Low pressure High pressure

  19. Particles have (1) no overlap or (2) partial overlap Increase T  more overlap density increase Increase P  more overlap diffusion increase Two length scales When T or P too high: Normal liquid again!

  20. 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 Melting line

  21. Changing the model To obtain a better understanding: try different potentials Hard Core + Linear Ramp Linear Ramp

  22. PT diagram Linear Ramp Hard Core + Linear Ramp

  23. Changing the model To obtain a better understanding: try different models Cut Ramp

  24. PT diagrams of Cut Ramp potential Several anomalies: • Density anomaly • Melting line with negative slope • Diffusion anomaly All within same pressure range!

  25. PT diagrams of Cut Ramp potential How can we explain this? Look at Radial Distribution Function!

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

  27. RDF of Linear Ramp (0% cut) RDF at T = 0.040 Low pressure(no anomalies)

  28. RDF of Linear Ramp (0% cut) RDF at T = 0.040 Low pressure(no anomalies)

  29. RDF of Linear Ramp (0% cut) RDF at T = 0.040 Low pressure(no anomalies)

  30. RDF of Linear Ramp (0% cut) RDF at T = 0.040 Medium pressure(inside anomaly region)

  31. RDF of Linear Ramp (0% cut) RDF at T = 0.040 High pressure(no anomalies)

  32. RDF of 50% Cut Ramp RDF at T = 0.040 Low pressure (no anomalies)

  33. RDF of 50% Cut Ramp RDF at T = 0.040 Medium pressure(no anomalies)

  34. RDF of 50% Cut Ramp RDF at T = 0.040 High pressure(no anomalies)

  35. Two “competing”length scales 50% cut: no anomalies 0% cut: anomalies Within anomaly region, someparticlesare on the ramp Particles are either near r=0 orr=1 but rarely on the ramp! HCLR

  36. For anomalies to occur, we require: • Needtwo length scales in potential • Liquid has two preferred liquid states • Length scales need to be “competing” • Anomalies occur when liquid is in between states Anomalies: conclusions Water has anomalies  does it have two length scales?

  37. Two length scales in water! When cooled super fast,it’spossible to createtwo types of “glassy” water! Low-DensityAmorphousice (LDA) High-DensityAmorphousice (HDA) Spontaneous crystallization Katrin Amann-Winkel (2013)Loerting Group, Universität Innsbruck

  38. 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) Liquid-liquid phase transition in water Hypothesis (Poole/Sciortino/Essmann/Stanley, Nat. 1992)

  39. Anomalies in water and simple models Liquid-liquid phase transition in water(using ST2 model) Liquid-liquid phase transition in silica Conclusions Outline

  40. ST2 water model + + – – Stillinger & Rahman, J. Chem. Phys. 60, 1545 (1974)

  41. Isochores in NVT ensemble NVT: Simulations with constant Number of molecules, constant Volume, and constant Temperature Isochores are found by connecting data points of the same density 0.80 g/cm3 Adapted from: Poole et al., JPCM 17, L431 (2005)

  42. Isochores in NVT ensemble NVT: Simulations with constant Number of molecules, constant Volume, and constant Temperature Isochores are found by connecting data points of the same density 0.81 g/cm3 0.80 g/cm3 Adapted from: Poole et al., JPCM 17, L431 (2005)

  43. Isochores in NVT ensemble NVT: Simulations with constant Number of molecules, constant Volume, and constant Temperature Isochores are found by connecting data points of the same density 0.82 g/cm3 0.81 g/cm3 0.80 g/cm3 Adapted from: Poole et al., JPCM 17, L431 (2005)

  44. Isochores in NVT ensemble NVT: Simulations with constant Number of molecules, constant Volume, and constant Temperature HDL LDL Isochores are found by connecting data points of the same density Isochores cross at the Liquid-Liquid Critical Point (LLCP) 0.80 g/cm3 Adapted from: Poole et al., JPCM 17, L431 (2005)

  45. 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 Measuring location (T, P) of the LLCP Will be explained on next few slides!

  46. “Phase flipping” in NPTensemble Density as a function of time: LDL HDL LLCP

  47. Phase flipping  histogram of density Density distribution LDL HDL

  48. Phase flipping  histogram of energy Energy distribution LDL HDL

  49. 2D histogram of energy & density Order parameter distribution HDL LDL

  50. 2D histogram of energy & density Order parameter distribution HDL Order parameter: M = r + 27.6 E LDL

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