Thermodynamic, Dynamic and Structural Anomalies in...
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Summary Our group What is the problem? Our Assumption Our Model Summary Thermodynamic, Dynamic and Structural Anomalies in Shoulder potentials Ney M. Barraz Jr. (UFRGS) Alan Barros de Oliveira (UFOP) Evy Salcedo (UFSC) Marcia C. Barbosa (UFRGS) 1 de julho de 2010
Transcript of Thermodynamic, Dynamic and Structural Anomalies in...
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Thermodynamic, Dynamic and StructuralAnomalies in Shoulder potentials
Ney M. Barraz Jr. (UFRGS)Alan Barros de Oliveira (UFOP)
Evy Salcedo (UFSC)Marcia C. Barbosa (UFRGS)
1 de julho de 2010
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1 Our group
2 What is the problem?
3 Our Assumption
4 Our Model
5 Summary
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Our Grouphttp : //www.if.ufrgs.br/ ∼ barbosa
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What is the Problem?[M. Chaplin, Water structure and science (2010).]
Density Anomaly
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What is the Problem?[ C. A. Angell, E. D. Finch, and P. Bach, J. Chem. Phys. 65, 3063 (1976) ]
Diffusion Anomaly
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What is the Problem?[ P. A. Netz, F. Starr, H. E. Stanley, M. C. Barbosa, Journal of Chem. Phys., 115, 344 (2001) ]
Diffusion Anomaly SPC/E
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How are the anomalies observed?[Angell, Finch, and Bach, J.Chem.Phys. 65, 3063 (1976)]
[Netz, Starr, Stanley, and Barbosa, J.Chem.Phys. 115, 344 (2001)]
There are experimental and simulational data.
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What is the main ingredient for anomaly?
Two Length Scales
The Second Scale has to be deeper
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Competition
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Effective Potential for Water[A. B. de Oliveira et. al JCP 124 84505 (2006),125 124503 (2006) ]
U(r) = 4ε[(σr
)12−(σr
)6]
+ aε exp
[−(r − r0c
)2]
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Phase Diagram
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Diffusion[A. B. de Oliveira et. al JCP 124 84505 (2006),125 124503 (2006) ]
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Integral Equations
βP = ρ− βρ
3N〈∑
~ri · ~∇Vi〉
βP = ρ− 2πβρ2
3
∫dV
drg(r)r3dr
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Radial Distribution Function
g(r) =dn
ρ4πr2dr
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Gas
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Liquid
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Solid
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Integral Equations
ggas(r) ∝ e−βV (r) Gas
gHNC(r) = e−βV (r)eh(r)−c(r) HNC
gPY (r) = e−βV (r)(1 + h(r)− c(r)) PY
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Ornstein-Zernike
h(r) = c(r) + ρ
∫c(|~r − ~r′|)h(r′)d3r′
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Correlations
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Percus Yevick: Phase Diagram
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Percus Yevick
c(r) = g(r)− gindirect(r)
c(r) = e−βW (r) − e−(βW (r)−βV (r))
c(r) = g(r)− eβV (r)g(r)
g(r) = e−βV (r)(1 + h(r)− c(r))
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HNC: Phase Diagram
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Hypernetted-chain
c(r) = g(r)− gindirect(r)
c(r) = e−βW (r) − e−(βW (r)−βV (r))
c(r) = g(r)− 1 + βW (r)− βV (r) = h(r)− Log[eβV (r)g(r)]
g(r) = e−βV (r)eh(r)−c(r)
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Inconsistency
βPfluc = ρ− 4π∫ ρ
0
∫ρ′r2c(r, ρ′)drdρ′
βPvirial = ρ− 2πβρ2
3
∫dV
drg(r)r3dr
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Roger Young
gRY (r) = e−βV (r)(1 +e(h(r)−c(r))f(r)−1
f(r))
f(r) = 1− e−αr
Pvirial = Pfluc
gRY = gPY r → 0
gRY = gHNC r →∞
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Roger Young: Phase Diagram
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gr[A. B. de Oliveira et. al European Physics Journal B 64 481 (2008)]
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Two length scales = density and diffusion anomalies
Integral Equations = help in choosing phase space forrunning simulations
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Effective Potential for Water[A. B. de Oliveira et. al JCP 132 164505 (2010) ]
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g(r)
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r2
