Poc

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Pocítacové simulace rozhraní pevná látka-kapalina
Milan Predota Katedra zdravotnické fyziky a
biofyziky ZSF JU
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Príklad 2D Isinguv model
SHOWISI.EXE
Program DEMO (demo.zip) lze stáhnout z www
stránky Jirího Kolafy http//home.icpf.cas.cz/jiri
/
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Connection between experiment and theory
REAL SYSTEM
MODEL SYSTEM
MAKE MODEL
CONSTRUCT APPROXIMATE THEORY
PERFORM EXPERIMENT
EXPERIMENTAL RESULTS
THEORETICAL PREDICTION
COMPARE
APPROXIMATE MODEL OR THEORY ?
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Connection between experiment and theory
REAL SYSTEM
MODEL SYSTEM
MAKE MODEL
CARRY OUT COMPUTER SIMULATION
CONSTRUCT APPROXIMATE THEORY
PERFORM EXPERIMENT
EXPERIMENTAL RESULTS
EXACT RESULTS FOR MODEL
THEORETICAL PREDICTION
COMPARE
COMPARE
TEST OF MODEL
TEST OF THEORY
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1. Predictive capabilities
REAL SYSTEM
MODEL SYSTEM
MAKE MODEL
CARRY OUT COMPUTER SIMULATION
CONSTRUCT APPROXIMATE THEORY
PERFORM EXPERIMENT
EXPERIMENTAL RESULTS
EXACT RESULTS FOR MODEL
THEORETICAL PREDICTION
COMPARE
COMPARE
TEST OF MODEL
TEST OF THEORY
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MeOHCO2 t50oC
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2. Development of theory
REAL SYSTEM
MODEL SYSTEM
MAKE MODEL
CARRY OUT COMPUTER SIMULATION
CONSTRUCT APPROXIMATE THEORY
PERFORM EXPERIMENT
EXPERIMENTAL RESULTS
EXACT RESULTS FOR MODEL
THEORETICAL PREDICTION
COMPARE
COMPARE
TEST OF MODEL
TEST OF THEORY
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Micellar solubilization
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2. Development of theorySystem
water/surfactant/oil

• Water/Surfactant/Oil systems were modeled by
  Larson, 1985
• Effective interaction

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3. Get insight to phenomena
REAL SYSTEM
MODEL SYSTEM
MAKE MODEL
CARRY OUT COMPUTER SIMULATION
CONSTRUCT APPROXIMATE THEORY
PERFORM EXPERIMENT
EXPERIMENTAL RESULTS
EXACT RESULTS FOR MODEL
THEORETICAL PREDICTION
COMPARE
COMPARE
TEST OF MODEL
TEST OF THEORY
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Klasifikace simulací
spojitého prostredí
molekulární
stavová rovnice Navier-Stokes Poisson-Boltzmann ve
dení tepla ...
elektronová struktura ? kvantové simulace
atomární struktura (B.-O.) ? klasické simulace
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Klasické molekulární simulace
modely se spojitými souradnicemi
diskrétní modely
Monte Carlo
Monte Carlo
molekulární dynamika
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Monte Carlo (MC)

• Strední hodnoty velicin jsou urceny souborovým
  stredováním (NVT, NPT, mVT) posloupnosti
  konfigurací generovaných náhodne s fyzikálne
  urcenou pravdepodobností za použití generátoru
  (pseudo)náhodných císel
• Stochastická metoda
• Primárne urcena pro rovnovážné simulace
• Posloupnost generovaných konfigurací se obecne
  jen podobá casovému vývoji nebo mu vubec
  neodpovídá
• Vhodná pro spojité i diskrétní systémy, spojité i
  nespojité potenciály

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Monte Carlo (MC) algoritmus

• Vygeneruj (stochasticky) zmenu konfigurace
• Zmena polohy cástice, zmena objemu, poctu cástic
• Spocti pravdepodobnost prijetí nové konfigurace
• Prijmi/neprijmi novou konfiguraci s vypoctenou
  pravdepodobností
• Ad 2. (zmena polohy), Metropolisuv algoritmus
• Ad 3.

prijmi novou konfiguraci neprijmi novou
konfiguraci
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Molekulární dynamika (MD)

• Modeluje realistický casový vývoj modelového
  systému
• Dynamika diktována fyzikálními zákony
• Strední hodnoty velicin jsou urceny casovým
  stredováním konfigurací
• Deterministická metoda
• Vhodná pro rovnovážné i nerovnovážné simulace
• Použitelná pouze pro spojité systémy, nevhodná
  pro nespojité potenciály

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Verletuv algoritmus MD
?
?
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Verletuv algoritmus MD
r
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Demonstracní programy
Program SIMOLANT 2002 lze stáhnout z www stránky
Jirího Kolafy http//www.vscht.cz/fch/software/si
molant/index-cz.html
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Molecular dynamics simulations

• Initiation
• Calculation of forces
• Propagation
• Measurement
• Finalization

• Typical timestep
• 1 fs 10-15 s
• Typical desired length of simulation
• at least 1 ns (10-9 s)
• biological systems 1??s 1 s ?? course grained
  techniques
• Typical number of MD steps
• at least 106

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Calculation of forces

• Pair potential interactions

• N atoms ?N(N-1)/2 pair interactions
• 10 000 atoms ? 50 mil. pairs

• Parallelization

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Computational resources

• Oak Ridge National Laboratory
• 704 processors 375MHz (1.3 GFlops)
• 864 processors 1.3 GHz
• National Energy Research Scientific Computing
  CenterBerkeley
• 2944 processors 1.5 GFlops
• nodes16 procs

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Negatively charged rutile surface, ? -0.2
C/m2Nonhydroxylated
Hydroxylated
OH-
terminal hydroxyl
hydroxylated terminal Ti
H
deprotonated bridging oxygen
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Study of adsorption of ions at interfaces

• rubidium
• chloride
• oxygen
• titanium

• hydrogen

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Model and potentials

• Rigid nonpolarizable model of water 2048 SPC/E
  molecules
• Ions (Rb,Na, Sr2, Ca2, Zn2) point charges
  LJ potential
• S. H. Lee and J. C. Rasaiah, JPC 100, 1420 (1996)
• B. J. Palmer, D. M. Pfund, and J. L. Fulton, JPC
  100, 13393 (1996)
• Structure and charges of TiO2 surface - ab initio
  calculations
• Matsui and Akaogi potential for bulk TiO2 (Mol.
  Sim. 6, 239 (1991))
• Relaxed surface structure and optimized
  water-TiO2 potentials potentials
• A. V. Bandura, D. G. Sykes, J. D. Kubicki, JPC B
  108, 7844 (2004)

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Water at the interface

• Diffusivity of water as a function of distance
  from the surface
• Parallel component Dxy and perpendicular
  component Dz
• Determination of contact and diffuse layers

• Axial density profile of oxygen
• Good agreement with X-ray data for all surfaces

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Axial density profiles of ions

• Comparison of MD results with XSWand CTR
  experimental data
• Better agreement for hydroxylated surface

Hydrox.
Nonhydrox.
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Lateral alignment of ions at negative surface

• rubidium

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Rubidium
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Strontium
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Zinc
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Adsorption sites from MD and X-ray
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Diffusivity profiles
Diffusivity calculated from mean square
displacement for times t1.2 ps to 2.4 ps ?
linear dependence, molecule does not diffuse to
distant bins ? local diffusivity
exp. value _at_ 298 K 2.7 10-9 m2/s
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Viscosity of water at 25 C, neutral surface, pure
water
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Axial profiles of electrostatics