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Transcript of maaza tiger
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Rotational & Translational
Dynamic Heterogeneities in
Supercooled Water
Collaborators: N. Giovambattista and F. W. Starr
Marco G. Mazza
Advisor: H. Eugene Stanley
Details: M.G. Mazza, N. Giovambattista, F.W. Starr, H.E. Stanley,
Relation between Rotational and Translational Dynamic Heterogeneities in Water, PRL 96, 057803 (2006)
Center for Polymer Studies and Department of Physics, Boston University
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Supercooling is the process of cooling a liquid
below its freezing point, without it becoming solid.
Water is metastable because it cannot overcome thefree energy barrier F
Upon cooling the energy barrier decreases, until
F kT, leading to homogeneous nucleation
stable
Free energy
= configurational parameter
metastable
F
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Ordinary single-component liquids in standard conditionsare correctly described as homogeneous
Overwhelming experimental evidence that supercooledliquids are instead heterogeneous
HETEROGENEITY = in one
region molecular translational
motion is orders of magnitude
faster than in another region afew nm distant
Overlapped snapshots of 2d atoms
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Questions:1. In addition to the well-studied translational heterogeneities, are there also
rotational heterogeneities?
2. If so, are rotational heterogeneities related to the translational
heterogeneities.?
Why bother?
Heterogeneous dynamics gives a mechanism for diffusion at very low T:
necessity of cooperative regions to overcome the energy barriers Heterogeneous dynamics explains relaxation in experimental correlationfunctions, which are not simple exponentials
0
/)(])/(exp[)( dePttCt
P(): spatial distribution ofrelaxation times
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Model: SPC/E(extended simple point charge potential)
= 3.166
= 0.650 kJ/mol
l1
= 1.0
= 109.47
q1= +0.4238 (e)
q2= -0.8476 (e)
Lennard-Jones interaction betweenoxygen atoms
Molecular dynamics simulation: Integrate numerically
Newtons equations in the canonical ensemble (NVT)
N=1728 water molecules
V=51.7 nm3
T=200350 K
Electrostatic interaction betweenall charged sites
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Translational mean square
displacement
(i)
(ii)
(iii)
Three dynamical regimes for translational mean square displacementdescribed by
Four dynamical regimes for rotational mean square displacement describedby
Rotational mean square
displacement
(i)
(ii)
(iii)
(iv)
Mazza et al., PRL 96, 057803 (2006)
First Results:
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The rotational diffusivity decreases by 3 orders of magnitude We need clusters of more mobile molecules: significant molecular motion in acold, dense fluid can only occur if the molecules rearrange their positions in a
concerted, cooperative manner.
Rotational Diffusivities for the three principal directions
Rt tDt 4)(
2
j
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Cluster definition
1. Rotational Mobility: maximum angular
displacement in t
2. Select the 7% of the most rotationally mobile
molecules
3. Define cluster at time t0for observation time t as
those molecules whose O-O distance is less than
0.315 nm
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Rotational mean square displacementAverage size of rotational clusters
3
2
1
3
21
Answer to question 1: yes, the most rotationally mobile moleculestend to form clusters.
The maximum size of these clusters occurs at the end of the cage
time regime (arrows).
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blue = Translat. mobile clusters
red = Rotationally mobile clusters
green = both
Clusters of rotationally mobile molecules
Disconnected clusters are part of a larger region of cooperative motion
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Fraction of molecules in both rotational & translational heterogeneities
blue = TH
red = RH
green = both
This fraction (of the clusters) can be as high as almost 30%
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Oxygen-Oxygen radial distribution function
probability of finding two molecules separated by distance r
Short range order, long range disorder
0.27
0.44
0.67
water forms atetrahedral structure
with its neighbors
Review:
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Three oxygen-oxygen radial distribution functions for heterogeneities
gR-R, gT-T, gR-T are similar to standard oxygen-oxygen radial distr. function
rotational and translational heterog. are correlated in space (answer to question 2)
gR-R :rotational clusters
gT-T: translational clustersgR-T : rotat. & transl. clusters
Blow-up of gR-T
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Peak at 0.31 nm bifurcated bond present in both rotational and translationalheterogeneities.
Bifurcated bonds provide extra mobility to molecules belonging to a heterogeneity.
Normalization by the standard radial distribution function
bifurcated bond: a hydrogen
shared between 2 other
oxygens
0.31 nm
Motivation: measure of some extra order beyond the bulkstructure
0.31
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Conclusions
1. Rotational and translational
heterogeneities form together a larger
more complex region of cooperative
motion.
2. The presence of a fifth oxygen (inside the
nearest neighbor shell) acts as catalystfor the restructuring of the hydrogen-
bonded network, therefore allowing amechanism for diffusion in cold water.