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7/29/2019 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.

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