a. soper : the structure of water in bulk and in confinement by

The structure of water in bulk and in confinement

by neutron and x-rayscattering

Alan K SoperISIS Facility, UK

April 2013

ISIS Disordered Materials Group

Alex Hannon

XRDSam Callear

Daniel Bowron,

Group Leader

Silvia ImbertiSANDALS

GEM

Tristan Youngs

NIMROD

Total scattering from disorderedmaterials

Q 4 sin

2

Sample

Detector

Incident radiation

Scattered radiation

Q 4 sin

SANDALS (liquids

diffractometer)

Incident neutron beam

Sample position

Scattering detectors

ILL – D4C

LANSCE – NPDF

X-ray diffractometer

Out of the instrument comes some data:

(Total scattering data from amorphous silica)

What does it tell us?

What we measure:

Site-site radial distribution functions

Atomic scattering lengths or “form factors”

Statistical factors

Partial structure factors, Hαβ(Q) = Sαβ(Q)-1

Self scattering

d σ

d Ω=∑

α

cα bα2+ ∑α ,β ≥α

(2−δ αβ ) cα cβ bαbβ {4πρ∫0

∞

r 2 (gαβ ( r )−1)sin Qr

Qrdr}

A much more tricky question:how do we interpret the data?

• For many years the next step was to simply invert the differential scattering cross-section:

d ( r ) =1

2 π2 ρ

∫0

∞

Q2 F d (Q )sin Qr

QrdQ

= ∑,α β ≥α

(2−δ αβ ) cα cβ bα bβ ( gαβ ( r )−1)

This leads to many problems

• Truncation errors.• Systematic errors.• Finite measuring statistics.• Some site-site terms are more strongly

weighted than others.• These all make interpretation of the

data unreliable.

Neutron kinematics

• Kinematics of neutron scattering:-

Q2=k i

2+k f

2−2 k i k f cos 2θ

ϵ=ℏ

2

2m (k i2−k f

2 )

Properties of the neutron differential cross section –

effect of inelastic scattering

• According to van Hove (1954) the dynamic structure factor, S(Q,ε), splits into two terms:

– The self term, Ss(Q,ε), and a distinct term, Sd(Q,ε).

• The total scattering cross section is related to:-

whered 2 σ

d dε~

k f

k i{ ⟨b2 ⟩S s Q , ε ⟨b⟩2 S d Q , ε }

F (Q)=∫cons.Q

d 2σdΩd ϵ

d ϵ=F s(Q )+F d (Q)

Neutron kinematics

• In a total scattering experiment the neutron detector integrates over all energy transfers ε.

• If this integral is done at Q ≈ constant, we get an instantaneous snapshot of the structure.

• In contrast, the crystallography experiment, by measuring only the Bragg peaks (ε ≈ 0) gives a time averaged view of the structure.

d 2σ

d Ωd ϵ

Time averaged structure

But there is another subtlety...

The total scattering experiment does not

integrate at constant Q!d2

σ

d Ωd ϵ

Fixed incident energy plotEi = 1eV

Increasing 2θ

Fixed incident energy plot Ei = 1eV

Reactor data

Time of Flight diffraction

• Energy dispersive.• Detector at fixed scattering angle.• Detector still integrates at constant

angle, but each time of flight channel corresponds to a range of incident energies:

1R k e

=1k i

Rk f

, k e=Qe

2sin

Constant time-of-flight plots:2θ = 30o

Pulsed Source Data

Effect of energy transfer• For distinct scattering (Placzek, 1952):-

• For self scattering:-

• Mp ≈ Mn means significant energy loss on scattering by protons.

∫Q Ss Q , d =

ℏ2Q 2

2M

∫Q Sd Q , d =0

Introduce: computer simulation

• Requires an atom-atom potential energy function.

• Place computer atoms in a (parallelpiped) box at same density as experiment.

• Apply periodic boundary conditions– the box repeats itself indefinitely

throughout space.• Apply minimum image convention.

Minimum image convention

D

Count atoms out to D/2

Monte Carlo computer simulation

1.Using the specifed atom-atom potential function, calculate energy of atomic ensemble.2.Displace one atom or molecule by a random amount in the interval ±.3.Calculate change in energy of ensemble, ΔU.4.Always accept move if ΔU < 05.If ΔU > 0, accept move with probabilityexp[- ΔU/kT].6.Go back to 2 and repeat sequence.

But there is a problem:

We don’t know the potential energy function!

Introduce Empirical Potential Structure Refinement, EPSR

• Use harmonic constraints to define molecules.

• Use an existing “reference” potential for the material in question taken from the literature (or generate your own if one does not exist).

• Use the diffraction data to perturb this reference potential, so that the simulated structure factor looks like the measured data.

You can read full details in:-

And you can download the software and try for yourself...

http://disordmat.moonfruit.com

Structure refinement of liquid water

Water data after structure refinement

Water partial g(r)’s

The spatial density function of water...

Water structure

(Courtesy Phil Ball, H2O: A Biography of Water)

This is WRONG!

zL

yL

xL

φL

θLr

Beyond g(r): the spatial density function

Choose distance range (0-5.7Å)

and a contour level

(% of all molecules in distance range)

Water under pressure

Water at 298K, 0kbar

Water at 268K, 0.26kbar

The structure of bulk water: two recent papers

The structure of bulk water: two recent papers

Soper 2013

Skinner et al. 2013

• Use separate x-ray and neutron total scattering datasets for H2O and D2O.

• Keep everything else the same except the OH bond length (0.976Å for D2O, 1.006Å for H2O).

Are quantum differences between H2O and D2O

observable?

Soper and Benmore, 2008

Compare with Zeidler et al. 2011

Water in confinement

MCM41 – dry and wet

• Hexagonal array of cylindrical pores in amorphous silica;

• Used to study gas and liquid absorption at the surface;

• Absorbed water claimed to undergo fragile-strong transition when supercooled;

• Claimed density minimum on cooling.

Total scattering pattern from MCM41

Porod (interfacial)scattering

Bragg peaks fromhexagonal lattice

of pores

Atomic structureof silica

Select four runs with increasing N

2 content...

Dry MCM H and D

H and D (100) peak heights almost identical

Wet MCM H and D

Scattering properties of MCM41

• The Bragg intensities depend on the density AND density PROFILE.

ab

(100)

(110)

I (Q)∼⟨∣C (Q)∣2⟩ΩQ

C (Q)=∫ dxdydz (ρ( x , y , z )−ρ0 )exp [i (Q . r)]

y

x


• Can't easily tell if scattering length density of water is > or < substrate.

– For bulk H2O ρs=-0.006

– For bulk D2O ρs=0.064

– For bulk SiO2 ρs=0.034

• H2O/D2O peak intensity changes by ~4.

• This means for D2O ρs= 0.054 or 0.014

• Density of water in pore 20% LOWER than bulk.


• No two samples of MCM41 are the same.

Zhang, PNAS 2011Liu, PNAS 2007 Kamitakahara, JPCM 2012

Mancinelli, JPCB, 2009

Sigma-Aldrich 2010


• We don't know the pore size!

Estimating the pore size.

b

Literature states amount of water absorbed is ~0.4-0.5g/g of substrate

M (r p)=ρW π rP

2 AW

( √32

d2−π rP2 )ρS AS

Literature also states r

P = 7.5Å

My analysis (2012)...Dry MCM H and D

H and D (100) peak heights almost identical

Dry MCM H and D - vary pore radius.

Wet MCM H and D

New EPSR simulations (preliminary results)

33.1ÅDRY

WET

New EPSR simulations

148Å

Dry EPSR MCM simulations

EPSR fits to data at 298K

DryDry

Wet

EPSR fits to data at 210K

Wet

Coordination numbers

210K

300K

LOW!

Coordination numbers

as a function of distance from pore

centre

Ow-Ow

OW-OW-OW triangle

distributions

q = 0.523

q = 0.540

q=1−94

∑ sinθP (θ)(cosθ+13 )

2

∑ sinθ P (θ)

300K

210K

θ

Variation of q across the pore

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

210K

298K

PureWater (2008)

r [Å]

q

Summary (1)

• Total neutron and x-ray scattering techniques provide a sensitive probe of structure in both bulk and confined water.

• Computer modeling of the data is becoming essential, particularly for water in complex environments.

Summary (2)

• For ambient bulk water we now have a set of radial distribution functions which are consistent with a large number of x-ray and neutron datasets.

• For confined water picture is much less clear. In particular the effect of the surface may proceed several molecular diameters into the liquid region

Summary (3)

• For MCM41 observed temperature behavior of (100) Bragg peaks CAN be obtained without changing density.

• For clay systems water strongly polarized by the surface

• Confined water has ~10 - 25% lower density than bulk water.

• Is it really bulk-like?• Increasing tetrahedrality on cooling.

Summary

• We appear to be moving into an era where water in confinement can be studied with considerable detail.

• Beware any experiment that does not first study AND model the total scattering!

Thank you!

a. soper : the structure of water in bulk and in confinement by

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