a. soper : the structure of water in bulk and in confinement by
TRANSCRIPT
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)
1%
2%
3%
4%
5%
7%
9%
12%
15%
18%
21%
25%
30%
Water under pressure
Water at 298K, 0kbar
Water at 268K, 0.26kbar
Water at 268K, 2.09kbar
Water at 268K, 4.00kbar
The structure of bulk water: two recent papers
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
Scattering properties of MCM41
• 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.
Scattering properties of MCM41
• No two samples of MCM41 are the same.
Zhang, PNAS 2011Liu, PNAS 2007 Kamitakahara, JPCM 2012
Mancinelli, JPCB, 2009
Sigma-Aldrich 2010
Scattering properties of MCM41
• 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!