Structure and dynamics of water in silica nanopores

Branka M. Ladanyi Department of Chemistry, Colorado State University

Fort Collins, CO 80523-1872, USA

National Science Foundation École de Physique des Houches

Back home in Fort Collins – snow most of this week: campus scenes

Monday

Wednesday

Acknowledgments

Dr. Anatoli A. Milischuk Colorado State University

Ms. Vera Krewald – IREU student from Univ. of Bonn, Germany (now a Ph.D. student at MPI-Mulheim)

Coworkers

Funding

National Science Foundation

Liquids in nanopores

Technological significance: Confined liquids play an important role in catalysis, lubrication, separations, oil recovery, cellular dynamics, and microfluidic technology.

Nanoporous silica materials: They have a wide range of applications. Materials with approximately cylindrical pores, with diameters in the nanometer range can be synthesized.

Nanoporous silica materials

Vycor glass (manufactured by Corning) – image constructed from TEM scan (D. P. Bentz, et al., Modell. Simul. Mater. Sci. Eng. 6, 211-236 (1998).

MCM-41 (MCM = Mobil Crystalline Material) http://www.chm.bris.ac.uk/motm/mcm41/mcm41.htm

MCM-41 synthesis

Our simulation of liquids in silica pores Study confinement effects on liquids in approximately

cylindrical pores in amorphous silica.

Study the properties of confined liquids in equilibrium with the bulk liquid phase under ambient conditions.

The focus for this talk: water confined in silica pores of diameters in the 20 – 40 Å range.

Investigation of effects of geometrical confinement and interactions with interface.

Calculation of properties that can be compared with experiments: for water - quasi-elastic neutron scattering (QENS) and optical Kerr effect (OKE).

Simulation procedure and system properties* Pores feature terminating OH groups with surface density

values close to those found in experiments (2−2.5 OH groups per nm2).

Approx. cylindrical pores in amorphous silica produced using cylinder-shaped resists.**

2-box Gibbs ensemble Monte Carlo simulations were conducted to obtain a realistic representation of filled pores at ambient conditions.

This distribution is used as input for molecular dynamics simulations.

*A.A. Milischuk and B. M. Ladanyi, J. Chem. Phys.135, 174709 (2011). ** T. S. Gulmen and W. H. Thompson, Langmuir 25, 1103-1111 (2009). using MCCCS Towhee: http://towhee.sourceforge.net/ using DL_POLY: http://www.cse.scitech.ac.uk/ccg/software/DL_POLY/

Pore parameters

z

Lz=40 Å

Lx = 60 Å

Ly =

60 Å

Diameters: approx. 20, 30, and 40 Å

From T. Yamaguchi, L6: Our pore sizes similar to: Material Diam./Å

MCM-41-C10 21 MCM-41-C14 28 MCM-41-C18 37

Potential parameters

12 6

0

Lennard-Jones + Coulomb potential:

( ) 4( )2 2 4

q qu r

r r rα β α β α β

αβ α β

σ σ σ σε ε

πε

+ + = − +

Water: SPC/E model: H. J. C. Berendsen, J. R. Grigera and T. P. Straatsma, J. Phys. Chem. 91, 6269 (1987). Silica nanopore: Lennard-Jones parameters from A. Bródka and T.W. Zerda, J. Chem. Phys. 104, 6319 (1996); partial charges from T. S. Gulmen and W. H. Thompson, Langmuir 22, 10919 (2006).

What do we calculate?

Interfacial structure and single-molecule translational and rotational mobilities.

Self-intermediate scattering functions – connection with quasi-elastic neutron scattering (QENS).

Polarizability anisotropy time correlations – connection with optical Kerr effect (OKE) response.

Water in silica pores:Snapshot of a pore cross-section

Snapshot of a 40 Å pore, looking down the z-axis.

: Si atoms, red spheres : oxygens, white spheres: hydrogens.

y

x

A.A. Milischuk and B. M. Ladanyi, J. Chem. Phys.135, 174709 (2011).

Water density profiles in pores of different diameters

H2O density in the pores (away from the interface) is about 89% of the bulk liquid water density. Consistent with neutron diffraction data: A.K. Soper - L5

Hydrogen bonding: water-water and water-silica

Mean squared displacements of water molecules

Fits to ‘free diffusion in a cylinder’ model* 2

22 2 1

2 2 21 1 1

t1

Axial direction: [ ( ) (0)] 2

Radial direction:

8[ ( ) (0)] 1 exp( 1)

: axial diffusion coefficient;: radial diffusion coefficient;

: pore radius;:

n

n n n

n

z t z D t

xt R D tx x R

DDRx n

∞

⊥=

⊥

− =

− = − − −

∑ρ ρ

h1

1

zero of ( ) / 0; ( ) : first order Bessel function of the first kind.

dJ x dxJ x

=

*A. Bródka, Mol. Phys. 82, 1075 (1994).

Fit to the model

9 2

9 2

and are in 10 m / s;

2.49 10 m / s bulk

D D

D

−⊥

−= ×

Diam./Å D⊥ D R (Å )

20 1.55 1.55 10.40 30 1.84 1.70 15.35 40 2.25 2.12 20.35

Water: interfacial shells – density and orientational profiles

n̂ OHˆ ˆcosθ = ⋅n u

Mean squared displacements in interfacial shells: 20 Å diam. pore

Mean squared displacement in interfacial shells

Water orientational time correlations: pore diameter dependence

, ,ˆ ˆ ˆ ˆ( ) [ (0) ( )] ; for ( ),l n l n n l OH n OHC t P t C t= ⋅ =u u u u

Water orientational relaxation by region

Dependence of orientational relaxation on nanopore diameter

Orientational relaxation at long times*

Water reorientation time correlation function C2(t), in hydrophilic (blue) and hydrophobic (red) silica nanopores (diam. = 2.4 nm), together with the bulk reference (black), in log-linear (a) and log-log (b) representations.

*From D. Laage and W.H. Thompson, J. Chem. Phys. 136, 044513 (2012)

Power-law decay

Core-shell model for reorientation

Comparison between the reorientational correlation functions C2(t) in silica pores directly obtained from the simulations (dashes ) and reconstructed from a two-state model (solid lines).

2

2 2 2 2 2

pore radius; shell thickness

2( ) ( ) ( ) ( )

.

R core shell core

R

C t C t C t C tR R

∆ ∆ ≅ + − −

= ∆ =

*From D. Laage and W.H. Thompson, J. Chem. Phys. 136, 044513 (2012)

Summary: dynamics of water in silica pores

• Confinement and affinity to pore walls both influence the dynamics.

• Long-time translational mobility is dominated by confinement dimensions.

• Dynamics is heterogeneous and non-bulklike in interfacial regions.

Quasi-elastic neutron scattering (QENS) experiments on water in silica pores

• QENS has been frequently used to study the dynamics of water in SiO2 pores.

• Dynamics are different from bulk: self-intermediate scattering function (ISF) shows pronounced nonexponential decay.

• We investigate* how confinement influences the dynamics observable by QENS.

*A. A. Milischuk, V. Krewald and B. M. Ladanyi, J. Chem. Phys. 136, 224704 (2012).

Example of experimental results: water in Vycor – Q = 1.13 Å-1

J.-M. Zanotti , M.-C. Bellissent-Funel, and S.-H. Chen, Phys. Rev. E 59, 3084 (1999): Fit to a stretched exponential decay:

( , ) ( ) expstF Q t A Q

β

τ = −

Recent experimental results and developments in data analysis for confined water: J.-M. Zanotti – L13 J. Swenson – L14

Quasi-elastic neutron scattering (QENS) • Momentum transfer (Q) typical range: 0.3 - 2.5 Å-1

• Incoherent neutron scattering cross-section for H is 20-30 times larger than the cross-sections for other nuclei.

• Thus the QENS signal is mainly due to water H’s.

Dynamic structure fa 1 (c ,tor: , ) ( )2

i tSS F t e dtωω

π

∞

−∞

= ∫Q Q

( )

( ) { }j

thj

j1

1, exp (0)

FT of the self intermediate scattering function ISF :

number of water H 's; position of the j H atom

)

.

(N

Sj

F t i tN

N=

= ⋅ −

= =

∑Q Q r r

r

Part of ISF due to molecular rotation and translation

CM= +r r b

[ ]{ }( , ) exp (0) ( )CMS CM CMF t i t= ⋅ −Q Q r r

( ) ( ) ( ){ }, exp 0RSF t i t = ⋅ − Q Q b b

rCM

r b

( ) ( ){ }rigid mol., ( ) ,S SF t V Q F t≅Q Q

( ) ( ){ }( ){ } ( ) ( )

rigid mol.

R,CM

, ,

, , ,

S S

R CMS S S

F t F t

F t F t F t

=

= ≅

Q Q

Q Q Q

Product approximation often used to analyze expts.– its accuracy can be checked via MD

Dominates at low Q

Becomes important at higher Q

Vibrational Debye-Waller factor

Product approximation test

( ) ( )( ) ( ) ( )

, ,

, , ,S P

R CMP S S

F t F t

F t F t F t

≅

=

Q Q

Q Q Q

Total ISF: dependence on pore diameter

Translational (CM) and rotational (R) contributions

Axial and radial components – total ISF

z

Axial and radial components – CM and rotational ISFs

Comparison with free diffusion in a cylinder model*

radial axial

*A. J. Dianoux, M. Pineri, and F. Volino, Mol. Phys. 46, 129 (1982).

Translational ISF in interfacial shells

Rotational ISF in shells: axial and radial components in shells

Water orientation relative to the interface

n̂ OHˆ ˆcosθ = ⋅n u

Summary of results relevant to QENS

Observable dynamics at longer times is dominated by molecules in interfacial layers.

In the range of silica pore sizes considered, these dynamics are mainly dependent on proximity of molecules to the interface.

Effects of pore anisotropy may be important, especially for experiments probing mainly translational dynamics.

Water dynamics: optical Kerr effect experiments

OKE results for water in silica pores (radii are indicated) and bulk water. The data sets have been displaced from one another for clarity. A. Scodinu, and J. T. Fourkas, J. Phys. Chem. B 2002, 106, 10292-10295.

( ) polarizability anisotropy time-correlation ( ) (in our notation)

collC tt

=

= Ψ

Comparison* to OKE experiment**

* A.A. Milischuk and B.M. Ladanyi, work in progress. ** A. Scodinu, and J. T. Fourkas, J. Phys. Chem. B 2002, 106, 10292-10295.

Polarizability anisotropy time correlation

M I= +Π Π Π

2

1( ) (0) ( )xz xzt tΨ = Π ΠΓ

1 1(; )

N NI

i ij jj

NM

ii ii

== ≠

≅ ⋅ ⋅= ∑∑∑ Π α T r αΠ α

2

5

3( ) rr−

=rr 1T r

2 2 /15NγΓ =

z

x ( ) ( ) ( )2 222 12 xx yy xx zz yy zzγ α α α α α α = − + − + −

3 3 3

3 3

1.04 1.00 Å , Å , Å

Å ,

1.17

1.07.1 4 Å0 5xx yy zzα

γ α

α α

=

= = =

=

Interaction-induced Molecular

*M.T. Sonoda, S.V. Vechi and M.S. Skaf, PCCP 7, 1176 (2005).

Molecular polarizability components*

Contributions to polarizability anisotropy relaxation

M I= +Π Π Π ( ))) ) ((( MM MI IIt ttt Ψ ΨΨ + +Ψ=

How much the response is due to water reorientation?

( )2

local field acting on molecular polarizability component

portion of interaction-induced polarizabi

;

(1 )

lity that is dy

;1

namic.

Rxz xz xzR Mxz xz xz

xz

M I Mxz xz xz xz

I Mxz xz xz xz

xz

GxzG

G

G

Π = Π + ∆Π

Π = + Π

+

= Π Π Π

∆Π = Π

=

=

− Π

∆Π ally

distinct from .MxzΠ

We can answer this by considering the local field effects that modify the effective molecular polarizability anisotropy.*

*T. Keyes and D. Kivelson, J. Chem. Phys. 56, 1057 (1972); D. Frenkel and J.P. McTague, J. Chem. Phys. 72, 2801 (1980).

(( )) ( )( )R RR t ttt ∆∆∆Ψ ΨΨ + +Ψ=

Implementing the projection scheme (( )) ( )( )R RR t ttt ∆∆∆Ψ ΨΨ + +Ψ=

Collective reorientation is the major relaxation mechanism.

Relaxation rates – collective vs. single-molecule reorientation

1

,2

2

1

15 (0) (0

15 (

)(

0) ( ))

)

(

;

Nxz xzi i

iMM s

M Mxz xz

N

M

Mi

i

M

tt

N

tNγ

α α

γ

=

=

Π ΠΨ =

=

=

Ψ

∑

∑

Π α

Relaxation rates – water in silica pores

Summary of results relevant to OKE

Relaxation rate is strongly dependent on pore diameter.

Rotational relaxation is the major contributor, despite small molecular polarizability anisotropy.

Collective reorientation contributing to OKE does not differ much for single-molecule reorientation.

Thank you for your attention!