X-ray Photon Correlation Spectroscopy from Liquid

Surfaces

Laurence Lurio

Department of Physics

Northern Illinois University

X-ray Photon Correlation Spectroscopy & Microbeam SAXS at NSLS-IIBrookhaven National Laboratory January 8, 2008

Collaborators

• Xuesong Xiao, Rakesh Vasudevan (NIU)• Zhang Jiang (PhD Thesis) , Mrinmay Mukhupadhyay,

Sunny Sinha (UCSD)• Hyunjung Kim (Sogang U. Korea) • Jyotsana Lal, Xuesong Hu (IPNS) • Suresh Naryanan, Michael Sprung, Alec Sandy (8-ID

ANL)• Simon Mochrie, Yale University• Miriam Rafaelovich, SUNY Stonybrook

Outline

• Surface XPCS from a liquid polymer (PS)

• Dynamics of a buried liquid-liquid interface (PS/PBrS)

• Future prospects for surface XPCS

• Implications for NSLS II

Example 1: Polystyrene Melts

Varnik et. al. EPJE, 2002

• A nice model liquid. Well characterized physical properties and slow dynamics.

• Study how polymer dynamics is modified by confinement.

• Study dynamics in a glass-forming thin film.

X-ray scattering as a Probe of Polymer Structure

• Traditionally polymer structural measurements are done using neutron scattering. Deuteration provides a contrast mechanism.

• X-ray scattering measures correlations in electron density, thus to see structure need a contrast mechanism, e.g. a density variation

• Melt/vapor interface gives a strong contrast between vacuum and polymer. Also can get contrast at a liquid/liquid or liquid solid interface.

Structure at the Liquid-Vapor Interface is dominated by thermally driven

capillary wavesLinearized Navier-Stokes Equation

2dvP v

dt

Note that for films whose thickness is comparable to the capillary wavelength, the dynamics of the capillary wave probe motion throughout the entire film.

Thermal Capillary Wave Roughness

• Each mode carries energy

• X-ray scattering intensity is approximately given by

Bk T

2( ) B

R

k TS q

q

2 22 2 ( )e e xy

dr A T T S

d

q

For small q

What you learn by scattering x-rays from capillary waves

• Amplitude of scattering measures surface tension.

• Relaxation rate of capillary waves probes viscoscity.

• Wavevector dependence of relaxation rate probes hydrodynamics within film.

• Wavevector dependent cut-offs measure Van der Waals forces and shear modulus.

Scattering Geometry

2 /

ˆ

f i

r

k

Q k k

Q Q n

8-ID-I at Advanced Photon Source

Diffuse scattering fits model exactly

Scattering of Coherent X-rays

( ) iQ re eI Q e r r r drdr

���������������������������� ��������������������������������������� ���

For incoherent x-rays the actual scattering represents a statistical average over many incoherent regions within the sample and one obtains:

e e e er r r r r r g r ����������������������������������������������������������������� �����

For coherent x-rays one measures the Fourier transform of the exact density distribution, not the average. What one observes is a speckle pattern superposed on the average scattering pattern.

Time correlation functions

2 2

( , ) ( , )( , )

( , )

I q t I q tg q

I q t

2 2

( ) ( )( )

I t I tg

I

Single Layer Dynamics• Time required for a surface mode of wavevector

q=2/ to relax.

• Use linear response theory to calculate the susceptibility of surface height fluctuations. For viscous fluid find overdamped modes which decay exponentially.

• Time correlation of the x-ray scattering pattern yields the decay times ( , ) exp 2 /g q t q

Single Layer Time Constants 2 2

2 sinh 2

2 1 2 cosh 2

k kh kh

h k hk

3 4

2 3 1 for 0

2kh

k kkh

2 1 for kh

k k

2

Overdamped /

For deep waves, use dimensional analysis

only dimension is wavevector,

Expect /

s

s

b k

k

k k

b k

k

J. Jäckle, J. Phys.: Condens. Matter 10 (1998) 7121.

For scaling arguments for thin films see Brochard and de Gennes, Capillarity and Wetting

Dynamics for PS films supported on Silicon(Thick films, T>>Tg)

Hyunjung Kim et. al. PRL 2003

1.0E+0q

||h

1.0E-3

1.0E-2

1.0E-1

1.0E+0

/h (

sec/

nm)

T = 150 °C

T = 160 °C

T = 170 °C

2.0E-1

84 nm (circ.), 177 nm (triang.), and 333 nm (diam.).

36.1 sec

q||= 8.92E-4 = 7.8 sec

q||= 1.23E-3 = 1.5 sec

1.00

1.05

1.10

124.0 sec

0.1 1.0 10.0 100.0

0.1 1.0 10.0 100.0time delay (sec)

0.1 1.0 10.0 100.0

1.00

1.05

1.10

1.00

1.05

1.10

1.00

1.05

1.10q||= 5.87E-4 =

g 2

q||= 3.85E-4 =

0.1 1.0 10.0 100.0

What about x-ray damage

• Samples begin to damage after around 1000s. • In poor vacuum samples last ~100s, probably

due to ozone.• Several ways to probe for damage:

– comparing correlation functions. – measurement of specular reflectivity before and after

exposure. – examination of sample under an optical microscope.

• Damage threshold ~108 Gy (vs. 107  Gy for protein crystallography (Tang & Moffat JSR 2000)

Why is the contrast so small?

• Longitudinal Coherence Length• • Coherence requires• In transmission• Coherence requires

L

2 21/

2PLD Q L k

42 10xq

cos cos /xPLD L q L k

/ 0.5μm

10.4nmxq

Close to Tg

T = 110Cq=.018 nm-1 , 129K 160 nm (thick film limit)

•Relaxation becomes a stretched exponential.

•Viscosity much smaller than bulk

Results for films with h~Rg Jiang et. al. PRL 2007

• Films thinner than ~2 Rg, q dependence changes.

• Fitting requires the addition of a shear modulus

• Films with ~1Rg appear to be static

( )G i

Example 2: Dynamics from a Buried Interface

• PS/PBrS bilayer• Independently

measure dynamics at interface and surface.

• Use x-ray standing wave for depth resolution.

Interest in Polymer bilayers

• Technologically important system– Co-extrusion of polymers– Mechanical toughness– Optical multilayers

• Physics of the polymer interface– Physical parameters: viscosity, interfacial

tension.– Intermixing, Entanglement, Slip– De-wetting Mechanisms– Tg depression

Select an interface using an x-ray standing wave excited through a grazing incidence beam

(0.14◦ and 0.18 ◦)

Autocorrelation functions-205oc

Single layer PS Bilayer

interface

surface

1 22/ /

2 1 (1 ) t tg t r e re

Wavevector Dependence of Dynamics

stick

slip

195C 100 nm PS/200 nm PBrS

Slow mode of top interface

Single mode of bottom interface

Mode of single layer PS

Fast mode of top interface

Results of Bilayer Measurements

•A PS film on-top of a PBrS layer shows faster dynamics than the same thickness PS film on a Si substrate

•Time independent dynamics consistent with the Maxwell relaxation time determined by a sheer modulus for a thin interfacial layer. Value is (within uncertainty) identical to that found for thin PS homopolymer films.

•Experiment inspired theory: Zhang et. al. PRE, 2006 (Separate interface region) , Henle & Levine PRE, 2007 (Slip length model, with only two layers)

•Results for separate interface model

2

2

/

18N / m

327Ns / m

Future Prospects for Surface XPCS

• Can the dynamics of biological systems in aqueous media be measured with XPCS?

• Start with something simpler: Dynamics of biomimetic membranes: e.g. phospholipid bilayers supported with a soft cushion on a substrate

• XPCS measures dynamics normal to the surface as opposed to Fluorescence techniques which measure in-plane dynamics.

From Tanaka, MRS Bull. 2006

Are the technical problems solvable?

• Dynamics in the microsecond to millisecond range: need enough coherent flux to get usable SNR.

• Easily flux damaged samples: don’t want too much flux.

Beam Damage• If present systems are close to the damage threshold,

does this mean it will be impossible to measure faster systems?

• Figure of merit:

• If you have as much coherent flux as you need and you are willing to translate the sample out of the beam once per correlation time then the beam damage is given by

• Thus for a fixed SNR, with a translated sample

• Measuring fast dynamics will give less rather than more beam damage

/corr meas corrSNR T T T

corrDamage T

/corr measDamage SNR T T

Is it doable?

• Measurements (so far unsuccessful) of XPCS from protein suspensions indicate a damage threshold ~100-1000 times lower than for polymers films. It is not clear where phospholipids would damage, but assume worst case.

• If dynamics are ~ 1 ms and if contrast can be brought up to 100% and if the detector efficiency can be brought to 100% than this implies a reduction in damage by

41000 1 15 10

.001 .05 .4

s

s

Can you can do even better?

• Blowing up the beam size reduces the SNR as the square root of the beam area. Damage is reduced as the area.

• Increasing the beam energy reduces the beam damage as E3 but only decreases the SNR as E-2.

• Note that both of these methods decrease the SNR however they decrease the damage even faster. They are only feasible with lots of coherent flux to waste.

Implications for NSLS II

• Surface XPCS experiments may require narrow energy resolution.

• Design beamlines for close to 100% coherence, even at some cost in SNR.

• Scatter at higher energies (15 keV) but only if there is enough flux to offset the cost in SNR

• Provide mechanisms to translate samples through the beam.

• Provide focusing options to increase or decrease beam size.

Detectors must be improved

• Fast readout

• High efficiency

• Low noise

• High spatial resolution

• Selective ROI readout

Thanks to:

• National Science foundation grants DMR-020954 and DMR-0706369