x-ray photon correlation spectroscopy€¦ · x-ray photon correlation spectroscopy anders madsen,...

XX--ray Photon Correlation Spectroscopyray Photon Correlation Spectroscopy

Anders Madsen ESRF

Coherence

X-ray Speckle

Photon Correlation Spectroscopy

Applications of XPCS

Coherence

Quantum mechanics probability amplitudes (waves) Optics Youngs double slit experiment interference X-ray (and neutron) scattering

Its all about probability amplitudes and interference

Example Youngs double slit experiment (Thomas Young 1801)[wave-character of quantum mechanical particles (photons)]

Plane mono-chromatic wave

P=|ΣjΦj|2Φ probability amplitudeΦj ~ exp[-i(ωt-klj)]ω=ck k=2πλ lj(Ly)

P(y) ~ cos2(πydλL)∆y=λLd

Anders Madsen X-ray coherence lecture series ESRF June 30 2008

Reasons for loss in (visibilityinterferencecoherence)

1) Incoherent superposition of probability amplitudes P=Σj|Φj|2(distinguishable alternatives uncertainty principle)

2) Intensity interference is only observed if event is repeated many times repetition under non-ideal conditions washes outthe visibilityUsing a (partially) coherent X-ray source 2) is a major limitation

Non-ideal conditions Ein Eout kin kout not well defined in the experiment Disorder in the scattering sample Limited detector resolution (temporal and spatial) The source is chaotic


Light sources

Chaotic sources (spontaneously emitted photons)Lab X-ray generatorsSynchrotron and Neutron sourcesRadioactive nuclei

One-mode sources (stimulated emission Glauber light)Unimodal lasers

Important parameter NC=photons pr coherence volumeNC ~10-3 for typical ESRF undulatorNC ~107 for typical optical laser

Beam direction

lv

lhCoherence volume Vc πlh lv ll 4horizontal vertical and longitudinal (temporal) coherence length

ll


Chaotic source (ESRF undulator) (spontaneous independent emission in all modes)

Longitudinal (or temporal) coherence

Spatial coherenceAnalogy with Youngs double slit experiment Transverse coherence length (vh) lvh=λLπdvh (~2-150 microm)

0ττ

2

(1) e

|E(t)|τ)(t)E(tE

)(g minus= prop

+τ

At times gtgt τ0 the field amplitudes from a chaotic source are no longer correlated due to the wavelength spread

τ0 = 1(π∆ν) = λ2(cπ∆λ) (~3fs)Longitudinal coherence length ll = cτ0 = λ(π∆λλ) (~1microm)

(Gaussian 1st order time-correlation function)


Important source parameters

Brilliance B = photonssec [source area times solid angle times bandwidth]

Lateral coherence area At=πlhlv4=(λL)2(4πdhdv) (~200 microm2)Νc=photons in Vc (Vc = Αt times ll)

Coherent solid angle ΩC=AtL2=λ2(4πdhdv)= λ216As

Νc=B times τ0 times As times λ216As times ∆νν = Β λ3 (16πc)Coherent intensity Ic = (ΝcVc) times c times At

= B times (λ4)2 times (∆λλ) (~1010 phs)

As=πdhdv4

Coherent intensity decreases with decreasing λ (increasing energy) Coherent scattering is very Brilliance-hungry


Coherence lengths

λ=21Aring d=11micromVisibility(β) ~ 80

Example Youngs double slit experiment with X-rays


∆y=λLdLeitenberger et al Physica B 336 36 (2003)

Transverse coherence length (vh) lvh=λLπdvh (~5-250 microm)

Longitudinal coherence length ll = cτ0 = λ2(π∆λ) (~1microm)

Contrast β asymp (coherence volume)(scattering volume)

ESRFvalues


Setup for coherent X-ray scattering

Coherence parametersTransverse coherence length lhv=λL(πdhv)Longitudinal coherence length ll=λ2(π∆λ)Contrast (degree of coherence) β=β (∆λλ )

IC prop B times λ2

ID10AIc ~2e8 phs (1997)Ic gt1e10 phs (2008)


Fraunhoferdiffraction

from slit


Coherent scattering What is the information we gain

If coherent light is scattered from a disordered system it gives rise to a random (grainy) diffraction pattern known as speckle A speckle pattern is an inter-ference pattern and related to the exact spatial arrangement of the scatterers in the disordered system (no averaging)

I(Qt) prop Sc(Qt) prop | sum e iQRj(t) |2j in coherence volume Vc=lv lh ll

D Abernathy et al

J Sync Rad 5 37 (1998)

Aerogel SAXSλ=1AringCCD (22 microm pixels)10 micron beamsize

speckle size ~λd


Longitudinal coherence length and scattering geometry

PLD Path Length Difference lt ll CSAXSPLD = t + BC - AC asymp d tan(2θ)

Bragg geometryPLD asymp 2(micro-1)sin2θ

Grazing Incidence PLD asymp 2Λsinαi

2θAd

Bt

θ

Condition PLD lt ll SAXS d=10microm λ=155Aring ∆λλ=14times10-4 rarr θMAX asymp1o rarr QMAX asymp 015Aring-1

Reflection micro-1Cu= 22microm λ=155Aring ∆λλ=14times10-4

rarr θMAX asymp 5o rarr QMAX asymp 07Aring-1


What is the contrast of the setup

Gamma-Poisson distribution of intensity coming from M statistically independent superimposed speckle patterns PM(I)=(MltIgt)MIM-1exp(-MIltIgt)Γ(M)σ2=ltIgt2M 1M=β

Coherent SAXS 8keV

Incoherent fraction

10 micron beam

VycorTM silica glass

Static speckle pattern

contrast β=1M=1281=356M ~ VscatteringVcoherence

Statistical speckle analysisPrinceton Instruments CCD1 Photon gives 879 adu2 Photons give 1758 adu


What is the shape of a speckle

200 400 600 800 1000 1200

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20 40 60

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20 40 60

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minus5 0 5

x 10minus4

0

001

002

003

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005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

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minus5 0 5

x 10minus4

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001

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∆Q

horizontal direction

0 002 0040

002

004

006

008

01

Q

20 40 60

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minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles


Pink beam ID10C (∆λλ=15)E=8keV 20microm beamsizeIcoherent gt 1x1011 phs

XPCS What is the information we gain

real space

non-coherent coherent

reciprocal space

ltI(Q)gt I(Qt) I(Qt)

DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ

Temporal intensityauto-correlation function

int int minussdotpropV V

mnmn tibbtf )])()0([exp()()(|)(| rrQQQQ

220 )()]([

1~)(QQ

QSΓ+minus ωω

ω

)(cos)2exp(1)( 02)2( τωττ Γminus+=Qg

)2exp(1)()2( ττ Γminus+=Qg

Dynamic structure factor(Lorentzian shape)

(propagating waves)

(Brownian motion overdamped waves)


Scattering Vector Q [Aring-1]

Length Scale [Aring]Fr

eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges

Non-ergodicity ie ltgtt ne ltgtφ (time average different from ensemble average)

systems that do not sample the entire allowed set of spatial configurations

Typical example samples with some degree of (quasi) static disorder (gels glasses etc)

To properly calculate g(2) the ensemble averaging ltgtφ must be performed explicitly

Pusey amp van Megen Physica A (1989)

I(t) I(t)

tt


Challenges



Solution move the beam around and average g(2) over many exposures

or (much better)

Use a 2D detector and catch many pixels with same |Q|

Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges

Non-equilibrium ie not all ∆t are equivalentg(2) depends on both ∆t and the absolute time (age)

Solution calculate the correlation function without time averaging (two-time correlation function)

φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1

Only with a 2D detector several Qs at same age can be recorded


2d detectors for multi-speckle XPCS

Advantages More efficient data-taking (Mpixels) with 2d detectorBeam induced sample damage minimized

Drawbacks 2d detectors are slow noisy have limited dynamic rangeare not always photon counting have limited resolutionradiation hardness can be a problem

Princeton Instruments Dalsa MedipixMaxipix


Limitations

sn ratio (more flux)

Speed and area of 2D detectors

Beam damage (minimize exposure)

Medipix-II detector 1kHz ff


Depletion gel

Inter-particle interaction potential

V(r)Complex phase diagramrgR (01) φ (20) cp (43mgcm3)

2rg

2R

r


The gel phase is transienthellip

W C K Poon et al Faraday Discuss 112 143 (1999)

delayedsedimentationageltt (latency time)


hellipbut the structure is constant in the accessible Q-range

Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG = Kohlrausch-Williams-Watts (KWW)

g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)


A jamming transition

(a) young gel(b) fully aged gel

relaxation timevs age

stretching exponentvs age

Phys Rev E 76 010401(R) (2007)


Jamming

Characteristic features

crowded media intermittent dynamics lt∆x2gt prop t2 (or Q prop Γ) cooperative behavior aging

Micro-collapses

Kohlrausch-Williams-Watts (KWW) g(2)(t) =1+exp(-2(Γt)γ) with γ~15

Bouchaud amp Pitard EPJE 6 231 (2001)

V Trappe et al Nature 411 772 (2001)


The Glass Transition(solid like behavior of liquids)

Characterized by several distinct relaxations in the super-cooled state TltTm

Non-Arrhenius behavior of the viscosity

Form glasses below Tg depending on the cooling rate

From Pablo G Debenedetti and Frank H Stillinger Nature (2001)


Recent results on surface dynamics

Capillary waves on highly viscous liquids Γ = 2γη Q

What happens as ηinfin ie at the transition from asupercooled liquid to a glass

What happens with the shear response as the liquid solidifies

RHEOLOGY (modulus=stressstrain)

Liquid deforms cont under stressSolid equilibrium deformation under stress

Liquid stress relaxes under a constant strainSolid constant stress level under constant strain


Grazing incidence XPCS

beamstop

αi lt αc

deflectingmirror

sample(liquid or solid)

monochromaticsynchrotron beam

Specklepattern

slits

2D detector

pinholeaperture

coherent intensity Ic prop Bλ2

Intensity fluctuations of the speckle pattern reflect the dynamics of the sample

2)(

)()0()(

tqI

tqIqItqg =XPCS Intensity auto-correlation function


CW dynamics on supercooled poly-propylene glycol (PPG)

All functions are simple exponential decays

Characteristic times change 5 ordersof magnitude from 280 to 214K (Tg ~ 205K)




qηγ2

=Γ

Newtonian liquid


Models for viscoelasticity

Liquids near the glass transition Viscosity and elasticity become important viscoelasticity

Kelvin-Voigt model(viscoelastic solid)

Maxwell-Debye model(viscoelastic liquid)

Over-damped capillary wavesNewtonian liquid

η

EE η

ηγ2q

=Γ

)()( ωωηω iG = EiG += 0)( ωηω

ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ

This is what we observeeven far above Tg

1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ




Combined Maxwell-Debye and Kelvin-Voigt model

EiG += )()( ωωηω

ωτηωηi+

=1

)( 0Maxwell Debye E Elasticity fromVoigt-Kelvin

10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0

Γ G(infin)η for q infin

q0=2Eγ


CW dynamics on poly-propylene glycol (PPG)

10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ


Viscoelasticity of poly-propylene glycol (PPG)

XPCS of CWs is a genuine way to measurelow frequency response of glass forming liquids

Low frequency elasticity of (supercooled) liquids is an extremely controversialtopic in the literature and non-invasive experimental methods are missing

η~exp(A(T-T0)) VTF law

E~exp(A(T-T0)) VTF law

Chushkin Caronna and Madsen EPL (in press)


Next topic Nano-particles in supercooled liquids

Or should I stop here


Dynamics of nano-particles in a glass forming solvent

Samples Nano-spheres in a glass forming solvent

Silica R=250nm

Solvent Propanediol (TG ~ 170K)Liquid at elevated temp (η ~ 01 Pas 290K)

httpwwwesrffrnewsspotlightspotlight39spotlight39xpcsAnders Madsen X-ray coherence lecture series ESRF June 30 2008

Simple Diffusion and Hyper-Diffusion

Ballistic motion x = vt lt[x(t)-x(0)]2gt = ∆x2 = v2t2 Q prop 1x prop 1t = Γ

Brownian (random walker) motion lt[r(t)-r(0)]2gt = 6D0t Q2 prop Γ

D0 self-diffusion constant

D0=kBT6πηR (Einstein 1905)

g(2) ~ 1 + exp( -2Γt ) Γ = D0Q2 for Brownian motion


Dispersion relations

Γ[s-1

]

QR

Silica nano-particles (1 vol) in supercooled propanediol

n=2(Brownian motion)

n1(Hyper diffusion)


Correlation functions

Results QR=675

240K simple exponential decay

205K decay faster than exponential

γ=1

γasymp17

Fits with empirical model (KWW) g(2) =1+exp(-2(Γt)γ)


XPCS results n = 2

n = 1

Lines are guides to the eyeAnders Madsen X-ray coherence lecture series ESRF June 30 2008

Model for particle dynamics

2)2( |)(|1)( tQftQg +=Continuous time random walk model

suminfin

==

0)()()(

Nt NQhNPtQf

)exp()( RQ sdotminus= αiNNQh

R

α=1 h(N+1)=h(N)h(1) (ballistic motion)

α=12 Brownian motion (simple diffusion)

αlt12 sub-diffusionαgt12 hyper diffusion

P(R) distribution of R (Gaussian)lt|R|gt=δ

))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α


The fits with the KWW form f(t) =exp(-(Γt)γ) are perfect The model explains the KWW exponent γ

α=1(ballistic)



Results

Caronna Chushkin Madsen and Cupane PRL 100 055702 (2008)


Results

Tg=170K (by DSC)

The transition from simple diffusion into event dominated hyper-diffusion is caused by elastic relaxations of the solvent kicking the particles

Those excitations become more important than diffusion at around 12Tg

This again shows that the solid like response of supercooled liquids dominates as the viscosity gets high close to Tg (to be continued)


Further reading

Magnetic colloids J Appl Cryst 40 250 (2007) J Phys Cond Mat 18 S2697 (2006)

X-ray fluorescence correlation spectroscopy J Appl Cryst 40 283 (2007)

Charge stab colloids J Chem Phys 126 104905 (2007) Phys Rev Lett 96 138303 (2006)

SrTiO3 displacive transition Phys Rev Lett 98 105501 (2007)

Nano-particles on the surface of thin polymer films Phys Rev Lett 98 047801 (2007)

Dynamical heterogeneity in colloidal gels Phys Rev E 76 051404 (2007)

Transient gelation Phys Rev E 76 010401(R) (2007)

Partially wetting thin liquid films Phys Rev Lett 99 096104 (2007)

Bulk fluctuations in a lamellar phase Phys Rev E 74 031706 (2006)

Coarsening dyn in alloys Phys Rev B 73 180101 (2006) Phys Rev E 74 041107 (2006)

Glass-glass transition in attractive colloids Phys Rev E 74 051504 (2006)

Ordering Kinetics in a Cu-Pd Alloy Phys Rev B 72 144201 (2005)

Grazing incidence XPCS J Sync Rad 12 786 (2005)

XPCS Microrheology J Phys Condens Matter 17 L279 (2005)

Dynamics of fluctuations in smectic membranes Phys Rev E 72 011704 (2005)

XPCS Journal of Alloys and Compounds 362 3 (2004)

General conclusion on XPCS

XPCS is the X-ray counterpart to PCS (DLS) with the obvious advantages of X-rays over visible light

Larger Q-range Surface sensitivity Penetration power

No (or only little) multiple scattering

Difficulties arise from the fact that the synchrotron is a chaotic source and intensity is lost when a coherent beam is defined

Brilliance hungry technique but samples are often radiation sensitive

Interesting perspectives with X-ray lasers coming on-line butXPCS at storage ring based sources (quasi DC) will remain competitive


Coherence

Quantum mechanics probability amplitudes (waves) Optics Youngs double slit experiment interference X-ray (and neutron) scattering

Its all about probability amplitudes and interference

Example Youngs double slit experiment (Thomas Young 1801)[wave-character of quantum mechanical particles (photons)]

Plane mono-chromatic wave

P=|ΣjΦj|2Φ probability amplitudeΦj ~ exp[-i(ωt-klj)]ω=ck k=2πλ lj(Ly)

P(y) ~ cos2(πydλL)∆y=λLd







Light sources




Beam direction

lv


ll





0ττ

2

(1) e

|E(t)|τ)(t)E(tE

)(g minus= prop

+τ











As=πdhdv4



Coherence lengths








ESRFvalues




IC prop B times λ2




from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading






























Light sources




Beam direction

lv


ll





0ττ

2

(1) e

|E(t)|τ)(t)E(tE

)(g minus= prop

+τ











As=πdhdv4



Coherence lengths








ESRFvalues




IC prop B times λ2




from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading




























0ττ

2

(1) e

|E(t)|τ)(t)E(tE

)(g minus= prop

+τ











As=πdhdv4



Coherence lengths








ESRFvalues




IC prop B times λ2




from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading































As=πdhdv4



Coherence lengths








ESRFvalues




IC prop B times λ2




from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Coherence lengths








ESRFvalues




IC prop B times λ2




from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading



























IC prop B times λ2




from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading


























from slit





D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading




























D Abernathy et al

J Sync Rad 5 37 (1998)


speckle size ~λd






2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading





























2θAd

Bt

θ







Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading



























Coherent SAXS 8keV

Incoherent fraction

10 micron beam







200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading


























200 400 600 800 1000 1200

200

400

600

800

1000

1200

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

vertical direction

0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q


0 002 0040

002

004

006

008

01

Q

20 40 60

10

20

30

40

50

60

70

20 40 60

10

20

30

40

50

60

70

minus5 0 5

x 10minus4

0

001

002

003

004

005

∆Q

diagonal direction

0 002 0040

002

004

006

008

01

Q

3

1

2

1 2 3

elongatedspeckles




real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading


























real space


reciprocal space


DynamicsKinetics


What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























What do we measure

2)2(

)(

)()()(

Q

QQQ

I

tItIg

ττ

+=

22~)2( |)(|1))((Re1)( tfSg QQQ +=+= ωτ




220 )()]([

1~)(QQ

QSΓ+minus ωω

ω




(propagating waves)





eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading



























eque

ncy

[Hz]

Energy [eV]

Raman

Brillouin

XPCSPCS

IXS

Spin-Echo

INS

NFS

Other techniques


Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Challenges






I(t) I(t)

tt


Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Challenges




or (much better)


Medipix-2

Ttp

Ttp

tpp

tItI

tItIQg

leleminuslele

+=

τφτφ

φτ

τ)()(

)()()(

0

)2(


Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Challenges



φφ

φ)()(

)()()(

21

2121 tQItQI

tQItQIttQG =

t1

t2

G(t1t2) age

τ

age ta=(t2+t1)2

lag time τ=t2-t1








Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading






























Limitations






Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Depletion gel



2rg

2R

r







Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading






























Phys Rev E 76 010401(R) (2007)


Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Two time analysis

φφ

φ)()(

)()()(

21

2121 tQItQI


g(2)(τ) =1+exp(-2(Γτ)γ)

γlt1

γ~1

γgt1

age

τ=t1-t2

Phys Rev E 76 010401(R) (2007)






Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading





























Phys Rev E 76 010401(R) (2007)


Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Jamming



Micro-collapses




















beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading








































beamstop

αi lt αc

deflectingmirror



Specklepattern

slits

2D detector

pinholeaperture



2)(

)()0()(

tqI









qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading































qηγ2

=Γ

Newtonian liquid







η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading






























η

EE η

ηγ2q

=Γ


ωτηωηi+

=1

)( 0

ωηωη

iE

+= 0)(

002 ηηγ Eq

+=Γ

0

)0(ηE

=Γ


1

0 21

2

minus

+=Γ

Gqq γ

ηγ

0)0( =Γ






ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading





























ωτηωηi+

=1


10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ

Γ Eη for q 0


q0=2Eγ



10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading


























10

0

0)(2)(1

2)( minus

infin

++

+=Γ

Gqqqq γ

ηγ














Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading





































Silica R=250nm











Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

































Γ[s-1

]

QR



n1(Hyper diffusion)



Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading


























Results QR=675



γ=1

γasymp17



XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























XPCS results n = 2

n = 1




suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading



























suminfin

==

0)()()(

Nt NQhNPtQf


R





))(exp()( 00

NttNP

Nt

ΓΓminus=

MSD ~ t2α



α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading


























α=1(ballistic)



Results



Results

Tg=170K (by DSC)





Further reading

























Results



Results

Tg=170K (by DSC)





Further reading

























Results

Tg=170K (by DSC)





Further reading

























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