andrei fluerasu, fluerasu@esrfandrei fluerasu, x-ray photon correlation spectroscopy and µbeam...
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X-ray photon correlation spectroscopy (XPCS) in microfluidic systems
Andrei Fluerasu, [email protected]
ID10A (Troïka), Soft Condensed Matter Group, ESRF, Grenoble, France
Flow = 15.0µl/hr
0.01 1.0
0.0
0.5
1.0
t(s)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 1
Outline
• Introduction to X-ray Photon Correlation Spectroscopy (XPCS)→ Coherence and Speckles→ Diffusive dynamics of colloidal suspensions→ “Standard” (single-speckle) and multispeckle XPCS
• XPCS-microfluidics: measuring the mesoscale dynamics in sheared complex fluids→ Motivations→ SAXS-compatible microfluidic devices→ XPCS in a shear flow→ “transverse” (Q⊥v), “longitudinal” (Q ||v) scattering geometry
• Slow dynamics and aging in colloidal gels→ Colloid / polymer mixtures: phase behaviour→ Non-equilibrium and non-stationary dynamics: two-time correlation functions→ Jamming phenomena; jamming transition in aging colloidal gels→ Colloidal gels in microfluidic devices
• Conclusions & Outlook→ XPCS-flow experiments in soft-matter model systems and biological systems
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 2
Coherent XRD: speckle, XPCS
Q =(4π
λ)
sin(Θ
2
)
I(Q, t) = Np∆ρ2V2pP(Q)S(Q, t)
P(Q) - particle form factor
Structure factor:
S(Q, t) = 1N
∑Ni, j=1
⟨
e−iQ(r i(t)−r j (t))⟩
ik
pinholeguard slits
sample
beamstop
CoherenceWhat interferes? Probability amplitudesΦ regarding microscopic states compatile with themacroscopic state of the system!P=|Φ|2: probability for a single event
I →P if the event is repeated several times (good statistics).
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 3
Coherent XRD: speckle, XPCS
Q =(4π
λ)
sin(Θ
2
)
I(Q, t) = Np∆ρ2V2pP(Q)S(Q, t)
P(Q) - particle form factor
Structure factor:
S(Q, t) = 1N
∑Ni, j=1
⟨
e−iQ(r i(t)−r j (t))⟩
ik
<I(Q,t)>
I(Q,t)
Thespeckle patternis observed only if the event is repeated several times (good statistics). There-occurence of an event under non-ideal conditions leads to theloss of the speckle pattern(phase information). E.g.:→ Ein, Eout, k in, kout are not well defined→ disorder in the sample
→ unsufficient detector resolution→ chaotic source . . .
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 4
X-ray Photon Correlation Spectroscopy,XPCS
10−4 10−3 10−2 10−11.00
1.05
1.10
q=1.4e−03 Å−1
q=1.5e−03 Å−1
q=1.5e−03 Å−1
q=1.6e−03 Å−1
q=2.2e−03 Å−1
q=2.4e−03 Å−1
q=2.5e−03 Å−1
q=2.7e−03 Å−1
q=3.6e−03 Å−1
t (s)
g 2(q
, t)
I
time
τ
• Intensity fluctuation autocorrelation functions:
g2(q, t) = <I(q,0)I(q,t)><I>2 = 1+β
∣
∣
∣
S(q,t)S(q,0)
∣
∣
∣
2
• X-ray photon correlation spctroscopy -XPCSX-ray Intensity Fluctuation Spectroscopy -XIFS
• complementary to Dynamic Light Scattering -DLS
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 5
XPCS: length and time scales
Can be used in a large variety ofexperimental configurations:
→SAXS, WAXS, GID, ...→transmission / reflection
l ≃ 1µm - 10Åt ≃ 106 - 10−3 Hz
from G. K. Shenoy,Nucl. Inst. and Meth. B199(2003), 1–9
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 6
Troïka I beamline @ E.S.R.F.
Troïka (ID10A) side station
2θ
q
Det.
S D
Slits
Mono δλ/λ
∆θ =λ/D
Mirror
Undulator sourceU27, U35, revolver U27/U35source size 928 x 23µm2 (h x v) FWHM
Multi-crystal single bounce monochromatorSi(111),∆λ/λ=10−4
Filtering and focussingSi mirror in the monochomatic beamBe CRLs
Coherent sourceHighly polished rollerblade slitsflux @ sample 109-1010 ph/s (8 keV, 10x10µm2 )brill. > 1020 ph/s/mm2/mrad2/0.1%bw/100mA @ 8 keV
Medipix 2pixel detectorSingle photon contingEnergy discrimination55 x 55µm2 pixel size256 x 256 pixels (12 mm x 12 mm)13.5 bits - 11800 cts/pixel (1 ADU/photon)1 kHz frame repetition rate
ESRF Detector SytemsX. Llopart et al.,IEEE Trans. Nucl. Sci.49, 2279 (2002)C. Caronna et al., ESRFSporlight on Science39 (2006)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 7
Hard-sphere suspensions
U(r)
r2R
10 nm
2R > 200 nm
• Spherical Poly(MethylMethacrylate)PMMA particles coated with poly-12-hydroxystearicacid in cis-decalin
• Entropic forces between the polymer layers -> infinite repulsion.
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 8
Hard-sphere suspensions
U(r)
r2R
10 nm
2R > 200 nm
• Spherical Poly(MethylMethacrylate)PMMA particles coated with poly-12-hydroxystearicacid in cis-decalin
• Entropic forces between the polymer layers -> infinite repulsion.
• The phase behaviour depends on the colloidvolume fraction
Φ = 43πR3N
V
P.N. Pusey & W. Megen, Nature320, 340 (1986).
Φ0.494 0.545 ~0.64 0.74
Fluid Fluid Crystal
Glass
+crystal
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 8
XPCS: Brownian dynamics in a PMMA / cis-decalin suspension (Φ=0.16)
4 6 80.1
1.0
10.0
qR
τq2
10−4 10−3 10−2 10−11.00
1.05
1.10
q=1.4e−03 Å−1
q=1.5e−03 Å−1
q=1.5e−03 Å−1
q=1.6e−03 Å−1
q=2.2e−03 Å−1
q=2.4e−03 Å−1
q=2.5e−03 Å−1
q=2.7e−03 Å−1
q=3.6e−03 Å−1
t (s)
g 2(q
, t)
• Intensity correlation functions:
g2(q, t) = <I(q,τ)I(q,τ+t)>τ<I(q,τ)>2
τ
= 1+β |g1(q, t)|2
• Intermediate scattering functions:
g1(q, t) = S(q,t)S(q,0)
g1(q, t) = exp(−Γt) = exp(
− tτ
)
• Diffusion
Γ = 1τ = Dq2
D = kBT6πηa (Einstein)
〈x(t)−x(0)〉2 = 2Dt (Fick)
L. Lurio et al., Phys. Rev. Lett84, 785 (2000)D. Lumma et al., Phys. Rev. E62, 8258 (2000)F. Zontone, A. Moussaïd,work in progress
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 9
Measuring dynamics in shear flow by X-ray photon correlation spectroscopy(XPCS)
a) Flow = 2.0µl/hrq = 2.1e−03 Å −1
q || v
0.01 1.0
0.0
0.5
1.0
b) Flow = 10.0µl/hr
0.01 1.0
0.0
0.5
1.0
c) Flow = 15.0µl/hr
0.01 1.0
0.0
0.5
1.0
norm
. cor
r.no
rm. c
orr.
t(s)
norm
. cor
r.
a) q = 1.4x10−3 Å−1
vflow = 0
vflow = 60 µm/s
10−4 10−3 10−2 10−1
0.0
0.5
1.0
b) q = 2.5x10−3 Å−1
10−4 10−3 10−2 10−1
0.0
0.5
1.0
c) q = 3.5x10−3 Å−1
10−4 10−3 10−2 10−1
0.0
0.5
1.0
norm
. cor
r.no
rm. c
orr.
t(s)
norm
. cor
r.
k iq
q ||
γ.
d=2R
flow: v,
x
z
q v
q v||
• the dynamics in anisotropic and measures a combination of diffusive and (flow induced)advective motion of the particles.G.G. Fullet et al., J. Fluid Mech. 1980
→ Heterodyne detection:g1(q, t) = exp(−Dq2t + . . .) ·exp(−iqv) ·∫
qδvC.Gutt et al., PRL 2004; F. Livet et al., J. Synch. Rad. 2006
→ Homodyne detection:g2(q, t) = exp(−2Dq2t + . . .) · ·[∫
qδv]2
• the diffusive component can be obtained by using correct experimental conditions (scattering geometry, flow/shear rate)
Andrei Fluerasu et al.,J. Synchrotron Rad., submitted; Sebastian Busch et al.,Eur. Phys. J. E., submitted;
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 10
XPCS & SAXS + microfluidics: motivations
• offers unique control possibilities over many parameters, and access to a large range of time scales; is anoriginal and movel way to study problems that cannot be studied by conventional means.
• Continuous flowmay help preventingsample damageby the X-ray beam.
→ opens new possibilities with biological samples
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 11
XPCS & SAXS + microfluidics: motivations
• offers unique control possibilities over many parameters, and access to a large range of time scales; is anoriginal and movel way to study problems that cannot be studied by conventional means.
• Continuous flowmay help preventingsample damageby the X-ray beam.
→ opens new possibilities with biological samples
E.G. Aggregation of fibroin (Anne Martel, Christian Riekel, ID13 ESRF)
fibroin
acid
0 500 10000.6
0.8
1.0
1.2
1.4
10+6
t (s)
Σ p
ix I 0 5 10
5.
6.
7.
8.
10+5
t (s)
Σ p
ix I
0.010.005
0.02
0.04
Γ ~ Q0.839096
q (Å−1)
rela
x. r
ate
Γ (s
−1)
A. Martel, S. Busch, A. Fluerasu, and C. Riekel, work in progress
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 11
XPCS & SAXS + microfluidics: motivations
• Microfluidic systems allowtime-resolvedstudies of processestaking place in mixing flowcells. The time-dependance ismapped into a space-dependance!L.Pollack et.al., Phys Rev. Lett.86, 4692, (2001).
t
t
t
1
3
2
courtesy of Anne Martel, ID 13 − ESRF
e.g. time-resolved studies formation of silica particles via sol/gel processes (ID 18, ID 2, ID 10, ESRF)
Qacid/Qsilicate
F. Destremaut, J−B. Salmon, J. Leng (LOF CNRS−Rhodia, Bordeaux) A. Fluerasu (ESRF) work in progress
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 12
X-ray compatible flow devices
• Microfluidic devicesR. Barret et al.,Lab. Chip.6, 494 (2006); A. Martel, PhD thesis (ID 13 - ESRF);
• “Milifluidic” devices - F. Destremaut, J.-B. Salmon, to be submitted; S. Busch et al.,Eur. Phys. J. E, submitted (2007);
“Table-top” fabrication method and technologies brought to ESRF as a part of the LTP SC-2266 & SC-2329project (ID 13, ID 2, ID 10, LOF CNRS-Rhodia, Bordeaux).
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 13
XPCS-microfluidics: the importance of scale
���������������������������������������������������������
���������������������������������������������������������
k iq
q ||
γ.
d=2R
flow: v,
x
zDiffusion
Shear rate:γ =-dv(r)dr (T−1)
Wi=γτ ≪ 1
Transit time effectsDeborah number:
De=τvs ≪ 1
Shear-induced effectsPeclet number:
Pe=γR2
D ≫ 1 !!!!Shear number:
S=q·vDq2 ≫ 1 !!!!
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 14
Shear flow
Volume rate of flowQ(L3T−1)=πR2v
Shear rate:γ =-dv(r)dr (T−1)
average shear rateγ ≈ 3vR
Reynolds numberRe=ρv(2R)η
(inertial forces) / (viscous forces)
η = 3.38 cP,ρ ≈0.9 g/cm3 (cis-decalin)
2R = 980µm, v = 100µm/s Re < 0.1
��������������������������������
��������������������������������
L>>R
r
v(r)R
S(beam size)
R − r
R
2 2
2v(r) = 2 v
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 15
XPCS in shear flow
• Brownian dynamics in shear flowAckerson, Clark,J. Physique42, (1981), 929-936;
g(2)(q, t)−1 = βexp
[
−2Γt
(
1− q⊥q‖q2 γt +
q2‖
q2 · (γt)2
3
)]
≈ exp[−2Γt] (if γt < 1)
• Doppler velocimetry (w. homodyne detection)G.G. Fuller et al.,J. Fluid Mech., 100(1980), 555
q ·δv - self beat frequency G(q, t) =∫
dr1dr2 ·exp[−iqδv]
G(q, t) =[
sin(ΓSt)ΓSt
]2(γ=const)=
|er f(√
iΓSt)|2ΓSt
(Poisseuille), withΓS ∝ q‖v
• Transit time effects
neglected if De≪1
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 16
XPCS in shear flow
• Brownian dynamics in shear flowAckerson, Clark,J. Physique42, (1981), 929-936;
g(2)(q, t)−1 = βexp
[
−2Γt
(
1− q⊥q‖q2 γt +
q2‖
q2 · (γt)2
3
)]
≈ exp[−2Γt] (if γt < 1)
• Doppler velocimetry (w. homodyne detection)G.G. Fuller et al.,J. Fluid Mech., 100(1980), 555
q ·δv - self beat frequency G(q, t) =∫
dr1dr2 ·exp[−iqδv]
G(q, t) =[
sin(ΓSt)ΓSt
]2(γ=const)=
|er f(√
iΓSt)|2ΓSt
(Poisseuille), withΓS ∝ q‖v
• Transit time effects
neglected if De≪1
With homodyne detection, the signal is modulated by a frequency determined by the Doppler shifts
between all pair of particles in the scattering volume (qδv(r)).
g(2)(q, t)−1 = βexp
[
−2Γt
(
1− q⊥q‖q2 γt +
q2‖
q2 · (γt)2
3
)]
·[
sin(vq‖t)vq‖t
]2
q⊥v: g(2)(q, t) = exp(−2Γt) q‖v: g(2)(q, t) ≈(
sinΓStΓSt
)2exp(−2Γt)
Transit : Γtr = v/s Diffusion: Γ = Dq2 Shear: ΓS = vq‖
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 16
XPCS-flow (q⊥v)
a) q = 1.4x10−3 Å−1
10−4 10−3 10−2 10−1
0.0
0.5
1.0
b) q = 2.5x10−3 Å−1
10−4 10−3 10−2 10−1
0.0
0.5
1.0
c) q = 3.5x10−3 Å−1
10−4 10−3 10−2 10−1
0.0
0.5
1.0
norm
. cor
r.no
rm. c
orr.
t(s)
norm
. cor
r.q⊥ v:Normalized correlation functions(g(2)(q, t) − 1)/β, obtained in atransverse scattering geometry,shown here for three differentvalues of q at zero flow (filledsymbols) and atv ≈ 58.5 µm/s(empty symbols).It can be seen that for this flow rate,the influence of the shear flow onthe correlation function is, in thefirst order, negligible. The solidlines show fits to thev ≈58.5µm/sdata with simple exponential relax-ations,
g(2) = 1+βexp(2Γt)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 17
XPCS-flow (q‖v)
a) v = 0.0 µm/s
0.001 0.01 0.1
0.0
0.5
1.0
b) v = 11.7 µm/s
0.001 0.01 0.1
0.0
0.5
1.0
c) v = 23.4 µm/s
0.001 0.01 0.1
0.0
0.5
1.0
norm
. cor
r.no
rm. c
orr.
t(s)
norm
. cor
r.
q‖ v:Normalized correlation functions(g(2)(q, t) − 1)/β, obtained in longitu-dinal scans, at q=1.3×10−3 Å−1 and threedifferent flow velocities - (a)v = 0 , (b) 11.7µm/s, and (c) 23.4µm/s.The dashed lines show the fits to the zeroflow correlation function (panel a). Solidlines are least square fits to the non-zero flowdata with,
g(2)(q, t) = 1+βexp(2Γt) ·[
sin(ΓSt)ΓSt
]2
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 18
XPCS - flow, latex / glycerol
a) Flow = 2.0µl/hrq = 2.1e−03 Å −1
q ⊥ vq || v
0.01 1.0
0.0
0.5
1.0
b) Flow = 10.0µl/hr
0.01 1.0
0.0
0.5
1.0
c) Flow = 15.0µl/hr
0.01 1.0
0.0
0.5
1.0
norm
. cor
r.no
rm. c
orr.
t(s)
norm
. cor
r.(De≈1)
q⊥v
g(2)(q, t) = 1+β ·exp[
−2Dq2t]
·exp[
−(νtrt)2]
q‖v
g(2)(q, t)−1 =
βexp[
−2Dq2t(
1+ γ2
3 t2)]
·exp[
−(νtrt)2]
· |er f(√
iΓSt)|2ΓSt
ΓS ∝ q‖v
S. Busch, T. Jensen, Y. Chushkin, and A. Fluerasu,submitted, EPJE (2007)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 19
XPCS-flow: measuring diffusive dynamics
4 6 810+5
10+6
10+7
10+8
v=0.00 µm/s γ=0.000 s−1.
v=58.50 µm/s γ=0.119 s−1.
v=117.00 µm/s γ=0.239 s−1.
qa
D=
Γq−
2 (Å
2 /s)
Diffusion constantD associated withthe Brownian dynamics of free col-loidal particles (radiusa) in shearflow as a function ofq measured ina transverse (q⊥v) scattering geome-try for three volume flow rates. Thesolid line shows the value for the dif-fusion constant calculated by usingthe Einstein-Stokes equation,
D0 = kBT6πηa.
The shear rates are estimated using,
γ = 3vR .
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 20
XPCS-flow: measuring diffusive dynamics
vflow = 0 Γ = Dq2
vflow = 58 µm/s
ΓS
Γtr
0.001 0.01
10.0
100.0
1000.
q (Å−1)
rela
x. r
ate
Γ (s
−1 )
Dispersion relationships:
• diffusion Γ = D0q2
• shear ΓS = vφq
• transit Γtr = v/s
||
V
φ
|
E.g. D0 ≈ 2.84·107 Å/s, φ ≈ 0.01 (0.5 deg)v = 58, µm/s
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 21
XPCS-flow: outlook
• Dynamics in high concentration suspensions under flow
• Aggregation phenomena in soft matter and biological systems
• Dynamics in attractive suspensions (depletion gels).
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 22
PMMA/PS depletion gels
R
rg
• Mixture of Poly(MethylMethacrylate)PMMA particles (spherical, R≈ 1000 Å)coated with poly-12-hydroxystearic acid andfree polymer(polystyrene) in cis-decalin
• Entropic forces between the polymer coat-ings layers→ infinite repulsion
• Depletion effect due to the free polymer→attractive potential
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 23
PMMA/PS depletion gels
R
rg
• Mixture of Poly(MethylMethacrylate)PMMA particles (spherical, R≈ 1000 Å)coated with poly-12-hydroxystearic acid andfree polymer(polystyrene) in cis-decalin
• Entropic forces between the polymer coat-ings layers→ infinite repulsion
• Depletion effect due to the free polymer→attractive potential
R+2 r g
U
R
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 23
PMMA/PS depletion gels
R
rg
• Mixture of Poly(MethylMethacrylate)PMMA particles (spherical, R≈ 1000 Å)coated with poly-12-hydroxystearic acid andfree polymer(polystyrene) in cis-decalin
• Entropic forces between the polymer coat-ings layers→ infinite repulsion
• Depletion effect due to the free polymer→attractive potential
R+2 r g
U
R
0.0 0.2 0.4 0.6 0.80.0
0.2
0.4
0.6
Φ
c p [m
g cm
−3 ] (
c* =0.
6 m
g cm
−3 )
rg/R~0.1
GELS
transient
sticky
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 23
PMMA/PS transient gels
time(from W.C.K. Poon et al., Faraday Discuss., 112, 143−154)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 24
Static analysis
(a)
(b)(c)
(d)
∝Q−4
102 205
10+0
10+2
10+4
QR
I(Q
)
0 5 100.0
0.5
1.0
1.5
2.0
QR
S(Q
)
The static scattering is constantduring the transient gelation pro-cess
SAXS profiles at 4 different timesduring the transient gelation pro-cess . The black line shows theform factor of polydisperse spheri-cal colloids resulting from a least-square fit with a hard sphere formfactor and a Schulz particle sizedistribution. The deviation be-tween data and model at lowQRis due to the structure factor (inset)caused by interactions between thecolloids. The dashed line is an eye-guide and has slope -4.
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 25
Two-time analysis∗
Two-time correlation functions:C(Q, t1, t2) =〈I(Q,t1)I(Q,t2)〉pix
〈I(Q,t1)〉pix〈I(Q,t2)〉pix
0 1000 2000 3000 4000 5000 0
2000
4000
t1 (s)
t 2 (
s)
C(q=3.18e−02 nm−1, t1, t2)
average time (“age”):ta = t1+t2
2
time difference:t = δt = |t1− t2|
∗ M.Sutton et al., Optics Express11, 2268 (2003).
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 26
Two-time analysis
Two-time correlation functions:C(Q, t1, t2) =〈I(Q,t1)I(Q,t2)〉pix
〈I(Q,t1)〉pix〈I(Q,t2)〉pix
0 1000 2000 3000 4000 5000 0
2000
4000
t1 (s)
t 2 (
s)
C(q=3.18e−02 nm−1, t1, t2)
0 100 200 300 400
1.0
0.2
0.5
t =|t1−t2| (s)
g 2(q
,t)
g2 = βexp(
−(Γt)γ)+g∞ Γ = 4.57e-3 s−1 γ = 0.57
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 27
Two-time analysis
Two-time correlation functions:C(Q, t1, t2) =〈I(Q,t1)I(Q,t2)〉pix
〈I(Q,t1)〉pix〈I(Q,t2)〉pix
0 1000 2000 3000 4000 5000 0
2000
4000
t1 (s)
t 2 (
s)
C(q=3.18e−02 nm−1, t1, t2)
0 100 200 300 400
1.0
0.2
0.5
t =|t1−t2| (s)
g 2(q
,t)
g2 = βexp(
−(Γt)γ)+g∞ Γ = 2.4e-3 s−1 γ = 0.82
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 28
Two-time analysis
Two-time correlation functions:C(Q, t1, t2) =〈I(Q,t1)I(Q,t2)〉pix
〈I(Q,t1)〉pix〈I(Q,t2)〉pix
0 1000 2000 3000 4000 5000 0
2000
4000
t1 (s)
t 2 (
s)
C(q=3.18e−02 nm−1, t1, t2)
0 100 200 300 400
1.0
0.2
0.5
t =|t1−t2| (s)
g 2(q
,t)
g2 = βexp(
−(Γt)γ)+g∞ Γ = 1.9e-3 s−1 γ = 1.61
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 29
Two-time analysis
Two-time analysis:g2(Q, ta, t) = βexp(
−(Γt)γ)+g∞
5000 6000 7000
5000
6000
7000
t1 (s)
t 2 (
s)
(a) (b)
0.5 1.010+4
0
500
1000
ta (s)
γ1/
Γ (s
)
1.51.00.5
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 30
Dynamics in “jammed” systems
“Signature” of a jammed system∗:
g1(t) = exp(
−(Γt)γ), with γ ≈1.5!
Γ ∝ Q; (< ∆r2 >∝ t2)
“Aging”
∗ L. Cipelletti et.al.,Faraday Discuss., 2003,123, 237∗ M. Bellour et al., PRE67, 031405 (3003).
C. Caronna et al., PRL, in press (2008)P. Falus et al., PRL97, 066102 (2006)A. Roshi et al., PRE74031404 (2006)B. Chung et al., PRL96228301 (2006)A. Robert et al., EPL75764 (2006)
V. Trappe et. al., Nature411772
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 31
Dynamics and aging in PMMA/PS transient gels
2 4 6 8 10
0.5
1.0
1.5
QR
γ
10.04.
0.01
0.002
0.02
0.005
QR
Γ (H
z)
Γ(ta≅4500 s)∝Q1.09
A. Fluerasu, A. Moussaïd, A. Madsen, and A. Schofield, Phys. Rev. E 76, 010401(R) (2007)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 32
Dynamics and aging in PMMA/PS transient gels
2 4 6 8 10
0.5
1.0
1.5
QR
γ
10.04.
0.01
0.002
0.02
0.005
QR
Γ (H
z)
Γ(ta≅4500 s)∝Q1.09
Γ(ta≅1e4 s)∝Q0.75
A. Fluerasu, A. Moussaïd, A. Madsen, and A. Schofield, Phys. Rev. E 76, 010401(R) (2007)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 33
Dynamics and aging in PMMA/PS transient gels
2 4 6 8 10
0.5
1.0
1.5
QR
γ
10.04.
0.01
0.002
0.02
0.005
QR
Γ (H
z)
Γ(ta≅4500 s)∝Q1.09
Γ(ta≅1e4 s)∝Q0.75
Γ(ta≅11 hr )∝Q0.55
A. Fluerasu, A. Moussaïd, A. Madsen, and A. Schofield, Phys. Rev. E 76, 010401(R) (2007)
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 34
Colloidal gels in microfluidic systems
x −> t1 1
x −> t
x −> t2 2
3 3
Q/2
Q/2
PMMA, Φ∼40%
PS, c~c*
Q=0.5µm/h, x=0 x=1 x=2 Q=50µm/h, x=0 x=1 x=2
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 35
Dynamical heterogeneities and “rare events”
Dynamical heterogeneities,g(4),χ4, . . ., talk by DJDDLS→ L. Cipelletti et al., DJD et al.XPCS→ V. Trappe, A. Robert, L. Cipelletti et al.,
PRE 2007
“Rare events”
A. Moussaïd, A. Fluerasu, work in progress
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 36
Conclusions and outlook
• XPCS + “microfluidics”: first studies have been performed oncolloidal suspensions undergoing (simple) Brownian motion→ it is possible to measure the diffusive dynamics
• X-ray + “microfluidics” studies ofnucleation, growth and aggre-gation phenomena in soft mattere.g.: sol-gel proc. - ongoing LT collaboration ESRF/CNRS-Rhodia Bordeaux
→ Colloidal gels, Aggregation of fibroin, etc.
• these methods mitigate beam damage, which is a major limiting factor in the study of softmatter and biological systems and will become even more important at future light sources
• Changes in the aggregation state of proteins are responsible e.g. for cataract formation inthe human eye lens and neuronal cell death involbed in Alzheimer’s disease.→ kinetics and the dynamics of such processes using XPCS + microfluidics.
Technical/operational requirements/wishes:
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 37
Conclusions and outlook
• XPCS + “microfluidics”: first studies have been performed oncolloidal suspensions undergoing (simple) Brownian motion→ it is possible to measure the diffusive dynamics
• X-ray + “microfluidics” studies ofnucleation, growth and aggre-gation phenomena in soft mattere.g.: sol-gel proc. - ongoing LT collaboration ESRF/CNRS-Rhodia Bordeaux
→ Colloidal gels, Aggregation of fibroin, etc.
• these methods mitigate beam damage, which is a major limiting factor in the study of softmatter and biological systems and will become even more important at future light sources
• Changes in the aggregation state of proteins are responsible e.g. for cataract formation inthe human eye lens and neuronal cell death involbed in Alzheimer’s disease.→ kinetics and the dynamics of such processes using XPCS + microfluidics.
Technical/operational requirements/wishes:
• MORE PHOTONS!higher current; long(er) in-vacuum undulators; lower emmitance;microfocus; faster (2D) detectors. . .
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 37
Conclusions and outlook
• XPCS + “microfluidics”: first studies have been performed oncolloidal suspensions undergoing (simple) Brownian motion→ it is possible to measure the diffusive dynamics
• X-ray + “microfluidics” studies ofnucleation, growth and aggre-gation phenomena in soft mattere.g.: sol-gel proc. - ongoing LT collaboration ESRF/CNRS-Rhodia Bordeaux
→ Colloidal gels, Aggregation of fibroin, etc.
• these methods mitigate beam damage, which is a major limiting factor in the study of softmatter and biological systems and will become even more important at future light sources
• Changes in the aggregation state of proteins are responsible e.g. for cataract formation inthe human eye lens and neuronal cell death involbed in Alzheimer’s disease.→ kinetics and the dynamics of such processes using XPCS + microfluidics.
Technical/operational requirements/wishes:• MORE PHOTONS!higher current; long(er) in-vacuum undulators; lower emmitance;
microfocus; faster (2D) detectors. . .
• complementary methods: direct observation, light scattering,microscopy, rheology,. . .
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 37
Collaborators
Anders Madsen, Abdellatif Moussaïd,Yuriy Chushkin, Federico Zontone(Troïka group, ESRF)
Anne Martel, Christian Riekel, Narayanan Theyencheri (ESRF)Ray Barret, Henry Gleyzolle (ESRF)
Jean-Baptiste Salmon, Jacques Leng, Fanny Destremaut(CNRS-Rhodia, Bordeaux)
Sebastian Busch (TU München), Torben Jensen (Univ. Copenhagen)Peter Falus (ILL)
Erik Geissler (Univ. Joseph Fourier, Grenoble)Mark Sutton (McGill University, Montreal)
http://www.esrf.eu/UsersAndScience/Experiments/SCMatter/ID10A/
Andrei Fluerasu, X-ray Photon Correlation Spectroscopy and µbeam SAXS at NSLS-II, Jan, 2008 38