I IL 18
Light, small angle neutron and X-ray scattering from gels.
Erik Geissler, Isabelle Morfin, Anne-Marie Hecht
Laboratoire de Spectrométrie Physique CNRS UMR 5588,
Université Joseph Fourier de Grenoble, 38402 St Martin d'Hères, France,
Ferenc Horkay
Section on Tissue Biophysics and Biomimetics, Laboratory of Integrative and Medical
Biophysics, National Institutes of Health, Bethesda MD 20892, USA
Abstract
Radiation is scattered by spatial variations in composition. Such variations occur in all
materials, owing to the presence of atoms, molecules or even supermolecular structures. In
polymer gels, variations arise from cross-links, which, by binding different polymer chains
together, imprint on the polymer network a permanent structure that yields a characteristic
pattern of elastic scattering. In addition, some gels simultaneously possess a liquid-like
character, in which mobile polymer segments continuously exchange their position with
solvent molecules. These thermally excited concentration fluctuations, which are related to
the osmotic pressure, have their own characteristic scattering pattern. The movement of the
molecules in the second contribution gives it a quasi-elastic character.
In neutral polymer gels, the different contributions to the scattering can be distinguished at
low values of the wave vector q by dynamic light scattering (DLS). At higher wave vectors,
where the important parameters defining the gel structure are revealed in small angle neutron
scattering (SANS), these components can be resolved by neutron spin echo (NSE)
observations. Generally, good agreement is found among NSE, SANS, DLS and macroscopic
osmotic measurements. In such systems, the scattering properties of the gels can usually be
described by two length scales, one for the osmotic component and the other for the elastic
component.
The case of neutralized polyelectrolyte gels is more complex, partly because the scattering
intensity is weak and partly because an additional length scale must be included to describe
the system. A striking feature of such gels is the volume transition that they exhibit when
placed in contact with a solution of divalent ions. As this transition occurs under physiological
conditions, it seems likely that it is important in biological systems. The role of the divalent
ions in modifying the thermodynamics of these systems has not, however, been ascertained.
Anomalous small angle X-ray scattering measurements will be described in an attempt to
characterize their spatial position in the polymer gel.
Light, small angle neutron and
X-ray scattering from gels
Erik Geissler
Laboratoire de Spectrométrie Physique
UMR 5588 CNRS Université J. Fourier de
Grenoble
Volume transition
of PNIPA hydrogels
in water/phenol and
water/resorcinol
mixtures at 20°C
Intensity correlation function
G(t) = <I(0)I(t)>/<I(t)>2
0.8
In soft gels(heterodyne detection):
G(t)-1 =β[2X(1-X)g(t) +
X= Idyn/(Idyn + Istat)
X2g2(t)]
g(t)
1
G(t)-1, g(t)
In liquids (homodyne detection):
G(t)-1 =β|g (t)|2
β ≤1: optical coherence factor
g(t) : field correlation function
1.2
X=0.426
0.6
X=0.314
0.4
X=0.178
0.2
X=0.075
0
0.0001
0.01
1
t (ms)
100
4
10
K. László et al. Macromolecules 36,
7771-7776 (2003)
Collective diffusion coefficient
Dc =
M os
fϕ
M os
Dc =
fϕ
∂ω 4
M os = ϕ
+ G
∂ϕ 3
If f increases, then Dc decreases.
Do phenol molecules stick to the PNIPA chains?
Light intensity scattered dynamically
from concentration fluctuations
kTϕ 2
Rdyn = K
M os
The product Rdyn Dc = K
kTϕ
is independent of Mos
f
⇒ f is insensitive to the phenol/resorcinol concentration
Hence, the aromatic molecules do not stick to the PNIPA chain
100
10
-1
)
Small Angle Neutron Scattering
gel
(cm
I(q)
poly(fluorosiloxane)
in acetone
1
uncross-linked
solution
0.1
0.001
0.01
0.1
q (Å


2
2 3
2
1
8π Ξ δϕ 
2  kTϕ
I (q) = ∆ρ
+
2
2
2
 M os 1+ q ξ
2 2 
1+ q Ξ


(
)
-1
)
1
Dynamic Light Scattering
8
(counts)
2.38 10
8
2.36 10
8
<I(t)I(t+ τ)>
2.37 10
0
0.0001
0.0002
0.0003
t (s)
0.0004
0.0005
Neutron Spin Echo
1
0.8
0.025 Å
-1
g(t)
0.6
0.4
0.05 Å
-1
0.2
0.1 Å
0
0
50
-1
100
t /ns
150
200
10
I(q)
/cm
-1
100
1
0.1
0.001
0.01
q /Å
0.1
-1
10
I(q)
/cm
-1
100
1
0.1
0.001
0.01
q /Å
0.1
-1
10
I(q)
/cm
-1
100
1
0.1
0.001
0.01
q /Å
0.1
-1
10
I(q)
/cm
-1
100
1
0.1
0.001
0.01
q /Å
0.1
-1
10
I(q)
/cm
-1
100
1
0.1
0.001
0.01
q /Å
0.1
-1
A.M.Hecht, F.Horkay et al. Macromolecules 35, 8552 (2002)
CONCLUSIONS 1
1 In fully swollen neutral gels, dynamic and static
fluctuations are separable.
2 The local chain motions are ergodic.
3 Changes in the diffusion coefficient are governed
principally by thermodynamic interactions rather
than by changes in the hydrodynamic interactions.
ASAXS
120
100
80
1/ϕ
poly(sodium acrylate) gel
in aqueous solutions of
NaCl and CaCl2 or SrCl2
at near-physiological
conditions
60
40
20
0
0
0.5
1
1.5
SrCl2 / mM
2
2.5
3
The number of electrons taking part in a scattering process is
proportional to f(E), which varies near an atomic absorption
threshold (ESr=16.104 keV)
I(q) = (ρsolvent-ρp)2Spp(q)+(ρsolvent-f(E))2SSrSr(q)
+ (ρsolvent-ρp) (ρsolvent-f(E)) SpSr(q)
Between 15.8 and 16.097 keV, f(E) decreases from 32.5 to 29.0
electrons
I(q)=F(E)S(q)
i.e., shape of scattering
curve is independent of
energy E
Comparison of ASAXS and SANS
100
10
SAXS
)
SANS
I(q) (cm
-1
1
0.1
0.01
0.001
0.001
0.01
0.1
q (Å
-1
1
)
I. Morfin et al. Macromolecular Symposia 200, 227-233 (2003)
CONCLUSIONS 2
1 Shape of ASAXS scattering curves S(q) unchanged with
energy
2 Intensity factor F(E) decreases as atomic absorption
threshold is approached
3 S(q) from ASAXS identical with S(q) from SANS
4 Therefore the Sr++ counterions do not form a diffuse cloud
around the polymer chain - they are condensed on it.
Coauthors
Ferenc Horkay
Anne-Marie Hecht
Krisztina László
Katalin Kosik
Isabelle Morfin
NIH (USA)
UJFG (France)
BUTE (Hungary)
BUTE (Hungary)
UJFG (France)
Acknowledgements
Françoise Bley
Cyrille Rochas
Françoise Ehrburger-Dolle
Tamás Horányi
Emese Fülöp
György Bosznai
European Synchrotron Radiation Facility, Grenoble
Institut Laue Langevin, Grenoble
National Institute for Science and Technology,
Gaithersburg, MD, USA
Hungarian National Research Fund