Small Angle Neutron Scattering Studies of the Initial

83 Pages·2005·7.17 MB·English

Small Angle Neutron Scattering Studies of the
Initial Stages of Phase Separation
Tim Rappl, Amy Lefebvre, Albert Pan
Nitash Balsara, David Chandler
University of California, Berkeley
Boualem Hammouda
National Institute of Standards and Technology
Financial Support:
NSF (indirect 1995-2003)
ACS PRF grant (2003-05)
Phase diagram of liquid
(polymer) mixtures
Binodal curve
Two Mechanisms:
(1) Nucleation (off-
1/T or P
critical systems)
(2) Spinodal
Decomposition
(critical systems)
Volume fraction
Question: Is there any difference between the 2 mechanisms?
(cid:1)(cid:1)(cid:1)(cid:1)(cid:2)(cid:2)(cid:2)(cid:2)(cid:3)(cid:3)(cid:3)(cid:3)(cid:4)(cid:4)(cid:4)(cid:4)(cid:5)(cid:5)(cid:5)(cid:5)(cid:6)(cid:6)(cid:6)(cid:6)(cid:7)(cid:7)(cid:7)(cid:7)(cid:3)(cid:3)(cid:3)(cid:3)(cid:4)(cid:4)(cid:4)(cid:4)
1. Classical nucleation theory
4
DG = - pr3DG + 4pr2s
r v
3
equilibrium droplet in an infinite "ocean"
(size)
Examples: clouds, rain, snow,
(R )
c
bones, crystallization, boiling,
melting, magnetization, phase
separation…
Experiments on liquid
mixtures
Metastable mixture Stable mixture
(one-phase) (two-phase)
Nucleation of A droplets
Krishamurthy and Goldburg (JCP 1982) write "Our observations of the
very initial stages of nucleation were severely limited by our microscope
technique, finite quench rates,… In our view, the same failing
characterizes all previous experiments.
Questions about nucleation
1. How to look for the critical nucleus (prove that
something is not there)?
2. Can scattering (a powerful tool for studying
critical systems) be used to study nucleation?
If nuclei are infinitely dilute, then scattering will not
work.
3. Theory is remarkably silent about measuring R .
c
Find each cluster and determine the probability of
growth/decay (experiments by Weitz and Vekilov).
Materials
[ CH CH CH CH ] [ CH CH CH CH ]
2 2 2 n 2 2 2 n
CH CH CH
3 2 3
PM PE
sample mol. wt. N Rg (nm)
desig. (kg/mol)
dPM 145 2055 15.2
hPE 195 2350 15.5

Blends:
B1, B2, B3 are
blend desig. vol fr. of dPM
also off-critical
B5 0.49 (critical)
blends (JCP,
B4 0.20 (off-critical)
2002)
Pressure Quench (off-critical)
Anneal above the
T
binodal at P=0.
a l
d
o
n
b i Quench in two
steps to final
(T,P).
a l
d
o
n
p i
s
Phase separation
triggered by the
pressure quench.
P
Determination of binodal and spinodal:
Lefebvre, et al., Macromolecules, 2002
Salient Features of our
Experiments
1. Molecular motion is extremely slow (t~0.1 s) and completely understood
(non-glassy).
2. Robust models for equilibrium thermodynamics are available; expressions
for R can be easily derived:
c
(cid:6) R (cid:3) 2 (cid:6) 2 c N (cid:3) 2 (cid:6) 1 1 2 (cid:3) (cid:6) 2 (cid:3)
(cid:4) g (cid:1) = (cid:4) (cid:1) f (1 - f )(cid:4) - 1 - - f (cid:1) (cid:4) 1 - (cid:1)
(cid:4) (cid:1) (cid:4) (cid:1) (cid:4) (cid:1)
(cid:5) R (cid:2) (cid:5) 0 .73 (cid:2) (cid:5) 2 2 c N (cid:2) (cid:5) c N (cid:2)
c
3. Nucleation triggered by pressure quench (faster and cleaner than
temperature quench).
4. Deuterium labeling enables detection of initial clustering by SANS.
SANS profiles merge
0.86 kbar 0.43 kbar
1000 10000
1 min
1 min
y 37 min y 48 min
1000
sit 100 58 min sit 75 min
n 74 min n 93 min
e e
114 min
nt nt 100
S I S I
N 10 N
A A 10
S S
q q
c c
1 1
0.01 0.1 0.5 0.01 0.1 0.5
-1 -1
q (nm ) q (nm )
Scattering Signature of Critical
Nucleus
0.19 kbar
1000
6 min
y 92 min
it 135 min
s 100
n 177 min
e
t
n
I

S
N 10
q
A c
S
1
0.01 0.10 0.50
-1
q (nm )
If none of the emerging structures are of size L then there will
be no scattering increase at the corresponding q~1/L.
None of the growing structures are smaller than R ~1/q
c c