Gel-like Aspect of Polymer Mixture with Dynamical Asymmetry
Studied by Small-Angle Neutron Scattering
Satoshi Koizumi
Advanced Science Research Center, Japan Atomic Energy Research Institute,Tokai, Japan
o
T ( C)
Many complex fluids, e.g., polymer melts and solutions, micellar solutions, gels and
suspensions, are intermediate between solid and liquid; they maintain their shape for some time like
a solid and eventually flow over a long time like a liquid. Hence these complex fluids are called
"viscoelastic". This intermediate character is due to (i) a molecular structure with a large number of
internal molecular modes and (ii) weak interactions among molecules, both of which are important
to determine a thermodynamic property of the complex fluids as well as rheology.
In this study, we aim to investigate the question "what is a gel ?", as related to a key word
of “dynamical asymmetry”, whereby two constituent components have a large difference in
mobility. It is well established from both experimental and theoretical sides that the large difference
in mobility enhances the viscoelasticity in the form of dynamical coupling between stress and
diffusion where a stress imbalance affects cooperative diffusion, phase separation or flow under
shear as well as the thermodynamic contribution.1
Along the same scenario, we performed small-angle neutron scattering (SANS)
measurements on the miscible mixture of polystyrene (PS) and poly (vinyl methylether) (PVME)
which has a large difference in glass transition temperature Tg. As temperature decreases to an
intermediate region between two Tg's, the large difference in Tg is expected to induce a large
difference in mobility between the two polymers and therefore "dynamical asymmetry enhanced by
temperature".
In this intermediate temperature region, we observed a new experimental phenomenon of
anomalous suppression of small-angle scattering at a quiescent state.2 Simultaneously, if a shear
flow is imposed on this mixture, we observed an established phenomenon; abnormal butterfly
scattering pattern due to shear-induced phase separation.3 Our interpretation for the suppression is
following3,4; the suppression behavior results
Two-Phase Region
200
TS
from two factors; (i) enhanced dynamical
asymmetry and (ii) a gel-like limit where the
TC
150
rheological relaxation is much slower than the
Single-Phase Region
concentration fluctuation relaxation. These
Dynamical Symmetry
factors are required to satisfy the gel state. As
Tg,PS
100
T
A
the temperature decreases between two Tg's,
(II)
dynamical asymmetry is simultaneously
50
Dynamical Asymmetry
enhanced by a temperature change. In this
TF
case, we expect that a long living shear
0
modulus (4/3G ) starts to suppress the
(I)
Glass Region
Tg,cal
concentration fluctuations at finite q values Tg,PVME
0.0
0.2
0.4 0.6
0.8
1.0
satisfying the gel-like limit, where q is a
PS
wavenumber (q=
sin( /2)).
Figure 1
4
Figure 1 is the phase diagram for the studied mixture. In addition to the spinodal and
binodal lines and the calorimetric glass transition temperature Tg,cal, the temperature region of
dynamical asymmetry, which was determined by SANS, is also included.
Characteristic Time (sec.)
Figure 2 shows a crossover between viscous and gel-like limits, which happens for the
mixture as the temperature decreases. The relaxational times for the concentration fluctuation at
q=0.003 Å-1 was determined by time-resolved SANS measurements observing (i) the initial stage of
spinodal decomposition above the spinodal line and the relaxation of shear-induced phase
separation in the intermediate temperature region. In the high temperature region above 100 oC, the
rheological relaxation is much faster than the concentration relaxation. Here we stress again that the
concentration relaxation is determined by the thermodynamics of the mixture. However, as the
temperature decreases below about 80 oC, two relaxational times of rheology and the concentration
at q=0.003 Å-1 merges and the mixture starts to behave as in the gel-like limit. The upturn of the
concentration relaxational time is attributed to temperature-change of the kinetic Onsager
coefficient in the thermodynamic contribution.
Figure 3 is a schematic diagram showing
9
10
DPS/PVME (50/50) Mixture
the suppression of small-angle scattering for the
8
4
10
dynamically asymmetric mixture in the gel-like limit.
Rheological
The suppression should disappear in the low q limit
Relaxation
7
10
Spinodal
R
(q 0) because the relaxational time for the
Temp.
6
10
concentration fluctuation becomes longer according
Ts
to q2 for the cooperative diffusion and the mixture
5
Concentration
10
Fluctuation
behaves as in the viscous limit again. In Figure 3,
-1
CF (= R(q) )
4
10
therefore, we draw the lower q-limit of the
at q=0.003 A-1
suppression at q=1/RL, which could not be detected so
3
10
far by the small-angle scattering technique due to the
2
10
limitation of q-resolution. We shortly comment on the
1
real gel, where polymer chains are permanently and
10
heterogeneously crosslinked. In this case, the static
0
10
inhomogeneity
coexists
with
the
thermal
0
20
40
60
80 100 120 140 160
Gel-Like Limit
Viscous
concentration fluctuations, which contributes to the
< Limit Temp. ( oC)
>
4
CF
CF
R
R
opposite behavior of excess small-angle scattering.
Figure 2
S(q) Polymer Mixture 1/R
L
lnS(q)
with Dynamical Symmetry
or
Dynamical Asymmetry
1/
1/RU
1/r0
S(0)
suppression
2
1/r'0 +4/3 G1
-2
Sth(q) Thermal Fluctuation
Sst (q) Static Inhomogeneity
S(q) Polymer Gel
-4
SANS
0.001
o
-1
ln q (A )
0.1
Figure 3
References:
1) Doi, M. and Onuki, A. J. Phys. II (France) 1992, 2,1631-1656.
2) Takeno, H., Koizumi, S., Hasegawa, H. and Hashimoto, T. Macromolecules, 1996, 29, 2440-2448.
3) Koizumi, S. J. Apply, Cryst. 2003, 36,381-388 (Conference Report of SAS2002).
4) S. Koizumi. Submitted to J. Polym. Sci. Part B: Polymer Physics (Special Issue of Neutron Scattering).