which implies that at interfaces the two components spontaneously diffuse towards
the directions of lower concentrations (downhill diffusion), resulting in sharper
interfaces, as illustrated at the left-hand side of Fig.9.6. Only concentration
fluctuations with large enough amplitude can lead to the emergence of new
phase, as illustrated at the right-hand side of Fig.9.6. Such a mechanism of the
phase separation is callednucleation and growth(NG) (Abraham 1974 ; Oxtoby
1998 ). The concentration regions of phase diagrams for different mechanisms of
phase separation are shown in Fig.9.5.
Polymer blends are the ideal system for scattering experiments to study the
phase separation kinetics with spinodal decomposition. This is because the diffu-
sion rates of polymer molecules are small in the bulk phase, leading to slow phase
separation process and thus allowing time-resolved scattering experiments to trace
the structural evolution during phase separation. The kinetic process of phase
separation is normally initiated by the concentration fluctuations in the homoge-
neous mixture. For such a homogeneous mixture, the scattering experiments based
on the visible lights (by the differences in polarizability or reflective index), neutron
beam (by the difference in neutron scattering sectional areas between deuterium
and hydrogen atoms) and X-ray (by the difference in the electron densities) can
measure the scattering intensity, which corresponds to the structure factor of the
concentration fluctuationsS(h)¼<Df^2 >. Here, the scattering vector
h¼4 psiny
l(9.21)
which reflects the length scale of scattering objects. De Gennes borrowed the
concept ofrandom-phase approximation(RPA) from the discussion of electron-
density fluctuations (de Gennes 1970 , 1979 ). He assumed that the scattering
intensity at a givenhis linearly integrated over the independent contributions
from each polymer chains in a field of average concentrations, so
1
SðhÞ¼
1
r 1 f 1 SDðh;r 1 Þþ1
r 2 f 2 SDðh;r 2 Þ 2 w (9.22)Fig. 9.6 Illustration of concentration fluctuations under different mechanisms of phase separa-
tion. Theleftside shows the features of concentration distribution and diffusion for the nucleation
and growth (NG) and the spinodal decomposition (SD), respectively, and therightside shows the
results of free energy changes due to small and large fluctuations
9.2 Kinetics of Phase Separation 173