Sy. Qi et Zg. Wang, KINETICS OF PHASE-TRANSITIONS IN WEAKLY SEGREGATED BLOCK-COPOLYMERS -PSEUDOSTABLE AND TRANSIENT STATES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(2), 1997, pp. 1682-1697
We study the kinetics of order-disorder and order-order transitions in
weakly segregated diblock copolymers using a time-dependent Ginzburg-
Landau (TDGL) approach. In particular, we investigate the microstructu
ral change as well as the order-parameter evolution after a sudden tem
perature jump from one phase to another. Direct numerical simulation o
f the TDGL equations shows that depending on the extent of the tempera
ture jump, these transitions often occur in several stages and can inv
olve nontrivial intermediate states. For example, we find that transit
ion from the lamellar phase to the hexagonal cylinder phase goes throu
gh a perforated lamellar state within a certain temperature range. The
numerical results are elucidated by a multimode analysis under the si
ngle-wave-number approximation. The analysis reveals that the geometri
c characteristics of the free energy surface, particularly saddle poin
ts and ridgelike features, are responsible for the nontrivial intermed
iate states on the kinetic pathways. On the basis of this analysis, a
generalized kinetic ''phase diagram'' is constructed, which is able to
account for all the different scenarios observed in the numerical sim
ulation. Our results are discussed in connection with available experi
mental observations. In particular, we suggest the possibility that th
e perforated-modulated lamellar structures obtained by Bales and co-wo
rkers [I. W. Hamley, K. A. Koppi, J. H. Rosedale, F. S. Bates, K. Almd
al, and K. Mortensen, Macromolecules 26, 5959 (1993); S. Forster, A. K
. Khandpur, J. Zhao, F. S. Bates, I. W. Hamley, A. J. Ryan, and W. Bra
s, Macromolecules 27, 6922 (1994)] may be kinetic, intermediate states
rather than new equilibrium phases.