Scaled structure factor

Allen S M and Cahn J W 1979 Acta. Metall. 27 1085 see also Ohta T, Jasnow D and Kawasaki K 1982 Phys. Rev. Lett. 49 1223 for the model A scaled structure factor... 

When the scaled structure factor F(x) is plotted against the reduced scattering vector x for an A/B binary blend in Fig. 12, F(x) becomes essentially universal... 

Fig. 23a,b. Scaled structure factor F(x) as a function of the reduced scattering vector for A/B/C-fo-D blend containing attractive block copolymers a with different interaction energies and Nbiock= 12 b with different chain length of A05f5 block copolymers [68]... 

The evolution of the parameters can be studied on the basis of power laws given by eqs. 2 and 3 in which a and p are the respective exponents characterizing the time-evolution of the pattern. In eq.3 F(x) is the scaled structure factor defined by... 

The scaled structure factor F(x) or F(x) characterizes morphological aspects of the growing pattern such as those shown in Fig. 2, while the size of the pattern at t is characterized by qm(t) or Am(t) (eq.2). If the pattern grows with the dynamical self-similarity at a given T and (t)> is invariant with t, F(x) is universal with t as shown schematically in Fig.3(b). Obtaining this universal scaling function F(x) confirms the validity of the dynamical scaling hypothesis. The... 

For this purpose F(x) is more convenient than F(x). The universal scaled structure factor with respect to both t and T was recently reported for the critical mixture of SBR/PB(12) and PI/PB(4, 19). 

Fig. 5. Scaled structure factors F(x) obtained at 40 C for SBR1/PB19 with 58/42 wt%/wt% mixture where the time elapses in the order of parts c to a. In part c, F(x) monotonically increases with time but in parts a and b it is essentially independent of time.

It is obvious that the dynamical scaling hypothesis is not valid through the dynamical percolation-to-cluster transition. This is because the pattern changes from the bicontinuous periodic structure to the cluster of spheres. In fact the scaled structure factor was found to substantially broaden before and after the transition. 

Universal scaled structure factor in polymer mixtures... 

Fig. 1 Scaled structure factor for a near-critical mixture (fj v/v) deuterated polybutadiane (DPB) and protonated polyisoprene (HPI) obtained from time-resolved light scattering experiments at various times in the late-stage SD at a quench depth JT = T — TsI = 3-9 °C where T, (36.1 °C) is spinodal temperature and T (= 40 °C) is phase-separation temperature [10]. The time covered corresponds to 6.4-118 in the reduced time t defined by t/t [3,8] (tc at 40 °C is 46.6 min)...

Figure 1 shows typical scaled structure factors obtained for a near-critical mixture of DPB/HPI in the late-stage SD process [10]. Details of the polymers used in this report are summarized in Table 1. As shown in this... 

Fig. 2 Comparisons of scaled structure factors Siqlq ) (proportional to F x) in Eq. (1)) obtained from the 3D LSCM image (unfilled circles), the TLS experiments for the PB/PI wt%/wt% mixture (crosses) and the computer simulations based on the 3D TDGL model (solid line) [14]...

Fig. 5 Comparison of the SAXS profile from the jiE equilibrium system at 22 °C with the TLS profile from the DPBl/HPIl mixture at a particular time in the late-stage SD (both shown by data points [29]). The solid lines are the best fit with the MB theory. The scaled structure factor F(x) for the DPBl/HPIl is identical to that for the DPB/HPI mixture shown in Fig. 1...

Fig. 12a,b Comparison of scaled structure factors, F x,t), obtained from LS (a) and from LSCM (b). F(x) shown by solid lines in a and b are identical and obtained from 3D computer simulation based on the TDGL equation with hydrodynamic interactions... 

In the late stage SD, since rj ty) becomes a constant equilibrium value, F x,t) does not depend on t if S qyt) becomes a time-independent universal scaling function, S( x ), which depends only on the form of the phase-separated structure. Consequently, in the late stage SD, F Xyt) can be rewritten as F x) ( universal scaled structure factor ), if this criterion is satisfied. 

The time evolution of the scaled structure factor, F x,t), the interfacial curvature distributions, P(H,iC t), and the interfacial area per unit volume, E(f), were also examined to study both the global and local features of the DPB/PB phase-separated structure. Depicted in Fig. 25 is the time evolution of X(f) for the thin and thick DPB/PB mixtures. As reported before [72], a power law behavior, was observed for the thick blend, while the... 

Figure 16 Comparisons of scaled structure factors, F ), obtained for critical mixtures of simple liquids (l/Wand L/W), polymer mixture (PB/PI, 50 50 v/v), and 3D simulation based upon the generalized TDGL equation with a system size of 128. From Hashimoto, T. J. Polym. ScL, Part B Polym. Phys. 2004, 42, 3207-3262. ...

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