Polydispersity scaling factor

Fig. 6a. Structure factor S(q, t) plotted vs time for a nearly symmetrical critical mixture (< >c = 0.486) of perdeuterated and protonated 1,4 polybutadiene degrees of polymerization Nh = 3180, Nd = 3550, polydispersity indices (Nw/Nn)h = 1.03 and ((Nw/Nn)d = 1.07 quenched from T0 75 °C to T 49 °C (Tc = 61.5 1.5 °C) for several representative scattering wave numbers q. Since the scattering intensity is plotted on a logarithmic scale, straight lines imply an exponential growth and their slope hence yields 2t 1 - Eq. (76). Arrows show the time tm where nonlinear effects start to limit the growth, b Cahn plot R(q) /q2 vs q2, for the quenching experiment of a), cf. Eq. (85). Deviations from linearity here are attributed to the neglect of thermal noise - i.e. only the first term on the right hand side of Eq. (76) is kept. From Bates and Wiltzius p6]...

FIGURE 6.14 SAXS results for 5% Brij 35/butanol/water ternary systems (black) with the result of the reference binary 5% Brij 35/water binary system (gray) at 25°C. (a) Experimental SAXS spectra on an absolute scale, (b) the GIFT results of some curves from Figure 6.11a p(r) functions, and (c) averaged structure factor S J.q). Inset Parameters of the modelled —volume fraction (j), interaction radius R, and polydispersity p. (d)... 

Photonic band gap (PBG) materials are a specific class of ordered stmctures containing a periodic variation in refractive index in two or three dimensions and are used in a variety of applications like low-loss waveguides, low threshold lasers to name a few. Colloidal self-assembly provides a very promising approach for the production of micron scale, three dimension photonic crystals with band gaps in the visible or infrared region. The limiting factor in the self-assembly process is the monodispersity of the colloids, as good quality crystals are only achieved with coUoids that have very low size polydispersity (<5 %). Braun et al. (2001, 2002) have recently employed colloidal crystallization of silica spheres to build photonic band gap crystals for different applications. 

To comment the results we can say firstly that the q dependence, for given and c values, can be analysed as controlled by a diffusive process, and secondly that the dynamical structure factor is not in general a simple exponential function of time. This last point cannot be analysed as a trivial polydispersity problem, as at fixed the profile of the structure factor changes tremendously as a function of concentration. Thus a single change in time scale is not useful to analyse the concentration dependence of the measurements. 

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