SPECTRAL TRANSPARENCY AND WAVE EXPONENT OF A POLYDISPERSE ENSEMBLE OFFRACTAL CLUSTERS

The spectral-turbidimetric theory of fractal clusters is generalized t o the case of polydisperse ensembles. With allowance for known cluster -mass distributions N(M) for the DLCA and RLCA aggregation regimes, ca lculations are performed to determine polydisperse scattering sections and the wave exponent in the spectral relation for turbidity T approx imately lambda(-w)BAR as a function of the parameter XBAR = 2piR(g)BAR /lambda (where R(g)BAR is mean cluster size). The calculations employ three literature models describing termination of the density correlat ion function, along with the parametric model of the scattering struct ure factor proposed by Lin. It is shown that in the limit XBAR > > 1 t he exponent wBAR = 4 - D (fractal dimension D < 2) or 2 (D greater-tha n-or-equal-to 2). On the basis of an analogy with the transition from scattering in the Rayleigh-Debye-Gans regime (WBAR greater-than-or-equ al-to 2) to scattering in the anomalous diffraction regime (wBAR less- than-or-equal-to 2), scaling relations are proposed for turbidity T ap proximately R(x)gBAR approximately M(x/D)2, Where M2 is the second mom ent of the distribution N(M), while the exponent x = D + wBAR - 4 for w greater-than-or-equal-to 2 and (D - 2)(wBAR - 1) for wBAR less-than- or-equal-to 2.