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MATERIALS RESEARCH

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Absorption length for photon propagation in highly dense colloidal dispersions Rajeev Garg, Robert K. Prud’homme, and Ilhan A. Aksay Department of Chemical Engineering and Princeton Materials Institute, Princeton University, Princeton, New Jersey 08544-5263

Feng Liu and Robert R. Alfano Department of Physics and Electrical Engineering, Institute for Ultrafast Spectroscopy and Lasers, New York State, Center of Advanced Technology for Ultrafast Photonic Materials and Applications, The City College and the Graduate Center of the City University of New York, New York, New York 10031 (Received 26 September 1997; accepted 8 April 1998)

The absorption length for photon propagation in highly concentrated colloidal dispersions calculated from temporal intensity profiles of 100 femto-second pulses is much longer than the absorption length obtained from the measurements of static light transmission in the pure continuous phase fluid. The difference between these two values is explained on the basis of small interparticle spacing at high particle concentration and hence shorter paths traveled by photons through the absorbing medium relative to the total diffusive path in the dispersion. The two values are in good agreement when the absorption length is rescaled with the interparticle separation.

I. INTRODUCTION

Light propagation in highly scattering and absorbing media is a problem of great technological importance and scientific interest for diverse fields such as colloidal dynamics, materials processing,1 biomedical diagnostics,2 and remote sensing.3 Our interest in this phenomenon arises from stereolithography (SL),4 a novel technique for processing complex shaped materials from colloidal suspensions. SL is a sequential layering process, converting a virtual object into a real, solid structure. It begins with a 3-dimensional, computer-aided design (CAD) model of an object of interest. The virtual object is computationally sliced into 2-dimensional, thin patterns. Each 2D pattern is then transmitted in turn to another computer which controls a patterning laser, each section is solidified by scanning the ultraviolet laser onto the surface of a photocurable polymer resin. A layer is built upon another by lowering the platform supporting the 3D object into the resin bath. Fresh, uncured resin flows over and covers the cured layer, and the next section is patterned on top of the preceding layer. The process is continued until the entire structure has been replicated in solid form. A precise manipulation of light penetration and the profile of the cured region in the colloidal suspension is of utmost importance for the success of this process. The “diffusion approximation” is now well established for modeling the light propagation in highly scattering and absorbing media.5 The essential approximation underlying the diffusion approach is that after going through a large number of scattering events, the phases of the scattered waves are randomized so that any J. Mater. Res., Vol. 13,