Sequential infiltration synthesis (SIS) is a process derived from ALD in which a polymer is infused with inorganic material using sequential, self-limiting exposures to gaseous precursors. SIS can be used in lithography to harden polymer resists rendering them more robust towards subsequent etching, and this permits deeper and higher-resolution patterning of substrates such as silicon. Herein we describe recent investigations of a model system: Al2O3 SIS using trimethyl aluminum (TMA) and H2O within the diblock copolymer, poly(styrene-block-methyl methacrylate) (PS-b- PMMA). Combining in-situ Fourier transform infrared absorption spectroscopy, quartz-crystal microbalance, and synchrotron grazing incidence small angle X-ray scattering with high resolution scanning transmission electron microscope tomography, we elucidate important details of the SIS process: 1) TMA adsorption in PMMA occurs through a weakly-bound intermediate; 2) the SIS kinetics are diffusion-limited, with desorption 10x slower than adsorption; 3) dynamic structural changes occur during the individual precursor exposures. These findings have important implications for applications such as SIS lithography.