  For the development of porous materials with improved transport properties, a
key missing ingredient is to determine the relations between growth kinetics,
structure, and transport parameters. Here, we address these relations by
studying solute diffusion through three-dimensional porous films produced by
simple deposition models with controlled thickness and porosity. We simulate
growing films with competitive aggregation rules that incorporate lateral
aggregation (relative rate proportional to $p$), which leads to pore formation,
and surface relaxation ($1-p$) that favors compaction. By connecting a solute
source at the basis and a drain at the top outer surface of the films, we
extract the effective diffusion coefficients from steady-state simulations. We
find that for a given film thickness, the larger the $p$, the larger the
effective porosity and diffusivity, but the smaller the tortuosity. Keeping
constant growth conditions (i.e., same $p$), the increase of thickness always
leads to an increase of effective porosity, but a nontrivial behavior in the
diffusivity occurs: for $p\leq 0.7$, the diffusion coefficient is larger in
thicker films; this is accompanied by a decrease of the tortuosity with the
thickness, thus indicating that growth continuously improves pore structure for
diffusion. Microscopically, such a result is associated with narrower
distributions of local solute currents at higher points of films. Particularly
for $p\geq 0.9$, in which film porosity is $\sim 0.65-0.7$, the tortuosity is
between $1.3$ and $2$, increases with the thickness, and has maximal changes
near $25\%$. Pairs of values of porosity and tortuosity that we obtain here,
for the thickest films, agree with those experimentally measured in some porous
electrodes. Noteworthy, the increase of film thickness is generally favorable
for diffusion in their pores, and exceptions have small losses in tortuosity.
