  A very promising approach to obtain efficient upconversion of light is the
use of triplet-triplet annihilation of excitations in molecular systems. In
real materials, besides upconversion, many other physical processes take place
- fluorescence, non-radiative decay, annihilation, diffusion - and compete with
upconversion. The main objective of this work is to design a proof of principle
model that can be used to shed light on the relevance of the interaction
between the different physical processes that take part in these kinds of
systems. Ultimately, we want to establish general principles that may guide
experimentalists toward the design of materials with maximum efficiency. Here
we show, in a 1D model system, that even in the presence of these processes
upconversion can be optimized by varying the ratio between the two molecular
species present in this kind of materials. We derive scaling laws for this
ratio and for the maximum efficiency of upconversion, as a function of the
diffusion rate J, as well as of the creation and of the decay rate of the
excitations.
