Jamming for nematic deposition in the presence of impurities

The deposition of one-dimensional objects (such as polymers) on a one-dimensional lattice with the presence of impurities is studied in order to find saturation conditions in what is known as jamming. Over a critical concentration of k-mers (polymers of length k), no further depositions are possible. Five different nematic (directional) depositions are considered: baseline, irreversible, configurational, loose-packing, and close-packing. Correspondingly, five jamming functions are found, and their dependencies on the length of the lattice, L, the concentration of impurities, p=M/L (where M is the number of one-dimensional impurities), and the length of the k-mer (k) are established. In parallel, numeric simulations are performed to compare with the theoretical results. The emphasis is on trimers (k=3) and p in the range [0.01,0.15], however other related cases are also considered and reported.