The effects of increasing the driving forces for a 1-D assembly of nanoparticles onto a surface are investigated with experimental results and models. Modifications, which take into account not only the particle-particle interactions but also particle-surface interactions, to previously established extended random sequential adsorption simulations are tested and verified. Both data and model are compared against the heterogeneous random sequential adsorption simulations, and finally, a connection between the two models is suggested. The experiments and models show that increasing the particle-surface interaction leads to narrower particle distribution; this narrowing is attributed to the surface interactions compensating against the particle-particle interactions. The long-term advantage of this work is that the assembly of nanoparticles in solution is now understood as controlled not only by particle-particle interactions but also by particle-surface interactions. Both particle-particle and particle-surface interactions can be used to tune how nanoparticles distribute themselves on a surface.