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.