The formation and structure of 2,2’-bipyridine (22BPY) and 4,4’bipyridine (44BPY) monolayers on Au(111) substrate have been studied as a function of the substrate potential. At high potentials, both molecules adsorb onto the substrate and stand vertically with their nitrogen atoms facing the Au(111). The vertically standing molecules stack, like rolls of coins, into polymer-like chains which pack closely in parallel to form ordered monolayers. Decreasing the potential to a critical value, the 22BPY chains become randomly oriented via a reversible order-disorder phase transition. The phase transition, as revealed by scanning tunneling microscopy, is driven by a potential dependent attractive force between the chains. The attractive force is believed to be a substrate-mediated effective force which arises as an adsorbed 22BPY perturbs its surrounding local surface potential and thus the nearby molecules. This hypothesis is supported by a quantitative investigation of the local surface potential using a self-consistent density functional method. In contrast to 22BPY, the 44BPY chains dissolve instead of becoming randomly oriented at low potentials. This behavior may be due to that 44BPY is not as strongly adsorbed on the surface as 22BPY because it has only one nitrogen facing the surface.