Langmuir-Blodgett films of 4-heptoxy-4'-carboxyazobenzene on mica transferred from pure water exhibit novel strip structures consisting of mono-molecular thick straight bands 80 nm wide and more than 100 mu m long. To examine a possibility that these bands are self-organized structures of small monolayer clusters, the effects of monovalent ions are investigated. The monovalent ions caused the mesoscopic bands to coagulate. The fraction of coagulated bands was measured as a function of ion concentrations at pH 7.0 by atomic force microscopy. K+ and Cs+ are shown to interact with the mica surface strongly and destabilize the bands by developing the hydration force. Na+ and Li+ cause critical coagulation without destabilization and have the critical concentrations at 3.0 and 1.6 mM, respectively. UV-vis reflection spectroscopy demonstrates that no molecular reorientation deviating from an H-aggregate-like state occurs during coagulation. X-ray photoelectron spectroscopy was used to obtain an adsorption isotherm of Na+. A comparison with a model monolayer described by Poisson-Boltzmann-Stern theory shows that the unusually large Na+ binding occurs prior to the coagulation. A comment is made on the importance of the characteristically large perimeter regions of monolayer clusters making up the band.