Patterned molecular assemblies on solid surfaces have important applications in a variety of industries, e.g., chemical engineering, electronics, optics, etc. They can also modulate the optoelectronic properties of 2D materials. Methods for precise control of pattern growth at the molecular level are therefore highly desired. The assembly of these molecular structures are impacted by a number of factors from the precursor solution and the substrate surfaces. Because of the interplay of so many factors, to precisely control the patterning remains a challenge, particularly for perfectly unidirectional formation. The authors developed a novel method using fast tip scanning with a Bruker FastScan AFM to perturb the system and guide the unidirectional growth of the SDS surfactant molecular assemblies on graphene surfaces. Without the perturbation, SDS molecules are uncharacteristically covered on the graphene surface as usual. The scanning of the AFM probe on the surface introduces nanomechanical symmetry breaking effects and strongly modifies the surface thermodynamics and additional anisotropy. This resulted in unidirectional growth of the SDS molecular assemblies. The authors found that the resulting ribbon-like 1D assembly highly depends on the symmetry axis of the graphene axis and the AFM tip scan direction. The experimental findings were further supported by extensive simulation studies. This work opens up opportunities for on-demand formation of targeted molecular assemblies on functional 2D surfaces.