Cells interact with both tethered and motile ligands in their extracellular environment to initiate and regulate signaling, adhesion, and migration. A quantitative and fundamental understanding of these receptor-ligand interactions is necessary for drug discovery, tissue engineering, and biomaterial fabrication. In this paper, we present a mean field approach to quantify the fundamental thermodynamics of interaction between the cell surface receptors and motile ligands in solvent. Our studies show that the free energy of interaction between the receptors and the nanosized ligands depends strongly on the ligand size and the effects at lower and higher concentrations show completely opposite trends that cannot be explained by simple scaling laws. In addition, we also observe various regimes of strong and weak adhesion as a function of ligand size and concentration. Our calculations provide insights into understanding cell-matrix interactions at a fundamental level as well as to identify potential avenues for fabrication of nanoligands for therapeutic and biotechnological purposes.