MPa, comparable to that of cross-linked polymer films. Free-standing nanoparticle membranes exhibit bending rigidity on the order of 10 eV, higher than what is predicted in theory for continuum plates of the same thickness, due to nonlocal microstructural constraints such as nonlocal coupling of particle rotational degrees of freedom. On the other hand, resistance to bending is found to be greatly reduced in nanoparticle monolayers that are supported at the air/water interface, possibly due to screening of ligand interactions in a wet environment. Surface chemistry In many different types of colloidal gold syntheses, the interface of the nanoparticles can display widely different character – ranging from an interface similar to a self-assembled monolayer to a disordered boundary with no repeating patterns. Beyond the Au-Ligand interface, conjugation of the interfacial ligands with various functional moieties (from small organic molecules to polymers to DNA to RNA) afford colloidal gold much of its vast functionality. Ligand exchange/functionalization After initial nanoparticle synthesis, colloidal gold ligands are often exchanged with new ligands designed for specific applications. For example, Au NPs produced via the Turkevich-style (or Citrate Reduction) method are readily reacted via ligand exchange reactions, due to the relatively weak binding between the carboxyl groups and the surfaces of the NPs. This ligand exchange can produce conjugation with a number of biomolecules from DNA to RNA to proteins to polymers (such as PEG) to increase biocompatibility and functionality. For example, ligands have been shown to enhance catalytic activity by mediating interactions between adsorbates and the active gold surfaces for specific oxygenation reactions. Ligand exchange can also be used to promote phase transfer of the colloidal particles. Ligand exchange is also possible with alkane thiol-arrested NPs produced from the Brust-type synthesis method, although higher temperatures are needed to promote the rate of the ligand detachment. An alternative method for further functionalization is achieved through the conjugation of the ligands with other molecules, though this method can cause the colloidal stability of the Au NPs to breakdown. Ligand removal In many cases, as in various high-temperature catalytic applications of Au, the removal of the capping ligands produces more desirable physicochemical properties. The removal of ligands from colloidal gold while maintaining a relatively constant number of Au atoms per Au NP can be difficult due to the tendency for these bare clusters to aggregate. The removal of ligands is partially achievable by simply washing away all excess capping