In my opinion, longer ligands can produce better luminescence. However when the length increased to a threshold length, no matter how long the ligands are, no luminescence increment occurs.

The chemical nature of the ligands matter too, as well as the function of the ligands.  Are the ligands mostly solubilizing/ passivated?  Are they filling trap states?  Are they protecting from degradation from air or water or whatever?  Can the ligands quench the emission?  

It depends on the functional groups of the ligand and the degree of crystallization in the short and long range. The length is not the most important factor in capping but the degree and nature of functional.  Some long chain ligand can quench luminescence especially the -OH groups.

Dear Louise,

OK. I am using carboxylic ligands with different lengths: ie, Oleic Acid, Myristic Acid, Octanoic Acid. I do not have any information about how they react with the nanoparticles or if they quench the emission or not. I do see changes in QY of the nanoparticles after ligand exchange, but, I am not sure if that is because of the new ligand or anything else such as impurities that are introduced during the ligand exchange process. But, I want to know, theoritially, if we have same PbS nanoparticles with different ligand length on the surface, does the ligand itself can play a role on changing the fluorescence lifetime of the nanoparticles or not. 

If the legend passivates the surface defects, it will decrease increase the decay lifetime since the decay lifetime is due to volume and surface recombination. So, passivating the surface would lead to smaller surface recombination velocity. The passivation effect is a matter of single layer of the legend. So, increasing the legend thickness will not appreciably increase the lifetime. \

The second effect is that the legend must have wider band gap such that it reflects the electrons and holes in side the quantum dot and confine them inside the core of the dot.

Best wishes