The dispersion of nanoparticles in ordered block copolymer nanostructures can provide control over particle location and orientation, and pave the way for engineered nanomaterials that have enhanced mechanical, electrical, or optical properties. Fundamental questions pertaining to the role of enthalpic and entropic particle-polymer interactions remain open and motivate the present work. We consider here a system of 10.6 nm silica nanoparticles (NPs) dispersed in ordered cylinders formed by hydrated poly(ethylene oxide)-poly(propylene oxide) block copolymers (Pluronic P105: EO(37)PO(56)EO(37)). Protonation of silica was used to vary the NP-polymer enthalpic interactions, while polar organic solvents (glycerol, DMSO, ethanol, and DMF) were used to modulate the NP-polymer entropic interactions. The introduction of deprotonated NPs in the place of an equal mass of water did not affect the lattice parameter of the PEO-PPO-PEO block copolymer hexagonal lyotropic liquid crystalline structures. However, the dispersion of protonated NPs led to an increase in the lattice parameter, which was attributed to stronger NP-polymer hydrogen bonding (enthalpic) interactions. Dispersion of protonated NPs into cylindrical structures formed by Pluronic P105 in 80/20 water/organic solvents does not influence the lattice parameter, different from the case of protonated NP in plain water. Organic solvents appear to screen the NP-polymer hydrogen bonding interactions.