A Theoretical Framework for Determining the Yield Stress of Nanoparticle Organic Hybrid Materials

Designing materials with desirable yield stresses is of interest due to their applications in additive manufacturing, soft robotics, and mimicking biological yield-stress fluids. One model class of materials with yield stress is Nanoparticle Organic Hybrid Materials (NOHMs), which are made up of inorganic nanoparticles with tethered oligomers on their surfaces. The apparent yield stress of NOHMs comes from the entropic penalty experienced by the oligomers that must fill the space between a deformed array of cores. We derive the evolution of the free energy of NOHMs in a deforming periodic array in the absence of a solvent as well as in the presence of an added solvent. For a solvent-free case, the tethered oligomers are at equilibrium for a given configuration of nanoparticles. This enables us to find the oligomer concentration field by minimizing the free energy of the system. Low values of yield stress are achievable by adding a solvent. In this case, the free energy is a result of oligomer configurational entropy, enthalpic affinity with solvent molecules, and solvent molecules configurational entropy. We model self-suspended poly (ethylene glycol)-tethered NOHMs and their solutions in water. We obtain the yield stress as the minimum stress necessary to continually deform the periodic array. We also obtain a simple estimate of the free energy barrier to thermally induced relaxation of the NOHMs microstructure as a function of core volume fraction, solvent concentration, and grafting density of oligomers.