NOVELTY - Method (M1) of coating a surface involves exposing the surface having hydroxyl groups to bidentate free radical crosslinking initiator; reacting hydroxyl group of the surface with each of the terminal ends of the bidentate free radical crosslinking initiator; cleaving the backbone of the bidentate free radical crosslinking initiator to produce a surface bound free radical at each cleaved end; initiating polymerization of a compound by the surface bound free radicals produced; and forming a coating of polymer on at least a portion of the surface.    USE - For coating surfaces e.g. silica nanoparticles to form monolithic products (claimed) useful to make superior body armor for police and other physical protection applications and in run flat tires; as media in chromatography columns, in lightweight thermal insulation, as acoustic insulation, as catalyst supports, in dielectrics in electrodes for fuel cells or other purposes, in optical sensors, in aircraft structural components, in polymer matrix composites, as hydrophobic coatings for glass, protective coatings for metals (such as aluminum), and other surfaces, as ultrafiltration nanoporous membranes, as nanoparticle-reinforced polymer nanoparticle composites, conductive substrates using conductive polymer coatings and a host of other applications.    ADVANTAGE - The monolithic product has a density less than 0.8 g/cc and a specific energy absorption less than 194 J/g. The crosslinked aerogels exhibit greatly increased strength with only nominal increase in density. The monolithic product has very high ultimate compressive strength. In this method the gelation process and the crosslinking process are deconvoluted by a single free radical crosslinking process, and especially through use of a surface bound bidentate free radical polymerization initiator in a single pot without interference of chemistry of one process with the other process and all polymer chains formed are surface bound so that subsequent solvent exchange steps may in principle be eliminated. Unlike the prior art methods where several solvent exchange steps are required.    DETAILED DESCRIPTION - Method (M1) of coating a surface involves providing a surface having hydroxyl groups; exposing the surface to a bidentate free radical crosslinking initiator comprising terminal ends each able to form a chemical bond with a hydroxyl group, and a backbone extending between the terminal ends, where the backbone is able to cleave to produce a pair of cleaved ends, each cleaved end having a free radical; reacting a hydroxyl group of the surface with each of the terminal ends of the bidentate free radical crosslinking initiator; cleaving the backbone of the bidentate free radical crosslinking initiator to produce a surface bound free radical at each cleaved end; initiating polymerization of a compound by the surface bound free radicals produced; and forming a coating of polymer on at least a portion of the surface. INDEPENDENT CLAIMS are included for the following:    (1) a monolithic product comprising a three dimensional assembly of nanoparticles with void space between nanoparticles having surfaces comprising hydroxyl groups, and a polymer coating covering at least some of the surfaces of the nanoparticles and filling at least some of the void space between nanoparticles, the polymer coating having been formed by surface initiated polymerization of constituent monomers of the polymer at locations on nanoparticle surfaces that had been modified by reaction of the hydroxyl groups on the surfaces with a bidentate free radical crosslinking initiator; and    (2) a method (M2) of producing monolithic product, comprising an assembly of three dimensionally dispersed, polymer coated, nanoparticles, involving providing a gel comprising nanoparticles having surfaces comprising a surface bound bidentate free radical crosslinking initiator; exposing the gel to compound able to polymerize; allowing the bidentate free radical crosslinking initiator to initiate polymerization of the compound at the gel surfaces; forming a polymer coating on at least a portion of the surfaces; and drying into a monolithic product.