Theoretical Foundations, Models, and Calculations of the Compositions of Particulate-Filled Polymers with Different Types of Structures and Properties

For the first time, the theoretical foundations for building the structure of particulate-filled polymer composite materials (PFPCMs) are presented from the standpoint of joint examination of Shklovsky-de Gennes model ideas concerning the formation of the structure of dispersed fillers in space and, proposed by us, a generalized model, including the creation of free space, its filling with a polymer matrix (binder) and its functional division into three components: φ_p = θ + B + M (θ is the proportion of the polymer phase-matrix for the formation of an interlayer between the filler particles; B is the proportion of the polymer phase-matrix at the maximum packaging of the dispersed phase; M is the proportion of the polymer phase-matrices in boundary layers). Correlation dependences between the parameters of heterogeneity in space (lattice parameters: Z and k_pac) and the generalized parameter θ were established, all PNPCMs were classified according to the structural principle [structure type: DS—diluted, LFS—low-filled, MFS—medium-filled (MFS-1 and MFS-2) and HFS—highly filled dispersed systems]. Generalized (θ, V, M) and reduced parameters (θ/V and θ/S_n) are proposed to describe the structure of the PFPCMs. Experimental methods have been developed for determining the main parameter of a dispersed filler for constructing PFPCMs structures—the maximum packing (k_pac) and the maximum content of dispersed fillers (parameter φ_m) of different sizes. It is shown that the construction of all possible types of structures and compositions of PFPCMs should begin with HFS at the content of dispersed filler equal to φ_m (fixed starting point), similar to the construction of the stepped CHICHEN ITZA PYRAMID with the apex—HFS, the base—a polymer matrix (PM) and with steps—different types of structures (MFS-2, MFS-1, LFS and DS). The dependences of the physicochemical, rheological, physicomechanical, electrophysical, thermophysical characteristics of PFPCMs on the generalized and reduced parameters, as well as on the lattice parameters Z and k_pac of the dispersed filler are established, and it is shown that the type of structure and its parameters determine the properties of PFPCMs. The obtained dependencies for the first time made it possible to compare the characteristics of PFPCMs with the same types of structures, and not at a constant value of the content of the dispersed phase (φ_f = const), which is not correct. This concept is the basis for the creation of high-tech, high-strength, heat-conductive and heat-insulating, as well as electrically conductive, etc. PFPCMs. New theoretical provisions can be extended to the construction of structures of composite materials based on metal and ceramic matrices.