A high kinetics rate electrochemical cell in which at least one of the electrodes is composed of a mesostructural electroactive material is comprising a three-dimensional framework structure of mesoporous texture forming a bicontinuous junction of large specific surface area with the electrolyte. The electrode material, which is suited for reversible ion intercalation and for electronic transport, is penetrated by an interconnected porous space filled with electrolyte the latter serving for ionic transport. The three dimensional framework structure of the electrode is designed in a manner to overcome impediment of ionic diffusion in the electrolyte encountered with conventional high surface area electrodes and to provide interconnectivity, mechanical stability of the solid phase as well as access of the electrolyte to the entire pore space. A low temperature method of preparation of the electrodes employs a high-speed deposition of the electrically active material in the form of a thin film. The application of said electrodes in high power lithium ion insertion batteries, photovoltaic cells, supercapacitors and fast electrochromic devices is disclosed.