NOVELTY - The method involves positioning a collection face of a collector substrate proximate an electrospinning apparatus, where the collector substrate includes an anode electrode (12) composed as either a positive or a negative electrode for an electrochemical battery cell (88) of a lithium ion battery. A non-woven polymer fiber mat comprising a fibrous mass of polymer fibers, is electrospun onto the collection face of the substrate to form an electrode-separator integral segment (10), where the polymer fiber mat includes a thickness that ranges from about 5 micrometers to about 50 micrometers.    USE - Method for making a single-layer separator that is placed between a negative electrode and a positive electrode in an electrochemical battery cell of a lithium ion battery to connect an electrical device e.g. electric motor, electrical loads and power-generating device, for hybrid electric vehicle and an extended range electric vehicle, for applications e.g. stationary applications, portable applications and vehicle applications.    ADVANTAGE - The method enables reliably producing a thermally stable and sufficiently porous separator from a robust array of polymer materials. The method enables the electrode-separator integral segment to be calendared in a calendaring apparatus to hot-press the various components of the segment together to improve mechanical performance and dimensional uniformity. The method enables the non- woven polymer fiber mat to render the separator sufficiently porous and ionically conductive, so that an infiltrated liquid electrolyte solution to facilitate the migration of lithium ions between the electrodes during operation of the lithium ion battery.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for an electrochemical battery cell of a lithium ion battery.    DESCRIPTION OF DRAWING(S) - The drawing shows a cross-sectional view of an electrochemical battery cell formed with the electrode-separator integral segment.    Electrode-separator integral segments (10, 110)    Electrodes (12, 92, 112)    Electrochemical battery cell (88)    Metallic current collectors (94)    Tabs (96)