NOVELTY - In a separator comprising porous film(s) of a polymer matrix, the matrix contains polyhedral oligomeric silicon-oxygen (Si-O) clusters, comprising units with Si and O in 1:1.5, 1:1, 2:2.5 and 2:2 ratio, each substituted by (hydr)oxy, alkoxy, carboxy, optionally alkyl- or alkoxy-substituted silyl, siloxy or silylalkyl, halogen, epoxy, ester, fluoroalkyl, (blocked) isocyanate, (meth)acrylate, nitrile, amino and/or phosphino group(s) and optionally also by other groups.    USE - The separators are used in lithium batteries (claimed) and other batteries, preferably primary and secondary (rechargeable) lithium, nickel metal hydride, nickel-cadmium, lead-acid, silver-zinc and zinc-air batteries, especially lithium high power batteries, including batteries for electric vehicles.    ADVANTAGE - Polyolefin separators (based on polyethylene or mainly polypropylene) have only limited heat resistance and can be destroyed by melt down. In extreme cases, the battery may explode if a short circuit occurs. Separators reinforced by particles have only slightly higher heat resistance. Ceramic-coated glass substrates withstand much higher temperatures, do not melt down and are very safe but have inadequate strength. The present separators have good thermal stability and very good mechanical stability. In particular, their tensile strength is much higher than that of existing ceramic separators. They also have good hardness, impact strength and flexural strength. These properties simplify processing, as there is less risk of tearing. The relatively high heat resistance of the separators allows rapid charging without damaging the battery.    DETAILED DESCRIPTION - In a separator comprising porous film(s) of a polymer matrix, the matrix contains polyhedral oligomeric silicon-oxygen (Si-O) clusters of formula (I);    ((RaXbSiO1.5)m (RcXdSiO)n (ReXfSi2O2.5.5)o (RgXhSi2O2)p) (I);    a, b, c = 0-1;    d = 1-2;    e, f, g = 0-3;    h = 1-4;    m + n + o + p = 4 or more;    a + b = 1;    c + d = 2;    e + f = 3;    g + h = 4;    R = H, (cyclo)alk(en)yl, (cyclo)alkynyl, (hetero)aryl or a polymer unit, which may be substituted or linked to other functionalized oligomeric polyhedral Si-O cluster units by a polymer unit or bridge;    X = (hydr)oxy, alkoxy, carboxy, optionally alkyl- or alkoxy-substituted silyl, siloxy or silylalkyl, halogen, epoxy, ester, fluoroalkyl, (blocked) isocyanate, (meth)acrylate, nitrile, amino and/or phosphino group(s), which may have substituents of type R    An INDEPENDENT CLAIM is also included for production of such a separator.