Scalar and vectorial percolation in compressed expanded graphite

DC electrical conductivity and elastic moduli of cubic samples made of two kinds of compressed expanded graphite are measured as a function of their a pparent density. Different percolation thresholds at which the physical pro perties under study are found to vanish are determined. The accuracy of the values is confirmed by the application of the usual scaling laws above but near these thresholds: the corresponding critical exponents are indeed fou nd to be very close to their universal values. The relationships between th e connectivity d(c) (i.e., scalar) and rigidity d(r) (i.e., vectorial) crit ical densities are discussed. It is shown that the ratio d(r)/d(c) is alway s almost equal to 8/5, which fact may be accounted by the so-called Kirkwoo d-Keating (KK) model. To our knowledge, it is the first time that such a co nstant value is observed in real materials. The KK model is also consistent with critical exponents of elasticity found in both kind of samples. Hence , compressed expanded graphite appears to behave like a disordered heteroge neous medium in which elastic forces are mostly of central nature but inclu de also bond-bending contributions. (C) 2001 Elsevier Science B.V. All righ ts reserved.