Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (h eat flow) J(q)(0) of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the siz es distribution of the pores. For porous glass with large pore size distrib ution, obtained by sol-gel technology, we show that in the domain of ice me lting, the heat flow J(q) is related to the melting: temperature depression of the solvent, DeltaT(m), by the scaling law: J(q)(0) similar to DeltaT(m )(-(1+D)). We suggest that the exponent D is of the order of the fractal di mension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron sca ttering and electronic energy transfer measurements on similar porous glass . The proposed scaling law is explained if one assumes that the pore size d istribution is self similar. In porous glass obtained from mesomorphic copo lymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate (q less than or e qual to 2 degreesC/min) is the most rapid and less expensive method for det ermining the pore distribution and the fractal exponent of a porous materia l.