ABSTRACT
From eqs. [II-26 to 29] the Hamaker constant All of a homogeneous material (1) in the condensed state (i.e., either liquid or solid) can be obtained via the Lifshitz (1955) approach; see Chapter II. However, the determination of the necessary spectroscopic data can be tedious and, in many cases, diffi cult. But if it can be shown that there is a reliable proportionality between All and the apolar surface tension component γ iLW of material (i), the determination of the Aii value of various liquid or solid materials can be much simplifi ed.* Using eq. [II-32]:
γ π
A =
which can be rewritten as:
Aii o iLW= 24 2π γ [III-1]†
that proportionality factor is 24 2π o. The minimum equilibrium distance o does not, in this case, take the Born repulsion (van Oss and Good, 1984; van Oss et al., Chem. Rev., 1988) into account, and thus is not an accurate measure of the “real” equilibrium distance, which may not be precisely measurable by this approach in any event (see below). For a fairly large number of cases, where All can be determined from permitivities and spectroscopic data (see Tables III-1 and 2), as well as from known values of γ iLW, a comparison can be made (see Table III-3). From this variegated collection of materials it can be seen that the value of o thus found in all cases is close to the average value of o = 1.57 Å, with a standard deviation (S.D.) of ±0.09 Å (van Oss et al., Chem. Rev., 1988). The proportionality factor 24 2π o then is 1.8585 (±0.0065 S.D.) × 10-14 cm2. Thus, for all practical purposes, for single, pure substances:
A S Dii iLW= ± × −1 8585 0 0065 10 14. ( . . .) γ [III-2A]
when γ iLW is expressed in ergs/cm2, or in mJ/m2, to obtain All in ergs. Or one may use:
A S Dii iLW= ± × −1 8585 0 0065 10 21. ( . . .) γ [III-2B]
(here also γ iLW is expressed in ergs/cm2, or in mJ/m2), to obtain Aii in J. Thus, the Hamaker constants of single pure substances in the condensed state
can be derived from their apolar surface tension component γ iLW via the above proportionality factor, e.g., eqs. [III-2A, 2B], or from the averaged o value of 1.57 Å using eq. [III-1], plus or minus less than 0.7% (S.D.).
