The gap between the measured and calculated liquid-liquid interfacial tensions derived from contact angles

We present our new findings about the causes of discrepancies between the m easured and calculated liquid-liquid interfacial tensions derived from cont act angles. The calculated ones are based on either the equation developed by Fowkes or that by van Oss, Chaudhury and Good (VCG), while the measured ones are based on the sessile drop, weight-volume by Janzuk et al. and the axisymmetric drop shape analysis (ADSA) by Kwok and Neumann. Indeed, there are deviations between the calculated and measured results. For an immiscib le liquid-liquid or liquid-solid interface, we prefer to employ Harkins spr eading model, which requires the interfacial tension to be constant. Howeve r, for the initially immiscible liquid-liquid pairs, we propose an adsorpti on model, and our model requires the interfacial tension to be varying and the surface tensions of bulk liquids at a distance from the interface to re main unchanged. Thus, the difference between the initial and final interfac ial spreading coefficients (S-i) equals the equilibrium interfacial film pr essure (pi(i))(e). According to our findings, the calculated interfacial te nsion represents the initial value (gamma(12))(0), which differs from the e quilibrium value (gamma(12))(e) obtained experimentally after some time del ay. This expected gap at a reasonable time frame is chiefly caused by the e quilibrium interfacial film pressure between the two liquids, The initial ( or calculated) interfacial tension can be positive or negative, while the e quilibrium (or measured) one can reach zero. In fact, the former is shown t o have more predictive value than the latter A negative initial interfacial tension is described to favor miscibility or spontaneous emulsification bu t it tends to revert to zero instantaneously. Thus, a miscible liquid mixtu re should have zero interfacial tension. In response to recent papers by Kw ok er al., we show that the disagreements between the calculated and measur ed interfacial tensions are definitely not caused by the failure of the VCG approach. Correct interfacial tensions are calculated for liquid pairs con taining formamide or dimethyl sulfoxide (DMSO) by using the dispersion comp onents cited in Fowkes et al.'s later publication. With the corrected surfa ce tension components, the equilibrium interfacial film pressures (pi(i))(e )'s for at least 34 initially immiscible liquid pairs have been calculated. These values are generally lower than the corresponding spreading pressure s pi(e)'s obtained by others using the Harkins model. Recently, we establis hed a relationship between these two film pressures with the Laplace equati on and found a new criterion for miscibility to be (pi(i))(e) = pi(e).