Previous cloud chamber experiments on freezing of supercooled cloud droplets with single immersed, size-selected 400 nm and 800 nm kaolinite particles revealed a sigmoidal increase of the fraction of frozen cloud droplets with decreasing temperature in the range from 243 to 236 K. Assuming uniformity of the particle composition and horizontal homogeneity of the phase compatibility, applying classical nucleation theory (CNT), and fitting the microscopic "ice contact angle" to these experimental freezing probabilities disclosed a negative temperature coefficient of the ice contact angle, revealing an apparent increase of the cryophobia of the freezing catalyzer. On the basis of Derjaguin's thermomechanic concept of the disjoining pressure, a conceptual model is proposed that links the semi-empirical ice contact angle to its generating molecular interaction forces by extrapolating macroscopic relations to microscopic scales. Within the framework of a closure study with consideration of a comprehensive set of physical constraints for the water/ice/kaolinite system, this model is used to determine the residual molecular interaction force, which is necessary to reproduce the experimentally derived ice contact angles. The residual interaction force is on the order of magnitude of steric oscillation forces at the kaolinite/ice interfacial layer and corresponds to a temperature-dependent negative line tension of -(5-28)pN. The line tension behavior is discussed in the light of previous findings on heterogeneous water nucleation on solid surfaces and computer simulations of the water/ice/kaolinit system. Uncertainties originating from the employed model assumptions, especially interference due to interparticle variability are analyzed. Finally, observational requirements for a conclusive discrimination between inter- and intraparticle effects are discussed.