The contact angles for liquids at heterogeneous rigid surfaces are discussed based on concepts that have recently been established for wetting and spreading phenomena at these surfaces. The discrete nature of the region in the vicinity of the three-phase contact line is critically reviewed and the excess energy associated with this region is analyzed. Also, the problem of classification of the surface heterogeneity with regard to the size of heterogeneous domains and their effects on contact angles is emphasized in this contribution.
The size, shape, and distribution of the heterogeneous pattern affect the advancing, receding, and equilibrium contact angles. There is, however, no universal theoretical model which describes all possible cases. It seems that the equilibrium contact angle for a liquid at a heterogeneous surface composed of macroscopic- and microscopic-sized patterns can be predicted based on the Cassie equation and the modified Cassie equation (including the line tension term) respectively. However, the contribution of the linear free energy, associated with a contorted three-phase contact line, to contact angles for liquids at heterogeneous surfaces still remains unclear. This is due to the controversial nature of the magnitude of the line tension and the effect of contortion of the three-phase contact line on the macroscopic ("apparent") contact angle. Also, both thermodynamic approaches, Cassie and modified Cassie equations, cannot predict contact angle hysteresis. The difference between the advancing and the receding contact angles depends on the position and contortion of the three-phase contact line at a heterogeneous surface. Although this phenomenon is well understood conceptually, an adequate model which could be easily adapted for real systems with randomly distributed heterogeneities of varying size and shape does not exist.
Further, the studies for systems with microscopic heterogeneities are almost exclusively limited to theoretical modelling. The systems with nanoscopic and molecular heterogeneities are poorly understood. There is still controversy with regard to the use of a theoretical model for describing the contact angles for liquids at these surfaces.
Finally, the characteristic features of a region in the vicinity of the three-phase contact line and their effects on the macroscopic contact angle are poorly understood. Both theoretical modelling and experimental investigation of this region are in an early stage and no general rules can be made.

The liquid-phase silylation of silica with various silanes is discussed. In each case, the reaction mechanism involved is more complex than often believed. Many reactions can occur simultaneously and the resulting surface layer depends largely on the synthesis conditions. Special attention should be given to the role of water in the synthesis. It can occur as physisorbed molecules on the substrate prior to modification, but it may be involved in the reaction mixture itself or even as humidity during the post-reaction curing step. In each case, the water molecules have an enormous impact on the modification reactions, causing a polymerization of the silane molecules and resulting in a thick but irreproducible and irregular surface layer.

Behavior of surfactant mixtures at solid-liquid interfaces was investigated using anionic-nonionic and cationic-nonionic surfactants of different structures. The results show that adsorption of nonionic surfactants on alumina was enhanced significantly by the coadsorption of ionic surfactants. The adsorption behavior of these binary surfactant mixtures was dependent upon the ratio of the two surfactants in the mixture. With an increase in the ionic surfactant content, the adsorption of nonionic surfactant increased and the isotherm shifted to lower surfactant concentrations. Synergism and competition between the ionic and nonionic surfactants were observed in different concentration ranges at different mixing ratios.

A pH-jump relaxation technique was developed for the investigation of proton transfer processes taking place at the oxide/aqueous interface. This approach is possible within narrow windows of equilibrium surface nonuniformity as revealed by the sample's proton affinity distribution (PAD). Within a restricted domain of the observed relaxation spectrum, a simple kinetic model coupled with appropriate charge balance allows for the determination of apparent kinetic constants of proton binding/release. This approach provides an independent estimate of the equilibrium constant which coincides with the mean PAD value of the specific nonuniformity domain.

The enthalpies of surface reactions at Si₃N₄/water interface are determined from the temperature dependence of the point of zero charge (p.z.c.). The p.z.c. is determined by the "mass titration method". According to the surface complexation model, the surface charge is a result of protonation and deprotonation of amphoteric surface sites. For Si₃N₄ the main surface groups are silanol (Si-OH) and silazane (Si₂=NH). The temperature dependence of p.z.c. yields the standard enthalpies of deprotonation of silanol groups (12 kJ mol^-1) and the standard enthalpy of protonation of silazane groups (-44 kJ mol^-1).

A theoretical analysis of the temperature dependence of the adsorption isotherms of simple ions, monitored experimentally under the conditions when the bulk concentration of the basic electrolyte ions is not constant, is presented. Recommendations how to conduct such measurement to extract the non-configurational enthalpic effects, accompanying the adsorption of ions, are given.

The experimental data of organic solute adsorption from dilute aqueous solutions on activated carbon are analyzed by using the model of liquid adsorption on heterogeneous solid surfaces. The effects of energetic heterogeneity and electrostatic interactions among charged adsorbent surface and adsorbed species are taken into account.

Density functional results are presented for adsorption of fluids on a surface bulit of two intersecting planes. It is shown that for a concave surface the wetting temperature is lower, whereas for the convex surface it is higher than for a flat wall.

Hydroxy-chromium smectites were prepared using hydroxy-chromium solutions with a OH/Cr content of about 1 and 2 aged for six weeks at 313 K. To study the thermal stability and oxidation resistance of hydroxy-chromium, interlayers materials were calcined at 473 K and 573 K in air. The extent of intercalation was evaluated using X-ray diffraction. The structural parameters such as surface areas, micropore volumes, and mesopore size distributions were evaluated from sorption of nitrogen. The surface chemistry was described in terms of the pK_a distributions calculated from potentiometric titration data using the SAIEUS procedure. The results obtained demonstrate that the properties of final materials depend on the OH/Cr content in the intercalating solution. When OH/Cr was about 1 the materials with a developed surface area and microporosity were obtained. The thermal stability and oxidation resistance of hydroxy-Cr smectites differ significantly. The sample obtained using OH/Cr about 1 is more oxidation resistant compared to this obtained with OH/Cr about 2. The differences in the observed behavior are likely related to the orientation and organization of hydroxy-chromium oligomers within the interlayer space of smectite.

The effect of chemical heterogeneity on the adsorption of phenol from aqueous solution by active carbon has been investigated. The carbon surfaces were oxidized, chlorinated and treated with ethylene. The changes in surface heterogeneity caused by these procedures were estimated by thermal desorption, chemical analysis, mass titration and acid-base depletion measurements. The influence of surface heterogeneity on adsorption from aqueous phenol is discussed in terms of the Dubinin-Radushkevich (DR) equation and calorimetric studies.
It was determined that the addition of a large number of oxide groups on the surface of the carbon, created by the use of a nitric acid treatment, resulted in the most pronounced changes to the phenol uptake from aqueous solution.

The adsorption of decyl- and tetradecylpyridinium chloride was studied on silicas with different pore sizes in the mesopore range and on nonporous silicas at pH 7. From adsorption isotherms of surfactant ions and their chloride counterions the part of surfactant, bound by ion exchange via electrostatic interactions and the part of surfactant, adsorbed by hydrophobic bonding, forming surface aggregates was evaluated. With decreasing pore size of the silicas surface aggregation decreases more than ion exchange on the surface. At pH 9 only the part of ion exchange is increased while total adsorption remains almost constant in a mesoporous support. An additional contribution of hydrophobic bonding even to the adsorption of surfactant ions via ion exchange is demonstrated by the different adsorption behavior of decyl- and tetradecylpyridinium ions to silica. From the saturation values of the surfactants on the silicas it is suggested that aggregate structures exist on the surface at pH 7 which are formed by a partial fusion of isolated aggregates formed at lower pH values.

Controlled Transformation Rate Thermal Analysis (CTRTA) and high resolution argon adsorption at 77 K treated by the Derivative Isotherm Summation (DIS) procedure were used for studying the retention mechanisms of phenol on activated carbons that are very heterogeneous adsorbents. The combination of these two techniques appears as a very powerful tool as it allows to identify the most energetic adsorption sites for phenol molecules on activated carbons. These sites are micropores which are filled by argon between Ln(P/Ps) = -12 to -7. Smaller and larger pores appear less energetic. The proposed methodology could certainly be applied to numerous adsorption systems at the solid/liquid interface.

Adsorption of a cationic surfactant, benzyldimethyldodecylammonium bromide (BDDAB), from aqueous solutions on negatively charged surfaces of precipitated silica S91-16 and crystalline quartz at 298 K and free pH has been studied using adsorption microcalorimetry. Differential molar enthalpy of displacement was correlated with the experimental adsorption isotherm and plotted as a function of the amount adsorbed. The general (qualitative) shape of the enthalpy curve appears to be dependent upon the crystalline structure of silica (amorphous-crystalline). The experimental calorimetric and adsorption data for BDDAB were compared with those for benzyltrimethylammonium bromide (BTMAB), a molecule containing no alkyl chain, in order to demonstrate an ion-exchange mechanism of individual surfactant adsorption onto silica S91-16 at low surface coverages.

The effect of grinding on the interfacial properties of talc has been studied. The enthalpies of immersion in n-heptane and water were measured calorimetrically for three talc samples: the original sample and two other samples obtained by grinding in a special grinder. A simple model of a heterogeneous talc surface with a bimodal distribution of surface sites (hydrophobic basal planes and hydrophilic lateral surfaces) was applied to elucidate changes in the enthalpy of immersion per unit surface area after grinding of the talc sample. The process of grinding is shown to modify the proportion between both surface components.