Fundamental studies of surface forces in foam films are carried out to explain the stability of foams and froths in froth flotation. The thin film pressure balance (TFPB) technique was used to study the surface forces between air bubbles in water from equilibrium film thickness and dynamic film thinning measurements. The results were compared with the disjoining pressure predicted from the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The contribution from the non-DLVO force was estimated by subtracting the electrostatic double-layer and van der Waals forces from the total force (or pressure) measured. The results obtained in the present work suggest that a strong attractive force (referred to as hydrophobic force) exists at very low surfactant concentrations, and that it decreases with increasing surfactant and/or electrolyte concentrations. In contrast, pH changes have only minor effects on the hydrophobic force. The changes in the hydrophobic force observed at low surfactant concentration region have been related to foam stability in flotation. In addition, an analytical model applicable to a broad range of surfactant concentration was developed to calculate film elasticity from surface tension. The model finds, however, that the film elasticities change little at low surfactant concentrations. It is, therefore, suggested that bubble coalescence and foam stability at low surfactant concentrations may be largely affected by hydrophobic force. The TFPB technique was also used to study the surface forces in the foam films stabilized with various frothers such as pentanol, octanol, methyl isobutyl carbinol (MIBC), and polypropylene glycol (PPG). The results were compared with the foam stabilities measured using the shake tests and the film elasticity calculated using the model developed in the present work. It was found that at a low electrolyte concentration foam stability is controlled by film elasticity and surface forces, the relative contributions from each changing with frother concentration and type. It is, therefore, proposed that one can control the foam stability in flotation by balancing the elasticities of foam films and the disjoining pressure in the films, particularly the contributions from the hydrophobic force. / Ph. D.

The extended DLVO theory was used to develop a flotation model by considering both hydrodynamic and surface forces involved in the process. A stream function was used to estimate the kinetic energies for thinning the water films between bubbles and particles, which were compared with the energy barriers, created by surface forces, to determine the probability of adhesion. A general expression for the probability of detachment was derived from similar mechanism for chemical reaction, and the kinetic energy for detachment was estimated with French and Wilson's model. The hydrophobic force parameter (K132) calculated from the rate constants of single bubble flotation tests showed that, K132 for bubble-particle interaction were close to the geometric means of K131 for particle-particle interactions and K232 for bubble-bubble interaction, indicating that the combining rules developed for dispersion forces may be useful for hydrophobic forces. The model was used to predict flotation results as functions of several important parameters such as contact angle, double-layer potentials, particle size, bubble size, etc. The predictions were consistent with experience, and could be explained in view of the various subprocesses considered in the model development. Furthermore, the model suggested optimum conditions for achieving the maximum separation efficiency. The extended DLVO theory was also used to determine the hydrophobic force between two oil/solution interfaces from the equilibrium film thicknesses of dodecylammonium chloride (RNH3Cl) solutions obtained using Thin Film Balance (TFB) technique. The results showed that, the oil droplets were inherently hydrophobic, and the hydrophobic force played an important role in the stability of emulsions. This force decreased with increasing surfactant concentration, and also changed with pH and the addition of electrolyte. The interfacial area occupied by molecules indicated that, the dodecane molecules might present between two surfactant ions at interface, thus the hydrophobicity of oil/solution interface was less sensitive to the addition of the surfactant than that of air/solution interface. Thermodynamic analysis suggested that, there might exist a relationship between the interfacial hydrophobicity and the interfacial tension. / Ph. D.

An atomic force microscope (AFM) has been used to conduct force measurements to better understand the role of hydrophobic forces in flotation. The force measurements were conducted between a flat mineral substrate and a hydrophobic glass sphere in aqueous solutions. It is assumed that the hydrophobic glass sphere may simulate the behavior of air bubbles during flotation. The results may provide information relevant to the bubble-particle interactions occurring during flotation. The glass sphere was hydrophobized by octadecyltrichlorosilane so that its water contact angle was 109 degrees. The mineral systems studied include covellite (CuS), sphalerite (ZnS) and hornblende (Ca₂(Mg, Fe)₅(Si₈O₂₂)(OH,F)₂). The collector used for all the mineral systems studied was potassium ethyl xanthate (KEX). For the covellite-xanthate system, a biopotentiostat was used in conjunction with the AFM to control the potential of the mineral surface during force measurements. This was necessary since the adsorption of xanthate is strongly dependent on the electrochemical potential (Eₕ) across the solid/liquid interface. The results show the presence of strong hydrophobic forces not accounted for by the DLVO (named after Derjaguin, Landau, Verwey and Overbeek) theory. Furthermore, the potential at which the strongest hydrophobic force was measured corresponds to the potential where the flotation recovery of covellite reaches a maximum, indicating a close relationship between the two. Direct force measurements were also conducted to study the mechanism of copper-activation of sphalerite. The force measurements conducted with unactivated sphalerite in 10⁻³ M KEX solutions did not show the presence of hydrophobic force while the results obtained with copper-activated sphalerite at pH 9.2 and 4.6 showed strong hydrophobic forces. However, at pH 6.8, no hydrophobic forces were observed, which explains why the flotation of sphalerite is depressed in the neutral pH regime. Direct force measurements were also conducted using hornblende in xanthate solutions to study the mechanism of inadvertent activation and flotation of rock minerals. The results show the presence of long-range hydrophobic forces when hornblende was activated by heavy metal cations such as Cu²⁺ and Ni²⁺ ions. The strong hydrophobic forces were observed at pHs above the precipitation pH of the activating cation. These results were confirmed by the XPS analysis of the activated hornblende samples. Force measurements were conducted between silanated silica surfaces to explore the relationship between hydrophobicity, advancing contact angle (CA), and the magnitude (K) of hydrophobic force. In general, K increases as Contact Angle increases and does so abruptly at Contact Angle=90°. At the same time, the acid-base component of the surface free energy decreases with increasing CA and K. At CA>90°, GammaS^AB approaches zero. Based on the results obtained in the present work a mathematical model for the origin of the hydrophobic force has been developed. It is based on the premise that hydrophobic force originates from the attraction between large dipoles on two opposing surfaces. The model has been used successfully to fit the measured hydrophobic forces using dipole moment as the only adjustable parameter. However, the hydrophobic forces measured at CA>90° cannot be fitted to the model, indicating that there may be an additional mechanism, possibly cavitation, contributing to the appearance of the long-range hydrophobic force. / Ph. D.

Between two neighboring air bubbles in a froth (or foam), a thin liquid film (TLF) is formed. As the bubbles rise upwards, the TLFs thin initially due to the capillary pressure created by curvature changes. As the film thicknesses (H) reach approximately 200 nm, the disjoining pressure created by surface forces in the films also begins to control the film drainage rate and affect the waves motions at the air/water interfaces. If the disjoining pressure is negative, both the film drainage and the capillary wave motion accelerate. When the TLF thins to a critical film thickness (Hcr), the amplitude of the wave motion grows suddenly and the two air/water interfaces touch each other, causing the TLF to rupture and bubbles to coalesce. In the present work, a new model that can predict Hcr has been developed by considering the film drainage due to both viscous film thinning and capillary wave motion. Based on the Hcr model, bubble-coarsening in a dynamic foam has been predicted by deriving the geometric relation between the thickness of the lamella film, which controls bubble-coalescence rate, and the Plateau border area, which controls liquid drainage rate. Furthermore, a model for predicting bubble-coarsening in froth (3-phase foam) has been developed by developing a film drainage model quantifying the effect of particles on pc. The parameter pc is affected by the number of particles and the local capillary pressure around particles, which in turn vary with the hydrophobicity and size of the particles in the film. Assuming that films rupture at free films, the pc corrected for the particles in lamella films has been used to determine the critical rupture time (tcr), at which the film thickness reaches Hcr, using the Reynolds equation. Assuming that the number of bubbles decrease exponentially with froth height, and knowing that bubbles coalesce when film drains to a thickness Hcr, a bubble coarsening model has been developed. The model predictions are in agreement with the experimental data obtained using particle of varying hydrophobicity and size. / Ph. D.

It is well known that water molecules at room temperature tend to form ‘iceberg’ structures around the hydrocarbon chains of surfactant molecules dissolved in water. The entropy reduction (times the absolute temperature T) associated with the iceberg structure can be considered as the net driving force for self-assembly. More recently, many investigators measured long-range attractive forces between hydrophobic surfaces, which are likely to result from structuring of the water molecules in the vicinity of the hydrophobic surfaces. Similarly, the hydrophobic nature of most gas hydrate formers may induce ordering of water molecules in the vicinity of dissolved solutes. In the present work, the surface forces between thiolated gold surfaces have been measured using an atomic force microscope (AFM) to obtain information on the structure of the thin films of water between hydrophobic surfaces. The results have been used to develop a new concept for the formation of gas hydrates.

In 1982, Israelachvili and Pashley reported the first measurements of a hitherto unknown attractive force between two mica surfaces hydrophobized in cetyltrimethylammonium bromide (CTAB) solutions. Follow-up experiments conducted by many investigators confirmed their results, while others suggested that the "hydrophobic force" is an artifact due to nanobubbles (or cavitation). Evidences for the latter included the discontinuities (or steps) in the force versus distance curves and the pancake-shaped nano-bubbles seen in atomic force microscopic (AFM) images. Recent measurements conducted in degassed water showed, however, smooth force versus distance curves, indicating that the hydrophobic force is not an artifact due to nanobubbles.1, 2 Still other investigators3, 4 suggested that the long-range attraction observed between hydrophobic surfaces is due to the correlation between the patches of adsorbed ionic surfactant and the patches of unoccupied surface. For this theory to work, it is necessary that the charged patches be laterally mobile to account for the strong attractive forces observed in experiment. In an effort to test this theory, AFM force measurements were conducted with gold substrates hydrophobized by self-assembly of alkanethiols and xanthates of different chain lengths. The results showed long-range attractions despite the fact that the hydrophobizing agents chemisorb on gold and, hence, the adsorption layer is immobile. When the gold surfaces were hydrophobized in a 1 Ã 10-3 M thiol-in-ethanol solution for an extended period of time, the force curves exhibited steps. These results indicate that the long-range attractions are caused by the coalescence of bubbles, as was also reported by Ederth.5 The steps disappeared, however, when the species adsorbed on top of the chemisorbed monolayer were removed by solvent washing, or when the gold substrates were hydrophobized in a 1 Ã 10-5 M solution for a relatively short period of time. AFM force measurements were also conducted between gold substrates coated with short-chain thiols and xanthates to obtain hydrophobic surfaces with water contact angles (ï ±) of less than 90o. Long-range attractions were still observed despite the fact that cavitation is thermodynamically not possible. Having shown that hydrophobic force is not due to coalescence of pre-existing bubbles, cavitation, or correlation of charged patches, the next set of force measurements was conducted in ethanol-water mixtures. The attractive forces became weaker and shorter-ranged than in pure water and pure ethanol. According to the Derjaguin's approximation6, an attractive force arises from the decrease in the excess free energy (ï §f) of the thin film between two hydrophobic surfaces.7 Thus, the stronger hydrophobic forces observed in pure water and pure ethanol can be attributed to the stronger cohesive energy of the liquid due to stronger H-bonding. Further, the increase in hydrophobic force with decreasing separation between two hydrophobic surfaces indicates that the H-bonded structure becomes stronger in the vicinity of hydrophobic surfaces. The force measurements conducted at different temperatures in the range of 10-40C showed that the hydrophobic attraction between macroscopic surfaces causes a decrease in film entropy (Sf), which confirms that the hydrophobic force is due to the structuring of water in the thin film between two hydrophobic surfaces. The results showed also that the hydrophobic interaction entails a reduction in the excess film enthalpy (Hf), which may be associated with the formation of partial (or full) clathrates formed in the vicinity of hydrophobic surfaces. The presence of the clathrates is supported by the recent finding that the density of water in the vicinity of hydrophobic surfaces is lower than in the bulk.8 / Ph. D.

Flotation is a process of separating particulate materials of different surface properties in a hydrodynamic environment, and is used extensively for separating different minerals from each other in the mining industry. In this process, air bubbles are introduced at the bottom of a particulate suspension (pulp), so that bubbles coated with hydrophobic particles rise to the top and form a froth phase while hydrophobic particles stay in suspension. The selectivity of the flotation process is determined by the hydrophobicity of the particulate materials involved, while the kinetics of the process is controlled by the hydrodynamic conditions and the disjoining pressures in the thin aqueous films between air bubbles and particles. In the present work, a mathematical model for the flotation process has been developed by considering both the hydrodynamic and surface chemical parameters. The model can describe the events occurring in both the pulp and froth phases of a mechanically-agitated flotation cell. The pulp-phase model is based on predicting the kinetics of bubble-particle attachment using the DLVO extended to include contributions from hydrophobic force and the theory of turbulent collision. The froth-phase model is based on predicting the rate of bubble-particle detachment by considering bubble coarsening and water recovery. The predictions from the overall flotation model are in general agreement with the results obtained in single-bubble flotation experiments and the flotation test results reported in literature. Since the model has been developed largely from first principles, it has predictive and diagnostic capabilities. / Ph. D.

This dissertation describes new methods for measuring surface forces using evanescent waves, and applications to non-DLVO forces. An evanescent wave, generated at a solid-liquid interface, is scattered by AFM tips or particles attached to AFM cantilevers. The scattering of this wave is used to determine absolute separation between surfaces and/or the refractive index as a function of separation in AFM measurements. This technique is known as evanescent wave atomic force microscopy (EW-AFM). The scattering of an evanescent wave by Si3N4 AFM tips is large and decays exponentially with separation from a refractive index boundary. Thus, scattering is a useful method for measuring the separation between a Si3N4 tip and sample. This method has been used to measure the absolute separation between a tip and sample in the presence of an irreversibly adsorbed polymer film. Measurement of the film thickness and time response of the polymer to applied loads has also been studied. These measurements are not possible using current AFM techniques. In addition to measurements in polymer systems, the simple scattering profile from Si3N4 tips was used to re-examine short range hydration forces between hydrophilic surfaces. Results presented in this thesis suggest this force does not depend on the hydrated radius of the ion between glass and silicon nitride. The scattering generated by a Si3N4 tip has also been used to measure the refractive index of bulk fluids and thin films between hydrophobic surfaces. Based on these results, I have shown that a long-range attraction between hydrophobic surfaces is accompanied by an increase in the refractive index between the tip and surface. From this I have concluded that the attractive force, measured in this study, is the result of an increase in the concentration of organic material between surfaces. Finally, I have shown that the scattering profile depends on the material and size of the scattering object. Scattering from silicon nitride tips is exponential with separation. In contrast, the scattering profile from silicon tips, which are similar in size and geometry, is not a simple exponential. The scattering profile of larger spherical particles attached to cantilevers is also not exponential. It is approximately the sum of two exponentials. The functional form of the scattering profile with separation is consistent with the transmission of evanescent light through flat planar films. This result would suggest that a re-examination of the separation-dependence of scattering in TIRM measurements is necessary. / Ph. D.

Surface force measurements previously conducted with thiolated gold surfaces showed a decrease in excess film entropy (£GSf), suggesting that hydrophobic force originates from changes in the structure of the medium (water) confined between hydrophobic surfaces. As a follow-up to the previous study, surface force measurements have been conducted using an atomic force microscope (AFM) with hydrophobic silica surfaces at temperatures in the range of 10 to 40¢XC. The silica sphere and silica plate were treated by both chemisorption of octadecyltrichlorosilane (OTS) and physical adsorption of octadecyltrimethylammonium chloride (C18TACl). A thermodynamic analysis of the results show similar results for both of the samples, that both ""Sf and excess film enthalpy ("Hf) become more negative with decreasing thickness of the water layer between the hydrophobic surfaces and decreasing temperature. |"Hf | > |T"Sf| represents a necessary condition for the excess free energy change ("Gf ) to be negative and the hydrophobic interaction to be attractive. Thus, the results obtained with both the silylated and C18TACl-adosrbed silica surfaces in the present work and the thiolated gold suefaces reported before show hydrophobic forces originate from structural changes in the medium. Thermodynamic analysis of SFA force measurements obtained at various temperatures revealed that "Sf were much more negative in the shorter hydrophobic force ranges than in the longer ranges, indicating a more significant degree of structuring in the water film when the two hydrophobic surfaces are closer together. It is believed that the water molecules in the thin liquid films (TLFs) of water form clusters as a means to reduce their free energy when they cannot form H-bonds to neighboring hydrophobic surfaces. Dissolved gas molecules should enhance the stability of structured cluster due to the van der Waals force between the entrapped gas molecules and the surrounding water molecules1, which may enhance the strength of the hydrophobic force. Weaker long-range attractive forces detected in degassed water than in air-equilibrated water was found in the present work by means of AFM force measurements, supporting the effect of dissolved gas on the structuring of water. At last, temperature effects on hydrophobic interactions measured in ethanol and the thermodynamic analysis revealed similar results as those found in water, indicating that the hydrophobic force originates from H-bond propagated structuring in the mediums. / Ph. D.

Hydrophobic interaction plays an important role in biology, daily lives, and a variety of industrial processes such as flotation. While the mechanisms of hydrophobic interactions at molecular scale, as in self-assembly and micellization, is relatively well understood, the mechanisms of macroscopic hydrophobic interactions have been controversial. It is, therefore, the objective of the present work to study the mechanisms of interactions between macroscopic hydrophobic surfaces in H-bonding liquids, including water, ethanol, and water-ethanol mixtures. The first part of the present study involves the measurement of the hydrophobic forces in the thin liquid films (TLFs) confined between two identical hydrophobic surfaces of contact angle 95.3o using an atomic force microscope (AFM). The measurements are conducted in pure water, pure ethanol, and ethanol-water mixtures of varying mole fractions. The results show that strong attractive forces, not considered in the classical DLVO theory, are present in the colloid films formed with all of the H-bonding liquids tested. When an H-bonding liquid is confined between two hydrophobic surfaces, the vicinal liquid molecules form clusters in the TLFs and give rise to an attractive force. The cluster formation is a way to minimize free energy for the molecules denied of H-bonding with the substrates. Thus, solvophobic forces are the result of the antipathy between the CH2- and CH3-coated surface and H-bonding liquid confined in the film. A thermodynamic analysis of the solvophobic forces measured at different temperatures support this mechanism, in which solvophobic interactions entail decreases in the excess film enthalpy and entropy. The former represents the energy gained by building clusters, while the latter represents loss of entropy due to structure building. Thus, hydrophobic interaction may be a subset of solvophobic interaction. The solvophobic forces are strongest in pure water and pure ethanol, and decrease when one is added to the other. Adding a very small amount of ethanol to water sharply reduced the solvophobic force due to the adsorption of the former with an inverse orientation. An exposure of the OH-group toward the aqueous phase decreases the antipathy between the surface and H-bonding liquid and hence causes the hydrophobic (or solvophobic) forces to decrease. The second part of the study involves the measurement of the hydrophobic forces in the wetting films of water using the force apparatus for deformable surfaces (FADS). This new instrument recently developed at Virginia Tech is designed to monitor the deformation of bubbles to determine the surface forces in wetting films. In effect, an air bubble is used a force sensor. The measurements have been conducted with gold, chalcopyrite, and galena as substrates. The results obtained with all three minerals show that hydrophobic force increases with increasing water contact angle, suggesting that hydrophobic forces are inherent properties of hydrophobic surfaces rather than created from artifacts such as preexisting nanobubbles and/or cavitation. A utility of the intrinsic relationship between hydrophobic force and contact angle is to predict flotation kinetics from the hydrophobicity of the minerals of interest. / Ph. D.