Statistical thermodynamics of fluids with orientation - dependent interactions : applications to water in homogeneous and heterogeneous systems

The aim of the present study was to develop a lattice theory for systems, homogeneous as well as heterogeneous, containing molecules with orientation- dependent interactions such as water. It was soon recognised that the so-called Bragg-Williams mean-field approximation is not capable of reproducing the typical temperature dependence of the thermodynamic properties of such systems. This is due to the neglect of correlations between positions and orientations of the molecules. To improve this, we based ourselves on the so called quasi-chemical approximation.In <strong>chapter I</strong> , some background information is given on the systems with which the present study is concerned and the theoretical methods that are employed.In <strong>chapter II</strong> the theory is derived in a general fashion, for an arbitrary collection of monomeric species. To model heterogeneous systems, the lattice is divided into parallel layers. The density of each monomeric species and the orientational distribution are allowed to be different for each layer. A partition function is derived as a sum over distributions of molecules over orientations and positions and over distributions of intermolecular contacts. From this, self- consistent field equations are obtained for the equilibrium distributions. Further, it is indicated how free-volume effects can be accounted for by allowing sites to be vacant. Expressions are obtained for energy, entropy, chemical potentials, pressure and surface tension etc..The self-consistent field equations are solved numerically by means of a modified Newton iteration. A major complication in the numerical problem associated with this theory is the necessity to simultaneously iterate the density distribution of the various molecular orientations as well as the distribution of contacts between molecules. With selfconsistent field theories that are based on the Bragg-Williams approximation such as that of Scheutjens and Fleer, the distribution of contacts is simply assumed to be random, even if there are non-zero interactions.At the end of chapter II, the capabilities of the method are illustrated by applying it to a number of specific systems containing molecules with orientation-dependent interactions. The coexistence curves that are calculated show that orientation-dependent interactions can give rise to an increasing solubility with decreasing temperature. Also for the interfacial properties the orientation- dependent nature of the intermolecular interactions is shown to be of great importance. For special model systems it is found that the tension of the interface between coexisting phases increases with increasing temperature. Of a system that exhibits a closed-loop coexistence curve, the interfacial tension of the interface between the coexisting phases vanishes at the lower critical solution temperature. Upon increasing temperature it increases, passes a maximum and decreases until it vanishes again at the upper critical solution temperature. The structural differences at the interface between temperatures at which the interfacial entropy is negative and where it is positive are discussed.Chapters III to VI are concerned with various properties of water.In <strong>chapter III</strong> , a lattice-gas model for water is introduced that is elaborated by the formalism of chapter II. This theory appeared to be capable of reproducing various anomalous thermodynamic properties of water. The calculated equation of state and liquid-vapour phase diagram agree at least qualitatively with the experimental behaviour of water. For instance, the maximum of the isobaric density as a function of temperature is reproduced. Within this model it is possible to analyse the relation between macroscopic behaviour and the microscopic structure of liquid water. The amount of intact hydrogen bonds can be calculated as well as that of the other intermolecular contacts. Over a large range of temperatures and densities, the fraction of intact hydrogen-bonds is close to unity. This confirms that liquid water can be considered as a percolating hydrogen-bonded network.The liquid-vapour interface is also investigated. A salient result is the increase of the interfacial thickness and the density-coherence length of liquid water upon decreasing temperature. This result still awaits experimental verification. Further, the minimum of the temperature coefficient of the interfacial tension as a function of temperature is reproduced by the theory.In <strong>chapter IV</strong> the so-called hydrophobic effect is addressed. It is made plausible that the physics underlying the anomalous thermodynamics of solvation by water of small apolar molecules is similar to that of the isobaric density maximum of pure water. An explanation is given for the exothermic solvation of apolar compounds below room temperature. This is attributed to a decrease of repulsive non-hydrogen bonding interactions between water molecules. The large entropy effect of solvating apolar compounds is also reproduced by the theory. For the explanation of these phenomena it appears to be unnecessary to invoke so-called iceberg formation around apolar molecules. Another interesting result is that the solvation thermodynamics of small molecules and of extended surfaces appears to be very different.In <strong>chapter V</strong> , hydration forces, water-structure mediated forces between surfaces, are the main subject. There is experimental evidence for the occurrence of such forces in systems as different as biological membranes and inorganic colloids. Both within a phenomenological approach based on a Landau expansion of the free-energy density as in results from the lattice-theory, it is found that these forces can be attractive or repulsive, depending on the properties of the surfaces. More specifically, the sign of the interaction depends on the type of ordering induced by the surfaces in adjoining water. If the solvation layers of two surfaces overlap in such a way that the ordering is enhanced, the ensuing interaction between the surfaces is attractive. This indicates that the accepted view, that the water-structure mediated interaction between hydrophilic surfaces is always repulsive, needs reconsideration. If the structuring is distorted by overlap, then a repulsive force is the result.<strong>Chapter VI</strong> contains some preliminary results on vapour adsorption and on wetting phenomena. For various model surfaces and temperatures vapour- adsorption isotherms are calculated. In this way, the understanding of the relation between the properties of surfaces and the adsorption of water vapour is improved. For a number of surfaces a transition from partial wetting to complete wetting is found with variation of the properties of the surface or of temperature. The interfacial tension of the solid-vapour and the solid-liquid interface at the saturation pressure has been calculated, as well as that of the liquid-vapour interface. Consequently, using Young's law, the contact angle can be obtained together with related quantities such as the reversible work of adhesion and the spreading coefficient.In <strong>chapter VII</strong> , the formalism of chapter II is extended towards systems containing chain molecules. Such molecules consist of segments, each occupying one lattice site. Generally, they can have a large number of conformations. It is indicated how the (semi)flexibility of chain molecules can be accounted for within the theory. Correlations due to the connected nature of segments are accounted for in firstorder approximation. This is consistent with the way correlations due to energetic interactions are accounted for. It has been possible to derive a recurrence relation for the statistical weight of chains of different lengths which allows an efficient evaluation of the statistical weight of each possible chain conformation.