Competitive Adsorption of Potential-determining Ions and Neutral Molecules by (Agl)n

The density of the charges of (AgI)n is in direct relation with the concentration of the potential determining ions (Ag+, i-), reaching its maximum at 1.1 ions per nm2, and is in inverse relation with the adsorption of neutral molecules (aliphatic alcohol). The adsorption of aliphatic alcohol (which reaches its maximum at 0.57 molecules per nm2 on the left side of the pzc) is in inverse relation with the adsorption of the potential determining ions. The adsorption of 1 molecule of alcohol is accompanied by desorption of 2 ions and vice versa

Zur Biostratigraphie der Selke-Mulde im Harz

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Norms of Ideals in Direct Sums of Number Fields and Applications to the Circulants Problem of Olga Taussky-Todd

This thesis, 'Norms of Ideals in direct sums of number fields and applications to the circulants problem of Olga Taussky-Todd,' presents wide-ranging material in the Mathematical areas of Algebraic and Analytic Number Theory. The work, which is substantially original, is set out in three chapters which are supported by appendices. As the title suggests, the main aim is to tackle a problem which was originally posed by Olga Taussky-Todd who asked what values can be taken by the determinant of a certain type of n X n matrix with integer entries - the circulant (see [15]). Hitherto fragmentary algebraic results have been proved by M.Newman, using matrix manipulation ([5],[6]). However, for a given circulant, he gave no indication as to what proportion of integers are values. The thesis solves this problem by utilising a well-known relationship between determinants of matrix transformations and "absolute" norms of fractional ideals in a direct sum of number fields. By working appropriately in the latter structure, asymptotic methods are made available to complete the solution. A sketch of the mathematical strategy is given in the preface. The overall approach is to start at the level of great generality in Chapter 1 where, by slight modification, there is a generalisation of some extensive results published by R.W.K.Odoni in recent mathematical journals (see e.g. [12]). Subsequently there is successive specialisation down to the case of the circulant. In Chapter 2, by using standard techniques of group characters and the arithmetic of cyclotomic fields there are proved a few new results for abelian group determinants. In the final chapter there are given new elementary proofs of results for particular circulants, first presented by Newman in [5,6]. Then the methodology of the first chapter is reprised to establish the most important original result of this thesis - that "almost all" integers with appropriate 'critical' exponents are values of a given circulant

Superhydrophobic surfaces: a model approach to predict contact angle and surface energy of soil particles

Wettability of soil affects a wide variety of processes including infiltration, preferential flow and surface runoff. The problem of determining contact angles and surface energy of powders, such as soil particles, remains unsolved. So far, several theories and approaches have been proposed, but formulation of surface and interfacial free energy, as regards its components, is still a very debatable issue. In the present study, the general problem of the interpretation of contact angles and surface free energy on chemically heterogeneous and rough soil particle surfaces is evaluated by a reformulation of the Cassie-Baxter equation, assuming that the particles are attached on to a plane and rigid surface. Compared with common approaches, our model considers a roughness factor that depends on the Young’s Law contact angle determined by the surface chemistry. Results of the model are discussed and compared with independent contact angle measurements using the Sessile Drop and the Wilhelmy Plate methods. Based on contact angle data, the critical surface tension of the grains were determined by the method proposed by Zisman. Experiments were made with glass beads and three soil materials ranging from sand to clay. Soil particles were coated with different loadings of dichlorodimethylsilane (DCDMS) to vary the wettability. Varying the solid surface tension using DCDMS treatments provided pure water-wetting behaviours ranging from wettable to extremely hydrophobic, with contact angles > 150°. Results showed that the critical surface energy measured on grains with the highest DCDMS loadings was similar to the surface energy measured independently on ideal DCDMS-coated smooth glass plates, except for the clay soil. Contact angles measured on plane surfaces were related to contact angles measured on rough grain surfaces using the new model based on the combined Cassie-Baxter Wenzel equation, which takes into account the particle packing density on the sample surface