Geometry of Thermodynamic Responses

As shown by these values, the pressure vector dominates the thermodynamic responsiveness of the ideal gas, conferring near one-dimensional character on its thermodynamic geometry. 

In a similar vein, Riemann s formalism finds useful application in expressing the global thermodynamic behavior of a system S. The metric geometry governed by M( ) represents thermodynamic responses (as before), while labels distinct states of equilibrium, each exhibiting its own local geometry of responses. The state-specifier manifold may actually be chosen rather freely, for example, as any/independent intensive variables (such as gi = T, 2 = P 3 = Mr, > = l c-p)- For our purposes, it is particularly convenient to... 

The spherical nature of the surfactant aggregates in reverse micelles is a response to a thermodynamically driven process. It basically represents a need for surfactants to reach an energetically favorable packing configuration at the interface, depending on the molecular geometry of the surfactant. The surfactant molecules can be represented as a truncated cone whose dimensions are determined by the hydrophilic and hydrophobic parts of the surfactant. Assuming that water-in-oil droplets are spherical, the radius of the sphere is expressed as... 

When applied to surface studies, vibrational spectroscopy provides primarily structural data such as molecular symmetry, geometry and bonding, when combined with statistical thermodynamics it allows the estimation of thermodynamic properties. In time-resolved experiments it monitors the transient response of surface species, thus giving an idea of possible intermediates involved in transformations on the solid surface and therefore being of high importance for kinetic investigations. 

This/2x / matrix (matrix of vectors), or the conjugate m matrix, contains the higher-order response functions needed to fully incorporate higher-order (U ") derivatives into the thermodynamic geometry. Geometrical identities for higher-order response functions can then be obtained in analogy to Sections 12.1-12.5. 

The key difficulty in extending thermodynamic geometry to higher-order response functions is the additional experimental data required. To obtain, for example, the m11 1 element of a homogeneous fluid,... 

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