Potential isobar-isothermal

The most stable compound of a multiphase binary system is often assumed to be the first to occur and grow at the A-B interface. The change, ArG , of the isobaric-isothermal potential (Gibbs free energy) in the reaction of formation of any compound from the elements under given conditions is usually considered to be a measure of its thermodynamic stability. The more negative the value of AfG°, the more stable the compound is. 

In the isobaric-isothermal ensemble [119-122], the probability distribution Pnpt(E, V T, V) for potential energy E and volume V at temperature T and pressure V is given by... 

After an optimal weight factor Wmu(E, V) is obtained, a long production simulation is performed for data collection. We employ the reweighting techniques [8] for the results of the production run to calculate the isobaric-isothermal-ensemble averages. The probability distribution / npt(A, V T, V) of potential energy and volume in the isobaric-isothermal ensemble at the desired temperature T and pressure V is given by... 

Fig. 4.4. Time series of potential energy E from (a) the conventional isobaric-isothermal MD simulation at To = 240 K and Vo = 0.1 MPa (b) the conventional isobaric-isothermal MD simulation at To = 298 K and Vo = 0.1 MPa (c) the conventional isobaric-isothermal MD simulation at To = 298 K and Vo = 300 MPa and (d) the multibaric-multithermal MD simulation...

When amorphous forms convert to crystalline, and finely dispersed materials to larger particles, the solubility should decrease and the isobaric-isothermal potential of mineral formation should increase (by an absolute value). 

From the graph of the dependence of variation in isobaric-isothermic potential on aging time, the duration of the individual stages of diagenetic... 

Thermodynamic properties and solubility of the sediments. From a comparison of the tabulated thermodynamic constants (Naumov et al., 1971) it follows that the transformation of glass into a-Si02 is accompanied by a 2.2 kcal/mol change in enthalpy. Values of the isobaric-isothermic potential of formation of amorphous silicas were calculated on the basis of a comparison... 

Under equilibrium conditions the change in isobaric-isothermal potential Gj- p) of the exchange reaction ... 

Isobaric-isothermic potentials of formation ( — AG , kcal/mol, from elements) of some minerals of iron-formations... 

Our purpose in this section is to derive a set of useful expressions for the chemical potentials starting with the principles of statistical mechanics. The expressions we shall obtain take the form of virial expansions similar to those of the Edmond and Ogston (6) but having a very different theoretical basis. Our model parameters are isobaric-isothermal virial coefficients which are about an order of magnitude smaller than the osmotic virial coefficients in the Edmond and Ogston model. We shall develop the theory neglecting the effect of polydispersity because we empirically did not find this to be very important at the level of accuracy commonly attainable in experimental phase diagrams for these systems. 

To outline the fundamental basis of the model, we follow the notation of Hill (10) and extend his derivation to a three component mixture. Component 1 is the solvent which in our case is water, component 2 is a solute or polyethylene glycol, and component 3 is another solute or dextran. We base the theory on an isobaric-isothermal ensemble first introduced by Stockmayer (14). This choice of ensemble is the most appropriate because it )delds expressions for the chemical potentials of the components with temperature, pressure, and solute molality or mole fraction as the natural independent variables, and these are the independent variables normally used in calculation, experiment, and industrial practice. 

The thermodynamics of the discontinuity surface can be examined by analyzing how the density of free energy f changes upon transition from one phase to another. From thermodynamics one can establish the relationship between the free energy, F, the isobaric-isothermal potential, f/, and the chemical potential, p, for a single component system ... 

A straightforward, but tedious, route to obtain information of vapor-liquid and liquid-liquid coexistence lines for polymeric fluids is to perform multiple simulations in either the canonical or the isobaric-isothermal ensemble and to measure the chemical potential of all species. The simulation volumes or external pressures (and for multicomponent systems also the compositions) are then systematically changed to find the conditions that satisfy Gibbs phase coexistence rule. Since calculations of the chemical potentials are required, these techniques are often referred to as NVT- or NPT- methods. For the special case of polymeric fluids, these methods can be used very advantageously in combination with the incremental potential algorithm. Thus, phase equilibria can be obtained under conditions and for chain lengths where chemical potentials cannot be reliably obtained with unbiased or biased insertion methods, but can still be estimated using the incremental chemical potential ansatz [47-50]. 

The sum U + PV - TS = F + PV = H - TS = Z characterizes extensive property called isobar-isothermal potential. It was introduced in 1874 by Josiah Willard Gibbs (1839-1903) and initially also called by him free energy, which caused confusion. To put things in order, this potential was renamed Gibbs free energy. In its content it is enthalpy without kinetic energy of motion. For this reason isobaric-isothermal potential is often called also free enthalpy. It follows from this that under the isobaric-isothermal conditions the measure of maximum useful work is free enthalpy... 

We considered energies of simple departure of Pt from the surface as cation by means of semiempirical method PM6. Activation energies are included into Table 5 in several possible species of complexes. These surface complexes are formed and stabilized by Pt cation interaction with molecules and ions from the environment. Our calculation confirmed existence of prevailing compound [Pt(OH) (Up) (under the condition of exclusion of other harmful ions), while it is accompanied by the largest changes of Gibbse isobar-isotherm potential, whereas the activation energy of its departure is the lowest. 

Direction of corrosion process is determined by thermodynamic properties of the system. The reactivity is determined by the change in isobaric-isothermal potential or Gibbs energy... 

Table 1 gives the phase compositions of the alloys used in our investigation, the chemical reactions responsible for the flow of the current in the galvanic cells, and the equations describing the changes in the isobaric-isothermal potential due to the formation of 1 mole of a given germanlde from the pure components. 

Just as one may wish to specify the temperature in a molecular dynamics simulation, so may be desired to maintain the system at a constant pressure. This enables the behavior of the system to be explored as a function of the pressure, enabling one to study phenomer such as the onset of pressure-induced phase transitions. Many experimental measuremen are made under conditions of constant temperature and pressure, and so simulations in tl isothermal-isobaric ensemble are most directly relevant to experimental data. Certai structural rearrangements may be achieved more easily in an isobaric simulation than i a simulation at constant volume. Constant pressure conditions may also be importai when the number of particles in the system changes (as in some of the test particle methoc for calculating free energies and chemical potentials see Section 8.9). 

This additive relationship may be applied to any other property of the system (i.e., viscosity, surface potential, etc.) under isothermal and isobaric conditions with the same result (Gaines, 1966). 

The enthalpy is useful in considering isentropic and isobaric processes, but often it becomes necessary to rather deal with isothermal and isobaric processes. In such case one needs a thermodynamic function of T and P alone, defining the Gibbs potential G = U(T, P, Nj) as the Legendre transform of U that replaces entropy by temperature and volume by pressure. This transform is equivalent to a partial Legendre transform of the enthalpy,... 

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