Condensed phases chemical potential

Chemical reaction dynamics is an attempt to understand chemical reactions at tire level of individual quantum states. Much work has been done on isolated molecules in molecular beams, but it is unlikely tliat tliis infonnation can be used to understand condensed phase chemistry at tire same level [8]. In a batli, tire reacting solute s potential energy surface is altered by botli dynamic and static effects. The static effect is characterized by a potential of mean force. The dynamical effects are characterized by tire force-correlation fimction or tire frequency-dependent friction [8]. 

Bash, P.A., Field, M.J.,Karplus, M. Free energy perturbation method for chemical reactions in the condensed phase A dynamical approach baaed on a combined quantum and molecular dynamics potential. J. Am. Chem. Soc. 109 (1987) 8092-8094. 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

In connection with the thermodynamic state of water in SAH, it is appropriate to consider one more question, i.e., their ability to accumulate water vapor contained in the atmosphere and in the space of soil pores. It is clear that this possibility is determined by the chemical potential balance of water in the gel and in the gaseous phase. In particular, in the case of saturated water vapor, the equilibrium swelling degree of SAH in contact with vapor should be the same as that of the gel immersed in water. However, even at a relative humidity of 99%, which corresponds to pF 4.13, SAH practically do not swell (w 3-3.5 g g1). In any case, the absorbed water will be unavailable for plants. Therefore, the only real possibility for SAH to absorb water is its preliminary condensation which can be attained through the presence of temperature gradients. 

The open-top floating roof tank design eliminates the potential for BLEVE. Further, the material being handled has no potential for chemical reactions or for condensed-phase explosions. Thus, these types of explosions can also be eliminated from consideration. 

Potential explosion phenomena include vapor cloud explosions (VCEs), confined explosions, condensed-phase explosions, exothermic chemical reactions, boiling liquid expanding vapor explosions (BLEVEs), and pressure-volume (PV) ruptures. Potential fire phenomena include flash fires, pool fires, jet fires, and fireballs. Guidelines for evaluating the characteristics of VCEs, BLEVEs, and flash fires are provided in another CCPS publication (Ref. 5). The basic principles from Reference 5 for evaluating characteristics of these phenomena are briefly summarized in this appendix. In addition, the basic principles for evaluating characteristics of the other explosion and fire phenomena listed above are briefly summarized, and references for detailed evaluation of characteristics are provided. 

A given phase may persist beyond the point at which transition to another phase should properly occur. On the T5 isotherm, for instance, it is possible to compress the vapour in clean conditions beyond point V, as shown by the dots, without condensation occurring. This vapour is supercooled, and Pv > Pl- When disturbed, the supercooled vapour condenses at once. In the same way, clean liquid may be superheated without boiling, in which case Pl > Pv Supercooled or superheated phases are metastable. They appear to be stable, but are thermodynamically unstable, since another state of lower chemical potential exists. 

For condensed phases (liquids and solids) the molar volume is much smaller than for gases and also varies much less with pressure. Consequently the effect of pressure on the chemical potential of a condensed phase is much smaller than for a gas and often negligible. This implies that while for gases more attention is given to the volumetric properties than to the variation of the standard chemical potential with temperature, the opposite is the case for condensed phases. 

In this section we will briefly review some of the main different approaches that have been used up to now in order to evaluate the potential energy of each configuration in a Monte Carlo run. As we have already stated, the force fields that describe intra- and intermolecular interactions are at the heart of such statistical calculations because the free energy differences that we want to evaluate are directly dependent on the changes of those interactions. In fact, the important advances of the last ten years in the power of computer techniques for chemical reactions in the condensed phase, that we have mentioned in the Introduction, have been due, to a great extent, to the continual evolution in force fields, with added complexity and improved performance. 

For Nf = 3 light flavors at very high chemical potential dynamical computations suggest that the preferred phase is a superconductive one and the following ansatz for a quark-quark type of condensate is energetically favored ... 

It is quite likely to find dense quark matter inside compact stars like neutron stars. However, when we study the quark matter in compact stars, we need to take into account not only the charge and color neutrality of compact stars and but also the mass of the strange quark, which is not negligible at the intermediate density. By the neutrality condition and the strange quark mass, the quarks with different quantum numbers in general have different chemical potentials and different Fermi momenta. When the difference in the chemical potential becomes too large the Cooper-pairs breaks or other exotic phases like kaon condensation or crystalline phase is more preferred to the BCS phase. 

In [25, 26] it is shown that at given pq the diquark gap is independent of the isospin chemical potential for Pi ) < Pic(Pq), otherwise vanishes. Increase of isospin asymmetry forces the system to pass a first order phase transition by tunneling through a barrier in the thermodynamic potential (2). Using this property we choose the absolute minimum of the thermodynamic potential (2) between two /3-equilibrium states, one with and one without condensate for the given baryochemical potential Pb = Pu + 2pd-... 

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

In a simplistic and conservative picture the core of a neutron star is modeled as a uniform fluid of neutron rich nuclear matter in equilibrium with respect to the weak interaction (/3-stable nuclear matter). However, due to the large value of the stellar central density and to the rapid increase of the nucleon chemical potentials with density, hyperons (A, E, E°, E+, E and E° particles) are expected to appear in the inner core of the star. Other exotic phases of hadronic matter such as a Bose-Einstein condensate of negative pion (7r ) or negative kaon (K ) could be present in the inner part of the star. 

---