Chemical potential protons

Khan, S. and Macnab, R.M. (1980). Proton chemical potential, proton electrical potential, and bacterial motility./. Mol. Biol. 138, 599-614. 

Each of the respiratory chain complexes I, III, and IV (Figures 12-7 and 12-8) acts as a proton pump. The inner membrane is impermeable to ions in general but particularly to protons, which accumulate outside the membrane, creating an electrochemical potential difference across the membrane (A iH )-This consists of a chemical potential (difference in pH) and an electrical potential. 

In an early work by Mertz and Pettitt, an open system was devised, in which an extended variable, representing the extent of protonation, was used to couple the system to a chemical potential reservoir [67], This method was demonstrated in the simulation of the acid-base reaction of acetic acid with water [67], Recently, PHMD methods based on continuous protonation states have been developed, in which a set of continuous titration coordinates, A, bound between 0 and 1, is propagated simultaneously with the conformational degrees of freedom in explicit or continuum solvent MD simulations. In the acidostat method developed by Borjesson and Hiinenberger for explicit solvent simulations [13], A. is relaxed towards the equilibrium value via a first-order coupling scheme in analogy to Berendsen s thermostat [10]. However, the theoretical basis for the equilibrium condition used in the derivation seems unclear [3], A test using the pKa calculation for several small amines did not yield HH titration behavior [13],... 

In Equation 50 the chemical potential of non-electrolyte A depends on the usual choice of standard-state conventions described above, and the chemical potentials of both H2(g) and H+(sod are taken to be zero (this defines e.s.s., the electrolyte standard state). By setting the standard-state free energy of the solvated proton equal to zero, this standard-state convention... 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

Because of charge neutrality, ye- t] B and is consequently negligible. That the same thing holds for yVe (and for yV/tI) is a postulate, but a very plausible one because otherwise we would have neutrino or antineutrino degeneracy with LV 2> B. The upshot is that the chemical potentials of neutrons and protons are equal and so from Eq. (2.43) one has a simple Boltzmann-type equilibrium ratio (n/p)eq = e-fa-mptflkT = g-1.29M eV/kT (4.36)... 

Use the formula Eq. (2.44) for chemical potential to show that the equilibrium number abundance of a nucleus i with mass number A, = Z, + /V, partition function u, and binding energy B, with respect to free protons and neutrons is given by... 

Models of hot isentropic neutron stars have been calculated by Bisnovatyi-Kogan (1968), where equilibrium between iron, protons and neutrons was calculated, and the ratio of protons and neutrons was taken in the approximation of zero chemical potential of neutrino. The stability was checked using a variational principle in full GR (Chandrasekhar, 1964) with a linear trial function. The results of calculations, showing the stability region of hot neutron stars are given in Fig. 7. Such stars may be called neutron only by convention, because they consist mainly of nucleons with almost equal number of neutrons and protons. The maximum of the mass is about 70M , but from comparison of the total energies of hot neutron stars with presupemova cores we may conclude, that only collapsing cores with masses less that 15 M have... 

In thermal equilibrium, within a quantum statistical approach a mass action law can be derived, see [12], The densities of the different components are determined by the chemical potentials ftp and fin and temperature T. The densities of the free protons and neutrons as well as of the bound states follow in the non-relativistic case as... 

There is also a topological term which is essential in order to satisfy the t Hooft anomaly conditions [32-34] at the effective Lagrangian level. It is important to note that respecting the t Hooft anomaly conditions is more than an academic exercise. In fact, it requires that the form of the Wess-Zumino term is the same in vacuum and at non-zero chemical potential. Its real importance lies in the fact that it forbids a number of otherwise allowed phases which cannot be ruled out given our rudimentary treatment of the non-perturbative physics. As an example, consider a phase with massless protons and neutrons in three-color QCD with three flavors. In this case chiral symmetry does not break. This is a reasonable realization of QCD for any chemical potential. However, it does not satisfy the t Hooft anomaly conditions and hence cannot be considered. Were it not for the t Hooft anomaly conditions, such a phase could compete with the CFL phase. 

R possesses a spherical core of radius a consisting of quark matter with CFL condensate surrounded by a spherical shell of hadronic matter with thickness R — a containing neutron and proton superfluids. The triangular lattice of singly quantized neutron vortices with quantum of circulation irh/jj, forms in response to the rotation. Since the quark vortices carry SttTj/fi quantum of circulation, the three singly quantized neutron vortices connect at the spherical interface with one singly quantized quark vortex so that the baryon chemical potential is continuous across the interface [19]. 

Contribution of pairing fluctuations to the specific heat in the hadron shell is minor for the case of the neutron pairing due to a small value of Tc < IMeV compared to the value of the neutron chemical potential f//, > 50 MeV). Therefore in the neutron channel fluctuations of the gap are relevant only in a very narrow vicinity of the critical point. However this effect might be not so small for protons, for which the chemical potential is of the order of several MeV, whereas the gap is of the order of one MeV. Therefore it seems that fluctuations may smear the phase transition in a rather broad vicinity of the critical point of the proton superconductivity. 

The state of unit activity of hydrated proton at the standard temperature 25X and pressure 1 atm. In elecfrodiemistry of aqueous solution, the scale of chemical potential for hydrated ions takes as the reference zero the standard chemical potential of hydrated protons at unit activity in addition the standard stable state energy of element atoms is set equal to zero. 

It follows from Eqn. 6-22 that the standard chemical potential of hydrated ions determined from the standard equilibrium potential of the ion transfer reaction is a relative value that is to the standard chemical potential of hydrated protons at unit activity, which, by convention in aqueous electrochemistry, is assigned a value of zero on the electrodiemical scale of ion levels. 

If we set at a value of zero according to the conventional chemical thermodynamic energy scale, the standard chemical potential of a hydrated proton,, is given by Eqn. 6-24 ... 

Upon comparison of eq 32 to 28, it is seen that the proton—water interaction is now taken into account. This interaction is usually not too significant, but it should be taken into account when there is a large gradient in the water (e.g., low humidity or high-current-density conditions). Upon comparison of eq 33 to 31, it is seen that the equations are basically identical where the concentration and diffusion coefficient of water have been substituted for the chemical potential and transport coefficient of water, respectively. Almost all of the models using the above equations make similar substitutions for these variables 15,24,61,62,128... 

In the new biochemical thermodynamic approach, the various protonated species of a metabolite are treated as pseudoisomeric forms having the same transformed chemical potential /x/ at a specified pH, such that they are collected in the term n/ (which is equal to 2 rii). 

At an electrode potential of U = V, the ORR is running with a high reaction rate. This situation would correspond to a short-circuited fuel cell where all elementary reaction steps are highly exothermic. At an electrode potential of U=1.23 V, where the chemical potential of the electrons is shifted by 1.23 eV, both protonation and electron transfer steps are activated. Process (26) or (28) are therefore rate-limiting under these conditions. 

The reader should be aware that considerable confusion exists with respect to names and definitions.176 For example, the AGH+ of Eq. 18-8 can also be called the proton electrochemical potential Ap,+, which is analogous to the chemical potential p of an ion (Eq. 6-24) and has units of kj/mol (Eq. 18-10). 

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