Mayer f function

Mayer s paper was an important milestone in the development of electrolyte theory and the principle ideas behind this theory and the main results at the level of the renormalized second virial coefficient will be presented below. It follows from Eqs. (3) and (11) that the Mayer f-function for the solute pair potential can be written as the sum of terms ... 

The model for weak electrolytes that I will discuss here is the sticky electrolyte model (SEM) in which a delta-function interaction is introduced into the Mayer f-function for the oppositely charged ions at a distance L < a, where a is the hard sphere diameter. This model was first introduced by Cummings and Stell (1984, 1985) to study association in uncharged systems and is closely related to Baxter s model (1968a) for... 

In the SEM the Mayer f-function for ions of opposite sign is defined... 

Steinbiichel A, Aerts K, Babel W, FoUner C, LiebergeseU M, Madkour MH, Mayer F, Pieper-Furst U, Pries A, Valentin HE et al (1995) Considerations on the structure and biochemistry of bacterial polyhydroxyalkanoic acid inclusions. Can J Microbiol 41(Suppl 1) 94—105 Stuart ES, Lenz RW, Fuller RC (1995) The ordered macromolecular surface of polyester inclusion bodies in Pseudomonas oleovorans. Can J Microbiol 41(Suppl 1) 84—93 Stuart ES, Foster LJR, Lenz RW, FuUer RC (1996) Intracellular depolymerase functionality and location in Pseudomonas oleovorans inclusions containing polyhydroxyocttmoate. Int J Biol Macromol 19 171-176... 

J. P. Desdaux, D. F. Mayers, F. O Brien. Relativistic atomic wave functions. /. Phys. B Atom. Molec. Phys., 4 (1971) 631-642. 

In the graphical representation of the integral shown above, a line represents the Mayer function f r.p between two particles and j. The coordinates are represented by open circles that are labelled, unless it is integrated over the volume of the system, when the circle representing it is blackened and the label erased. The black circle in the above graph represents an integration over the coordinates of particle 3, and is not labelled. The coefficient of is the sum of tln-ee tenns represented graphically as... 

Separating out the volume element fceU dr of one lattice cell, V0 and introducing the cell average Mayer function, (f), defined as ... 

Ilk, N. Kosma, P. Puchberger, M. Egelseer, E. M. Mayer, H. F. Sleytr, U. B. Sara, M. Structural and functional analyses of the secondary cell wall polymer of Bacillus sphaericus CCM 2177 that serves as an S-layer-specific anchor. J. Bacterial. 1999,181,7643-7646. 

Sanchez C, Soler-Illia G, Ribot F, Lalot T, Mayer CR, Cabuil V. Designed hybrid organic-inorganic nanocomposites from functional nanobuilding blocks. Chem Mater 2001 13 3061-3083. 

As a major deficit, in both DH and MSA theory the Mayer functions fxfi = exp —f q>ap(r) — 1 are linearized in ft. This approximation becomes unreasonable at low T and near criticality. Pairing theories discussed in the next section try to remedy this deficit. Attempts were also made to solve the PB equation numerically without recourse to linearization [202-204]. Such PB theories were also applied in phase equilibrium calculations [204-206]. 

Explicit solutions of Eqs. (88) or (97) are not known, even for the Flory-Stock-mayer model. The concentrations of individual species Cy(f) for that model are available, but only by recursive solution of appropriate kinetics equations (before they are summed up to yield Eqs. (88) or (97)). The function ci(t) + Hx(t) + Hy(t) which is needed to solve the equations is... 

These data are from calculations made by D. H. Whiffen and co-workers based on wave functions developed by A. J. Freeman, D. F. Mayers, C. J. Roothaan, R. E. Watson, and others. 

Goellner, J. F., Neyman, K. M., Mayer, M., Nortemann, F., Gates, B. C., and Rosch, N., Ligand-free osmium clusters supported on MgO. A density functional study. Langmuir 16, 2736 (2000). 

Good, J.L., Khurana, R.K., Mayer, R.F., Cintra W.M., Albuquerque, E.X. (1993). Pathophysiological studies of neuromuscular function in subacute organophosphate poisoning induced by phosmet. J. Neurol. Neurosurg. Psychiatry 56 290. ... 

Figure 6.3 Compare with Fig. 6.1. Here again the solid lines indicate factors of Mayer / functions as in Eq. (6.25) and further discussed as Ursell functions beginning on p. 126. The second term shown is / f(r )p6 r r)d r for a simple fluid. The shaded regions with m-l black disks and one white disk represent conditional densities (rj,..., r). That white disk, rightmost here, corresponds to the real atom positioned at r on which the averages are conditioned. The other white disk, leftmost here, corresponds to the test particle.

C. Sanchez, G. Soler-IUia, F. Ribot, T. Lalot, C.R. Mayer, and V. Cabuil, Designed Hybrid Organic-inorganic Nanocomposites from Functional Nanobuilding Blocks. Chem. Mater., 2001, 13, 3061-3083. 

At those times the term biosphere already existed. It is known that early in the nineteenth century the Zellinhaltskoerper , discovered with the help of the microscope, were often understood in the light of Leibniz monadology and were seen as the bearers of the life functions. These monads were named the biospheres by A.F.T. Mayer (1837)(Jahn, 1982, p. 361). 

F. Tolle, G. Mayer, Dressed for success— applying chemistry to modulate aptamer functionality, Chem. Sci. (Cambridge) 4 (1) (2013) 60-67. 

Marla Mayer prepared a summary of the above development In April 1944 (27) which was reviewed by Edward Teller at the request of H. C. Urey and M. Kilpatrick. Included in the summary paper were some applications of equations (12) and (18) to the possible chemical separation of the uranium Isotopes. Edward Teller recognized that In Eq. (18) we had generalized the Herzfeld-Teller theorem to the case of chemical equilibrium In polyatomic molecules. A lucid summary of this development and some of the research it initiated Is summarized by Clyde A. Hutchison, Jr. (29). Late In 1946 Marla Mayer and I were encouraged by W. F. Libby and H. C. Urey to prepare a summary of our work which could be published In the open literature (29). It was then that Libby called our attention to Waldmann s Independent formulation of the reduced partition function ratio and the development of a mathematically equivalent form of Eq. (12) (30). 

We have just shown that for equilibrium systems, it is possible to express the two-particle distribution function as a power series in the density in terms of the single-particle distribution function, by using Mayer s cluster expansion method. We are now going to show that the same method can also be extended to nonequilibrium systems, so that one can express F2(xi, X2, t) as a power series in the density in terms of Fi(Xj, t), similar to Eq. (191). This nonequilibrium expansion of F2 in terms of Fi, when inserted into the first hierarchy equation, will then enable us to derive the Boltzmann equation and to extend it to higher densities. We begin by constructing a set of functions Pr( i Jt2,..., x 0 that satisfy the s-particle Liouville equation for s = 1,2,3,..., which we will use to derive cluster expansions for F,(xi,..., x t) similar to those for F (xi,..., X3) in terms of the W 5(xi,..., x ). The functions Ds satisfy... 

Many methods have been proposed to calculate bond orders from SCF MO wave functions. One useful definition is due to Mayer [1. Mayer, Chem. Phys. Lett., 97,270 (1983)]. For a closed-shell molecule whose occupied MOs are i= 2 the Mayer bond order Bcd between atoms C and D is defined as... 

Hildebrand, H.F., Blanchemain, N., Mayer, G Chai, F., Lefebvre, M., and Bosdiin, F. (2005) Surface coatings for biological activation and functionalization of medical devices. Surf. Coat. Technol, 200, 5318-5324. 

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