If the differential distribution function is exponential in Q (Section XVII-14A), the resulting Q(P, T) is that known as the Freundlich isotherm [Pg.699]

Figure A2.3.8 Atom-atom distribution functions aiid for liquid water at 25 °C detemrined |

Figure A2.3.7 The radial distribution function g r) of a Lemiard-Jones fluid representing argon at T = 0.72 and p = 0.844 detennined by computer simulations using the Lemiard-Jones potential. |

Figure C2.2.10. Orientational distribution functions for (a) a highly oriented liquid crystal phase, (b) a less well |

Leadbetter A J and Norris E K 1979 Distribution functions in hree liquid crystals from x-ray diffraction measurements Moiec. Phys. 38 669-86 [Pg.2568]

Flere g(r) = G(r) + 1 is called a radial distribution function, since n g(r) is the conditional probability that a particle will be found at fif there is another at tire origin. For strongly interacting systems, one can also introduce the potential of the mean force w(r) tln-ough the relation g(r) = exp(-pm(r)). Both g(r) and w(r) are also functions of temperature T and density n [Pg.422]

Integral equation approximations for the distribution functions of simple atomic fluids are discussed in the following. [Pg.480]

Toby B FI and Egami T 1992 Accuracy of pair distribution function analysis applied to crystalline and noncrystalline materials Aota Crystaiiogr.k 48 336-46 [Pg.1383]

Hiroike K 1972 Long-range correlations of the distribution functions in the canonical ensemble J. Phys. Soc. Japan 32 904 [Pg.554]

Between the limits of small and large r, the pair distribution function g(r) of a monatomic fluid is detemrined by the direct interaction between the two particles, and by the indirect interaction between the same two particles tlirough other particles. At low densities, it is only the direct interaction that operates through the Boltzmaim distribution and [Pg.468]

In the limit of zero ion size, i.e. as o —> 0, the distribution functions and themiodynamic fiinctions in the MS approximation become identical to the Debye-Htickel limiting law. [Pg.495]

Here the bar indicates an average over the orientational distribution function.Here cos — 4)is the [Pg.2555]

Binder K 1981 Finite size scaling analysis of Ising-model block distribution-functions Z. Phys. B. Oondens. Matter. 43 119-40 [Pg.2285]

Thus D(r) is given by the slope of the V versus P plot. The same distribution function can be calculated from an analysis of vapor adsorption data showing hysteresis due to capillary condensation (see Section XVII-16). Joyner and co-woikers [38] found that the two methods gave very similar results in the case of charcoal, as illustrated in Fig. XVI-2. See Refs. 36 and 39 for more recent such comparisons. There can be some question as to what the local contact angle is [31,40] an error here would shift the distribution curve. [Pg.578]

This can be inserted in equation (02.2.3) to give tlie orientational distribution function, and tlius into equation (02.2.6) to deteniiine the orientational order parameters. These are deteniiined self-consistently by variation of tlie interaction strength iin equation (c2.2.7). As pointed out by de Gemies and Frost [20] it is possible to obtain tlie Maier-Saupe potential from a simple variational, maximum entropy metliod based on tlie lowest-order anisotropic distribution function consistent witli a nematic phase. [Pg.2556]

It is instructive to see this in temis of the canonical ensemble probability distribution function for the energy, NVT - Referring to equation B3.3.1 and equation (B3.3.2I. it is relatively easy to see that [Pg.2247]

Born M and Green H S 1946 A general kinetic theory of liquids I. The molecular distribution functions Proc. R. Soc. A 188 10 [Pg.551]

Microscopic theory yields an exact relation between the integral of the radial distribution function g(r) and the compressibility [Pg.647]

We are going to carry out some spatial integrations here. We suppose that tire distribution function vanishes at the surface of the container and that there is no flow of energy or momentum into or out of the container. (We mention in passing that it is possible to relax this latter condition and thereby obtain a more general fonn of the second law than we discuss here. This requires a carefiil analysis of the wall-collision temi The interested reader is referred to the article by Dorfman and van Beijeren [14]. Here, we will drop the wall operator since for the purposes of this discussion it merely ensures tliat the distribution fiinction vanishes at the surface of the container.) The first temi can be written as [Pg.684]

In either case, first-order or continuous, it is usefiil to consider the probability distribution function for variables averaged over a spatial block of side L this may be the complete simulation box (in which case we [Pg.2266]

It is conventional to express tlie stmctiiral infomiation in temis of a pair distance distribution function, or PDDF [5], which is defined by p(r) = p-P(r). Using this, equation (Bl.8.10 becomes [Pg.1370]

We have seen various kinds of explanations of why may vary with 6. The subject may, in a sense, be bypassed and an energy distribution function obtained much as in Section XVII-14A. In doing this, Cerefolini and Re [149] used a rate law in which the amount desorbed is linear in the logarithm of time (the Elovich equation). [Pg.709]

The analysis of the direct data, namely, volume penetrated versus pressure, is as follows. Let d V be the volume of pores of radii between r and r - dr d V will be related to r by some distribution function Z)(r) [Pg.578]

In general, it is diflfieult to quantify stnietural properties of disordered matter via experimental probes as with x-ray or neutron seattering. Sueh probes measure statistieally averaged properties like the pair-correlation function, also ealled the radial distribution function. The pair-eorrelation fiinetion measures the average distribution of atoms from a partieular site. [Pg.131]

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