Maximum density

We observe that association leads to pronounced differences in the behavior of the system. In particular, we find that for the thick film the increase of the association energy leads to the increase of the height of the first local density peak. In contrast, the height of the local density maximum decreases at the region of small adsorption (below the prewetting transition). One can say that for increasing association energy the film structure becomes more ordered and its layered structure is more visible. 

In de-aerated 10sulphuric acid (Fig. 3.45) the active dissolution of the austenitic irons occurs at more noble potentials than that of the ferritic irons due to the ennobling effect of nickel in the matrix. This indicates that the austenitic irons should show lower rates of attack when corroding in the active state such as in dilute mineral acids. The current density maximum in the active region, i.e. the critical current density (/ ii) for the austenitic irons tends to decrease with increasing chromium and silicon content. Also the current densities in the passive region are lower for the austenitic irons... 

In order to apply the crack nucleation approach, the mechanical state of the material must be quantified at each point by a suitable parameter. Traditional parameters have included, for example, the maximum principal stress or strain, or the strain energy density. Maximum principal strain and stress reflect that cracks in rubber often initiate on a plane normal to the loading direction. Strain energy density has sometimes been applied as a parameter for crack nucleation due to its connection to fracture mechanics for the case of edge-cracked strips under simple tension loading. ... 

Chemical Energy Density (maximum heat of decomposition constrained only by stoichiometry). For the first criterion, substances are placed in four different hazard classes based on enthalpy of reaction/decomposition as indicated in Table 2.10. 

FIG. 5 The density of liquid and supercooled water as a function of temperature, illustrating the anomalous liquid phase density maximum of water (data from Lide, 2002-2003). 

Pyramidalization is also a well-established indicator of increased reactivity of alkenes where the 7r-type HOMO makes the major contribution to the reaction.12 This increased reactivity is specific to the more open (convex) face, and contributes to the well-known exo-selectivity of attack on bicyclo[2,2,l]hept-2-enes [60]. The electron density distribution of a derivative of [60] showed a measurable displacement of the electron-density maximum of the double bond in the exo direction (Irngartinger et al.,... 

At a critical point, Vp(r) equals zero because each of the three contributions to Eq. (6.18) are zero. The classification of critical points is based on the second derivatives, which as noted above are all negative for a density maximum, but have different signs for saddle points and minima of the distribution. 

A first study refers to liquid water [77]. The signals AS q,x) and A5[r,r] were measured using time-resolved X-ray diffraction techniques with 100 ps resolution. Laser pulses at 266 and 400 nm were employed. Only short times x were considered, where thermal expansion was assumed to be negligible and the density p to be independent of x. To prove this assumption, the authors compared their values of AS q, x) to the values of AS q) obtained from isochoric (i.e., p = const) temperature differential data [78-80]. Their argument is based on the fact that liquid H2O shows a density maximum at 4 °C. Pairs of temperatures Ti, T2 thus exist for which the density p is the same constant density conditions can thus be created in this unusual way. The experiment confirmed the existence of the acoustic horizon (Fig. 8). 

Moreover, because the nuclei are effectively point charges, it should be obvious that their positions correspond to local maxima in tlie election density (and these maxima are also cusps), so the only issue left to completely specify the Hamiltonian is die assignment of nuclear atomic numbers. It can be shown diat diis information too is available from the density, since for each nucleus A located at an electron density maximum Fa... 

Fig. 2.7 (a) Pictorial representation or the electron density in a hydrogen-like 2p orbital compared with lb) the electron density contours Tor the hydrogen-like 2pr orbital of carbon. Contour values are relative to the electron density maximum The xy plane is a nodal surface. The signs (+ and —) refer to those of the original wave function. [The contour diagram is from Ogryzlo, E. A4 Porter G. B J. Client. Ethic. 1963.40. 258. Reproduced with permission. ... 

The molecular dynamic technique has been validated for water structures through comparison of calculated properties with experimental thermodynamic water data, such as the density maximum, the high heat capacity, and diffraction patterns (Stillinger and Rahman, 1974) as well as the hydrate infrared (vibrational) spectral data by Bertie and Jacobs (1977, 1982). With acceptable comparisons of many computed and experimental properties of water structures, there is little doubt that a substance similar to water has been simulated. 

For methane hydrate, the minimum water depth is 381 m in freshwater and upto 436 m in seawater, respectively, at 277 K. In the world s oceans at water depths greater than 600 m, the temperature is typically uniform at 277 K, due to the density maximum in seawater. Lower bottom water temperature exceptions can be found with strong subbottom currents from Antarctic and Arctic environments such as the north of Norway or Russia. Methane-phase equilibrium data in Chapter 6, indicate that 3.81 MPa are required to stabilize methane hydrates at 277.1 K. Using the rule of thumb 1 MPa = 100 m water, hydrates in pure water would be stable at depths greater than 381 m. 

The density maximum at 4 °C is induced by the sum of two effects. The normal lowering of density with increasing T by the increase of the volume of thermal vibrations and the rise of p with T by an increase of the content of 0F. The structure near the orientation defects is more like non-polar liquids with their densed package and higher coordination number. 

The T of the density maximum is decreased linearly by the concentration of added salts (Despretz effect60,61 ). The constant of molar decrease depends on the type of ions31). There is a distinct but small difference in this constant between Na+ and K+-ions. Large anions like I- or NO3 give bigger effects than small anions like Cl or Br . The Despretz effect can be understood by the assumption that the ions destroy the loosely packed ice like H-bonded structure near 0 °C. 

In the Gibbs model of an ideal interface there is one problem where precisely do we position the ideal interface Let us therefore look at a liquid-vapor interface of a pure liquid more closely. The density decreases continuously from the high density of the bulk liquid to the low density of the bulk vapor (see Fig. 3.2). There could even be a density maximum in between since it should in principle be possible to have an increased density at the interface. It is natural to place the ideal interface in the middle of the interfacial region so that T = 0. In this case the two dotted regions, left and right from the ideal interface, are equal in size. If the ideal interface is placed more into the vapor phase the total number of molecules extrapolated from the bulk densities is higher than the real number of molecules, N < caVa + c V13. Therefore the surface excess is negative. Vice versa if the ideal interface is placed more into the liquid phase, the total number of molecules extrapolated from the bulk densities is lower than the real number of molecules, N > caVa + surface excess is positive. 

Donation of electron density from the ligand to an unoccupied metal p- or s-orbital in a cr-fashion (i.e. the electron density maximum lies along a line joining the two atomic centres—the inter atomic vector) (Figure 3.54a). 

The density maximum point in the La hemispheric density distribution, which corresponds to the most probable La atom position, locates adjacent to the center of a six-membered ring inside the C82/C2V cage. The nearest neighbor distance between the most probable La atom position and the carbon atom is 2.55(8) A. The distance from the cage center to the La atom is 1.96(9) A. This value is very close to those reported by theoretical calculations [19-21]. Furthermore, the obtained feature of the La atom density resembles a theoretically deduced electrostatic potential inside the C82/C2y [21]. 

Limiting current density Maximum (diffusion-limited) current density at which a given electrode reaction can proceed. Above this limit another electrode reaction commences. 

---