Statistical effects

Sorescu D, Thompson D L and Raff L M 1994 Statistical effects in the skeletal inversion of bicycio (2.1.0)pentane J. Chem. Phys. 101 3729—41... 

Carpick et al [M] used AFM, with a Pt-coated tip on a mica substrate in ultraliigh vacuum, to show that if the defonnation of the substrate and the tip-substrate adhesion are taken into account (the so-called JKR model [175] of elastic adliesive contact), then the frictional force is indeed proportional to the contact area between tip and sample. Flowever, under these smgle-asperity conditions, Amontons law does not hold, since the statistical effect of more asperities coming into play no longer occurs, and the contact area is not simply proportional to the applied load. 

London [11] was the first to describe dispersion forces, which were originally termed London s dispersion forces. Subsequently, London s name has been eschewed and replaced by the simpler term dispersion forces. Dispersion forces ensue from charge fluctuations that occur throughout a molecule that arise from electron/nuclei vibrations. They are random in nature and are basically a statistical effect and, because of this, a little difficult to understand. Some years ago Glasstone [12] proffered a simple description of dispersion forces that is as informative now as it was then. He proposed that,... 

For the PIMC study of quantum statistics effects in He systems and additional references see Refs. 90, 91. 

Factors responsible for this order include the trans-effect, charge neutralization, and statistical effects. 

Statistical Effects. In a symmetrical diprotic acid, the first dissociation constant is twice as large as expected since there are two equivalent ionizable... 

From the image sequences, information on the velocities of nano-particles can be extracted. The statistical effect of Brownian motion on the flowing speed of the mixed liquid is found small enough to be ignored as shown in Fig. 37 where most of the particles trajectories in the liquid are straight lines and parallel with the wall basically. Therefore, Brownian diffusive motion is ignorable. 

At the second stage of chlorine substitution in the tetramers there is a greater statistical probability for the incoming nucleophile to attack the phosphorus adjacent to =P(C1)(NHR), viz. P4 or P8, rather than the remote phosphorus, viz. P6 (Fig. 9). However, this statistical effect is countered by the electron releasing effect of the substituent already present on P2, which tends to deactivate P2 as well as P4 and P8 towards further nucleophilic substitution. It is observed that reactive amines such as dimethylamine (94) or ethylamine (95) react with N4P4C18 and... 

Voors AW, Johnson WD, Shuman MS. 1982. Additive statistical effects of cadmium and lead on heart related disease in a North Carolina autopsy series. Arch Environ Health 37 98-102. 

Statistical effects, in CA resists, 75 182 Statistical market research data analysis, 75 636... 

One approach that has overcome this dichotomy of substituent effects is the use of a combination of statistical effects and cooperativity in dendrimeric catalysts. 

The dendrimer wedges with two, three, and four organotelluride groups and the first-generation Frechet-type dendrimers based on 3,5-dihydroxybenzyl alcohol and l,l,l-tris-4-hydroxyphenylethane shown in Fig. 26 illustrate statistical effects in thiolperoxidase-like reactions. Nearly linear increases in reactivity on a molar basis with increasing numbers of organotelluride groups were observed in the oxidation of... 

Bjerrum divided this value into two terms S +i, which accounts for statistical effects and L +i, which accounts for all effects attributable to the nature of the hgand, including electrostatic effects. 

For a metal cation of = 6 that complexes with a monodentate hgand (one with a single binding site), the statistical effect gives the following relationship for Ki through and for (3i throngh P4... 

These values determined for kt are listed in Column 4 of Table I. From these values it is possible to determine the constants kp belonging to each reagent (Column 5) as well as the constant kp per atom of reactive hydrogen. The value of kp, which is deduced from kp by compensating for the statistic effect caused by the number of hydrogen atoms, is thus very significant in discussing reactivity in function of structure. 

Dunkle s Syllabus (1957-1958) Shock Tube Studies in Detonation (pp 123-25) Determination of Pressure Effect (144-45) Geometrical and Mechanical Influences (145-48) Statistical Effects of Sensitivity Discussion on Impact Sensitivity Evaluation (148-49) Pressure in the Detonation Head (175) Temperature of Detonation (176) Charge Density, Porosity, and Granulation (Factors Affecting the Detonation Process) (212-16) Heats of Explosion and Detonation (243-46) Pressures of Detonation (262-63) A brief description of Trauzl Block Test, Sand Test, Plate Dent Test, Fragmentation Test, Hess Test (Lead Block Crushing Test), Kast Test (Copper Cylinder Compression Test), Quinan. Test and Hop-kinson Pressure Bar Test (264-67) Detonation Calorimeters (277-78) Measurements... 

The switching efficiency of lumophore-spacer-receptor systems can be improved by using multiple receptor modules. The PET rate is increased in the device when free of guest ions since more than one site can provide the transiting electron. The simplest cases, such as 4, are those where the receptor units are well separated to prevent interdependent ion binding with an interposed lumophore to minimize the lumophore-receptor spacing for maximum PET rates. Besides this statistical effect, receptors may also cooperatively participate in PET. This may be the case in 5 and 6. ... 

It is worth noting that a statistical effect (different combinations of the various complexants) may result in mixtures of complexants binding more strongly to a cation than would be expected based on the individual stability constants of the complexants [2]. 

This is a classical example of a statistical effect reflecting changes in the symmetry numbers of the various species involved in ionization equilibria. Furthermore, the acidity constant K, corresponding to ... 

For the light molecules He and H2 at low temperatures (below about 50°C.) the classical theory of transport phenomena cannot be applied because of the importance of quantum effects. The Chapman-Enskog theory has been extended to take into account quantum effects independently by Uehling and Uhlenbeck (Ul, U2) and by Massey and Mohr (M7). The theory for mixtures was developed by Hellund and Uehling (H3). It is possible to distinguish between two kinds of quantum effects— diffraction effects and statistics effects the latter are not important until one reaches temperatures below about 1°K. Recently Cohen, Offerhaus, and de Boer (C4) made calculations of the self-diffusion, binary-diffusion, and thermal-diffusion coefficients of the isotopes of helium. As yet no experimental measurements of these properties are available. 

Statistical effects. In a symmetrical diprotic acid, the first dissociation constant is twice as large as expected since there are two equivalent ionizable hydrogens, while the second constant is only half as large as expected because the conjugate base can accept a proton at two equivalent sites. So K IKi should be 4, and approximately this value is found... 

---