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Neighbors

A component in a vapor mixture exhibits nonideal behavior as a result of molecular interactions only when these interactions are very wea)c or very infrequent is ideal behavior approached. The fugacity coefficient (fi is a measure of nonideality and a departure of < ) from unity is a measure of the extent to which a molecule i interacts with its neighbors. The fugacity coefficient depends on pressure, temperature, and vapor composition this dependence, in the moderate pressure region covered by the truncated virial equation, is usually as follows ... [Pg.37]

The b3TJroduct, DCD, is not required for this project. Hydrogen chloride can be sold to a neighboring plant. Assume at this stage that all separations can be carried out by distillation. The normal boiling points are given in Table 4.1. [Pg.102]

One may consider a molecule in the surface region as being in a state intermediate between that in the vapor phase and that in the liquid. Skapski [11] has made the following simplified analysis. Considering only nearest-neighbor interactions, if n, and denote the number of nearest neighbors in the interior of the liquid and the surface region, respectively, then, per molecule... [Pg.52]

The next point of interest has to do with the question of how deep the surface region or region of appreciably unbalanced forces is. This depends primarily on the range of intermolecular forces and, except where ions are involved, the principal force between molecules is of the so-called van der Waals type (see Section VI-1). This type of force decreases with about the seventh power of the intermolecular distance and, consequently, it is only the first shell or two of nearest neighbors whose interaction with a given molecule is of importance. In other words, a molecule experiences essentially symmetrical forces once it is a few molecular diameters away from the surface, and the thickness of the surface region is of this order of magnitude (see Ref. 23, for example). (Certain aspects of this conclusion need modification and are discussed in Sections X-6C and XVII-5.)... [Pg.56]

This region has been divided into two subphases, L and S. The L phase differs from the L2 phase in the direction of tilt. Molecules tilt toward their nearest neighbors in L2 and toward next nearest neighbors in L (a smectic F phase). The S phase comprises the higher-ir and lower-T part of L2. This phase is characterized by smectic H or a tilted herringbone structure and there are two molecules (of different orientation) in the unit cell. Another phase having a different tilt direction, L, can appear between the L2 and L 2 phases. A new phase has been identified in the L 2 domain. It is probably a smectic L structure of different azimuthal tilt than L2 [185]. [Pg.134]

The effects of electric fields on monolayer domains graphically illustrates the repulsion between neighboring domains [236,237]. A model by Stone and McConnell for the hydrodynamic coupling between the monolayer and the subphase produces predictions of the rate of shape transitions [115,238]. [Pg.139]

If the interaction between atoms that are not nearest neighbors is neglected, then the ratios B/A are each equal to the ratio of the number of nearest neighbors to a surface atom (across the dividing plane) to the number of nearest neighbors for an interior atom. The calculation then reduces to that given by Eq. Ill-15. [Pg.266]

The calculation of the surface energy of metals has been along two rather different lines. The first has been that of Skapski, outlined in Section III-IB. In its simplest form, the procedure involves simply prorating the surface energy to the energy of vaporization on the basis of the ratio of the number of nearest neighbors for a surface atom to that for an interior atom. The effect is to bypass the theoretical question of the exact calculation of the cohesional forces of a metal and, of course, to ignore the matter of surface distortion. [Pg.269]

Westwood and Hitch suggest, incidentally, that the cleavage experiment, not being fully reversible, may give only a bond-breaking or nearest-neighbor type of surface energy with little contribution from surface distortion. [Pg.280]

Make the following approximate calculations for the surface energy per square centimeter of solid krypton (nearest-neighbor distance 3.97 A), and compare your results with those of Table VII-1. (a) Make the calculations for (100), (110), and (111) planes, considering only nearest-neighbor interactions, (b) Make the calculation for (100) planes, considering all interactions within a radius defined by the sum... [Pg.286]

Taking into account only nearest-neighbor interactions, calculate the value for the line or edge tension k for solid argon at 0 K. The units of k should be in ergs per centimeter. [Pg.286]

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... [Pg.286]

The various spectroscopic methods do have in common that they typically allow analysis of the surface composition. Some also allow an estimation of the chemical state of the system and even of the location of nearest neighbors. [Pg.306]

A LEED pattern is obtained for the (111) surface of an element that crystallizes in the face-centered close-packed system. Show what the pattern should look like in symmetry appearance. Consider only first-order nearest-neighbor diffractions. [Pg.312]

Some studies have been made of W/O emulsions the droplets are now aqueous and positively charged [40,41 ]. Albers and Overbeek [40] carried out calculations of the interaction potential not just between two particles or droplets but between one and all nearest neighbors, thus obtaining the variation with particle density or . In their third paper, these authors also estimated the magnitude of the van der Waals long-range attraction from the shear gradient sufficient to detach flocculated droplets (see also Ref. 42). [Pg.508]

The quantity zoi will depend very much on whether adsorption sites are close enough for neighboring adsorbate molecules to develop their normal van der Waals attraction if, for example, zu is taken to be about one-fourth of the energy of vaporization [16], would be 2.5 for a liquid obeying Trouton s rule and at its normal boiling point. The critical pressure P, that is, the pressure corresponding to 0 = 0.5 with 0 = 4, will depend on both Q and T. A way of expressing this follows, with the use of the definitions of Eqs. XVII-42 and XVII-43 [17] ... [Pg.614]

Such attractive forces are relatively weak in comparison to chemisorption energies, and it appears that in chemisorption, repulsion effects may be more important. These can be of two kinds. First, there may be a short-range repulsion affecting nearest-neighbor molecules only, as if the spacing between sites is uncomfortably small for the adsorbate species. A repulsion between the electron clouds of adjacent adsorbed molecules would then give rise to a short-range repulsion, usually represented by an exponential term of the type employed... [Pg.700]

Yarkoni [108] developed a computational method based on a perturbative approach [109,110], He showed that in the near vicinity of a conical intersection, the Hamiltonian operator may be written as the sum a nonperturbed Hamiltonian Hq and a linear perturbative temr. The expansion is made around a nuclear configuration Q, at which an intersection between two electronic wave functions takes place. The task is to find out under what conditions there can be a crossing at a neighboring nuclear configuration Qy. The diagonal Hamiltonian matrix elements at Qy may be written as... [Pg.382]

As for the trough states, a statistical analysis has been earned out for the calculated cone states [12]. The nearest neighbor spacings are calculated by... [Pg.600]

The values due to the two separate calculations are of the same quality we usually get from (pure) two-state calculations, that is, veiy close to 1.0 but two comments have to be made in this respect (1) The quality of the numbers are different in the two calculations The reason might be connected with the fact that in the second case the circle surrounds an area about three times larger than in the first case. This fact seems to indicate that the deviations are due noise caused by CIs belonging to neighbor states [e.g., the (1,2) and the (4,5) CIs]. (2) We would like to remind the reader that the diagonal element in case of the two-state system was only (—)0.39 [73] [instead of (—)1.0] so that incorporating the third state led, indeed, to a significant improvement. [Pg.711]

While smooth pair potentials are the rule in the literature, surface terms have traditionally been discontinuous the only potential using smooth surface terms seems to appear in Lund et al. [19], where the surface term is a function of a smooth approximation to the number of neighbors of a Ca atom.)... [Pg.215]

Fig. 2. Patches divide the simulation space into a regular grid of cubes, each larger than the nonbonded cutoff. Interactions between atoms belonging to neighboring patches are calculated by one of the patches which receives a positions message (p) and returns a force message (f). Shades of gray indicate processors to which patches are assigned. Fig. 2. Patches divide the simulation space into a regular grid of cubes, each larger than the nonbonded cutoff. Interactions between atoms belonging to neighboring patches are calculated by one of the patches which receives a positions message (p) and returns a force message (f). Shades of gray indicate processors to which patches are assigned.

See other pages where Neighbors is mentioned: [Pg.105]    [Pg.65]    [Pg.65]    [Pg.196]    [Pg.571]    [Pg.108]    [Pg.270]    [Pg.286]    [Pg.588]    [Pg.613]    [Pg.692]    [Pg.701]    [Pg.702]    [Pg.729]    [Pg.301]    [Pg.342]    [Pg.355]    [Pg.393]    [Pg.393]    [Pg.465]    [Pg.499]    [Pg.500]    [Pg.500]    [Pg.516]    [Pg.600]    [Pg.603]    [Pg.306]    [Pg.475]    [Pg.476]   
See also in sourсe #XX -- [ Pg.102 ]




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3-Bromo-2-butanol, neighboring group

Activate neighboring functional groups

Alkenes neighboring group effects

Amides, neighboring group participation

Amorphous near-neighbor atom

Amorphous nearest-neighbor distance

Amorphous nearest-neighbor region

Amorphous second neighbor

Anchimeric assistance (Neighboring group

And neighboring group effects

And neighboring groups

And neighboring-group participation

And the neighboring group

Anisotropy effect neighbor

Atoms changing neighbors

Bonded neighbors

Boronic neighboring group effect

Bromination neighboring groups

Carboxylic cleavage with neighboring

Chiral neighboring group participation

Clustering) nearest neighbor

Commonality between nearest neighbors

Conditions for and Features of SN Reactions with Neighboring Group Participation

Control by Neighboring Groups

Coulomb nearest-neighbor repulsion

Critical nearest-neighbor distance

Crystal constant neighbor distance)

Cyclopropanes neighboring group

Displacement reactions neighboring group effects

Effect, directive neighboring groups

Electronic Couplings Between Neighboring Pairs

Entanglement nearest-neighbor

Esters neighboring group participation

Ethers neighboring group participation

Excluded neighbors

Extrapolated from neighboring values

Fc-nearest neighbors

First neighbor approximation

First neighbors

First-neighbor distance

Functionalized negative neighboring group effect

Gene neighbor method

Genome neighbors

Getting by with Help from Friends, or a Least Neighbors Neighboring Group Participation

Goodman, Leon, Neighboring-group

Goodman, Leon, Neighboring-group Participation in Sugars

Group Neighboring Heavy Atoms into CG Particles

Halogenation neighboring groups

He-Like and Neighboring Ions

Heteroatoms as Neighboring Groups

Hopping nearest-neighbor

Hydrogen bonding, between neighboring water molecules

Hydrogen neighboring group effects

Hydrogens nonequivalent neighboring

INDEX neighboring

Increased Rate through Neighboring Group Participation

Interaction nearest-neighbor

Interactions with neighboring chains

Interactions, first neighbor

Interactions, first neighbor entropy

Ising model with next nearest neighbors

Junction topological neighbor

K nearest neighbor algorithm

K nearest-neighbor

K nearest-neighbor, KNN

K-nearest neighbor classification

K-nearest neighbor method

Koenigs-Knorr reaction neighboring group participation

Koenigs-Knorr reaction neighboring-group effect

Leaving groups neighboring group participation

Machine nearest neighbors

Many-neighbor interactions

Mechanism, neighboring

Mechanism, neighboring group groups

Mechanism, neighboring stereochemistry

Mechanism, radical neighboring group effects

Mechanisms neighboring-group

Metalation neighboring group assistance

Method nearest-neighbor distance

Methyl groups, neighboring

Methyl groups, neighboring group participation

Missing neighbor

Molecule nearest-neighbor

Molecule next-nearest neighbor

Multiple neighboring groups

N-nearest neighbors

NEIGHBOR program

Ne-Like and Neighboring Ions

Near-neighbor interaction

Near-neighbor shell

Near-neighbor spectra

Nearest neighbor analysis

Nearest neighbor bond, weakening

Nearest neighbor broken bond model

Nearest neighbor distance

Nearest neighbor distance contributions

Nearest neighbor distribution

Nearest neighbor free energy parameters

Nearest neighbor frequencies

Nearest neighbor random walks

Nearest neighbor site

Nearest neighbor spacing distribution

Nearest neighbor technique

Nearest neighbor techniques representation

Nearest neighbors

Nearest neighbors methods

Nearest- neighbor characterized

Nearest- neighbor concurrence

Nearest-Neighbor Dominance in Cooperative Luminescence

Nearest-neighbor approximation

Nearest-neighbor arrangement

Nearest-neighbor atoms

Nearest-neighbor base sequences

Nearest-neighbor bond lengths

Nearest-neighbor bond network

Nearest-neighbor bond potential

Nearest-neighbor correlation parameter

Nearest-neighbor coupling

Nearest-neighbor distance reversible

Nearest-neighbor distance theory

Nearest-neighbor distribution function

Nearest-neighbor electronic couplings

Nearest-neighbor exchange interaction

Nearest-neighbor graft points

Nearest-neighbor hoppings

Nearest-neighbor interaction model

Nearest-neighbor interaction model excitation

Nearest-neighbor interaction model pair approximation

Nearest-neighbor interactions, protein

Nearest-neighbor level spacings

Nearest-neighbor lists

Nearest-neighbor models

Nearest-neighbor nucleotide

Nearest-neighbor selection

Nearest-neighbor sequence analysis

Nearest-neighbor site probability (

Nearest-neighbor spacing

Negative neighboring group effect

Neighbor anisotropy term

Neighbor atom effects

Neighbor atom potential

Neighbor contributions

Neighbor effect

Neighbor effect, plants

Neighbor exclusion principle

Neighbor group assistance

Neighbor joining analysis

Neighbor joining method

Neighbor list

Neighbor lists a time-saving trick

Neighbor relations

Neighbor tables

Neighbor tables, molecular dynamics

Neighbor-joining algorithm

Neighbor-joining trees

Neighboring Amides

Neighboring Group Displacement Reactions

Neighboring Group Participation and Intramolecular Reactions

Neighboring Group Participation by Other Functional Groups

Neighboring acetal functions

Neighboring amino

Neighboring atoms

Neighboring bonds, conformational changes

Neighboring clusters

Neighboring clusters centers

Neighboring concept

Neighboring defects

Neighboring dehydrohalogenation

Neighboring exclusion

Neighboring functional groups

Neighboring group

Neighboring group assistance in displacement reactions

Neighboring group assisted opening

Neighboring group contribution

Neighboring group effect intramolecular)

Neighboring group effect, macromolecular

Neighboring group effect, nucleophilic substitutions

Neighboring group effects

Neighboring group effects anchimeric assistance

Neighboring group effects reaction mechanism

Neighboring group effects reaction rate

Neighboring group effects remote

Neighboring group effects stereochemistry

Neighboring group free radical

Neighboring group inhibition

Neighboring group participation

Neighboring group participation chiral auxiliaries

Neighboring group participation decreasing

Neighboring group participation definition

Neighboring group participation for hydroxyl inversion

Neighboring group participation glycosylation

Neighboring group participation groups

Neighboring group participation, studies

Neighboring group participation. See

Neighboring group participation: in reactions

Neighboring groups, alkenes

Neighboring groups, alkenes hydrogen

Neighboring groups, powerful

Neighboring hydrogens

Neighboring hydroxyl group participation

Neighboring n Systems

Neighboring occupied sites

Neighboring participation

Neighboring-group assistance

Neighboring-group model

Neighboring-group participation anomerization

Neighboring-group participation donors

Neighboring-group participation trichloroacetimidate

Neighboring-group participation, in sugars

Neighboring-group reactions

Neighboring-group-effect 846 Subject

Neighboring-interaction model, ferrocene

Next neighbors

Next-nearest neighbors

Next-neighbor effects

Nuclear energy neighboring

Nucleophile substitution, neighboring group

Opening hydroxy neighboring group

Oxiranes neighboring group

Oxygen neighboring group

Participation s. Neighboring

Petasis Borono-Mannich Reaction Iminium Ions Possessing Neighboring Heteroatom Functionality

Petasis iminium ions possessing neighboring

Placing neighbors

Probability factor nearest neighbor sites (

Protecting neighboring-group participation

Protein Structure Is Determined by Attractions Between Neighboring Amino Acids

Protein neighbor

Proton transfer neighboring-group participation

Proximity s. Neighboring

Proximity s. Neighboring group

Quantitative nearest neighbors

Rate, increased with neighboring

Rate, increased with neighboring group participation

Reactions neighbor effects

Reactivity neighboring group effect

Rearrangement neighboring group effects

Reciprocal nearest neighbor

Remote Neighboring Group Participation

SO Effects on Nuclear Shieldings of Neighbor Atoms

Second nearest neighbor interactions

Second nearest neighbors

Second-neighbor hopping

Sequence Neighbors link

Simulation neighbor lists

Single Bonds as Neighboring Groups

Solvolysis neighboring-group participation

Spacing between neighboring energy

Spatial neighbor

Spin correlations between neighboring sites

Stereoselectivity with neighboring group participation

Structure Neighbors links

Substitution reactions neighboring group participation

Sugars neighboring-group participation

Sugars neighboring-group reactions

Surface-neighbor effects

Surfaces nearest neighbor interactions

Syntheses Substitutions and Rearrangements Involving Neighboring Group Participation of Dihetero-tricyclodecanes

The Good Neighbor

Three neighboring-group participation mechanism

Topological neighbors

Transition probabilities nearest-neighbor

Treat Many-Neighbor Interactions

Two Neighbor Segments with Different Filling

Two Neighbor Segments with Equal Filling

Two Neighboring Double Bonds Conjugated Dienes

Verlet neighbor list

Vertex Neighbor Sum Rule

Water nearest neighbor distribution

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