Okahara’s one-pot approach

Often the divergence in costs shown in Figure 14.11 does occur, and must be managed. The objective is to maintain production in a safe and environmentally responsible manner, while trying to contain or reduce costs. The approach to managing this problem is through reviewing  [c.345]

A rather different approach is to investigate possible adsorption isotherm forms for use with Eq. X-43. As is discussed more fully in Section XVII-7, in about 1914 Polanyi proposed that adsorption be treated as a compression of a vapor in the potential held U x) of the solid with sufficient compression, condensation to liquid adsorbate would occur. If Uq(x) denotes the held necessary for this, then  [c.377]

An important aspect of the stabilization of emulsions by adsorbed films is that of the role played by the film in resisting the coalescence of two droplets of inner phase. Such coalescence involves a local mechanical compression at the point of encounter that would be resisted (much as in the approach of two boundary lubricated surfaces discussed in Section XII-7B) and then, if coalescence is to occur, the discharge from the surface region of some of the surfactant material.  [c.505]

The preceding discussion on site energy distributions has made the implicit assumption that each kind of site occurred in patches at least large enough that boundary effects could be neglected. In effect, each patch is treated as a small adsorption system within which lateral interaction between adsorbate molecules would occur. At the other extreme, sites of varying energy are randomly distributed on the surface, and only as lower energy sites b ame occupied would there be a developing probability of adjacent sites being occupied. A complete description of surface heterogeneity would have to include the distribution of site energies adjacent to a site of given energy. At this point there are probably too many variables to be extracted from adsorption data alone, although the comparison of isotherms for adsorbates of varying size may help (e.g., nitrogen versus butane—see Ref. 162). A formal statistical mechanical approach to the problem was made by Steel [166].  [c.660]

The model illustrated in figure A3.9.7 is primarily diabatic, the molecule jumps suddenly from one type of bonding, represented by a potential energy curve, to another. However, much of the understanding in gas-surface dynamics derives from descriptions based on motion on a single adiabatic PES, usually the ground-state PES. In the Leimard-Jones model, this would approximately correspond to whichever of (a) and (b) has the lower energy. Although this approach is successfiil in describing H2 dissociation, it will not be adequate for reactions involving very sudden changes of electronic state [43]. These may occur, for example, in the O2 reaction with simple metal surfaces [44] they are so energetic that they can lead to light or electron emission during reaction [45].  [c.907]

The probability of a collision between an electron and a target depends upon the impact parameter, b, which is the perpendicular distance between the line of travel of the electron and the centre of force exerted by the target on the electron. The impact parameter is equivalent to the distance of closest approach if no potential is present between the electron and the target. For a hard-sphere collision between an infinitesimally small projectile and a target of radius r, the impact parameter must be less than r for a collision to occur, and, from simple geometry, the scattering angle 0=2 arccos (b/r). The scattering angle is large for small impact parameters, while for grazing collisions, where b approaches r, the scattering angle is small. The probability  [c.1308]

The separation of the electionic degrees of freedom from nuclear motions through adiabatic approximation has brought success to the ab initio quantum chemistry computations, but it is also the reason why we are confronted with the very difficult problem of potential energy crossing, in particular, the conical intersections. There may be other approaches, however, in which the energies of the states depend neither functionally nor parametrically on the nuclear configuration, and hence no crossing of energy levels may occur. If an approach like this can  [c.400]

Identification of mass spectra is typically performed by searching for similarities of the measured spectrum to spectra stored in a library. Several MS databases and corresponding software products are used routinely [81, 82], A more challenging problem is the interpretation of mass spectra by means of computational chemistry, and different strategies have been applied to the problem of substructure recognition. The use of correlation tables containing characteristic spectral data together with corresponding substructures has been successfully applied to spectroscopic methods. However, because of the complexity of chemical reactions that may occur in mass spectrometers and because of the lack of generally applicable rules, this approach has been less successful with MS.  [c.534]

Gasteiger and co-workers followed an approach based on models of the reactions taking place in the spectrometer [94, 95). Automatic knowledge extraction is performed from a database of spectra and the corresponding structures, and rules are saved. The rules concern possible elementary reactions, and models relating the probability of these reactions with physicochemical parameters calculated for the structures. The knowledge can then be applied to chemical structures in order to predict a) the reactions that occur in the spectrometer, b) the resulting products, and c) the corresponding peaks in the mass spectrum.  [c.535]

In each of the examples cited above, symmetry reduction occurred as a molecule or atom approached and interacted with another species. The "path" along which this approach was thought to occur was characterized by symmetry in the sense that it preserved certain symmetry elements while destroying others. For example, the collision of two Nitrogen atoms to produce N2 clearly occurs in a way which destroys spherical symmetry but preserves axial symmetry. In the other example used above, the formaldehyde molecule was postulated to decompose along a path which preserves C2v symmetry while destroying the axial symmetries of CO and H2. The actual decomposition of formaldehyde may occur along some other path, but if it were to occur along the proposed path, then the symmetry analysis presented above would be useful.  [c.187]

The simplest approach to computing the pre-exponential factor is to assume that molecules are hard spheres. It is also necessary to assume that a reaction will occur when two such spheres collide in order to obtain a rate constant k for the reactants B and C as follows  [c.165]

In this model, reaction is considered to occur preferentially at that position in the aromatic molecule to which the approach of the electrophile causes the smallest increase in zero energy. In molecules possessing polar or dipolar groups, long range electrostatic forces will initially be the most important.  [c.130]

Physically a change in a is caused by the electrostatic field of the reagent, and a change in yS by the modification of the atom from an sp to an sp state, with the concomitant isolation of the atom from the delocalized system. In considering the approach of electrophilic reagents, which usually have marked polar properties, considerable changes in a occur long before any significant changes in hybridisation.  [c.131]

A major problem with the diester approach is the fact that one P—O" group of the phosphate always remains free. Since this group is also activated by condensing agents branched pyrophosphates or triesters may also be formed. Cyclization may also occur when the protecting group of the 3 -OH group is removed before a third nucleotide is condensed to it. These side-reactions drastically reduce yields, especially if the condensing reagent is used repeatedly on a growing oligonucleotide chain with several phosphodiester groups.  [c.217]

Finally, the development of this procedure did not occur in a single, linear pass through the analytical approach. As research progressed, problems were encountered and modifications made, representing a cycle through steps 2, 3, and 4 of the analytical approach.  [c.8]

Selecting the Wavelength and Slit Width The choice of wavelength is dictated by the need for sensitivity and freedom from interference due to unresolved emission lines from other constituents in the sample. Because an atomic emission spectrum usually has an abundance of emission lines, particularly when using a high-temperature plasma source, it is inevitable that some overlap will occur between emission lines. For example, an analysis for Ni using the atomic emission line at 349.30 nm is complicated by the atomic emission line for Fe at 349.06 nm. Narrower slit widths provide for better resolution. The easiest approach to selecting a wavelength is to obtain an emission spectrum for the sample and then to look for an emission line for the analyte that provides an intense signal and is resolved from other emission lines.  [c.437]

Quantitative information about a chemical reaction can be made using any of the techniques described in the preceding chapters. For reactions that are kineti-cally slow, an analysis may be performed without worrying about the possibility that significant changes in concentration occur while measuring the signal. When the reaction s rate is too fast, which is usually the case, significant errors may be introduced if changes in concentration are ignored. One solution to this problem is to stop, or quench, the reaction by suitably adjusting experimental conditions. For example, many reactions involving enzymes show a strong pli dependency and may be quenched by adding a strong acid or strong base. Once the reaction is stopped, the concentration of the desired species can be determined at the analyst s convenience. Another approach is to use a visual indicator that changes color after the reaction occurs to a fixed extent. You may recall that this variable-time method is the basis of the so-called clock reactions commonly used to demonstrate kinetics in the general chemistry classroom and laboratory. Finally, reactions with fast kinetics may be monitored continuously using the same types of spectroscopic and electrochemical detectors found in chromatographic instrumentation.  [c.634]

In discussing Fig. 4.1 we noted that the apparent location of Tg is dependent on the time allowed for the specific volume measurements. Volume contractions occur for a long time below Tg The lower the temperature, the longer it takes to reach an equilibrium volume. It is the equilibrium volume which should be used in the representation summarized by Fig. 4.15. In actual practice, what is often done is to allow a convenient and standardized time between changing the temperature and reading the volume. Instead of directly tackling the rate of collapse of free volume, we shall approach this subject empirically, using a property which we have previously described in terms of free volume, namely, viscosity.  [c.251]

Our approach to the problem of gelation proceeds through two stages First we consider the probability that AA and BB polymerize until all chain segments are capped by an Aj- monomer then we consider the probability that these are connected together to form a network. The actual molecular processes occur at random and not in this sequence, but mathematical analysis is feasible if we consider the process in stages. As long as the same sort of structure results from both the random and the subdivided processes, the analysis is valid.  [c.316]

An alternative mechanism of substitution is unimolecular and involves ionization of the leaving group to give a carbenium ion which reacts rapidly with the reagent. The lifetime of this carbenium ion determines the stereochemical course of the reaction - inversion if it is short, racemization if it is long. In the examples quoted above the Ag20 reaction invi)lves the formation of a carbenium ion, but the carboxyl group forms a weak bond with the developing centre of positive charge so that the approach of the reagent from this side is blocked and must occur from the side of the leaving group. The original optical configuration is thus retained because of neighbouring group participation in the reaction.  [c.424]

A somewhat different point of view is the following. Since 7sv and 7sl always occur as a difference, it is possible that it is this difference (the adhesion tension) that is the fundamental parameter. The adsorption isotherm for a vapor on a solid may be of the form shown in Fig. X-1, and the asymptotic approach to infinite adsorption as saturation pressure is approached means that at the solid is in equilibrium with bulk liquid. As Deijaguin and Zorin [144] note (see also Refs. 10 and 18S), in a contact angle system, the adsorption isotherm must cross the line and have an unstable region, as illustrated in Fig. X-IS. See Section XVII-12. A Gibbs integration to the first crossing gives  [c.374]

This insulation does, in fact, seem to occur. It was remarked on in connection with Fig. XVII-21 and was very explicitly shown in some results of Dubinin and coworkers [139]. Nitrogen adsorption isotherms at -185°C were determined for a carbon black having various amounts of preadsoibed benzene. After only about 1.5 statistical monolayers of benzene, no further change took place in the nitrogen isotherm. A similar behavior was reported by Halsey and co-workers [140] for Ar and N2 adsorption on Ti02 having increasing amounts of preadsorbed water. In this case, a limiting isotherm was reached with about four statistical layers of water, the approach to the limiting form being approximately exponential. Interestingly, the final isotherm, in the case of  [c.654]

Many of the fiindamental physical and chemical processes at surfaces and interfaces occur on extremely fast time scales. For example, atomic and molecular motions take place on time scales as short as 100 fs, while surface electronic states may have lifetimes as short as 10 fs. With the dramatic recent advances in laser tecluiology, however, such time scales have become increasingly accessible. Surface nonlinear optics provides an attractive approach to capture such events directly in the time domain. Some examples of application of the method include probing the dynamics of melting on the time scale of phonon vibrations [82], photoisomerization of molecules [88], molecular dynamics of adsorbates [89, 90], interfacial solvent dynamics [91], transient band-flattening in semiconductors [92] and laser-induced desorption [93]. A review article discussing such time-resolved studies in metals can be found in  [c.1296]

The mechanism by which a transition is induced by electron impact depends on the nature of the coupling between the projectile electron and the target this in turn is influenced by the velocity and closeness of approach of the projectile to the target. There is a wide range of possibilities. A high-energy projectile electron may pass quickly by, delivering only a photon-like electric-field pulse to the target at the mstant of closest approach. Less probable are hard, billiard-ball-like collisions between tlie projectile and one target electron. At low energies, slower, more intimate collisions are characterized by many-electron interactions. Depending upon tlie mechanism, the momentum transferred from projectile to target can vary from the minimum necessary to account for the transition energy to many times more. The interaction influences the type of transition that can be induced and the way in which the projectile is scattered. It is even possible for the projectile electron to be exchanged for a target electron, thus allowing for electron-spin-changing transitions. This state of affairs is a contrast to optical excitation where the momentum transfer is a constant and only dipole-allowed transitions occur with significant probability.  [c.1307]

The complications which occur with bifiircation, i.e. when more than one product arrangement is accessible, can be solved by various methods. Historically, the first close-coupling approaches for multiple product chaimels employed fitting procedures [ ], where the close-coupling equations are simultaneously propagated from each of the asymptotes inwards and then are fitted together at a dividing surface. This approach has been replaced in recent calculations by two methods. One is based on using absorbing potentials to turn the reactive problem into an inelastic one, as explained later. The other is to use hyperspherical coordinates for carrying out the close-coupling propagation [41, 42, 43, 44 and 45]. The hyperspherical coordinates consist of a single radius p, which is zero at the origin (when all nuclei are stuck together) and increases outwards, and a set of angles. For the collinear problem as well as the atom-diatom problem (mvolving tliree independent distances) the hyperspherical coordinates are typically just the regidar spherical coordinates. Close-coupling propagation starts at p = 0 and moves outward until a large value of p is reached. When the asymptote are reached one fits the wavefunction to have the fonn of equation (B3.4.4) and thus obtains the scattering matrix.  [c.2297]

Altematively, tire polymer layers may overlap, which increases tire local polymer segment density, also resulting in a repulsive interaction. Particularly on close approach, r < d + L, a steep repulsion is predicted to occur. Wlren a relatively low molecular weight polymer is used, tire repulsive interactions are ratlier short-ranged (compared to tire particle size) and the particles display near hard-sphere behaviour (e.g., [11]).  [c.2679]

One can study a slow (minutes or longer) chemical reaction by mixing two chemicals in the sample compartment of a standard UV-vis spectrophotometer and measuring the spectmm as a function of time. Though perhaps not often thought of as such, this is a fonn of transient spectroscopy, albeit a slow one. To carry out such a measurement for a reaction which is complete on a time scale of milliseconds to seconds one needs to mix the chemicals and measure the spectra much more rapidly. For gases, this can be done by releasing reactants into a discharge flow apparatus, where they are mixed by diffusion and turbulence while being carried down a tube in an inert carrier gas such as helium. This is not, strictly speaking, a transient kinetic method, however, as the progress in time of the reaction is measured by the steady state detection of concentration as a function of distance travelled down the tube. For liquids, achieving satisfactory mixing times (not to mention conserving reactant) usually requires the use of a stopped-flow apparatus, as in figure C3.1.2 in which chemicals are rapidly forced into a sample cuvette by syringes whose plungers are quickly actuated at a specific time. A probe detection system is triggered immediately after the sample is mixed in this transient technique. Conductance may be monitored in the case of ionic solutions, whereas spectrophotometry provides a more general method for detennining concentrations. Electronic detection methods provide the time resolution needed (oscilloscopes and transient recorders with response frequencies up to a few GFtz are available) to monitor the conductance or spectral changes that accompany the reaction taking place. The rapid mixing approach is limited to the study of reactions taking place on time scales of milliseconds or longer simply because it takes this long for mixing to occur (although ultrarapid techniques have been developed to mix reactants on a 100 microsecond time scale [7].  [c.2949]

A convenient technique to study the sign flip of the wave function is the line-integral approach suggested by Baer [85,86] (an alternative, though more combersome approach, will be to monitor the sign of the wave function along the entire loop [74]). Calculations have been reported [5] using such a line-integral approach for H3, DH2, and HD2 using the 2x2 diabatic DMBE potential energy surface [1]. First, we have shown that the phase obtained by employing the line-integral method is identical (up to a constant) to the mixing angle of the orthogonal transfomiation that diagonalizes the diabatic potential matrix (see Appendix A). We have also studied this angle numerically along the line fomied by fixing the two hyperspherical coordinates p and 0 and letting


Diamonds are found in South Africa, India, South America and Russia. The largest ever found was the Cullinan diamond which weighed about 600 g. The structure is as shown in Figure 8.2. (There are four possible crystalline arrangements all of which are found to occur naturally.) The interatomic bonds are very strong (mean thermochemical bond energy 356kJmor ). This high bond strength is reflected in the great hardness and high melting point of diamond. Diamond also has a high refractive index and is the densest form of carbon (density 3.5gcm ). The many uses of diamond are largely dependent on its great hardness, for example for cutting and grinding.  [c.164]

The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the  [c.137]

An examination of the application of IM to MD shows very good numerical properties (e.g., energy conservation and stability) for moderate timesteps, larger than Verlet [62, 41]. However integrator-induced resonance artifacts limit the application of this approach to larger integration stepsizes. Essentially, resonance occurs at special timesteps that are related in a complex way (via the stepwise propagation transformation) to the various timescales of the motion [63, 64, 6, 65]. At those timesteps, a concerted effect stemming from one component of the motion (e.g., heating of a bond-stretch vibrational mode) leads to very large energetic fluctuations or instability (e.g., bond rupture). Thus, resonance problems lead in general to erratic, rather than systematic, error patterns as a function of timestep. They are also method and system dependent [63, 66, 67], occur for both implicit and explicit schemes (e.g., Verlet and IM [63, 62]), and depend strongly on the fastest frequency in the system and possibly on the coupling strength to other vibrational modes.  [c.241]

The HOMO-LUMO interaction depends on various factors, including the geometry of approach (which affects the amount of overlap), the phase relabonship of the orbitals and their energy separation. For example, the HOMO and LUMO of ethene are illustrated pictorially in Figure 5.34. The most obvious mode of interaction between the two molecules involves suprafacial attack shown in Figure 5.34 to give cyclobutane. However, the symmetries of the overlapping orbitals must have the same phase for a favourable interaction to occur and this is not possible for ethene unless an energetically unfavourable antarafacial approach is adopted. By contrast, the interaction between etliene and the butadiene does occur in a suprafacial sense with both HOMO/LUMO pairs of orbitals having the appropriate phase relationship (Figure 5.34).  [c.307]

In a Lagrangian framework the coordinate system in which the governing flow equations are formulated moves with the flow field. Therefore flow equations written in such a system do not include any convection terms. In particular, the free surface continuity equation (Equation (3.69)) is reduced to a simple time derivative expressed as dFIdt) = 0. However, the integration of this derivative is not trivial because in a free boundary domain it should be evaluated between variable (i.e. time-dependent) limits. In addition, a method should be adopted to prevent computational mesh distortions that will naturally occur in a Lagrangian framework. Various methods based on adaptive re-meshing are used to achieve this objective (e.g. see Morton, 1996). However, some of these techniques lack geometrical flexibility (e.g. they are only suitable for domains that do not include curved boundaries) or they require high CPU times. A robust and geometrically flexible method with implementation that requires relatively moderate CPU times is described in this section. This method is based on the tracking of fluid particle trajectories passing through each node in the computational domain and provides an effective technique for regeneration of the mesh at the end of each time step (Petera and Nassehi, 1996). The free surface continuity equation can be readily integrated using this approach.  [c.104]

A recent estimate places the number of prescrip tion and over the counter drugs marketed throughout the world at about 2000 Approxi mately one third of these are either naturally occur ring substances themselves or are prepared by chemical modification of natural products Most of the drugs derived from natural sources are chiral and are almost always obtained as a single enantiomer rather than as a racemic mixture Not so with the over 500 chiral substances represented among the more than 1300 drugs that are the products of synthetic or game chemistry Until recently such substances were with few exceptions prepared sold and adminis tered as racemic mixtures even though the desired therapeutic activity resided in only one of the enan tiomers Spurred by a number of factors ranging from safety and efficacy to synthetic methodology and eco nomics this practice is undergoing rapid change as more and more chiral synthetic drugs become avail able in enantiomerically pure form  [c.296]

Consider, for instance, the precipitation of AgCl from a solution of AgNOa, using NaCl as a precipitant. Early in the precipitation, when NaCl is the limiting reagent, excess Ag+ ions chemically adsorb to the AgCl particles, forming a positively charged primary adsorption layer (figure 8.5). Anions in solution, in this case and OH , are attracted toward the surface, forming a negatively charged secondary adsorption layer that balances the surface s positive charge. The solution outside the secondary adsorption layer remains electrically neutral. Coagulation cannot occur if the secondary adsorption layer is too thick because the individual particles of AgCl are unable to approach one another closely enough.  [c.242]

In this chapter we analyse a wide class of equilibrium problems with cracks. It is well known that the classical approach to the crack problem is characterized by the equality type boundary conditions considered at the crack faces, in particular, the crack faces are considered to be stress-free (Cherepanov, 1979, 1983 Kachanov, 1974 Morozov, 1984). This means that displacements found as solutions of these boundary value problems do not satisfy nonpenetration conditions. There are practical examples showing that interpenetration of crack faces may occur in these cases. An essential feature of our consideration is that restrictions of Signorini type are considered at the crack faces which do not allow the opposite crack faces to penetrate each other. The restrictions can be written as inequalities for the displacement vector. As a result a complete set of boundary conditions at crack faces is written as a system of equations and inequalities. The presence of inequality type boundary conditions implies the boundary problems to be nonlinear, which requires the investigation of corresponding boundary value problems. In the chapter, plates and shells with cracks are considered. Properties of solutions are established existence of solutions, regularity up to the crack faces, convergence of solutions as parameters of a system are varying and so on. We analyse different constitutive laws elastic, viscoelastic.  [c.69]

It is well known that the classical approach to the crack problem is characterized by the equality type boundary conditions considered at the crack faces in particular, the crack faces are assumed to be stress-free. This means that displacements found as solutions of these boundary value problems do not provide a nonpenetration condition between crack faces. There are practical examples showing that interpenetration of crack faces may occur in these cases. An essential feature of the book is that a restriction of Signorini type is considered at the crack faces which does not allow the opposite crack faces to penetrate each other. The restriction can be written as an inequality for the displacement vector. As a result a complete set of boundary conditions at crack faces is written as a system of equations and inequalities. The presence of inequality type boundary conditions implies the boundary problems to be nonlinear, which requires the investigation of corresponding boundary value problems.  [c.393]

See pages that mention the term Okahara’s one-pot approach : [c.166]    [c.611]    [c.92]    [c.1832]    [c.2679]    [c.2768]    [c.389]    [c.506]    [c.27]    [c.451]    [c.14]    [c.94]    [c.109]    [c.350]   
Macrocyclic polyether syntheses (1982) -- [ c.46 ]