Kinetic secondary

If secondary isotope effects arise strictly from changes in force constants at the position of substitution, with none of the vibrations of the isotopic atom being coupled into the reaction coordinate, then a secondary isotope effect will vary from 1.00 when the transition state exactly resembles the reactant state (thus no change in force constants when reactant state is converted to transition state) to the value of the equilibrium isotope effect when the transition state exactly resembles the product state (so that conversion of reactant state to transition state produces the same change in force constants as conversion of reactant state to product state). For example in the hydride-transfer reaction shown under point 1 above, the equilibrium secondary isotope effect on conversion of NADH to NAD is 1.13. The kinetic secondary isotope effect is expected to vary from 1.00 (reactant-like transition state), through (1.13)° when the stmctural changes from reactant state to transition state are 50% advanced toward the product state, to 1.13 (product-like transition state). That this naive expectation... 

These studies had therefore found the tunneling phenomenon, with coupled motion, as the explanation for failures of these systems to conform to the expectations that the kinetic secondary isotope effects would be bounded by unity and the equilibrium effect and that the primary and secondary effects would obey the Rule of the Geometric Mean (Chart 3), as well as being consistent with the unusual temperature dependences for isotope effects that were predicted by Bell for cases involving tunneling. 

However, a much coarser approach can yield significant results. Several authors, for example, have attempted to relate the kinetic-secondary-electron coefficient to the stopping-power relationships used for the analysis of atomic ion ranges in solids. A very lucid paper on this approach has been presented by Beuhler and Friedman and their perspective will be summarized in the following paragraphs. 

The three pieces of information needed for a kinetic-secondary-electron yield calculation can now be related to the model of Beuhler and Friedman ... 

The numerical factors in equations (70) to (73) are again statistical. The factors involving l raised to a power imply kinetic secondary isotope effects. The replacement of one protium atom by one deuterium atom increases the rate constant by i . This inverse isotope effect is qualitatively intelligible since the non-transferred nuclei are more tightly bound in the transition state than they were in the reactants. The existence of the secondary isotope effect also means that the ratio of rate constants in H20 and D20 ( H/fcD) Is not a measure of the primary isotope effect, whereas h o/3 h,do is- To obtain the primary isotope effect it is necessary to divide H/feD by Z2 - (For experimental evaluations of primary and secondary isotope effects see Kreevoy et al.t 1964 ... 

As isotopes of the same element have the same number of electrons, they display the same chemical reactivity. Isotope fractionation, also referred to as mass fractionation, describes the subtle differences noted in reaction kinetics (speed) displayed by different isotopes of the same element. This is noted as mass (m), velocity (v), and energy (E) are all interrelation through E = l2mv. Isotope fractionation can be useful in defining chemical reaction kinetics, secondary ion emission studies (see Section 3.3.1.2.3), and of course chronology (see Section 1.2.3). 

Figure Al.7.12. Secondary electron kinetic energy distribution, obtained by measuring the scadered electrons produced by bombardment of Al(lOO) with a 170 eV electron beam. The spectrum shows the elastic peak, loss features due to the excitation of plasmons, a signal due to the emission of Al LMM Auger electrons and the inelastic tail. The exact position of the cutoff at 0 eV depends on die surface work fimction.

Typically elimination by the El mechanism is observed only for tertiary and some secondary alkyl halides and then only when the base is weak or m low con centration Unlike eliminations that follow an E2 pathway and exhibit second order kinetic behavior... 

Radiation Damage. It has been known for many years that bombardment of a crystal with energetic (keV to MeV) heavy ions produces regions of lattice disorder. An implanted ion entering a soHd with an initial kinetic energy of 100 keV comes to rest in the time scale of about 10 due to both electronic and nuclear coUisions. As an ion slows down and comes to rest in a crystal, it makes a number of coUisions with the lattice atoms. In these coUisions, sufficient energy may be transferred from the ion to displace an atom from its lattice site. Lattice atoms which are displaced by an incident ion are caUed primary knock-on atoms (PKA). A PKA can in turn displace other atoms, secondary knock-ons, etc. This process creates a cascade of atomic coUisions and is coUectively referred to as the coUision, or displacement, cascade. The disorder can be directiy observed by techniques sensitive to lattice stmcture, such as electron-transmission microscopy, MeV-particle channeling, and electron diffraction. 

Autooxidation. Liquid-phase oxidation of hydrocarbons, alcohols, and aldehydes by oxygen produces chemiluminescence in quantum yields of 10 to 10 ° ein/mol (128—130). Although the efficiency is low, the chemiluminescent reaction is important because it provides an easy tool for study of the kinetics and properties of autooxidation reactions including industrially important processes (128,131). The light is derived from combination of peroxyl radicals (132), which are primarily responsible for the propagation and termination of the autooxidation chain reaction. The chemiluminescent termination step for secondary peroxy radicals is as follows ... 

Only 20—40% of the HNO is converted ia the reactor to nitroparaffins. The remaining HNO produces mainly nitrogen oxides (and mainly NO) and acts primarily as an oxidising agent. Conversions of HNO to nitroparaffins are up to about 20% when methane is nitrated. Conversions are, however, often ia the 36—40% range for nitrations of propane and / -butane. These differences ia HNO conversions are explained by the types of C—H bonds ia the paraffins. Only primary C—H bonds exist ia methane and ethane. In propane and / -butane, both primary and secondary C—H bonds exist. Secondary C—H bonds are considerably weaker than primary C—H bonds. The kinetics of reaction 6 (a desired reaction for production of nitroparaffins) are hence considerably higher for both propane and / -butane as compared to methane and ethane. Experimental results also iadicate for propane nitration that more 2-nitropropane [79-46-9] is produced than 1-nitropropane [108-03-2]. Obviously the hydroxyl radical attacks the secondary bonds preferentially even though there are more primary bonds than secondary bonds. 

Radical Scavengers Hydrogen-donating antioxidants (AH), such as hindered phenols and secondary aromatic amines, inhibit oxidation by competing with the organic substrate (RH) for peroxy radicals. This shortens the kinetic chain length of the propagation reactions. 

The distribution of current (local rate of reaction) on an electrode surface is important in many appHcations. When surface overpotentials can also be neglected, the resulting current distribution is called primary. Primary current distributions depend on geometry only and are often highly nonuniform. If electrode kinetics is also considered, Laplace s equation stiU appHes but is subject to different boundary conditions. The resulting current distribution is called a secondary current distribution. Here, for linear kinetics the current distribution is characterized by the Wagner number, Wa, a dimensionless ratio of kinetic to ohmic resistance. 

Various racemic secondary alcohols with different substituents, eg, a-hydroxyester (60), are resolved by PFL neatly quantitatively (75). The effect of adjacent unsatuiation on enzyme-catalyzed kinetic resolutions was thoroughly studied for a series of aHyUc (61), propargyUc (62), and phenyl-substituted 2-aIkanols (76,77). Excellent selectivity was observed for (E)-aHyhc alcohols whereas (Z)-isomers showed poor selectivity (76). 

This assumes that the gas-solid exchange kinetics at the interface is rapid. When this process affects the exchange kinetics significantly dieii analysis of concentrations layer by layer in die diffused sample is necessaty. This can be done by the use of SIMS (secondary ion mass spectrometry) and the equation used by Kihier, Steele and co-workers for this diffusion study employs a surface exchange component. 

Ethylene oxide secondary oxidation with C-tagged ethylene oxide, to clarify the source of CO2, was done at Union Carbide but not published. This was about 10 years before the publication of Happel (1977). With very limited radioactive supply only a semi-quantitative result could be gained but it helped the kinetic modeling work. It became clear that most CO2 comes from ethylene directly and only about 20% from the secondary oxidation of ethylene oxide. 

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