The kinetic method

The kinetic method [42,43] is a relative method for thermochemical data determination which is based on measurement of the rates of competitive dissociations of mass-selected cluster ions. This method was introduced by Cooks [44] for proton affinity determination. Later, an extension of this method was proposed by Fenselau [45]. 

Proton affinity determination by the kinetic method, (a) This method is based on competitive dissociation of heterodimer clusters, (b) Potential energy diagram for proton-bound dimer dissociation. 

The above equation can be simplified to give an equation that shows the relation of the proton affinity (PA) with the rate constant ratio of the decomposition reaction  

This equation is verified by the assumption that both the differences in the entropy changes for the competitive dissociation channels and the reverse activation barriers for the dissociation of the proton-bonded dimer are negligible or similar. In these conditions, gi = Qix and E — E2 = PA2 - PAi = APA. The entropy effects are generally comparable when the competing dissociations involve species that are similar in structure. 

The rate constant ratio of the competitive decomposition reaction is equal to the ratio of the two fragment ion intensities (/x) if the comparison is made for competitive dissociation of a weakly proton dimer having no other decomposition channel. In these conditions, 

The network build-up is described by a (infinite) set of kinetic differential equations for the concentration of each i-mer. This approach has been developed mainly by Kuchanov et al. (cf., e.g., Refs. and is demonstrated here on two examples  

Assuming bimolecular kinetics, the time (t) dependence of the concentration c,, reads 

The set (25) can be converted into a single differential equation (27) for the generating function g(z) 

In these equations, i, m, o are molar concentrations of the initiator I, monomer M, and polymer of degree of polymerization i, respectively t = kpt and 

The kinetic theory can also be used for polyfunctional systems with unequal reactivities of groups and substitution effects, but an explicit solution of the partial differential equation corresponding to Eq. (23) derived for the equireactive system is not possible. One can use, however, the method of moments for derivation of certain averages as was explained in 

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Assay of Enzymes In body fluids, enzyme levels aie measured to help in diagnosis and for monitoiing treatment of disease. Some enzymes or isoenzymes are predominant only in a particular tissue. When such tissues are damaged because of a disease, these enzymes or isoenzymes are Hberated and there is an increase in the level of the enzyme in the semm. Enzyme levels are deterrnined by the kinetic methods described, ie, the assays are set up so that the enzyme concentration is rate-limiting. The continuous flow analyzers, introduced in the early 1960s, solved the problem of the high workload of clinical laboratories. In this method, reaction velocity is measured rapidly the change in absorbance may be very small, but within the capabiUty of advanced kinetic analyzers. 

PMSA is easily synthesized reagent and its diluted aqueous solutions (10 -10 M) ai e stable in time. PMSA is stronger oxidizer than both widely used in the kinetic methods of analysis and K S O. ... 

Following this procedure urea can be determined with a linear calibration graph from 0.143 p.g-ml To 1.43 p.g-ml and a detection limit of 0.04 p.g-ml based on 3o criterion. Results show precision, as well as a satisfactory analytical recovery. The selectivity of the kinetic method itself is improved due to the great specificity that urease has for urea. There were no significant interferences in urea determination among the various substances tested. Method was applied for the determination of urea in semm. 

The kinetic method of determining relative acidity suffers from one serious complication, however. This complication has to do with the fate of the ion pair that is formed immediately on removal of the proton. If the ion pair separates and difiuses into the solution rapidly, so that each deprotonation results in exchange, the exchange rate is an accurate measure of the rate of deprotonation. Under many conditions of solvent and base, however, an ion pair may return to reactants at a rate exceeding protonation of the carbanion by the solvent. This phenomenon is called internal return ... 

The greater dependence of rate coefficient upon acidity for detritiation compared to dedeuteration is apparent for benzene as it was for toluene and is more marked, but in view of the errors in the benzene work (which appear to arise only from measuring the acid concentration but could possibly arise from some feature of the kinetic method) and element of doubt must remain here. Nevertheless, this phenomenon (which is understandable on the basis that when the reactions are infinitely fast they will then both take place at the same rate, and the more reactive the compound and the stronger the acid, the more closely this situation is approached) seems to be general, for Gold et a/.460 found that the log rate coefficient... 

The methods have been modified by Sax and co-workers and by Amador and Salvatore, who stabilized the final color by the addition of appropriate buffers at pH 3, optimized the substrate concentrations, and showed that acceptable correlation existed with the revised kinetic method (26). Automated continuous flow methods for these dyes, as well as for the kinetic method are now available (26). 

The resulting pyruvate may be measured by coupling the reaction with lactic dehydrogenase and NADH, or chemically by using dini-trophenylhydrazine. The kinetic method has been revised by Henry and co-workers to optimize the analytical conditions, and still is the method of choice (28). 

The kinetic method, developed by Cooks et al., is commonly nsed to measnre acidities for systems that readily form proton-bound clnster ions. For example, acidities are determined from the branching ratios for dissociation of proton-bonnd cluster ions of anions and reference. In the simplest form, there is assnmed to be a semi-logarithmic relationship between the CID branching ratio, r, and the difference in the free energies for the two processes (Eq. 5.2). 

Although the kinetic method as a thermochemical tool has been debated, it is ultimately a refined bracketing approach, using branching ratios to interpolate a more precise location of the thermochemical property (as opposed to jnst between those of HA and HC). Therefore, the kinetic method should be at least as reliable as bracketing for the measnrement of gas-phase thermochemistry. The kinetic method has a... 

Other variations of the kinetic method have been proposed. ... 

Wenthold and co-workers have used this approach to generate the negative ion of 5-dehydro-m-xylylene (Eq. 5.19). ° Using bracketing experiments to determine the gas-phase acidity at the 5-position of m-xylylene, and the kinetic method to determine the triradical electron affinity, the BDE at the 5-position of m-xylylene was measured (Eq. 5.20). 

In our studies we mainly used the kinetic method of detection which was initially proposed in paper [75]. The advantages of this method if compared to the method of measurements of the stationary electric conductivity deal (apart from fast availability of the data) with the fact that in several cases it enables one to obtain information concerning concentration of detective particles even during development of certain surface reactions in which these particles directly participate. The most simple example is provided by (lie surface recombination whose study... 

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

Recently, Cooks and coworkers176 determined the electron affinity (EA) of 1,3,5,7-cyclooctatetraene by using the kinetic method, that is, by performing CID of the cluster anions of the cycloolefin with a number of reference molecules of known EA. The value obtained (EA = 0.58 0.10 eV) was found to be in excellent accordance with that reported previously by Wentworth and Ristau177. 

The kinetic method was introduced by Cooks and co-workers about twenty years... 

A wide range of thermochemical properties can be measured, including not only proton affinity or gas-phase basicity, but also electron affinity, ionization energy, gas-phase acidity and cation affinity Entropy changes upon attachment of an ion to a molecule are also accessible and provide information on both the nature of the bonding and fragmentation mechanisms in cluster ions, especially in biological compounds. Thermochemical determinations by the kinetic method also provide very useful structural information e.g., two-electron three-center bond has been observed in the gas phase by means of the kinetic method. " In the last years, the kinetic method has been also applied to characterize chiral ions in the gas phase. 

At this point, it is worthwhile to return on the theoretical basis of the kinetic method, and make some considerations on the assumptions made, in order to better investigate the validity of the information provided by the method. In particular some words have to been spent on the effective temperamre The use of effective parameters is common in chemistry. This usually implies that one wishes to use the form of an established equation under conditions when it is not strictly valid. The effective parameter is always an empirical value, closely related to and defined by the equation one wishes to approximate. Clearly, is not a thermodynamic quantity reflecting a Maxwell-Boltzmann distribution of energies. Rather, represents only a small fraction of the complexes generated that happen to dissociate during the instrumental time window (which can vary from apparatus to apparatus). 

At the beginning of this paragraph, it has been mentioned the application of the kinetic method to characterize chiral ions. If A is an unknown chiral molecule and ref is a reference molecule of defined configuration, the stability difference between their homochiral and heterochiral complexes with I, [A -Lref] and [A -Lref], can be determined by the dissociation of the corresponding [A -L(ref)2] and [A -L(ref)2] clusters (Scheme 4). 

The differences between the A(AG) values of diastereomeric complexes (AA(AG) = A(AG) — A(AG) in Table 9) demonstrate that the kinetic method can be used to enantiodifferentiate chiral ions and molecules in the gas phase. 

The kinetic method [102,104-106] compares the relative rates of the competitive dissociations of a proton-bound adduct [A-H-B] formed by admitting a mixture of A and B to a Cl ion source. [104,105] There, the proton-bound adduct [A-H-B] is generated amongst other products such as [AH] and [BH]. Using standard tandem MS techniques, e.g., MIKES, the cluster ion [A-H-Bref] is selected and allowed to undergo metastable decomposition ... 

Fig. 2.23. Determination of the proton affinity of cyclohexanecarboxamide (a) by the kinetic method, and (b) by the thermokinetic method. The horizontal lines show the indicative values ln[AH]V[BrefH] = 0 in (a) and REs according to different authors in (b). [101] Adapted from Ref. [109] by permission. IM Publications, 2003.

Proton transfer is one of the prominent representatives of an ion-molecule reaction in the gas phase. It is employed for the determination of GBs and PAs (Chap. 2.11.2) by either method the kinetic method makes use of the dissociation of proton-bound heterodimers, and the thermokinetic method determines the equilibrium constant of the acid-base reaction of gaseous ions. In general, proton transfer plays a crucial role in the formation of protonated molecules, e.g., in positive-ion chemical ionization mass spectrometry (Chap. 7). 

Figure 3. Generation of species using the kinetic method.

Gal and coworkers measured relative LCAs for amides of the structure RC(0)NRR (R, R = H, Me) ° using the kinetic method. From this work, the effect of methyl substituent at the amide nitrogen and the alpha carbon can be derived (Table 4). 

Similar estimations have been made (Laidler et al., 13) by means of calculations involving the transition states. This method offers the advantage of using more exact data for the available degrees of freedom in the activated state of the reactant. Beyond this, it does not differ essentially from the kinetic method. The vibration in the direction that leads from the former to the new atomic arrangement is replaced by a translation, and the frequency v by a transition probability kT/h, giving... 

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