Third-Order Measurements

Researchers have used a variety of techniques to measure the third-order hyperpolarizabilities of organometallic complexes, Z-scan in particular being very popular over the past few years. Data have been collected at several wavelengths with varying pulse lengths using these various techniques, and in many instances with 

Ferrocene was the first organotransition metal complex for which third-order NLO properties were reported, and metallocenes and their derivatives remain popular (Tables XII and XIII). Ferrocene itself has been measured several times. Early values obtained from optical power limiting (OPL) measurements were very high compared to later values from DFWM and probably because OPL is 

The carbonyl complexes in Table XIV are of three types, tricarbonylchromium r] -arene complexes, pentacarbonyltungsten o-pyridine complexes, and car-bonylruthenium o-alkenyl complexes, the first two possessing low y values. For the first two types, lengthening the 7i-system or replacing acceptor by donor substituent on the tricarbonylchromium-coordinated arene ring results in 

Molecular Third-order NLO Results of Other Metallocene Complexes 

Data for phosphine-substituted molybdenum carbonyl complexes reported as either y or as a ratio of collected in Table XV. These studies were carried 

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The typical approach taken when attempting to vary the concentration of intermolecular modes is the use of binary mixtures. When one considers the many body nature of the intermolecular modes and the complexity of binary mixtures, it is not directly evident that there is any proportionality between the ill-defined concept of concentration for intermolecular modes and the binary mixture fraction. An additional complication in the use of binary mixtures comes from the significant changes in the polarizability weighted density of states as a function of binary mixture fraction. In other words, the intermolecular spectrum is changing with binary mixture fraction. These types of effects are clearly evident in third-order measurements of CS2 in binary mixtures (3). 

Figure 5.5. Example of a third-order measurement of combinatorial materials. Oxidative stability of polymers from measurements of UV-VIS reflection spectra from each polymeric composition in a materials array as a function of reaction temperature and time. (A) General view of the materials array on a gradient temperature heater (B) representative UV-VIS spectra from a single material in the array as a function of reaction time and temperature. Reaction temperatures Ti> T2> T. Reaction progress is shown as spectra changes from spectrum 1 to spectrum 7.

Adding two more independent variable parameters to the response of a first-order system obviously makes it a third-order measurement approach. An example of such system is spectroscopic monitoring (wavelength is the variable parameter 7) of the reaction progress of combinatorial materials (time is the variable parameter J) at different process temperatures (temperature is the variable parameter K). Alternatively, a second-order system can be implemented for the measurements as a function of one or more independent parameters. Examples of second-order systems are excitation-emission luminescence measurement systems, GC-MS, and HPLC-diode array UV systems, among others. An example of one of our third-order measurement approaches for combinatorial screening is illustrated in Figure 5.5. It was implemented for the determination of oxidative stability of polymers under different process conditions (temperature / and time J). 

First-order nitrations. The kinetics of nitrations in solutions of acetyl nitrate in acetic anhydride were first investigated by Wibaut. He obtained evidence for a second-order rate law, but this was subsequently disproved. A more detailed study was made using benzene, toluene, chloro- and bromo-benzene. The rate of nitration of benzene was found to be of the first order in the concentration of aromatic and third order in the concentration of acetyl nitrate the latter conclusion disagrees with later work (see below). Nitration in solutions containing similar concentrations of acetyl nitrate in acetic acid was too slow to measure, but was accelerated slightly by the addition of more acetic anhydride. Similar solutions in carbon tetrachloride nitrated benzene too quickly, and the concentration of acetyl nitrate had to be reduced from 0-7 to o-i mol 1 to permit the observation of a rate similar to that which the more concentrated solution yields in acetic anhydride. 

The best fit, as measured by statistics, was achieved by one participant in the International Workshop on Kinetic Model Development (1989), who completely ignored all kinetic formalities and fitted the data by a third order spline function. While the data fit well, his model didn t predict temperature runaway at all. Many other formal models made qualitatively correct runaway predictions, some even very close when compared to the simulation using the true kinetics. 

The measured relationships between piezoelectric polarization and strain for x-cut quartz and z-cut lithium niobate are found to be well fit by a quadratic relation as shown in Fig. 4.4. In both materials a significant nonlinear piezoelectric effect is indicated. The effect in lithium niobate is particularly notable because the measurements are limited to much smaller strains than those to which quartz can be subjected. The quadratic polynomial fits are used to determine the second- and third-order piezoelectric constants and are summarized in Table 4.1. Elastic constants determined in these investigations were shown in Chap. 2. 

Bimolecular rate constants determined at temperatures giving conveniently measurable rates and calculated for the temperature given in parentheses, except for some of the catalyzed reactions (lines 1-4 and 14—19) which are third-order. 

For each EA spectrum, the transmission T was measured with the mechanical chopper in place and the electric field off. The differential transmission AT was subsequently measured without the chopper, with the electric field on, and with the lock-in amplifier set to detect signals at twice the electric-field modulation frequency. The 2/ dependency of the EA signal is due to the quadratic nature of EA in materials with definite parity. AT was then normalized to AT/T, which was free of the spectral response function. To a good approximation [18], the EA signal is related to the imaginary part of the optical third-order susceptibility ... 

There have been comparatively few kinetic studies of the decompositions of solid malonates [1103]. The sodium and potassium salts apparently melt and non-isothermal measurements indicate second-order rate processes with high values of E (962 125 and 385 84 kJ mole-1, respectively). The reaction of barium malonate apparently did not involve melting and, from the third-order behaviour, E = 481 125 kJ mole-1. 

The vast majority of the kinetic detail is presented in tabular form. Amassing of data in this way has revealed a number of errors, to which attention is drawn, and also demonstrated the need for the expression of the rate data in common units. Accordingly, all units of rate coefficients in this section have been converted to mole.l-1.sec-1 for zeroth-order coefficients (k0), sec-1 for first-order coefficients (kt), l.mole-1.sec-1 for second-order coefficients (k2), l2.mole-2.sec-1 for third-order coefficients (fc3), etc., and consequently no further reference to units is made. Likewise, energies and enthalpies of activation are all in kcal. mole-1, and entropies of activation are in cal.deg-1mole-1. Where these latter parameters have been obtained over a temperature range which precludes the accuracy favoured by the authors, attention has been drawn to this and also to a few papers, mainly early ones, in which the units of the rate coefficients (and even the reaction orders) cannot be ascertained. In cases where a number of measurements have been made under the same conditions by the same workers, the average values of the observed rate coefficients are quoted. In many reactions much of the kinetic data has been obtained under competitive conditions such that rate coefficients are not available in these cases the relative reactivities (usually relative to benzene) are quoted. 

Nitromethane has been used as a solvent for molecular bromination297. The bromination of polymethylbenzenes in nitromethane, acetic acid, and 1 1 mixtures of these solvents at 30 °C, showed that rates were much faster (about 330-fold) in nitromethane than in acetic acid. With nitromethane, in the bromine concentration range 0.01-0.02 M, the reaction was third-order in bromine. The relative deactivating effects of m-halogen substituents were measured in terms of the time taken for 10 % reaction to occur, and these values are given in Table 71 from which the relative reactivities in the different solvents are apparent the deactivating effects of the m-nitro substituent were obtained by comparison with the reactivity of chloromesitylene at different concentrations (0.035, 0.055 M) of reactants. The results for the nitro compounds were interpreted in the same way... 

Third-order kinetics, equation (166), have also been obtained330 for the iodination of mesitylene and pentamethylbenzene by iodine monochloride in carbon tetrachloride, the negative activation energies of —4.6 and —1.6 (from measurements at 25.2 and 45.7 °C) obtained being attributed to a mildly exothermic preformation of ArHICl complexes (c/. molecular bromination, p. 123) which subsequently react with two further molecules of iodine monochloride to give the products, viz. equilibria (167) and (168)... 

An explanation for the effect of excess catalyst has been offered by Corriu et al. 16, who measured the rates of the aluminium chloride-catalysed reaction of benzoyl chloride with benzene, toluene, and o-xylene. The observed rate coefficients were analysed in terms of a mixture of second- and third-order reactions (the latter being second-order in the halide-catalyst complex), the following results being obtained benzene (40 °C), k2 = 2.5 xlO-5, fc3 = 3.3 xlO-5 toluene (2.5 °C), k2 = 0.75 xlO"4, k3 = 3.83 xlO-4 o-xylene (0 °C), k2 = 1.83 x 10-3, k3 = 4.50 x 10-3. They suggest the equilibrium... 

There have been very few measurements made on the physical properties of Tg derivatives, their relative greater difficulty of preparation when compared with the Tg analogs has meant little interest in their properties. However, TglOSiMeslg has been found to show photoluminescence in the blue region of the spectrum, third-order nonlinear optical properties for TgMeg have been modeled, and electronic properties for and TgMeg have been calculated. 

Similar expressions can be written for third-order reactions. A reaction whose rate is proportional to [A] and to [B] is said to be first order in A and in B, second order overall. A reaction rate can be measured in terms of any reactant or product, but the rates so determined are not necessarily the same. For example, if the stoichiometry of a reaction is2A-)-B—>C- -D then, on a molar basis, A must disappear twice as fast as B, so that —d[A]/dt and -d[B]/dr are not equal but the former is twice as large as the latter. 

Rao reported measurement of third-order optical non-linearity in the nanosecond and picosecond domains for phosphorus tetratolyl porphyrins bearing two hydroxyl groups in apical position [89]. Strong nonlinear absorption was found at both 532 nm and 600 nm. The high value of nonlinearity for nanosecond pulses is attributed to higher exited singlet and triplet states. Time resolved studies indicate an ultra-fast temporal evolution of the nonlinearity in this compound. 

Fig. 8. Examples of some of the donor-acceptor substituted TEEs prepared for the exploration of structure-property relationships in the second- and third-order nonlinear optical effects of fully two-dimensionally-conjugated chromophores. For all compounds, the second hyperpolarizability y [10 esu], measured by third harmonic generation experiments in CHCI3 solution at a laser frequency of either A = 1.9 or 2.1 (second value if shown) pm is given in parentheses. n.o. not obtained...

The first-generation dendrimer 51 was directly observed by transmission electron microscopy (TEM). The TEM image showed that the dimensions of individual molecules are about 50 A, which is consistent with the calculated one [36]. Third-order NLO measurements showed a significant enhancement of two-photon absorption upon proceeding from the constituent molecules to the dendritic complex [35]. 

The reaction between Fe(IlI) and Sn(Il) in dilute perchloric acid in the presence of chloride ions is first-order in Fe(lll) concentration . The order is maintained when bromide or iodide is present. The kinetic data seem to point to a fourth-order dependence on chloride ion. A minimum of three Cl ions in the activated complex seems necessary for the reaction to proceed at a measurable rate. Bromide and iodide show third-order dependences. The reaction is retarded by Sn(II) (first-order dependence) due to removal of halide ions from solution by complex formation. Estimates are given for the formation constants of the monochloro and monobromo Sn(II) complexes. In terms of catalytic power 1 > Br > Cl and this is also the order of decreasing ease of oxidation of the halide ion by Fe(IlI). However, the state of complexing of Sn(ll)and Fe(III)is given by Cl > Br > I". Apparently, electrostatic effects are not effective in deciding the rate. For the case of chloride ions, the chief activated complex is likely to have the composition (FeSnC ). The kinetic data cannot resolve the way in which the Cl ions are distributed between Fe(IlI) and Sn(ll). 

Figure 75-2 shows third-order data or a hyperspectral data cube where the spectral amplitude is measured at multiple frequencies (spectrum) with X and Y spatial dimensions included. Each plane in the figure represents the amplitude of the spectral signal at a single frequency for an X and Y coordinate spatial image. 

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