Second-Order Measurements

Results of Bulk Second-Order Measurements on Films and Composites... 

Rank annihilation factor analysis treats the special situation in which there are only two slices, where each slice contains the second-order measurements of one sample. One sample is usually a pure standard containing only the analyte of interest in a known concentration and the other is an unknown sample containing unknown interferents as well as the analyte of interest. The purpose in rank annihilation factor analysis is to estimate the concentration of the analyte of interest in the unknown sample. It is assumed that the signal from the analyte of interest corresponds to a rank-one component with the intensity proportional to the concentration. Thus the standard sample, say Xi, can be described... 

II. Ilf represents the F norm of a matrix, which is the square root of the sum of the squares of all elements. The matrix E is the error matrix of the second-order measurements. 

Figure 5.4 Example of a second-order measurement of combinatorial materials. Sensor materials as a 48-element sensor materials array. (A) general view of the sensor materials array in a gas flow-through cell (B) representative absorption spectra from a single material in the array collected over a period of time of reaction of this sensor material with a vapor of interest.

When measurements are done with a first-order instrument, and there is another independent variable involved, this constitutes a second-order measurement approach. This type of screening was used for the in situ monitoring of melt-polymerization reaetions (see Section 5.4) and for the evaluation of the sensor materials. Figure 5.4A shows a 48-element array of sensor materials positioned in a gas fiow-cell for the monitoring of the materials response upon exposure to vapors of interest. For the evaluation of sensor materials, absorption speetra were colleeted over a period of time of reaction of these sensor materials with a vapor of interest. Results of these measurements are illustrated in Figure 5.4B. 

Convexity represents an attempt to remedy the drawbacks of duration. A second-order measure of interest rate risk uses second-order derivatives. It measures the curvature of the price-yield graph and the degree to which this diverges from the straight-line estimation. Convex-... 

The measurement of a from the experimental slope of the Tafel equation may help to decide between rate-determining steps in an electrode process. Thus in the reduction water to evolve H2 gas, if the slow step is the reaction of with the metal M to form surface hydrogen atoms, M—H, a is expected to be about If, on the other hand, the slow step is the surface combination of two hydrogen atoms to form H2, a second-order process, then a should be 2 (see Ref. 150). 

The applications of this simple measure of surface adsorbate coverage have been quite widespread and diverse. It has been possible, for example, to measure adsorption isothemis in many systems. From these measurements, one may obtain important infomiation such as the adsorption free energy, A G° = -RTln(K ) [21]. One can also monitor tire kinetics of adsorption and desorption to obtain rates. In conjunction with temperature-dependent data, one may frirther infer activation energies and pre-exponential factors [73, 74]. Knowledge of such kinetic parameters is useful for teclmological applications, such as semiconductor growth and synthesis of chemical compounds [75]. Second-order nonlinear optics may also play a role in the investigation of physical kinetics, such as the rates and mechanisms of transport processes across interfaces [76]. 

The matrix gp, represents the components of a covariant second-order tensor called the metric tensor , because it defines distance measurement with respect to coordinates To illustrate the application of this definition in the... 

Kinetic measurements were performed employii UV-vis spectroscopy (Perkin Elmer "K2, X5 or 12 spectrophotometer) using quartz cuvettes of 1 cm pathlength at 25 0.1 C. Second-order rate constants of the reaction of methyl vinyl ketone (4.8) with cyclopentadiene (4.6) were determined from the pseudo-first-order rate constants obtained by followirg the absorption of 4.6 at 253-260 nm in the presence of an excess of 4.8. Typical concentrations were [4.8] = 18 mM and [4.6] = 0.1 mM. In order to ensure rapid dissolution of 4.6, this compound was added from a stock solution of 5.0 )j1 in 2.00 g of 1-propanol. In order to prevent evaporation of the extremely volatile 4.6, the cuvettes were filled almost completely and sealed carefully. The water used for the experiments with MeReOj was degassed by purging with argon for 0.5 hours prior to the measurements. All rate constants were reproducible to within 3%. 

As the medium is still further diluted, until nitronium ion is not detectable, the second-order rate coefficient decreases by a factor of about 10 for each decrease of 10% in the concentration of the sulphuric acid (figs. 2.1, 2.3, 2.4). The active electrophile under these conditions is not molecular nitric acid because the variation in the rate is not similar to the correspondii chaise in the concentration of this species, determined by ultraviolet spectroscopy or measurements of the vapour pressure. " ... 

For nitrations in sulphuric and perchloric acids an increase in the reactivity of the aromatic compound being nitrated beyond the level of about 38 times the reactivity of benzene cannot be detected. At this level, and with compounds which might be expected to surpass it, a roughly constant value of the second-order rate constant is found (table 2.6) because aromatic molecules and nitronium ions are reacting upon encounter. The encounter rate is measurable, and recognisable, because the concentration of the effective electrophile is so small. 

A similar circumstance is detectable for nitrations in organic solvents, and has been established for sulpholan, nitromethane, 7-5 % aqueous sulpholan, and 15 % aqueous nitromethane. Nitrations in the two organic solvents are, in some instances, zeroth order in the concentration of the aromatic compound (table 3.2). In these circumstances comparisons with benzene can only be made by the competitive method. In the aqueous organic solvents the reactions are first order in the concentration of the aromatic ( 3.2.3) and comparisons could be made either competitively or by directly measuring the second-order rate constants. Data are given in table 3.6, and compared there with data for nitration in perchloric and sulphuric acids (see table 2.6). Nitration at the encounter rate has been demonstrated in carbon tetrachloride, but less fully explored. ... 

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 rates of reaction of phenacyl bromide with thiosemicarbazide and its phenylated derivative were determined by conductivity measurements in ethanol (517). The reaction is second order up to 85% completion. The activation energies are 10.5 to 11.3 kcal/mole with the phenyl thiosemicarbazide and 8.5 to 9.3 kcal/mole for the unsubstituted derivatives. 

The concentration of aluminum in serum can be determined by adding 2-hydroxy-1-naphthaldehyde p-methoxybenzoyl-hydrazone and measuring the initial rate of the resulting complexation reaction under pseudo-first-order conditions.The rate of reaction is monitored by the fluorescence of the metal-ligand complex. Initial rates, with units of emission intensity per second, were measured for a set of standard solutions, yielding the following results... 

Earlier we noted that a response surface can be described mathematically by an equation relating the response to its factors. If a series of experiments is carried out in which we measure the response for several combinations of factor levels, then linear regression can be used to fit an equation describing the response surface to the data. The calculations for a linear regression when the system is first-order in one factor (a straight line) were described in Chapter 5. A complete mathematical treatment of linear regression for systems that are second-order or that contain more than one factor is beyond the scope of this text. Nevertheless, the computations for... 

According to the conception of the development of the system of spectra of additive properties stated by I.G. Per kov the use of spectra of second order, represented by AS arrays, measured concerning two axes the length of a wave and water phase pH in monophase, pseudomonophase (micellar solutions) and twophase systems is of great interest. 

Chemoinformatics (or cheminformatics) deals with the storage, retrieval, and analysis of chemical and biological data. Specifically, it involves the development and application of software systems for the management of combinatorial chemical projects, rational design of chemical libraries, and analysis of the obtained chemical and biological data. The major research topics of chemoinformatics involve QSAR and diversity analysis. The researchers should address several important issues. First, chemical structures should be characterized by calculable molecular descriptors that provide quantitative representation of chemical structures. Second, special measures should be developed on the basis of these descriptors in order to quantify structural similarities between pairs of molecules. Finally, adequate computational methods should be established for the efficient sampling of the huge combinatorial structural space of chemical libraries. 

There is no entirely satisfactory way of measuring flow. In the BS 2782 flow cup test an amount of moulding powder is added to the mould to provide between 2 and 2.5 g of flash. The press is closed at a fixed initial rate and at a fixed temperature and pressure. The time between the onset of recorded pressure and the cessation of flash (i.e. the time at which the mould has closed) is noted. This time is thus the time required to move a given mass of material a fixed distance and is thus a measure of viscosity. It is not a measure of the time available for flow. This property, or rather the more important length of flow or extent of flow, must be measured by some other device such as the flow disc or by the Rossi-Peakes flow test, neither of which are entirely satisfactory. Cup flow times are normally of the order of 10-25 seconds if measured by the BS specification. Moulding powders are frequently classified as being of stiff flow if the cup flow time exceeds 20 seconds, medium flow for times of 13-19 seconds and soft flow or free flow if under 12 seconds. 

The intermediate diphenylhydroxymethyl radical has been detected after generation by flash photolysis. Photolysis of benzophenone in benzene solution containing potential hydrogen donors results in the formation of two intermediates that are detectable, and their rates of decay have been measured. One intermediate is the PhjCOH radical. It disappears by combination with another radical in a second-order process. A much shorter-lived species disappears with first-order kinetics in the presence of excess amounts of various hydrogen donors. The pseudo-first-order rate constants vary with the structure of the donor with 2,2-diphenylethanol, for example, k = 2 x 10 s . The rate is much less with poorer hydrogen-atom donors. The rapidly reacting intermediate is the triplet excited state of benzophenone. 

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