Isopotentials

Figure 2-125. Different isovalue-based surfaces of phenylalanine a) isoelectronic density b) molecular orbitals (HOMO-LUMO) c) isopotential surface and d) isosurface of the electron cryo-microscopic volume of the ribosome of Escherichia coii.

Fig. U (o) Isopotential curves for the adsorption of He on the (100) face of solid Xe. The interval between the isopotential lines is 1-24 x 10 J. [b) Isopotential curves for the adsorption of He on the (III) face of solid Xe. The interval between the isopotential lines is 1-66 x 10 J. (After...

In addition, most devices provide operator control of settings for temperature and/or response slope, isopotential point, zero or standardization, and function (pH, mV, or monovalent—bivalent cation—anion). Microprocessors are incorporated in advanced-design meters to faciHtate caHbration, calculation of measurement parameters, and automatic temperature compensation. Furthermore, pH meters are provided with output connectors for continuous readout via a strip-chart recorder and often with binary-coded decimal output for computer interconnections or connection to a printer. Although the accuracy of the measurement is not increased by the use of a recorder, the readabiHty of the displayed pH (on analogue models) can be expanded, and recording provides a permanent record and also information on response and equiHbrium times during measurement (5). 

In the simplest case of one-dimensional steady flow in the x direction, there is a parallel between Eourier s law for heat flowrate and Ohm s law for charge flowrate (i.e., electrical current). Eor three-dimensional steady-state, potential and temperature distributions are both governed by Laplace s equation. The right-hand terms in Poisson s equation are (.Qy/e) = (volumetric charge density/permittivity) and (Qp // ) = (volumetric heat generation rate/thermal conductivity). The respective units of these terms are (V m ) and (K m ). Representations of isopotential and isothermal surfaces are known respectively as potential or temperature fields. Lines of constant potential gradient ( electric field lines ) normal to isopotential surfaces are similar to lines of constant temperature gradient ( lines of flow ) normal to... 

Fig. 3-2. Molecular electrostatic potential with 6-31G //3-21G basis set in the molecular plane of (ii)-nitrous acid. Black dots refer to four different protonation sites in potential minima. For values of isopotential contours see Nguyen and Hegarty, 1984.

On the isopotential map three minima (III, IV, V) are separated by barriers. They can be reached by decreasing of the distance R between the educts (I) via an activated complex (II). A detailed discussion of this potential energy surface also under the influence of a solvent will be given in part 4.3.1. 

Therefore, in most cases, pH values measured at high temperatures in dilute solution should be considered approximate values only. In cases where the investigators address this problem and are careful to select a suitable electrode (namely, one that manufacturers claim to have almost hysteresis-free pH measurement and a stable isopotential point over the temperature range), the error associated with electrode performance will be small, and differences in reported pH values will correspond to differences in actual pH. In cases where pH is measured in concentrated sucrose solutions, the reported pH value should be considered as a nominal value only, and the differences in nominal pH values might not correspond to actual differences in hydrogen ion activity. 

When appreciable temperature differences between calibration and measurement unavoidably occur, a correction must be applied either by calculation or most practically by instrumental means. It is in this instrumental method that the concept of the isopotential suggested by Jackson plays a basic role, and can be explained as follows. 

Note from the definition is follows that the pH of the isotherm intersection point in Fig. 2.13 represents the isopotential pHf of the Metrohm EA121 combined electrode.)... 

Hence, by applying a bias emf corresponding to 2.3026RT/F pH, or by offsetting the mechanical zero of the potentiometer by pH units, the zero shift is compensated for any temperature within the range (about 20° C) over which pH is fairly constant. Modern instruments often include the possibility of varying the pH, bias (to allow the use of different electrode systems) by incorporating the isopotential bias into the meter circuits. 

In practice, electrode suppliers can provide the relevant isopotential data and a few dpH/d T coefficients of electrolytes are known from the literature or can be obtained from measurements at two different temperatures in the area of practical interest. Nevertheless, it may be necessary to carry out some separate determinations of isopotential values67. 

Automatic zero shift compensation by previously setting the isopotential values of pHi(electrodes) or even pHi(overaii, may be especially attractive for on-line control of process streams. 

Also, in modem, accurate apparatus there is a general trend to have a digital display not only of pH units or millivolts but often also of isopotential setting and solution temperature in the more sophisticated instruments all this can be actuated by a push-button via a microprocessor. 

Keyboard sixteen push-buttons for entry of data and instructions for manual or automatic calibration, based on the three National Bureau of Standards (NBS) buffers of pH 4, 7 and 9, whose values as a function of temperature have been permanently and separately stored to three decimal places and at intervals of 0.1° C. Hence there is no need to enter pH values, as the electrode automatically identifies the buffer in use and the apparatus immediately retrieves and displays the temperature-adjusted buffer value the isopotential adjustment is defaulted to pH 7.000. 

Naray-Szabo, G. 1979. Electrostatic Isopotential Maps for Large Biomolecules. Int. J. Quant. Chem. 16, 265. 

The resulting isopotential point confirms that H-Tg-H reacts to produce a new electroactive species without side reactions. The optical absorption of the electrochemically generated product is red-shifted and its cathodic peak potentials upon discharging (reduction) lie negative to those of the educt, indicating that the product consists of larger molecules with a more extended redox system. If experiments are carried out at higher sweep rates (v > 100 m V s ), broad waves are... 

Figure 7. Top panels Schematic diagram of 3-D cylindrical battery arrays in parallel row (left) and alternating anode/cathode (right) configurations. Middle panels Isopotential lines between cathode (C) and anode (A) for unit battery cells. Bottom panel Current densities (in arbitrary units, a.u.) at the electrode surfaces as a function of the angle 9 (see middle panel for definition of 9). The area of the cathodes and anodes is equal throughout the diagram. (Reprinted with permission from ref 19. Copyright 2003 Elsevier.)...

E° [equation (15.4)] is also referred to as the offset, the zero potential point, or the isopotential point, since theoretically it is defined as the pH that has no temperature dependence. Most pH electrode manufacturers design their isopotential point to be 0 mV at pH 7 to correspond with the temperature software in most pH meters. The offset potential is often displayed after calibration as an indication of electrode performance. Typical readings should be about 0 30 mV in a pH 7 buffer. In reality, E° is composed of several single potentials, each of which has a slight temperature coefficient. These potentials are sources of error in temperature compensation algorithms. 

The study of the reactivity of the nucleic acid bases utilizes indices based on the knowledge of the molecular electronic structure. There are two possible approaches to the prediction of the chemical properties of a molecule, the isolated and reacting-molecule models (or static and dynamic ones, respectively). Frequently, at least in the older publications, the chemical reactivity indices for heteroaromatic compounds were calculated in the -electron approximation, but in principle there is no difficulty to define similar quantities in the all-valence or allelectron methods. The subject is a very broad one, and we shall here mention only a new approach to chemical reactivity based on non-empirical calculations, namely the so-called molecular isopotential maps. 

The study of the nucleic acid bases is interesting because they possess many possible sites of protonation or electrophilic attack. Isopotential maps have been constructed for adenine, cytosine, and thymine.244 They may be used to study theoretically the proton affinities of the different atoms in these molecules. It is well known that protonation of cytosine, its nucleotide or nucleoside, occurs at N-394,245-247 (cf. Section II) alkylation also occurs at N-3.103-248-249 Nevertheless protonation of the oxygen of cytosine in DNA has been reported.250 The basic pA of cytosine is higher than that of adenine. The isopotential map in the molecular plane of cytosine (Tig. 8) shows that the potential well is deeper for N-3 than for 0 and the minimum for N-3 in cytosine is deeper than for any nitrogen in adenine. These maps, and their confrontation with the experimental facts have been discussed228-244... 

Figure 3.8 Edge dislocation in an isotropic elastic body. Solid lines indicate isopotential cylinders for the portion of the diffusion potential of any interstitial atom present in the hydrostatic stress field of the dislocation. Dashed cylinders and tangential arrows indicate the direction of the corresponding force exerted on the interstitial atom.

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