Null-point method

To lessen experimental time, the null-point method may be employed by locating the pulse spacing, tnun, for which no magnetization is observed after the 180°-1-90° pulse-sequence. The relaxation rate is then obtained directly by using the relationship / , = 0.69/t n. In this way, a considerable diminution of measuring time is achieved, which is especially desirable in measurements of very low relaxation-rates, or for samples that are not very stable. In addition, estimates of relaxation rates for overlapping resonances can often be achieved. However, as the recovery curves for coupled spin-systems are, more often than not, nonexponential, observation of the null point may violate the initial-slope approximation. Hence, this method is best reserved for preliminary experiments that serve to establish the time scale for spin-lattice relaxation, and for qualitative conclusions. 

Ostwald also discusses the background of the Null point method (14) in his text and quotes extensively from von Helmholtz, Wied. (1882), 1, 35. One von Helmholz quotation is the following ... 

The composition of the hydrogen + water vapour mixture, which had a total pressure of 1 atm, was adjusted until the cell produced zero e.m.f., that is, until the same chemical potential of oxygen existed at both electrodes. This oxygen potential was calculated from the known hydrogen and water vapour pressures. Thus, by arranging the conditions in such a way that the method becomes a null-point method, interference by electronic conduction is made as small as possible and the range of utility of stabilized zirconia as an electrolyte is extended. 

Fluorescent dyes have also been used to measure transmembrane potential. A lipophilic fluorescent dye, the cation di-S-C3-(5), is taken up, and its fluorescence quenches as a function of an internal negative potential. The membrane potential is also calibrated by a null point method, in which the K -selective ionophore, valinomycin, is added to set the membrane potential to that generated by the transmembrane K" gradient. Then K" is added until there is no fluorescence quench (i.e., PD = 0), and then the internal K" is known, because when there is no membrane potential, [K ],n = [K"]out. From this known value of [K%y the membrane potential with the addition of valinomycin and then before addition of valinomycin can be calculated. 

Apart from the necessity of excluding interferences from any diffusion potential, normal potentiometry requires accurate determination of the emf, i.e., without any perceptible drawing off of current from the cell therefore, usually one uses the so-called Poggendorff method for exact compensation measurement the later application of high-resistance glass and other membrane electrodes has led to the modern commercial high-impedance pH and PI meters with high amplification in order to detect the emf null point in the balanced system. 

In the null-point instruments use is made of the well-known compensating method according to Poggendorf, by which the emf of the cell under test is compared with that of a standard cell. The circuit diagram of such a method54 is illustrated in Fig. 2.14. 

In the direct-reading instruments the emf of the cell is led through an (operational) amplifier across a standard high resistor yielding a current that is measured by a milliammeter calibrated to be read in pH units or millovolts. So, while the null-point system provides a truly potentiometric (non-faradaic) measurement where the off-balance adjustment remains limited to an interrupted temporary current draw-off, the direct-reading system represents an amperometric measurement where a continuous steady-state current draw-off takes place as long as the meter is switched on. In fact, the latter is a deflection method as a pointer indicates the pH units or millivolts by its deflection on the meter scale. 

If the matrix Q is positive semidefinite (positive definite) when projected into the null space of the active constraints, then (3-98) is (strictly) convex and the QP is a global (and unique) minimum. Otherwise, local solutions exist for (3-98), and more extensive global optimization methods are needed to obtain the global solution. Like LPs, convex QPs can be solved in a finite number of steps. However, as seen in Fig. 3-57, these optimal solutions can lie on a vertex, on a constraint boundary, or in the interior. A number of active set strategies have been created that solve the KKT conditions of the QP and incorporate efficient updates of active constraints. Popular methods include null space algorithms, range space methods, and Schur complement methods. As with LPs, QP problems can also be solved with interior point methods [see Wright (1996)]. 

Winefordner, J. D., and M. Tin Separation of Trace Quantities of Bromide from Large Amounts of Chloride by a Distillation Method and Measurement of the Bromide by Precision Null-Point Potentiometry. Anal. Chem. 35, 382 (1963). 

Malmstadt, H. V., and J. G. Winefordner Precision Null-Point Potentiometry. A Simple, Rapid and Accurate Method for Low Concentration Chloride Determination. Anal. Chim. Acta 20, 283 (1959). 

The simplest method of measurement with ion-selective electrodes is direct potentiometry by use of the Nemst equation. However, this makes extreme demands on the reproducibility of the junction potential, and there is the problem of variation of activity with ionic strength. Concentration-cell techniques have proved to be very precise, especially in terms of null-point potentiometi... 

The simplest method of beam microbalance operation is to measure the deflection of the ends of the beam by optical magnification. This method has the disadvantage that the maximum weight change that can be observed is limited and the vacuum system must usuaUy be opened to reset the zero point. However, a beam microbalance can be readily converted to a null point instrument by electromagnetic adjustment. A commercially available instrument which features electromagnetic compensation and automatic recording is shown schematicaUy in Fig. 10. 

The vapour pressures over CuSe03(cr) and Cu0 CuSe03(cr) were measured with a membrane null manometer and with a Knudsen effusion cell with mass spectro-metric detection by Makatun, Rat kovskii, and Pechkovskii [71MAK/RAT]. The dew point method was used by Bakeeva et al. [72BAK/BUK] for the same purpose. 

T-90°-data acquisition [9] in which the time interval, x, is chosen such that the water resonance, which is expected to have the longest T, in the sample, has zero magnetization after the 90° pulse [113, 114], The CPMG spin-echo pulse sequence 90°-(t-180°-t) n-data acquisition (n = number of repetitions), has been used with the pulse interval, r, adjusted to attenuate the water signal, for example, from erythrocyte and protein suspensions [113], The technique is improved by the addition of ionic species such as ammonium chloride which increases the chemical exchange of the water protons and thus shortens T2 relative to the compounds of interest. This method is known as WATR (Water Attenuation by T2 Relaxation) [114]. Solvent suppression can also be achieved by selective excitation of the spectrum with special pulses such that the water resonance occurs at a point of null excitation [115-119]. However, distortion of peaks near the null point may occur. 

Gordon and Campbell (2) have summarized the various methods that have been employed to detect the deviation of a balance beam from its horizontal or vertical position in the null-point balances. They are ihe following ... 

The best device, however, is the quartz coil manometer, the coil of which can be heatedto500°C(in special cases to 600-700°C). In all cases the null point of the instrument must be checked after each measurement. Therefore the manometer should be provided with a heating coil, which doe snot need to be at the test temperature but must nevertheless be at a sufficiently high temperature to prevent condensation in the coil and in the capillary connections (which are likewise provided with a heating coil). With compensation to zero, the pressure is read off on the Hg manometer. In those cases where it cannot be ascertained by the usual method (with a thermometer and distillation flask) the boiling point is determined more accurately by extrapolation of the vapor pressure curve. 

The precision of the differential potentiometric method can be improved by using null-point potentiometry [15—19]. The ion concentration is measured, not from a single potential reading, but by adjusting the composition of one of the half-cell solutions to matdi the other until a potential (the null, or bias poten-... 

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