Double subtraction technique

Sometimes, small structural differences in morphology of polymer samples can be isolated by using a double subtraction technique. For example, with polyethylene terephthalate) PET, differences in the amorphous phase of the melt-quenched polymer and solution-cast polymer can be isolated by first subtracting out the contribution due to the trans isomer and then subtracting the two difference spectra from each other 214). (Fig. 16) shows the resultingdifference spectrum obtained after the second subtraction. Obviously the two amorphous structures are different from each other. 

The CO chemisorption blank on Carbolac was found to be 0.09 cc/g when reduced at 500°C and zero when reduced at 700°C. The uptake on the Carbolac support was subtracted from the values for all the samples described in this table employing the double isotherm technique. 

Fig. 8.13 The steps involved in the subtractive technique for the manufacture of printed circuit boards. A very simplified schedule is shown to obtain a double-sided board, i.e. one which has copper tracks on each side interconnected by plated-through holes.

In addition techniques, the test substance concentration is determined from the difference in the ISE potentials obtained before and after a change in the sample solution concentration. The main advantage Ues in the fact that the whole measurement is carried out in the presence of the sample matrix, so that results with satisfactory accuracy and precision can be obtained even if a substantial portion of the test substance is complexed. Several addition techniques can be used, namely, single, double or multiple known addition methods, in which the sample concentration is increased by additions of a test substance standard solution single, double or multiple known subtraction methods, in which the sample concentration is decreased by additions of a standard solution of a substance that reacts stoichiometrically with the determinand and analyte addition and subtraction methods, in which the sample is added to a test substance solution or to a reagent solution. 

The motivation behind the considerable effort that was exerted in the development of DCV [42, 49, 50, 69] was based on the need to make CV and LSV quantitative tools for the study of electrode kinetics. At that time, there were three major problems that had to be overcome. These were (a) the precision in the measurement of Ep and AEp, (b) the problem with accurately defining the baseline for the reverse sweep and (c) the problem as to how to handle Rn in a practical manner. The development of DCV did indeed provide suitable solutions to all three of these problems, although the methods developed to handle the Ru problem [41, 42] only involve the derivative of the response in terms of precision necessary for the measurements. More recent work [55, 57] is indicative that the precision in Ep/2, Ep) and AEP measurements can be as high as that observed during DCV (see Sect. 3.4). Also, a recent study in which rate constants were evaluated using CV, DCV, and double potential step chronoamperometry for a particular electrode reaction showed that the precision to be expected frcm the three techniques are comparable when the CV baseline, after subtracting out the charging... 

In order to estimate this term with sufficient accuracy, its magnitude has to be at least 10% of the total value of q(t) at the shortest accessible time, say t> 100 ps. This leads to the condition l < ca. 900 s 1/2, which corresponds to k values between 0.1 and lcms-1. However, the time-independent double-layer contribution, qc, has to be subtracted from q(t) first and this may reduce the accuracy of the kinetic information. Therefore, an upper limit for kt similar to that of the chronoampero-metric technique seems more realistic. The value of qc has to be determined separately from a chronocoulogram recorded in the absence of the electroactive species. 

Once the background is subtracted, the component of the spectrum due to the annihilation of ortho-positronium is usually visible (see Figure 6.5(a), curve (ii) and the fitted line (iv)). The analysis of the spectrum can now proceed, and a number of different methods have been applied to derive annihilation rates and the amplitudes of the various components. One method, introduced by Orth, Falk and Jones (1968), applies a maximum-likelihood technique to fit a double exponential function to the free-positron and ortho-positronium components (where applicable). Alternatively, the fits to the components can be made individually, if their decay rates are sufficiently well separated, by fitting to the longest component (usually ortho-positronium) first and then subtracting this from the... 

In situ techniques are based primarily on the determination of the charge stored in the H adsorption region of the CV of the electrocatalyst (Fig. 21). As shown in this figure, the double-layer charge must be subtracted for a reliable measurement. The currently recommended normalization value, based on a 1 1 H to Pt chemisorption is 210 pC cm-2, which roughly corresponds to the surface density of Pt(lll) [38],... 

The alteration of ships silhouettes to render them unrecognisable, a tactic known as dynamic camouflage, was another technique widely used by the combatants of both World Wars. Apart from the addition or subtraction of funnels, a particularly ingenious trick was to create the effect of a symmetrical, double-ended vessel, with navigation bridges and... 

The technique is based on the fact that the double contrast of standard minus placebo subtracted from that of experimental minus standard eliminates the effect of the standard. One is thus left with an indirectly established contrast of experimental versus placebo. Assuming a so-called fixed-effects model, its variance is equal to the sum of the variances of the two contrasts used in its construction and it therefore follows that, however large the current trial, its variance cannot be lower that that pertaining to the (historical) comparison of the standard treatment with placebo. 

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