Mass insertion

Evaluating this for renormalized critical mass Uj = 0 and taking the limit k 0 one recovers the standard first order contribution to F. The same applies to the mass insertion generated by the derivative However, we are interested in the behavior of terms of linear and possibly higher order in k. So we evaluate the general derivative... 

Then, with FqY we recover the standard mass insertion while the one loop approximation to Fj f is the term considered by MH. The generalized two loop contribution to the bare vertex function may be written as... 

To detemiine k E) from equation (A3.12.9) it is assumed that transition states with positivefomi products. Notmg that / f = p dqf/dt, where p is the reduced mass of the separating fragments, all transition states that lie within and + dq with positive will cross the transition state toward products in the time interval dt = pj dqf p. Inserting this expression into equation (A3.12.9), one finds that the reactant-to-product rate (i.e. flux) through the transition state for momenPim p is... 

Dissolve 57 g. of dry malonic acid in 92 5 ml. of dry P3rridine contained in a 500 ml. round-bottomed flask, cool the solution in ice, and add 57 g. (70 ml.) of freshly distilled n-heptaldehyde (oenanthol) with stirring or vigorous shaking. After a part of the aldehyde has been added, the mixture rapidly seta to a mass of crystals. Insert a cotton wool (or calcium chloride) tube into the mouth of the flask and allow the mixture to stand at room temperature for 60 hours with frequent shaking. Finally, warm the mixture on a water bath until the evolution of carbon dioxide ceases (about 8 hours) and then pour into an equal volume of water. Separate the oily layer and shake it with 150 ml. of 25 per cent hydrochloric acid to remove pyridine. Dissolve the product in benzene, wash with water, dry with anhydrous magnesium sulphate, and distil under reduced pressure. Collect the ap-nonenoic acid at 130-13272 mm. The yield is 62 g. 

These thin wires are supported on a special carrier that can be inserted into the ion source of the mass spectrometer after first growing the whiskers in a separate apparatus. Although the wires are very fragile, they last for some time and are easily renewed. They are often referred to as emitter electrodes (ion emitters). 

Positive ions are obtained from a sample by placing it in contact with the filament, which can be done by directing a gas or vapor over the hot filament but usually the sample is placed directly onto a cold filament, which is then inserted into the instrument and heated. The positive ions are accelerated from the filament by a negative electrode and then passed into a mass analyzer, where their m/z values are measured (Figure 7.1). The use of a suppressor grid in the ion source assembly reduces background ion effects to a very low level. Many types of mass analyzer could be used, but since very high resolutions are normally not needed and the masses involved are quite low, the mass analyzer can be a simple quadrupole. 

Although simple solutions can be examined by these electrospray techniques, often for a single substance dissolved in a solvent, straightforward evaporation of the solvent outside the mass spectrometer with separate insertion of the sample is sufficient. This situation is not true for all substances. Peptides, proteins, nucleotides, sugars, carbohydrates, mass organometallics, and many... 

Liquids examined by FAB are introduced into the mass spectrometer on the end of a probe inserted through a vacuum lock in such a way that the liquid lies in the target area of the fast atom or ion beam. There is a high vacuum in this region, and there would be little point in attempting to examine a solution of a sample in one of the commoner volatile solvents such as water or dichloromethane because it would evaporate extremely quickly, probably as a burst of vapor when introduced into the vacuum. Therefore it is necessary to use a high-boiling solvent as the matrix material, such as one of those listed in Table 13.1. 

In practice, direct insertion of samples requires a somewhat more elaborate arrangement than might be supposed. The sample must be placed on an electrode before insertion into the plasma flame. However, this sample support material is not an electrode in the usual meaning of the term since no electrical current flows through it. Heating of the electrode is done by the plasma flame. The electrode or probe should have small thermal mass so it heats rapidly, and it must be stable at the high temperatures reached in the plasma flame. For these reasons, the sort of materials used... 

Schematic diagram of a mass spectrometer. After insertion of a sampie (A), it is ionized, the ions are separated according to m/z value, and the numbers of ions (abundances) at each m/z value are plotted against m/z to give the mass spectrum of A. By studying the mass spectrum, A can be identified,...

For solids, there is now a very wide range of inlet and ionization opportunities, so most types of solids can be examined, either neat or in solution. However, the inlet/ionization methods are often not simply interchangeable, even if they use the same mass analyzer. Thus a direct-insertion probe will normally be used with El or Cl (and desorption chemical ionization, DCl) methods of ionization. An LC is used with ES or APCI for solutions, and nebulizers can be used with plasma torches for other solutions. MALDI or laser ablation are used for direct analysis of solids. 

Direct-exposure probe. Provides for insertion of a sample on an exposed surface, such as a flat surface or a wire, into (rather than up to the entrance of) the ion source of a mass spectrometer. 

Direct-inlet probe. A shaft or tube having a sample holder at one end that is inserted into the vacuum system of a mass spectrometer through a vacuum lock to place the sample near to, at the entrance of, or within the ion source. The sample is vaporized by heat from the ion source, by heat applied from an external source, or by exposure to ion or atom bombardment. Direct-inlet probe, direct-introduction probe, and direct-insertion probe are synonymous terms. The use of DIP as an abbreviation for these terms is not recommended. 

The key to solving these problems is to design the vessel for a mass flow pattern. This involves consideration of both the hopper angle and surface finish, the effect of inserts used to introduce gas and control the soHds flow pattern, and sizing the outlet valve to avoid arching and discharge rate limitations. In addition, the gas or Hquid must be injected such that the soHd particles ate uniformly exposed to it, and flow instabiHties such as fluidization in localized regions are avoided. 

As before, the mass of the beam can be reduced by reducing t, but only so far that it does not deflect too much. The thickness is therefore constrained by eqn. (7.5). Solving this for t and inserting it into the last equation gives ... 

The various SNMS instruments using electron impact postionization differ both in the way that the sample surface is sputtered for analysis and in the way the ionizing electrons are generated (Figure 2). In all instruments, an ionizer of the electron-gun or electron-gas types is inserted between the sample surface and the mass spectrometer. In the case of an electron-gun ionizer, the sputtered neutrals are bombarded by electrons from a heated filament that have been accelerated to 80—... 

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