Ionization ratio

In ion beam deposition, hydrocarbon gas such as methane or ethyene is ionized into plasma by an ion source such as the Kaufman source [3]. The hydrocarbon ions are then extracted from the ion source and accelerated to form an ion beam. The ions and the unionized molecules condense on the substrate surface to form DEC coating. However, in this method, ionized ratio of precursor gases could hardly exceed 10 %. In order to obtain a better quality of DEC coatings. 

Writing equation (6) in logarithmic form results in equation (7). Again by convention, the log ionization ratio, log / = log(CfiH+ /Cb), is defined, with the ionized form on top. Equations (6) and (7) are thermodynamically exact the problem with them has always been what to do about the unknown activity coefficient ratio term. The first person to tackle this problem was Hammett,21 22 who defined an acidity function, H0, as in equation (8) ... 

H0 is defined so as to be similar to pH, and to reduce to it in dilute solution, i.e. to pH = pKa — log I. The idea is that versions of equation (8) can be written for weak base indicators that protonate to different extents in the same add solutions (overlapping indicators indicators because they indicate the solution acidity) subtracting two of these (say for indicators A and B) leads to equation (9), and if the activity coefficients for A and B, and for AH+ and BH+, approximately cancel, the value of pA bh+ can be calculated from the measured ionization ratios for A and B if pAah+ is known ... 

A is an anchor compound, one whose ionization ratios are measurable in dilute aqueous add pAbh+ = 100 for p-nitroaniline is used for H0.22 23 Equation (9) is known as the cancellation assumption using it on a series of overlapping weak base indicators of similar type (primary aromatic amines in the case of Ho) leads to Ho values covering a wide addity range according to equation (8), once all the P bh+ values are known. 

It was soon realized that there are problems with this approach.24,25 Log ionization ratios for weak bases that are not primary aromatic amines, while linear in H0, do not give the unit slope required by equation (8). This soon led to many other acidity functions, defined for other types of weak base, HA for amides,24 Hq for tertiary aromatic amines,25 C0 or HR for carbocations,26,27 and so on. In a recent review of addity functions,28 28 different ones were listed... 

For an anchor compound B (say p-nitroaniline), whose ionization ratios are measurable in dilute acid, we can write the thermodynamically exact equation (14) ... 

Carpentier and Lemetais60 have published ionization ratios for the protonation of some secondary aromatic amines in aq. H2S04, and these are illustrated as an excess acidity plot (log I - log Cn > vs. X, using the values in Table 3) in Fig. 4. In all the calculations in this section the data have been weighted using an... 

It is well known23 that ionization ratios / can be determined from spectra using the expression /=( > — DB)/ D — D), where D is the measured UV-vis optical density or NMR chemical shift and DA and Z>B refer to the values for the pure acid form (i.e. BH+) and pure base form (i.e. B), respectively. Recasting this in terms of D gives equation (27) ... 

Comparing the ionization ratio, %, of any weak base (B) to that, li , of a Hammett indicator (In), we have... 

The ionization ratios CArCH(OH)o-/CArCHO needed were calculated from experimentally accessible absorbancies, using Equation 5... 

Values of CArcH(OH)cr/CArCHO f°r eac benzaldehyde derivative were measured at 10-15 different sodium hydroxide concentrations in solutions containing fixed ethanol or DMSO concentrations ranging from 1 to 90 vol %. Since spectra obtained in the presence of 1% ethanol were indistinguishable from spectra recorded in purely aqueous solutions, it was possible to use absorbancies obtained in 1% ethanolic solutions for the calculation of pX2(H20) values. Ionization ratios were also determined in benzaldehyde solutions containing a constant concentration of sodium hydroxide (0.01M) and an ethanol or DMSO content which was varied between 1 and 98 vol %. 

The pKa s of protonated benzoic acid and its derivatives are readily measured by conventional spectrophotometric methods. Data for over forty compounds have been obtained by Stewart and Granger34 and Stewart and Yates35 and the results have been summarized by Arnett36. Substituted benzoic acids are well-behaved Hammett bases, with slopes of the logarithm of the ionization ratio plots close to 1.0. But, as explained by Arnett36, this is only true, for benzoic itself t any rate, in its region of protonation. In more dilute acid a sudden sharp change in activity coefficient occurs, which means that the observed... 

Aliphatic esters do not behave even approximately as expected for Hammett bases. Plots of the logarithms of the ionization ratios against — H0 are linear, but have a slope of 0.62 for simple acetates37. Lane et al.3t< have found a similar slope, 0.65, for ethyl acetate38. 

Lane38 measured the rate of hydrolysis of ethyl acetate at 25°C in 11 -79% sulphuric acid by both spectrophotometric and dilatometric techniques. He also measured spectrophotometrically the concentration of the conjugate acid of the ester in solution by measuring the absorptivity at 190 nm, and extrapolating to zero time, and by the change in the chemical shift of the acetyl protons. He found a linear relation between the ionization ratio and Hammett s acidity function... 

Figure 25. Associative Penning ionization total ionization ratio as function of collision energy for Ne(3P2 0)-Kr. Results obtained by three different experimental methods are compared.

Since two product molecules are produced from two reactant molecules, the ionization ratio of the acid is expressed as the product of the product concentrations divided by the product of the reactant concentrations). This numerical ratio can be used to compare the strengths of acids. It is very important to realize just how simple this notion is. The equilibrium constant (in this case the ionization constant of an acid) is merely a ratio of the molecules which have donated a proton to water to those which have not. 

The immediate changes in UV spectra57 exhibited by the substrates on addition of mineral acids are consistent with a rapid protonation equilibrium, S+H+ < SH+, to form the conjugated acid. In order to interpret the rate data, one must first correct the observed values of k,j, for the amount of protonated substrate. Spectrophotometric methods are widely applicable for determination of the ionization ratio, I = CSH+ /Cs, of moderately basic substrates74. For A-f-butylbenzaldoxime and 2-/-butyl-3-phenyloxaziridinc, however, the rate of the hydrolysis reaction (t /2 = 1 min) at the maximum in the profile at 24.2 °C made it impossible to measure the zero-time absorption of the substrates. However, allowing for medium effects in the absorption spectra, the substrates appeared to be essentially fully protonated in solutions of CH+ > 2 M in all three acids. 

The protonation of amides (A) to yield the conjugated acids (AH+) in aqueous sulphuric acid takes place on the carbonyl oxygen158-161 and the ionization ratio (I = [AH+]/[A]) has been found to depend on the acidity of the solution as measured by the Ha acidity function25,162 163 where A ah+ is the thermodynamic dissociation constant of the conjugated acid (equations 33 and 34). 

FIGURE 16. Variation of ionization ratio of iV-benzoylthiourea in 35-60% sulphuric acid with acidity function (0, A, Hq)... 

From Eq. (1.14) it is apparent that the main experimental difficulty in determining acidities is the estimation of the ratio between the free base and its protonated ionic form of a series of indicators, their so-called ionization ratios. 

In the early work of Hammett and Deyrup8 the measurement of the ionization ratio was based on the color change of the indicator. The solutions containing the indicator were compared at 25°C in a colorimeter with a standard reference. This reference was water, when the indicator was colorless in its acid form, and 96% sulfuric acid (or 70% perchloric acid), when the indicator was colorless in the basic form. 

For example, when the indicator was colored in water the authors define a stoichiometric color intensity relative to water 7W = Cw/Ca, where Ca and Cw are the stoichiometric concentrations of indicator in solution A and in water. On the other hand, the specific color intensity of the colored form relative to water is defined as Sw = [B]w/[B]a, where [B]w is the concentration of the colored base in water and [B]ais concentration in solution A. Because the indicator exists only in its basic form in water, [B]w = Cw and in solution A, Ca = [B]a+ [BH+]a. The ionization ratio is given by Eq. (1.22). 

C is the concentration of the absorbing species, l is the length of the cell, andis the molar absorptivity (or extinction coefficient). If at a given wavelength A, eBH +, eB, and sK are the extinction coefficients, respectively, of acid form of the indicator, its basic form, and of the unknown solution, the ionization ratio is given by Eq. (1.24). 

The pAfBH + value is easy to determine, when the ionization ratio can be measured in dilute aqueous solution [Eq. (1.25)]. 

Figure 1.4. The ionization ratio as measured for a series of indicators in the 0-100% H2S04-...

NMR spectroscopy, which was developed in the late 1950s as a most powerful tool for structural analysis of organic compounds, has also proven to be useful for acidity determinations. The measurement of the ionization ratio has been achieved by a variety of methods demonstrating the versatility of this technique. If we consider the general acid-base equilibrium Eq. (1.26) obtained when the indicator B is dissolved in the strong acid HA, then Up, and fcd, respectively, are the rates of protonation and deprotonation. 

Depending on these conditions, various NMR methods have been proposed and used to calculate the ionization ratio of weak bases in a superacid medium. 

Chemical Shift Measurements. Under slow-exchange conditions, the ionization ratio cannot be measured. In fact, one of the major advantages of the superacidic media is the ease with which weak bases can be fully protonated and directly observed by NMR. Because it is known that the protonation rates are practically diffusion-controlled ( 409 liter mol-1 s-1), under these conditions (< 10 2 s 1) the indicator is totally in the acidic form described by the NMR spectmm and no variable is available to measure the ionization ratio. 

However, because the measurement of the ionization ratio requires the presence of a minimum of 5% of one of the forms of the indicator, it necessitates the availability of a family of structurally similar compounds of varying basicity to cover a large domain of acidity. This condition has been met by Sommer and co-workers22,43 using the para-methoxybenzhydryl cations as useful indicators for the strongest superacids. 

Both methods have been exploited to determine ionization ratios. 

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