Proton curves

Figure 14 Proton beam irradiation of a deep-seated large tumor. Single Bragg peaks of different energy are combined, in adequate proportions, to obtain a homogeneous dose distribution at the level of the SOBP. The depth-dose curve of a photon beam, shown for comparison, is inferior compared to the proton curve. However, an optimized multifield photon treatment allows to reach better irradiation conditions. (From Ref 43.)...

Figure 1.5. Acidity-dependent H NMR chemical shift variations protonation curve for acetaldehyde.42 CF3C00H-H2S04, A CF3COOH-CF3SO3H.

Figure 1.7. Protonation curves of indicator 3 in the superacid systems (from left to right) HF SbFs, HS03F SbFs, and CF3SO3H SbFs22...

Fig. 11. Molecular stopping power of water for protons (curve 1, data of Ref. 159) and electrons (curve 2 -----, data of Ref. 161 ----, data of Ref. 160).

The kinetics of the photochemical reductive dissolution of lepidocrocite (y-FeOOH) with oxalate as the reductant depends strongly on pH both the rate and the overall rate constant, k> decrease with increasing pH. This behavior means that the pH dependence of the rate does not simply reflect the pH dependence of oxalate adsorption at the lepidocrocite surface. Between pH 3 and 5, the log k() values can be fitted with a straight line. The dependence of k on the concentration of surface protons, >FeOH2+, can be estimated from the slope of this line and from the protonation curve of lepidocrocite k0 >FeOHf I6. The value of 1.6, which can be considered only a rough estimate, is not too different from the theoretically expected value of 2 for the proton-catalyzed detachment of reduced surface iron centers (i.e., of surface metal centers with the formal oxidation state of II). 

As described by Wieland et al. (8), the same protonation curve applies for various oxide minerals if the surface concentration of protons, >MOH2+, is plotted as a function of pH - pH = ApH, where the index zpc denotes the zero point of charge caused by binding or dissociation of protons. In the range ApH > 1, a straight line fits all the experimental data within a factor of 2. Therefore, a suitable approximation can be given by a Freundlich master isotherm ... 

Figure 6. Saturation surface Mo(vi) concentration achieved at various temperatures as a function of the concentration of the protonated (curve a) and neutral (curve b) surface hydroxyls regulated by varying the temperature of the impregnating suspension of y-aiumi-na. Temperature values are indicated in degrees centigrade.

Figure A3.8.3 Quantum activation free energy curves calculated for the model A-H-A proton transfer reaction described 45. The frill line is for the classical limit of the proton transfer solute in isolation, while the other curves are for different fully quantized cases. The rigid curves were calculated by keeping the A-A distance fixed. An important feature here is the direct effect of the solvent activation process on both the solvated rigid and flexible solute curves. Another feature is the effect of a fluctuating A-A distance which both lowers the activation free energy and reduces the influence of the solvent. The latter feature enliances the rate by a factor of 20 over the rigid case.

Fig. 3. Time evolution of the distance between the Zr atom and each of the three hydrogen atoms belonging to the methyl group (the original methyl group bonded to the Zr) in the zirconocene-ethylene complex. The time-evolution of one of the hydrogen atoms depicted by the dotted curve shows the development of an a-agostic interaction. Later on in the simulation (after about 450 fs) one of the other protons (broken curve) takes over the agostic interaction (which is then a 7-agostic interaction).

As the atom (A) to which H is bonded becomes more electronegative the polarization H—A becomes more pronounced and H is more easily lost as H An alternative approach to the same conclusion is based on the equation for proton transfer especially with regard to the flow of electrons as shown by curved arrows... 

Use curved arrows to show the bonding changes in the reaction of CIS 4 tert butylcyclohexyl bromide with potassium tert butoxide Be sure your drawing correctly represents the spatial relationship between the leaving group and the proton that is lost... 

Chemical shifts of pyridine and the diazines have been measured as a function of pH in aqueous solution and generally protonation at nitrogen results in deshielding of the carbon resonances by up to 10 p.p.m. (73T1145). The pH dependence follows classic titration curves whose inflexions yield pK values in good agreement with those obtained by other methods. 

If a sample contains groups that can take up or lose a proton, (N//, COO//), then one must expect the pH and the concentration to affect the chemical shift when the experiment is carried out in an acidic or alkaline medium to facilitate dissolution. The pH may affect the chemical shift of more distant, nonpolar groups, as shown by the amino acid alanine (38) in neutral (betaine form 38a) or alkaline solution (anion 38b). The dependence of shift on pH follows the path of titration curves it is possible to read off the pK value of the equilibrium from the point of inflection... 

Figura 3 Calculated detection limits for trace eiements in 1 mg/cm specimens of carbon, aiuminum, and caidum (100 xC of 3-MeV protons). The dashed curves represent the detection limits if the background radiation is due oniy to secondary eiectron bremsstrahiung.

It must be appreciated that the selection of the best model—that is, the best equation having the form of Eq. (6-97)—may be a difficult problem, because the number of parameters is a priori unknown, and different models may yield comparable curve fits. A combination of statistical testing and chemical knowledge must be used, and it may be that the proton inventory technique is most valuable as an independent source capable of strengthening a mechanistic argument built on other grounds. 

The shapes of the titration curves of weak electrolytes are identical, as Figure 2.13 reveals. Note, however, that the midpoints of the different curves vary in a way that characterizes the particular electrolytes. The pV, for acetic acid is 4.76, the pV, for imidazole is 6.99, and that for ammonium is 9.25. These pV, values are directly related to the dissociation constants of these substances, or, viewed the other way, to the relative affinities of the conjugate bases for protons. NH3 has a high affinity for protons compared to Ac NH4 is a poor acid compared to HAc. 

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