Dimer Equilibria

The variation in chemical shift was analyzed assuming dimer formation. The equations are as follows  

Below the data section lies an extensive table (not shown), used to obtain the smooth calculated curve, in rows 20 to 118. 

To plot the theoretical binding curve, generate Scale for a range of [U], as follows. In cell A20 type 0.000, in A21 type 0.001, then use AutoFill to generate values from 0.000 to 0.100 in steps of 0.001. Copy the expression for [U] and Paste in cell C20. Fill Down to end of table. Transfer the expression for Scale from any cell in row D to cell F20 (Copy to D20, Cut and Paste to F20 to transfer correctly). Fill Down to end of table. 

2 (Chemical shift d of hiqh field urea proton)  

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The "chemical" theory postulates that there is a dimerization equilibrium of the type... 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

The dithionite ion has a remarkable eclipsed stmcture of approximate C2v symmetry (Fig. 15.32b). The extraordinarily long S-S distance (239 pm) and the almost parallel SO2 planes (dihedral angle 30°) are other unusual features. Electron-spin-resonance studies have shown the presence of the S02 radical ion in solution ( 300ppm), suggesting the establishment of a monomer-dimer equilibrium 8204 ... 

Zollinger (1971) calculated the actual rate constant referring to the monomeric diazo component from the (overall) measured rates and the dimerization equilibrium constant. The ratio of rates of the first to the second azo coupling reaction of the biphenyl-4,4 -bis-diazonium ion with the trianion of 2-naphthol-3,6-disulfonic acid at 15 °C, k /k2 9 is 80. 

In contrast to disproportionation, in the dimerization equilibrium at lower temperatures the reaction product is favored. The contributions coming from partition functions and from the exponential term are presented together with the temperatures and logarithms of equilibrium constants of the reaction (103) in Table XI. 

With radicals of the benzyl type, 11 through 18, the dimerization equilibrium depends on the relative magnitudes of the energy gain arising from the C-C bond formation and of the ir-electron energy loss which results from a reduction of the conjugated system. 

With radical ions, the dimerization equilibrium is strongly influenced by the solvation and association of radical ions with counter ions. It has been shown that the free ions dimerize much more slowly than do the respective contact ion pairs e.g., the quinoline radical anion does not dimerize in the powerfully solvating hexamethylphosphoramide, but it does dimerize rapidly in tetra-hydrofuran (160). Thus, two equilibria should be distinguished (160), viz. 

Baryshnikova OK, Sykes BD (2006) Backbone dynamics of SDF-lalpha determined by NMR interpretation in the presence of monomer-dimer equilibrium. Protein Sci 15 2568-2578 Becker EB, Bonni A (2004) Cell cycle regulation of neuronal apoptosis in development and disease. Prog Neurobiol 72 1-25... 

Absorbance measurements on mixtures of Sb(V) and Sb(III) in hydrochloric acid media, have led Whitney and Davidson - to propose a dimeric equilibrium... 

Veldkamp CT, Peterson FC, Pelzek AJ, Volkman BF. The monomer-dimer equilibrium of stromal cell-derived factor-1 (CXCL 12) is altered by pH, phosphate, sulfate, and heparin. Protein Sci 2005 14 1071-81. 

Until very recently, the only example of a quasi-3-coordinate aluminum phosphide was (Me3SiCH2)2AlPPh2,76 which was reported to exist in solution as a monomer-dimer equilibrium. However, a crystal structure of... 

Pt/Al2C>3-cinchona alkaloid catalyst system is widely used for enantioselective hydrogenation of different prochiral substrates, such as a-ketoesters [1-2], a,p-diketones, etc. [3-5], It has been shown that in the enantioselective hydrogenation of ethyl pyruvate (Etpy) under certain reaction conditions (low cinchonidine concentration, using toluene as a solvent) achiral tertiary amines (ATAs triethylamine, quinuclidine (Q) and DABCO) as additives increase not only the reaction rate, but the enantioselectivity [6], This observation has been explained by a virtual increase of chiral modifier concentration as a result of the shift in cinchonidine monomer - dimer equilibrium by ATAs [7],... 

Typical examples are the conversion of the neutral form of an amino acid into its zwitterionic form, the helix-coil transitions in polypeptides and polynucleotides, and other conformational changes in biopolymers. Reactions of higher molecularity in which reactants and products have different dipole moments are subject to the same effect (association of the carboxylic acids to form hydrogen-bonded dimers). Equilibrium involving ions are often more sensitive to the application of an electric field ... 

The color of the quinonoid compounds that may be obtained by disproportionation can be sufficiently like that of the radicals to cause confusion if visual observation or broad-band spectrophotometry is used.11 For example, Preckel and Selwood, using paramagnetism as a measure of the amount of radical, reported that solutions of triphenyl-methyl derivatives more or less rapidly lost their paramagnetism. The decomposed solutions were still highly colored, but the color was no longer dependent on the temperature as it is in the case of a radical-dimer equilibrium mixture. What is more striking, and an even more subtle and dirtier trick on the part of nature, is the fact that Preckel and Selwood s non-paramagnetic solutions were still rapidly bleached by exposure to the air. It is clear that radical-like reactivity is not a safe criterion for the presence of radicals. It is also clear that the ebullioscopic method is particularly unsatisfactory in view of the excellent chance for decomposition. 

Variable temperature C NMR data of the Y derivative were consistent with a monomer/dimer equilibrium for compounds 85 in solution as depicted in Scheme... 

Scheme 26. Proposed monomer/dimer equilibrium for compounds 85.

A series of titanasilsesquioxane alkoxides, including [R7Si70i2Ti0zPr] (107, R = C-C5H9 108, c-CfiHn = 1,2) and [Cy7Si70i2Ti(p-0Me)(Me0H)]2 (109) were published by Crocker and co-workers. " Treatment of Cy7Si70i2Ti(0Pr) (108) with methanol affords the six-coordinate titanasilsesquioxane dimer [Cy7Si70i2 Ti(p-OMe)(MeOH)]2 (109), which was structurally characterized. The monomer/ dimer equilibrium of 108 and the formation of 109 are depicted in Scheme 34. " ... 

The structure of [CofCNljNO] " has been studied by spectral means. I.r. and electronic spectra indicate it should be reformulated as [(CN)5Co(N202)-CoICNjs] - however, the appearance of v(NO) in range 1770—1860 cm" in dilute solution is taken as evidence for a monomer-dimer equilibrium. ... 

McGarrity and Ogle examined the aggregation of BuLi in THF by using H and Li NMR spectroscopy and determined that BuLi exists as a tetramer in equilibrium with a dimer in THF. Activation and equilibrinm parameters were measured for the tetramer-dimer equilibrium (equation 2). No evidence was obtained for a monomer at concentrations of BuLi down to 0.1 mM. ... 

Fluorescence quantum yield and emission maximum determinations as a function of peptide concentration may also permit the detection of peptide self-aggregation at concentrations below 10-4 M, because the peptide fluorophore is likely to be located in a different environment in the peptide aggregate. For example, the concentration-dependent changes in the tryptophan fluorescence emission maximum of mellitin were monitored to determine the equilibrium dissociation constant and thermodynamic parameters of the monomer-tetramer self-association reaction of this peptide. 25 Similarly, measurement of the changes in the tryptophan fluorescence intensity of gramicidin A as a function of its concentration permitted the determination of an average monomer-dimer equilibrium con-stant. 26 ... 

The effect of phase upon the monomer-dimer equilibrium is pronounced. The quantum yields for dimer formation in liquid-aerated water solution are low (from zero for thymine to 10"2 for other pyrimidines) but the quantum yields for dimer formation in frozen aqueous solutions or in single crystals are much higher (reaching unity in frozen water solution for thymine). The quantum yields for monomerization are uniformly high and are about the same in solution or in solid phase. The net result of this phase effect is that even at optimum wavelengths for dimer formation, the yields of dimers are low in solution and high in solid phases, for all the single bases, nucleosides, or nucleotides. 

In 1976, Lappert and co-workers " reported the first stable dialkylstan-nylene (154, Scheme 14.71) in solution. They found that 154 exists as a monomer in the gas phase and as a dimer 153 in the solid state, whereas it exists as a monomer-dimer equilibrium mixture in solution. Extensive studies on the reactions of 154 were carried out, especially on oxidative addition and insertion reactions leading to a variety of new organotin compounds such as 165 and 166 (Scheme... 

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