Dimerization association constants

Due to the apparent very high stability constant of the dimer and the lack of solubility in more competitive media, estimation of the association constant of the dimer formation was made by comparing the association constants of various smaller components in which the strength of the individual interactions could be calculated and used to give an approximate value of the dimer association constant in DMSO-<7rt of 1012 M 1. 

Auto-association of A-4-thiazoline-2-thione and 4-alkyl derivatives has been deduced from infrared spectra of diluted solutions in carbon tetrachloride (58. 77). Results are interpretated (77) in terms of an equilibrium between monomer and cyclic dimer. The association constants are strongly dependent on the electronic and steric effects of the alkyl substituents in the 4- and 5-positions, respectively. This behavior is well shown if one compares the results for the unsubstituted compound (K - 1200 M" ,). 4-methyl-A-4-thiazoline-2-thione K = 2200 M ). and 5-methyl-4-r-butyl-A-4-thiazoline-2-thione K=120 M ) (58). 

Metal-modified base pairs have been reported some time ago for identical (119), complementary (120), and non-complementary bases (59,121-126). These may assemble into a type I quartet through dimerization, as seen for trassociation constant of 59.1 M 1 in d6-DMSO (123). Rather unusual is the involvement of the aromatic C-H5 proton in the hydrogen bond-... 

The aniline-zinc porphyrin interaction has also been exploited to form dimers. Hunter (60) reported the dimerization of porphyrins functionalized at one meso position with ortho or meta aniline groups (47, 48, Fig. 15). Both compounds showed concentration-dependent H NMR spectra with large upfield shifts for the aniline protons. The dimerization constants are 160 and 1080 M-1 respectively for 47 and 48, and these values are an order of magnitude higher than the association constants of simple reference complexes (K — 10 and 130 M 1 respectively), which is indicative of cooperative self-assembly. The complexa-tion-induced changes in chemical shift were used to obtain three-dimensional structures of the dimers. 

Hunter (60) reported a self-assembled open polymer formed by a zinc porphyrin bearing one para-aniline substituent at the meso position. The ortho- and mela-analogs discussed above form closed dimers, but the geometry of the para-derivative precludes this, and polymerization is the only alternative (76, Fig. 31). Although the dilution experiments could be fitted to a non-cooperative polymerization model with a pairwise association constant (K = 190 M 1) practically identical to that found for simple aniline-zinc porphyrin complexes (K = 130 M 1), broadening of the 4H NMR spectrum at high concentrations is characteristic of oligomerization. 

Reinhoudt at al. have recently reported [48] the preparation of a calix[4]arene functionalized with two Zn(II) centers 25, which is highly efficient on transesterification of HPNP. The dimer complex is reported to be 50 times more active (in 50 (v/v)% acetonitrile-water at pH = 7.4 and I = 298 K) than the corresponding monomer (26) which is itself 6 times more active than 27, implying the contribution of the calix[4]arene moiety in the mechanism. The saturation kinetic experiments showed high association constant for the catalyst-substrate complex (K -... 

We shall examine the simplest association in the vapor phase, dimerization. Any conclusions drawn may be extended to higher polymerizations. For the comparison salt AX, which has a characteristic size parameter d0, the association constant for the equilibrium... 

Several studies have appeared (12,13,14) in which the propagation reactions involving styryllithium were examined in mixed solvent systems comprising benzene or toluene and ethers. The kinetics were examined under conditions where the ether concentration was held constant and the active center concentration varied. In most cases, the kinetic orders of the reactions were identical to those observed in the absence of the ether. Thus, in part, the conclusion was reached (13,14) that the ethers did not alter the dimeric association state of polystyryllithium. The ethers used were tetrahydrofuran, diphenyl ether, anisole, and the ortho and para isomers of ethylanisole. 

The state of association of poly(dienyl)lithium compounds in hydrocarbon solutions is a matter of current controversy (15-18). Aggregation states of two (.16 and four (.15) have been reported based on light-scattering and concentrated solution viscosity measurements. The most recent concentrated solution viscosity studies ( 1 6 J 7.) > which include results of various endcapping and linking techniques, provide convincing evidence for predominantly dimeric association of poly(isoprenyl)lithium in hydrocarbon solution. The effect of tetrahydrofuran on the degree of association of poly(isoprenyl)lithium has also been examined by concentrated solution viscosity measurements (13). These results indicate that the equilibrium constant for the process shown in eq 3 [PILi = poly(isoprenyl)lithium] exhibits an equilibrium... 

In the MWC treatment, the assumption is made that the mixed dimer AB can be neglected entirely. However, a more general treatment requires that we consider all dimeric forms. The formation constants KAA, Km, and KAB are defined as follows13 113 (Eqs. 7-32 to 7-34 note the statistical factor of 2 relating KAB to the association constant Kt) ... 

Though the five-coordinate complexes, except for p-oxo dimers, coordinate sixth ligands, the association constants are low (K < 103 M-1) because of the strong trans effect of the anionic ligand (equation 13).18 In the presence of excess ligand, the anionic ligand may be displaced (equation 14).13... 

The reactions of poly(styryl)lithium in benzene with an excess of diphenyl-ethylene 272) and bis[4-(l-phenylethenyl)phenyl]ether158) also were found to proceed by a first order process. However, the reactions of poly(styryl)lithium with the double diphenylethylenes l,4-bis(l-phenylethenyl)benzene and 4,4 bis(l-phenyl-ethenyl)l,l biphenyl gave l58) non-linear first order plots with the gradients decreasing with time. This curvature was attributed to departure from a geometric mean relationship between the three dimerization equilibrium constants (Ka, Kb and Kab). The respective concentrations of the various unassociated, self-associated and cross-associated aggregates involved in the systems described by Equations (49) to (51) are dependent upon the relative concentrations of the two active centers and the respective rate constants which govern the association-dissociation events. 

Insulin monomers are in equilibrium with more stable dimers and hexamers with known association constants fCdimer= 1.1 x 105 m-1, fChexamer = 2.89 x 108 m-2. 

By studying the concentration dependence of the H NMR spectra performed in DMSO-c/6 the association constant of the dimer could be calculated at 673 M"1 at 298 K. This value is surprisingly high for a cationic species in a polar solvent such as DMSO and is indicates that the binding within the dimer is not the result purely of hydrogen bonding, with ji-stacking and hydrophobic interactions potentially important. 

The hetero-dimerization behavior of dye-modified -cyclodextrins with native CDs was investigated by means of absorption and induced circular dichroism spectroscopy in aqueous solution [43], Three types of azo dye-modified /i-CDs show different association behavior, depending on the positional difference and the electronic character of substituent connected to the CD unit in the dye moiety. p-Methyl Red-modified fi-CD (1), which has a 4-(dimethylamino)azobenzene moiety connected to the CD unit at the 4 position by an amido linkage, forms an intramolecular self-complex, inserting the dye moiety in its / -CD cavity (Figure 13). 1 also associates with native a-CD by inserting the dye residue into the a-CD cavity. The association constants for such hetero-dimerization are 198 M"1 at pH 1.00 and 305 M 1 at pH 6.59, which are larger than the association constants of 1 for / -CD (43 M 1 at pH 1.00). 

In a similar approach, the aggregation of phenyl-acetylene macrocycles 65 (Chart 1) in solution have been studied with H NMR spectroscopy.169 170 They have determined the association constant for dimerization, iCssoc, by curve fitting the concentration dependence of the proton chemical shift to a model for monomer—dimer equilibrium. The results obtained from NMR studies, e.g., aggregation constants and aggregate size, have independently been verified by vapor pressure osmometry experiments. Further, it has been well documented in the literature that... 

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