Thermodynamic distribution

Scheme 20 Kinetic and thermodynamic distributions of the product isomers in the Friedel-Crafts methylations...

Addition of Bu3SnLi or McsSnI.i to 4-t-butylcyclohexanone affords mixtures of trans and cis adducts in ratios that depend on reaction conditions (Table ll)68. In THF, a 93 7 mixture is obtained with both reagents. This ratio is thought to represent the thermodynamic distribution—the axial stannane being favored. In ether, the cis isomer predominates, suggesting a kinetic preference for equatorial addition. Each of the two isomers can be lithiated with BuLi. Subsequent treatment with alkyl halides or carbonyl compounds affords the substituted alkoxy cyclohexanes with retention of stereochemistry. 

This reaction occurs rapidly at room temperature using a small excess of alkyne and either pinacol- (HBpin) or catecholborane (HBcat). When an excess of borane was used, the Z/E ratio of the products was slowly eroded, eventually attaining a thermodynamic distribution of isomers. Equilibration presumably occurs via addition/elimination of excess Rh-H. Miyaura s method provides a useful synthetic complement to knovm cis-hydroboration methods. Under optimized conditions, good yields and high stereoselectivity (>90 10) were achieved for a variety of alkenylboronates (Table 9.8). The best selectivities were generally obtained with the use of catecholborane and Et3N as an additive. As in related reactions, the presence of base seems to suppress undesired reaction pathways. 

This unprecedented kinetic preference for isomerization of the internal olefin to a terminal olefin is in stark contrast to the strong thermodynamic preference for the conjugated isomer 2PN the thermodynamic distribution at 50°C is 78.3 20.1 1.5 (2PN 3PN 4PN). It should be emphasized that the ratio of 4PN 3PN never goes above the equilibrium ratio of about 0.07 1, but arrives at that equilibrium ratio before any significant production of 2PN occurs. This may result from coordination of nitrile prior to olefin, thereby directing the nickel-hydride addition to the olefin as illustrated in 18. In the... 

Because 1-octanol is a good surrogate phase for lipids in biological organisms, the octanol-water partition coefficient, a ratio of concentrations in 1-octanol and water, represents how a chemical would thermodynamically distribute between the lipids of biological organisms and water. It further represents the lipophilicity and the hydrophobicity of the chemical substance. It usually is referred to as Kow or P, or in its 10-based logarithmic form as log I, w or log P, and is unitless. For more detail see Chapter 5. 

The thermodynamic distribution coefficient is introduced when one of the components can be considered as a solute in each phase, and when we choose the reference states of that component to be the infinitely dilute solution in each phase. For discussion, we designate the first and second components as those that form the solvents and the third component as the solute. Equations (10.245), (10.246), (10,248), and (10.249) are still applicable when we choose the pure liquid phase as the standard state for each of the two components. When we introduce expressions for the chemical potential of the third component into Equation (10.247), Equation (10.250) becomes... 

With the definition of the thermodynamic distribution coefficient, Equation (10.252) can be written as... 

For those samples that are not compatible with GC, the first question to ask involves the size (molecular weight) of the solute molecules. Their size should be compared to the pores of the packing materials that can be used in LC. If the size of the molecules is not negligible relative to the (average) pore size, then part of the pores and hence part of the stationary phase present in the column will not be accessible to the solute molecules. Hence, the simple relationship between chromatographic retention and thermodynamic distribution (eqn.l. 6) loses its significance. To avoid that, wide pore materials can be used for the separation of large molecules (e.g., proteins) based on their distribution over the two phases [202]. 

A solute undergoing chromatographic migration partitions between the stationary and mobile phases, a process driven by thermodynamic equilibrium. At equilibrium (established fully only at the zone center), the concentration in the stationary phase (c,) relative to that in the mobile phase (cm) is given by the thermodynamic distribution constant K, as shown by comparing Eqs. 2.18 and 2.19. Thus... 

For a homogeneous, low-viscosity fluid the probability P(p,M) is essentially a delta function centered at

and and the linear result is recovered. However, when Vyqr is much greater than one, there should be a thermodynamic distribution of density and modulus for a region of size 2ir/q. 

Indeed, it was shown mat cyclic oligomers are always formed in the cationic polymerization of cyclic acetals and their distribution agrees well with the thermodynamic distribution calculated on the basis of Jacobson-Stockmayer theory (with exception of small rings with n = 2-4) [89]. 

The fact that thermodynamic distribution of ring sizes is attained in the course of polymerization provides another indication that involved processes are relatively fast. 

The thermodynamic distribution coefficient requires that equilibrium be maintained between the crystallizing solid and the parent liquid. However, diffusion rates in the solid are so slow that there is negligible interchange between trace elements in the crystal and trace elements in solution except at the surface. The measured empirical distribution coefficients describe an instantaneous or surface partitioning. This requires that a careful distinction be made between a static system, such as a closed pocket or pond from which crystals are growing and a flow-through system in which the growing crystals are continuously bathed in fresh solution. 

Independent of which model is used to calculate the diflerential heat of adsorption, one must verify that the experimental q-0 curve represents the thermodynamic distribution of surface sites with respect to a given adsorbate under specified conditions. Specifically, one must confirm that the adsorption... 

Relative similarity is dependent on an alignment constraint (an external reference frame) while the absolute similarity is alignment independent. This methodology accounts for the thermodynamic distribution of conformer states of a molecule and is able to provide measures of similarity with respect to the whole molecule as well as pharmacophoric features of the molecule. 

---