Entropic separation

Establishing a metric that provides an intuitive measure of the graphical separation between value distributions of two databases being compared is also useful. Eor this purpose, the Entropic Separation (ES) was defined... 

Two conclusions can be derived from these results. First, it is feasible to use entropy-based information theory to select fewer than 10 chemical descriptors that can systematically distinguish between compounds from different sources. Second, when selecting descriptors to distinguish between compounds, it is important that these descriptors have high information content that can support separability or differentiate compounds between the datasets. The power of the entropic separation revealed in this analysis gave rise to the development of the DSE and, ultimately, the SE-DSE metric, as described earlier. 

The well defined contact geometry and the ionic structure of the mica surface favours observation of structural and solvation forces. Besides a monotonic entropic repulsion one may observe superimposed periodic force modulations. It is commonly believed that these modulations are due to a metastable layering at surface separations below some 3-10 molecular diameters. These diflftise layers are very difficult to observe with other teclmiques [92]. The periodicity of these oscillatory forces is regularly found to correspond to the characteristic molecular diameter. Figure Bl.20.7 shows a typical measurement of solvation forces in the case of ethanol between mica. 

Examples of entropically driven separations are chiral separations and separations that are dominated by size exclusion. However, it must be emphasized that chromatographic separations can not be exclusively "energetically driven" or "entropically driven" but will always contain both components. It is by the careful adjustment of both "energetic" and "entropic" components of the distribution that very difficult and subtle separations can be accomplished. 

Temperature can also be used to optimize enantioselectivity in SFC. The selectivity of most CSPs increases as temperature decreases. For this reason, most chiral separations in SFC are performed at ambient or subambient temperatures [50, 74]. Subambient temperatures are particularly useful for compounds having low conformational stability [75]. Stringham and Blackwell explored the concept of entropically driven separations [76]. As temperature increased, enantioselectivity decreased until the enantiomers co-eluted at the isoelution temperature. Further increases in temperature resulted in reversal of elution order of the enantiomers. The temperature limitations of the CSP should be considered before working at elevated temperatures. 

The entropic hypothesis seems at first sight to gain strong support from experiments with model compounds of the type listed in Table 9.1. These compounds show a huge rate acceleration when the number of degrees of freedom (i.e., rotation around different bonds) is restricted. Such model compounds have been used repeatedly in attempts to estimate entropic effects in enzyme catalysis. Unfortunately, the information from the available model compounds is not directly transferable to the relevant enzymatic reaction since the observed changes in rate constant reflect interrelated factors (e.g., strain and entropy), which cannot be separated in a unique way by simple experiments. Apparently, model compounds do provide very useful means for verification and calibration of reaction-potential surfaces... 

This separation is an impressive example of an entropically driven distribution system where the normally random movements of the solute molecules are restricted to different extents depending on the spatial orientation of the substituent groups. For further information the reader is directed to an excellent review of chiral separations by LC (Taylor and Maher (12)) and a monograph on CYCLOBOND materials from ASTEC Inc. (13). 

The more useful types of chirally active bonded phases are those based on the cyclodextrins. There are a number of different types available, some of which have both dispersive or polar groups bonded close to the chirally active sites to permit mixed interactions to occur. This emphasizes the basic entropic differences between the two isomers being separated. A range of such products is available from ASTEC Inc. and a separation of the d and / isomers of scopolamine and phenylephrine are shown in figure 4. The separations were carried out on a cyclodextrin bonded phase (CYCLOBOND 1 Ac) that had been acetylated to provide semi-polar interacting groups in close proximity to the chiral centers of the cyclodextrin. The column was 25 cm long, 4.6 mm in diameter and packed with silica based spherical bonded phase particles 5pm in diameter. Most of the columns supplied by ASTEC Inc. have these dimensions and, consequently, provide a... 

Interactive LC systems are those where solute retention is predominantly controlled by the relative strengths of the molecular interactions between solute molecules with those of the two phases. In such systems, exclusion and entropically driven interactions will be minor contributions to retention. The three basically different types of molecular interaction, dispersive, polar and ionic give rise to three subgroups, each subgroup representing a separation where one specific type of interaction dominates in the stationary phase and thus governs solute retention. The subgroups are as follows ... 

It is sometimes informative to separate AG into hypothetical enthalpic and entropic terms, and then the Arrhenius factors may be related to the transition state activation parameters by Eqs 10.4 and 10.5. Thus, the Arrhenius activation energy can be approximately related to the potential energy of a transition state, and the preexponential A value includes probability factors. 

The last several years have seen an enormous growth in the number and use of chiral stationary phases in liquid chromatography [742,780-791]. Some problems with the gas chromatographic approach are that the analyte must be volatile to be analyzed and larger-scale preparative separations are frequently difficult. For entropic reasons relatively high temperatures tend to minimize the stability differences between the diastereomeric complexes and racemization of the stationary phase over time may also occur. The upper temperature limit for phases such as Chirasil-Val is about 230 C and is established by the rate of racemization of the chiral centers and not by column bleed. Liquid chromatography should be s ior in the above... 

As has been pointed out, both entropic and enthalpic interactions affect the chromatographic behavior of macromolecules. They are adjusted to the required type of separation by selecting appropriate stationary and mobile phases. In a third mode of liquid chromatography of polymers, liquid chromatography at the critical condition (LCCC) (Entelis etal., 1985,1986 Pasch, 1997), the adsorptive interactions are fully compensated by entropic interactions. This mode is also referred to as liquid chromatography at the critical point of adsorption. Hence, TAS is equal to AH and therefore, AG becomes zero. K is 1 irrespective of molar mass and, consequently, homopolymer molecules of different molar masses coelute in one chromatographic... 

Water-soluble polymers in general, and especially polyelectrolytes, are often difficult due to their specific and long range electrostatic interactions, which complicate all analytical techniques that rely on single particle properties that are usually realized by high dilution. In most cases the ionic strength of the solution must be increased by the addition of salt in order to screen electrostatic forces. Ideally, SEC separation is predominantly governed by entropic interactions,... 

---