Linear retention relationships

Neue, U.D. (2006) Non-linear retention relationships in reversed-phase chromatography. Chromatographia, 63, 45-53. 

T. Baczek and R. Kaliszan, Combination of linear solvent strength model and quantitative structure-retention relationships as a comprehensive procedure of approximate prediction of retention in gradient liquid chromatography. J. Chromatogr.A 962 (2002) 41-55. 

With binary and ternary supercritical mixtures as chromatographic mobile phases, solute retention mechanisms are unclear. Polar modifiers produce a nonlinear relationship between the log of solute partition ratios (k ) and the percentage of modifier in the mobile phase. The only form of liquid chromatography (LC) that produces non-linear retention is liquid-solid adsorption chromatography (LSC) where the retention of solutes follows the adsorption isotherm of the polar modifier (6). Recent measurements confirm that extensive adsorption of both carbon dioxide (7,8) and methanol (8,9) occurs from supercritical methanol/carbon dioxide mixtures. Although extensive adsorption of mobile phase components clearly occurs, a classic adsorption mechanism does not appear to describe chromatographic behavior of polar solutes in packed column SFC. 

Parameters describing the linear relationship between the slope and the intercept of linear retention vs. composition curves in RPLC (eqn.3.46). Data taken from refs. [322] and [333] (1). 

Linear relationships are preferred, but not mandatory. For non-linear retention lines... 

Many attempts to correlate the analyte structure with its HPLC behavior have been made in the past [4-6], The Quantitative structure-retention relationships (QSRR) theory was introduced as a theoretical approach for the prediction of HPLC retention in combination with the Abraham and co-workers adaptation of the linear solvation energy relationship (LSER) theory to chromatographic retention [7,8],... 

The reliable range of is less than one and a half decades. When dealing with a series of analytes of diverse retentive properties it is hence necessary to determine Rm values at several compositions of binary eluents and next to extrapolate linearly the relationship between R and the volume percent of one of the eluent components to a fixed value. In the case of reversed-phase TLC extrapolation is usually performed to pure water (buffer) as a hypothetical eluent. Such an extrapolated Rm value is usually denoted by... 

RP-LC, multivariate analysis methods such as principle component analysis (PCA) and nonlinear mapping (NML), or comparative molecular field analysis (CoMFA) approaches and linear free energy-related (LFER) equations have been used to derive structure-retention relationships in chiral chromatography [16-18]. 

A similar linear logarithmic relationship, known as a van t Hoff plot, usually exists between adjusted retention data and the reciprocal of column temperature in gas, liquid (constant composition) and supercritical fluid (constant density) chromatography. The effect of temperature on retention is based on the Gibbs-Helmholtz equation and has a sound thermodynamic basis, Eq. (1.9)... 

The retention and the selectivity of separation in RP and NP chromatography depend primarily on the chemistry of the stationary phase and the mobile phase, which control the polarity of the separation systems. There is no generally accepted definition of polarity, but it is agreed that it includes various selective contributions of dipole-dipole, proton-donor, proton-acceptor, tt-tt electron, or electrostatic interactions. Linear Free-Energy Relationships (LFER) widely used to charactaize chemical and biochemical processes were successfiiUy apphed in liquid chromatography to describe quantitative structure-retention relationships (QSRR) and to characterize the stmctural contributions to the retention and selectivity, using multiple linear correlation, such as Eq. 

As apparent from Eqs. (11), (12), and (18), the free energy of cavity formation is proportional to the surface area of a protein or peptide. Therefore, retention differences between proteins or peptides will reflect the incremental changes in their surface areas as a consequence of adsorption to the stationary phase ligands. In the presence of an organic solvent in RPC, or when the salt concentration is sufficiently high in HIC, the retention relationship for a specific protein or peptide takes the simplified linear form [8,160,207]... 

A different approach to the systematic characterization of stationary phases is the correlation of analyte structure and retention in a given chromatographic system with the help of quantitative structure retention relationships (QSRR), a distinct discipline of linear free energy relationships (LFER). In QSRR, the total retention of an analyte is separated into individual contributions such as dipole-dipole, K-n, acid-base, and hydrophobic interactions. This approach enables strict interrelations on the basis of fundamental mechanistic aspects in order to improve the physico-chemical understanding of chromatographic retention. 

As indicated by these equations, both retention factor and separation factor are controlled by an enthalpic contribution, which decreases with the elevation of temperature, and an entropic contribution, which is independent of the temperature. The selectivity is a compromise between differences in enantiomeric binding enthalpy and disruptive entropic effects. The enthalpy term is a function of overall interactions between each enantiomer and the chiral selector. By plotting ln(o ) vs. 1 /T, all processes that do not contribute to the enantiomeric discrimination cancel out and the plot is linear, the slope being the difference between the enthalpy of association of the enantiomers with the stationary phase. The linear inverse relationship between In a and temperature demonstrates the enhancement of selectivity with a decrease in temperature. There exists a Tiso where - (AG ) = 0 owing... 

On nonpolar columns, the compounds of a homologous series separate as a function of their boiling points, and linear relationships have been established between the logarithms of the retention volumes and the number of carbon atoms in the 2-, 4-, and 5-positions (see Fig. III-l). 

Concentrations of moderator at or above that which causes the surface of a stationary phase to be completely covered can only govern the interactions that take place in the mobile phase. It follows that retention can be modified by using different mixtures of solvents as the mobile phase, or in GC by using mixed stationary phases. The theory behind solute retention by mixed stationary phases was first examined by Purnell and, at the time, his discoveries were met with considerable criticism and disbelief. Purnell et al. [5], Laub and Purnell [6] and Laub [7], examined the effect of mixed phases on solute retention and concluded that, for a wide range of binary mixtures, the corrected retention volume of a solute was linearly related to the volume fraction of either one of the two phases. This was quite an unexpected relationship, as at that time it was tentatively (although not rationally) assumed that the retention volume would be some form of the exponent of the stationary phase composition. It was also found that certain mixtures did not obey this rule and these will be discussed later. In terms of an expression for solute retention, the results of Purnell and his co-workers can be given as follows,... 

The column was operated in the normal phase mode using mixtures of n-hexane and ethanol as the mobile phase. Equation (13) is validated by the curves relating the corrected retention volume to the reciprocal of the volume fraction of ethanol in Figure 19. It is seen that an excellent linear relationship is obtained between the corrected retention volume and the reciprocal of the volume fraction of ethanol. 

From the general framework of the Snyder and Soczewinski model of the linear adsorption TLC, two very simple relationships were derived, which proved extremely useful for rapid prediction of solute retention in the thin-layer chromatographic systems employing binary mobile phases. One of them (known as the Soczewinski equation) proved successful in the case of the adsorption and the normal phase TLC modes. Another (known as the Snyder equation) proved similarly successful in the case of the reversed-phase TLC mode. 

The following Soezewinski equation is a simple linear relationship with respect to logA, linking the retention parameter (i.e., R,J) of a given solute with quantitative eomposition of the binary eluent applied ... 

Baczek, T., Markuszewski, M., Kaliszan, R. Linear and quadratic relationships between retention and organic modifier content in eluent in reversed phase high-performance liquid chromatography a systematic comparative statistical study. 

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