Temperature dependence of the Kováts retention index

Journal of Chromatography A, 1137 (2006) 84–90

Temperature dependence of the Kov´ats retention index The entropy index Mikl´os G¨org´enyi a,∗ , Jo Dewulf b , Herman Van Langenhove b a

b

Department of Physical Chemistry, University of Szeged, Rerrich B´ela t´er 1, H-6721 Szeged, Hungary Research Group ENVOC, Faculty of Bioscience Engineering, Ghent University, Coupure Links 653, B-9000 Ghent, Belgium Received 4 August 2006; received in revised form 28 September 2006; accepted 29 September 2006 Available online 20 October 2006

Abstract According to a novel equation, the temperature dependence of the Kov´ats retention index, dI/dT is proportional to the difference of the Kov´ats retention index, I, and the new entropy index, I(S), defined similarly as the retention index, but based on solvation entropy instead of the free energy of solvations. The new relationship was tested with the experimental retention and thermodynamic data published by Kov´ats and coworkers for 32 compounds on 6 different stationary phases. Very good correlations (r > 0.99) were observed for dI/dT versus (I − I(S)) and dI/dT versus ␦Cp , the molar heat capacity difference of the solute and the hypothetical n-alkane, which has the same retention index as the solute. Deviations in the dI/dT versus ␦Cp relationship were observed only for alcohols, suggesting a different solvation mechanism for alcohols as compared with other compounds. © 2006 Elsevier B.V. All rights reserved. Keywords: Kov´ats retention index; Temperature dependence of retention index; Entropy of solvation; Molar heat capacity of solvation; Entropy index

1. Introduction The Kov´ats retention index, I, is a well-documented concept for the qualitative identification of organic compounds [1]. Identification can be achieved via the agreement of the Kov´ats index on at least two columns with different polarities. The temperature dependence of the retention index, dI/dT, provides additional support in the refinement of the compound identification, e.g. in the distinction of isomers where the mass spectra do not differ. Multidimensional GC offers an attractive, combined method of identification via the retention index and its temperature increment [2]. For alkylbenzenes, a fine structure versus retention correlation exists [3,4]; a branched, more compact alkane molecule has a larger temperature dependence in the retention index on squalane than that of a straight-chain compound [5]; cisalkene isomers have higher temperature coefficients than those of trans isomers on both apolar and polar phases [6], etc. Cyclic compounds exhibit higher temperature dependence in

∗

Corresponding author. Tel.: +36 62 544628; fax: +36 62 544652. E-mail address: [email protected] (M. G¨org´enyi).

0021-9673/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.chroma.2006.09.091

the retention index as the size of the molecule increases [7–9]. The dI/dT value is positive [10] or negative. It is negative for mainly polar molecules, e.g. alcohols [11], fluorinated compounds [12], tetraalkoxy siloxanes [13], esters of acrylic and methacrylic acids [14], alkylbenzenes [15] and halogenated hydrocarbons [16]. For polar or moderately polar compounds on an apolar phase both positive and negative temperature dependence in the retention index were recently observed, i.e. a minimum in the retention index versus temperature relationship [17–20]. Some general tendencies concerning the position of the minimum have already been recognized, e.g. a shift in the position of the minimum to lower temperatures with increasing molar mass [18,19]. The temperature dependence of the retention index has been reported to depend mainly on structural properties. Studies of the retention of alkylbenzenes on polar 1,2,3triscyanoethoxypropane and apolar (squalane) phases revealed that the temperature dependence of the retention index is inversely proportional to the symmetry of the molecule and the size of its alkyl groups. The dimensions and structural groupings of branched paraffin molecules are major factors that influence the temperature dependence [21]. For apolar stationary phases

M. G¨org´enyi et al. / J. Chromatogr. A 1137 (2006) 84–90

and solutes, the temperature dependence of the Kov´ats index has been observed to depend on the free energy and entropy changes during the partitioning. An equation has been deduced for the temperature dependence of the retention index which is based on these thermodynamic quantities and the retention index [22]. However, this equation has subsequently not been discussed. These and other results may have resulted in the statement that the temperature dependence of the retention index is connected with entropy changes during partitioning [10]. Experimental observations have been utilized to derive empirical expressions describing the relationship I versus T: (a) The retention index is independent of the temperature. Strictly, this case is very rare and is limited to a rather narrow temperature range. (b) The retention index is suggested to change linearly with temperature [23–29], which is common for alkanes for instance: I = aT + b

(1)

On the assumption that the retention index changes according to Eq. (1), the slope a (dI/dT) is determined by the solvation enthalpies, Hi , and entropies, Si , of the solutes, i, and the n-alkane (reference compound) with carbon number z in Eq. (1) [10]:

Both ϕ values are indirectly proportional to the free energy of the CH2 unit, but ϕ1 is proportional to the solvation entropy and ϕ2 is proportional to the solvation enthalpy of the CH2 unit [10]. (c) The empirical reciprocal equation β (2) T is used more rarely [25,30]. (d) In a larger temperature range, the curvature in the I versus T graph reflects a hyperbolic (Antoine type) temperature dependence [31]: I =α+

B T +C

(3)

where A, B and C are empirical constants, but they have thermodynamic meaning [32,33]. Two types of hyperbola have been presumed to exist: either a concave (increasing I–T) or a convex (decreasing I–T) curve [34]. Accordingly, the hyperbola concept cannot be used for the descending part of the I versus T curve with minimum where the curve is concave. (e) The polynomial I = I 0 + a1 T + a 2 T 2

(4)

yields a good description of the temperature dependence of the minimum behaviour too [12,35]. (f) A combined reciprocal and logarithmic equation [18,36]: I =A+

B + C ln T T

seems to be applicable in several cases. This equation was considered to be better than Eq. (1) for the characterization of the retention index of, e.g. substituted aromatic compounds [37] and plant volatiles [38] and can be well used instead of parabolic equation (Eq. (4)). Although numerous experimental observations have been made on the value of dI/dT and a number of expressions have been used to describe the temperature dependence of the retention index, a general equation with a thermodynamic explanation which can be used in all cases is not yet available. In the present paper we deduce a thermodynamic expression for interpretation of the temperature dependence of the retention index. To test the new relationship, the thermodynamic and retention data reported by Kov´ats et al. for 32 selected solutes on a standard C78 stationary alkane and on its derivatives have been used. 2. Theory The thermodynamic definition of the retention index is I = 100

Gx − Gz + 100z Gz+1 − Gz

(6)

or

a = ϕ1 (HiS − HzS ) + ϕ2 (SiS − SzS )

I =A+

85

(5)

I = 100

␦Gx−z + 100z G(CH2 )

(6a)

where Gx , Gz and Gz+1 are Gibbs energy differences in the solvation of solute x, z and z + 1: n-alkanes preceding and following the solute x in the chromatogram having carbon numbers z and z + 1, ␦ denotes the difference between the given properties of two substances. The temperature dependence of the standard free energy difference at a given temperature is [39]   ∂G = −S (7) ∂T P Introducing the variable I in Eq. (6a): I =

␦Gx−z = 0.01I − z G(CH2 )

(8)

Reordering and differentiation of Eq. (8) result in ␦S(x−z) G(CH2 ) ␦G(x−z) S(CH2 ) dI  =− + dT G2 (CH2 ) G2 (CH2 )

(9)

Multiplication by G(CH2 ) and division by S(CH2 ) results in the equation ␦S(x−z) dI  G(CH2 ) = I − dT S(CH2 ) S(CH2 )

(10)

In gas chromatography, both G(CH2 ) and S(CH2 ) are negative. Let us introduce a new expression, I (S) similarly to Eq. (8): I  (S) =

␦S(x−z) S(CH2 )

(11)

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Table 1 S(CH2 ) and S(CH2 )/G(CH2 ) × 103 ratiosa in different stationary phasesb at different temperatures T (K)

C78

POH

PCN

PCl

MTF

TMO

Average

363

S(CH2 )/G(CH2 S(CH2 )

) × 103

2.50 −5.88

2.52 −5.89

2.61 −6.12

2.45 −5.72

2.54 −5.92

2.60 −6.09

2.54 ± 0.06 −5.94 ± 0.14

383

S(CH2 )/G(CH2 ) × 103 S(CH2 )

2.44 −5.47

2.48 −5.51

2.55 −5.67

2.42 −5.39

2.47 −5.48

2.54 −5.65

2.48 ± 0.05 −5.53 ± 0.10

403

S(CH2 )/G(CH2 ) × 103 S(CH2 )

2.38 −5.08

2.43 −5.15

2.48 −5.25

2.40 −5.08

2.39 −5.06

2.48 −5.24

2.43 ± 0.04 −5.14 ± 0.08

423

S(CH2 )/G(CH2 ) × 103 S(CH2 )

2.32 −4.71

2.38 −4.80

2.40 −4.85

2.37 −4.79

2.31 −4.66

2.40 −4.84

2.36 ± 0.04 −4.78 ± 0.07

a b

Ratio

S(CH2 ) is in J K−1 mol−1 , S(CH2 )/G(CH2 ) is in K−1 calculated from the data set. Meaning of the abbreviations of the 6 stationary phases see Section 3.

or, similarly to Eqs. (6) and (8), at a given temperature: I(S) = 100I  (S) + 100z = 100

Sx − Sz + 100z Sz+1 − Sz

(12)

Eq. (12) is similar to the definition of the Kov´ats retention index, but the Gibbs energy differences are replaced by appropriate entropies of solution. The I(S) of an n-alkane is equal to 100z, similarly as for the retention index. Hence, I(S) may be called the entropy index. In the case of the entropy index, it is not the retention of the solute and the reference n-alkane are compared, but the changes in “freedom” during the dissolution from the gas phase into the solvent. As the entropy index does not include retention data, it can only be calculated from the solvation entropies of the solute and the reference n-alkanes. The entropy index is roughly proportional to the difference in solvation entropy of the solute and the n-alkane, as the denominator of Eq. (12) is almost independent from the selected n-alkane pairs at a given temperature, although they do display some tendencies, depending on the stationary phase (Table 1). Finally, after using Eqs. (8), (10)–(12), we obtain: dI S(CH2 ) = (I − I(S)) dT G(CH2 )

(13)

Eq. (13) clearly suggests that the temperature dependence of the retention index increases with the difference between the retention and entropy index. In these equations the retention index, the entropy index and the temperature dependence of the retention index refers to a given temperature. The temperature dependence of the retention index can be: (a) positive, if I > I(S); (b) negative, if I < I(S); (c) zero, if I = I(S). In this case, the I versus T curve exhibit an extreme (minimum) at the minimum temperature. The retention index at this temperature depends on the solvation entropy relationships, i.e. the entropy index. 3. Experimental and calculations The experimental data are based on the publications of Kov´ats and coworkers relating to 32 representative solutes

on 6 different stationary phases: on a C78 branched alkane, 18,23-dioctadecyldotetracontane, having four methyl (ethyl) endgroups [12] and on its nearly isochor and isomorph polar derivatives, where one of the methyl groups is replaced by primary OH (POH) (363–483 K) [12], chloro (PCl) (358–433 K) [40], cyano (PCN) (363–483 K) [41] and CF3 (MTF for monotrifluoromethyl) (363–483 K) [42]. In the case of the sixth solvent the four ethyl groups are replaced by OCH3 (TMO for tetrakismethoxy) (363–483 K) [41]. These data were recently partially corrected in [43]. We have used the corrected data set. An attempt was made to minimize the adsorption by careful preparation of the packing material [12]. The retention indices at different temperatures, I(T), were generally calculated from Eq. (14) by using the linear temperature dependence: I(T ) = I(T ◦ ) + AT T + ATT T 2

(14)

where T = T − T◦ , A

T and ATT are parameters determined from the experimental retention index data; I(T◦ ) is the retention index at the reference temperature, T◦ = 403 K. Generally ATT is zero. However, for alcohols, the quadratic term, ATT is not zero. All of these parameters are available in the data set. The temperature dependence of the retention index at given temperature were calculated from the derived form of Eq. (14). The standard molar enthalpy, entropy and heat capacity of solvation are given for 403 K. The method of their determinations are summarized in [44]. The enthalpy and entropy data at other temperatures were calculated with the help of molar solvation heat capacities. The statistical calculations were performed with StatisticaTM software (Version 6.0, Statsoft Inc. Tulsa, Oklahoma, USA).

4. Results and discussion The entropy indices, calculated via Eq. (12) from the published S data and the experimental retention index values of the 32 representative solutes on 6 stationary phases at 403 K are listed in Table 2. From the comparison of the retention and entropy index data at 403 K, it follows that, if dI/dT < 0, then I < I(S) and, if dI/dT > 0, then I > I(S) (the more general case). This is in agreement with Eq. (13). To the contrary, the temperature dependence of the

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87

Table 2 Kov´ats retention indices, I and entropy indices, I(S) of 32 characteristic compounds on 6 phases at 403 K Solute

Stationary phases C78

2,2-Dimethylbutane 2,3-Dimethylpentane 2,3,4-Trimethylpentane 1-Hexene 2-Hexyne Cycloheptane Benzene Ethylbenzene 1-Fluorohexane 1-Chlorohexane 1,1,1-Trifluorodecane 1-Cyanopropane 1-Nitropropane 1-Acetoxybutane 1-Pentanol 2-Pentanol 2-Methyl-2-butanol 2-Butanethiol 2-Butanone Pentanal Dibutyl-ether Fluorobenzene Hexafluorobenzene Bromobenzene Pyridine Hexamethyldisiloxane 1,4-Dioxane cis-Hydrindane Naphthalene 2,3-Dimethylpyridine Nitrobenzene Anisole

POH

PCN

PCl

MTF

TMO

I

I(S)

I

I(S)

I

I(S)

I

I(S)

I

I(S)

I

I(S)

540.8 679.4 765.1 585.9 642.0 837.5 677.2 875.4 656.8 843.7 920.9 587.0 660.5 739.4 698.3 644.5 597.5 716.6 537.6 646.9 854.4 664.9 546.8 960.0 724.4 597.4 670.1 1035.6 1214.1 934.3 1049.4 909.0

497.5 636.0 709.3 559.9 651.9 662.7 562.0 747.5 653.3 774.1 1014.3 531.9 582.1 762.4 659.8 626.0 543.0 579.4 502.5 586.3 851.9 565.0 648.4 738.3 575.8 712.8 559.8 793.5 895.9 798.4 820.4 781.4

541.1 679.9 766.4 588.5 655.8 841.6 694.2 891.8 669.8 860.1 932.2 642.9 706.1 782.3 766.2 704.8 653.3 733.2 583.7 688.8 870.6 682.7 555.4 982.2 787.8 597.1 717.4 1041.1 1248.1 1004.2 1095.7 935.7

487.5 624.9 698.4 570.8 658.4 664.7 547.7 743.5 662.0 768.9 1032.6 617.9 623.3 831.9 1007.4 897.1 826.2 643.1 602.5 712.9 888.7 567.4 646.2 734.7 779.6 688.1 649.1 790.2 975.1 1012.8 869.0 813.9

540.8 679.5 765.7 589.9 658.1 839.9 701.8 899.2 682.5 870.8 947.5 675.5 746.7 781.1 764.8 699.8 646.7 742.2 594.3 697.4 867.0 695.8 577.9 995.0 778.1 597.8 710.8 1038.9 1257.0 984.9 1131.1 951.9

503.4 642.4 703.3 590.1 687.9 657.8 578.2 756.1 680.4 789.5 1047.3 640.7 709.8 811.5 819.3 741.1 669.1 652.1 598.4 668.5 867.3 601.6 680.8 771.1 647.5 708.0 613.6 793.6 906.3 852.6 898.7 828.9

540.9 680.0 765.5 588.0 648.3 839.0 686.7 884.8 666.2 853.4 928.4 615.5 687.9 754.0 715.0 659.3 610.9 727.0 556.8 664.9 858.7 675.9 554.3 972.9 743.8 596.9 684.6 1038.1 1231.5 952.2 1077.6 924.7

504.9 636.2 696.0 572.6 657.7 660.1 546.7 744.6 665.4 776.4 1027.5 568.0 612.5 779.0 680.6 622.9 564.2 607.5 544.9 621.3 862.1 568.0 656.5 747.0 586.5 719.0 582.7 804.3 905.8 804.1 853.0 798.1

542.2 688.4 766.3 586.7 645.8 835.6 684.8 882.3 667.1 852.0 939.1 618.8 687.6 757.3 713.6 659.9 610.6 721.0 560.5 665.7 858.9 674.7 563.7 966.0 742.1 604.6 684.2 1033.8 1224.8 950.1 1081.9 921.8

494.2 630.4 697.0 566.3 670.9 660.9 552.4 744.4 668.2 781.9 1032.9 591.1 628.5 788.5 685.9 637.9 597.0 597.2 563.8 640.7 866.5 573.7 627.1 731.4 618.7 695.7 584.4 786.9 911.6 806.5 892.6 810.2

541.8 688.4 766.4 593.3 665.0 840.5 706.1 902.9 684.5 873.8 950.5 669.4 747.3 785.4 797.9 727.5 669.8 746.7 590.2 696.1 869.2 704.8 583.7 1002.9 781.0 602.3 717.5 1040.2 1262 983.2 1136.6 957.1

492.8 634.7 700.2 574.7 681.5 648.8 579.4 769.1 688.1 799.8 1068.1 638.0 701.2 812.1 906.3 826.9 738.2 649.0 583.4 675.8 872.8 613.3 711.8 792.5 647.7 723.0 618.1 804.2 948.7 835.5 915.6 843.5

Solutes with negative dI/dT or dI(S) /dT are indicated in bold. The experimental I data are taken from refs [12,40–43], the I(S) values were calculated by Eq. (12). Symbols of stationary phases see Section 3.

entropy index does not display any correlation with that of the retention index. For the cyclic compounds, with the exception of hexafluorobenzene, I(S) < < I (I – I(S)) ≈ 100 index units) (Table 2), as S for these compounds is more positive than that for the reference n-alkanes (the nominator is positive, and thus I (S) < 0), in agreement with the larger entropy penalty for the n-alkane, as the long chains can be more structured in the solution than the cyclic molecules, the liquid structure of which is destroyed during dissolution [45]. The temperature dependence of the retention index in the data set is about ±0.1 index unit/K. The temperature dependence of the entropy index, dI(S)/dT, is linear in the temperature range 363–423 K. Generally, it is slightly negative or positive (±0.01–0.3 entropy index unit/K); the larger absolute values are exhibited by the substituted aromatic compounds and cishydrindane. Alcohols have large, (−0.5–(−5)) negative dI(S)/dT values. Particularly large temperature dependence in the entropy index was observed on the POH phase. Fig. 1 presents retention indices, calculated at different temperatures with Eq. (14) and entropy indices, calculated with

Fig. 1. The Kov´ats retention index, I, (open symbols), and the entropy index, I(S), (closed symbols), for benzene (), 1,1,1-trifluorodecane () and 2-pentanol () on POH stationary phase as a function of temperature, T.

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The correlation equations seem to be quite linear, but the slope decreases slightly with temperature (Eqs. (15)–(17)): dI = (0.00257 ± 0.000009)(I − I(S)) dT +(−0.0049 ± 0.0106) at 363 K, n = 192; r = 0.9989; F (1, 190) = 90218; s = 0.0131

(15)

dI = (0.00242 ± 0.000009)(I − I(S)) dT +(0.000892 ± 0.00113) at 403 K, n = 192; r = 0.9986; F (1, 190) = 69958; s = 0.0135

Fig. 2. Temperature dependence of the Kov´ats retention index, dI/dT, vs. the difference of the retention index, I, and the entropy index, I(S), for 32 solutes on 6 stationary phases at 363 K. Number of data points: 192.

Eq. (12) for benzene (I > I(S)), 1,1,1-trifluorodecane (I < I(S)) and 2-pentanol at different temperatures. For 2-pentanol the large differences in the retention and entropy indices gradually decrease with increasing temperature, at the minimum the difference is zero and finally the differences start to increase with temperature with opposite sign (I > I(S)). This minimum behavior is due to the very large solvation heat capacity changes of alcohols (e.g. 2-pentanol) as compared with the reference nalkane. To test the new Eq. (13), G(CH2 ) was determined from the slope of G(n-alkane) versus the number of carbon atoms and S(CH2 ) from that of S(n-alkane) versus the number of carbon atoms, respectively. Ratios S(CH2 )/G(CH2 ) are shown in Table 1. Next dI/dT was depicted versus I − I(S) (Eq. (13)) for all 32 solutes on all 6 phases at 363 and 423 K (Figs. 2 and 3, respectively). The very good correlations suggest that the relationship may be general for all GC stationary phases and for all solutes.

(16)

dI = (0.00238 ± 0.00001)(I − I(S)) dT +(0.00201 ± 0.00168) at 423 K, n = 192; r = 0.9969; F (1, 190) = 30904; s = 0.0196

(17)

where r is the correlation coefficient, n is the number of data points included, F is the result of the Fischer statistics and s is the standard error of estimation. The slopes of Eqs. (15)–(17) agree well with the ratio S(CH2 )/G(CH2 ) calculated from the data set (Table 1). The slight decrease in the slope with increasing temperature (Eqs. (15)–(17)) is caused by the small temperature dependence of S(CH2 )/G(CH2 ). Further statistical evaluation (residual analyses) of Eqs. (15)–(17) and Figs. 2 and 3 show that: (a) Eq. (13) is not perfectly linear, i.e. there is some deviation from linearity (higher residuals) for compounds with higher positive (naphtalene on all, cis-hydrindane and nitrobenzene on some phases,) and negative (hexamethyldisiloxane, hexafluorobenzene on all phases and alcohols on POH) dI/dT values. (b) the intercept at 403 and 423 K is not significant (significance level, p > 5%), i.e. the fitting with an one parameter equation is better than the two parameter equation, in agreement with Eq. (13), which is an one parameter equation. The one-parameter fitting at 403 K results into dI = (0.00243 ± 7.8 × 10−6 )(I − I(S)), n = 192; dT r = 0.9990; F (1, 191) = 95001; s = 0.0135

Fig. 3. Temperature dependence of the Kov´ats retention index, dI/dT, vs. the difference of the retention index, I, and the entropy index, I(S), for 32 solutes on 6 stationary phases at 423 K. Number of points: 192.

(18)

According to Eq. (13), the temperature dependence of the retention index is closely related to the entropy index, which is connected with the change in the structure of the solution during the transfer of solutes or n-alkanes from the gas phase to the liquid phase. These changes can hardly be studied independently by GC methods. However, the solvation of non-electrolytes has been intensively studied by calorimetric methods [45,46]. Among the thermodynamic functions, the excess entropy is determined rather by the general randomness, while the excess heat capacity, is more sensitive to the structural change in the solution [47].

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Fig. 4. Temperature dependence of the retention index, dI/dT, vs. the difference in solvation heat capacities, ␦Cp for the 32 solutes and the reference hypothetical alkanes, on the C78 stationary phase at 403 K. The symbols of the alcohols are circled. The alcohols were excluded from the linear fitting. Number of points: 32.

If we accept that n-alkanes behave ideally in the 6 phases, and there is no special interaction with the stationary phase, then the possible structural differences observed in solvation (e.g. outlier points) are not due to the behavior of the n-alkane, but to the solute. In our case, therefore the difference of the molar solvation heat capacities of the solute x and that of a hypothetical n-alkane, ␦Cp should be a more appropriate function for characterization of the structural differences during solvation, if any, than the entropy function. The hypothetical n-alkane with carbon number ξ has the same retention index at the given temperature than the solute, i.e. ζ = Ix /100 and hence Ix (T) = Iζ (T) and ␦Cp = Cp,x − Cp,ζ . The solvation molar heat capacity of the hypothetical nalkane, Cp,ζ can be calculated by Eq. (19). Cp,ζ = (Cp,z+1 − Cp,z )

(Ix − 100z) + Cp,z 100

(19)

The calculated ␦Cp is a measure of structure formation and contributes to the temperature dependence of the retention index. Fig. 4 depicts dI/dT versus ␦Cp on C8 phase. The statistical evaluation shows that the correlation equation for the solutes with the exception of alcohols on C78 phase is better without an intercept: dI = (= 0.0257 ± 0.00021)␦Cp , dT n = 29; r = 0.9985; F (1, 28) = 14951; s = 0.0135

(20)

The fitting indicates a good correlation with the exception of the alcohols, however some curvature can be observed. The largest deviation for alcohols is observed on the POH phase. The findings for all the solutes and phases (with the exception of the alcohols) are depicted in Fig. 5. Some outlier points are from hexamethyldisiloxane and hexafluorobenzene. The linear fitting for all solutes with

89

Fig. 5. Temperature dependence of the Kov´ats retention index, dI/dT, vs. the difference in solvation heat capacities, ␦Cp of the 32 solutes and the reference hypothetical alkanes, on all stationary phases at 403 K. The alcohols were excluded from the linear fitting. Number of points: 174.

the exception of alcohols on 6 phases at 403 K results in Eq. (21): dI = (−0.0250 ± 0.00016)␦Cp , dT n = 174; r = 0.9947; F (1, 172) = 24316; s = 0.0259 (21) The exceptional case of alcohols may support the hypothesis that some special structural effect exists for alcohols (as e.g. aggregate formation [48]) which is not present in the partitioning of other medium polar compounds. Further thermodynamic studies are necessary to understand this effect. Eq. (13) is more suitable form for characterization of the temperature dependence of the retention index than Eq. (21), but the latter is more indicative for explanation the structural effects, which determine the retention index or its temperature dependence. 5. Conclusions The new equation dI/dT = (S(CH2 )/G(CH2 ))(I − I(S)) excellently describes the temperature dependence of the retention index as a function of the difference of the Kov´ats retention index and the entropy index. The general relation between the retention and the entropy index is that, if dI/dT < 0, then I < I(S), and if dI/dT > 0, then I > I(S). For cyclic compounds, the entropy index is about 100 units smaller than the retention index. A minimum in the I versus T graph is observed at a temperature, where the retention index equals to the entropy index. Eq. (13) works excellently for all the solutes and phases studied at the given temperature. While the plots of dI/dT versus (I − I(S)) do not demonstrate clearly significant differences in partitioning mechanism, dI/dT versus ␦Cp suggests an exception for alcohols.

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