Prediction of Gas Chromatographic Retention Times of Esters of PDF 44-3-148.pdf

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The linear free energy of solution (ΔG) relationship (ΔG = ΔG o zδG) for compounds of different carbon atoms (z) in the same homologous series is expanded and modified to cover compounds with two dif ferent hydrocarbon side chains. The expanded equation is successfully used to predict the retention times (t R of standard esters of long chain alcohols and fatty acids of different chain lengths in both isothermal and temperature- programmed gas chromatography (TPGC). Approximately 90% of the 125 predicted t R values have a difference of less than 1.00% from the actual t R and the highest difference is 1.26%. Two different temperature gradients in TPGC are tested. The expanded equation can be used to forecast the tR of TPGCwith good accuracy. The highest difference is ± 1.40% and ± 1.00% for the temperature gradients of 2°C and 4°C/min, respectively. However, the increments in free energy per carbon atom (zδG) of the alcohol and acid are approximately equal but have slightly dif ferent temperature sensitivities. Therefore, it is very dif ficult to separate esters of different acid and alcohol chain length but with the same total carbon numbers. Furthermore, the difference in temperature sensitivities for the acid and alcohol side chains renders them to be inversely eluted at different temperatures.

Introduction

Kovats" retention index system has been used extensively as an aid in gas chromatographic (GC) identification of organic com- pounds (1-3). Using n-alkanes as the references has a draw back, especially for the identification of high molecular weight and polar compounds, which requires high molecular n-alkanes (4). Thus, other similar systems, which use different standard refer- ences compounds [e.g., equivalent chain length, carbon number (5,6), or ketone number (7)] have been set up. Waxes are ubiqui- tous in nature, but there is no identification system for them. Furthermore, retention indices are not available. With the price of GC-mass spectrometers (MS) low enough now that many lab-

oratories can afford them, waxes are then identified by their massspectra (8-10). Otherwise, they are usually identified by compar-ison of their retention times (t

R ) with reference waxes, which are difficult to obtain in chemically pure forms. Therefore, tentative identification of a wax, for those without access to an MS, requires standar d wax as the r efer ence. However, beeswax may be hydrolyzed to long chain alcohols and acids (9), which are easier to identify, and the relatively expensive reference waxes are avoided, but the identity of the wax is lost. With recent advances in knowledge of solute migration along the GC column, the tR of several solutes can be forecast with good accuracy, but there is no report on the prediction of t R of waxes. In this study, a thermodynamic model is proposed to predict the t R of waxes of different alcohols and fatty acids. The basic equation pr oposed by Krisnangkura et al. (equation 1) (11), which is used to predict the t

Rof fatty acid methyl esters (FAMEs) of fixed

alcohol chain length, is expanded to cover alcohols of variable chain lengths. Eq. 1 where a, b, c, and dare thermodynamically related column con- stants. The well-known free energy of solution (ΔG) equation of James and Martin, equation 2, is further expanded to equation 4. Eq. 2 where z i is the carbon number of fatty acid. ΔG o is the free energy of a solution of hypothetical acid of a zero carbon atom (with a fixed number of carbon atoms of the alcohol). δG iis the incre- ment in free energy of solution per carbon atom of the acid. When the alcohols vary, James and Martin"s equation is repeated as shown in equation 3. Eq. 3 where z j is the carbon number of alcohol, and ΔG oo is the free energy of a solution of hypothetical ester of a zero carbon atom of both alcohol and acid. δG j is the increment in free energy of solu- tion per carbon atom of the alcohol. 148

Abstract

Prediction of Gas Chromatographic Retention Times

of Esters of Long Chain Alcohols and Fatty AcidsKaruna Katsuwon, Kornkanok Aryusuk, andKanit Krisnangkura*

Biochemical Division, School of Bioresources and Technology, King Mongkut"s University of Technology, Thonburi, 83 Moo 8,

Tientalay 25 Rd., Takham, Bangkhuntien, Bangkok 10150, Thailand Reproduction (photocopying) of editorial content of this journal is pr ohibited without publisher"s permission. Journal of Chromatographic Science, Vol. 44, March 2006 * Author to whom correspondence should be addressed: email kanit.kri@.km itt.ac.th. ln k= a+ bz+

ΔG= ΔGo

z i δG i ΔG o ΔG oo z j δG j c+dz T T Downloaded from https://academic.oup.com/chromsci/article/44/3/148/482012 by guest on 03 July 2023 Journal of Chromatographic Science, Vol. 44, March 2006 149
If there are no interactions between the two side chains of the acid and alcohol, equations 2 and 3 are directly combined. Eq. 4 Fr om basic thermodynamics, the free energy of solutions in equation 4 can be expanded to: Eq. 5 or Eq. 6 where Eq. 7 Eq. 8 Eq. 9

Eq. 10

Thus, equation 6 is proposed for prediction of t

R of waxes of variable chain lengths in the acid and alcohol moieties.

Experimental

Fatty acids (14Ð18 carbon atoms) and long chain alcohols (14Ð22 carbon atoms) were purchased from Sigma Chemical Co. (St. Louis, MO). Natural beeswax was obtained from a grocery stor e (Bangkok, Thailand). Esterification of long chain fatty acid and long chain alcohol was modified from Kalayasiri et al. (12) for methyl ester with 2% H 2 SO 4 as the catalyst, but the reaction time for esterification of long chain alcohols and acid was extended to

24 h at 80

°C.

GC GC analysis was performed on a Shimadzu (Kyoto, Japan) model 17A. The instrument was equipped with a flame ionization detector and split/splitless injector. Separation of the esters was perfor med on an AT-5 high-temperature capillary column (10-m ¥0.1-mm i.d., 0.1-µm film thickness) from Alltech Assoc. (Deer field, IL). Nitrogen was used as carrier gas at the flow rate of

0.18Ð0.2 mL/min. Injector and detector temperatures were set at

350°C. The column oven was held isothermally at intervals

between 290 °C and 310°C. Temperature programming condi- tions are reported in the text. Δetermination of the constants of eθuation 6 Determination of the six numeric constants of equation 6 can be done by holding each variable constant at a time.

When the fatty acid carbon number (

z i ) is fixed, equation 6 is reduced to:

Eq. 11

where

Eq. 12

Eq. 13

Equation 11 is similar to that proposed by Krisnagkura et al. (11). Thus the four numeric constants of equation 11 can be solved as described. Combining terms (with constant z j ), equation

11 is further reduced to:

Eq. 14