An Experimental Study of Column Efficiency in Liquid-Sol id Adsorption Chromatography HETP Values as a Function of Separation Conditions L. R. Snyder Union Oil Company ,of California, Union Research Center, Brea, Calif. The separation efficiency of columns in liquid-solid adsorption chromatography has been studied in terms of column theoretical plate numbers. Height equivalent of a theoretical plate (HETP) values have been studied as a function of all the important separation variables associated with normal liquid-solid column chromatography: sample retention volume, sample size, adsorbent type, adsorbent activity, adsorbent particle size, solvent type, solvent flow rate, column packing procedure, and column diameter. Bed permeability values are given also in order to establish the column pressure drop required in a given separation. These data permit the calculation of theoretical plate numbers for any set of operating conditions and the rapid selection of optimum conditions for a given separation. Comparisons of the present data with contemporary theory and previous experience show certain interesting anomalies.
THERELATIVE SEPARATION of a mixture by any chromatographic process is determined by two separate factors: the selectivity of the process or the relative differences in the affinities of different sample components for the stationary phase--e.g., the adsorbent-and the efficiency of the process or the number of theoretical plates in the chromatographic bed. In the case of liquid-solid adsorption chromatography (LSAC) much attention has been given to selectivity as a function of sample type and separation conditions, and a good understanding of this aspect of such separations now existse.g., (I). Much less is known concerning the basis of bed efficiency in LSAC separation and its variation with experimental conditions. A vast amount of experience which is related to separation efficiency has been acctimulated during the past 30 years, but almost all of this information is qualitative in nature and of questionable validity--e.g., (2) for a review. In most of these cases the complexity of the chromatographic systems studied precludes firm conclusions, or the separations are so far from optimum that extrapolation of the results to reasonably high efficiency separations appears unwarranted. More recently a comprehensive theory of bed efficiency in liquid-solid chromatography has been developed by Giddings (3-5). See also the discussion of Horne et a f . (6). Unfortunately certain of the physical parameters involved in this treatment have not yet been determined with sufficient precision to permit better than order-of-magnitude estimates of bed plate numbers or HETP values (bed length (1) i.R. Snyder, “Chromatography,” 2nd ed.. E. Heitmann,
EL
Reinhold, New York, 1967, chap. 4. (2) Ibid.,chap. 5 (3) J . C. Giddings, “Dynamics of Chromatography, Part E. Priaciples and Tneory,” Dekker, New York, 1965. ( 4 ) J. C . Giddings, J . Chromatog., 13, 301 (1964). ( 5 ) 3 . C . Giddings, ANAL.CHEM., 37,60 (1965). ( 6 ) D. S. Horne, J. H. Knox, and L. !VcLarcii, S e p S.;., I..53. (1966).
498 *
ANALYTICAL CItiEMkTR”
divided by bed plate number). At the same time the contribution of bed packing structure to bed efficiency in liquidsolid chromatography seems particularly important (particularly in the light of the present investigation), yet this is surely the most complex and least well understood aspect of such separations. For these reasons a thorough experimental study of bed efficiency in liquid-solid chromatography seems long overdue. The present study is limited to the measurement of column HETP values over a range 0:’ conditions that are either typical of present separations or which are readily attainable. The possibility of marked improvement in separation efficiency by extreme departures from normal operating conditions has been noted by vaiious workers; e.g., turbulent flow (3), capillary columns (7), or “accelerated microparticulate bed liquid chromatography” (8). These separation modes, although promising, are beyond the present capability of most chromatographers. EXPERIMENTAL
Materials. The solvents used were 99% plus pure (Phiiiips Petroleum Co.) and were further purified by passage over activated silica gel. Alcoa F-20 alumina was screened into approximate, narrow-mesh fractions, heated in air at 400 C , and deactivated with 4% added water. Davison Code ti2 silica gel was similarly screened, heated in air at 170‘ C for a minimum of 2 hours, and deactivated with varying amounts of added water (4x in most cases). Portions of the final adsorbent fractions were rescreened to determine the exact adsorbent particle size distribution. The range in particle sizes about the mean was of the order of *lO.-2!lz (standard deviation) for each fraction. Equipment. The chromatographic unit was constructcd of standard stainless steel parts. Two connected solvent tanks (5OOO-psi rating) of 2100-ml total capacity are pressured by a compressed nitrogen cylinder and are connected t o a sample introduction unit (SIU). The SIU consists of a 12-cm length of 0.125-inch tubing (0.3-mi voiume) connected (Ai; each side to 3-way valves which are in turn connected to 2-way valves. The 3-way valve on the solvent tank side is equippeci with a glass sample holder, and one line from the other ?-way valve leads to E waste container. The chromatographic column is connected directly to the SIU on tnz side awal from the solvent vesseis Ali valves are low hoid up taper Seal Series, High Pressure Eiquipment Co., h i e , Pa.), arid the total volume withir? the valves ana connec:ir!u tuhing, !xtween column and SIU IS less than 0.5 mi. T h e cnlunin: ;!.re 4-foot (122 cm.) iengths or stainless steef t u h q or p i p of varying diameteyi, fitted with !ow hold-up COIIIXC~.ions kt e m : end. Largr-diameter columns (;.d. > C.77 cm arc taper?: at each end. Most separations were carried out e i t h diameter coiumrIs. The column is connected ’n:.! (2. T&JR tubing IO a iletectw: a. continuous i
fractometer (Waters Associates, Framingham, Mass.) with a sensitivity of lo-’ refractive index units, equipped with a 100-mV recorder of 1 second full scale deflection time. Total solvent volume between the column end and the detector cell ( Ve)was 3.0 ml. Procedure. Solvents were normally deaerated and charged by vacuum to the solvent tanks. However, deaeration is unnecessary if a slight pressure is maintained on the outlet side of the detector during separation. For separations on silica the solvent was pre-equilibrated with water to give 50% relative saturation, in order to avoid drying the deactivated adsorbent during separation--e.g., (9). Columns were packed with adsorbent in various ways. The normal procedure involved si:epwise addition of dry adsorbent with manual vibration of the column by horizontal tapping and gentle bouncing. T h IS was continued until no further settling of the column packinit occurred. Other packing procedures are described in the t’ext. The packed column was attached to the unit and solvent flow through the column was begun under nitrogen preswre. Deaeration of the column was facilitated by momentary constriction of the exit line from the detector at interbals, until solvent issuing from the detector was free of bubbles. The desired flow rate for a given separation was established by varying the pressure on the solvent tanks and/or the constriction of the exit line from the detector. No significant changes in solvent flow rate during the course of a separation were observed. The two 2-way valves were next turned off, the sample holder was filled with sample, and the two 3-way valves were opened. After 2-3 ml of sample had flowed through the SIU, the 3-way valves were closed. The 2-way valves were opened and the recorder was started. Solvent flow was continued until the sample had cleared the column. All separations were ,3t 24” f 2“ C. The sample was in a solution of the solvent used for separation, at a concentration sufficientto give a sample size of gram per gram of silica or 5 x 1 0 - ~gram per gram of alumina. Sample sizes were somewhat smaller for separation on 0% H20-Si02: In every case, sample sizes were well below the linear capacity of the column-i.e., sample retention volumes were independent of sample size. Calculation of HETP Values. For the separation of a given compound (usually dibenzyl on silica, naphthalene o n alumina) under a certain set of conditions the total plate number N of the column was calculated from elution bands in the usual way:
iV
=
16(R’/~)~.
(1)
The retention volume R ‘ is the total volume required to elute the band center, minus P‘-i.e., corrected for the holdup in the tubing between ccilumn end and detector cell. w is the base width of the barid (equals 4 times the variance), determined by drawing tangents to the sides of the band and measuring the eluate ,dolume between intersects on the base line. All elution bands observed in the present study were symmetrical, except for a very slight skewing or tailing in the usual direction. H E r P values were calculated in centimeters, equal 122/N. Extra-column contributions to band widening were studied by connecting the lines from the two column ends (eliminating the column) and passing a sample band through the SILI and detector in the usual way. The normal 0.3-ml sample was found to broaden in the lines between the SIU and detectcr cell to give an approximately Gaussian band of width K’ c-iual 1.8 f 0.1 mi (independent of solvent viscosity 3nd ~ J Wrate). Reported values of H E T P a r e L-cxrected r i ;iis extra-column contribution to I.,an.d wltl::niiig; :.e., i-TP (true) = HETP {observed) ,:iE7’.~iextr : - L ~ U ~ U T I ~ :f. f E P iex?ra-coiumn) is g:veri as
1.0 -
-
0.8-
5
c.
n 0.6 -
b W
I
0.4
-
0.21 I .o I .5 v (cm /sec )
0.5
2.0
Figure 1. Linear dependence of HETP on solvent Row rate Elution of dibenzyl from 4% H20-Si0* by pentane 0 dpequals 0.0181 cm dp equals 0.0128 cm V dp equals 0.0057 cm 122/N’, where N‘ is equal to 16 (R’/1.8)*. In only a few cases was HETP (true) significantly different from HETP (observed). RESULTS
ERect of Solvent Flow Rate on HETP. The variation of HETP with solvent flow rate for any chromatographic system can usually be expressed in terms of the well known van Deemter equation: HETP = A f B/v
+ CU.
(2)
The A term of Equation 2 refers to contributions to HETP from so-called “eddy diffusion,” E / u arises from longitudinal diffusion of the band along the column in the moving phase, and CUrepresents slow mass transfer of sample between moving and stationary phases. This simple dependence of HETP on solvent flow rate may be complicated by “coupling” effects in some systems - e . g . , (3)-but the slower diffusion of sample in the liquid phase makes coupling less important in liquid-solid chromatography. As we shall see, the A term of Equation 2 for the systems currently under study is invariably larger than predicted, while any effect of coupling should tend to give smaller values. We shall accordingly ignore the possible effect of coupling on the present separations. Because of slow diffusion in the liquid phase, the B term of Equation 2 is expected to be small. In most practical separations by liquid-solid column chromatography (IO) it is desirable to operate at solvent flow rates u such that s/(;makes a negligible contribution to HETP, and under these conditions Equation 2 reduces to HETP
=
A
- c‘u.
(24
A s illustrated in Figure 1 , for somc representative separations carried out in the present study, Lquation 2a provides satisfactory description of the depzt2dence of N.CTP on c cver jhc: r’jnge *)f flow rates irwestigated i n the present study,
I "
A
8
I
-1
-- 80 60
!/
-
- 40 -
U
n I
E
c 0
- 20 ' N
-9 Y
-10
i./ P i -
0.6
2.8 dpo'60
10-5
10-4 WT SAMPLE WT ADSORBENT
10-3
Figure 2. Dependence of HETP and sample retention volume on sample size Dibenzyl (sample), pentane (solvent), 4.0 H20-SiO2, mean particle size dp0.0066 cm, u equals 0.47 cm/sec O R W HETP
-"
0.30
0.2
0.20
0.15
1
I
/, .,-, , , I 1
' '
0.01 dp(cm)
-5
2
L'O.10
0.IO
Figure 3. Variation of A , C, and K with mean particle size d, of the adsorbent Elution of dibenzyl from 4% H20-SiOz by pentane V
.c
A
o K
Assuming that B is of the same magnitude as the sample diffusion coefficient (3), -10-6 cmZ/second (cf. I]), it can be calculated that the contribution of B/o to HETP is negligible ( K1) L = column length (cm) = number of repeat determinations n = number of theoretical plates in an adsorbent N bed; defined by Equation 1 = maximum value of N achievable under some NUUX set of limiting operating conditions (defined for optimum resolution, Kzequals 2 Vo/w> = pressure drop across column (atm) P R' = sample retention volume (ml); the volume of eluate required to elute the band center from the column R = sample equivalent retention volume (ml/gram); equal to (R' V o ) / W R" = linear isotherm value of R_ (ml/gram) = retention volumes (R')of bands 1 and 2 (Rz> R1, Rz
-
R 1)
R.
RF t u
V0 W w1,
resolution function; defined in Equation 3 of following paper = distance traveled by sample along bed (in TLC), divided by distance traveled by solvent front (relative to sample origin) = time (sec) required to elute center of band 2 = solvent linear flow rate through column (cmisec) = void volume of column (ml); equal to the total volume of solvent plus sample in a saturated column = base line width (ml) of an eluted band = base line widths ( w ) of bands 1 and 2 = weight of adsorbent in column (grhms) = a constant less than one = linear capacity of the column (grimsjgram); equals the weight of sample (grams) per gram of adsorbent for which & equals 0.9 R " = solvent viscosity (centipoise) = solvent viscosity (centipoise) at 20" C =
w2
W x
eo.l Y v20
ACKNOWLEDGMENT
The assistance of F. 0. Wood in the present investigation is appreciated. The author is also obliged to G . H. Stewart of Gonzaga University for a prepublication copy of his paper, and to G. H. Stewart, J. C . Giddings (University of Utah), and J. C . Sternberg (Beckman Instruments) for helpful comments in connection with the present and following papers.
1967.
-
(21) G . Hesse and H. Engelhardt, 1. Chromatog., 21,228 (1966).
