Evaluating Dispersion in Gel Chromatography Dispersion Due to Permeation Richard N. Kelley’ and Fred W. Billmeyer, Jr. Departments of Materials and Chemistry, Rensselaer Polytechnic Institute, Troy, N . Y . 12181
Dispersion (peak broadening) in gel chromatography was measured under identical operating conditions with nonporous and porous column packings. The difference between the results, the contribution of permeation alone to dispersion, is a linear function of flow rate, suggesting that the separation may be diffusion-controlled with a linear permeation isotherm. For a porous glass (Porasil) packing, dispersion arising from permeation is the major contribution to peak broadening; for a poly(styrene-divinylbenzene) (Styragel) packing, dispersion due to mobile-phase effects is predominant. These results are qualitatively explained in terms of differences in the gel structures of the two packing materials.
GEL CHROMATOGRAPHY, which we take to include gel filtration ( I ) , gel permeation chromatography (GPC) (2), and molecular sieve chromatography (3), is a technique for separating molecular species according to their volumes in solution. Mass transfer of solute is effected between the mobile liquid phase and the pores of porous column packings (gels), larger solute molecules being able to penetrate a smaller fraction of the internal volume of the gel and thus being eluted earlier than smaller molecules, in contrast to gas chromatography. Both the efficient design of gel chromatographic systems and the interpretation of results require understanding of the basic factors affecting resolution and their relation to operating variables. Two major problems are the prediction of elution volume and of dispersion or peak broadening. Others have attacked the prediction of elution volume, calculating distribution coefficients from models based o n steric exclusion (4-6), restricted diffusion (7), simple diffusion (8), o r thermodynamic considerations (9-11). Our efforts fall in the group of theories (12-25) developed to describe dispersion in gel chromatog-
Present address, Roll Coating Division, Eastman Kodak Co., Kodak Park Works, Rochester, N. Y. 14650. (1) J. Porath and P. Flodin, Nature, 183, 1657 (1959). (2) J. C. Moore, J . Polymer Sci., A-2, 835 (1964). (3) G. K. Ackers, Biochemistry, 3,723 (1964). (4) J. Porath, Pure Appl. Chem., 6, 233 (1963). ( 5 ) P. G. Squire, Arch. Biochem. Biophys., 107, 471 (1964). (6) T. C. Laurent and J. Killander, J . Chromatog., 14, 317 (1964). (7) G. K. Ackers and R. L. Steere, Biochem. Biophys. Acta, 59,
137 (1962). (8) W. W. Yau and C. P. Malone, J . Polymer Sci., B-5,663 (1967). (9) A. J. de Vries, Preprint 139, IUPAC Meeting, Prague, 1965. (10) E. F. Casassa, J . Polymer Sci., B-5, 773 (1967). (1 1) E. F. Casassa and Y. Tagarni, Macromolecules, 2, 14 (1969). (12) W. B. Smith and A. Kollmansberger, J . Phys. Chem., 69, 4157 (1965). (13) J. B. Carrnichael, Macromolecules, 1,526 (1968). (14) J. C. Giddings and K. L. Mallik, ANAL.CHEM.,38,997 (1966). (15) F. W. Billmeyer, Jr., G. W. Johnson, and R. N. Kelley, J . Chromaton., 34, 316 (1968). (16) F. W. -Billmeyer, Jr., and R. N. Kelley, J. Chromatog., 34, 322 (1968). (17) R: N. Kelley and F. W. Billrneyer, Jr., ANAL.CHEM.,41, 874 (1969). (18) J. Coupek and W. Heitz, Makromol. Chem., 112, 286 (1968). (19) W. Heitz and J. Coupek, “Column Eficiency in GPC,” 5th International Seminar on Gel Permeation Chromatography, London, England, May 19-22, 1968.
raphy. Many approaches to the solutions of both problems have recently been reviewed (26). We have separated the causes of dispersion into two independent contributions, mobile-phase effects arising outside the gel and mass-transfer effects. With contributions from the instrument itself suitably minimized (16), we studied dispersion in columns packed with nonporous glass beads (17), showing that the axial dispersion observed is satisfactorily described by a model (15) incorporating molecular diffusion, eddy diffusion, and velocity-profile effects. In this paper we describe experiments with porous glass column packings, using operating conditions identical to those utilized in the studies with nonporous beads. We subtract the contribution of mobile-phase effects from the over-all peak broadening, leaving only the contribution arising from permeation. The major operating variables examined are porosity of the packing, solute diffusivity, and solvent flow rate. Differences in the broadening behavior of porous glass (Porasil) and porous poly(styrene-divinylbenzene) (Styragel) packings are discussed in terms of the pore structures of these gels. EXPERIMENTAL
Apparatus and Materials. A Waters Associates (Framingham, Mass.) Model 100 gel permeation chromatograph was used with toluene as the solvent at room temperature. A microrefractometer detection cell having a volume of 10 p1 was used with a ‘/Ie-inch null glass. The flow system of the chromatograph was slightly modified as previously described (16) to permit accurate dispersion measurements with single 4-foot length columns with inside diameter of 0.305 inch. Bead sieving procedures and column packing techniques were identical with those employed previously (17). Porous silica beads [Porasil, manufactured by PechineySaint-Gobain (27) and distributed by Waters Associates] were used. Their preparation was identical to that utilized for the nonporous beads (17), except that after solvent washing and drying, the beads were degassed twice to a pressure of 25 microns to remove entrapped air. While the beads were still under vacuum, toluene was introduced to ensure that the internal pore structure became well saturated with solvent. The beads, saturated with toluene, were then utilized for column packing. Data obtained earlier (16) with poly(styrene-divinylbenzene) beads (Styragel, Waters Associates) are referred to. The six types of Porasil beads described in Table I were studied, covering a wide range of porosity. Photomicrographs of these beads after size separation showed them t o be well sieved and approximately spherical in shape. (20) W. Heitz and W. Kern, Angew. Makromol. Chem., 1, 150 (1967). (21) J. G. Hendrickson, J . Polymer Sci., A-2, 6, 1903 (1968). (22) M. LePage, R. Beau, and A. J. de Vries, J. Polymer Sci., C-21,119 (1968). (23) J. F. K . Huber, J . Chromatog. Sci., 7, 85 (1969). (24) L. H. Tung, J. Appl. Polymer Sci., 10, 375, 1271 (1966). (25) J. J. Hermans, J. Polymer Sci., A-2, 6, 1217 (1968). (26) K. H. Altgelt, in “Advances in Chromatography,’’ Vol. 7, J. C . Giddings and R. A . Keller, eds., Marcel Dekker, New York, 1968. (27) Pechiney-Saint-Gobain, French Patents 1,473,240, 1,475,929 (1967). ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
399
Characteristics of Porasil Beads. Average pore Type of Porasil Surface area, m*/g diameter, Ab A 480 100 B 200 100-200 C 50 200-400 400-800 D 25 E 4 800-1 500 F 1.5 1500 a Based on data of Waters Associates. Waters Associates designation. Table I.
Table 11. Characteristics of Porasil Columns
Type of porasil A B
Molecular weight Void fraction Plates/fta exclusion limitb 0.37 625 3.0 x 104 0.37 865 1.0 x 105 C 0.37 850 4.0 x 105 D 0.37 650 7 . 0 x 105 E 0.37 475 2 . 0 x 108 F 0.37 625 > 2 . 0 x 106 a Measured at 1 cc/min flow rate with cyclohexane solute. Approximate values based on polystyrene standards. See also Figure 1.
0 0.01
I
I
l
l
I
0.I REYNOLDS NUMBER
1.0
Figure 2. HETP us. Reynolds number for 120-140mesh Porasil columns Data for cyclohexane solute. Legend and conditions same as in Figure 1
diameter of the Porasil, the greater the molecular weight exclusion limit for the column. These curves break sharply at both the high and low molecular weight ends, indicative of a rather narrow pore-size distribution. To eliminate broadening of the chromatograms resulting from a distribution of molecular sizes, only the monodisperse solutes cyclohexane and hexatriacontane (Humphrey & Wilkinson, Inc.) were used. Procedure. The height equivalent to a theoretical plate, HETP, was used as a measure of column efficiency. BY measuring the retention time, t,, and broadening u of-an injected sample pulse, the number of theoretical plates was calculated as N = (tJu)*, and the HETP as LjN where L is the column length. Viscosity (viscous fingering) and concentration effects were minimized by using the lowest practical solute concentration, and sorptive effects were minimized by using relatively nonpolar solutes. HETP was measured as a function of Reynolds number, N R= ~ d,,Up/p, where d, is the effective particle diameter, U is the average interstitial velocity, p is the solution density, and p is the solution viscosity. From these data for a Porasil column the corresponding data obtained with nonporous beads was subtracted. The results, representing the broadening contribution due to permeation, were then subjected t o a least-squares analysis to determine the order and coefficients of the polynomial required for the best statistical fit of the data. Subtracting the mobile-phase contribution from the over-all HETP assumes that this contribution and that due to permeation are independent and additive.
Characteristics of the packed Porasil columns of 120-140mesh particle size are given in Table 11. The void fractions of these columns (0.37) agree fairly well with the void fraction of the 120-140-mesh nonporous glass bead column (0.39). An indication of the range in porosity of the various Porasils is obtained from the polystyrene calibration curves of these columns shown in Figure 1. The larger the average pore
Y W
IC
I
i?
W
3 K -I
I
Reynolds numbers, calculated from the average linear velocity of a nonpermeating solute, ranged between 0.04 and ~ 0.164 corresponded 0.5 for 120 to 140-mesh beads; N R = to a flow rate of 1 cc per minute. The average particle diameter was taken as 115 microns, based on the mesh size of the screens used. The density of the solutions was 54.3 pound per cu foot, and their viscosity was 0.555 cp.
3 W u
i
RESULTS AND DISCUSSION 0 ELUTION
V O L U M E (COUNTS)
Figure 1. Calibration curves for Porasil columns Polystyrene standards in toluene. Room temperature; flow rate Icc/min; 120-140-mesh particle size. 0, Porasil A ; 0 , Porasil B; A, Porasil C; A, Porasil D; 0,Porasil E; ., Porasil F 400
a
Results with Porasil Columns. HETP data obtained with the six Porasil columns covering a wide range of porosity and the two solute molecules are shown in Figures 2 and 3. The level of dispersion, as measured by HETP, for both cyclohexane and hexatriacontane increases sharply with increasing Reynolds number, but is approximately the same for a given solute regardless of the porosity of the column
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
loo,
I
I
I
/
/
I
POROUS GLASS 2 0
%
-.. L
-
4.
w 4.0 I
I.o
20 NON-POROUS GLASS
0
Figure 3. HETP cs. Reynolds number for 120-140-mesh Porasil columns Data for hexatriacontane solute. as in Figure 1
Legend and conditions same
packing. Both cyclohexane and hexatriacontane could easily permeate into the pores, and therefore the amount of steric exclusion was minimized. Under these conditions, no influence of column porosity o n dispersion was observed. It is possible that for molecules just large enough to enter the pores, a n effect of porosity o n dispersion may be noticeable as the porosity of the packing material is changed. Since the results from the various Porasil columns studied were in relatively close agreement, the data from only two sets of columns were subjected to detailed analysis. The Porasil A and Porasil E columns were selected as representing different average porosities. Least-squares analyses were carried out using linear, quadratic, and several higher-power functions of flow rate. Linear functions of Reynolds number deviated least from the experimental data for over-all dispersion obtained for cyclohexane and hexatriacontane. The linear relationships indicate that the contribution due to the mass-transfer term in the HETP equation is also linear with velocity. Dispersion data obtained with cyclohexane in the Porasil A column are compared with mobile-phase dispersion data, obtained with nonporous glass beads under equivalent operating conditions, in Figure 4. The increased broadening associated with the permeation process leads to significantly higher HETP values for the porous glass system. The rapid linear increase in HETP with Reynolds number in the Porasil columns differs greatly from the concave-downward HETP curves (12, 16, 18, 19) obtained with small molecules using Styragel column-packing gels. Possible explanations for these differences are discussed below. LePage et al. (22) reported concave-downward dispersion data with Porasil over a lower and more limited range of flow rates than that employed in this study. In addition, dispersion increased greatly with increasing particle size. Differences between our data and those of LePage et af. may be explained, in part, by the fact that we degassed the beads thoroughly prior to column packing, making their deep internal pore structure more readily available to the diffusing molecules. Effect of Permeation on HETP. Having HETP data obtained with porous and nonporous glass beads under the same operational conditions, as shown in Figure 4, the data for the nonporous case could be subtracted from the porous,
I
0
REYNOLDS NUMBER
I
I
l
I
l
I
l
l
.
Figure 4. Comparison of Porasil A dispersion with nonporous data using cyclohexane solute Conditions same as in Figure 1
leaving HETP values due only to permeation into and out of the porous particles. The over-all dispersion data for the Porasil columns were statistically fitted by least squares, and from the calculated points, corresponding values of the mobile-phase dispersion were subtracted. The resulting data for the two sets of columns with two solutes, describing the effects of permeation o n broadening, were again fitted by least squares to determine the order and coefficients of the equations giving the best statistical fit. The HETP results, shown in Figures 5 and 6, were found to be linear functions of Reynolds number over the region investigated. The slopes of the HETP curves are greatly affected by the diffusivity of the solute molecules and the intercepts are small. Within experimental error, the contribution to HETP resulting from the mass-transfer effects associated with the 7.0I
I
I
02
03
I
6oI 30i 50
c I
20
0
0
01
REYNOLDS
04
05
06
NUMBER
Figure 5. Effects of permeation on HETP as a function of Reynolds number Data for 120-140-mesh Porasil A. 0, cyclohexane; 0, hexatriacontare. Toluene solvent at room temperature ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
401
7.0I
I
I
I
I
,
The over-all dispersion number, D , is expressed as
D
=
where
L1
OO
01
02
I
0.3
I
I
04
05
REYNOLDS NUMBER
Figure 6. Effects of permeation on HETP as a function of Reynolds number Data for Porasil E. Conditions and legend same as in Figure 5
permeation process of these small molecules may be expressed as a term with the form CU, where U is the average linear velocity and C is a constant depending upon the solute material and column packing. Such a linear relationship is also encountered in gas chromatography and results from a linear adsorption isotherm. It therefore suggests that a linear permeation isotherm may be present in gel chromatography. Proof would, of course, require measurement of the solute concentraticln in the mobile and stationary phases, which we have not done. Since the time for diffusion varies inversely with solute diffusivity and residence time is inversely proportional to HETP, the linearity of HETP with flow rate suggests that it may also be linearly related to diffusivity. In analogy with gas chromatography, this may imply that, under the conditions studied, the permeation process may be controlled by a diffusion mechanism. A linear contribution justifies the original assumption that the mobile-phase dispersion effects and mass-transfer effects associated with permeation are, to a first approximation, independent and additive quantities in their effect o n the overall HETP. An equilibrium diffusion mechanism for retention is consistent with many theories previously proposed, including those of Yau and Malone (8), Casassa ( I O , I / ) , and Hermans (25). Over-All Model for Dispersion. The dispersion process for small solute molecules permeating porous beads is a linear function of flow rate, suggesting that the process is diffusioncontrolled. In addition, a model (15) incorporating molecular diffusion, eddy diffusion, and velocity-profile effects as the major causes of axial dispersion in the mobile phase was shown (17) to give good agreement, both qualitatively and quantitatively, with experimental data obtained in the absence of permeation. The over-all equation describing the HETP in gel chromatography with small molecules is therefore proposed to have the form HETP
402
=
2D/U Mobile-phase effects
+
cu Permeation effects
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
+DL Molecular difl’usion
+
XUd, Eddy diffusion
+
hR2U2/(+DL+XUdp) Velocity-profile effects
+
= 213 is a tortuosity factor Dl = molecular diffusivity in the mobile phase X = 1/11 is a n eddy-diffusion proportionality factor h = a velocity-profile constant R = column radius
The magnitude of the term describing velocity-profile effects depends greatly on the average radial dispersion coefficient. This in turn describes radial gradients within the column resulting from molecular diffusion and eddy diffusion. The velocity-profile constant h can be calculated (17) as a function of the ratio of the column diameter to the particle diameter, as shown by Johnson (28). This approach to describing dispersion phenomena is applicable to both gaseous (28, 29) and liquid (17) systems and gives valuable insight for the design of columns and optimization of’operational variables. There are indications in our data that the eddy-diffusivity proportionality factor, X, is not strictly constant but may vary with the diffusivity of the solute species, the velocity, and the interchannel distance through which the molecule must diffuse to achieve perfect mixing. Our model does not include such effects as stagnant regions, boundary-layer phenomena, natural convection effects due to density gradients, adsorption effects, viscous fingering, o r other concentration-depend$nt effects. All these could be present to varying degrees within the column systems used and would be expected to lead to poor agreement between theory and data. Because of the generally good agreement of theory with experimental data, we feel that effects not included in the model are secondary and cause no significant error. It is probable that stagnant regions or “dead volume” areas exist within the system. In fact, the pores themselves may be considered dead volume, since the local fluid velocity within them is very low compared to the velocity in the channels between the particles. Transfer into and out of such dead volume is diffusion-controlled and should give a linear contribution to HETP. At the flow rates encountered in this study, boundary layers developed around the particles should be very thin and should not appreciably affect the observed dispersion. Convective effects are insignificant, and the experimental design was such as to minimize adsorption, viscous fingering, and similar concentration-dependent effects. Differences in Dispersion in Porasil and Styragel. HETP data for small solute molecules are concave downward with decreasing flow rate for Styragel columns (12, 16, 18, 19). This behavior is similar to the mobile-phase dispersion results, in both magnitude and curve shape. With Porasil columns, dispersion increases linearly with increasing flow rate, giving much larger values of HETP. It seems likely that mobilephase dispersion effects are controlling in Styragel columns, while the mass-transfer effects associated with permeation are predominant in the Porasil columns. To predict the band-broadening behavior in detail for any porous column packings would be extremely difficult, requiring detailed information on pore structure. It is, however, (28) G. W. Johnson, Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, N. Y . , February 1967. (29) S. T. Sie and G. W. A. Rijnders, Anal. Chirn. Acta, 38, 3
(1967).
possible to explain our results qualitatively from knowledge of the differences in pore structure of the two materials. Mercury porosimetry data (30) for Porasil beads indicate a relatively narrow distribution of pore sizes. The slopes of the volume-pressure curves are steep, suggesting that once mercury has penetrated a pore opening it takes a very small increase in pressure to force it all the way into the pore network. On the other hand, mercury porosimetry data for Styrageltype particles (31) indicate a much broader range of pore-size distribution. Scanning electron micrographs furnished by Godwin (32) and Moore (31) indicate very great differences in pore structure between Styragel and Porasil. While the range of sizes of pore openings is narrower in Porasil, these openings are frequently followed by enlargements down the pore channel within the particle. In addition, large cavities are encountered within Porasil beads, with many interconnected pore channels leading into them. Styragel particles have a wider range of pore sizes but a structure that does not exhibit as many gross irregularities as in Porasil. Basically, the deep internal pore structure of the glass beads is much more accessible from the pores near the surface of the bead than in the case of the poly(styrene-divinylbenzene) beads. Therefore, once a molecule enters a pore in Porasil, it has more freedom to continue diffusing toward the center of the particle than in Styragel. Such diffusion greatly increases the observed dispersion over that due to mobile-phase effects. We feel that at normal GPC flow rates, because of such differences in pore structure, dispersion in these porous glass bead columns is primarily controlled by permeation (mass-transfer) effects, while in the poly(styrene-diviny1benzene)-packed columns dispersion is primarily controlled by mobile-phase effects oc-
curring outside the gel. These results demonstrate the importance of understanding both the origin of mobile-phase dispersion and the influence of pore structure on dispersion in order to tailor such size-separation techniques for maximum efficiency. While the broadening associated with Porasil is greater than that with Styragel, porous glass packings may offer significant practical advantages such as structural rigidity, chemical inertness, and compatibility with selected solvents, in comparison to other materials. The direct comparison of our dispersion data obtained o n Styragel and Porasil columns is difficult, since the particle size of the Porasil packing used was approximately two to three times as large as that of the Styragel. The larger particle size leads to greater interparticle diffusion distances and therefore greater dispersion. In addition, pore depth is much greater in the Porasil system, leading to greater broadening effects due to permeation. We expect that the level of dispersion with a Porasil system can be significantly reduced by going to smaller gel particle sizes and lower flow rates. ACKNOWLEDGMENT
We thank G . W. Johnson and J. C. Moore for many helpful discussions, and R. W. Godwin and J. C. Moore for allowing us to examine unpublished scanning electron micrographs.
(30) A. J. de Vries, M. LePage, R. Beau, and C. L. Guillemin, ANAL. CHEM.,39, 935 (1967). (31) J. C. Moore, Dow Chemical Co., Freeport, Tex., private communication, 1969. (32) R . W. Godwin, Celanese Fibers Co., Charlotte, N. C., private communication, 1969.
RECEIVED for review September 26, 1969. Accepted November 17, 1969. Presented in part at an ACS Division of Petroleum Chemistry Symposium on Gel Permeation Chromatography, Houston, Tex., February 1970. Work supported by The Dow Chemical Co. and Waters Associates. One of us (R.N.K.) thanks Hercules, Inc., for fellowship support. Work performed in Rensselaer’s Materials Research Laboratory, a facility supported by the National Aeronautics and Space Administration.
Application of the Trichloroacetyl Isocyanate Reaction with Terpene Alcohols to Quantitative Fractionation of Essential Oils P. A. Hedin, R. C. Gueldner, and A. C.Thompson Etitomology Research Dirision, Agricultural Research Seroice, Utiited States Department of Agriculture, State College, Miss. 39762
The quantitative reaction of trichloroacetyl isocyanate (TCAIC) with alcohols was used to fractionate essential oils. The TCAIC esters were extracted from the oil with dilute alkali in aqueous methanol with concomitant hydrolysis to carbamates. When the alcohols were regenerated by refluxing with 10% KOH in 80% aqueous methanol the recovery was essentially quantitative except in the case of the tertiary sesquiterpenoids. The method was evaluated with 15 alcohols, a phenol, a sterol, a synthetic mixture, and cotton bud essential oil.
difficult to separate from other oxygenated classes by column chromatography and were dehydrated during GLC. Several procedures that involve masking or reaction with the hydroxyl function have been reported. Hefendehl ( I ) added boric acid to the stationary phase of gas-liquid chromatographic (GLC) columns to achieve selective removal of Primary and secondary alcohols; Grechukhina and Nesmelov (2) converted primary and secondary aliphatic alcohols to the corresponding alkyl nitrites; and Larkhan and Pagington (3)
IN THE COURSE of our investigations of the essential oil of the cotton plant (Gossypium hirsutum L. var. Deltapine Smoothleaf) for constituents attractive to the boll weevil, Anthonornus grandis Boheman, we found several tertiary alcohols that were
(1) F. Hefendehl, Nuturwissenshuftetz, 51, 138 (1964). (2) F. N. Grechukhina and V. V. Nesrnelov, Zh. Prikl. Khim., 39,
w.
2574 (1966). w. Larkhan and (1967).
(3) T,
J.
s. Pagington, J . C/lromatogr., 28, 422
ANALYTICAL CHEMISTRY, VOL. 42, NO. 3, MARCH 1970
403
