SOMEASPECTSOF
4157
GELPERMEATION CHROMATOGRAPHY
Some Aspects of Gel Permeation Chromatography
by William B. Smith and Anthony Kollmansberger Department of Chemistry, Texas Christian University, Fort Worth, Texas (Received June 14, 1966)
The separation of a number of alkanes and aromatic compounds by chromatography through cross-linked polystyrenes has been carried out using tetrahydrofuran as the eluting solvent. It was established that molecular volume is fundamental in determining the degree of separation. The variation of the height equivalent to a theoretical plate with flow rate was studied, and a comparison of‘ the elution volumes with diffusion coefficients for a series of compounds was also made. These data are compared to the expectations from recent chromatographic theory.
It has been known for some time that molecular separation can be effected by the passage of solutions through solvent-swollen, cross-linked gels. While much of this work ‘has been done with water solutions and hydrophilic gels, recently the use of organic solvents and hydrophobic gels has been reported. Using a vulcanized rubber latex with heptane as the solvent, Brewer separated polymers from low molecular weight compounds.2 Vaughan3 has reported the separation of low molecular weight polystyrenes upon passage through a cross-linked polystyrene swollen with benzene. Recently, Moore4* and Moore and Hendricksondb have described an elegant proceldure for obtaining polymer molecular .weight distributions by chromatography of the polymer sample through cross-linked polystyrenes of permeabilities, B~ calibrating these columns withi carefully characterized polymers, relating the elution it was possible to prepare volume to the logarithm of the average molec1ilar chain length. It was observed that these calibration curves were often linear over a large range of chain lengths. From the calibration CULrve, the mOkxular weight distribution of unknown samples could then be calculated. Moore has termed this process as “gel permeation chromatography” Which Seems more descriptive of the process involved than the previously used term “gel filtration.” The simplest model conwith this method of separation envisions the permeation of the solute into the @;elfrom the flowing solution. I n both aqueous and nonaqueous solvents
and with both hydrophilic and hydrophobic gels, it is observed that larger, higher molecular weight materials are eluted from the columns first since, presumably, these substances diffuse less rapidly (or not at all) into the gel structure when compared to smaller molecules. In view of the importance which gel permeation chromatography is likely to assume in polymer chemistry, it seems highly desirable that the details of the mode of separation be ascertained.6 In order to eliminate the difficulties in working with poorly defined high molecular weight mixtures, it was decided that separations with smaller molecules should be used in this study. Experimental Section used in this study Benzene and the were all commercial products with properties in agreement with the literature The iodobenzene and p-diiodobenzene were distilled and recrystallized, respectiveb, before use. The normal hydrocarbons (1) For a review of these techniques see P. Flodin and J. Porath, “Chromatography,” E. Heftmann, Ed,, Reinhold Publishing Corp., New Yorkt N. y.r 196l9 Chapter 13. (2) P. S. Brewer, Nature, 188, 935 (1960). (3) M. F. Vaughan, ibid., 188, 55 (1960). (4) (a) J. C. Moore, J . Polymer Sci., A2,835 (1964); (b) J. C. Moore and J. G. Hendrickson, ibid., C 8 , 233 (1965); see also (e) D. J. Harmon, ibid., C8, 243 (1965); and (d) L. E. Maley, ibid., C8, 253 (1965). ( 5 ) For recent attempts t o define the separations with aqueous systems see: P. Flodin, J . Chromatog., 5 , io3 (1961); J. Porath, Pure Aml. Chem., 6 , 233 (1963); G. K. Ackers, Biochemistry, 3, 723 (1964); and M. Kubin, Collection Czech. Chem. Commun., 30, 1104 (1965).
V’olume 69, Number 18 December 1966
4158
WILLIAMB. SMITHAND ANTHONY KOLLMANSBERGER
were high purity materials obtained from the Aldrich Chemical Co. as was the 2-methylpentane. Each checked as one compound upon vapor phase chromatography, and each gave the correct index of refraction.6 The preparations of 2-methyloctane1 3-methyloctane1 3-ethyloctane1 3-methylnonane1 4-ethylnonane1 and 4-methyldecane each proceeded in the same fashion. The appropriate Grignard reagent was reacted with either 2-octanone or 3-octanone, and the resultant alcohol was dehydrated by distillation from a trace of iodine. The crude distillate, consisting of a mixture of olefins and some of the starting ketone, was hydrogenated with Adams' platinum in acetic acid, and the hydrogenated material was washed with cold, concentrated sulfuric acid. Each substance was then washed with water, dried over magnesium sulfate, distilled, checked for purity by v.P.c., index of refraction, and infrared spectroscopy. Tetrahydrofuran was refluxed for a t least 1 day over solid potassium hydroxide and was then distilled before use. Gel Permeation Chromatography. A commercial instrument manufactured by Waters Associates, Framingham, Mass., was used in this study. The i?strument was equipped with two 4-ft. columns of 40-A. gel and one 4-ft. section of 20-8. gel in series (permeabilities Tetrahydrofuran assigned by the manufacturer) was used as the solvent throughout. All determinations were carried out a t the ambient temperature (2325"). Since the instrument uses a differential refractometer as the detector, the concentrations of solutes used in this study were determined, in part, by the refractive index differences between the solutes and the solvent (THF). I n one study a mixture containing 0.020 g., respectively, of benzene and p-dibromobenzenelml. of tetrahydrofuran was used to determine the variations caused by differing flow rates. The same sample size was injected in each case. The peaks were symmetrical and cleanly separated to the base line. The total number of plates in the column for each substance was calculated from the usual chromatographic formula: , Ve is the elution volume plates = ( ~ V , / W ) ~where to the peak from the time of injection, and w is the width in volume a t the base of the peak and is determined by drawing the tangents to the inflection points on each side of the peak. The height equivalent to a theoretical plate (HETP) was determined by dividing the total number of plates into 12 ft., the length of the columns. The results of this study are given in Table I. Elution volumes a t a constant flow rate were then de-
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The Journal of Physical Chemistry
Table I: HETP vs. Flow Rate
Solute
a
Flow rate, d./ min.
Vet
%
ml.
HETP x IO',
ml.
ft.
Benzene DBB"
0.074
99.51 92.54
2.70 3.12
0.55 0.85
Benzene DBB
0.286
104.89 97.55
3.60 4.13
0.88 1.34
Benzene DBB
0.390
105.34 97.55
4.17 4.39
1.18 1.51
Benzene DBB
0.744
107.94 100.12
5.08 5.17
1.66 2.00
Benzene DBB
1.612
109.64 102.01
6.63 6.63
2.75 3.17
p-Dibromobenzene.
Table 11: Elution Volumes (at 0.736 ml./min.) in THF Concn., Compound
g./ml.
ve,
HETP x 105 ft.
ml
.
n-Pentane %-Hexane n-Heptane n-Octane n-Nonane *Decane n-Undecane n-Dodecane
0.02 0.03 0.05 0.09 0.20 0.20 0.15 0.13
98.48 95.19 91.98 89.17 86.67 83.41 81.86 79.97
1.36 1.28 1.49 1.39 1.30 1.42 1.69 1.70
2-Methylpentane 3-Methyloctane 2-Methyloctane 3-Methylnonane 3-Ethyloctane CMethyldecane 4-Ethylnonane
0.04 0.11 0.10 0.20 0.11 0.14 0.11
94.01 86.29 85.76 84.39 84.78 81.91 82.32
1.66 1.34 1.45 2.01 2.30 1.52 2.30
Benzene Chlorobenzene Bromobenzene Iodobenzene p-Dichlorobenzene p-Dibromobenzene p-Diiodobenzene
0.02 0.02 0.02 0.02 0.02 0.02 0.02
107.39 101.96 102.83 102.21 97.30 99.70 97.30
1.57 1.61 1.77 1.81 2.06 1.88 2.06
termined for a series of normal alkanes, branched alkanes, and aromatic compounds. The results of these determinations are presented in Table 11. Both here (6) All boiling points, indices of refraction, and densities were taken from R,., R. Dreisbach, "Physical Properties of Chemical Compounds, Vol. I, American Chemical Sooiety, Washington, D. C., 1956.
(7) The instrument has been described in ref. 4d,and the preparation of the gels in ref. 4a.
SOMEASPECTSOF GXLPERMEATION CHROMATOGRAPHY
and in the flow rate study described above, at least three determinations of V , and w per compound were carried out, and the values reported are the average values. Values of V,,were reproducible with an average deviation of 3t0.05--0.07%, while values of w agreed with average deviations of h 1-27&. Diffusion Coeficicnts. The apparatus and techniques used in the determination of the diffusion coefficients were similar to those described by The diffusion cell coinsisted of a glass tube bisected by a medium-porosity glass frit (2-cm. diameter). The ends of the glass tube were pulled down and joined to stopcocks (one at each end) which were mounted axially. Ten small glass beads were sealed in each compartment for stirring purposes. The two cell compartments so formed contained 13.31 and 10.15 ml., respectively. The cell was mounted horizontally in the constant-temperature bath. The glass tubing leading away from each stopcock was used as an axle and mounted in small ball bearings. Stirring was accomplished by turning the cell axially about its mounting using a motor-driven rubber pulley. The temperature bath was maintained at 25.0 0.02'. The compartments were filled and emptied with the cell mounted vertically using a long hypodermic needle and syringe. The larger side was first filled with pure solvent, and solvent was allowed to fill the frit. The cell was then inverted, and the solvent which passed through the frit was withdrawn. This compartment was then filled with the desired solution. The cell was placed in its mounting and stirred for the appropriate length of time. Upon completion of a run, the cell was againvertically clamped with the smaller compartment, containing the more concentrated solution, uppermost. The end tubes were washed with acetone and dried with an air jet. This compartment was quickly emptied with the syringe. Then the lower compaxtment was emptied. The concentrations of the solutions in each compartment were determined from the refractive indices a t 25". Calibration curves for each solute a t various concentrations in THF were prepared in advance. Once the diffusion time and the two concentrations were determined, the diffusion coefficient was obtained by the relation: D = (l/KT) log [CI/(C~ - C3)], where D is the diffusion coefficient, T is the temperature, C, is the initial concentration (g./ml.) of the solution, 4 and CSare the final concentrations of the initial solution and solvent, side, respectively, and K is the cell constant. I n order to determine the cell constant, three runs were made using biphenyl in b e n ~ e n e . ~ An average value of 0.112 was found with a precision of fractional standard deviation of 5.2701,.
*
4159
I n order to check the accuracy of the method, the diffusion coefficient for toluene in hexane was determined with a fractional deviation of 4.5401, as 4.10 X for three runs. The reported value is 4.21 X 10-6.10 The results for the seven compounds used in this study are given in Table 111. Table I11 : Diffusion Coefficients in THF at 25" Fractional std. dev..
Initial Solute
ooncn., g./ml.
D X 10-6
%
Benzene Chlorobenzene Bromobenzene Iodobenzene p-Dichlorobenzene p-Dibromobenzene p-Diiodobenzene
0.0704 0.1026 0.1392 0.1844 0.1354 0.2080 0.2961
3.84 3.28 2.69 2.06 2.21 1.94 1.69
4.07 1.38 1.06 3.62 2.87 9.61 3.52
Apparent Molar Volumes. The apparent molar volumes of the aromatic compounds used in this study were determined in THF solution by a standard technique.ll The results were as follows where the value in parentheses are the molar concentrations: benzene, 89.15 ml. (0.9004) ; chlorobenzene, 100.07 ml. (0.9000); bromobenzene, 103.36 ml. (0.9002) ; iodobenzene, 109.78 ml. (0.9003) ; p-dichlorobenzene, 113.49 ml. (0.8999) ; p-dibromobenzene, 119.79 ml. (0.9000) ; and p-diiodobenzene, 128.67 ml. (0.8999).
Results and Discussion The separation of various mixtures into discrete molecular species by means of gel permeation chromatography presumably depends on the relative rates of diffusion of the various species into the gel. I n the polymer systems studied previ~usly,~ calibration of the columns was carried out on the basis of an average molecular chain length calculated from the numberaverage molecular weight and assuming a planar zigzag backbone structure. While this procedure has been found empirically to give useful results, intuitively it would seem that molecular volumes would be a more fundamental parameter with which to calibrate the columns. The elution volumes for a series of normal and ~
(8) R. H. Stokes, J. Am. Chem. Soc., 7 2 , 763 (1950). (9) R. M i l l s , J. Phys. Chem., 67, 600 (1963). (10) P. Chang and R. C. Wilke, &id., 59, 592 (1955). (11) N. Bauer and S. Z. Lewin, "Technique of Organic Chemistry," Vol. I, A. Weissberger, Ed., Interscience Publishers, Inc., New York, N. Y., 1959, pp. 141, 142.
Volume 69, Number 1.2 December 1966
4160
WILLIAMB. SMITHAND ANTHONY KOLLMANSBERGER
Table IV : Chain Length vs. Molar Volume Comparisons
Length,
Compound
A=
n-Pentane n-Hexane n-Heptane n-Octane n-Nonane n-Decane n-Undecane n-Dodecane 2-Methylpentane 3-Methyloctane 2-Methyloctane 3-Methylnonane 3-Ethyloctane PMethyldecane P-Ethylnonane Benzene Chlorobenzene Bromobenzene Iodobenzene p-Dichlorobenzene p-Dibromobenzene p-Diiodobenzene
9.0 10.3 11.7 13.1 14.4 15.8 17.2 18.6 9.0 13.1 13.1 14.4 13.1 15.8 14.4 7.1 8.4 8.8 9.1 9.7 10.5 11.1
Effeotive length,
A.
10.1 14.6 15.0 15.8 15.5 17.3 17.0 6.4 7.9 7.6 7.8 9.5 8.6 9.5
%
Molar vol.,b
error
ml.
12.2 11.5 15.3 9.7 18.4 9.5 11.8 9.9 6.0 13.6 14.3 2.0 20.0 16.8
116.1 131.6 147.5 163.5 179.7 195.9 212.2 228.6 132.9 178.9 180.8 195.0 193.3
... ...
89.2 100.1 103.4 109.8 113.5 119.8 128.7
Effective molar vel., ml.
136 179 182 191 188 210 206 85 104
100 103 122 113 122
% error
2.3 0.0 0.5 2.1 2.6
... ...
4.5 4.0 2.9 6.4 8.0 5.8 5.4
’
Measured from LaPine-Leybold models prepared according t o Stuart and Briegleb, LaPine Scientific Co., Chicago, 111. Molar volumes determined from the densities a t 25” for the alkanes. For the aromatic compounds, the values are apparent molar volumes in THF a t 25’.
branched alkanes, as well as a series of aromatic compounds, are given in Table 11. Plots of log (chain length) and log (molar volume), respectively, vs. V , for the normal hydrocarbons gave very good straight lines. Using these lines as calibrations then allows one to determine an “effective chain length” and an “effective molar volume” for the other compounds in the series. The comparison of the chain lengths and molar volumes determined by the g.p.c. is given in Table IV. For 14 compounds, the “effective chain lengths” were found to show a 12.101, average deviation; while for 12 cases, the molar volumes gave only a 3.7% average deviation. As expected, the molecular volume is the more fundamental yardstick relating elution volume to molecular structure. Regarding the model to be used in considering the g.p.c. process, we first rather naively assumed that the general chromatography equation would apply. l2 According to this equation (known as the van Deemter equation when applied to gas chromatography) the height equivalent to a theoretical plate is given by: HETP = A B/u Cu, where A is a constant describing the “multipath” or eddy diffusion effect which is a function of the packing and particle size of the
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The Journal of Physical Chemistry
column packing; the term B / u describes the longitudinal diffusion of the solute into the bulk of the solvent and varies inversely as the flow rate, u; and Cu is a term describing the state of the partition equilibrium between solute in the bulk solution and the packing. According to this equation, the variation in HETP with flow rate follows a hyperbola with HETP decreasing with flow rate until a minimum is reached. At slower flow rates, the HETP then increases rapidlyowing to the longitudinal diffusion term. A plot of the data in Table I is given in Figure 1, and it is clear that the behavior expected, based upon the above reasoning, is not observed. At the lowest flow rate used in this study, benzene was eluted after over 24 hr. on the column. The deleterious effect of longitudinal diffusion, even over this long period, has not yet started to evidence itself. Others have noted chromatographic behavior at odds with that expected from the above equation, and a t least two theories have been proposed to account for the departure. Giddings13 has proposed a modifica(12) See ref. 1, pp. 27, 97,and 170. (13) J. C. Giddings, AnaE. Chem., 35, 1338 (1963); see also ref. 1, p. 98.
SOMEASPECTS OF GEL PERMEATION CHROMATOGRAPHY
4161
I/ '
I
I
I
0.3 0.4 0.6 1/D, seo./cm.2 X 10-5.
L
I
0.6
Figure 2. A plot of HETP vs. the reciprocal of the diffusion coefficientsfor a series of aromatic compounds. The point off the line is p-dichlorobenzene. I
I
1.0
0.5
1 -
1.5
Flow rate, ml./min.
Figure 1. A plot of flow rate vs. HETP for the g.p.c. data with benzene (lower) and p-dibromobenzene (upper).
tion of the eddy diffusion term to take into account mass-transfer . processes in the mobile phase. His theory, known as %he coupling theory, may be summarized by the equat,ion HETP =
AEu -tcu A AEu
+
where the first term replaces the former term for eddy diffusion, and E is a constant (or better a series of constants) proportional to the square of the channel diameter and the reciprocal of the diffusion coefficient of the solute in the mobile phase. The longitudinal diffusion term has been omitted here as it seems to make no important contribution under the conditions of this study. Waltonl4 has proposed a modified equation to account for behavior in ion-exchange chromatography. Walton's equation, as defined by his film diffusion theory, is HETP = A
cu + Bu -+De ( 1 + Fu)DL
where A again describes the eddy diffusion effect; B, C, and F are composites of several constants; and D, and D1 axe (diffusion coefficients for the solute in the gel and the aliffusion of solute through a static liquid film surrounding the gel particles. No obvious choice between the two above equations is suggested by the data in Figure 1. Both should lead to linear behavior a t the extremes of flow rate with
a nonlinear intermediate region. The curves in Figure 1 exhibit just such behavior. Furthermore, both models suggest a higher slope for the curve a t lower flow rates in agreement with Figure 1. Giddings13 has offered considerable data to support his theory and has criticized the film diffusion theory.15 Examination of the details of either theory suggests a reciprocal relation between HETP and the diffusion coefficients for the different solute species. It is evident from the data in Table I1 that HETP increases with molecula,r size, and, of course, diffusion coefficients vary in the opposite fashion. Unfortunately, there is no exact theory relating molecular size or shape to diffusion coefficients for small molecules at this time. A plot of 1 / D os. HETP for the aromatic compounds is shown in Figure 2, and, with the unexplained exception of dichlorobenzene, a linear relation is observed. I n summary, it is evident from this study that useful separations of small molecules may be effected by this technique and that molecular volume is the important parameter influencing the degree of separation. The variation of HETP with flow rate follows either of the two most current chromatographic equations and shows a linear inverse variation with the diffusion coefficients for various solutes.
Acknowledgment. The authors wish to acknowledge the financial support of the Dow Chemical Co. in the conduct of this research. Grateful thanks is also expressed to J. C . Moore for helpful discussions. (14) H. F. Waltan, ref. 1, p. 299. (15) J. C.Giddings, Anal. Chem., 34, 1186 (1962).
Volume 69, Number 19 December 1966
