Molecular Size Analysis Using Gel Permeation Chromatography J. G . Hendrickson The Dow Chemical Co., Freeport, Texas Molecular sizes of solutes in tetrahydrofuran were re-examined with some new test compounds; in general, they gave the expected molecular size based on additive structural elements determining the effective size. The effective size of phenols was consistently larger than one might predict, and phenols typically appeared to be 4.67 carbon atoms larger than the corresponding aromatic hydrocarbon. A range of 2,2,4-trimethyldioxolane derivatives were studied, and they gave the expected sizes. The gases studied eluted at a molecular size slightly smaller than propane. Some implications of this observation are given. General uses and advantages of the method are listed and some predictions as to future developments are given. A chromatogram of 13 solutes in GPC is included to show the efficiency of the separation. A PRIOR PAPER from this laboratory ( I ) developed simple rules that predicted the elution volumes of small molecules in gel permeation chromatography (GPC); the object was to further define the probable basis under which both small molecules and polymers are separated. In the GPC process, the molecules are separated based on some measure of molecular size; the large molecules penetrate into the gel the least and hence are eluted first. As further examples, iso-octane eluted at virtually the same point as did n-octane, and ethylbenzene appeared a little smaller than did n-pentane. Tetrahydrofuran (THF) was found ( I ) to be a preferred elution solvent in GPC for many reasons. It was a good solvent for a large range of compounds and polymers, and its refractive index was different from most polymers. The prior work showed also that THF hydrogen bonded to the nonhindered alcohols, acids, phenols, and other active hydrogen species; hence, small and medium size molecules of these types remained in solution, instead of being sorbed on the gel surface. However, further work was undertaken to test the accuracy of the prior guidelines and to further define the mechanism of the GPC separation.
fed into a computer t o obtain the best fit to an equation of the form Elution = V,
The effective chain lengths for heteroatoms used in the prior paper ( I ) were again used (see Table I). This technique gave the constants listed below for the above equation when applied to the columns used in the current work. These constants and the equation were then used to compute molecular size for newly studied compounds. Results are also included for a few compounds studied with the columns used in the prior work; these columns have long since been replaced. Column A B C D E F
Length, ft
TPFa
vz
810 580
187.0 94.5 96.39 95.66 91.14 140.3
16 8 8 8 8 12
600
933 900 lo00
Theoretical plates per ft (TPF)
Table I.
Atom
C
c
/ \
C
/ \
N
...
0.62
...
16 (ml to elution)* Ft (ml at base of pea=
C
/\
C
/ \
C1
Br I
1.00
1.25
0.27
1.84
1.09
2.60
1.32
2.88
1.54
3.15
0.0
1.25
0.61
2.00
I
C
/ \
1.14
Br
C
/ \
0.91
c1
C
/ \
0.84
F
C
/\
0.67
R
C
/ \
1.25
R
S
F
1 .o
R
N
S
0
... ... ...
c
0
0
H (1) J. G . Hendrickson and J. C. Moore, J. Polymer Sci., A-1-4, 167 (1966). (2) J. C. Moore and J. G . Hendrickson, Ibid., 8C, 233-42 (1965). (3) L. E. Maley, Ibid., pp. 243-52.
=
R
S 73.0 35.8 36.36 36.29 32.31 52.5
Values Used as Effective Chain Length of Various Atoms - Chain length No. of Group c basis A
C
EXPERIMENTAL
The experimental techniques of the prior work were again used ( I , 2). Briefly, the solvent was tetrahydrofuran pumped at 1 ml/minute through 8 to 16 feet of 3/*-inch stainless steel columns that contained a divinylbenzene-styrene copolymecized gel. This gel can be purchased commercially as4O-A gel. It was just barely permeable to C40 alkanes, showing a useful separation range below 450 molecular weight for these alkanes. The gel was sized a t 80% between 20 to 40 p . The runs were made with a Waters Associates commercial GPC unit previously described (3), and the data are given in the enclosed tables. The columns were calibrated with n-alkanes and di-n-alkyl ethers, and then the elution us. effective chain length data was
+ Sx log (number of C atoms + R).
H
\ C=O
/ ~
VOL 40, NO. 1, JANUARY 1968
~
0
_
49
_
_
50 C
200
1oc 60 110
150
130 ML. ELUTED
Figure 1. Molecular volume cs. elution using four 40-A columns 0
Hydrocarbons
X Halides = O compounds
+
0 Aromatics
*
Alcohols
0 Others
DISCUSSION
Many bases exist for comparing molecules to try t o obtain a correlation of molecular domain us. elution volume in GPC, and this problem was re-examined. I n our early work ( I ) , 130 compounds were studied, and the generalization was proposed that structural elements were additive and that the angstrom length of a straight chain compound has its effective length. A little later, other workers (4) chose molecular volume as a basis for correlations. A comparison of the two methods would seem in order. Figure 1 shows a plot of molecular volume in cubic angstroms us. elution volume for the compounds of the prior work where densities were readily available. The range of the data would typically be +20%. This corresponds to a compound with a molecular volume of n-pentane being, at times mistaken for n-heptane, which is about a 5- to 10-fold increase in error compared to the method of additive structural element lengths. The latter method allows one to remember structural element lengths and thereby to compute good approximations for the size of newly evaluated compounds. Further tests were made to test molar volumes as a basis for expressing G P C results. Molecular volumes were determined for n-pentane, n-hexane, and ethylbenzene in tetrahydrofuran, benzene, and chloroform. These nine runs showed that the molecular volumes in solution differed from that of the pure compounds by less than 2 in every case, and the actual Thus, in tetrahydrodifference was probably less than 1 furan, ethylbenzene had a molar volume very close to nhexane, but its size based on elution was slightly smaller than n-pentane, indicating a 20z error. Indeed, the sum of molecular volumes for T H F and a random sample of alcohols also fell within the calibration scatter in Figure 1. A group of compounds were studied that were new to GPC evaluation and which had a basic structure similar to those compounds of the prior study. In most cases, these were calibration standards for routine work; hence, a variety of columns were used for the study. The results in Table I1 show that the experimental results conformed to the theory in the
z
z.
(4) W. B. Smith and A. Kollmansberger, J . Phys. Chem., 69, 4157 (1965).
50
a
ANALYTICAL CHEMISTRY
cases reported, but a few of the test compounds deserve special comment. Results for cumyl peroxide were quite close to the expected size, when one gives credit for all the methyl groups in the center of the molecule. Cumene hydroperoxide was hydrogen bonded, as anticipated. Some more aromatic compounds were studied to evaluate GPC as a method for predicting elution volume and to recalibrate the size of a phenyl group. An equivalent chain length of 2.85 carbon atoms per phenyl group was used in the prior study and currently. This value gave the results given in Table 111, and they were in quite good agreement with the predicted values. Rules for predicting elution were further defined for some polyphenyl ethers, and the phenyl groups appeared to be 2.85 number of carbon atoms long, in agreement with the general assignments in the previous work. In the early work, a value of 2.4 number of carbon atoms was the assigned length of a buried benzene ring, but at present this appeared to reflect the rigidity of the terphenyl, etc., studied. Amines were studied, and they gave varying amounts of hydrogen bonding that reflected the acidity of the N-H group and steric hindrance. A group of phenols were examined, and a correction of four carbon atoms per OH group appeared to correspond to additional chain length due to hydrogen bonding. This data is given in Table IV. Some compounds with the 1,3-dioxolane structure were studied to see if this structure had a uniform size and if the derivatives also conformed to the prior rules. This was the case, as shown by the data in Table V. Tetrahydrofuran was established in the prior work as being 2.85 number of carbon atoms in size, and this was also the size of the 1,3-dioxolane structure. Indeed, a range of compounds from alcohols t o ketals was studied, and the agreement with the predicted results was quite good. As in almost every case in this work, the effective chain length was predicted with an average error considerably below 4z, and the number of cases where the error is above 6 is very small. Some esters were studied, since the early studies indicated that these molecules looked smaller than one would predict based on the sum of the lengths of the pendent groups. Initial evaluation of simple esters led to good correlation by not adding in any effect for such a pendent carbonyl oxygen. Using this basis, the results in Table VI were obtained. It can be seen that the theory works fairly well if the molecule is not too highly esterified. The light gases eluted in GPC at a point earlier than predicted by prior work ( I ) . With these gases, there appeared t o be a penetration limit, and as an extrapolated value, methane and helium eluted at a comparative size of about 2.5 number of carbon atoms. Hence, one must assume that elution delayed past this point is due to adsorption, permeation, chemisorption, partition, etc. With the gases studied, one may assume that major adsorption forces were not present, since elution varied continually as a function of molecular size. Methyl iodide and ethyl iodide penetrated further into the gel matrix or were adsorbed, compared to the light gases; there is n o strong evidence for making a choice between these possibilities, and indeed both probably occurred to a degree. The 2.5 number of carbon atom penetration limit for the gases is quite interesting. Since it is quite close to the measured size of the solvent (THF), one has a new measure of the interaction of gases in solution at gel interfaces. This suggests that the bonding of inert gases could be conveniently studied as a function of their size in solution. The possibility still exists that there is some form of bonding of the gases to the solvent in the current system, although this is discounted by the elution data in benzene, where the same size was observed.
Compound Cumene peroxide Cumene hydroperoxide n-Butylbenzene Di-@-chloroethyl) ether p-Cymene Phenethyl ether Mesitylene 2-Bromobutane Styrene Anisole Benzaldehyde Isopropyl chloride
Table 11. GPC Results with Standard Compounds with 40-A Columns Elution, ml Compared chain length (No. ____ of C basis) Column To peak At base TPF Theory Obsd 0 - T 13.03 56.3 5.20 237 12.66 -0.37 C 10.03 10.21 59.7 4.67 327 -0.18 C 66.0 348 6.85 0 . no 6.85 5.00 C 6.85 64.8 4.30 454 7.15 E +O. 30 C +O. 32 385 6.72 6.40 66.3 4.78
C C C C C C
Compound Benzene Benzoic acid THF Salicylic acid . THF Phenyl salicylate rn-Diphenoxybenzene rn-Phenoxyphenol . THF rn-Hydroxybenzoic acid * (THF)* p-Hydroxybenzoic acid . (THF)* Polyphenyl oxide [4-(0-+)3--0- -41 -41 Polyphenyl oxide [+-(O-4)a-O" Using column PF. +
70.8 70.8 71.6 73.7 71.4 72.2
Column
Amines Methylamine Aniline Diphenylamine PhenyLi3-naphthyIamine Di benzylamine Di benzylphenylamine H (Q-N-6)2 Bonded Phenols Phenol p-Chlorophenol o-Cresol rn-Cresoi p- Methoxyphenol @-Naphthol Hydroquinone Bisphenol A Bisphenol S Ionol Using 16-foot columns. * Using 4.0 number of C per
379 468 426 413 432 564
5.40 5.32 4.85 4.52 4.46 4.08
5.05 5.32 4.80 4.20 4.86 4.62
Table 111. GPC Results with Aromatic Compounds. Chain length Elution, ml (No. of C basis) To peak At base Theory Obsd 113.0 4.12 3.31 (3.40) 7.71 93.7 5.04 8.00 8.61 8.67 91.25 4.88 8.67 91.50 4.69 8.50 88.0 4.84 9.91 9.88 85.4 4.24 11.10 10.55 11.96 12.17 83.7 4.83 82.8 4.54 12.6 12.2 74.4 16.82 4.42 17.99 70.8 20.14 5.47 21.07
Table IV.
Compound
5.14 4.63 4.90 5.13 4.86 4.24
To peak
-0.35 0.0
-0.05 -0.32 $0.40 $0.54
Error ~
(0 - TI
-0.09 -0.29 -0.06 -0.17 -0.03 -+0.55 -0.21 +0.4 +1,17 +O. 93
GPC Results with Amines and Phenols Compared chain length Elution, ml (No. of C basis) At base TPF Theory Obsd
Error (Ob - T)
"7
/o
3.6 0.7 2.0 0.3 5.2 1.7 3 7.0 4.6
7; H
Bonding
A A E E B E
160.3n 126.6a 62.0 60.0 60.7 59.8
5.04 5.90 4.35 5.24 5.04 5.94
1020 46 1 406 262 290 202
2.0 3.76 6.51 7.66 8.71 10.36
2 6.68 8.59 9.30 8.79 9.95
2.92 2.08 1.64 0.09 -0.41
102 73 58 3
E
51.0
4.96
211
12.32
18.09
5.67
200
A A C C C C
123.0° 116.8O 63.4 62.8 62.8 61.9 118.5a 50.7 51.3 109.2
5.68 5.64 4.96 4.82 4.80 4.94 5.48 4.88 4.43 6.63
469 427 327 339 343 314 467 216 268 270
3.52 4.51 4.52 4.52 5.19 4.68 3.73 9.13 8.13 12.15
7.53 9.15 8.07 8.39 10.44 8.88 8.61 18.05 17.36 11.63
4.00 4.34 3.55 3.87 4.23 4.20 4.88 8.92 8.23
1OOb
A
C C A
0
...
0
0
108 89 97 105 122 223 206 0
0
OH bonded in phenols.
The current results also lead to a better understanding of prior GPC work with some other small molecules. Such compounds looked bigger than predicted by the early theories and calibrations. Comparisons can be made when one transfers the chain lengths found earlier t o the upper curve in Figure 2 and then projects the observed point to the lower curve a t the same elution volume. The prior results with benzene, cyclohexane, and methanol bonded t o tetrahydrofuran gave apparent chain lengths about 0.4 to 0.5 number of carbon atoms
bigger than one might expect. The current results show that the size of benzene is probably nearer to the expected 2.85 number of carbon atoms length that one would predict from the size of a phenyl group in other compounds. Also, cyclohexane on a readjusted basis was observed t o be 3.15 number of carbon atoms long, compared to the theoretical 3.35. Similarly, results with methanol appeared more in line when interpreted in light of Figure 2. Further evaluation was undertaken with other cyclic comVOL 40, NO. 1, JANUARY 1968
51
* t,
h
pounds and a case of borderline hydrogen bonding. The prior study measured propargyl chloride as having T H F bonded in an equilibrium with the acetylenic hydrogen. In the current study, propargyl alcohol also looked longer than n-propyl alcohol, and this corresponded to about one and a half T H F molecules bonded per molecule. In the prior work, an oxygen atom in an epoxide was not counted because of the restricted rotation that it produced. In the current studies, a cyclopropyl group gave parallel results. Indeed, a slightly improved answer was obtained by using about 1.7 number of carbon units for the value of this CBgroup. In the early work, cyclohexane was valued at 3.35 number of carbon atoms long. Now, bicyclohexyl and bicyclohexanone have been tested, and they fall in line with the expected values, as shown by the data in Table VII. This paper would not be complete without a prediction as to the general conditions one might some day use and a curve of the current separations obtained. Such a demonstration of the separating power is shown in Figure 3. Here 13 compounds were separated with about twice the efficiency that one would expect with a 3/8-inchgas chromatography column of equal length, and there is room on the chromatogram for even more peaks to be present and measured for analysis. One might further predict that smaller diameter columns, faster
10
5 8 0
L 6 I
I-
4
$ W
-I
zQ I
2
0 W
2 I-
E LL
1 70
60
W LL
80
ELUTION VOLUME (ml.) Figure 2. Elution in GPC of methane, nitrogen, and propane (for a 12-foot co~umnof 40-A gel)
Table V.
GPC Results with 2,2,4Trimethyl Dioxolane Derivatives Comoared chain length Elution, mla (No. of C basis)Compound To peak At base TPF Theory Obsd 0 - T 2,2-Propane-di-4a,4’a-(2,2,4-trimethyldioxolane) ketal 53.1 4.96 16.03 229 15.50 -0.53 Di-4~~,4’a-(2,2,4-trimethyldioxolane) ether 258 56.5 12.50 4.97 12.37 +O. 13 2,2-Propane-methyl-4-(2,2,4-trimethyldioxolane) ketal 59.5 292 10.34 4.92 11.18 -0.84 2a-Chloro-4a-hydroxy-(2,2,4-trimethyldioxolane) 305 59.2 4.80 10.47 10.53 +0.07 4a-Hydroxy-(2,2,4-trirnethyldioxolanej 61.2 350 4.63 9.37 9.28 -0.08 2a-Hydroxy-(2,2,4-trimethyldioxolanej 62.2 8.71 361 4.63 9.37 -0.66 4a-Chloro-(2,2,4-trimethyldioxolane) 64.9 5.04 7.34 331 6.94 +0.40 Parent compound 68.4 372 5.88 5.02 5.85 $0.03 rrans-4a-Hydroxy-(2,4-dimethyldioxolane) 63.3 387 8.12 4.55 8.37 -0.25 cis-4a-Hydroxy-(2,4-dimethyldioxolane) 390 4.55 8.02 63.5 8.37 -0.35 a Using column C. Table VI.
GPC Results with Carboxylic Esters
Comoared chain length Compound Diethylene glycol diacetate Dimethyl adipate P-Hydroxyethyl acrylate P-Methoxy ethyl acetate Ethyl carbonate Methyl butyrate Methyl benzoate Ethyl acetate
Column C
E C C
C C C
To peak 60.2 61.8 61.4 68.3 68.3 69.9 70.4
-
Column C
-
52
...
4.62 4.54 5.0
(No. of C basis) -
TPF 292 386 430
...
437 473 397
B
Table VII.
Compound Propargyl alcohol THF Dicyclopropyl ketone Cyclopropanecarboxylic acid THF Bicyclohexyl CBicyclohexanone
Elution, ml At base 5.0 4.45 4.19
ANALYTICAL CHEMISTRY
C C C
C
To peak 64.1 72.1 66.0
66.0 65.2
Theory 10.01 9.33 9.19 6.32 6.32 5.67 5.52 4.67
Obsd
9.89 8.72 9.16 5.92 5.92 5.35 5.18 4.17
0 - T -0.12 -0.61 -0.03 -0.40
-0.40 -0.32 -0.34 -0.60
GPC Results with Other Compounds
Elution, ml At base 4.15 5.04 5.27 5.08 5.38
TPF 478 409 314 337 294
Compared chain length (No. of C basis) Theory Obsd 0-T 6.54 7.72 + l . 18 5.61 4.65 -0.95 7.15 6.70 7.31
6.85 6.85 7.20
-0.29
+O. 15 -0.09
Figure 3. Separation efficiency in a 12-foot 40-Acolumn flow rates, and longer columns would be increasingly important. One can foresee using ‘/8-inchcolumns run at 2 ml/minUte with 50 feet of column at above 1000 psi inlet pressures. Advantages could include a constant diffusivity throughout the column, a predictable elution, gentler treatment of samples, and better resolution per pass. It appears likely that G P C for small molecules will become a new basic tool that could be called a “liquid phase size spectrometer.” In this application, a major use is to measure the size of new compounds in mixtures, especially those compounds which cannot be measured conveniently by other analytical methods, such as gas chromatography or mass spectrometry. By assuming that the structural elements are additive in their effect, one may calculate molecular size in GPC from elution data, and in general both G P C and size analysis have some interesting features. Quantitative methods can be obtained in GPC, based either on the area under the GPC curve or ratioing peak heights t o internal standards. A range of R.I. values in the literature helps in the prediction of both refractive index calibration factors and elution solvents with a preferred R.I. High quality columns of 1200 to 1800 T P F are now being made; also, increased flow rates appear practical for speeding up the separations, based on diffusion studies. The method requires a minimum calibration of elution position with the bulk of the solutes studied in a solvent such as THF. There is a range of gels available, so that a range of molecular sizes can be brought into focus; sorption can be increased if desired by changing gels.
The order of elution can often be dramatically changed by using different elution solvents because of the changes in hydrogen bonding that such changes will produce. By choosing poorer solvents, adsorption forces can further be brought into play. The method requires a minimum of time and/or man-hours to carry out, especially during automatic operation. In many laboratories, the G P C equipment is already available, including automatic injection equipment. The method is nondestructive of the sample. The sample is not contaminated by pyrolysis products of a stationary phase or a high temperature heating chamber. The method can be used to measure both volatile and nonvolatile compounds and their mixtures. With the 40-A columns, the high polymers will all elute at the same time, so that total polymer yields can be figured from results at a single point. The “highs” are measured and they do not interfere with the analysis of the “lows.” Research samples almost always can be run without a preliminary devolatilization or other treatment. Indeed, such treatments are undesirable to the degree that they allow further polymerization or reaction of the sample, change the sample composition, or affect the accuracy of the analysis.
RECEIVED for review August 31, 1967. Accepted October 24, 1967. Paper presented at the Fourth International Gel Permeation Chromatography Symposium, May 22, 1967, Miami Beach, Fla.
VOL 40, NO. 1, JANUARY 1968
e
53
