Evaluation and Comparison of Gel Permeation Chromatography and Thermal Field-Flow Fractionation for Polymer Separations J. Calvin Giddings, Young H e e Yoon, and Marcus N. Myers Department of Chemistry, University of Utah, Salt Lake City, Utah 84 1 72
The efficacy of gel permeation chromatography (GPC) and thermal field-flow fractionation (TFFF) in separating polymers is evaluated using several appropriate parameters. The two methods are assumed lo have a similar capability in generating theoretical plates. Given this, TFFF has roughly a fourfold advantage in peak capacity, the maximum number of peaks resolvable over a method’s range of practical operation. Another indicator, the resolution over a llmited range of molecular weights, is characterized by the fractionating power, equal to the molecular weight over the separable increment in molecular weight. Equations are derived expressing this parameter as a function of theoretical plates and the nature of the retention curve. For a like number of theoretical plates, it is shown that TFFF provides a maximum fractionating power roughly twice as large as that provided by GPC. Furthermore, the superior fractionating power of TFFF is maintained over a much greater molecular weight range. These results suggest that TFFF might be a highly useful tool for the fractionation of polymers.
The efficient separation of close-lying polymer fractions is a long-standing goal of polymer chemists. Progress toward this goal received an enormous boost with the development of gel permeation chromatography (GPC) by J. C. Moore in 1964 ( I ) . Until this time, chromatographic methods were applied to macromolecules only with considerable difficulty and limited success. The GPC method combined the efficacy of chromatography with a simple and practical mechanism of separation based on the differential exclusion of polymer molecules of different sizes from a porous gel medium. The advantages of the method were quickly recognized and widely applied. The method has been greatly refined both in terms of efficiency and speed. GPC may now be regarded as the standard technique for polymer separations and the method against which any new technology must be compared for potential acceptance. Field-flow fractionation (FFF) is a class of separation methods applicable to macromolecules (2, 3 ) . It is a flowelution technique; hence, the external experimental features resemble liquid elution chromatography. However, the mechanism of separation is different. An appropriate field is applied to solute zones in a channel, forcing each zone toward one wall where it forms a narrow “layer” of unique thickness. The differential flow profile present in laminar flow along the channel carries the zones downstream at different velocities depending on how far the layer extends into the faster streamlines toward the center. The unequal zone velocities lead to separation in elution sequence ( 4 1. Of the various methods of FFF, only one, thermal fieldflow fractionation (TFFF)-still in the developmental stage-has been studied in adequate depth to make possible an evaluation of its potential in polymer separations (5-8). Here we will attempt such an evaluation, and compare the results with those obtained for GPC. 126
Two general objectives of poymer fractionation are: 1, to achieve the resolution of specific, close-lying fractions, and 2, to maintain fractionating power over a wide range of molecular weights. These objectives must, of course, be achievable with reasonable speed and convenience. Objective 1 must be attained in order to generate valid molecular weight distributions, when these are the objective of the study.
THEORETICAL PLATES, N The comparison of different separation tools can be made by employing various parameters denoting the effectiveness of fractionation. One of the broadest indexes for characterizing any zonal separation method is the number of theoretical plates (or, for the speed of separation, the rate of generation of theoretical plates). The value and drawbacks of this parameter in comparing chromatographic systems has been discussed (9, 1 0 ) . Theoretical plates have also been used to characterize such diverse methods as sedimentation and electrophoresis ( I 1 ). The number of theoretical plates can be defined as the square of the displacement of a zone of homogeneous material, X 2, divided by zone variance, u2, equivalent to (9, I 1 )
N = (X/a)2
(1)
Narrow, sharply resolved zones or peaks are characterized by a small u and thus by a large number of plates, N. No clear limit has emerged on the maximum number of theoretical plates obtainable by GPC and TFFF. The potential of TFFF is known to be outstanding-up to 12,000 plates per foot-but this has not been realized in practice (12). Hence, neither technique is assumed to have an advantage over the other. Parameter N is fundamental to a number of other parameters. These include peak capacity, resolution, and resolving power (to be defined). These parameters reflect more directly the utility of separation.
PEAK CAPACITY, n Peak capacity, n, is defined as the maximum number of distinct peaks that can be successfully resolved over the operating range of the instrument under prescribed conditions ( 1 3 ) .I t is calculated very simply as the largest number of peaks that can be physically emplaced, without undue overlap, into the operating range (measured in elution time or volume) of the designated instrument. As displacement X increases to u-which is about one quarter of the zone width-more peaks can be so resolved. Thus, peak capacity increases with N . The relationship is of the form (12) IZ = 1
+
(N/16)’/‘ In (Vmax/Vmio)
(2)
where V,,, and Vmin define the maximum and minimum of the practical retention-volume range. GPC exhibits an immediate and almost unique defect when viewed in this way. The retention volume range is limited to approximately (Vma,/Vmin) = 2.3. The minimum volume, Vmin is the interstitial volume, VO, and the
A N A L Y T I C A L CHEMISTRY, VOL. 47., N O . 1, J A N U A R Y 1975
maximum volume, V,,,, is the interstitial volume plus the internal pore volume, Vo V,. All peaks must be eluted in the limited range between these extremes. Essentially all other forms of chromatography, by contrast, have a N,,, limited only by peak dilution and waiting time, since in theory elution and separation can go on indefinitely for the more highly retained components. Similarly, TFFF has no concrete upper bound to retention volume. The lower bound, V,,,, is simply the volume of the TFFF column, while the upper bound may, in practical terms, be from 10 to 50 times larger. Assuming for the moment that (Vmax/ V,,,) = 25, the peak capacity from Equation 2 is
+
12
=
1
+
0 . 8 ~ " ~
(TFFF)
6c
F
A . Gel Permeation Chrornotogrophy
(3)
Since (Vmax/Vm,,) for GPC is about 2.3, peak capacity in this case is approximately ( 1 3 ) TZ
= 1
+
0.2h"12
(GPC)
(4)
The above equations show that for a given number of theoretical plates, N , T F F F can resolve roughly four times as many peaks as GPC. In order to bring the peak capacities to the same level, the GPC column would require about 16 times as many plates as the TFFF column, as the above equations show. Since GPC has no inherent advantage in the generation of theoretical plates, the above limit is a drawback to GPC. One can compensate somewhat by making the GPC column longer, but to gain approximate equality a 16-fold multiplication of length is necessary. This is generally impractical. Figure 1 helps illustrate the significance of these conclusions. Figure 1 A shows the elution distribution of each of 5 different polystyrene polymer fractions reported in the literature for GPC ( I ) . The column, 3.66 m in length and 0.775 cm in diameter, is identical in kind to that used in a subsequent study of GPC ( 1 4 ) . Peaks in Figure 1 are identified by molecular weight, and alongside, by the number of theoretical plates, N The average N for the five peaks is 304. Below this, in Figure l B , is shown a fractogram generated on a 0.36 m long T F F F column. The 5 polystyrene fractions differ considerably in molecular weight from those employed in the GPC run. However two similarities between these runs provide a basis for comparison. First, the molecular weight ratios of the extreme peaks in each separation are comparable: 41 from GPC and 32 for TFFF. Second, the average number of theoretical plates for the 5 peaks is comparable in the two runs. In fact, GPC in this particular case shows a slight advantage: 304 plates for GPC us 208 for TFFF. Despite the moderate apparent advantage of the GPC column, the TFFF column shows a much cleaner resolution of 5 polymer peaks. In fact, if we draw a summation curve for the 5 fractions in GPC-showing the nature of an actual fractogram-very little peak resolution is discernible (Figure 1A ), In view of the previous discussion, the inferiority of the GPC separation in Figure 1 can be ascribed mainly to the small retention volume range of the GPC method. All fractions must be crowded into a limited region, and peak overlap is thereby encouraged. The retention volume range for TFFF, by contrast, is much larger, and can be considered to extend off the right-hand margin of the figure. More peaks are separable even with fewer theoretical plates, as the equations predict. In general, peak capacity is a useful index of separation because it reflects the system's capability for separating close-lying polymer peaks or for covering a broad molecular weight range, or for achieving both of these two objectives to some intermediate degree.
LC
I;
;-
i-
