Anal. Chem. I90g9 61 2449-2455
2449
Isocratic Elution of High Molecular Weight Monodisperse Polystyrenes C. H. Lochmuller* and Mary Beth McGranaghan Department of Chemistry, Duke University, Durham, North Carolina 27706 The retention mechanism of high molecular weight, organic polymers was examined by using binary solvent mobile phases and hydrocarbon bonded phases. Under carefully controlled conditions, nonzero but finite &’ values were obtained for polystyrenes of molecular weights up to 3.0 X 10’. The &’values obtained can be used to predict the gradient eiutbn time composition values quite accurately, udng weliknown relationships based on ordinary chromatographic theory. Such &’ values can be observed If adequate mixing of solute and mobile phase prlor to column exposure Is assured. Failure to achieve such mixing plays a significant role in the chromatographic behavior of these macromolecules. Furthermore, dze excludon effects are present and necessitate the use of a wide-pore stationary phase. The conclusion drawn is that whlie experimental conditions must be adapted to accommodate the special characteristics of polymer materials, traditional chromatographic theory is adequate to predict their retention.
INTRODUCTION The separation of synthetic macromolecules by high-performance liquid chromatography (HPLC) has been an area of active research for several years. Typically, separations are achieved by means of gradient elution, but the fundamental basis for such gradient separations is the subject of substantial controversy. It is held that the traditional chromatographic theory, first applied to the partitioning or adsorption behavior of small molecules, is equally applicable to polymer separations. Counter to this, other theories based on purely mobile-phase control of solute retention have been put forth. A clear, definitive model is needed in order to accelerate the realization of the full potential of macromolecular separations by HPLC. Central to the development of such models is the development of experimental approaches to the measurement of isocratic retention volumes for the macromolecules. Armstrong et al. reported the nonaqueous fractionation of polystyrenes using a binary solvent mobile phase in conjunction with “reversed-phase” thin-layer chromatography (TLC) and HPLC (1-4). They concluded that the separation of polystyrene is controlled by the composition of the mobile phase and pose the existence of a critical composition, directly dependent on the molecular weight of the polymer, at which the dissolved polymer would precipitate and, conversely, the precipitated polymer would dissolve. They argued that the fractionation of any molecular weight range of polymers can be accomplished strictly by altering the solvent ratio in the mobile phase (I). Armstrong contends that traditional theories which do not account for either inter- or intrapolymer segment-segment interactions are incomplete and cannot fully explain macromolecular separations (2). In support of the conclusions of Armstrong et al., Martire and Boehm developed a model for the equilibrium distribution of infinitely dilute and, therefore, isolated, flexible polymer molecules between a binary solvent mobile phase and a planar stationary phase based on the Flory-Huggins lattice model (5-7). Although precipitation was invoked in the earliest work published and has never been clearly withdrawn as a mechanism (4), in this 0003-2700/89/0361-2449$01.50/0
model infinitely dilute sample solutions are assumed and the phase preference depends on the degree of polymerization, the solvent composition and chemical nature of the solvent, solute, and surface interactions. The Martire-Boehm explanation has drawn considerable criticism from proponents of linear solvent strength (LSS) chromatographic theory. Snyder and co-workers argue that this traditional theory is adequate to describe the fractionation of macromolecules by gradient elution and suggest that while a key feature of these polymer solutes is the potentially strong dependence of retention on mobile-phase composition, this possibility need only be considered in terms of optimizing the separation (8,9).Snyder et al. compared the “critical solution theory” with data previously presented in the literature (10). They concluded that the arguments supporting the unique effects due to critical solution behavior lacked credibility. In addition the same group examined the precipitation-redissolution process proposed by Glockner and co-workers (11, 12) and concluded that retention occurs either by sorption of molecules to the stationary phase or by precipitation-redissolution processes and that the precise mechanism of retention depends on the solubility of the sample (13). We have examined the retention of a series of polystyrenes under carefully controlled conditions. The results support the description of macromolecular separations in LSS chromatographic terms. Thin-layer chromatographicexperiments yield identical R, values for polystyrene samples spotted on dry adsorbent and on adsorbent wetted with the “good” solvent prior to mobile-phaseexposure. These results suggest that migration is due to an adsorption process rather than one completely controlled by the alteration of the solvent ratio in the mobile phase. HPLC further supports this claim. Under isocratic conditions, finite, nonzero capacity factor values (k 7 were attained for 600-dalton, 4-kdalton, 17.5kdalton, 35-kdalton, 104-kdalton, 300-kdalton, and 2.8Mdalton polystyrene. These observable changes were detected by using small changes in the solvent composition of several solvent pairs. A linear relationship of log k’versus volume percent of good solvent in the binary mixture (+) is obtained in all cases. Further, it is observed that separation is greatly influenced by treatment of the solute prior to its contact with the column. Previously reported experiments appear to have used the most favorable mobile-phase component as the solvent for the polystyrenes to be studied (2,3). In the work reported here, it was found that conventional behavior is obtained only if steps are taken to adequately mix the sample into the mobile phase prior to column contact. If the measures described in the discussion of results are not taken, at least part of the polystyrene sample apparently remains well solvated by the sample solvent throughout the chromatographic experiment and is, thus, completely insulated from both mobile- and stationary-phase effects. What is clear from our results is that the insurance of uniform elution conditions throughout the experiment can eliminate some of the retention anomalies reported to date.
EXPERIMENTAL SECTION X
Materials. Whatman KC18F reversed-phase TLC plates (20 5 cm) were used in the TLC fractionation of polystyrene.
0 1989 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
Table I. Rr Values for TLC ExDeriments Using Saturated Plates (A), Dry Plates (B), and Plates Preequilibrated with Vapor
(0 strong solvent-
6OOQ
%
4000"
100000Q
35000"
A
B
C
A
B
C
100 90 80 70 60 50
1.00 1.00 1.00 1.00 0.76 0.76
1.oo 1.oo 1.00 1.00 0.72 0.68
1.00 1.00 1.00 1.00 0.75 0.67
1.00 1.00 1.00 1.00 0.70 0.58
1.00 1.00 1.00 1.00 0.68 0.58
1.00 1.00 1.00 1.00 0.69 0.58
100 81 78 76 70 0
1.00 1.oo 1.oo 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00
1.00 0.98 0.74 0.57 0.52 0.00
1.00 0.99 0.75 0.56 0.52 0.00
1.00 0.97 0.74 0.57 0.52 0.00
100 60 55 50 40 0
1.00 1.00 1.00 1.00 1.00 1.00
1.00 1.00 1.oo 1.00 1.00 1.00
1.00 1.00 1.00 1.00 1.00 1.00
1.00 0.66 0.52 0.50 0.10 0.00
1.00 0.66 0.53 0.50 0.09 0.00
1.00 0.65 0.52 0.50 0.09 0.00
A
B
280O00Oa
C
A
B
C
A
C
1.00 1.00 0.92 0.78 0.51 0.21
1.00 1.00 0.81 0.60 0.32 0.00
1.00 1.00 0.81 0.59 0.32 0.00
1.00 1.00 0.82 0.61 0.32 0.00
1.00 1.00 0.70 0.54 0.00 0.00
1.00 1.00 0.69 0.53 0.00 0.00
1.00 1.00 0.72 0.54 0.00 0.00
1.00 0.74 0.51 0.41 0.19 0.00
1.00 0.52 0.32 0.25 0.00 0.00
1.00 0.53 0.30 0.26 0.00 0.00
1.00 0.53 0.32 0.26 0.00 0.00
1.00 0.31 0.00 0.00 0.00 0.00
1.00 0.31 0.00 0.00 0.00 0.00
1.00 0.30 0.00 0.00 0.00 0.00
1.00 0.34 0.27 0.00 0.00 0.00
1.00 0.20 0.12 0.00 0.00 0.00
1.00 0.21 0.13 0.00 0.00 0.00
1.00 0.20 0.12 0.00 0.00 0.00
1.00 0.06 0.00 0.00 0.00 0.00
1.00 0.07 0.00 0.00 0.00 0.00
1.00 0.06 0.00 0.00 0.00 0.00
THF/MeOHb 1.00 1.00 0.91 0.78 0.51 0.20
1.00 1.00 0.92 0.79 0.53 0.21
MeC1/MeOHc 1.00 0.74 0.51 0.42 0.19 0.00
1.00 0.74 0.51 0.40 0.19 0.00
MeCl/ACNc 1.00 0.34 0.26 0.00 0.00 0.00
1.00 0.34 0.28 0.00 0.00 0.00
Molecular weight of polystyrene. * THF used as the stronger solvent in the binary mobile-phase pair. MeCl used as the stronger solvent in the binary mobile-phase pair. Whatman Partisil lO,ODS-2 bonded phases and Alltech Hypersil wide-bore C8 bonded phases were used in the HPLC columns. HPLC grade acetonitrile (ACN),methanol, methylene chloride, tetrahydrofuran (THF),and water were obtained from American Burdick and Jackson Co. From Polyscience, Inc., were purchased pdystyrene standards of the following molecular weights (M,/M, values in parentheses): 600 (1.3), 2000 (1.06), 4000 (1.04), 35000 (1.06),100000 (1.06),104000 (1.04), 300000 (1.06), 2800000 (1.2), 3 000 000 (1.04). A "crocheted" column reactor from Applied
Biosystems was used to enhance mixing. TLC. TLC fractionation was carried out in an airtight 113/4 in. long, 4 in. wide, and lo3/, in. high developing chamber. The mobile phase consisted of various ratios of good/poor solvent pairs, (methylene chloride/methanol, tetrahydrofuran/methanol, methylene chloride/acetonitrile). Accurate volume ratios were obtained by weight by using the known density. Solvent composition was then checked by refractive index with the use of a Bausch and Lomb Abbe refractometer. Each polymer standard was dissolved in the stronger solvent of the solvent pair to concentrations of 2 mg/mL. Approximately 1pL of each solution was spotted on the TLC plates. After being spotted, but prior to developing, the plates were subjected to one of three possible treatments. They were (1) equilibrated with solvent vapor, (2) saturated with 100% of the more favorable solvent by fully dipping the plate in that solvent, or (3) not subjected to any equilibrationor treatment of any kind. Detection was accomplished by fluorescence quenching. HPLC. Both isocratic and gradient HPLC of polystyrene were carried out with a Perkin-Elmer Series 4 liquid chromatograph and Perkin-Elmer LC420B autosampler. Detection was accomplished with a Varian Varichrom variable wavelength detector (270 nm) or a Hewlett-Packard 1070-A diode array detector. Retention data was collected by using the Nelson Analytical chromatography package. Columns 5 and 10 cm in length were utilized for retention studies. A 25-cm column was used for the preliminary studies of the separation of high molecular weight oligomers. Samples were dissolved by using a mixture of the good and poor solvents to a concentration of 2 mg/mL for most experiments and in keeping with the reported work of Armstrong et al. (1-5). Additional experiments were performed to assess any dependence of V,/ on sample concentration. Flow rates of 1 and 2 mL/min and a sample size of 10 pL were used. Connecting tubing from sample loop to column and column to detector was initially straight stainless steel (i.d. = 0.25 mm). Improved mixing prior to the column was achieved by replacing this connecting
tubing with "serpentine" stainless steel (i.d. = 0.25 mm), and finally, a "crocheted reactor" constructed from poly(tetrafluor0ethylene) (PTFE) tubing was placed in line prior to the column (14-16). Capacity factor calculations were carried out by using the retention time of each polymer under nonretaining conditions, t,. For small molecules t , = to; for large molecules t, < to since the solvent-swollen polymer may be excluded from regions accessible to the smaller solvent molecules. RESULTS AND DISCUSSION TLC. Thin-layer chromatography was employed to examine the role of the mobile phase in polystyrene separation, as well as to establish the most desirable binary mobile-phase composition for the fractionation of these homopolymers. Previous reports suggest that the depletion of the thermodynamically "good" solvent from the advancing mobile phase caused the polymer to precipitate selectivelyon the TLC plate. One might expect that if the TLC plates are saturated by exposure to the good solvent prior to development, the mobile phase would migrate the length of the plate without a loss of its better solvent by fractionation. Table I lists the R, values obtained from TLC experiments using dry and preequilibrated ODS-3 plates. Those plates saturated in the good solvent prior to spotting and development yielded R, values comparable to those of plates that were dry. This suggests that the mechanism of separation is not one of selective precipitation. Rather, it appears that the solute undergoes an equilibrium sorption process involving the mobile phase and stationary phase and its fiial placement is the result of migration slower than that of the mobile-phase front. The values in Table I further suggest that for each binary mobile-phase pair there exists a finite region in which a polymer will go from being highly retained by the stationary phase to being eluted with the mobile phase. In each case the lower molecular weight polystyrene exhibits a wider range over which notable migration takes place; yet even for polystyrenes up to molecular weight 2.8 X lo6, a region of migration was noted. HPLC. High-performance liquid chromatography (HPLC) was used to observe the polymers' elution behavior and to establish the practical parameters needed for an efficient separation. Initial efforts focused on a mobile phase consisting
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
of methylene chloride as the "good" solvent and methanol as the "poor" solvent. Isocratic elution data were generated for several polystyrene homopolymers, (600dalton, 4 kdalton, 17.5 kdalton, 35 kdalton, 104 kdalton, 300 kdalton, and 2.8 Mdalton). It was observed that variations in 4 as small as 0.001% indeed resulted in a change of k'from a very low to a very high value. While these data closely paralleled previously reported work, several features of the chromatograms were anomalous. First, decreases in the 4 of the good solvent in the isocratic mobile phase resulted in elution at the void time (to)as opposed to the elution time initially observed for the polymer when the mobile phase consisted only of the more favorable solvent ( t J . Second, all retained peaks appeared nonsymmetrical with severe tailing. The tailing significantly worsened with mobile phases consisting of larger volume fractions of poor solvent, and incomplete recovery of the polystyrene samples was noted. These observationssuggested that while some of the solute was eluting with the solvent plug, at least a portion of the injected polystyrene sample was being retained on the column. This was confirmed by using a diode array detector and adding a gradient to the end of the isocratic program. The UV spectrum of the species eluted at the void volume was identical with that eluted with the gradient. Neither peak was detected with the injection of pure solvent nor was there any indication of the presence in significant amounts of low molecular weight oligomers, monomers, or related compounds in any of the solvent systems studied. Further, when columns of varying lengths were used, it was noted that, under the same mobile-phase conditions, a sample eluting from a 5-cm column at the void volume showed complete retention on a 10-cm column. This suggested that the polystyrene was actually being spread over the length of the column as a result of poor mixing of the sample into the mobile phase in the injection step. We observe that mixing of the sample plug and the mobile phase prior to the column plays a particularly important role in the chromatography of polymer molecules. A macromolecule differs from its smaller counterpart in that there exists a volume within the molecule where favorable solvent is sorbed and unfavorable solvent and other polymer segments are excluded (17). The presence of this "excluded volume" allows a large molecule to remain well solvated from its interior until the external solvent environment is so thermodynamically hostile that segment-segment interactions are favored above all those of segments and solvents. Thus, a polymer can exist in several conformations, exhibiting a swollen form in good solvent and a contracted form in poor solvent. The polymer's ability to change shape and sue in response to its environment results in a nonuniform sample distribution as the more favorable solvent plug mixes with the poorer mobile phase, causing varied retention behavior of the polymer molecules. This problem can be further complicated if the interconversion from one conformation to another occurs on a time scale longer than that of the chromatographic process. When the samples are prepared in mixtures of the same binary solvents used in the mobile phase and adequate mixing prior to the column is provided, a more uniformly solvated sample can be attained and retention behavior examined. Figure 1illustrates the effect of the solvent in which samples are prepared. Under equivalent isocratic conditions the same 35 000-dalton polystyrene prepared in various proportions of THF/H20 yielded four different chromatograms. The initial sample prepared in 100% of the good solvent, (THF), shows elution at the void volume (k'= 0) for a mobile phase of 86/14 THF/H20. With increases of H20 in the preparative solvent, however, this void volume peak diminishes and a peak at t , = 3.65 min (k' = 5.64) becomes increasinglyprominent. This procedure was continued until the polymer was no longer
0 - 1 5 MLn. S c a l e :
2451
5 0 Hv
Flgure 1. Chromatogramsof a 35kdaton polystyrene prepared in four different solvents: (a) 100% THF, (b) 9515 THF/H,O, (c) 90/10 THF/H,O, (d) 86/14 THF/H,O, and eluted isocratically with a mobile phase of THF/H,O (86114).
soluble at concentrations of 2 mg/mL. It is apparent that while some polystyrene is eluting at the void volume, a portion of the sample experiences a different environmentand exhibits an adsorption type behavior. Greater mixing of the solute between the sample loop and the column was initially achieved by replacing the short straight stainless steel tubing with a longer piece that had been bent into a "serpentine shape", so as to minimize band broadening. Katz and Scott previously demonstrated the ability of this serpentine shape to induce a secondary, radial flow that disturbs the parabolic flow profile common in straight tubing (14). Thus, an additional length added to provide mixing would not result in significant band dispersion. A second means of providing precolumn mixing was the use of a tightly crocheted PTFE reactor (15). These chambers have been found useful as mixing cells for postcolumn derivatization reactions (16). With the use of a commercially available model, a volume of 0.5 mL was placed prior to the column. The difference in peak shape for a 35000-dalton polystyrene is shown in Figure 2. The initial peak eluting at t owhen no added mixing is provided is no longer observed when adequate mixing is applied. These results were typical of all polymer samples up to 1.04 X 105dalton. With the larger molecular weight polymer samples, 3.00 X lo5 and greater, a single peak chromatogram was unattainable on the C18, 100-8, bonded phase. Following the method described by Birks et al. (14),larger mixing chambers were constructed and placed in line to yield 1.5-2.0 mL of mixing prior to the column. This allowed for at least partial mixing of the higher molecular weight samples. What is noteworthy is that the sample size is the same for all these experiments. One would expect that 10 pL of sample volume would be adequately mixed in a volume independent of the sample molecular weight. The need for more and more mixing volume as the molecular weight increases implies a need for increased contact
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
0-15 nln.
rcnls!
SO
nv
Flgure 2. Chromatograms of a 35-kdalton polystyrene eluted by a THF/H,O (86.5/13.5) mobile phase: (a) without added mixing prior to the column, (b) with a commercial mlxer placed between injector and column.
1 . 6 LO
A 0 +
I kD 11.5 k0
.
35 ko
104 k0
300 1 0
2800 1 0
+ *IC1
Flgure 3. Plots of log k'vs 4 for polystyrene eluted isocratically by using a binary moblle phase: (top) THF/H,O (bottom) MeCVACN with a C18 bonded phase (100-A pore size).
time with the mobile phase on the part of the solute molecules. Whiie the transition from swollen coil to collapsed coil occurs abruptly in polymers over a narrow composition range, this process may have a rate that is significantly slow on the chromatographic time scale. This rate can only be speculated upon a t this time, and future experiments are planned to elucidate this observation. Figure 3 shows the log k'vs 4 plots for polystyrene eluted by using two different binary mobile phases, THF/H20 and MeCl,/ACN, on a C18 bonded phase. Linear relationships were observed for each solute. It is clear that small additions of the poorer solvent to the mobile-phase composition exhibited a direct and significant influence on the value of the capacity factor. Yet, for each polymer a distinct region did exist wherein nonzero, finite k'values could be measured. The range of this region is dependent upon the molecular weight of the sample, with the large molecular weight polystyrenes showing a more abrupt change in k' values as opposed to the smaller polystyrenes, which display a more gradual progression.
Flgure 4. Plots of the S value, A log k'lA4, obtained kom polystyrene retention data vs molecular welght: C18 bonded phase, (100-A pore size); MeCVACN mobile phase.
The parameter S is a measure of the slope of log k'vs 4 plots from isocratic data. When S is plotted for each polymer as a function of its molecular weight, as in Figure 4, a monotonic increase is noted for those samples up to 104 X 103 but styrenes of higher molecular weight yield S values significantly lower than anticipated. One avenue of explanation is to consider the effect of pore exclusion. The C18 bonded phase has an average pore size of 100 A. Smaller solutes are able to penetrate the pores with relative ease. As the molecular diameter of the solute gets larger, this ability to diffuse into the pores decreases. Thus, the surface area available for interaction with these larger solutes is significantly less. This results in decreased retention volumes and reduced k 'values. Since the effect is constant throughout the isocratic experiment, plots of log k'vs 4 are still linear, but the slopes of such plots are significantly lower than predicted from the plots of the lower molecular weight polymers. Another possibility is sample loading, but as will be seen later, sample size has little effect on retention. If loading were a problem, one would have expected this to be exaggerated when a lower capacity column was used. The observation is that the use of a larger pore, albeit lower capacity, column eliminated the problem. Figure 5 shows plots of log k'vs 4 obtained with the same binary mobile phase and a C8 bonded phase with an average pore size of 300 A. Again linear relationships were observed for all polystyrene samples, as well as the molecular weight dependence of the transition region. However, a plot of S values as a function of molecular weight yielded a monotonic increase for all samples up to 300 000 as shown in Figure 6. This plot was constructed with data from the MeCl/ACN mobile phase since the C8 phase required weaker mobile-phase strength for elution and resulted in a solubility limitation for the larger molecular weight samples. It is believed that the larger 2.8 X lo6 sample would exhibit the same behavior, but the ability to examine its behavior is limited by our ability to control the chromatographic conditions needed to detect its elution. The change in good solvent over which measurable retention will occur is predicted to be less than O.OOOl% . To
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
2453
5
4
3
0
Vr
0
0
0
0
0
0
0
0
2
1
I
Figure 5. Plots of log k’vs 4 for polystyrene eluted lsocratlcally by using a binary mobile phase: (top) THF/H,O; (bottom) MeCVACN with a C8 bonded phase (300-A pore size).
YIlkD)
Flgm 6. Plots of the S value, A log k’lA4, obtalned from polystyrene retention data vs molecular weight: C8 bonded phase (300-A pore size); MeCllACN moblle phase.
accurately and reproducibly administer this change in solvent composition is beyond the scope of the existing experimental apparatus. Thus, we believe that while the same retention process governs these larger molecules, the demands on the chromatographic system are much more stringent due to the larger excluded volume present in the higher molecular weight polystyrenes, the smaller change in solvent composition needed to induce a shift in their elution behavior, and the exclusion of these large samples from the pores of the stationary phase. An important consideration is the possible effect of chain-chain interactions between high molecular weight polymers in high concentration sample bands. High sample
.2
log
1
concmtratlon
0
1
[mglml]
Figure 7. Plots of retention volume, V,, vs log sample concentration from three MeCI/ACN mobile-phase ratios (A)50150, (0) 51/49, (0) 52/48. Sample concentrations range from 20 to 2 X mg/mL.
loadings could also result in exclusion of solute from the stationary phase and, subsequently, unexpected effects on retention behavior. We examined the effect of sample concentration on isocratic retention over the range 20 mg/mL to 2 x mg/mL and found no dependence. Figure 7 illustrates this for three mobile-phase solvent compositionsfor a nominally monodisperse polystyrene of MW = 35 000 over 5 orders change in concentration. At 2 mg/mL, a 35-kdalton polystyrene is likely a “semidilute” solution, and if this were likely to have a significant effect, some sample concentration dependence should be seen. Again, both TLC and isocratic HPLC data suggest that the separation of high molecular weight polystyrenes can well be described by relationships derived from classical, conventional chromatographic theory. As a further verification, gradient liquid chromatography was used to predict the isocratic retention data for these molecules. A convenient approach to obtaining such data has been suggested based on the LSS model (18). Here two gradient runs can be used to develop the generally accepted reversed-phase approximation log k’ = log k , (1) where S represents the change in log k‘for unit change in C#J in isocratic elution. The term k , is the capacity factor in pure water. The use of linear gradients enables eq 1to be expressed as log ki = log ko - b(t/to) (2) since the condition for LSS behavior is satisfied. Here ki represents the value of k’at the column inlet during gradient elution (ko = ki when t = 0) and b is proportional to the steepness parameter, which has been defined in terms of experimental conditions of mobile-phase volume, dead time, composition change, and flow rate as b = A4SVm/tz (3) Gradient retention time (t,) for a given solute is related to b by t, = (to/b) log (2.3kob(tg/to) + 1) + t o + t d (4) where ko equals the k’value at the beginning of the gradient
2454
ANALYTICAL CHEMISTRY, VOL. 61, NO. 21, NOVEMBER 1, 1989
Table 11. Comparison of Gradient Derived S Values with Isocratic Measurements; C8 Bonded Phase, 300-A Pores
S MW
predicted
b
actual
THF/HZO" 4000 17 500 35 000
0.097 0.282 0.308
4000 17 500 35 000 104000 300 000 3 000 000
0.059 0.072 0.087 0.143 0.184 4.226
11.43 33.12 46.14
11.51 35.21 47.39
MeCI/ACN* 3.46 16.93 23.17 44.02 91.87 2113.10
5.75 13.03 17.51 43.69 95.33
"Tetrahydrofuran/water gradient, b1 = 0.5, $r = 1, t , = 10 min, bMethylenechloride/acetonitrilegradient, = 0.2, = 0.7, tl = 20 min, t z = 30 min.
t 2 = 15 min. $f
Table 111. Comparison of Gradient Times Predicted from Isocratic Data with Those Obtained from Gradient Elution; C8 Bonded Phase, 300-A Pores
t, MW
predicted
actual
4 000 17 500 35 000
8.14 9.15 9.28
8.20 9.37 9.57
% THF at elution predicted actual
79.65 84.75 85.35
79.95 85.80 86.81
% MeCl at elution
t,
MW
predicted
actual
predicted
actual
4 000 17 500 35 000 104000 300 000
4.28 12.45 14.18 15.89 16.83
4.57 12.90 14.49 16.29 16.90
38.68 45.73 50.05 54.33 56.67
44.61 46.85 50.83 55.33 56.85
Figure 8. Chromatogramof the individual oligomers of a polystyrene standard ( M , = 2000; M , / M , = 1.06) obtained with gradient RPLC: mobile phase, THF/H,O; A 4 = 0.1 (70% THF to 80% THF); t , = 25 min; flow rate, 2 mL/min; column, ODS-3, 25 cm. (Top) Full scale = 50 mV. (Below) Full scale = 15 mV.
and t d represents the delay time between the pump and the column. If one carries out several gradient runs with different gradient times ( t G l , t ~eq ~4 allows ) for the explicit solution of the steepness parameter b by
bi = ( t o log @ ) / [ t i- ( t z / P ) - ( t o
+ ~ D ( P- 1)/P)1
(5)
where p is In turn, rearrangement of eq 3 allows the S value to be determined. This S value represents the change in log k'with changing solvent composition as produced by the gradient. Gradient chromatography was used as described here for the purpose of estimating the plot of log k'vs 4 for each of the polystyrenes studied. The data from the gradient runs was used to calculate the b parameter from which the S value of eq 1 was derived and compared with the plots obtained through isocratic elution. A comparison of the derived and experimental values is summarized in Table 11. In both mobile phases employed, the gradient data predicts quantitatively the same dependence of log k'vs 4 as was found under isocratic conditions. Alternatively, these same relationships can be used to predict the gradient elution time and composition of the mobile phase from isocratic data. Table I11 shows the gradient times, t,, and the corresponding volume percent of the good solvent at elution. In this case the values generated isocratically agree well with those obtained when gradient chromatography is employed. This ability to interrelate the two methods of elution based on ordinary chromatographic theory further argues that polymer retention is adequately described by classical, conventional LSS theory
over the molecular weight range studied. This study considered polymers with molecular weights separated by an order of magnitude or more. With the understanding provided here, the mechanism controlling the separation process can now be exploited to develop the potential of these separations. Work is currently under way to demonstrate the ability of gradient reversed-phase liquid chromatography to separate individual high molecular weight oligomers by molecular weight. Figure 8 shows the resolution of the individual oligomers of a nominally monodisperse polystyrene standard (MW = 2000 and M J M , = 1.06) using precolumn mixing as described in this paper. Future studies will include the application of both solvent and temperature gradients toward the attainment of this goal.
CONCLUSION Various theories for the separation of large molecular weight polymers by high-performance liquid chromatography have been proposed. Our results clearly demonstrate that there exists for each molecular weight styrene polymer studied, a region where finite, nonzero k' values can be obtained under isocratic conditions. While these regions narrow in volume percent with increasing molecular weight, definite areas of transition are clearly observed; that is, slopes of A log k' vs A 4 become large but not infinite. The Boehm-MartireArmstrong-Bui theory does predict a transition from high retention to low over a narrow range of composition a priori and provides a molecular basis for that observation. The LSS theory makes no such predictions a priori but can be used to predict the observed behavior of molecules within the region of finite retention. It would appear that some of the experimental findings reported by Armstrong et al. could be artifacts of the experimental method used. Adapting experimental conditions to accommodate the needs of these large
Anal. Chem. 1989, 61, 2455-2461
flexible solutes (i.e., providing adequate mixing of solute and phase and using stationary phases) results in complete agreement with conventional chromatographic theory. Registry No. Polystyrene, 9003-53-6.
LITERATURE CITED Armstrong, Armstrong, Armstrong,
D.W.; Bui. K. H. Anal. Chem. 1982, 5 4 , 706. D.W.; Boehm, R. E. J. Chromatogr. Sei. 1984, 22, 378. D.W.; Boehm, R. E.;Bui, K. H. J . Chromatogr. 1983, 6 ,
1
Armstrong, D. w.; Boehm, R. E.; Bui, K. H. J . c h ~ o m t o g r .1984, 288, 14. Boehm, R. E.; Martire, D. E. Anal. Chem. 1989, 67, 471. Boehm, R. E.; Martire, D. E.;Armstrong, D. W.; Bui, K. H. Macromolecubs 1983. 16,466. Boehm, R. E.; Martire, D. E.; Armstrong, D.W.; Bui, K. H. Macromolecubs 1984, 17,400. Snyder, L. R.; Stadalius, M. A,; Quarry, M. A. Anal. Chem. 1983, 55,
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(9) DeStefano, J. J.; Goldberg, A. P.; Larmann, J. P.; Snyder, L. R.; Stadalius, M. A.; Stout, R. W. J . Chromatogr. 1983, 255, 163. (10) Stadalius, M. A.; Quarry, M. A.; Mourey, T. H.; Snyder, L. R. J . Chromatogr. 1988.358, 17. (11) Glockner, G. Pure Appl. Chem. 1983, 55, 1553. (12) Glockner, G.; van der Berg, J. H. M. J . Chromatogr. 1988, 352, 151. (13) Stadalius. M. A.; Quarry, M. A.; Mourey, T. H.; Snyder, L. R. J . Chrom t o g r . 1986, 358,I. (14) Katz, E. D.;Scott, R. P. W. J . Chfomatogr. 1983, 268, 169. (15) Poulsen, J. R.; Birks, K. S.; Gandelman, M. S.;Birks, J. W. Chromatographic 1966, 22,231. (16) Blrks. J. W.; Frei, R. W. TRAC, Trends Anal. Chem. (Pers. Ed.) 1983, 7 , 361. (17) . , Fiorv. P. J. I n Princides of Polvmer Chemise; Cornel1 University Preis: Ithaca, NY, 1953;p 519: (18) Quarry, M. A.; Grob, R. L.; Snyder, L. R. Anal. Chem. 1986, 58, 907.
RECEIVED for review May 5, 1989. Accepted August 3, 1989. The authors acknowledge the support, in part, of a grant (to c* Lochmuller) from the National Science Foundation CHE-8500658.
CORRESPONDENCE Random-Walk Theory of Nonequilibrium Plate Height in Micellar Electrokinetic Capillary Chromatography Sir: Micellar electrokinetic capillary chromatography (MECC) is a highly efficient separation technique implemented in a narrow-bore capillary tube, along which is applied a large electric field. Separation is based on the partitioning of electrically neutral analytes between a mobile liquid electrolytic phase, whose motion arises from field-induced electroosmosis, and a micellar phase of electrically charged micelles, whose lesser motion arises from the combined fieldinduced effects of electroosmosis and electrophoresis. The differential migration of the two phases spatially separates the components of a mixture, when the components' partition coefficients differ (1-3). A significant distinction between MECC and the parent technique on which it is based, capillary zone electrophoresis (CZE), is that the plate heights of certain analytes resolved by MECC, under typical experimental conditions, appear to be govemed by nonequilibrium effects when the electric field strength exceeds roughly 7-20 kV/m ( 4 , 5 ) . In other words, a contribution to the plate height increases with the electric field strength, apparently in a linear manner, and becomes the dominant source of plate height at field strengths greater than these. In contrast, only small nonequilibrium-likeeffects are observed in CZE at these field strengths (6, 7), unless the analytes readily adsorb to and desorb from the capillary wall, as do proteins (8, 9). Ultimately, plate heights in CZE do increase with field strength, but only when the field exceeds 30 kV/m or so, under typical experimental conditions (10). In general, rapid separations in MECC, as in any electrophoretic method, require large field strengths. Because plate heights ultimately increase with increasing field strength, one can simultaneouslyobtain rapid and efficient separations only if one reduces or minimizes these (apparent) nonequilibrium effects. To minimize them, one must have some physicochemical understanding of their origin. In a recent work, Sepaniak and Cole argued that these effects originate from transchannel mass transfer ( 4 ) . An equation for this mass transfer that agrees fairly closely with experiment, and thus supports this conclusion, is derived below. 0003-2700/89/0361-2455$01.50/0
THEORY In a recent work, Terabe et al. examined several possible sources of nonequilibrium dispersion in MECC, including sorption-desorption kinetics, intermicelle diffusion, the effect of temperature gradients, and electrophoretic dispersion (11). They developed theories for each source of dispersion and concluded that only electrophoretic dispersion could explain their experimental results. Their work is most instructive in demonstrating that many plausible sources of dispersion do not, in fact, govern the nonequilibrium plate height. In this paper, the author will consider again a source of dispersion first addressed by them and also a new source of dispersion, which seems to explain much experimental data. In both cases, the magnitudes of these dispersions will be estimated from the theory of a random walk, and these estimates will then be compared to experiment. In this approximate but heuristic theory, one assumes that any representative analyte molecule is displaced along the flow direction an average distance 1 from the center of a zone formed from a statistically large number of analyte molecules. After n displacements, the breadth of the resultant analyte distribution is described by the variance u2 = 12n. The nonequilibrium plate height H is then calculated as
H
=
." = -12n L
L
(1)
where L is the column length. Several applications of random-walk theory to chromatography are discussed by Giddings (12).
The basic assumptionsare herewith stated. One will assume that any analyte molecule has two characteristic velocities. The first of these, u,, is the velocity of the molecule in the mobile phase; the second, um0 is the velocity of the molecule in a micelle. For dilute zones, the velocities u, and u,, essentially equal the velocities of the analyte-free mobile and micellar phases, respectively. The average velocity v of the analyte molecule, by definition, is a weighted average of u, and u,, 0 1989 American Chemical Society
