Determination of pore size distributions of liquid chromatographic

950

Anal. Chem. lg84, 56,950-957

this concentration. Bulky ions, such as I- and Clod-, showed a positive error because their ion pair with EV was extracted into toluene. Application to the Determination of Boron in Seawater. As described above, the coexisting ions usually present in seawater did not interfere with the determination when the seawater was diluted 50-fold. The results obtained by the standard procedure are shown in Table 111. The recovery tests conducted by adding a known amount (0.109 pg) of boron to the sample solution confirmed that the recoveries were satisfactory (97.2 to 100.9%). Reaction and Extraction Mechanism. The reaction mechanism of the formation of the boron complex with DBC (HzR) and the extraction mechanism of the ion pair with EV are considered to be as follows:

HzR + (H&)org

(dye+)(HR-),,,

+ dye+

+ H+

(2)

+

( ~ Y ~ + ) ( B R ~ - ) 3, ,H~ z 0 + H+ (3)

+ HzO

slow

(Dye-OH),,, (carbinol)

+ (HZR)org (4)

HA

LITERATURE CITED

(1)

dye+ + (H2R)org+ (dye+)(HR-),,,

HSB03 + 2(HzR)o,g

The spectroscopic study indicates that reactions 3 and 4 are rather time-consuming states. The presence of hydrogen peroxide markedly facilitates reaction 5, yielding the colorless carbinol within 1 min which shows its characteristic absorbance at 350 nm. On the other hand, the absorption spectra of DBC around 290 nm in toluene remained unchanged after adding hydrogen peroxide. These results suggest that hydrogen peroxide presumably catalyzes the transformation of the colored EV to the colorless carbinol. Registry No. Boron, 7440-42-8; 3,5-di-tert-butylcatechol, 1020-31-1;ethyl violet, 2390-59-2; water, 7732-18-5.

(dye+)(HR-)org+ HzO fast- (dye-OH),,,

+ (H2R)org

(5)

(1) Kuwada, K.; Motomlzu, S.; Toei, K. Anal. Chem. 1978, 50, 1788-1792. (2) Toei, K.; Motomizu, S.; Oshima, M.; Watari, H. Analyst (London) 1981, 106, 778-78 1. (3) Oshima, M.; Motomlzu, S.; Toei, K. Bunseki Kagaku 1983, 32, 268-272. (4) Sato. S.; Uchikawa, S. Anal. Chim. Acta 1082, 143, 283-287. (5) Sato, S. Anal. Chim. Acta 1983, 757, 465-472. (6) Hakoila, E. J.; Kankare, J. J.; Skarp, T. Anal. Chem. 7972, 4 4 , 1857-1860. (7) Schulze, H.; Flalg, W. Justus Liebigs Ann. Chem. 1052, 575, 231-241.

RECEIVED for review November 3, 1983. Accepted January 16, 1984.

Determination of Pore Size Distributions of Liquid Chromatographic Column Packings by Gel Permeation Chromatography F. Vincent Warren, Jr., and Brian A. Bidlingmeyer* Waters Associates, 34 Maple Street, Milford, Massachusetts 01757

A method for the determlnatlon of “effective” pore slre dlstrlbutlons (PSDs) and median pore dlameters (MPDs) by gel permeatlon chromatography Is applled to 37 commerclally avallable columns. A practlcal dlscusslon of the technlque addresses preclslon, alternatlves for data presentatlon, and the use of n-hydrocarbons to supplement the polystyrene standards ordlnarlly used. The resultlng MPD values are In general agreement with the nominal pore sires speclfled by column manufacturers. I n a few cases, the MPDs are as much as 50% below the antlclpated value.

There is presently a need for more information concerning the median pore diameter (MPD) and pore size distribution (PSD) of commercially available chromatographic column packings. The need for this information is quite significant as many chromatographersare now suggesting that differences in chromatographic performance are due to pore size differences among the various packings (1-7). Unfortunately, the chromatographic behaviors attributed to pore size are frequently baaed on information which is limited. Often, specific details concerning MPDs and PSDs are not available to chromatographers. In some situations these are proprietary

to the manufacturer. In others, a specification comes from the silica supplier, and in still other cases, some information is not even known. Another problem is that the average pore size information may result from one of several different methodologies; therefore, comparisons based upon these data become meaningless. When a nominal pore size (NPS) is available, some ambiguity may still remain as this value may not reflect batch to batch variations. If the measurement technique used by a manufacturer to determine the NPS is not stated and if the width of the pore size distribution is not provided, it is difficult to make accurate claims regarding pore size effects. There is no guarantee that a nominal pore size specified by the manufacturer is closely related to the mean of the pore size distribution. For instance, if the nominal pore diameter is determined by the Wheeler equation (8),then the stated values give only a rough indication of the mean of the pore size distribution (9). Clearly, for chromatographic columns, there is a need to standardize the method used to determine pore size distribution and mean pore diameter. There are two common techniques for the direct measurement of pore size distributions: mercury intrusion and gas condensation/evaporation (9). Using either af these techniques has not been practical for most chromatographic

0003-2700/84/0356-0950$0 1.50/0 0 1984 American Chemical Society

ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984

laboratories. First, the equipment required for either of these techniques is costly, as is its maintenance. In qddition, these methods can only be applied to dry, rigid solids, and it is not clear how effectively they may be used to characterize porous polymers or chemically modified materials. Heither method is representative of the type of penetrations which would occur in a chromatographic system. A simpler means for the measurement of nore size distribution is based upon gel permeation chromatography (GPC). By use of probes in solution, the information obtained will be more indicative of the molecular diffusion which takes place in a liquid chromatographic separation. This method, introduced in 1975 by Halasz (10) and described more fully later (11-17), uses polystyrene standards as pore size probes. Similar techniques have since been discussed by others (18-21). The standards are eluted from a chromatographic column with a strong solvent such as tetrahydrofuran. A packed column may be analyzed by this procedure and may be returned to normal use after determination of the pore size distribution. The required equipment is an isocratic liquid chromatograph, which is commonly available to most chromatographers. The measurements can be completed in a few hours and the calculations are easily performed with a microcomputer or handheld calculator. A systematic comparison of the GPC technique for measurement of PSDs with the results of mercury intrusion and gas condensation/evaporation is obviously of great interest. However, such a study is beyond the scope of this paper. Halasz has addressed this issue (11),although additional work is needed to establish a detailed relationship between the alternative sources of PSD information. In the absence of a more complete understanding of this relationship, we consider the results of the GPC technique to be'"effective" PSD information, and we interpret the assigned values (see below) as "effective" pore diameters. The goal of this report is to describe the application of the GPC technique for the determination of PSDs for a variety of columns. We have expanded the applicability of the GPC method by incorporating two needed modifications. These are the use of hydrocarbon standards for better probing the small pores of the PSD and the use of polynomial curve fitting for objective determination of the pore size distribution and median pore size. The quantitative characterization of various pore size distributions using this method is shown to be simple and informative and should provide the basis for more valid studies of pore size effects in LC. Ohmacht and Halasz have published PSD data for a number of commercially 'supplied silicas (22) which were subsequently compared chromatographically (23). This paper will demonstrate the broad applicability of the GPC method for the evaluation of PSDs of commercially available packings. A variety of examples are reported including silica, chemically modified silica, alumina, pellicular packings, and styrene-divinylbenzene gels.

THEORY Polystyrene standards are eluted from a packed column with a strong solvent such as methylene chloride, tetrahydrofuran, or chloroform. The size and geometry of the column are unimportant. These standards serve as pore size probes, because each standard is of a known molecular weight and is associated with a characteristic random coil diameter in solution. On the basis of an empirical relationship developed by Halasz and Martin (11) (eq l),it is possible to

4 = 0.62 MW0.59

(1)

associate with each polystyrene standard a pore diameter 4 (in angstroms) which corresponds to the smallest pore allowing W n d e r e d access to the standard of a given molecular weight (MW). The significance of this equation, which closely re-

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Flgure 1. Cumulative PSD for a Waters pbndagel E500 column. The

dashed line is a fifth-order polynomial, fit to the experimental data. loo

1

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Flgure 2. Point-by-point derivative of Figure 1.

sembles the well-known Mark-Houwink relationship, is discussed elsewhere (11,24). The elution volumes ( Vd for the polystyrene standards may be expressed according to eq 2, provided that a t least one standard is totally excluded from the column pore volume (Vex)and that at least one standard is totally included (Vi").

A plot of R vs. log 4 is the cumulative PSD for the column packing and will resemble the typical curve shown in Figure 1. This is clearly seen when R is interpretql as the percentage of the total pore volume to which a given polystyrene probe has access. The 4 value which corresponds to R = 50.0% denotes the median pore diameter (MPD) of the material. That is, a polystyrene probe having this 4 value would be excluded from half of the pore volume. The & I value is, therefore, a useful figure for the characterization of column PSDs. Calculation of the point-by-point derivative of Figure 1gives a representation of the PSD, as shown in Figure 2. Here the quantity (AR/A log 4) X 100 is plotted as a function of the geometric mean of each pair of log 4 values. While the plot is useful for the visualization of differences among PSDs, little quantitative information can be directly extracted from Figure 2. However, the PSD can often be fitted satisfactorily to a Gaussian. The mean and standard deviation of the fitted curve can then be used to characterize the PSD. The

952


Table I. Summary of Column and PSD Information

columnu supplierg d,, Mm Ultrasil Octyl 1 10 Ultrasp here Oct yl 5 1 Bakerbond Widepore C18 2 10 RP18 Lichrosorb 5 3 RP300 Aquapore 10 3 Zorbax ODS 5 4 Chromegabond C18 5 10 Vydac Polar Bonded Phase 6 10 Vydac 218TP 6 10 Spherisorb ODS 5 7 LC18 8 5 LC318 5 8 RP-P C18 9 6.5 RP18 Lichrosorb 10 10 Universil C18N 11 10 alumina 11 10 pBondapak C18 12 10 pPorasil 10 12 pPorasil GPC 60A 12 10 @Bondage1E l 25 12 10 @Bondage1E500 12 10 pBondagel El000 12 10 pBondage1 EHIGH 12 10 @Bondage1ELINEAR 10 12 Radial-PAK Silica 5 12 Radial-PAK C8 5 12 Corasil 37-50 12 Bondapak C 18/Corasil 37-50 12 I125 Protein Analysis 10 12 I250 Protein Analysis 10 12 Radial-PAK PAH 12 f Prep Bondapak C18 55-105 12 Novapak C18 5 12 RP8 Lichrosorb 10 12 RP18 Lichrosorb 12 10 Ultrastyragel 500A 12 10 Protesil 300 13 10

bonded type e phase I C8 S C8

nom pore size 100 80 330 100 3 00 75 100 330 330 80 100 300 300 100

$10

417 891 1133 851 1000

$25

200 132 603 200 575

$50

100 72 263 89 275 57 79 263 251 71 98 209 245 76

@75

d d

@ 90

corr coeff

0.999 62 0.999 70 S C18 110 0.998 96 I C18 d 0.999 64 S f 129 63 0.998 78 S C18 d d 37 29 0.985 44 d C18 776 166 d d 0.999 53 S 1175 f 575 136 91 0.998 27 C18 S 1162 562 110 0.999 22 15 S C18 24 5 126 d d 0.998 76 S C18 234 646 d d 0.998 91 S C18 912 468 95 52 0.998 26 S C18 1162 562 105 0,999 14 19 I C18 794 158 d d 0.999 59 I b C18 1950 81 d d 170 0.999 38 I b 3090 355 79 d d 0.999 28 I C18 125 417 214 100 50 30 0.999 74 I 125 5 50 251 110 50 0.998 39 27 S 60 288 63 d f d 129 0.996 82 I 125 41 7 d 200 95 51 0.997 93 f I 500 631 302 1122 135 f 63 0.999 03 I 1000 955 1660 457 209 105 f 0.998 68 I 1995 3311 955 347 56 f 0.999 39 f I 1259 3020 347 98 42 0.999 69 f f S 90 275 148 71 36 23 0.995 87 S C8 90 135 1862 72 d d 0.998 21 P b d 2754 89 d 263 0.997 65 P C18 b d 2089 59 d 309 0.998 8 3 I 125 d 315 87 d 162 0.999 76 f I 2 50 912 468 214 95 f 48 0.998 93 S 140 575 d 24 5 120 71 0.999 02 f I C18 d 170 69 d 125 112 0.997 81 S C18 d 90 2630 759 68 d 0.997 8 1 I C8 100 d 776 95 d 195 0.999 61 I C18 100 d 174 1820 81 d 0.999 47 G 500' 93 158 46 24 16 0.999 1 9 I C8 653 d 300 35 5 162 78 0.998 88 a All brand names covered by a trademark. Not available. Exclusion limit specification (see text). Polynomial deviates from data, e Type of particle. Key: I, irregular silica; S, spherical silica; P, pellicular; G, gel. f Proprietary. P Key: 1,Altex-Beckman, Berkeley, CA; 2, J. T. Baker Research Prod., Phillipsburg, PA; 3, Brownlee Labs, Santa Clara, CA; 4,Du Pont, Wilmington, DE; 5, E. S. Industries, Marlton, NJ; 6, The Separations Group, Hesperia, CA; 7, Spectra Physics, Santa Clara, CA; 8, Supelco, Bellefonte, PA; 9, Synchrom, Linden, IN; 10, Unimetrics, Anaheim, CA; 11, Universal Sci., Atlanta, GA; 12, Waters Associates, Milford, MA; 13, Whatman Chemical Separation, Clifton, NJ.

agreement between Ra and the mean of the Gaussian provides a useful check on internal consistency.

EXPERIMENTAL SECTION Chromatographic System. Elution volumes for the polystyrene and n-hydrocarbon standards were determined with a Waters Associates (Milford, MA) Model ALC 244 which included a Model 6000A solvent delivery system, a Model 401 differential refractometer, a Model 440 absorbance detector operating at 254 nm, and a WISP automatic injector. The analog outputs of the differential refractometer and UV absorbance detector were recorded with a Model 730 Data Module (printer, plotter, integrator) (Waters). A simplified system without automated components could equally well be used for the determination of PSD information. For the present work, use of the absorbance detector is optional. The columns indicated in Table I are listed alphabetically by their suppliers. Columns from Waters Associates were obtained in Radial-PAK cartridges (0.8 X 10 cm) whenever possible. Polystyrene standards were obtained from Waters (mol w t 3K, 8K, 17.5K, 35K, llOK, 250K, 390K, 2700K) and Toyo Soda (Atlanta, GA) (2.8K, 6770K, 8420K). Styrene monomer and normal hydrocarbons (C12436) were obtained from various suppliers. o-Dichlorobenzene (ODCB) was obtained from Aldrich (Milwaukee, WI) and used without further purification. HPLC grade THF (unstabilized) and methylene chloride were obtained from Waters. The solvents were filtered through 0.5 fim filters (Millipore, Bedford, MA) ahd degassed before use.

d d d d

Measurement Technique. For each PSD determination, the column to be tested was prepared by passing at least five column volumes 'of eluent (generally THF) through the column. A flow rate of 1.0 mL/min was used throughout the experiments. Fresh standards were prepared weekly in the eluent. Styrene, ODCB, and n-hydrocarbons were prepared as approximately 0.15% (w/v) solutions, except for the C12-Cl3 hydrocarbons (0.32%) which showed a weak response on the differential refractometer. Polystyrene standards were prepared as 0.03% (w/v) solutions. The standards were injected individually by the WISP, and elution volumes were automatically determined by the Data Module. For standards with molecular weight greater than 8000, it was convenient to include an ODCB or styrene internal standard. In this manner, all elution volumes could be reported relative to a constant elution volume for ODCB. For lower molecular weight standards, the standard peak sometimes overlapped with the ODCB peak and these standards (2800,3000,8000)were therefore analyzed without the ODCB marker. Data Analysis. Normal hydrocarbons were assigned "polystyrene-equivalent" molecular weights using an empirically derived correction factor. This factor of 2.3 was determined (25) from the inspection of calibration curves for polystyrenes and nhydrocarbons, generated under identical chromatographic conditions using the same column. The calibration lines for the two sets of standards were observed to be parallel. Multiplication of the hydrocarbon molecular weights by 2.3 generates polystyrene-equivalent molecular weights such that all calibration data fall on the same curve.


953

Table 11. Correlation Coefficients for Various Polynomial Fits column Du Pont Zorbax ODS Supelco LC318 Whatman Protesil Octyl

+so,

57 209 162

2

1

0.873 04 0.966 26 0.967 15

degree of polynomial 3 4 0.967 23 0.998 57 0.998 40

0.94249 0.998 15 0.994 62

0.942 47 0.967 78 0.994 62

5

6

0.985 44 0.998 26 0.998 78

0.995 57 0.999 59 0.998 17

Table 111. Cumulative PSDs with and without n-Hydrocarbons column Du Pont Zorbax ODS Supelco LC318 Waters pBondapak C18 Waters pPorasi1 Waters Radial-PAK Silica

$10

with without with without with without with without with without

2089 1820 91 2 871 417 3 89 550 550 275 21 9

The raw molecular weight vs. elution volume data were converted to log @ vs. R values by a BASIC computer program (PORESIZE) executed on an Apple I1 Plus microcomputer (Apple Computer, Cupertino, CA). The regulting values were then fit to a polynomial using the CURVE FITTER software package (Interactive Microware, Inc., State College, PA). A fifth-order polynomial was generally found to give the most satisfactory fit. By interpolation routines present in the CURVE FITTER package, the log @ value corresponding to any specified value of R could be determined and converted to the corresponding value of in angstroms. The @ values at R = lo%, 25%, 50%, 75%, and 90% were determined for all column packings (Table I). The PORESIZE program also calculated the point-by-point derivative of the R vs. log @ curve. The PSD thus determined was plotted with the APPLE PLOT software package (Apple) to facilitate visual comparison of PSDs. For a more quantitative comparison, selected R vs. log @ data were fit to a Gaussian distribution by manual plotting on probability paper.

RESULTS AND DISCUSSION Table I summarizes information concerning the cumulative pore size distributions of 37 commercially available columns. The values of 4 corresponding to 10,25,50,75, and 90% of the pore volume are listed. These were determined from fifth-order polynomial curves having the correlation coefficients indicated. The $s value gives the column MPD. Other @ values can be used to specify the width of the PSD (e.g., 80% of the pores have a diameter between and 490). In many cases, 475and &,, values are not reported because the polynomial fit was judged (visually) to deviate significantly from a portion of the data. Selection of Polynomial Curve Fit. GPC calibration data are often fit to a first-order (linear) or third-order polynomial. Alternatively a 'best fit" smooth curve may be drawn by hand, but this approach is inherently more subjective. h,drder to ensure an objective and reproducible treatment-of the data, we pref6rre'd to fit a polynomial to the cumulative PSDs summarized in Table I but did not wish to a s k m e that a third-ordbr fit would be optimal. In order to select the best polynomial for all the column data, first-order through sixth-order fits were generated for three representative cumulative PSDs having median pore diameters ranging from 57 A to 209 A. The correlation coefficients for these curve fits are summarized Table 11. From the data presented, it appears that a sixth-order fit would be the best choice. Visual inspection of the actual polynomial curves does not corroborate this selection. Figure 3 shows the six curves generated for a Supelco LC318 column. The fifth-order fit is visually selected as superior, particularly in its fifth-order fit is visually selected

$25

@SO

100

57 38 209 219

98 468 479 214 191 251 209 148 129

100

98 110

102 71 76

075

37 20 95 93 50 58 50 60 36 50

@,

29 14 52 41 30 43 27 44 23 39

corr coeff 0.985 44 0.997 1 2 0.998 26 0.999 2 1 0.999 74 0.999 67 0.998 39 0.998 28 0.995 87 0.999 85

as superior, particularly in its fit to data at the extremes of the cumulative PSD. Other curves from Table I1 reinforced this conclusion. Interestingly, the fifth-order fit for the Whatman Protesil Octyl column has the best correlation Coefficient in addition to appearing superior visually. On the basis of these comparisons, a fifth-order polynomial was used to fit all the cumulative PSDs. Columns having an extremely narrow PSD will not be well suited by any polynominal fit between first and sixth order. Of the 37 columns studied, only one (Zorbax ODS) demonstrated this problem. The curves generated for this column are presented in Figure 4. The correlation coefficients are given in Table 11. From an inspection of the curves in Figure 4, it is apparent that even the value of the median pore diameter (MPD) will be influenced by the choice of polynomial. This is not a general problem. In Figure 3, for example, the central portion of the cumulative PSD is adequately fitted by polynomials of fourth, fifth, and sixth order. For the Zorbax ODS column, however, an MPD of 57 A is obtained from the fifth-order fit, while the sixth-order fit yields an MPD of 49 A. Visually, the latter value appears to better represent the data. For an unusual cumulative PSD of the type shown in Figure 4, a "best fit" smooth curve drawn by hand might provide the most reliable interpretation of the data. A set of three straight lines could also give a workable solution. Fortunately, visual inspection of the fifth-order polynomial fits for each of the 37 columns studied revealed that problems with the polynomial fits were limited to the Zorbax ODS column. Based on our experience, visual inspection is always advised when calibration data are fit to a polynomial curve. A good correlation coefficient does not guarantee an acceptable fit to the full range of the data. Use of Normal Hydrocarbons. ,For columns having an MPD less than 4s = 100 A, polystyrene standards may not provide sufficient information about small pores of the PSD. Inspection of the cumulative PSDs for a variety of columns of this type reveals a lack of information for R > 50%. This problem leads to the missing @75 and @w values in Table I. Figure 5 provides a specific example of this problem for a Waters Radial-PAK silica column. The quality of the polynomial fit for R > 50% is questionable. If only a value for the MPD is desired, the data are sufficjent; however, if values such as @75 and @w are desired, more data are required to fill in the plot and generate a better polyhomial fit. Previously, a series of alkyl-substituted benzenes was used to supplement polystyrene standards (26). Hydrocarbon standards can also be used to provide the additional data points.

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Several columns were analyzed with a full set of standards including both polystyrene standards and n-hydrocarbons. The resulting 4 values are summarized in Table 111. Polystryene-equivalent molecular weights (MW,) for each hydrocarbon were determined from the empirical equation (25)

MWp = 2.3 MWH

(3)

where MWHis the hydrocarbon molecular weight. In all cases the use of hydrocarbons provided a visually superior polynomial fit over the entire range of the cumulative PSD. This is not generally reflected in the correlation coefficients given in Table I11 and series to further reinforce the need for visual inspection of fitted polynomial curves. Columns having the

highest MPD values show the smallest relative changes in 4 values with the inclusion of n-hydrocarbons. This is to be expected, because the smallest polystyrene probes are able to penetrate a significant proportion of the pore volume for these columns. For columns having MPD less than about 6% = 100 A, inclusion of hydrocarbons is particularly desirable, as indicated by Figure 5 for a column having 4% = 71 A. In general, the use of hydrocarbons is useful for any determination of cumulative PSD. If only a value for 6% is needed, polystyrene standards alone will frequently suffice. For all but the Zorbax ODS column in Table III, the 6% values for each column agree within 7% for first- through sixth-order polynomials. It might appear that polystyrene oligomer mixes


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hydrocarbons are used to supplement polystyrene standards.

could be used in place of n-hydrocarbons, with the advantage that no refractive index detector would be needed. In practice, however, the analysis of oligomer standards will make the correct assignment of V, more difficult due to the presence of multiple peaks for the closely related oligomers which are present. The use of alkyl-substituted benzenes (26)may provide a useful alternative. Nominal Pore Size. The nominal pore sizes listed in Table I can be considered to give a rough indication of the manufacturers expectation for the mean of the PSD. A comparison of the NPS and 4so(i.e., MPD) values from Table I indicates that the experimental values are generally less than the corresponding nominal pore sizes. This is not surprising for bonded phase materials, since the nominal values are typically based on analysis of unbonded base material. Additional batch-to-batch variations are to be expected. Nonetheless, some of the discrepancies seen in Table I are too large to be dismissed on the basis of these considerations. Halasz estimates the thickness of a C18 bonded phase to account for about a 20 A difference in MPD (11). Batch-to-batch varia-

958

ANALYTICAL CHEMISTRY, VOL. 56, NO. 6, MAY 1984 too,

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I


Figure 6. Column fingerprints: point-by-point derivative PSDs of Waters Radial-PAK C8 and Radial-PAK C18 columns, showing good qualitative agreement because the same base silica is used for both columns.

tions might contribute similarly. This fails to explain the discrepancies observed for some materials in Table I, for which the NPS values are nearly twice the corresponding MPDs. This indicates the inadvisability of relying on nominal pore sizes in evaluating and comparing commercially available columns. For gel permeation columns such as the Waters Ultrastyragel column, a direct comparison between the MPD and NPS values cannot be made. By historical definition ( 2 3 , the nomenclature for the angstrom value of the column refers to the exclusion limit of the column. In the case of an U1trastyragel500 A column, the nominal value of 500 A is not the NPS but rather indicates that polystyrene molecules having a chain length equal to or greater than 500 A will be excluded from all pores in the gel. Thus the MPD of 450= 46 A is not expected to compare favorably with the nominal 500 A designation. Representation of the PSD. When the derivative of Figure 1 is calculated, the plot shown in Figure 2 is obtained. This plot may be interpreted, with some caution, as a rough outline of the PSD. At first glance, Figure 2 appears to indicate bimodality, but this cannot be correctly inferred on the basis of Figure 2 alone. The value plotted on the Y axis is a quotient, and standards of similar molecular weight which elute a t nearly the same volume may give an inappropriately large or small value. The apparent bimodality of Figure 2 is due to a single data point corresponding to a polystyrene standard having mol wt 17 500. In comparing the PSDs for a variety of columns, this same data point was frequently found to be out of place. This probably indicates a problem with the molecular weight assigned to this standard. For quantitative purposes, the cumulative PSD is more useful than the point-by-point derivative PSD. This is particularly true when a polynomial fit is used t~ smooth the data. The most useful application of the point-by-point derivative is as a “column fingerprint”. Figure 6 shows the PSDs for two closely related materials. The fact that the base silica is the same despite a different bonded phase is apparent from inspection of the curves. This approach may be useful for visual ”pattern recognition“ and classification of columns according to their base material regardless of bonded phase. A Gaussian distribution can often be fit to the experimental PSD. For example, Figure 7 allows a visual comparison of the Gaussian PSD with the point-by-point derivative (Figure 2) for a pBondagel E500 column. Data from the cumulative PSD for any column may be plotted on probability paper to

Figure 7. Overlay of point-by-point derivative PSD and Gaussian PSD for a Waters IBondagel E500 column.

ggL

90

\.

80

o

= 0.42

10 : : b 1 . 7

1

0.1

1

k 2

3

Lag(0)-

Figure 8.

Plot on probability paper of cumulative PSD data for a Waters Ultrastyragel 500 A column, indicating the determination of p and u for the Gaussian PSD.

Table IV. Gaussian PSDs for Selected Columns column Bakerbond Widepore C18 Supelco LC18 Vydac Polar Bonded Phase Waters WBondagel E l 2 5 Waters pBondagel E500 Waters PBondagel El000 Waters Ultrastyragel 500A Whatman Protesil Octyl

W

2.40 2.02 2.46 2.02 2.47 2.62 1.70 2.24

0

0.59 0.64 0.51 0.38 0.48 0.46 0.42 0.52

log @so

2.42 1.99 2.42 1.98

2.48 2.66 1.66 2.21

yield values for a Gaussian fit. An example of the method used to fit cumulative PSD data to a Gaussian distribution is shown in Figure 8 for a Waters Ultrastyragel 500.4 column. The mean (I) and standard deviation (u) of the Gaussian PSD may be read directly from the plot. The mean is the log d, value corresponding to 50% of the area under the Gaussian, while the standard deviation is the difference between the mean and the log d, value corresponding to 16% (or 84%) of the area under the Gaussian. Mean and standard deviation values for several representative columns are presented in Table IV. For comparison, log @50 values are also listed. The agreement between p (in A) and log d,50 is a good indication of internal consistency for the method. The agreement between the two curves in Figure 7 indicates that reasonable


values for the mean and standard deviation have been obtained. Unfortunately, not every PSD can be adequately represented by a Gaussian distribution. Some plots on probability paper reveal two intersecting straight lines rather than a single line, This might represent data from a bimodal PSD. Our experimentation with synthetic overlapped Gaussian8 demonstrated that the values of p and u extracted from such a plot will be in error. This limits the utility of the Gaussian PSD. The cumulative PSD with a polynomial curve fit will still give accurate information, however, since no assumption is made concerning the nature of the PSD. Precision. For most of the columns studied, ODCB was included in all standards of mol w t MOO0 as an internal check on reproducibility of elution volume (Vg). The variation in V, was generally no more than a few hundreths of a milliliter for ODCB. When the variation exceeded 0.1 mL, the pump and on-line fiter were checked and the column was reanalyzed. As a further check on reproducibility of V,, selected columns were analyzed in triplicate by use of a full set of standards (styrene, 7 n-hydrocarbons, and 12 polystyrenes). Relative standard deviations for the elution volumes ranged from 0.0 to 0.5%,with most standards showing no variation in V , over three runs. We have experienced no problem in analyzing the same column on different days using different standards or even different instruments. The resulting cumulative PSDs can generally be overlaid and give nearly identical &, values. When this is not the case, a system problem has generally been discovered.

CONCLUSION A GPC method for PSD determination has been applied to 37 commercially available columns of widely varying characteristics. The 950 values presented in Table I indicate that the nominal pore sizes quoted by manufacturers may give only an approximation of the MPD. Most 950 values were within 20% of the nominal pore size, but a few &, values were 40-50% lower than the manufacturer’s claim. For the study of pore size effects in HPLC, PSDs determined by GPC may provide a useful starting point. Normal hydrocarbons can be successfully used as a supplement to polystyrene standards, to improve the applicability of the method to columns having a large volume of small ((100 A) pores. The cumulative plot is most useful for obtaining quantitative information regarding the column PSD. A fifth-order polynominal generally provides a good fit to the data and allows an objective means for calculating the MPD ($50) and other 4 values.

957

In our experience, the GPC method gives reproducible results for both manual and automated runs. Due to its convenience and simplicity, we routinely use this approach in our investigations (24,28),both as a source of physical data regarding column packings and as a tool for the monitoring pore size effects. We anticipate that other chromatographers will find this method useful in their research.

ACKNOWLEDGMENT The authors gratefully acknowledge the assistance of J. Newman in preparing the manuscript as well as P. Watson and T. Lewtas for assistance with the figures. LITERATURE CITED (1) Vanacek, G.; Regnler, F. E. Anal. Biochem. 1980, 709, 345. (2) Walters, R. R. J . Chromatogr. 1982, 249, 19. (3) Lewis, R. V.; Fallon, A.; Stein, S.; Glbson, K. D.; Udenfrlend, S. Anal. Biochem. 1980, 704, 153. (4) Van Der Rest, M.; Bennett, H. P.J.; Soloman, S.; Florieux, F. H. Biochem. J . 1980, 197, 253. (5) Pearson, J. D.; Mahoney, W. C.; Hermodson, M. A,; Regnier, F. E. J . Chromatogr. 1981, 207, 325. (6) Pearson, J. D.; Lin, N. T.; Regnler, F. E. Anal. Biochem. 1982, 724, 217. (7) Wilson, K. J.; Van Wlerlngen, E.; Klauser, S.; Berchfold, M. W.; Hughes, G. J. J . Chromatogr. 1982, 237, 407. (8) Engelhardt, H. Unlversitat des Saarlandes, Saarbrucken (G.F.R.), personal communicatlon, 1982. (9) Unger, K. K. ”Porous Slllca”; Elsevler: Amsterdam, 1979. (10) Halasz, I.Ber. Bunsenges Phys. Chem. 1975, 7 9 , 731. (11) Halasz, I.; Martin, K. Angew. Chem., I n f . Ed. Engl. 1978, 77, 901. (12) Halasz, I.; Vogtel, P. Angew, P. Angew, Chem., Int. Ed. Engl. 1980, 19, 24. (13) Werner, W.; Halasz, I. Chromafographia 1980. 73,271. (14) Nikolov, R.; Werner, W.; Halasz, I. J . Chromatogr. Sci. 1980, 78, 207. (15) Werner, W.; Halasz, R. J . Chromatogr. Sci. 1980, 78, 277. (16) Groh, R.; Halasz, I. Anal. Chem. 1981, 53, 1325. (17) Crlspln, T.; Halasz, I. J . Chromatogr. 1982, 239, 351. (18) Freeman, D. H.; Polnesca, 1 . C. Anal. Chem. 1977, 49, 1183. (19) Schram, S. B.; Freeman, D.H. J . Liq. Chromatcgr. 1980, 3 , 403. (20) Freeman, D. H.; Schram, S. B. Anal. Chem. 1981, 5 3 , 1235. (21) Kuga, S. J . Chromatogr. 1981, 206, 449. (22) Ohmacht, R.; Halasz, 1. Chromatographla 1981, 74, 155. (23) Ohmacht, R.; Halasz, I. Chromatographia 1981, 74, 216. (24) Warren, F. V.; Bldllngmeyer, 8. A.; Richardson, H.; Ekmanis, J. In “Recent Advances in Slze Exclusion Chromatography”; Provder, T., Ed.; American Chemical Society; Washington, DC, ACS Symposium Series, In press. (25) Ekmanis, J., Waters Associates, Milford, MA, personal communicatlon, 1983. (26) Halasz, I.; Vogtel, P.; Groh, R. 2. Phys. Chem. (Wiesbaden) 1978, 172, 235. (27) Cazes, J. J . Chem. Educ. 1986, 43, A587. (28) Warren, F. V.; Bldlingmeyer, B. A. Paper presented at Pittsburgh Conference on Analytical Chemistry and Applied Spectroscopy, Atlantic City, NJ, March 7-12, 1982; Abstract No. 136.

RECEIVED for review August 22,1983. Accepted January 24, 1984.

Determination of pore size distributions of liquid chromatographic

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