3036
Anal. Chem. 1986, 58,3036-3044
Hydrodynamic Chromatography of Macromolecules in Open Microcapillary Tubes Robert Tijssen,* J a a p Bos, a n d M. Emile van Kreveld
KoninklijkelShell-Laboratorium,Amsterdam (Shell Research B. V . ) ,Badhuisweg 3, 1031 CM Amsterdam, The Netherlands
The development of an ultravlolet “on-column” detection technique with Improved signal-to-ndse ratlo allows the study of the separation mechanism in mlcrocapillary hydrodynamic chromatography (HDC). For polystyrene standards, for which data on the molecular slzes in solutions are avallable, the experimental residence tlmes almost exactly follow the modffled theorles after DIMarzio-Guttman and Brenner-Gaydos, at least with good solvents such as tetrahydrofuran. These modlfied theorles use the effective radius of macromolecules, Le., the radius based on the largest size of the chain, rather than hydrodynamic or other theoretical radll. Mlcrocaplllary HDC separatlons are efflclent and dlrectly reflect the size dlstrlbutlon (and hence the molecular weight distribution) of polymer samples. Futthermore, mkrocaplllary HDC is well-suited to studying size effects of polymer molecules In solutlon.
Hydrodynamic chromatography (HDC) is a relatively new technique, mainly used for the separation of colloidal particles of different sizes. The pioneering work was done by Small (1-3), who demonstrated its practicability for separating mixtures of polymer latexes and colloidal dispersions using packed beds as the separation column. Pedersen ( 4 ) , Mori et al. ( 5 ) ,and more recently Prud’homme et al. (6) showed that in principle large molecules such as proteins, polystyrenes, and water-soluble polymers can also be separated into fractions of different molecular weights by applying packed bed separation columns. For an extensive review of packed-column HDC, the reader is referred to a recent article by McHugh (7) and a somewhat earlier one by Dodds (8). Mullins et al. (9, l o ) , Brough et al. ( l l ) and , Shuster et al. (12) demonstrated experimentally that HDC separation of differently sized particles can also be effected in a single open tubular capillary column with a diameter of the order of several tenths of a millimeter. Elie and Renaud (13)succeeded in separating fibrous particles in paper fiber suspensions using even wider open tubes (id. = 1 cm). The particle separation technique called field flow fractionation (FFF), which was developed by Giddings et al. (14), is carried out in open channels with parallel walls. FFF is closely related to open tubular capillary HDC (15) and is also suited to the separation of macromolecules (14). More recently (16)we extended the working range of open tubular or capillary HDC to include microcapillaries of 1-10 pm i.d. for the separation of polystyrene macromolecules from small molecules like toluene. It was found that a qualitative agreement could be obtained between experimental residence (“retention”) times and theoretical ones as predicted by an adapted theory of “separation-by-flow“, which was originally put forward by DiMarzio and Guttman (DG) ( I 7-19). A test of more quantitative agreement with ‘either DG or the more sophisticated Brenner-Gaydos theory (BG) (20) had to await developments in detector technology. The present contribution reports the experiments carried out after an improvement of our UV detector had enabled the
signal-to-noise ratio to be increased by about 1 order of magnitude. The experimental results will be interpreted in terms of the modified DG and BG theories. EXPERIMENTAL SECTION The microcapillary columns as used in this work have internal diameters down to about 1pm and column volumes not exceeding 20 nL. The corresponding flow rate of mobile phases is of the order of 1 nL/min, which precludes the use of standard LC techniques for liquid-phase flow, sample introduction, and detection of sample zones. A schematic representation of the apparatus used in shown in Figure 1. Just as in our earlier work on microcapillary LC and HDC ( 1 6 ) ,we prefer the use of a split technique as the method of introducing sample and mobile phase. This allows the use of commercially available LC pumps and injectors, while at sufficiently high splitting ratios peak broadening outside the column is carefully controlled and kept within practical limits. We used a standard M 6000 HPLC pump (Waters Assoc., Milford, MA) set to deliver a flow rate of 1 mL/min through a U 6 K injector (Waters Assoc., Milford, MA). The injector outlet is connected to a metal T-piece via a metal tubing of 0.5 mm i.d. and 10 cm length. The microcapillary HDC column to be used (fused silica, SGE, North Melbourne, Australia) is stuck into the T-piece such that the column entrance protrudes 2 cm into the 10-cm connecting tubing with the injector. The split ratio (flow through the column/flow split off via the T-piece) is now determined by the dimensions of the interchangeable resistance capillary, for which we also used fused silica capillaries (50-100 pm id.) of different lengths. The pressure drop across the resistance capillary determines the pressure within the T-piece and so the required inlet pressure and flow for the HDC microcapillary. Flows and pressure for each particular capillary used were estimated by Poiseuille’s law. After the sample loop of the injector has been loaded with sample solution, the required amount of sample is injected by switching the injector into the “inject” position for a time of say 3-10 s depending upon the split ratio. Subsequent switching back into the “load” position ensures that the injected sample zone is cutoff into a more or less blocklike shape. In this way peak shapes after transport through the HDC column are not significantly affected by the injection process. As before (16),by burning off a small length of the polymer coating at the end of the fused silica microcapillary columns, this end section can be used as the detector cell for on-column UV detection of eluting sample zones. In this way sample concentrations are relatively high, and additional peak broadening in connections and in the flow cell of the detector is avoided. In principle, the apparatus used was the same as that reported in our earlier work (16),with a few alterations: (1)The splitter had been constructed from a standard Waters Assoc. compression screw T-piece with graphite ferrule connections. This allowed, among other things, the connection of a pressure transducer (Bell and Howell 4-366-0001-OIMO; range 0-5000 psi), necessary for determining pressure drop vs. flow relationships. (2) Data were recorded on an HP 7004B X-Y recorder (rise time 1 s ) or, alternatively, were digitally stored on an HP 3357 lab automation system after 8-Hz AD conversion (HP 18652A). Digital data handling was carried out either on an HP 9836C or on an HP 85 desk-top computer. (3) The UV-vis detector had been replaced by a Jasco UVIDEC 100-111variable-wavelength detector, which is twice as sensitive as the former UVIDEC 100-11. The commercially available apparatus had been adapted in two ways. First,
0003-2700/86/0358-3036$01.50/00 1986 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 58, NO. 14, DECEMBER 1986
3037
2
HPLC PUMP
A
INTERCHANGEABLE WASTE RESISTANCE CAPILLARY
)‘I
I
I
I I WASTE
I ON COLUMN UV DETECTOR INJECTOR HDC MICRO CAPlLL ARY COLUMN
Flgure 1. Schematic representation of the apparatus for microcapillary hydrodynamic chromatography.
the measuring cell holder had been equipped with an adjustable slit consisting of two carefully manufactured knives. The angle of the sharp knive edges was such that the main part of the relatively thick quartz wall of the “on-column”detection cell was covered. This limited the occurrence of stray light considerably, improving the signal-to-noise ratio by a factor of 5. Second, optimization of the electronic circuit yielded a further gain in signal-to-noise ratio by a factor of 3. The total gain by a factor of 30 in signal-to-noiseratio as compared with that of the detector mentioned in ref 16 allowed us to work with considerably lower polymer concentrations than before, a prerequisite for meaningful data interpretation. All measurements were carried out at a wavelength of 215 nm. Materials. Fused silica microcapillaries were supplied by SGE (North Melbourne, Australia). Solvents. All solvents were used without further purification. Tetrahydrofuran (HPLC reagent no. 9441), diethyl malonate (practical grade no. 7028), and methyl ethyl ketone (analyzed reagent no. 8052) were obtained from Baker (Deventer,Holland). trans-Decaline (zur Synthese no. 821745) was purchased from Merck (Darmstadt, FRG). Polymers. The following narrow-molecular-weight-distribution polystyrene standards were used (M, is weight average molecular weight; Mp is peak molecular weight, while the value given in parenthesis represents the polydispersity): Polystyrenes of M , = 51 K ( u(rl) in Figure 2). The resulting couple of forces makes the spheres rotate, which influences the translational velocity up(( r ) ) . This hydrodynamic problem was investigated theoretically by DiMarzio and Guttman (17-19) for polymer molecules that are permeable and later by Brenner and Gaydos (20) for hard-sphere particles, with the result that all effects can be described using an increased quadratic term in eq 9 as follows: 7
= (1 + 2x -
cxy
All theories, including the foregoing simple linear and quadratic models as well as the DiMarzio-Guttmann (DG) and the Brenner-Gaydos (BG) theories, are unified by eq 10. Table I shows how upon the choice of the value for C the different models result from eq 10. For instance, in the simple linear model I, C = 0 and the residence time mechanism is exclusion alone. In the simple quadratic model 11, C = 1, which accounts for the parabolic velocity profile. In the DG model for free-draining permeable and rotating polymer spheres C = 1 + 2y, where y is a parameter defined by DiMarzio and Guttman as
(8)
The average residence time for particles with aspect ratio X thus amounts to tp = L/iip, and so = t,/t,
ref 17-19; eq 13
C = 1 2yM = 2.698, y M = 2 / , ( r g / T ) 2= ref 16, 27, 28; eq 25 0.849
permeable spheres
where 2ii = uo,the maximum velocity at the tube center ( r = 0), and u is the average velocity,
7
+
C = 1 2 y D G = 1.465, yDc = 2 ~ / 2 7= 0.233
C, = 0.32
u ( r ) = 2ii
up
ref 17-19, 29; eq 14
'/3
C = 1 + 2yHS + 8C3 = 4.89, yHS=
the polymer sizes. In practice this means that R < 1 pm is desirable. Quadratic Models 11-VIII. Simple Quadratic Model: Model II. The above reasoning is highly idealized as it does not take into account any hydrodynamic effects. The first effect to be reckoned with is the existence of the undisturbed fluid velocity profile after Poiseuille for the solvent point molecules. The local velocity u ( r ) for a stream line at radial position r is well-known to be parabolic in nature,
up =
ref and eq
T
hard spheres and permeable spheres hard spheres and permeable spheres hard spheres
only
I1
C in eq 10
particles types equation of calibration curve
+ 2X - x2)-'
This result, which we call the simple quadric model, or simply model 11, has been obtained several times before (8,21-23) and still only reflects exclusion of particle centers from the wall, taking into account the fluid velocity profile. The quadric correction term X2 as compared with the linear term 2X is very small, and for h < 0.02 the linear model I (eq 2) almost equals
where aDGis the polymer radius according to DiMarzio and Guttman (12) with rg representing the radius of gyration of the polymer chain. As a result, from eq 11 and 12 one finds YDG
= 2 ~ / 2 7= 0.233
(13)
It is interesting to note that the DiMarzio-Guttman theory
ANALYTICAL CHEMISTRY, VOL. 58, NO. 14, DECEMBER 1986
3039
RADIUS, pm
k = ( a / R ) = P A R T . / C O L U M N RADIUS
io 0 r
'o-2k t
io3
TO-'
05
06
os
07 T
VIII.
can also be applied to rotating hard spheres by equating rgHS = aHS(instead of eq 12), giving
y3
(14)
which is the same result as reported by Brenner (29) for particle transport near the center of the tube. Brenner and Gaydos (20), who refined this result by taking into account the different types of hydrodynamic behavior in the central region and the wall region, obtained
C = 1 + 2yHS+ 8C3 = 4.89
(15)
where 7HSis the same as in eq 14 and C3 is a hydrodynamic wall effect constant with a value of 0.32. As indicated by the authors themselves, their analytical solution, which leads to eq 15, is only an approximation and the error in C is about 20%. Still, the difference from DiMarzio-Guttman's solution is substantial, and it is up to the experiments (see Results and Discussion) to decide which theory is best. T o resolve this question, Table I contains one further model description (VII), in which 7DG (as in eq 13) for polymer particles replaces yHS. The models V and VI11 are modified quadratic models in which the effective radius, p, replaces a; we will revert to this point later on. Figure 3 compares several of the theoretical models, plotted as X vs. T in the fashion of GPC calibration curves. Clearly, all these models have the same limiting behavior for very small X (Le., T l),similar to that observed for the simple linear model. For higher X values (X > 0.02) the models differ much more from each other. Again, the experiments should discriminate between the various possibilities. All theories agree in one respect, viz. that the residence times in HDC are mainly determined by the aspect ratio X = a / R , i.e., the ratio of particle and column radii. The next paragraphs deal with the determination of these two radii. Molecular Size. The determination of correct size parameters for macromolecules in solution is a long-standing problem, e.g., in GPC,where the discussion is still unsettled (27,28,30,31),partly because of the difficult modeling of the porous packing. In open tubular HDC, the geometry of the flow tube is well-defined (see next paragraph), and so this technique is much better suited than GPC for determining the size parameters of macromolecules. As stated in the former paragraph, DiMarzio and Guttman calculated on a statistical basis the radius uDG of a polymer
-
I
io7
I
IO*
mw
+
=
I
io6
Figure 4. Molecular radii of polystyrene molecules in THF and 6
chromatography,from bottom to top: simple (linear)model, nonrotating (hard)spheres, model I; simple (quadratic)model, nonrotating (hard) spheres, model I I; quadratic model, DiMarzio-Guttman, rotating permeable spheres, 1 27 = 1.4654, model IV; quadratic model, corrected DiMarzio-Guttman, 1 27 = 2.698, model V; quadratic model, corrected after Brenner-Gaydos, 3.56 + 27 = 5.26, model
YHS
I
io5
09
t ( P O L Y S T Y R E N E ) / t (TOLUENE1 = t p l t M
Figure 3. Comparison of theories for residence times in hydrodynamic
+
I
io4
solvents as derived from experiments on the radius of gyration (cf. Table 11). chain close to a wall; cf. eq 12. Their calculation overlooks the fact that as a consequence of the very fast succession of all spatial configurations (cf. Van Kreveld and Van den Hoed (27,28)),the molecule cannot approach the wall closer than the average distance determined by the outer segments. Hence, we prefer the use of half of the mean maximal cross section (32),to be called effective radius, F, as proposed by Van Kreveld and Van den Hoed (27, 28):
a = 7 = (&/2)rg
= 0.886rg
(16)
This is a factor */6, i.e., roughly half, times the polymer radius uDG (cf. eq 12), and the experiments should clearly distinguish these two possibilities. Several authors (30, 31) suggested candidates for the polymer radius other than aDG and 7, such as the hydrodynamic radii (rh)obtained from viscosity (rh?)or from diffusivity (rhD)(33). Reliable measurements of rh are available for polystyrenes (PS)in several solvents but hardly any are known for other polymers. For tetrahydrofuran (THF) as the solvent Benoit et al. (34) reported viscosity data as
rhQ= (1.31
X
10-5)Mw0.567 (pm)
(17)
This almost equals the diffusivity data determined by Mandema and Zeldenrust (35) via light scattering, rhD
= (1.37 x 1 0 - 5 ) ~ w 0 5(pm) 64
(18)
Equations 17 and 18 should be compared with similar expressions for ax and F, which can be obtained from eq 12 and 16 since rg is known from the light-scattering experiments by Schulz and Baumann (36) for PS in THF:
rg = (1.39
X
10-5)Mw0588(wm)
(19)
So, eq 12 becomes ~ D G =
(2.35 X 10-5)Mw0.588 (pm)
(20)
and eq 16
r = (1.23 X
10-5)Mw0.588 (pm)
(21)
All polymer radii mentioned can be represented by the general equation a = pMwg
(22)
which has been reported earlier in GPC studies (27,30). Table I1 collects all possible values for p and q. Figure 4 shows plots of u vs. M,., after eq 22. Column Radius. Establishment of the correct value of the column radius ( R ) is as important as that of molecular radius ( a ) because both determine A, being defined as alR. As
3040
Table
ANALYTICAL CHEMISTRY, VOL. 58, NO. 14, DECEMBER 1986 11.
Polymer Size Relationships after
a = pMwqa
eq 22
values, Fm
polymer/
solvent
size type
1o"p
PS/THF PSI#
1.39 0.588 LS 2.737 0.500 LS
o;
ref and eq
technique*
q
ref 36 ref 33
+ VISC
solvents
PS/THF PS/THF PS/THF PSiTHF a
aDG= 1.683rg 2.35 f = 0.886rg 1.23 rhe 1.31 rhD 1.37
Equation 22.
LS LS VISC LS
0.588 0.588 0.567 0.564
eq 20 eq 21
ref 34 ref 35
LS, light scattering; VISC, viscometry.
M.
05
06
07
0 8
09 T :I
-1 p/f)*
Figure 6. Theoretical calibration curves for HDC of PS in THF: influence of column radius after the modified DG model (V). The GPC curve is the same as in Figure 5.
Table 111. Pressure Drop vs. Flow Experiments with THF" at 22 "C and Toluene as the Tracer column
A
e5
I
I
I
06
07
7 8
\L 09 7 -
:F
Figure 5. Theoretical calibration curves for HDC of PS in THF after several models: column radius, R = 1 pm; molecular size after eq 21 for 7 except for model IV (DG) where eq 20 for aDGis used The GPC calibration curve is experimental for PL gel (5 pm and 10' A).
microscopic techniques only yield local values (e.g., inlet and outlet diameter), these methods cannot account for possible variations in column diameter. Somewhat more accurate are methods that are based on filling the capillary with, e.g., liquid mercury and weighing the contents or measuring the electrical resistance (37). We prefer, however, a hydrodynamic method of characterizing the columns, viz., by measuring the pressure drop as a function of flow. This method provides information on the column radius on the basis of the same flow process as that used for the HC experiment itself, but this time for point molecules. Furthermore, this hydrodynamic method yields important information on the validity of the Poiseuille flow profile, which is a basic assumption of the theory. For Poiseuille flow. hydrodynamics requires that ii = LpR2//8vL
(23)
from which R follows when v, L , A p and ii are known or measured. For microcapillaries, in which impractically small flows of only a few microliters per hour prevail, a simply follows from a residence time determination for pointlike molecules (e.g., toluene) and eq 6. It is useful to carry out several experiments a t different pressure drops and to plot IL (or tb1-I for that matter) vs. Ap. For Poiseuille flow, this plot should be linear and the slope R2/8qL (or R2/8vL2)then readily yields the average R value. Theoretical HDC Calibration Curves. Adopting GPC nomenclature, we can call the relation between M and 7 a calibration curve. Theoretical calibration curves can be obtained by combining eq 10 and 22 as follows: 7 =
[ (
1 + 2 p:q) -
Typical plots for M , vs.
T,
-
C(
p$)2]-1
B
1 tM
(24)
using F as the molecular dimension
C
i p , bar
L,* cm
tM,Cs
R, Urn
R (av), Fm 0.630
42 98 174
72/85 72/85 72/85
1686.6 742.8 401.4
0.631 0.622 0.636
96.4 159.0 159.8 226.0
280/293 280/293 280/293
4420.2 2751.0 2754.6 1864.2
0.887 0.875 0.873 0.892
104 145 200
323/330 323/330 323/330
2286.6 1637.4 1166.4
1.33'7 1.338 1.350
0.882
1.342d
"Viscosity THF = 0.488 mPa.s (cP) at 22 "C as determined in our laboratory. *Lengths are given as from inlet to detector/from inlet to outlet. tM is corrected for note b; Le., it is valid for the total length. dIndependent of flow properties the total column volume can be obtained by filling the column with toluene and determining the toluene concentration (UV absorption) after displacement with THF. The duplicate result in terms of R is R = 1.345 um. (eq 21) for PS in THF and a column radius of 1 pm, are depicted in Figure 5 for several of the competing theories. For comparison, the calibration curve of a modern GPC material, PL Gel, is also shown; it is more or less parallel with the HDC curves; in other words HDC and GPC are expected to show a nearly equal separation power. The working ranges are somewhat different (GPC: M , < lo6 and r = 0.3-1; HDC: M, > lo4 and r = 0.75-l), although there is a broad overlapping area: lo4 < M, < lo6. Figure 6 shows the calibration curves after eq 24 (with C = 1 + 2 y M ,i.e., model V) and the column diameter as the parameter. It becomes clear that for practical applications of HDC to polymers, columns should have diameters of the order of 1 pm, but preferably less. RESULTS AND DISCUSSION Flow Experiments. First of all we determined the average column radii of available microcapillaries from the pressure dropresidence time relationship (by combining eq 6 and 23). The experimental results obtained are gathered in Table 111. The viscosity of THF, as determined in our laboratory, was found to be 0.488 mPa-s a t 22 "C. It shows that the relationship between experimental A p and t M - l values is linear, which implies that the assumption of Poiseuille flow is realistic, even for the very small column diameters considered here. HDC Experiments w i t h PS i n THF. Typical HDC chromatograms of mixtures of PS standards with narrow
ANALYTICAL CHEMISTRY, VOL. 58, NO. 14,DECEMBER 1986
I
I
ll n 1
COLUMN P R :.63 pm
1390
1 4 3 0 1470 1510
1
1550 1 5 9 0
COLUMN 0 R : 8 8 2 urn
082
084
086
088
090 7 -t
I
I
2350 2 4 0 0
I
3041
I
2450
I
1
2500 2550
I
2600
COLUMN C
092 0 9 4 396 098 1 (POLYSTYRENE) /t (TOLUENE)
Flgure 8. Experimental points for columns A, 6, and C (from bottoln to top) with theoretical curves according to the modified DG model (V): (0)column radius, 1.342Km: (0)column radius, 0.882pm; ( 0 )column radius, 0.630pm. M O L WEIGHT I P O L Y S T Y R E N E I
0
1030
1050 1070 1 0 9 0 1110 1130 RETENTION T I M E ( 5 )
Figure 7. Comparison of the separations effected using three different column radii ( R ) for a test mixture containing toluene, PS 68K,127K, 41 lK,and 775K (from right to left) in concentrations of 1 mg/mL each in THF. Column dimensions are shown in Table 111. The injection time for all three chromatograms was 5 s. Inlet pressures are as follows: column A, 40 bar: column 6,160 bar; and column C, 200 bar.
molecular weight distribution (polydispersity M J M , < 1.1) are shown in Figure 7 for all three columns (A, B, and C) characterized by the data in Table 111. It appears that peak shapes are quite symmetric (except for very high molecular weight samples ( M , > 5 X lo5), in contrast to the skewed peaks obtained in earlier work (16). This is a direct result of the 10-fold lower concentrations used in the present work (ca. 0.1% m/m), which are made possibly by the 30-fold increase of the signal-to-noise ratio of the UV-vis detector (see Experimental Section). Consequently, the sample solutions are far less viscous and concentration effects on the polymer sizes, as indicated before (16),less important. Thus, we are much better equipped to test the validity of the various residence time theories, which all assume infinite dilution. Yet, particularly for the higher molecular weights, concentrations of about 1 mg of polymer/mL of T H F are necessary to obtain any signal at all. This is rather close to the critical concentration (38)where the polymer molecules are able to interact with each other through entanglement and hence change in shape and size. Consequently, peaks for M , > 5 x lo5 are still skewed and further detector improvement remains necessary. The low molecular weights (M, < 5 x lo5) can be studied safely, however, without interference from concentration effects. Figure 7 shows that the separation of one particular mixture of PS standards clearly improves upon using smaller inside diameter microcapillaries, in line with theory. Further, it is observed that the signal-to-noise ratio becomes ever smaller with decreasing column radius. Clearly, the present detector is limited to columns above 1 pm i.d. for acceptable signalto-noise ratios. The HDC chromatogram in Figure 7A, obtained using the smallest column available to us (R = 0.63 wm), shows the PS peaks to be less wide than the toluene peak. This is qualitatively in accordance with the Taylor-Aris-Golay
082
OS4
086
088
090 T
=
t
092 0 9 4 0 9 6 098 1 (POLYSTYRENE / t (TOLUENE I
Figure 9. Experimental points for columns A, 6, and C (from bottom to top) and polystyrene in THF with theoretical curves according to the column radius, 1.342pm; (0)column modified BG model (VIII): (0) radius, 0.882pm; (0)column radius, 0.630 pm.
convective dispersion theory (cf. our earlier discussion (16)), which yields that for the case of Figure 7A (in contrast to 7B,C) toluene is below optimum velocity conditions (peak spreading mainly by axial molecular diffusion), whereas for PS 68K and 127K near optimum conditions are valid. The high number of theoretical plates obtained for the polymer peaks ( N = 3 X lo5 for PS 68K) illustrates how efficient microcapillary HDC in fact is, considering that the larger part of the peak widths observed is due to polydispersity of the standard samples. Using the peak maxima for the residence times, we show in Figures 8-10 all our measurements of T in all three columns for a broad range of PS standards in comparison with two of the possible residence time theories (drawn lines), viz., the modified DG and the BG models (V and VIII, respectively, cf. Table I for the model equations). The molecular weight of the standards has been taken at the top of their molecular weight distribution. The other models differ quite substantially from the experimental results and are not shown for clarity. The modified DG and BG models (V and VIII) use the same X values and only differ in the magnitude of the quadratic term (C in Table I). The use of eq 21 (cf. Table 11) enables us to draw plots of X vs. T for all our experiments with different columns and molecules in one graph. This graph can be compared with the curves in Figure 3, as is done in Figure 10. It appears that indeed all the experimental data points fall along one smooth line with very little scatter of the
3042
ANALYTICAL CHEMISTRY, VOL. 58, NO. 14, DECEMBER 1986 i
= ('/Rl:
E F F E C T RADIUS M O L E C U L E / R A D I U S COLUMN
... ( ',,.........) C
080
082
084
086
090
088
T :t
092
0 9 4 096
098
1
b
(POLYSTYRENE! / t (TOLUENE!
Flgure 10. Universal calibration curve for HDC. For experimental points see Figures 8 and 9: (-) quadratic model corrected after model V and quadratic model corrected after model V I I I . (-e)
.
MOL WEIGHT ( P O L Y S T Y R E N E ) x
4X1O6r
082
I
I
I
I
1
I
I
084
OS6
088
090
092
094
096
r
:t
098
1
(POLYSTYRENE) /t (TOLUENE)
Figure 11. Comparison of experimental points and several theoretical models. Column A radius is 0.63 pm. Experimentalpoints are in THF. Theoretical models are as follows: (-) DiMarzio-Guttman, unmodiied, model IV; (-) simple linear, model I; (- - -) simple quadratic, -) modified DiMarzio-Guttman, model V; (- -) modified model 11; Brenner-Gaydos, model V I I I . (-e
-
points. The modified DG model seems slightly in favor. It is, however, too early to discard the modified BG model altogether as the data points for the high molecular weights, as mentioned above, probably still suffer from concentration effects. This is also clear from the rather triangular peak shapes for M , > lo6. Figure 11shows the experimental results obtained in column A only ( R = 0.63 pm) in comparison with several other models. Clearly, only the modified models based on F agree with the experiments. This finding strongly favors the choice of the effective radius, p, as the measure of molecular size in exclusion separation methods like HDC and GPC (27,28). The original DG theory, therefore, is not justified. Further evidence in support of this finding should be obtained by using P S molecules of different sizes (e.g., in other solvents; see next paragraph) and other polymers. As a practical example, Figure 12 shows HDC chromatograms of a polydisperse polymer sample and several standard mixtures. In partial answer to the question how these separations compare with state-of-the-art GPC, Figure 13 shows current GPC chromatograms of the same mixtures as shown in Figure 12; the total analysis time in these two figures is about the same as in HDC and GPC (ca1400 s). It is seen that the HDC chromatograms are far more efficient, which implies a much higher peak capacity. Indeed, we estimate that the peak broadening shown in the standard HDC chromatograms
iL,
1250 1290 1330 1370 1410 1450 RETENTION TIME ( s )
Flgure 12. Hydrodynamic separation of a polydisperse polystyrene sample on column C: R = 1.342 pm; injection time, 5 s; inlet pressure, 170 bar; (a) 4 mg/mL broad molecular weight range polystyrene obtained from BDH; (b) calibration mixture containing (from right to left) toluene, PS 127K, 411K, and 775K, 1 mg/mL each; (c) calibration mixture containing toluene, PS 68K, 186K, and 675K, 1 mg/mL each.
mainly originates from the polydispersity of the standards themselves, the instrumental contribution to peak widths being very limited. Consequently, a microcapillary HDC chromatogram is a direct reflection of the size (and hence molecular weight) distribution of the sample. This contrasts with GPC where only a comparison with standards can be made. Figure 13 further shows that the chromatogram of sample mixture a covers the complete GPC working range from the lower limit of exclusion (ca. 700 s) up to the higher limit of exclusion (ca. 1300 9). The HDC chromatogram on the contrary has a working range, which extends to about 1000 s as the lower analysis time limit (according to the modified DG model). Hence, it shows considerable separation capacity for the higher molecular weights, which cannot be handled by GPC as no suitable gels are available. A further practical advantage of microcapillary HDC over GPC is that no equilibration is needed. HDC E x p e r i m e n t s with PS in O t h e r Solvents. In order to change the size of the polymer molecules, with a view to obtaining different X values, we investigated several solvents other than THF. Nonpolar solvents like trans-decaline, a B solvent for PS at 23.8 "C (33),could not be applied because the PS molecules then adsorb onto the inner wall of the fused
ANALYTICAL CHEMISTRY, VOL. 58,NO. 14, DECEMBER 1986
t 5
10 088
,
,
1
090
, 092
,
, 094
r = t
3043
, 096
098
I
(POLYSTYRENE) /! (TOLUENE)
Figure 14. Comparison of experiments in THF and in diethyl malonate: column C, R = 1.342 pm. Experimental points are as follows: ( * ) THF at 22 "C, (0)diethyl malonate at 23 "C, and ( 0 )diethyl malonate at 35 "C. Theoretical curves according to modified DiMarzio-Guttman theory, model V, are given by the following: (-) a = i , (---) a = i o ,and ( - - - ) a= r g o with y = 2/3 (model 111).
600
760
920
1000 1240
1400
RETENTION TIME (S) Figure 13. State-of-the-art GPC separation of a polydisperse polystyrene sample. Composttion of mixtures a-c is the same as in Figure 12: injection sizes, 5 pL; column, 300 X 7.7 mm PL Gel; particle size, 5 pm; pore size, lo5 A; mobile phase, 0.5 mL/min THF at 23 "C; UV detection at 254 nm.
silica columns. Experiments in polar solvents like methyl ethyl ketone (MEK) were successful in this respect: HDC separations of PS samples without adsorption effect could be achieved but the results hardly differed from the T H F data. Apparently, PS molecules in T H F and in MEK, both good solvents, possess almost the same dimensions. The largest change in size of the polymer molecules can be obtained by switching to a 0 solvent in which the molecules are supposed to behave ideally and show a characteristically small (unperturbed) dimension (33). A suitable polar 0 solvent is, e.g., diethyl malonate, which exhibits 8 properties at about 31-36 "C (33). Performing HDC a t this temperature, by immersing column C in a water bath maintained at 35 "C, yields good HDC chromatograms of the PS standards. The 7 values as compared with the T H F data are shifted toward higher values, which indicates that X values are indeed lower, as should be the case for the smaller polymer sizes in the 8 solvent. Figure 14 shows the experimental data a t the 0 temperature (35 "C) and a t room temperature (23 OC) in comparison with the T H F data from Figure 8 obtained using the same column and the same PS standards. It clearly shows that the 7 values for the 0 solvent are systematically higher than those for the good solvent THF. This agrees with the fact that polymer sizes are smaller in the 0 solvent than in a good solvent. As a tentative conclusion we further observe that experiments in microcapillary HDC are sufficiently precise and repeatable to show the slight effect of temperature on polymer size in going from 23 to 35 "C. The 7 values at 23 OC are all systematically higher than those a t 35 "C.
If we now want to match the experimental data with the models that are so successful with T H F as the solvent, we need the polymer size in the 0 solvent. Just as for THF, we obtain the data on the radius of gyration in 0 solvent from reported measurements using viscosity and light scattering (33);these data are also contained in Table 11, as rgo. Provided that eq 16 also holds for 8 solvents, the effective radius, To (=0.886rgo), yields the calibration curve (eq 24), shown in Figure 14 as the broken-line curve. This theoretical curve, however, does not represent the experimental data as well as has been the case with THF. Further study should reveal whether this is due to shortcomings in the HDC models or to changes in polymer statistics when, e.g., hindered internal rotation in the 0 state, the polymer chain being rather collapsed, plays a role. If so, polymer molecules in the 8 state behave more like rigid spheres than those in the expanded state in the good solvent. Then the factor 0.886 in eq 18 becomes more like 1(for hard spheres aHS= rgHS and yHS= 2/3, eq 14). Indeed, the line in Figure 14, obtained by using rgoas the characteristic molecular radius with y = 2 / 3 (i.e., model 111), is found to approach the experimental data much better. This conclusion is somewhat speculative, and further work should reveal that it is justified.
-.-
ACKNOWLEDGMENT We thank J. F. Lambregts and B. S. Douma for their contributions in detector development. Registry No. PS, 9003-53-6.
LITERATURE CITED Small, H. J . Colloid Interface Sci. 1974, 4 8 , 147. Small, H. Adv. Chromatogr. 1977, 15, 113-129. Small, H. Anal. Chem. 1982, 5 4 , 892A-898A. Pedersen, K. 0. Arch. Biochem. Biophys. Suppl. 1962, 1 , 157. Mori, S.; Porter, R. S.;Johnson, J. F. Anal. Chem. 1974, 4 6 , 1599. Hoagland, D. A.; Larson, K. A.; Prud'Homme, R. K. I n Modern Methods of Particle Size Analysis; Barth, H. G., Ed.; Wiley: New York, 1984; Chapter 9, pp 277-301. McHugh, A. J. CRC Crit. Rev. Anal. Chem. 1984, 15, 63-117. Dodds, J. Analusis 1982, 10, 109-119. Muiiins, M. E.; Orr, C. Int. J. Multiphase Now 1979, 5. 79-85. Noel, R. J.; Gooding, K. M.; Regnier. F. E.;Ball, D. M.;Orr, C . ; Mullins. M. E. J. Chromatogr. 1978, 166, 373. Brough, A. W. J.; Hillman, D. E.; Perry, R. W. J . Chromatogr. 1981. 208, 175. Shuster, C. D.; Schroeder. J. R.: McIntyre, D. Rubber Chem. Technol. 1981, 5 4 , 882-891. Elie, P.; Renaud, M. Entropie 1984, 20, 109-119. Giddings, J. C. Sep. Sci. Technol. 1984-85, 19, 831-847. Glddings, J. C. Sep. Sci. Technol. 1978, 13, 241-254. Tijssen, R.; Bleumer. J. P. A.; van Kreveld, M. E. J. Chromatogr. 1983, 260, 297-304. DiMarzio, E. A.; Guttman, C. M. J . Polym. Sci.. Pari B 1969, 7 , 267. DiMarzio, E. A.; Guttman, C. M. Macromolecules 1970, 3, 131, 681.
3044
Anal. Chem. 1986, 58,3044-3047
(19) DiMarzio, E. A,; Gunman, C. M. J . Chromatogr. 1971, 55, 83-97. (20) Brenner, H.; Gaydos, L. J. J . Colloid Interface Sci. 1977, 58, 312-356. (21) Prieve, D. C.;Hoysan, P. M. J . Colloid Interface Sci. 1978, 6 4 , 201 (22) Stoisits, R. F.: Poehiein, G. W.: Vanderhoff. J. W. J . Colloid Interface Sci. 1976, 57, 337. (23) Silebi, C. A.; McHugh, A. J. AIChE J . 1978, 2 4 , 204. (24) Buffharn, B. A . J . Colloid Interface Sci. 1978, 67, 154. (25) Nagy, D. J.; Silebi, C. A.; McHugh, A. J. J . CoNoid Interface Sci. 1981, 79,264. (26) Ruckenstein, E.;Marmur, A.; Gill, W. N. J . Colloid Interface Sci. 1977, 67,183-191. (27) van Kreveld, M. E.; van den Hoed, N. J . Chromatogr. 1973, 83, 111 (28) van Kreveld, M. E. J . Polym. Sci.. Polym. Phys. Ed. 1975, 73, 2253-2257. (29) Brenner, H. I n Advances in Chemical Engineering: Academic Press: New York. 1966; Voi. 6, pp 287-438.
(30) Squire, P. G. J . Chromatogr. 1981, 270,433-442. (31) Casassa, E. F. Macromolecules 1976, 9 , 182-185. (32) Volkenstein, M. V. Configurational Statistics of Polymeric Chains ; Wiley-Interscience: New York. 1963. (33) Polymer Handbook,2nd ed.; Brandrup, J., Irnrnergut, E. H.,Eds.; Wiley: New York, 1975. (34) Benoit. H.; Grubisic, Z.; Rernpp, P.; Decker, D.: Zilliox, J. G. J . Chim. Pbys. 1966, 63, 1507. (35) Mandema, W.: Zeldenrust, H. Po/ymer 1977, 78, 835. (36) Schulz, G. V.; Baumann, H. Makromol. Chem. 1968, 7 1 4 , 122-138. (37) Jorgenson, J. W.; Guthrie, E. J. J . Chromatogr. 1983, 255, 335. (38) Lipatov, Y. Progr. Colloid Polym. Sci. 1976, 67,12-23.
RECEIVED for review November 7 , 1985. Resubmitted July 9, 1986. Accepted July 29, 1986.
Effect of Solvent on Solid-Supported Reactions on Styrene/Divinylbenzene Copolymeric Macroreticular Resin Jack M. Rosenfeld,* Shahin Yeroushalmi, and Emmanuel Y. Osei-Twum Department of Pathology, Faculty of Health Sciences, Health Sciences Center (3N10), McMaster University, 1200 M a i n Street W e s t , Hamilton, Ontario, Canada L8N 325
Pentafluorobenrylatlon of organic acids on XAD-2 can be positively and negatively affected by organic solvent used as a dlhtent for the reagent, pentafluorobenzyl bromide (PFBBr). The increase or decrease in yield Is determined by the nature of the solvent and the functional group undergoing derlvatiration. When 200 mg of XAD-2 is impregnated with 10 pL of PFBBr In 90 pL of certaln organlc solvents, rather than with the pure reagent, there is an increase in yield of pentafluorobenzyl (PFB) esters. Such Increases are found with 1,1,2-trichloroethylene (TCE), saturated hydrocarbon (e.g., hexane), monochlorobenzene, and dlchlorobenzene. I n contrast, other aromatk hydrocarbons and hydroxylic solvents can decrease the yield by as much as 5- to 10-fold. Derlvatlzation of phenols is also increased by dllutlng PFBBr in TCE as well as in other solvents, but most Important the yield is also Increased when the diluents are hydroxylic solvents. As a result, simply by changing the organic solvent used as a diluent, it is possible to achieve a 5- to 10-fold enrichment in the derlvatiratlon of phenolic analyte relative to the carboxylic acid background that is present In plasma.
Reactions on solid support are an approach to the automation of those methods that are predicated on analytical derivatization reactions. Such reactions can be used in both the on-line and off-line mode (1-3). The advantages and disadvantages of using these techniques have been recently discussed (1,3). One intriguing possibility is the development of superior specificity for derivatization using solid-supported reagents (3). Such specificity can be particularly important as it would simplify subsequent chromatographic separations. In developing the off-line reactor approach for automating analyses of organic analytes from biological matrix, we investigated the styrene/divinylbenzene copolymer, XAD-2, as a solid support for analytical derivatization reactions (4-9). Solid-supported reaction on XAD-2 has been used to determine carboxylic acid ( 7 , 8 ) and phenolic analytes (9) from simple matrices such as incubates (7, 8) as well as more
complex matrices such as plasma (9). This macroreticular resin is suited to biological applications in that such samples are predominantly aqueous and analytes are both basic and acidic. Thus, the support used for the reaction must be stable a t both alkaline and acidic pH and XAD-2 meets these requirements. In addition, the resin is also compatible with all organic solvents which are required for eluting adsorbed compounds from the resin. In these methods, organic solvent was used as a diluent for the reagent (PFBBr) during the impregnation step. It was suggested that this resulted in a more homogeneous distribution of the reagent throughout the beads and pores of the resin, which led to an increase in the yield of reaction (6, 7 , 9). Subsequent investigation, however, demonstrated that the solvent used as a diluent for PFBBr exerted unexpected effects on the reaction yield of carboxylic acids and this in turn could be used to enhance the specificity for derivatization of phenolic analytes.
EXPERIMENTAL SECTION Apparatus. The pentafluorobenzyl derivatives of pure anal* were determined on a Hewlett-Packard (H-P) 5710 gas chromatograph equipped with a pulse linearized electron capture detector. These determinations were carried out on a 2.8-m X 4.6-mm-i.d. glass column packed with 3% SE-30 on 100-120 mesh Supelcoport. The output of the detector was monitored on a H-P 3380A recording integrator. Plasma extracts were analyzed on an H-P 5790 gas chromatograph also equipped with a pulse linearized electron capture detector. In this case the output of the detector was monitored on a H-P 3390A recording integrator. The column was a J & W DB-17N with a thickness of 0.15 pm and a length of 15 m (0.23 mm i.d.). On the H-P 5710 gas chromatograph the carrier gas was 10% methane in argon maintained at a flow rate of 20 mL/min; on the H-P 5790 instrument, the carrier gas was hydrogen with a linear velocity of 40 cm/s at 200 "C. In the latter case, 10% methane in argon was also used as make-up gas at a flow rate of 15 mL/min. Reagents. Pentafluorobenzyl bromide was purchased from Caledon Laboratories, Georgetown, Ontario. The macroreticular resin, XAD-2, a cross-linked copolymer of styrene/divinylbenzene was obtained from BDH Laboratories, Toronto, Ontario. Solvents were bought from a variety of the usual commercial suppliers,
0003-2700/86/0358-3044$01.50/0 0 1986 American Chemical Society
