Anal. Chem. 1992, 6 4 , 896-904
898
Separation of Poly(styrenesu1fonates) by Capillary Electrophoresis with Polymeric Additives Janet Beebe Poli*st and Mark R. Schure*v* Analytical Research and Computer Applications Research, Rohm and Haas Company, 727 Norristown Road, Spring House, Pennsylvania 19477
The addition of hydroxyethyl colluhe to the carrier solution employed h the capMary elwtrophare6bmprratbn of poly(styrenewifonate) is shown to drrmrtkatly increase resoiution over a wide range of #holwuhw o w , allowing for the development of a hlgh-resoiutbn separation method. Waiicoated capillaries are utlked to reduc6 electroomnotic flow and to provide a surface wlth minimal interaction. This technique b compared with rlte-exclwion chromatography (SEC) and found to be favorably competitive for the analyels of poly(styrenewifonates) in terms of resolution, efflclency, and fractionating power: however, the speed of analysis is found to be approximately three tlmes faster than SEC. The mechanism of separation, as determined by empklcai curve Wing and inrpecuonofmobllltypbts, bthought to a r k from dze-selective sieving, as is the case for the separation of #opdymen by tradttbnai dab gel ebctrophoredr. However, moMlHy does not adhere to the clardcai theoretkai behavlor of -r e c k o p h o r e ~whkh b mOa ilkdy due to the very large e M r k fW that Is utlllzed in these experhnents. The advantages of the addithre methodology for the analyds of synthetic polyelectrolytes of industrial significance are discussed In detail.
INTRODUCTION
A number of variations now exist for the parent technique of capillary electrophoresis (CE). These variations, for the most part, center on the type of carrier solution which is utilized during separation. For example, in micellar electrokinetic capillary chromatography (MECC),'+ a surfactant is added to the carrier solution to form micelles; the micelles facilitate the migration of uncharged species through a differential partitioning process involving moving phases. To extend the limited migration range of MECC, organic modifiers have been added to the carrier s ~ l u t i o n . In ~ *CE, ~ resolution of enantiomers has been demonstrated in a number of studies by the addition of chiral components to the carrier solution; these studies have been summarized in a recent publication.' In addition, carrier solution modification by organic solvents in CE has been reported.s In contrast to micelles and low molecular weight organic solvents, relatively little work has been done with polymeric additives in CE. For example, a number of different polymeric additives, such as methyl cellulose and poly(ethy1ene glycol), have been shown to enhance the resolution of the separation of DNA fragments and monomer, dimer, and trimer albumins? The enhanced resolution is believed to occur because of size-dependent sieving of the charged macromolecule as it moves through the polymeric n e t ~ o r k .In ~ another study utilizing the additive hydroxyethyl cellulose,1° mechanisms similar to those found in slab gel electrophoresis were demonstrated for the differences in DNA fragment mobility, as a function of molecular weight and additive concentration. 'Analytical Research. 1 Computer Applications Research. 0003-2700/92/0364-0696$03.00/0
DNA restriction fragments have also been shown to exhibit high-resolution separations using methyl cellulose," hydroxypropyl methyl cellulose,l2 and poly(acry1amide) (non-crosslinked) additive^'^ in the CE experiment. The use of hydroxypropyl starch and dextran additives has been given for the CE separation of pharmaceutical drugs and protein^,'^ based on hydrophobic interaction mechanisms. The use of non-cross-linked poly(acrylamide) additives for the separation of biomolecules has been demonstrated previously in slab gel electroph~resis.'"'~ Polymeric cellulose derivatives have also been used in electrophoresis for the reduction of electroosmotic flow,w23whereby the adsorption of the cellulose onto the silica capillary surface is thought to mask charged silanol groups?' Most applications of CE, and electrophoresis in general, have focused on molecules of biological interest. Recentlyz4 the applicability of CE has been expanded to include the high-resolution and very fast separation of low molecular weight ions, although these types of separations were demonstrated many years agozowhen detector technology was in its infancy. Synthetic polyelectrolytes of industrial significance have not been previously analyzed by CE; however, a number of studies demonstrate the potential of electrophoretic methods for the separation of this class of solutes. For instance, slab gel electrophoresis and size-exclusion chromatography (SEC) have been comparedz5for the separation of poly(styrenesu1fonate) (PSS); although the slab gel experiments take about 10 times longer than SEC, outstanding resolution and wider range of molecular weight were demonstrated for the slab gel technique. Earlier work26has confirmed that poly(acry1ic acid) can be separated by slab gel electrophoresis, although the molecular weight range studied was limited and zones were broad. The present work describes the effect of the additive, hydroxyethyl cellulose (HEC), on the migration behavior of various molecular weight PSS in the context of CE; analysis of the resulting zones will be compared to the elution behavior of SEC and will be shown to be superior to SEC in terms of analysis time, applicable molecular range, and fractionating power. This work will attempt to demonstrate the potential of molecular weight determination that is possible for synthetic polyelectrolytes using CE methodology. EXPERIMENTAL SECTION Instrumentation. The CE instrument used for these studies was assembled in our laboratory. The apparatus consists of a high-voltage power supply (0 to -30 kV, Peshel Instruments, Model HBOYS, Cape Coral, FL) as well as a variable-wavelength UV detector (Linear Instruments, Model 200,Reno, NV) modified by the manufacturer for capillary on-column detection. The carrier electrolyte reservoirs are 13.5- X 65-mm borosilicate glass vials fitted with poly(trifluoroethy1ene)-faced silicone septa with phenolic screw caps. A total of three openings were made in each septa; two to allow passage of the capillary and the platinum wire electrode,and the third to allow for pressurization. Pressurization of the vial is accomplished by pumping air in with a syringe, which in turn forces the solution through the capillary for rinsing. The apparatus, including power supply, is housed in a Plexiglas case which has a voltage-interlockedcover to ensure operator safety. The capillaries used in this work were CElect-H15O (Supelco, 0 1992 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
Bellefonte, PA); these capillaries are precoated with an organic phase to minimize adsorption and reduce electroosmotic flow. The capillaries have dimension 50-pm i.d., 375-pm o.d., and 50-cm length (35 cm to detector) and are rinsed with carrier solution for 30 s between injections. Solute migration was monitored at 235-nm wavelength. SEC experiments were performed using a coupled column system which employs a guard column of dimensions7.5" i.d. and 7.5cm length, and two analytical columns, each of dimensions 7 . 5 " i.d., Wcm length. All columns are from Varian Aasocitea Inc. (Sunnyvale,CA). The guard column (part no. 03-913082-01) is packed with Toso Micropak TSKgel, type GSWP, and the analytical columns (part nos. 03-912021-74 and 03-912022-74) employ Toso Micropak TSK type 3000SW and 4000SW gels. These gels are silica-based with a chemically-bonded organic coating to minimize solute adsorption. The aqueous mobile phase employed in all SEC experiments was 0.15 M sodium sulfate and was driven by a Waters pump (Model 510, Waters division of Millipore, Milford, MA) with flow rate of 1.1mL/min. The solute was introduced via a Rheodyne Model 7010 injection valve (Rheodyne Inc., Cotati, CA) equipped with a 100-pLsample loop. Detection was performed using a UV detector (LinearInstruments, Inc. Reno, NV) operating at 225-nm wavelength. Chemicals. Water was deionized with a Milli-QWater System (Millipore, Inc., Bedford, MA). HEC (molecularweight between 60000 and 1 million) was obtained from Aldrich Chemical Co., Inc. (Milwaukee,WI). PSS standards of molecular weight 1800, 8000,18000,46000,100000,400000,780000,and 1200000 (abbreviated in the text as 1.8K, 8K, 18K, etc.) were purchased from Polymer Laboratories,Inc. (No. 2100-0100, Amherst, MA 01002). These standards were characterized for polydispersitywith SEC by the manufacturer; the weight average to number average molecular weight ratio given is less than 1.10. In addition, these solutes are stated by the manufacturer to be nearly 100% monosulfonated. AU chemicals were used as received without further purification. The buffer used in these studies is 25 mM KHZPO4 (Fisher Scientific, Fair Lawn, NJ), pH 5.0. The appropriate amount of additive was dissolved in buffer to obtain the desired concentration; no pH change was detected upon addition of the neutral additives at the stated concentrations. All solutions were filtered through a 1-pm Gelman No. 4226 filter (Fisher Scientific, Fair Lawn, NJ) prior to use. The concentration of each PSS standard is approximately 375 pg/mL in 25 mM KHzP04,pH 5.0, with no additive. Procedures. Absolute viscosity, q, of the additive solutions was calculated from kinematicviscosity; these kinematicviscosities were determined using series 13-617 Ubbelohde viscometer tubes (Fischer Scientific, Fairlawn, NJ). Densities were determined using a Mettler/PAAR DMA 24 densitometer (Anton PAAR USA, Inc., Warminster,PA). The volume fraction of additive in solution, 4, is calculated according to 4 = ( p - pL)/(ph - pL) where p is the density of the solution containing additive, pL is the density of the pure solution including the 25 mM KHzP04without additive, and Ph is the hydrated density of the pure additive. Using a linear least-squares analysis of p vs additive concentration, C,, yielded a ph value of 1.400 g/cm3. The volume fraction is expressed in this paper as a percentage, obtained by multiplying 4 by 100. Table I s u m " the concentrationsand physical measurements of the carrier solutions, including the electroosmoticmobility, pea, described below. The injection times for electroosmotic and solute mobility studies were 1and 2 s, respectively, and the field strength used in these experiments was 400 V-cm-'. These experiments were performed at ambient temperature; the temperature of the capillary at the detector was monitored and was typically 28-30 "C. Operating current was typically 30 FA. Electroosmotic mobility measurementswere performed on the coated capillaq with benzyl alcohol;fiua,was typically 2.21 X lo4 cmZ.V-'.s-' with no additive present, in agreement with the value provided by the manufacturer. The reproducibility of these measurements, as given in Table I, is hindered by primarily two factors. First, the manipulation of the capillary is performed manually. Before and after injection of solute, siphoning is introduced by this operation, which affects the size, shape, and reproducibility of the solute plug in the capillary. Second, as discussed in the concluding remarks section, the power supply rise time and decay time may influence
897
Table I. Solution Concentrations and Physical Parameters of HEC Solutions (Symbols Given in Text)
c*
Pa
7
# fJ
(mg/mL) (g/mL)
(cp)
(%)
0.9968 1.OOOO 1.0014 1.0034
1.00 1.18 3.97 12.0
0 0.0740 0.372 0.714
0 1.037 5.234 10.03
lrwlb
%
(cm*.V-'.s-')
RSDc
lo4
9.68 2.35 9.25 7.93
2.21 X 2.13 X 2.25 X 2.40 X
lo-' lo-' 1G4
Five significant digits have been used here with a typical error of fl in the last digit after calibration with a reference. bAverage of four replicate measurements. Percent relative standard deviation of four replicate measurementsof the electroosmotic mobility. reproducibility because of the relatively small migration times. This level of reproducibility is also present in the electropherograms to be presented below. When uncoated capillaries are used, the traditional approach is to inject solute at the positive end of the capillary and detect at the negative end, regardless of the charge on the s01ute.~With coated capillaries, the electroosmoticvelocity is diminished below the level of electrophoretic velocity for the PSS solutes; hence, injection is made electrokinetically at the negative end of the capillary and detection is performed at the positive end. Electroosmotic mobility measurement is performed by reversing the polarity of the experimental configuration so that injection of benzyl alcohol is made at the positive end of the capillary. Migration order and identity was established by the injection of single solutes or groups of solutes. Data were acquired by a Nelson Analytical Data System (Model 6000, Nelson Analytical, Inc., Cupertino, CA). Data Analysis. Peaks with moderate to large resolution are characterized in this paper by resolution,R,, operationally defied by the well-known relationship, R, = AtN/2(u1-t uZ), where AtN is the difference in net migration time and ul and uz are the standard deviations of two successive peaks (in units of time). All peaks, for the purpose of parameter estimation in this study, are assumed to be Gaussian. The width at half-height is used to estimate u for well-separated peaks. For highly fused peaks, a least-squares computer program, which utilizes both the Nelder-Mead simplex minimization algorithmz8and the Marquardt minimization algorithm,Bis used to fit the peaks to sums of Gaussian functions from which individual u and tN values are obtained. This least-squares program is also used to fit models to the mobility data. Additional quantities of characterization , include the number of theoretical plates, N, equal to ( t N / ~ ) zthe rate development of theoretical plates, N / t , and the molecular weight-based fractionating power, Fm. The fractionating powe9J' allows the quantitation of selectivity,weighted by separation efficiency, and has been shown to be useful for the comparison of different macromolecular separation techniques such as SEC and thermal field-flow fractionation (thermal FFF). Fm is equal to d7&9Mw/4,and the molecular weight-based selectivity, Sw, is equal to Id log tN/d log M,I; M , is the molecular weight in grams per mole. The derivative operation used in obtaining Sm is performed by fitting a quasi-Hermite cubic spline interpolation function32to the log M,, log t~ pairs, and then using the algebraic derivativeof the spline coefficients evaluated at each log M , value. This spline algorithm is also used for the graphical presentation of mobility and efficiency data given below. RESULTS AND DISCUSSION HEC Electropherograms. Electropherograms of all eight PSS standards are given in Figure 1 for the three concentrations of HEC given in Table I and with no additive present. The data in Figure 1are summarized in terms of R,, N, and N / t in Table I1 and SMw and F- in Table 111. These data are presented for comparison purposes in Figure 2. As can be seen Figure 1, as the HEC additive concentration is increased, peak definition increases. Although better overall resolution is obtained for the highest HEC concentration experiments where 4 = 0.714%, as shown in Figures 1 and 2 (except between the 8K and 18K solutes), the migration time
898
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
Table 11. Evaluation of Resolution, Theoretical Plates, and Plates per Unit Time technique
quantity 1.8K
CE with HEC additive 6 = 0.372% CE with HEC additive 6 = 0.714% SEC"
R,
N N/t
1.02
N Nlt R, N Nl t
0.632
3110 1280
R,
2940 1120 0.992
2470 819
" Conditions as in Figure 4.
1.08 2920 1060
0.382 1790 546
1.21 1280 61
molecular weight of poly(styrenesu1fonate) 18K 46K l00K 400K
8K
0.579
1.60 4350 1090
6.82
2.10
0.412 6600 840
b
3080 380 b
b b
2330 181
b b
7650 1720
9710 1350 b
0.843 1760 127
1200K b
1.39 3190 776
1510 330
0.912 286 18
4.00 4190 1330
1.68 986 288
866 78
1.18 6530 2220
780K
b b
b b
*Value could not be reliably estimated because of low resolution.
Table 111. Evaluation of Selectivity and Fractionating Power
a
molecular weight of poly(styrenesulf0nate) 18K 46K l00K 400K
780K
1200K
0.0528 0.715
0.0622 0.840
0.0721 1.46
0.102 1.65
0.145 2.12
0.0826 1.81
b b
0.0614 0.763
0.0581 0.616
0.101 0.796
0.168 2.76
0.178 1.73
0.207 5.10
G.0846 1.72
0.0161 0.224
0.0849 0.758
0.146 0.844
0.142 0.601
0.143 1.50
0.0620 0.748
b b
b b
b b
technique
quantity
1.8K
8K
CE with HEC additive $I = 0.372%
sMW FMW
0.0461 0.642
CE with HEC additive = 0.714%
sMW FMW
SEC"
SMW FMW
Conditions as in Figure 4. *Value could not be reliably estimated because of low resolution.
is approximately twice that of the more dilute experiment where = 0.372%, as shown in Figure 1. Under conditions of zero additive concentration there appears to be no useable resolution of the eight solutes; this stems from the fact that the effective charge to friction coefficient ratio which governs mobility in free solution is approximately constant. Injection of individual solutes shows that all solutes are mobile with zero additive concentration; preliminary experiments with uncoated capillaries demonstrate irreversible adsorption of the solutes with no detectable migration. Further discussion will center on the two highest concentrations of additive a t C#J = 0.372% and 4 = 0.714%, which are analytically useful. Separation efficiency, as judged from the number of theoretical plates given in Table I1 and Figure 2, appears to be better for the smaller additive concentration (4 = 0.372%), with the exception of the 400K PSS,where close to 10000 plates were observed for the 4 = 0.714% experiment. The experiment with highest additive concentration (4 = 0.714%) is, however, more desirable as judged from the selectivity, S-, and the fractionating power, F M W . This situation has been observed before, in the comparison of SEC and thermal FFF, where separation by SEC delivers more plates; however, thermal FFF yields higher selectivity and fractionating power.30,31With a factor of two analysis time advantage for the 4 = 0.372% experiment, the number of theoretical plates per unit time, N l t , is larger for the more dilute additive, as shown in Table I1 and Figure 2. These results suggest that it is more desirable to utilize HEC concentrations for the molecular weight characterization of PSS at or above 4 = 0.714% when analysis time is not a critical issue. The physical reasons for the double peak behavior seen in Figure 2 for N , N l t , and F M W are not clear. Since these experiments are run with a very polydisperse additive, the possibility exists that this regional enhancement is due to the unique size distribution of the additive. Another reason could possibly be due to the polydispersity of the solute itself; the lOOK solute shows relatively broad peaks in Figure 1,at both
I
E
4
14 b
1'
2'
3'
4'
6'
e'
A'
JJU
I'
a'
e'
10'
TIME WIN)
Flguro 1. Electropherogramsof the eight PSS solutes in solutions of HEC. (A) C, = 0 mg/mL; (B) C, = 1.037 mglmL; (C) C, = 5.234 mg/mL; (D) C, = 10.03 mg/mL. Peak numberlng is as follows: 1 = 1.8K, 2 = 8K, 3 = 18K, 4 = 46K, 5 = 100K, 6 = 400K, 7 = 780K, 8 = 1200K. Conditions as described In the text.
relevant additive concentrations, indicative of a larger polydispersity than the 46K or 400K solutes which would cause a local minimum to be displayed in N , N l t , and F M w This, however, is not supported by cursory inspection of the zone width of the lOOK PSS peak from SEC shown in Figure 3. As will be described below, the mechanism of electrophoresis changes for solutes greater than l00K in molecular weight, and this may partially explain the double peak behavior seen in Figure 2. Since absolute polydispersity measurements are extremely difficult for this class of solutes, in the molecular weight range studied here, accurate quantification of the peak dispersion due to column processes and due to solute polydispersity prohibit the establishment of the true efficiency
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
0.0
-1
high selectivity in separations, the number of plates in the SEC separations is small; the fractionating power reflects the bias of smaller plate number and shows that the overall quality of SEC separation tends to degrade above 46K molecular weight. The number of plates per unit time for the SEC experiment is especially smaller than that for CE with HEC additive. This suggests that CE with HEC additive is potentially more desirable in the separation of PSS or similar polyelectrolytes;the two techniques are relatively competitive in performance, but the results given here demonstrate that CE with additive is approximately 3-5 times faster than SEC. One of the well-known limitations of SEC is the relatively small peak capacity, where peak capacity is defined as the maximum number of component peaks which can be uniformly packed into a chromatogram or electropherogram a t a stated r e s ~ l u t i o n .In ~ ~SEC the retention volume is limited between the interstitial volume and the total column volume which includes interstitial and pore volume. In conventional CE and MECC, peak capacity is affected by electroosmotic a critical factor in determining the maximum differential displacement that can be obtained. The CE technique reported here is also limited in peak capacity due to electroosmotic flow; solutes with electrophoretic mobilities equal to or leas than the electroosmoticmobility of the fluid-additive mixture will not migrate through (nor be injected into) the capillary. For this reason, additives must be chosen which do not contribute to the electroosmotic flow and capillaries with low electroosmotic mobility must be used for maximum peak capacity. However, a small amount of electroosmotic flow may be useful for keeping the additive concentration uniform throughout the capillary length. For the case where peak variance is not constant throughout the separation range, the peak capacity, n,, is equal to33
I
8000.0 4000.0 0.0 2400.0
I
0.0
!
I
0.25
I
I
0.00
I
J
2
.o
0.0
...-:
,,-. *
, 1.5
1,
4
,I
3.0
5.0
4.0
800
6.0
log M W Flgure 2. Qraphlcal presentatlon of the data given In Tables I 1 and 111 fw resdutkn, R,, selecthrity, Sw, plates per unlt time, Nlt, plates, N , and the fractlonatlng power, F,. Dotted line: SEC. SolM Ilne: CE with HEC addltlve at C , = 5.234 mglmL, 4 = 0.372%. Dashed line: CE with HEC additbe at C , = 10.03 mglmL, 4 = 0.714%. Average values of M, are used in the plot of R,.
n
4
0
5
10
15
20
25
30
35
40
TIME WIN)
Flgure 9. Slre-excluslon chromatography of PSS standards. Peak numbering Is as follows: 1 = 1.8K, 2 = 8K, 3 = 18K, 4 = 46K, 5 = 100K. CondMons as described In the text.
of the CE technique with HEC additive. In that regard, these resulta should be interpreted as comparative, since the same solutes are used in all experiments. In all cases, the highest M, standard was not resolved to the point of unique peak identity. Comparison with SEC. A typical chromatogram of the solute mixture up to molecular weight lOOK is given in Figure 3 for the SEC analysis of five of the eight solutes. This range is studied because resolution is lost in the molecular weight range above 350K for these columns. As indicated in Tables I1 and 111, and Figure 2, four of the five descriptors of separation quality over most of the molecular weight range are smaller for SEC than that found for the CE experiments. The exception is the selectivity, which is higher at the lower half of the molecular weight range. Although it is desirable to have
where Navis the average number of theoretical plates and t , and t- are defied here as the maximum and minimum time for peak production under useable resolution conditions. Using the values from Table I1 and Figures 1and 3 of t- = 12 min, t,, = 25 min, and N,, = 1300 plates for SEC, and tmh= 2.9 min, t,, = 8.5 min, and Nav= 3800 plates for CE a t 4 = 0.7149'0, eq 1, evaluated a t unit resolution, yields n, = 8 for SEC and n, = 17 for the CE experiment. Thus CE with additive is clearly more favorable in the ability to contain more peaks over the migration time range as is SEC under conditions of similar plate number; this is of great importance when characterizing complex samples. Electroosmotic Flow. Because any electrophoresis mechanism study requires the examination of electrophoretic mobilities corrected for electroosmotic mobility, and the experimental configuration is different from that normally used in CE,n a complete description of this correction is given here. It should be noted that because vectors are used, the assignment of magnitude and sign is unambiguous as long as the experimental reference frame is rigorously defined. The electrophoretic velocity, v, is equal to 'the product of the electrophoretic mobility, p, and the electric field vector, E, such that v = pE (2) Because the electric field vector, E, is essentially one-dimensional in CE, E takes the form% E = 10,0,- k aV/az), where V is the scalar potential difference across the capillary length L, and k is the unit vector in the z (migration)direction. All vedor quantities are denoted in boldface and p is assumed to be a scalar whose sign is indicative of the excess charge. For example, when is negative, as is the case for PSS in weak
GOO
0
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
acid solution, the velocity will be positive for the experimental reference frame where Vis positive at z = L, (the case given in this paper). We assume no chemical potential gradients exist in the z direction so that aVJaz = VJL,. Further discussion will consider only the z component of these vectors. The positive net solute velocity, vN, obtained experimentally by the quotient LdltN, where Ld is the length from injection at z = 0 to the detector, is identified with the vector sum of the electrophoretic and electroosmoticflow velocities: V N = v v., Hence, the electrophoretic mobility, p, is expressed as the dot product
+
P =
- veo).E-' = PN - peo
(3) Because v, is negative in the laboratory reference frame used for PSS migration experiments, the electrophoretic mobility is the sum of the absolute values of the velocities given in eq 3, divided by the z component of the electric field vector. As shown in Table I, IbJ appears to increase slightly as the additive concentration is increased; however, a one-way analysis of variance (ANOVA)%on the 16 values of Ip,l (four measurementa at each Ch gives only an 18% probability that these 1~4 are Werent. The calculatedF ratio for the ANOVA was 0.31 for 3 degrees of freedom associated with the four C, and 12 degrees of freedom associated with the measurement error. This suggests that the additive does not cause significant chemical modification of the surface of the coated capillary, which would subequently modify the electroosmotic flow characteristics of the capillary. Although the coating on the capillary is assumed to be complete, masking all of the silenol groups, it should be noted that agarose, commonly used in slab gel electrophoresis, also has a small electroosmotic flow,%even though agarose is considered electrically inert. The extent to which the additive flows with respect to the liquid electroosmotic velocity is exceedingly difficult to measure (by microbalance or other methods) and is presently unknown. Because q5 and q are relatively small, we expect the additive to flow with the electroosmoticvelocity of the liquid. The volume fraction of HEC where polymer entanglement occurs has been estimated to be approximately q5 = 0.4%;1° it is expected that at some point of high entanglement, at additive concentrations higher than that used here, viscous retardation of the additive at the capillary wall will severely restrict the motion of the additive in the capillary. Model Fitting and Mechanism. A relationship of the form log ( p / p 0 ) = - C O W + R)" (4) where po is the free-solution electrophoretic mobility, co is a constant, C is the concentration of the immobilized gel, r is the gel fiber radius, and R is the radius of the biopolymer, is often observed for the electrophoresis of bi~polymers~'-~~ at small C, E,and R. The constant, n, is equal to 1, 2, or 3, depending on whether the geometry of gel-macromolecule spatial interaction is poinblike, surfacelike, or volumelike.38a In this region of operation, DNA and other biopolymers are able to penetrate through gel pores with minimal conformational change by a simple drift mechanism. Nonspherical solutes are treatad as spheres because diffusional mechanism allow the solute to sample all configurational states; hence, R is identified with an average molecular size.37-" Although the linear relationship between log p and C was first observed by Fergmon$' the region of C, E,and R where eq 4 is obeyed is called the Ogston region, because the theoretical form of eq 4 was derived by O g ~ t o n ,who ~ * treated ~~ the problem in the context of the distribution of spheres amongst fibrous rods. Hence, separation based on size differences in the Ogston region is driven by entropic f a ~ t o r s . ~ ~ , ~ Deviations from the Ogston sieving mechanism are wellknown for biological electrophoresis38smas R gets large. For (vN
-7.00
-I
h -1.25
J .r(
.rl d
P 0
E
-1.50
ho 0
4
-1.15
-8.00
I 0.0
2.0 4.0 6.0 8 . 0 10.0
Conc. Additive (mglml) 4. tog (baae e)electrophoreUc mobility for the eight PSS Soluteg wlth HEC addlthre, versus C, from the data given in Flgure 1. Solutes are labeled as follows: plus sign = 1.8K, triangles = 8K, diamonds = 18K, squares = 46K, hexagons = 100K, asterick = 400K, X = 780K, ckcles = 1200K. The curves A-H correspond to the spline interpoleted pkts for the molecular weights 1.8K, 8K, 18K, 46K, loOK, 400K, 780K, and 1200K, respectively.
instance, at high C, and/or large R, but low E,electrophoretic mobility asymptotically approaches an inverse molecular weight dependence where very small changes in mobility are observed for large changes in solute molecular weight. In this region, known as the "reptation" region?' in reference to the 'snake-like" behavior of a flexible rod moving head first through a highly entangled gel matrix, most resolution is lost. Between the Ogston and reptation region is a transition region where there is a mixture of head group-directed movement and limited configurational state ampl ling.^' Although the mechanical mechanisms of biopolymer electrophoresis which comprise the Ogaton, transition, and reptation regions have been identified for low E separations by visualization40and computer-simulation methods,qsv46only limited experimental data and no simulation data are available for the very high E region where fEed-gel and polymer solution CE is performed. Although straight-line plots of log p vs C are suggestive of the Ogston sieving mechanism, the molecular weight dependence carried implicitly in R must also be quantitatively obeyed for strict adherence to this mechanism. In one studylo of DNA separation where the C, dependence on p was examined at high E using HEC additive, straight-line plots of log p vs C , were found over the small C , region, suggesting Ogston region behavior. However, verification that the experimental R was equal to its theoretical value in eq 4 was not performed. For protein and peptide separation using fixed-gel capillaries at high E,p was found to be proportional to the logarithm of the molecular weight;47this behavior is clearly not consistent with the Ogston mechanism given in eq 4. The migration characteristics of the eight PSS standards with different additive concentrations are summarized in Figure 4 by plotting log p vs C,. These data are given in different form in Figure 5 where plots of p w log M , are given with spline fitting and with the result of function fitting, based on an empirical function described below. Although some linearity is present in log p as a function of C,, as shown in Figure 4, for adherence to the Ogston model of electrophoresis given in eq 4,the slope of the data should be proportional to (r + R)", assuming R to be a linear function of M,, as would be the case for a rod-like solute. For example, the slopes should vary for the range of solute molecular weights used here
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
I*
0.0010 0.0009
I
6
0.0008
5 =0.0007 .I
z0.0006 0.0005 0.0004
0.0003 310
410
510
Log M W
6:O
3.0
4.0
5.0
6.0
Log M W
Figure 5. Electrophoretic mobility in cm2.V-'.s-' for the eight PSS as a function of log (base 10) M, for the data given in Figure 1. I n plot A interpoletknis by spine, plot B shows the result of curve fitling with eq 5. Cuve A, C, = 0 mglml; 8, C, = 1.037 mglml; C, C, = 5.234 mglmL; D, C, = 10.03 mg1mL.
over at least a factor of 1000 for n = 1 if the data were to completely adhere to eq 4;obviously they do not. If we m u m e that the solute is not a rod but rather a worm-like R is not linearly dependent on M,, but still does not scale in adherence to the requirements of eq 4; hence, the solute does not behave as predicted by the classical Ogston sieving model of electrophoresis. In an attempt to mathematically describe the data in Figurea 4 and 5A, over 30 different model equations have been utilized in fitting the electrophoretic mobility, as a function of the independent variables of additive concentration and solute molecular weight for the three concentrations of HEC additive employed in this study (the free-solution mobility data are not included in the parameter estimation). Some of these model equations were empirical, based soley on mathematical functions capable of describing the data over the limited range of independent variables used in this study. These model equations include forms with log, power law, linear additivity, multiplicative terms, and various combinations of these. Other models were utilized that have been previously shown to describe electrophoresis data in slab gel experiments. These forms include variants of the Ogston a logarithmic semiempirical form used to describe sieving of double-stranded models based on biasedreptati~n,~' models used to describe the sedimentation of polymers through polymer networks,= and models used in SEC theoryasl The models that worked the best, as judged from the goodness of fit criterion of relative standard deviation, were power law functions of the form
where A1-A6 are constants. The values of the constants obtained by least-squares fit with 3.82% relative standard deviation and shown by fitting in Figure 5B are AI = -2.603 X Az = 2.693 X A3 = 1.907 X lo2,A4 = 4.387 X A5 = 0.6506, and AB = -3.697 X lo-'. Equation 5 has the equivalent mathematical form 1.1
= f(ca,
Mw)
=
A1 + Az expl-A4(CaA6- A6) In (MW/A3)J(6) As seen in Figure 5, the addition of HEC, at 6 = 0.0740%, causes a larger average mobility as compared to the zero additive experiment. This suggests that the additive sterically shields the solute from some retentive mechanism, such as adsorption, on the capillary coating. The free-solution mobility can be roughly estimated by setting ABand C, in eq 5 to zero; the s u m of the Al and A2 terms gives = 9 X lo4 cm2-V-l.s-'
901
which is slightly larger than the mobility of solutes at 4 = 0.0740% shown in Figure 5. The functiond form of the exponential term in eq 6 contains two contributing fadors to the electrophoretic mobility; one being the molecular weight dependence of the solute and the other being the concentration of additive. The logarithmic dependence on solute molecular weight has been previously found in treatments of the entropy of an ideal polymer chain in a polymer melt.52 The power law dependence of the additive concentration in the exponential term of eq 6 is found in treatments of percolation processes,53where scaling laws are derived which are independent of the topology of the gel network. It is noted that the estimated value of A6 is very close to the theoretical value of 2 / 3 found in the correlation length exponent from percolation the0ry.6~The correlation length of a gel network has been recently to be equal to the average pore size which polymers in solution form during entanglement. This suggests that the high E problem in gel electrophoresis may be treated theoretically as an entropically-driven percolation process of solute moving through a lattice network. However, the velocity of additive relative to the electroosmotic velocity must be ascertained before the exponent of C, can be reliably utilized, and computer simulation must be used to verify this suggestion. In the limit as r 0, 1 - r; the same limit may be applied to the functional form of eq 6 for small values of the exponent. Noting that A4, which controls this scaling is particularly small; for constant C,, eq 6 reduces to 1.1 a bl bz log M, (7)
-
S=
+
where bl and b2 are general constants, unique at constant C,. Equation 7 has the same functional form as that found for protein and peptide analysis with fixed gel capillaries at high E4' and commonly found in SEC,58when retention volume is used instead of mobility. Although the curve fit given in Figure 5B illustrates the trend of the data, plots of cc vs M;' demonstrate a linear relationship for the three highest solute M, a t the two highest additive concentrations. This suggests that reptation is controlling the migration process for solute M, in ex= of 106 at the two analytically useful C,. This also suggests that no one comprehensive theory can be used as a model for the data presented here, as was the case in the study of the CE separation of DNA using HEC additives.1° The curves shown in Figure 5B do not give good detailed fitting; as has been recently demonstrated for SEC,67s68it may be necessary to include details of the pore size distribution into the theory to obtain reasonably detailed fits. For M, less than lo5, mobility can be qualitatively explained by considering the solution conformation of HEC and PSS,and the relevant length scales involved; this will now be discussed in detail. Length Scales. In both water and acid solution, HEC is thought to exist as a stiff extended coil,%with a large amount of hydration; hydration is thought to occur primarily through hydrogen bonding with the poly(ethy1ene oxide) side chains@ and is thought to be tightly bound with little free drainage over the length of the macromolecule. Other means of solvent interaction have been suggested.60 During the entanglement process, it is estimated that the pore length scale of HEC is of the order of 200-300 A.l0 We note that gels used in agarose gel electrophoresis possess a bundled filament structure;36the pores formed by this network are typically of length scale 500-1000 A.36 In dilute solution, PSS,as studied by electric birefringence,Bl is rod-like with limited flexibility. The diameter of the rod has been estimated to be 10 A.61 In semidilute and concentrated solution, PSS tends to coil so as decrease neighboring interactions.61 The length of the rod can be approximated as the contour length of PSS,for which a convenient formula exists:62 1 = 2.5Mw/M,, where 1 is the contour length of the
802
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
macromolecule in angstroms and M, is the molecular weight of one monomer unit, equal to 206 g/mol for PSS. For solute M, of 1.8K, 18K, 46K, 100K, and 1200K, this formula yields 1 values equal to 22,218,558,1210, and 14500 A, respectively. We will assume that under conditions of high E, PSS chains are oriented parallel with the electric field lines and are somewhat stretched so that the contour length is of the same order as the chain length. These wumptions are well founded from visualizationa and ~ i m u l a t i o n . ~The ~ - ~consequences of this are as follows. Because the HEC particle is not free-draining, penetration of the additive by the solute is expected to be extremely limited at low additive concentrations where the solute can move around the additive particle. For additive concentrations where C$ is equal to or greater than the entanglement threshold (4 > 0.4%), solute is forced to move through the porous polymer network head first, which is the accepted mode of transport through sieving matrices at relatively high E.45 In Figure 5 it is seen that the slope of the mobility for the highest additive concentration (the D curve) appears to decrease for M, in excess of 18K; at this point it is hypothesized that the solute with 1 > 218 A can no longer assume all configurations and restriction occurs, although some thermally-induced reorientation may still be possible. For solutes in excess of M, equal to loOK, this restriction becomes severe (at length scales in excess of 1210 A), and the solute has essentially little, if any, free movement. In this region, reptation controls migration where motion is governed by head-group movement and molecular weight discrimination rapidly degrades. For additive concentrations near or lees than the entanglement threshold, as viewed from curve C of Figure 5, the multiple slope change does not occur until the onset of reptation at M, in excess of lOOK because migration can occur, albeit with some loss of configurational sampling, by migration around pore sites. We note the analogy for solutes of M, less than 46K, for both relevant additive concentrations, with the Ogston region where configurational sampling is not restricted except, of course, by the spacing between pores. However, at high E, the mobility is such that the time for complete configurational sampling is very limited. In this regard, deviations from any local equilibrium configurational sampling are high and the rate of change of mobility with respect to solute molecular weight, dp/dM,, is smaller than that which could be obtained at small E. Because of the multiple restrictions in a straight-line trajectory of the solute and because of some degree of coiling at larger M,, the tail may on occassion become the head group as high E drives the migration of solute. This is well-known for flexible biopolymer^;^^ however, biopolymers tend to get pinned around small circumference pore systems due to flexibility. This pinning is doubtful here because of the limited flexibility of the solute and because the smallest mobility observed in Figure 5 is fairly large; mobility of the largest M , solute being about half the value of the smallest M, solute. Although this is speculative, the techniques of computer simulation and experimental visualization must be used to provide a higher level of understanding for this problem. Concluding Remarks. The results presented in this paper suggest that molecular weight analysis of synthetic polyelectrolytes may be accomplished by CE with hydroxyethyl cellulose additive. In particular we have noted that faster separation occurs at slightly higher fractionating power with CE as compared to SEC. Although HEC has been shown to give useful results as a sieving material, other additives have been tried with rather poor results. For instance, the separation of PSS with poly(ethy1ene glycol) (PEG) additives has been attempted, based on the known enhanced resolution of DNA with PEG? Only the 1.8K PSS was resolved in the best
results; we note that there may be a chemical incompatibility in this case because some plastics are known to be attacked by PEG.63 In addition, polydextran additive of 500 000 molecular weight appears to cause some fractionation of both the 1.8K and 8K PSS; bands were generally broad and were not analytically useful. Due to the marked similarity between the mobility as a function of molecular weight relationship seen in these experiments, and the elution characteristics of SEC, an investigation of more controlled dispersity additives may reveal higher CE performance. In that regard, as is known from SEC,'j4 future CE experiments with additive should be attempted with two relatively monodisperse sizes of additive at the higher and low ends of the molecular weight range. It may be difficult to find cellulose derivatives which meet these criteria, but not impossible. In preliminary experiments, the separation of PSS solutes has been attempted using a poly(acry1amide) fixed-gel capillary of 5 % mas~loading and 70-cm totallength. The results of these experiments were comparable in terms of resolution, to the CE experiment with additive at C$ = 0.714%;however, migration times were much longer; for example, the migration time of the 46K solute was approximately 55 min. If a shorter length of capillary is used so that migration time is comparable with the results of Figure 1,as was the case for the fixed-gel capillary separation of proteins and peptides with a capillary length of 10 or 20 ~ m , the ~ ' field strength will be higher for the same potential difference acrw the capillary. In this case, resolution should be roughly the same or better as the electropherograms in Figure 1,considering the loss of separation space due to smaller length. This scenario cannot be carried out, however, because the fiied-gel capillary manufacturer's maximum suggested E would be greatly exceeded and our instrument cannot utilize capillaries of leas than approximately 30 cm in length, due to geometrical constraints. This geometrical constraint is, in fact, present in the commercially available instrument we use for routine CE analysis. In addition, the fixed-gel capillaries are fragile, possess a short lifetime even with mild samples, are extremely restrictive in solvent selection, are easily fouled by reactive sample matrices, and cannot be regenerated. The advantagesof the "renewable" sieving matrix provided by mobile polymeric additives, as used in this paper, allows a wider choice of solvent selection, a deemphasis on sample preparation, and longer capillary life when molecular weight analysis is to be performed for synthetic polyelectrolytes. Injection of solute by means of pressure, impossible for the fixed-gel capillaries, is easily accomplishedwith additives. Finally, HEC does not have an appreciable absorptivity in the ultraviolet, nor is scattering a significant concern, alloying for the transparent detection of the solute. In these regards, the use of polymer additives is very desirable. The drawback here is that the direct coupling of polymer solution CE to a mass spectrometer may be very difficult. The degree of sulfonation was known to be uniform in these experiments. For most industrial polymers where the purity of monomer is carefully controlled and the charged site responsible for electrophoresis is present in the monomer, variability of charged site substitution is minimal, resulting in electrophoretic migration which is a monotonic function of molecular weight. Because some stretching is known to take place for chain molecules at even moderate E,40*45*46 polymers that show conformational changes over the molecular weight range of interest in free solution may still exhibit monotonic mobility over the molecular weight range due to stretching. However, for block copolymer polyelectrolytes,where mixtures of segment lengths from different polymers are grafted together, the situation may be entirely different. Further in-
ANALYTICAL CHEMISTRY, VOL. 64, NO. 8, APRIL 15, 1992
vestigation on the migration order of these species should determine if this type of polymer is amenable to molecular weight analysis by CE with additive methodology. Although we have focused attention on the comparison of CE with polymer additives and SEC, comparison of CE with polymer additives and thermal FFF are unnecessary because thermal FFF appears to be confined to the separation and quantification of macromolecules in nonaqueous environmenta, whereby CE must be run in an aqueous environment to promote solute mobility. Hence, CE with additives may have good analytical potential for polyelectrolytes in aqueous environments, SEC may be the mainstay of techniques for the analytical and small-scale preparative separation of aqueous and nonaqueous macromolecules, while thermal FFF is generally useful for the high-resolution analytical and small-scale preparative separation of nonaqueous macromolecules. The extent to which the molecular weight analysis of synthetic polymers can be performed using the CE with additives methodology for non-polyelectrolytes remains an open question. If one is to utilize a calibration curve, as in SEC, with the technique described in this paper for the molecular weight determinations of unknowns, the calibration curve must be stable relative to experiments done at a later time. In this regard, CE with polymer additives may be ideal because the well-known entropic mechanism which governs SECM is known to be relatively insensitive to temperature. If, in fact, the mechanism of the technique described in this paper is primarily entropic with minimal thermal energy contributions, the mobility dependence with respect to temperature is expected to be minimal, suggesting a high degree of reproducibility inherent in the technique. Although not competetitive for the analysis of large macromolecules, it should be noted that a large dependence of the distribution coefficient with temperature has been shown to occur for MECC.2s6 Because of the very short migration times characteristic of this and other CE types of experiments where the migration time is used for the prediction of physical parameters, stringent demands are placed on the power supply in terms of accurate voltage reproducibility in the rise time and decay time for the electrokinetic injection sequence65and the rise time for migration. It may be necessary in future work to incorporate some type of feedback system, similar to the three-electrode system used in analytical voltammetry, to guarantee a more precise temporal control of the applied field. The analysis of many synthetic polyelectrolytes appears to be advantageously characterized by this technique; work in our laboratory with proprietary poly(acry1ic acid) mixtures has repeatedly demonstrated high-resolution separations of these substances with HEC additive. Finally, because the mechanism of migration may vary depending on the chemical nature and concentration of additive, we refer to this technique simply as capillary electrophoresis with polymer additives (CEPA); considering the ease of implementation, obtainable resolution, and speed, we expect a considerable utilization of this methodology in the future.
ACKNOWLEDGMENT We thank Dennis Nwogwugwu for performing the size-exclusion chromatographic analysis reported in this paper, Susan Lokey for assistance in the analysis of variance calculation, and Clarence H. Freeman, Jr., for technical assistance. In addition, we thank David Soane, Department of Chemical Engineering at the University of California, Berkeley, for making available the preprint of his work (ref 10).
SYMBOLS A,-&
bl,b2 CO
least-squares determined parameters general constants constant in the Ogston model of gel electrophoresis
003
concentration of gel in traditional slab gel electrophoresis concentration of polymeric additive in solution electric field vector molecular weight-based fractionating power unit vector in the z direction length of capillary length from point of injection to detector molecular weight of solute monomer molecular weight of solute polymer number of theoretical plates spatial exponent used in the Ogston equation peak capacity resolution fiber radius in gel electrophoresis molecular weight-based selectivity time net migration time minimum and maximum times used in peak capacity voltage drop across the capil!ary length net migration velocity vector of the solute electroosmotic velocity vector electrophoretic velocity vector of the solute general variable spatial coordinate in the migration direction electrophoretic mobility free-solution (4 = 0) electrophoretic mobility electroosmotic mobility net solute mobility contour length of solute in solution volume fraction of solution occupied by additive density of solution with additive density of hydrated additive density of solution without additive 9 solution viscosity with additive u, ul,u2 standard deviation of Gaussian peaks Registry No. HEC, 9004-62-0.
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RECEIVED for review October 7,1991. Accepted January 21, 1992.
Polymer Molecular Weight Distributions by Thermal Field Flow Fractionation Using Mark-Houwink Constants J. J. Kirkland*,+and 5.W. Rementer E. I. DuPont de Nemours Company, Experimental Station, P.O. Box 80228, Wilmington, Delaware 19980-0228
Molecular wdght dktrlbutkns (MWD) of polymers measured by thermal fleld flow fractionation (TFFF) typically must be accanp#l.d by catlbrathg wtth polymer standards of known ch8racterWcs. I n this dudy, the MWD of a variety of known polymers k wccerrfully determined by TFFF wing callbratlonr estaMhhed wlth publhhed Mark-Houwlnk (M-H) constants. The procedure uses a combhation of the concentrathdependont refractive Index detector wlth a senaitlve online clrpllrrv vhcometer detector. The accvacy of me(#wod molecular wdght (MW) values Is dependent on the MarkHouwlnk conatants avallable for the callbratlon process. Wdght-average MW (M,) measurements on wdl-characterked polymers typkally show average differences of 10% from reported values ushg the best-avallabk M-H constants for callbratlon. However, M, values can vary as much as 20% with dHerent M-H constants for the same polymer/ solvent system. For all polymers studled, average M, difference from reported values was < I 5 % . TFFF k wltable for MWD mearurements of many organlc-aolubh polymers, pcutlcubrly hlgh MW mat.rlrdr that are dllficu# to charactedze by more conventlonal methods ruch as rlz+exclu&n chromatography.
INTRODUCTION Thermal field flow fractionation (TFFF) is useful for measuring the molecular weight distribution (MWD) of a 'Current addreas: Rockland Technologies, Inc., 538 First State Blvd., Newport, DE 19804. 0003-2700/92/0364-0904$03.00/0
range of organic-~oluble~~~ and certain water-soluble polymers! TFFF methods often show higher molecular weight (MW) accuracy than those based on size-exclusion (gel permeation) chromatography? An important feature of TFFF is that it is especially suited for characterizing fragile polymers of very high molecular weight because of the gentle nature of this separations meth~d.~JO TFFF separations typically use a single solvent. A large thermal gradient is applied across a very thin channel formed by two highly polished, parallel metal plates. This thermal gradient causes sample components to be pushed against the cooler accumulation wall. The essentially laminar flow created within the channel results'in a very steep velocity profile of flow streams near the walls. Higher MW components that are pushed closer to the accumulation wall by the temperature gradient are swept down the channel by slower flow streams and elute after lower-MW components. The result is a fractogram that resembles a chromatogram, with the lowest-MW component eluting f i t , the highest-MW component last. When characterizing polymer samples with a wide range of molecular weights, the force field (temperature difference between the plates) often is systematicallydecreased during the separation. This approach allows samples with a wide MW range of components to be characterized in a practical analysis time. Temperature programming can be carried out with a variety of p r o ~ e d u r e s . ~ - ~One J J ~ particularly J~ useful method involves time-delay, exponential-decay force-field programming.3*5v7 The TFFF fractogram can be used to determine the MWD of a polymer sample, providing a suitable calibration is 0 1992 American Chemlcal Society
