Anal. Chem. 1995, 67, 3229-3233
On-Line Coupling of Flow Field-Flow Fractionation and Multiangle Laser Light Scattering for the Characterization of Polystyrene Particles Heiko Thielking, Dierk Roessner, and Wemer=MichadKulicke* lnstitut fur Technische und Makromolekulare Chemie, Universitat Hamburg, Bundesstrasse 45, 20146 Hamburg, Germany
The on-line coupling of a flow field-flowfractionator (P) and a multiangle laser light scattering detector (MALLS) produces a novel analytical system for dispersed samples. Absolute distributionmeasurements are obtainedfor the molar mass and radius of gyration, which is directly related to the particle diameter. In this work, polystyrene latex standards (50, 105, and 304 nm and a mixture) dispersed in water were used to investigate the accuracy of a system with on-linecoupling of P and MALLS. Tests were carried out in a constant field of force and for the first time in a programmed field of force mode. The results show that it is possible to use MALLS and a decreasing cross-flowfor separation and that, even with changing cross-flow and under nonideal elution conditions, coupling to MALLS gives more reliable results than those obtained with a F4 system alone. Flow field-flow fractionation (F4) is probably the most universally applicable fractionation method for dissolved or dispersed particles involving polymer molecules (nonionic and ionic) ,l aggregates,! colloids? proteins: or virus samplesS5Separation in P is based on differences in diffusion coefficients. F4 has a dynamic separation range from =lo4 to 10l2 in molar mass and requires only that the sample be soluble or dispersible in some camer liquid.6 There are no problems with adsorption, charge repulsion, or degradation, as known from other separation technique^.',^ Multiangle laser light scattering (MALLS) is one of the few absolute methods available for the determination of molar mass and particle size over a broad range (between a few thousand and several million) .a An absolute MAUS experiment yields the molar mass and the corresponding radius of gyration without any need for polymer standards. However, if MAUS is not coupled with a fractionation method, these results will only be average values. Often there is a great demand for information on the distributions of size and mass. In technical applications for latices, these distributions are crucial in controlling the properties of the product. The production of paper or water-based paints, for (1) Benincasa, M. A; Giddings, 1.C.Anal. Chem. 1992,64, 790. (2) Giddings, J. C.; Benincasa, M. C. Polym. Mater. Sci. Eng. 1991, 65, 21. (3) Ratanathanawongs, S. IC; Giddings, J. C. Polym. Mater. Sci. Eng. 1991, 65, 24. (4) Giddings, J. C.; Yang, F.; Myers, M. N. Anal. Biochem. 1977,81, 395. (5) Giddings, J. C.; Yang, F.; Myers, M. N. 1. Mrol. 1977,21, 131. (6)Kirkland, J. J.; Dilks, C. H.; Rementer, S. W. Anal. Chem. 1992,64, 1295. (7) Kulicke W.-M.; Bose N. Colloid Polym. Sci. 1984,262, 197. (8)Wyatt, P. J. Anal. Chim. Acta 1993,272, 1.
0003-2700/95/0367-3229$9.00/0 0 1995 American Chemical Society
example, calls for broadly distributed latices because the small particles increase the adhesive power and the larger ones are responsible for a smooth and shiny surface. On-line coupling of P and MAUS makes it possible to sort particles according to their size and analyze their molar mass and dimensions one by one in order to obtain the absolutely determined distributions of molar mass and radius of gyration for broadly dispersed samples. Our very first results obtained on latices and dextran were published re~ently.~ Naturally, there are some limitations and problems associated with tandem techniques. As described in publications about the coupling of MALLS with other fractionation methods, a concentration detector (e.g., a differentialrefractive index detector, DRI) is needed.s The sensitivity of MALLS/DRI requires extremely pure solvents and samples.I0 In the case of P,there is a great demand for a well-poised flow and pressure balance. To improve the detectability and the separation speed of broadly dispersed samples, it is sometimes useful to work with decreasing instead of constant cross-flow. To obtain an ideal, programmable crossflow, it is necessary to have computer control over all flows at any one time. In addition, when the flow is switched between the cross-flow pump pistons, there is no active field of force for a fraction of a second. During this period, some of the sample may be eluted and be well detected by the MAUS but not recognized by the DRI (which leads to unwanted spikes). The aim of this work was to test the accuracy of F4/MALLS/ DFU investigations on very well-characterized (transmission electron microscopy, TEM) polystyrene latex standards using a constant cross-flow to analyze individual samples. An additional aim was to try to establish a programmable cross-flow which could improve the efficiency and detection quality of this method for very broadly dispersed samples. The programmable F4/MALL.S/ DFU was tested by mixing the standards so that they could be analyzed in one run. THEORY
Flow field-flowfractionation is probably the most generally useful of all of the FFF methods for the separation/characterization of macromolecules and particulates.6 F4 separates particles according to their diffusion coefficients using two streams of the same liquid flowing perpendicularly against each other. The general theory was developed by Giddings et al.' Simple equations relate the diffusion coefficient of a species to its retention time. The Einstein-Stokes equation gives the relation between the diameter and the diffusion coefficient for homogeneous (9) Roessner, D.; Kulicke W:M. J. Chromatogr. A 1994,687, 249. (10) Kulicke W.-M.; Kniewske R Makromol. Chem. 1980,1, 719.
Analytical Chemistry, Vol. 67, No. 18, September 15, 1995 3229
11UI I
photcdiode
Control and evaluation unit
scattering
angle
lasermonitoi
MALLS
r
\
cross flow
Figure 1. Schematic representation of the flow field-flow fractionator on-line coupled to the multiangle laser light scattering detector with its flow cell and the 18 photodiodes (only six to be seen) and the differential refractive index detector.
spherical particles. Equation 1gives the Stokes diameter d p as a function of elution time t~ (approximation for ,IQ: 1)) where E and E are the volume velocities of the two flows, w the channel thickness, and 7 the viscosity of the eluent.
MuMimgle Laser light Salter& Early formulations of the theory of light scattering were put forward by Einstein." Debye,13and 73"' and can be found in any modem textbook (e.g., ref 15). Multiangle laser light scattering means measuring the intensity of the scattered light emitted by the sample particles under different scattering angles e. With a modem MALLS photometer, it is possible to monitor continuously the scattering by means of several detectors mounted at different angles. This allows the MALLS photometerto be coupled with any fractionation method and then used to cany out absolute measurements. The values for the molar mass M, and the radius of gyration (R,3!.5 at each "slice" along the distribution can be calculated using the following equations:
where K is a light scattering constant, containing the wavelength ,IO of the incident light, the refractive index noof the pure eluent, and the refractive index increment dn/dc; c i s the concenhtion; A2 is the second vinal coefticient Ro is the excess Rayleigh ratio; and P(0) is a general form of a scattering function. For very diluted concenhations, the second and higher order terms in eq 2 can usually be neglected and Ro becomes dirrctly proportional to MwP(0). Plotting RdKc against sin2(0/2) gives M, from the (11) Einstein. A Ann. mp.1910.33. 1275. (12) Raman C. V. h d J Fit,% 1927.2. 1. (13) Debye P.J. AM-f. fifi 1944, 15.338 (14) Zmm B. H.J Chmt. PIP. 1945.13.141. (15) Kralcchvil P.In &-hi Sconedwj%m h/mnSdutim Huglin. M.B..Ed.: Academic Pres: London. 1981.
3230 Afla/ytic.?f Chemistry, Vol. 67, No. 18, September 15, 1995
intercept with the ordinate and ( R Gfrom ~ the angular dependence of the intensity of the scattered light, which is included in UI and higher order terms of eq 3. The dehition of the *average square radius of gyration, in the event that a distribution of molecular size is present, is given by eq 4.
The values obtained for (R&P5 are independent of dn/dc (assumed constant), M,, or even c (sufficiently small) and therefore insensitive to errors! When interpreting the value obtained for the molar mass,it is necessary to bear in mind that two assumptionsof the light scattering theory for molecules might not have been fulfilled in the case of latices. The drst assumption is that the wave Wnt is not altered on its passage through the sample, and the second is that the refractive index difference between sample and solvent is small. UBERIMEWTAL SECTION Apparatus. Figure 1 is a schematic diagram of the system used in this study. ?he fractionator was a model F-100 from FFFractionation. Inc. (Salt Lake City, VT). The 250 pm Teflon spacer (28.5 cm tiptetip length, 2.0 cm width) was bound by ceramic frits with a pore size of 3-5 pm. The lower frit was covered with a cellulose membrane, type YM 10. The channel flow was delivered by an MGlOOO HPLC pump from Costa Mehics (LDC Analytical, Riviera Beach, FL) at constant rates. The crossflow was provided by a double piston precision pump from Reichelt (Reichelt ChemietechnikGmbH & Co.. Heidelberg, Germany). With inlet and outlet flow under computer control, the magnitude of the crossflow could be varied as desired. The channel effluent was directed through a DAWN-DSP-F light scattering photometer (Wyatt Technology Corp., Santa Barbara, CA) and then into a RI SE51 differential index detector (Showa Denko KK, Tokyo, Japan). Materials. The samples were narrowly dishibuted polystyrene latex spheres from Duke Scientific (Palo Alto, CA) with nominal diameters of 50 f 2,105 f 3,and 304 f 6 nm and were certified to as calibrated with methodology traceable to the US. National Institute of Standards and Technology. The carrier solution was deionized, and doubledistilled water containing
0.005% (w/w) sodium dodecyl sulfate was used as a dispersant and 0.02% (w/w) of sodium azide as a bactericide. The solution was puriiied by filtration (0.1 pm) lo and on-line degassed (Knauer, Germany). Procedures. The particles were dispersed by immersion in a low-power ultrasonic bath for 15-30 s. The injection volume was 50 pL, with an amount ranging from 0.08 to 1.00 mg for samples consisting of a single size of latex particles and 1.00 mg (Duke 50, 0.71 mg; Duke 105, 0.27 mg; Duke 304, 0.08 mg) for the particle mixture. Following injection, samples were allowed to relax into their equilibrium distribution under the influence of the cross-flow but with a bypassed channel flow. This stopflow condition was maintained until -1.5 channel volumes of crossflow had passed across the channel. The calibration of the DAWN was done with ultrapure toluene, and the normalization of the k e d 18 scattering angles was performed with a disperse solution of gold with known diameter. For determination of the interdetector volume, the "spider" plot method* was used. The signal of the DRI detector was routed to the DAWN, which was interfaced to an AT computer. RESULTS AND DISCUSSION To get an ideal, programmable cross-flow, we connected the frit inlet and the frit outlet of the channel with one and the same pump so as to form a closed circuit. Having this pump under computer control means that there are no unwanted changes in the flow balance. However, when a suction pump is fitted on the frit outlet side, it becomes necessary to provide as much back pressure on the channel outlet side as the membrane generates in order to prevent the system from drawing in air. The second problem of spiking was controlled by installing pulse damping and pressure restriction on both pumps. The use of a MALLS photometer enables the radius of gyration to be calculated for each eluting slice. The calculation is independent of experimental parameters, Le., flow rates, detector delay, calibration, concentration, the refractive index increment, interdetector volume, and band broadening. The only source of error lies in the accuracy with which the sensitivity of the 18 detectors has been normalized. For this reason, the determination of the radius of gyration is very useful in checking the quality of a fractionation method. The scattering function gives a linear graph for small particles and a more curved one for larger parti~1es.l~ Therefore, it is useful to use different order fits of eq 3 for different particles sizes. Figure 2 shows the angular dependence for the samples Duke 105 and 304 at the peak maxima. The plot of RdKc against sin2(8/2) for the sample Duke 105 was fitted to a second-order function and that for the Duke 304 sample to a third-order function in order to give the minimized squares of the errors. Figure 3 shows the radius of gyration calculated from the angular dependence of the three single runs. The radius for each individual fraction is plotted against the elution time. In order to gain an impression of the concentration at each point, the elution profile has been included in the background. For greater clarity, the data for the Duke 304 sample were shifted 10 min to a higher elution time in Figure 3. It can be seen that there is a gentle slope in the radius of gyration plots with higher elution volumes for all three samples. This means that even narrowly distributed standards can be fractionated with this method. The width of the elution profile is not only a result of the band broadening. Taking both pieces of information ((R,3°.5 and c) separates
3,2E8
0
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-1
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c
-2E9
I
L
L-
0,o
0,6 sin2(9/2)
02
0-4
1,o
0,8
Figure 2. Representation of the angle dependence of the intensity of the scattered light for the samples Duke 105 and 304 at the peak maximum
h
v
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Figure 3. Radius of gyration for the samples Duke 50, 105, and 304 plotted against the elution time (the elution profiles have been plotted as dotted lines). For greater clarity, the data for the Duke 304 sample were shifted 10 min to a higher elution time (V, = 1.08 m U min; Duke 50, V, = 0.75 mumin, Duke 105, Vx = 0.42 mumin, and Duke 304, Vx = 0.13 mumin). 160
Duke 304
10
100 radius of gyration ( nm )
I000
Figure 4. Differential distribution of the radii of gyration for the samples Duke 50, 105, and 304. Fractionation and detection were performed with CFF F4/MALLS/DRI ( T = 298 K, in water containing 0.005°/~(w/w) sodium dodecyl sulfate and 0.02% (w/w) sodium azide, 1 = 632.8 nm, 0 = 3°-1600).
polydispersity from band broadening, because the evaluation involves adding fractions of the same size, and thus the true distribution of the radius of gyration is the result (see Figure 4). Analytical Chemistry, Vol. 67, No. 18, September 15, 1995
3231
Table 1. Calculated Mean Values of Molar Mass and Radius of Gyration for Duke Sampler 50, 105, and 304 Determined by MALLSDRI and the Stokes Diameter Calculated from the Retention Time Using F4Theory'
Duke 50
Duke 105 3.20 x 108 (12%) 3.22 x 108 (12%) 1.01 37.8 (+2%) 105 (13) 98 128
3.73 3.85
107 (13%) 107 (f3%) 1.03 18.9 (12%) 50 (f2) 48 48
(I
Duke 304 8.30 8.34
109 (13%) 109 (%3%) 1.00 116.5 (f2%) 304 (f6) 300 366
The errors indicated are the percentage standard deviation of the results from five experiments.
It can be seen that the polydispersity decreases from Duke 50 to Duke 304. If F4 theory had been employed alone, it would not have been possible to distinguish polydispersity from band broadening. This error in F4 has been discussed by AndreevlG among others. Table 1 gives the numerical results (polydispersity of the molecular mass distribution and the mean values of molar mass and radius of gyration) which were obtained with CFF F4/ MALLS/DRI. The percentage error indicated gives the standard deviation for five identical runs. Equation 5 enables the diameter to be calculated for homogeneous spherical particles by using the radius of gyration measured by light scattering (Table 1). This allows the results
Figure 5. Scattering intensity of the MALLS detectors from 3" to 160" versus elution time for a mixture of three Duke standards. Measurement performed with PFF F4/MALLS/DRI.The channel flow was V, = 1.08 mumin, and the cross-flow il,, decreased from 1.5 down to 0.07 mUmin in 140 min ( T = 298 K, in water containing 0.005% (w/w) sodium dodecyl sulfate and 0.02% (w/w) sodium azide, i= 632.8 nm).
to be compared with the nominal diameters given by TEM. In addition, the Stokes diameter of the particles can be calculated from the retention time using eq 1 (Table 1). There is good agreement between the light scattering data and the nominal diameters for all samples. For the Duke 50 sample, there is also good agreement with the results obtained from the retention time using F4theory. For the larger samples, we found deviations of -20% from the nominal diameter. This may be the result of a nonideal elution process. The best fractionation conditions chosen for the larger latices may not have been the best possible. A lot of possible errors and deviations from ideal elution theory are discussed in the l i t e r a t ~ r e . ~However, ~J~ using MALLWDRI for detection instead of DRI or W gives more reliable results, even if the ideal elution conditions are not known. To discover how well F4/MALLS/DRI analysis performs over a broad size range and to see how the MALLS/DRI detection reacts to a changing field of force in P,we mixed the three Duke samples in different amounts and separated them in one run using a programmed field of force. As can be seen in Figure 5, there is no problem in obtaining good baseline separation. Figure 5 shows the response of 17 MALLS detectors against the elution time. A semilogarithmicplot was chosen because of the large scattering intensity differences of the 50 the 304 nm Duke samples (see boxed figure). The different angular dependencies for small and large particles are particularly visible. The numeric results are comparable with those reported for the single runs with constant field (Table 1). (16)Andreev V. P.: Stefanovich L. A Chromatografihio 1993,37,325. (17) Litzen A.; Wahlund IC-G. J. Chromatog. 1991,548,393.
3232 Analytical Chemistty, Vol. 67, No. 18, September 15, 7995
ACKNOWLEDGMENT This work was kindly supported by the Deutsche Forschungsgemeinschaft (DFG). This work is dedicated to Prof. Dr. J. Klein on the occasion of his 60th birthday. GLOSSARY second virial coefficient in the 2i"-Debye
Az al,
a2, ..
CFF C
D DRI dp
4s dnldc FFF
F4 K k k M Mw
MALLS no
equation
virial coefficiens constant field of force concentration diffusion coefficient differential refractive index Stokes diameter obtained from F4 theory diameter obtained from light scattering theory refractive index increment field-flow fractionation flow FFF light scattering constant, equal to 4 ~ t ~ ( d n / d c ) ~ n o ~ / N ~ & ~ Boltzmann constant constant, equal to 2nn0/& molar mass weight average molar mass multiangle laser light scattering refractive index of pure solvent
Avogadro number programmed field of force scattering function radius of gyration z-average radius of gyration excess Rayleigh factor distance from the center of gravity absolute temperature transmission electron microscopy retention time void volume flow rate of cross flow
K W
8 rl
1 10
flow rate of channel flow channel thickness scattering angle viscosity retention parameter, equd to DV/VJ.~? wavelength of incident light
Received for review February 23, 1995. Accepted June
20,1995.8 AC9502012 @Abstractpublished in Advance ACS Abstracts, August 1, 1995.
Analytical Chemisrty, Vol. 67, No. 18, September 15, 7995
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