Anal. Chem. 1996, 68, 1169-1173
On-Line Coupling of Flow Field-Flow Fractionation and Multiangle Laser Light Scattering for the Characterization of Macromolecules in Aqueous Solution As Illustrated by Sulfonated Polystyrene Samples Heiko Thielking and Werner-Michael Kulicke*
Institut fu¨ r Technische und Makromolekulare Chemie, Universita¨ t Hamburg, Bundesstrasse 45, 20146 Hamburg, Germany
Seven sulfonated polystyrene standards (18 0003 000 000 g/mol), taken as model substances for macromolecular polyelectrolytes, were dissolved in aqueous 0.1 M sodium nitrate solution and characterized by multiangle laser light scattering coupled on-line to flow field-flow fractionation. The distributions of molar mass and root mean square radius and the diffusion coefficients were obtained for each sample using a constant field of force for separation. Relationships between molar mass and root mean square radius [〈RG2〉z0.5 ) (2.71 × 10-2)Mw0.56] or diffusion coefficient [D ) (7.10 × 10-8)Mw-0.68] were calculated. To investigate the static analytical range of this novel hyphenated technique a mixture of all seven samples was fractionated applying a programmed field. The relationship obtained between root mean square radius and molar mass was used to calculate a Mark-Houwink equation [[η]calcd ) (2.99 × 10-2)Mw0.68]. To verify this result, the intrinsic viscosities for all samples were measured at low shear rate and found to be in good agreement [[η]calcd ) (2.77 × 10-2)Mw0.67]. The on-line coupling of a flow field-flow fractionator (F4) and a multiangle laser light scattering detector (MALLS) produces a novel analytical system for the characterization of dissolved macromolecules and dispersed particles. We have previously reported on the experimental method and the measurement of particles.1,2 Nevertheless, the real advantages of combining these methods lie in the characterization of macromolecules. Separation in F4 is achieved by means of two streams of the same liquid flowing perpendicularly against each other and is based on differences in diffusion coefficients. By varying the flow rates of the two streams, it becomes possible to optimize the separation power for various analytical problems. F4 has a dynamic separation range from ∼104 to 1012 g/mol in molar mass and requires only that the sample be soluble in some carrier liquid.3 In standard applications, F4 is equipped with a concentration detector. The result obtained is a distribution of diffusion coefficients. To calculate molar masses from this, an empirical relationship between the diffusion coefficient and the molar mass is needed. (1) Roessner, D.; Kulicke, W.-M. J. Chromatogr. A 1994, 687, 249. (2) Thielking, H.; Roessner, D.; Kulicke, W.-M. Anal. Chem. 1995, 67, 3229. (3) Kirkland, J. J.; Dilks, C. H.; Rementer, S. W. Anal. Chem. 1992, 64, 1295. 0003-2700/96/0368-1169$12.00/0
© 1996 American Chemical Society
Multiangle laser light scattering 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 grams per mole).4 A MALLS experiment yields the molar mass and the corresponding root mean square radius without need for polymer standards. However, if MALLS 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 clinical use, for instance, high molar mass tails in blood volume expander can be life-threatening.5,6 On-line coupling of F4 and MALLS should make it possible to sort molecules according to their size and to analyze their molar masses and dimensions one by one, in order to obtain the absolutely determined distributions of molar mass and root mean square radius, even for broadly dispersed samples. Correlations of these values enable an interpretation of the solution structure of the sample investigated. In this paper, seven sulfonated polystyrene standards in aqueous 0.1 M sodium nitrate solution will be investigated as model substances for charged macromolecules, both as individual samples and in a mixture to simulate high polydispersity. Measurements are carried out with constant cross flow fields and with linearly decreasing fields to improve the efficiency and detection quality for broadly dispersed samples. THEORY Flow Field-Flow Fractionation. F4 separates molecules according to their diffusion coefficients, which can be empirically related to their molar mass. In this work, we used the standard approximation7 for calculation. Equation 1 gives the diffusion coefficient D as a function of elution time tR:
D ) w2V˙ x/6tRV˙ z
(1)
where V˙ x and V˙ z are the volume velocities of the cross and the channel flows, respectively, and w is the channel thickness. A full theoretical description of F4 can be found elsewhere.7,8 (4) Wyatt, P. J. Anal. Chim. Acta 1993, 272, 1. (5) Kulicke, W.-M.; Roessner, D.; Kull W. Starch/Sta ¨ rke 1993, 45, 445. (6) Ljungstro ¨m, K. G. Infusionsther. Transfusionsmed. 1993, 20, 206. (7) Benincasa, M. A.; Giddings, J. C. Anal. Chem. 1992, 64, 790. (8) Giddings, J. C.; Yang, F. J.; Meyers, M. N. Anal. Chem. 1974, 46, 1912.
Analytical Chemistry, Vol. 68, No. 7, April 1, 1996 1169
Table 1. Calculated Mean Values of Molar Mass and Root Mean Square Radius for the Samples 1-7 Determined by MALLS/DRI, the Diffusion Coefficients Calculated from the Retention Time Using F4 Theory, and the Intrinsic Viscosities Measured at Low Sheara sample 1 Mnominal ( g/mol)c Mn (g/mol) Mw (g/mol) Mz (g/mol) Mw/Mn Mz/Mn 〈RG2〉z0.5 (nm) [η] (mL/g) D (m2/s)
2
3
4
5
6
7b
1.80 × 104
4.75 × 104
8.01 × 104
1.755 × 105
3.530 × 105
1.000 × 106
2.746 × 106
1.56 × 104 ((7%) 1.56 × 104 ((7%) 1.56 × 104 ((5%) 1.004 1.008
3.85 × 104 ((5%) 3.85 × 104 ((5%) 3.88 × 104 ((6%) 1.005 1.011
9.04 × 10-11
5.18 × 10-11
7.94 × 104 ((3%) 7.98 × 104 ((3%) 8.04 × 104 ((3%) 1.005 1.012 18 ((9%) 36 3.61 × 10-11
1.79 × 105 ((7%) 1.82 × 105 ((6%) 1.84 × 105 ((6%) 1.016 1.032 22 ((3%) 119 2.09 × 10-11
3.38 × 105 ((3%) 3.44 × 105 ((4%) 3.50 × 105 ((5%) 1.017 1.035 32 ((3%) 175 1.35 × 10-11
9.91 × 105 ((6%) 1.07 × 106 ((6%) 1.20 × 106 ((7%) 1.076 1.208 69 ((6%) 340 4.77 × 10-12
3.15 × 106 ((4%) 4.27 × 106 ((4%) 6.55 × 106 ((4%) 1.318 2.050 152 ((3%) 614 2.58 × 10-12
a The errors indicated are the percentage standard deviations of the results from five experiments. Samples 1 and 2 were too small for the radius to be measured with MALLS. b Sample 7 has been investigated in PFF mode. c Values from manufacturer, obtained by relative size exclusion chromatography.
Multiangle Laser Light Scattering. Formulations of the theory of light scattering were put forward by Einstein,9 Raman,10 Debye,11 and Zimm,12 and concise, well-presented summaries of their work can be found in any modern textbook (e.g., ref 13). Multiangle laser light scattering means measuring the intensity of the scattered light emitted by the sample molecules at different scattering angles ϑ. With a modern MALLS photometer, it is possible to continuously monitor the scattering by means of several detectors mounted at different angles. This allows the MALLS photometer to be coupled with any fractionation method and then used to carry out absolute measurements. For each elution slice, a weight average molar mass (Mw) can be calculated using the following equations:
1 Kc ) + 2A2c + ... Rϑ MwP(ϑ)
(2)
and
P(ϑ) ) 1 - a1[2k sin(ϑ/2)]2 + a2[2k sin(ϑ/2)]4 - ... (3)
where K is a light scattering constant, containing the wavelength λo of the incident light, the refractive index no of the pure eluent, and the refractive index increment dn/dc, c is the concentration, A2 is the second virial coefficient, Rϑ is the excess Rayleigh ratio, and P(ϑ) is a general form of a scattering function. For very low concentrations, the second and higher order terms in eq 2 can usually be neglected, and Rϑ becomes directly proportional to MwP(ϑ). Plotting R(ϑ)/Kc against sin2 (ϑ/2) gives Mw from the intercept with the ordinate; from the angular dependence of the intensity of the scattered light, which is included in a1 and higher order terms of eq 3, a z-average root mean square radius 〈RG2〉z0.5 can be derived. This latter quality is defined in terms of the distribution of the volume elements of the molecule with respect (9) Einstein, A. Ann. Phys. 1910, 33, 1275. (10) Raman, C. V. Indian J. Phys. 1927, 2, 1. (11) Debye, P. J. Appl. Phys. 1944, 15, 338. (12) Zimm, B. H. J. Chem. Phys. 1945, 13, 141. (13) Kratochvil P. In Light Scattering from Polymer Solutions; Huglin, M. B., Ed.; Academic Press: London 1981.
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to the square of the distance from its center of gravity:
〈RG2〉z0.5 )
∫
1 2 r dV V
(4)
The calculation of the values for 〈RG2〉z0.5 is independent of dn/dc (assumed constant), Mw, and even c (sufficiently small) and therefore is insensible to errors. The only source of error lies in the accuracy with which the sensitivity of the 18 detectors has been normalized. For molecules below about 10 nm (∼λ/20), the precision of the root mean square radius derived from light scattering at 633 nm begins to deteriorate rapidly. EXPERIMENTAL SECTION Apparatus. A schematic diagram of the system used in this study can be found in ref 2. The fractionator was a Model F-1000 from FFFractionation, Inc. (Salt Lake City, UT). The 250 µm Teflon spacer (28.5 cm tip-to-tip length, 2.0 cm width) was bounded by ceramic frits with a pore size of 3-5 µm. The lower frit was covered with a cellulose membrane, type YM 10 from FFFractionation, Inc. The channel flow was delivered by a Hewlett Packard 1050 pump (Hamburg, Germany) at constant rates. The cross flow was provided by a double piston precision pump, Pharmacia LKB P-500 (Freiburg, Germany). With inlet and outlet flow under computer control, the magnitude of the cross flow 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 from there into an Optilap 903 differential index detector (Wyatt Technology Corp.). Refractive Index Increment. The refractive index increment was measured after equilibrium dialysis with a Wood RF-600 (Newtown, PA); the four samples measured gave a constant value of dn/dc ) 0.195 mL/g. The intrinsic viscosities were measured on a Zimm-Crothers rotary viscometer (Krannich, Go¨ttingen, Germany). Materials. The samples were narrowly distributed sulfonated polystyrene standards from Polymer Standard Service (Mainz, Germany) with nominal molar masses from 18 000 to 3 000 000 g/mol (see Table 1). They were certified by size exclusion chromatography. The carrier solution was deionized and double-
Table 2. Values of Molar Mass and Root Mean Square Radius for Samples 1-7 Determined by MALLS/DRI at Peak Maximuma sample 1
2
3
4
5
6
7b
Constant Field Mp (g/mol) 1.54 × 104 ((7%) 3.88 × 104 ((4%) 7.80 × 104 ((3%) 1.80 × 105 ((4%) 3.40 × 105 ((4%) 1.00 × 106 ((3%) 4.75 × 106 ((10%) 〈RG2〉p0.5 (nm) 17 ((7%) 22 ((3%) 31 ((2%) 68 ((4%) 117 ((7%) Programmed Field Mp (g/mol) 1.53 × 104 ((3%) 3.73 × 104 ((3%) 7.23 × 104 ((2%) 1.78 × 105 ((2%) 3.32 × 105 ((3%) 1.21 × 106 ((2%) 5.65 × 106 ((15%) 〈RG2〉p0.5 (nm) 14 ((10%) 21 ((5%) 32 ((4%) 66 ((3%) 156 ((5%) a The constant field values were single measurements in CFF mode. The programmed field values were measured in PFF mode separating a mixture composed of all seven standards. The errors indicated are the percentage standard deviations of the results from five experiments. Samples 1 and 2 were too small for a radius to be measured with MALLS. b Sample 7 has been investigated in PFF mode.
distilled water containing 0.1 M sodium nitrate as electrolyte and 0.02% (w/w) of sodium azide as a bactericide. The solution was purified by filtration (0.1 µm)14 and degassed on-line (ERC-3522, Alteglofsheim, Germany). Procedure. The samples were dissolved in the carrier solution overnight without stirring. The injection volumes were 50 and 100 µL, with an amount ranging from 0.08 to 0.4 mg for samples consisting of a single species and from 0.15 to 1.50 mg (see Table 2) for the mixture. To exclude overloading effects the results were double-checked by injecting one-half and one-tenth of the usual amount. 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 stopped flow condition was maintained until 1.5 channel volumes of cross flow had passed across the channel. The calibration of the DAWN was done with ultrapure toluene, and the normalization of the fixed 18 scattering angles was performed with a disperse solution of gold of known diameter. The “spider” plot method was used for determining the interdetector volume.4 The signal of the DRI detector was routed to the DAWN, which was interfaced to an AT computer. RESULTS AND DISCUSSION First, the individual samples were measured by applying a constant cross flow (constant field of force mode, CFF). The separation conditions were then optimized for each sample with a channel flow of 0.48 mL/min so as to obtain short analysis times (about 30 min); i.e., the cross flow imposed was just sufficient to suppress a void peak in the light scattering detector. The use of a MALLS photometer enables the molar mass and the root mean square radius to be calculated for each fraction eluted. Figure 1 shows the root mean square radius and the molar mass calculated from the intensity and the angular dependence of the scattered light for the sample with a mean molar mass of 182 000 g/mol. The values for each individual fraction are plotted against the elution volume. To gain an impression of the concentration at each point, the elution profile from the DRI detector has been included in the background as dotted lines. As noted above, the calculation of the root mean square radius is independent of experimental parameters, i.e., flow rates, detector delay, and calibration, and for this reason the determination of the radius is a very useful instrument for checking the success of (14) Kulicke, W.-M.; Kniewske, R. Makromol. Chem. 1980, 1, 719.
Figure 1. Root mean square radius and molar mass for sample 4 plotted against the elution volume (the elution profile has been plotted as a dotted line; V˙ z ) 0.48 mL/min, V˙ x ) 1.25 mL/min, CFF mode).
Figure 2. Differential distribution of the molar mass for samples 1-7. Fractionation and detection were performed with CFF F4/MALLS/ DRI, except for sample 7, which was measured in PFF mode (T ) 298 K, in 0.1 M sodium nitrate solution containing 0.02% (w/w) sodium azide, λ ) 632.8 nm, ϑ ) 3°-160°).
a fractionation method. The width of the elution profile is primarily a result of band broadening and, to a limited degree, polydispersity. The gentle slope of the radius versus elution volume plot in Figure 1 means that even this narrowly distributed standard can be fractionated with F4. By adding all slices of the same size, reliable distributions of the root mean square radius and the molar mass evolved from band broadening can be obtained.2 Figure 2 is a compilation of the molar mass distributions for all seven samples measured individually. It can be seen that the polydispersity is very low and increases with molar mass, indicated numerically by the ratios Mw/Mn and Mz/Mn in Table 1. This table also lists the average values for molar mass and root mean square radius obtained by light scattering, the diffusion Analytical Chemistry, Vol. 68, No. 7, April 1, 1996
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theory can also be applied to dissolved polymers in good solvents.17,18
[η] ) φ
〈RG2〉3/2 ) φkν3M3ν-1 M
(8)
Where φ is the Flory constant, with
Figure 3. Elution profiles and molar masses under different F4 conditions for sample 7: (- -) CFF mode, V˙ z ) 0.48 mL/min, V˙ x ) 23 mL/h; (s) PFF mode, V˙ x ) 45 mL/h f V˙ x ) 5 mL/h, over 20 min.
coefficients calculated by F4 theory, and the intrinsic viscosities. In the first row, labeled nominal, are the manufacturers’ values for the molar mass, obtained by relative size exclusion chromatography against other NaPSS standards. The intrinsic viscosities have been measured at a low shear rate (γ˘ ) 0.1 s-1). There is a good agreement between the light scattering data and the nominal results, except for the last sample. Figure 3 presents two different elution profiles of this sample. The dotted line gives a typical elution profile for this sample under CFF conditions. It can be seen that there is not enough separation power to divide the sample peak from the void peak. Applying more cross flow would move the peak away from the void but would also extend it more, leading to a lower signal-to-noise ratio and longer analysis times. The continuous line in Figure 3 shows the elution profile from a run with a decreasing cross flow (programmed field of force mode, PFF). The initial cross flow was double that of the CFF measurement and decreased linearly from the moment of injection down to almost zero (V˙ x ) 45 mL/h f V˙ x ) 5 mL/h, over 20 min). The slope of the root mean square radius versus elution volume plot (included in Figure 3) illustrates the fractionation process. The calculated mean values (see Table 1) are higher than the manufacturers’ values but match the intrinsic viscosity. The polydispersity of this sample is much higher than the polydispersity of the other samples. This example demonstrates that a programmable cross flow can improve the efficiency and detection quality of this method for high molar mass polymers and for broadly dispersed samples. It enables the fractionation power to be optimized with respect to the analytical problem. To describe the solution structure of macromolecules, often the intrinsic viscosity and the root mean square radius are related to the molar mass. From the experimental data (Table 1), it is possible to formulate the following three relationships:
[η] ) kaMwa ) (2.77 × 10-2)Mw0.67
(5)
〈RG2〉z0.5 ) kνMwν ) (2.71 × 10-2)Mw0.56
(6)
D ) kdMwd ) (7.10 × 10-8)Mw-0.68
(7)
The connection between the root mean square radius and the intrinsic viscosity is given by the Flory-Fox equation for the unperturbed state. By introducing expansion coefficients, the 1172
Analytical Chemistry, Vol. 68, No. 7, April 1, 1996
φ ) φ° (1 - 2.63 + 2.862)
(9)
) 2ν - 1
(10)
and
The Flory constant for the unperturbed state, φ°, is calculated to be φ° ) 3.69 × 1024 mol-1 for uncharged molecules and φ° ) 2.10 × 1024 mol-1 for polyelectrolytes. If eqs 8-10 are taken into account, the following links can be established between relationships 5 and 6, which therefore enables Mark-Houwink equations to be calculated from light scattering data:
a ) 3ν - 1
(11)
ka ) φkν3
(12)
The values from eq 6 yield eq 13, which is in very good agreement with the experimentally obtained relationship 5:
[η]calcd ) kcalcdMwcalcd ) (2.99 × 10-2)Mw0.68
(13)
These results also agree very well with published data.15,16 The exponents of the Mark-Houwink-like relationships describe something like the conformation of the polymer. For linear chain molecules forming a θ coil, the Mark-Houwink exponent has a value of 0.5. The better the solvent, the more open the structure of the coil becomes, and the Mark-Houwink exponent increases up to a value of 2 for ideal rods. A value of a ) 0.67 for sulfonated polystyrene in aqueous 0.1 M sodium nitrate solution takes account of the fact that a polyelectrolyte is concerned. To investigate the static separation range, we mixed the seven samples in nearly equal amounts and analyzed them in one PFF FFFF/MALLS measurement. Figure 4 gives the elution profile and the corresponding molar masses. It can be seen that separation and detection over a polydispersity range of Mw/Mn ≈ 14 is possible. In Table 2, the molar masses, the root mean square radius, and the diffusion coefficients at peak maximum are compared with the results from the CFF FFFF/MALLS/DRI measurements. The deviation is
