Anal. Chem. 2000, 72, 3896-3901
The Influence of Temperature on the Characterization of Water-Soluble Polymers Using Asymmetric Flow Field-Flow-Fractionation Coupled to Multiangle Laser Light Scattering Christer Viebke* and Peter A. Williams
Centre for Water Soluble Polymers, The North East Wales Institute, Plas Coch, Mold Road, Wrexham, LL11 2AW, U. K.
Asymmetrical flow field-flow fractionation coupled to multiangle laser light scattering has been shown to be an effective method to determine the molar mass distribution of polysaccharides. Two polymer standards, dextran and pullulan, were analyzed in the temperature range 30-60° at intervals of 10 °C. The weight average molar mass and molar mass distribution obtained at each temperature agreed well with quoted values. The diffusion coefficient, hydrodynamic radius, radius of gyration, and activation energy of diffusion were calculated and all agreed well with literature data obtained by dynamic and static light scattering. The asymmetry factor Rg/Rh suggests a flexible random coil conformation for both polymers, which was supported by the molar mass dependence of both the radius of gyration and the hydrodynamic radius. The results show the potential of asymmetric flow field fractionation coupled to multiangle laser light scattering in undertaking measurements of molar mass distribution as a function of temperature.
Natural biopolymers are extensively used as thickeners and gelling agents in many industrial sectors including food, cosmetics, and pharmaceutical products. The main parameters that govern the functional behavior of a biopolymer are the molar mass, molar mass distribution, molecular size, and conformation. Further, the solution behavior of biopolymers is also highly dependent on the temperature and solvent composition. The determination of such parameters is important in understanding the resulting properties of a product. The determination of molar mass distributions is normally done by gel permeation chromatography (gpc) coupled to a suitable detector. However, this method has a few restrictions that prevent the analysis of some polymers. A problem sometimes observed is that the polymer may adsorb, either completely or partly, to the packing material in the columns. Another problem is the total exclusion of very high molecular mass molecules from the pores of the packing material, which then will not be fractionated. Further, it has also been reported that degradation of high molar mass polymers can occur1 due to the high shear forces generated in the gpc column during elution. * Corresponding author: (e-mail)
[email protected]; (tel.) INT+441978293321
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Field-flow fractionation2 (FFF) has been developed to overcome these problems. Recently a number of publications have demonstrated that a wide range of polymers can be fractionated and analyzed by FFF combined with either a light-scattering and/or a refractive index (RI) detector.3-9 It has also been demonstrated that molecular parameters can be obtained by utilizing FFF.3,4,7,8,10,11 Thus, it is now established that FFF can be successfully combined with light scattering, but to be truly useful in the analysis of a number of polymer systems, it is often necessary to be able to perform measurements at elevated temperature. For example, many biopolymers undergo a temperature-induced orderdisorder transition which, in some cases, at room temperature, leads to aggregation and, if the polymer concentration is high enough, to gelation. A few examples are gelatin, carrageenan, and xanthan gum all used as thickeners and/or gelling agents.12 It has also been shown that it is necessary to thermostat13 the flow field-flow fractionation (FFFF) system to obtain accurate diffusion coefficients or to resolve small changes in fractograms. The aim of this study was to evaluate the effect of temperature on FFFF/MALS measurements using two polymer standards, i.e., pullulan and dextran. Pullulan is a linear polysaccharide where the repeating units are maltotriose connected through R-1, 6 glycosidic linkages. Dextran consists of R-1, 6 linked glucose units; however, a small portion of the units are joined through 1, 4-, 1, 3-, and 1, 2- linkages, giving rise to branching. THEORY Multiangle Laser Light Scattering. The scattering of light from a macromolecule solution depends on the molar mass and (1) Kulicke, W.-M.; Bo ¨se, N. Colloid Polym. Sci. 1984, 262, 197-202. (2) Giddings, J. C. Science (Washington, D.C.) 1993, 260, 1456-1465 (3) Thielking, H.; Kulicke, W.-M. J. Microcolumn Sep. 1998, 10, 51-56. (4) Thielking, H.; Kulicke, W.-M. Anal. Chem. 1996, 68, 1169-1173. (5) Roessner, D.; Kulicke, W.-M. J. Chromatogr., A 1994, 687, 249-258. (6) Benincasa, M. A.; Giddings, J. C. Anal. Chem. 1992, 64, 790-798. (7) Adolphi, U.; Kulicke, W.-M. Polymer 1997, 38, 1513-1519. (8) Wittgren, B.; Wahlund, K.-G. J. Chromatogr., A 1997, 760, 205-218. (9) Wittgren, B.; Borgstro ¨m, J.; Piculell, L.; Wahlund, K.-G. Biopolymers 1998, 45, 85-92. (10) Pauck, T.; Co ¨lfen, H. Anal. Chem. 1998, 70, 3886-3891. (11) Liu, M.-K.; Giddings, J. C. Macromolecules 1993, 26, 3576-3588. (12) Guiseley, K. B.; Stanley, N. F.; Whitehouse, P. A. In Industrial gums; Davidson, R. L., Ed.; McGraw-Hill: New York, 1980; Chapter 5. (13) Litze´n, A. Doctoral Dissertation, University of Uppsala, Uppsala, Sweden, 1992. 10.1021/ac991205x CCC: $19.00
© 2000 American Chemical Society Published on Web 07/15/2000
the radius of gyration of the macromolecule according to the following equation14
Kc/R(θ) ) 1/[MwP(θ)] + 2A2c
given data
(1)
where c is the concentration of the macromolecule, Mw is its weight average molar mass (Mw ) ∑ciMi/∑ci where Mi is the molecular weight and ci is the concentration of species i), and A2 is the second virial coefficient. The excess Rayleigh ratio, R(θ), which is a function of the intensity measured at different angles, is given by the instrument. The radius of gyration enters the equation through the particle scattering function, P(θ), which is a function of the size and shape of the molecule. For a polydisperse sample, the measured quantity is the z-average radius of gyration (Rg,z)2)∑iCiMi/∑ciMi where Mi, i are the molecular weight and the mean square radius of species i and ci is the concentration. K is an optical constant given by
K ) 2π2n02(dn/dc)2λ0-4NA-1
Table 1. Given and Measured Data on the Studied Samples
(2)
where n0 is the refractive index of the solvent at the incident wavelength (λ0), dn/dc is the refractive index increment, and NA is Avogadro’s constant. The molar mass and the radius of gyration may be obtained from a Debye plot of R(θ)/Kc vs sin2(θ/2), through an extrapolation to zero concentration and zero angle. When light scattering is used “on-line” coupled to a gpc fractionation column or FFFF channel, the scattered intensity is measured at 15 angles simultaneously but only at a single very low concentration which is assumed to be approximately zero. A2 is also assumed to be zero. Asymmetrical Flow Field-Flow Fractionation. The fundamentals of FFFF are described in detail in the work of Litzen and Wahlund,13,15-18 and below only a short description of the asymmetrical version of FFFF will be given. The separation mechanism in FFFF is based on differences in the rates of diffusion of the molecules. As diffusion is a function of the size and shape of the molecules, both of these parameters will influence the separation process. The separation principle described below is valid for particles less than 0.5 micrometers where diffusion is the governing force. When larger particles (>0.5 micrometer) are analyzed, they will separate according to a different principle2 (steric FFF). In this case, the larger species will elute before the smaller ones. The essential component of the system is the separation channel. This channel consists of an upper solid wall and a lower wall permeable to liquid (accumulation wall). A membrane is fitted at the accumulation wall in order to retain the polymer molecules in the channel. During measurements, a flow profile is created in the channel where the longitudinal velocity is close to zero at the accumulation wall and reaches a maximum near the center of the channel. The eluent will exit through the membrane (accumulation wall) and at the outlet at the end of the channel into the detectors. Restriction at either of these two outlets determines the ratio (14) Kratochvil, P. Classical light scattering from polymer solutions; Elsevier: Amsterdam, 1987. (15) Litze´n, A.; Wahlund, K.-G. J. Chromatogr. 1991, 548, 393-406. (16) Wahlund, K.-G.; Litze´n, A. J. Chromatogr. 1989, 461, 73-78. (17) Litze´n, A. Anal. Chem. 1993, 65, 461-466. (18) Litze´n, A.; Wahlund, K.-G. Anal. Chem. 1991, 63, 1001-1007.
0.1 M NaNO3
sample
Mw
P
Mw
P
dxt150 dxt410 T2000 P100 P400 P800
148 000 410 000
1.47 1.66
112 000 404 000 788 000
1.12 1.13 1.23
153 000 447 000 2 410 000 122 000 424 000 887 000
1.45 2.66 20.5 2.51 1.10 1.21
between the cross and channel flow rates. The cross-flow forces the molecules toward the accumulation wall where they form a characteristic concentration distribution. Low molecular mass molecules with a higher diffusion coefficient will reside at a higher elevation from the accumulation wall and, thereby, due to the flow profile, flow quicker through the channel. This leads to a separation that is opposite to the one found in gel permeation chromatography, in which the larger molecules elute first. The diffusion coefficient can be directly calculated from the channel thickness, w; channel volume, V0; retention time, tr; void time, t0; and the applied cross-flow rate, Vc
D ) (w2Vct0)/(6V0tr)
(3)
which is valid within19 10% if tr/t0 g 2.4. By using the StokesEinstein relation, the above equation can be rewritten to give a relationship between the hydrodynamic radius, Rh, and the retention time according to the following equation
Rh ) (kTA)/(π ηt0Vcw)
(4)
where k is Boltzmann’s constant, T the temperature, A the area of the membrane, and η the viscosity coefficient of the solvent. Thus, FFFF enables the hydrodynamic properties of macromolecules to be determined. EXPERIMENTAL SECTION Materials. Two dextran standards (dxt150 and dxt410) were purchased from Polymer Standard Service (Mainz, Germany). A third dextran sample (T2000) was purchased from Pharmacia (Uppsala, Sweden). Three pullulan standards were purchased from Polymer Standard Service (P100, P400, and P800). The weight average molar mass and polydispersity index of all samples as given by the suppliers are listed in Table 1. The salt used was sodium nitrate (Sigma, Lot. 97H1564). Preparation of Samples. Pullulan or dextran dry powder was dissolved in 0.1 M sodium nitrate by tumbling for approximately 30 min to give a sample concentration varying from 2 to 5 mg/ mL. The higher sample concentration was used for the low molar mass samples to improve the light-scattering intensity. The solvent was taken from the same batch used for elution. The eluent was filtered through a 0.22-micrometer filter. The sample was filtered through a 0.45-micrometer filter prior to injection onto the channel. (19) Wittgren, B.; Wahlund, K.-G.; De´rand, H.; Wessle´n, B. Macromolecules 1996, 29, 268-276.
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Figure 1. Molar mass versus elution time (volume) for dextran 150 (line). The circles represent the RI signal and the squares the 90° light-scattering signal. The measurement was done in 0.1 M sodium nitrate at 60 °C. The cross-flow rate was 1 mL/min, and the channel flow rate was 1 mL/min. Sample concentration was ∼8 mg/mL. A 0.250-mL injection loop was used.
FFFF/MALS. The FFFF experiments were carried out using an Asymmetric FFFF channel supplied by ConSenxus (OberHilbersheim, Germany) using a trapezoidal geometry. The channel was 28.6 cm long, and the trapezoid breadths were 2.12 and 0.47 cm, respectively. The area cut off at the inlet end was 2.25 cm2, and the total area enclosed by the spacer was 36.09 cm2. The nominal spacer thickness was 190 µm and the resulting channel volume 0.68 mL. The accumulation wall consisted of a Nadir UF10C10 ultrafiltration membrane of regenerated cellulose (Hoechst, Germany). The software for the flow control was CSC 1.2 supplied by ConSenxus. A Constant Metric 3200 pump was used to generate the flow in the channel. The injection of a sample was made with a Knauer pump (Microstar K100). The eluent (filtered using a 0.22-µm filter) was degassed before entering the channel by an ERC 3215R degasser. An in-line filter (0.1-µm) was installed between the pump and the FFFF channel. Eluent detection was performed using light scattering coupled with refractive index. Light scattering was undertaken using a Dawn F MALS photometer (Wyatt Tech., Santa Barbara, CA) equipped with a 5 mW He-Ne linearly polarized laser at a wavelength of 632.8 nm. Pure toluene with a known Rayleigh ratio was used to calibrate the instrument. The intensity of scattered light was measured at 15 different angles. The software used to process the data was ASTRA 4.50. A Wyatt Tech. Optilab DSP, an interferometric refractometer, working at the same wavelength as the light-scattering laser, was used as a mass-sensitive detector. In all calculations, a refractive index increment of 0.147 mL/g for dextran and 0.138 mL/g for pullulan has been used. The light-scattering and RI detector could be independently thermostated, and the FFFF channel was submerged in a thermostated water bath. IV. RESULTS AND DISCUSSION Molar Mass and Molar Mass Distribution. In Figure 1 the molar mass versus elution time (volume) is displayed for dextran 150 (60 °C) together with the corresponding RI and 90° lightscattering signal. In accordance with FFFF theory, the smaller molecules elute first. The RI and light scattering signals do not overlap due to the polydispersity of the sample, since the RI detector is only mass sensitive whereas the light-scattering signal is also sensitive to the molecular size. The two peaks will only 3898 Analytical Chemistry, Vol. 72, No. 16, August 15, 2000
Figure 2. Molar mass versus elution time (volume) for pullulan 400 (line). The circles represent the RI signal and the squares the 90° light-scattering signal. The measurement was done in 0.1 M sodium nitrate at 60 °C. The cross-flow rate was 1 mL/min, and the channel flow rate was 1 mL/min. Sample concentration was ∼4 mg/mL. A 0.250-mL injection loop was used.
overlap for a monodisperse sample. The noise in the molar mass curve at the high and low ends of the elution volume is due to the low concentration of polymer, which makes the calculated molar mass unreliable in this region, although it will not have any significant influence on the weight average molar mass calculated over the entire peak. In Figure 2, the molar mass versus elution time is displayed for pullulan 400, and once again, the scattering signals are shown. The P-400 sample is less polydisperse than dxt150 since the variation in molar mass as a function of elution time is smaller. Figures 1 and 2 are typical for the elution profiles observed for all six samples. The analysis times for P800 and T2000 were about 20 min (P800 and T2000), but in general, the measurements were less than 15 min. The run time varied with flow conditions and temperature. We obtained well-defined fractograms for all six polymers using the same cross-flow/ channel flow rate ratio of 1. The dxt150 and P400 sample were run at a channel flow rate of 1 mL/minute and subsequently a cross-flow rate of 1 mL/minute. The other four samples were run at a channel flow rate of 0.5 mL/minute and cross-flow rate of 0.5 mL/minute. The obtained parameters are independent of flow rate. For the very polydisperse dextran sample (T2000) it was found that, to decrease the analysis time significantly, a gradient in the cross-flow rate had to be introduced. This did not affect the resolution or recovery but it complicates the calculation of hydrodynamic parameters.20 The analysis time more or less halved (constant flow conditions) when the temperature was changed from 30 to 60 °C with no significant reduction in separation. The experiments were performed at least twice at each temperature for all polymers. The variation in the calculated weight average molar mass was less than 7%. The calculated weight average molar mass for each polymer is independent of the temperature. The molar masses were calculated from the light-scattering measurements not from FFFF calibration. The recovery was generally above 80% with the exception of the low molar mass pullulan sample (P100) where the recovery was between 65 and 75%. The lower recovery might be due to loss of sample through the membrane, which has a cutoff of 10 000 g/mol. The refractive index increment is independent of the temperature for both dextran and pullulan.21 In (20) Hecker, R.; Fawell, P. D.; Jefferson, A.; Farrow, J. B. J. Chromatogr., A 1999, 837, 139-151. (21) Nordmeier, E. J. Phys. Chem. 1993, 97, 5770-5785.
Table 2. Diffusion Coefficients for Dextran and Pullulan in 0.1 M Sodium Nitrate at Different Temperatures
Figure 3. Differential weight fraction versus molar mass for dextran 150. Conditions were as in Figure 1. 30 °C (filled square), 40 °C (open circle), 50 °C (open square), and 60 °C (filled circle).
Figure 4. Differential weight fraction versus molar mass for pullulan 400. Conditions were as in Figure 2. 30 °C (filled square), 40 °C (open circle), 50 °C (open square), and 60 °C (filled circle).
Table 1, the weight average molar mass and the polydispersity index obtained in 0.1 M sodium nitrate (average from the four temperatures) for each polymer, together with the quoted values supplied by the manufacturers, are presented. It is clearly seen that the weight average molar masses agree within 5-10% with the given values. Further, the polydispersity index, P, for P400, P800, and dxt150 is in good agreement with the data given by the manufacturers. For T2000 there was no data available on the weight average molar mass or polydispersity. However, our results regarding both these parameters agree well with data found in the literature8 on the same sample. For the low-molar-mass pullulan, P100, and dxt410, the obtained polydispersity indices differ significantly from those reported by the manufacturers. The reason for this is not clear; however, the results were reproducible. In Figures 3 and 4 the differential weight fractions versus molar masses are displayed for dextran 150 and pullulan 400, respectively. It is clearly observable that the distribution does not change with temperature for either polymer, which is expected, as no association or aggregation occurs. As can be seen in Figure 3 (dextran 150), a separation of molar masses from below 50 000 up to almost a million has been achieved in an experiment taking less than 15 min, demonstrating the quick analysis time of a fairly polydisperse sample. It was possible to separate molecules from 10 000 g/mol, for the low molar mass pullulan (P100), up to well above 10 million, for the high molar mass dextran sample (T2000), without any change of the channel setup. The distribution data for the other four polymers are similar (data not shown).
sample
Mw (g/mol)
dxt150 dxt410 T2000 P-100 P-400 P-800
105 000 240 000 2 100 000 100 000 425 000 820 000
D30° × 107 D40° × 107 D50° × 107 D60° × 107 (cm2/s) (cm2/s) (cm2/s) (cm2/s) 4.66 2.43 1.17 2.50 1.35 0.78
5.16 2.72 1.45 3.18 1.77 1.11
5.20 2.86 1.69 3.56 2.27 1.39
7.65 3.15 2.04 nd 2.85 1.72
The data above show that the separation performance of the channel is not affected as the temperature is increased. Diffusion Coefficient. As has been described in the theory section above, the retention time is inversely proportional to the diffusion coefficient (eq 3). The calculated diffusion coefficients are presented in Table 2. The retention time was taken at the peak maxima of the RI signal, with the exception of T2000), for which the RI peak maxima corresponds to a molar mass of about 200 000 g/mol, which reflects its high polydispersity as seen in the P value of around 20. Here, instead, the retention time was chosen (from the molar mass versus elution time plot) where the molar mass was 2 million. The other weight average molar masses were 105 000 g/mol for dextran 150 and 240 000 g/mol for dextran 410. For the pullulan samples, the molar masses were 100 000 g/mol for P-100, 425 000 g/mol for P-400, and 820 000 g/mol for P-800. It should be noted that each diffusion coefficient refers to a monodisperse fraction and is not an average depending on the polydispersity of the sample. The diffusion coefficients presented in Table 2 have not been extrapolated to infinite dilution. However, considering that the polymer concentration at the selected points never exceeds 0.2 mg/mL for the high molar mass samples and is less than 0.5 mg/mL for the low molar mass samples (data not shown), the concentration effect should be negligible.21 The diffusion coefficients at 30 °C agree well with values found in the literature obtained by FFF7,8 dynamic light scattering21-23 and by other techniques.24 The molar mass dependence of the diffusion coefficients can be described by the following relationship:24
D ) C1M-R
(5)
where R equals 0.33 for a compact sphere, 0.5 for a random coil in theta solvent, 0.6 for a random coil in a good solvent, and 1 for a rigid rod. M is the molar mass, and C1 is a constant. In Table 3, a complete list of R values obtained at the different temperatures is presented. The values for dextran are between 0.4 and 0.44 with the exception of 0.35 at 50 °C. These values agree with literature values of 0.4421 and 0.38.8 The values for pullulan are between 0.48 and 0.53, which is slightly lower than that found by dynamic light scattering,21 0.54, and by FFFF,8 0.58, but in the same range as other studies by dynamic light scattering,22,23 0.52 and 0.51. The slight decrease in the R value observed for pullulan (22) Kato, T.; Katsuki, T.; Takahashi, A. Macromolecules 1984, 17, 1726-1730. (23) Nishinari, K.; Kohyama, K.; Williams, P. A.; Phillips, G. O.; Burchard, W.; Ogino, K. Macromolecules 1991, 24, 5590-5593. (24) Pavlov, G. M.; Korneeva, E. V.; Yevlampieva, P. Int. J. Biol. Macromol. 1994, 16, 318-323.
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Figure 5. A plot of the logarithm of the diffusion coefficient versus 1/T for dextran in 0.1 M sodium nitrate: (diamonds) Mw ) 2 100 000, (squares) Mw ) 240 000), and (circles) Mw ) 100 000.
Figure 6. A plot of the logarithm of the diffusion coefficient versus 1/T for pullulan in 0.1 M sodium nitrate: (diamonds) Mw ) 820 000, (squares) Mw ) 425 000), and (circles) Mw ) 100 000.
Table 3. Scaling Exponent r
Table 4. Activation Energy of Diffusion
polymer
temp (°C)
R
sample
Mw
D0/104
Ed (kJ)
dextran
30 40 50 60 30 40 50
0.44 0.40 0.35 0.40 0.53 0.49 0.48
dextran
105 000 240 000 2 100 000 100 000 425 000 820 000
0.03 0.1 0.5 1.2 5.4 4.7
4.5 9.4 15.3 15.6 20.9 21.9
pullulan
pullulan
as the temperature increases might indicate that the solvent quality becomes worse but the change is too small to be confident that this is the case. The same trend has been observed by dynamic light scattering.21 The data suggest that pullulan is a more extended polymer than dextran, which agrees well with the fact that dextran usually contains some branching.26 The diffusion coefficient will vary with temperature due to the faster Brownian fluctuations of the molecules as the temperature is increased. The change in diffusion coefficient was clearly seen as a change in the elution time of the sample as the temperature was increased. The temperature dependence of the diffusion coefficient is often described by the following semiempirical equation21
D ) D0 exp(-Ed/RT)
(6)
where R is the gas constant, Ed the activation energy for diffusion, and D0 a prefactor. In Figures 5 and 6, ln D versus 1/T are displayed for dextran and pullulan, respectively. As can be seen, they are straight lines; thus, eq 6 can be used to describe the obtained data. The corresponding activation energies are displayed in Table 4. It can be seen that for dextran and pullulan the activation energy depends on the molar mass. The highest value of 15.3 kJ for dextran is slightly lower than the value of 19 kJ found by dynamic light scattering.21 The value for pullulan is around 20-21 kJ, which agrees well with the value of 19 kJ found by dynamic light scattering.21 The different values obtained for dextran and pullulan probably reflect their different molecular structures. (25) Richards, E. G. An Introduction to physical properties of large molecules in solution; Cambridge University Press: Cambridge, UK, 1980. (26) Kennedy, J. F.; White, C. A. Comphrensive Organic Chemistry, Vol. 5; Haslam, E., Ed.; Pergamon Press: Oxford, UK, 1987; Chapter 26.
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Size and Shape. The hydrodynamic diameter can be calculated using eq 4 or directly from the diffusion coefficient using the Stokes-Einstein equation. This parameter gives the equivalent sphere diameter of a macromolecule in solution. The solvent quality should change as a function of temperature for both polymers, and this would affect the value of the hydrodynamic diameter. However, within experimental error, both the radius of gyration and the hydrodynamic diameter are independent of the temperature. The calculated radius of gyration for dxt150 is 10 ( 2 nm; for dxt410, 23 ( 2 nm; and for T2000, 41 ( 1 nm; the corresponding hydrodynamic diameters are 14 ( 3 nm, 27 ( 5 nm, and 48 ( 2 nm. For pullulan we obtain 12 ( 1 nm, 25 ( 3 nm, and 38 ( 1 nm for the radius of gyration and 21 ( 2 nm, 39 ( 3 nm, and 61 ( 7 nm for the hydrodynamic diameter for P100, P400, and P800, respectively. The results for pullulan, in regard to the radius of gyration, agree with results obtained by light scattering in the temperature range27 15-45 °C. The radius of gyration for the low-molar-mass dextran and pullulan might be unreliable since the light-scattering detector cannot measure sizes below 10-15 nm accurately. The hydrodynamic diameter was independent of both flow conditions and of the spacer thickness. In one run on dextran 150, a 350-micrometer spacer was used (instead of a 190-micrometer), and this gave the same results regarding the hydrodynamic radius (and diffusion coefficient). The combination of the radius of gyration and the hydrodynamic radius7 gives information about the polymer structure. The following dimensionless factor is often defined21
p ) Rg/Rh
(7)
For a compact sphere, this ratio is 0.775; for a flexible polymer, it varies between ∼1.5 and ∼1.9 for a theta and good solvent, (27) Buliga, G. S.; Brant, D. A. Int. J. Biol. Macromol. 1987, 9, 71-76.
Figure 7. Logarithm of the radius of gyration and the hydrodynamic radius versus the logarithm of the molar mass for dextran in 0.1 M sodium nitrate. Filled circles denote the radius of gyration and open circles the hydrodynamic radius.
respectively. In our case, we obtain values of 1.1-1.5 for P-400 and 1.1-1.3 for P-800. For the dextran samples we obtained 1.31.7 for dextran 410 and from 1.4 to 1.5 for dextran 2000. The scatter in the data is relatively large as has been observed in other studies;7,21,22 however, the ratios are all reasonable. As for the diffusion coefficient, the radius of gyration and the hydrodynamic radius molar mass dependence can be described by a power law expression as follows25
Rh ) C2Mβ
(8)
Rg ) C3Mγ
(9)
and
where β ) γ have values of 0.33 for a sphere, 0.5 for a random coil in theta solvent, 0.6 for a random coil in a good solvent, and 1 for a rigid rod. M is the molar mass, and C2 and C3 are constants. In Figures 7 and 8, the logarithm of the radius of gyration and the hydrodynamic radius as a function of the logarithm of the molar mass are displayed for dextran and pullulan, respectively. As the radius of gyration and the hydrodynamic radius are more or less independent of temperature, an average of the data obtained at each temperature has been used in the plots. The resulting power law values are, for dextran, β ) 0.44 and γ ) (28) Kato, T.; Okamoto, T.; Tokuya, T.; Takahashi, A. Biopolymers 1982, 21, 1623-1633.
Figure 8. Logarithm of the radius of gyration and the hydrodynamic radius versus the logarithm of the molar mass for pullulan in 0.1 M sodium nitrate. Filled circles denote the radius of gyration and open circles the hydrodynamic radius.
0.49, and, for pullulan, β ) 0.55 and γ ) 0.64. The data are consistent and reasonable for both sets of data and agree well with data found in the literature.22,27,28 The higher values found for pullulan once again support the notion that pullulan has a more extended structure compared with the slightly branched dextran. Concluding Remarks. This study has shown that it is possible to use FFFF at elevated temperature to obtain reliable results regarding weight average molar mass, z-average radius of gyration, and molar mass distribution. This is a great advantage for a number of biopolymers in which association and aggregation occur at room temperature. Further, we have shown that the coupling of MALS and asymmetric FFFF is a powerful tool to derive information about molecular parameters. The diffusion coefficient and hydrodynamic radius, in connection with the radius of gyration, provide information about the polymer structure in a given environment. We have demonstrated that the data obtained for dextran and pullulan is consistent with data in the literature obtained by dynamic and static light scattering regarding diffusion coefficients and activation energy of diffusion. Further, our results suggest that pullulan is more extended than dextran. This is expected because the dextran molecules are usually slightly branched whereas pullulan is linear. ACKNOWLEDGMENT We thank the E. U. for a supporting Grant (Contract no. FAIR CT97-9521). Received for review October 20, 1999. Accepted May 5, 2000. AC991205X
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