Environ. Sci. Technol. 2000, 34, 3508-3513
Diffusion Coefficients and Polydispersities of the Suwannee River Fulvic Acid: Comparison of Fluorescence Correlation Spectroscopy, Pulsed-Field Gradient Nuclear Magnetic Resonance, and Flow Field-Flow Fractionation J A M I E R . L E A D , †,§ K E V I N J . W I L K I N S O N , * ,† E R I C B A L N O I S , † BENJAMIN J. CUTAK,‡ CYNTHIA K. LARIVE,‡ SHOELEH ASSEMI,# AND RONALD BECKETT# CABE (Biophysical and Environmental Analytical Chemistry), University of Geneva, Sciences II, 30 Quai E. Ansermet, CH-1211, Geneva 4, Switzerland, Department of Chemistry, University of Kansas, Lawrence, Kansas 66045, and CRC for Freshwater Ecology, Water Studies Centre and Department of Chemistry, Building 19, Monash University, Wellington Road, Clayton, Victoria 3800, Australia
Diffusion coefficients of the Suwannee River fulvic acid (SRFA) obtained using fluorescence correlation spectroscopy (FCS), pulsed-field gradient nuclear magnetic resonance spectroscopy (PFG-NMR), and flow field-flow fractionation (FlFFF) were compared as a function of pH (4.0-8.5) and ionic strength (5-500 mM). Diffusion coefficients of the SRFA ranged between 1.9 and 3.5 × 10-10 m2 s-1. These values were fairly constant as a function of both pH and ionic strength and comparable to the limited literature values available. Polydispersity data are shown indicating that there is some degree of size and chemical heterogeneity for this humic sample including a small fraction of SRFA components with a diffusion coefficient smaller than 1 × 10-10 m2 s-1. The results imply that the majority of SRFA components have hydrodynamic diameters between 1.5 and 2.5 nm.
Introduction Knowledge of the diffusion coefficients, D, of humic substances is essential in order to understand the fate and behavior of humic-bound trace pollutants (1-3). For example, complexation by humic substances is generally acknowledged to reduce contaminant bioavailability (4), possibly due to a decreased diffusive flux of contaminant to the organism surface. Although there is some degree of consensus on the values of D, in general, the values are not * Corresponding author phone: (4122) 702 6051; fax: (4122) 702 6069; e-mail:
[email protected]. † University of Geneva. ‡ University of Kansas. § Current address: Institute of Environmental Health and Risk Management, University of Birmingham, Edgbaston, Birmingham, B15 2TT, U.K. # Monash University. 3508
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easily obtained, due in large part to the inherent complexity and heterogeneity of the humics. Furthermore, techniques used for their determination often (i) require concentrations which are higher than natural levels (e.g. dynamic light scattering (5, 6)), (ii) are based upon indirect measurements (e.g. voltammetry (6, 7)), or (iii) require the interaction of the humics with a solid phase (e.g. chromatography (8)). These factors may lead to artifacts due to the easily modifiable nature of the humics and their ability to be sorbed to most surfaces. Suwannee River fulvic acid (SRFA) is a standard, wellcharacterized HS with little tendency to aggregate, even at high concentrations (9). The evaluation of diffusion coefficients of complex and polydisperse samples such as HS requires the use of analytical methods that do not perturb the sample as a consequence of the measurement. In this paper, we have attempted to validate the minimally perturbing and complementary techniques of fluorescence correlation spectroscopy (FCS), pulsed-field gradient nuclear magnetic resonance (PFG-NMR), and flow field-flow fractionation (FlFFF) by determining average diffusion coefficients of the SRFA. In addition, a quantitative indication of the polydispersity of SRFA is given. Each of these techniques has been used previously for the measurement of average diffusion coefficients of natural organic macromolecules (10-15); however, differences in solution conditions or the exact nature of the organic matter has precluded an absolute comparison. In any case, some uncertainty still exists in the literature as to the size of humic macromolecules and their aggregates, their degree of polydispersity, and the conditions under which aggregates form. Much of the difficulty in interpreting the results stems from the fact that each of the analytical techniques used to determine diffusion coefficients (or hydrodynamic sizes) has its own advantages and limitations. Furthermore, each technique measures an average value which is weighted in a different manner. For this work, we have examined a standard fulvic acid under similar conditions by comparing the diffusion coefficients and polydispersities obtained with FCS, PFG-NMR, and FlFFF.
Experimental and Theory Samples were prepared under a range of solution conditions: pH (pD for NMR) 4.0-8.5; ionic strength 5-500 mM in NaCl; humic concentrations 10-5000 mg L-1. To correct for the isotope effect in D2O solutions, pD measurements were determined by adding 0.40 to the pH meter reading (16). Stock solutions of standard SRFA obtained from the International Humic Substances Society were prepared from the freeze-dried solids without further treatment and left for 24 h to ensure rehydration. For the three techniques, ‘average’ diffusion coefficients, DP, were determined as the most probable diffusion coefficients. For FCS and NMR, DP was derived from the maximum in the calculated diffusion coefficient distribution, while in FlFFF this value corresponds to the peak maximum. The number average diffusion coefficient, DN, was determined using the relationship ΣiniDi/ Σni where n is the number based signal from FCS. This relationship was also used in the analysis of the NMR results; however, the signal in this case is weighted by the number of protons comprising a peak and therefore is influenced by both the number and size of the molecules giving rise to an integrated signal. The relationship ΣmiDi3/ΣmiDi2 was used in the calculation of DN from the FlFFF results where m is the mass based signal obtained from FlFFF. Hydrodynamic diameters (dH) were estimated using the Stokes-Einstein equation (17, 18) under the assumption that the molecule 10.1021/es991195h CCC: $19.00
2000 American Chemical Society Published on Web 07/08/2000
exists as a compact sphere (eq 1)
n
∑c ) G(0) (1)
where k is the Boltzman constant, T is the temperature, and η is the viscosity. Polydispersities were determined from the quotient of the weight average (dW) and number average (dN) hydrodynamic diameters. In the case of FlFFF, polydispersities were calculated directly from the UV signal (eq 2 (19)), whereas in PFG-NMR and FCS, dW and dN are determined from a derived size distribution using eq 3 (20).
Σimidi Σimi Polydispersity ) Σimi/di
(2)
Σimi/d2i Σinidi3 (3)
Fluorescence Correlation Spectroscopy (FCS). The FCS method has been discussed in detail elsewhere (21-23). In brief, laser light (excitation at 488 nm) is focused into the sample of interest using confocal optics. In this manner, a small, illuminated volume element (approximately 0.5-1.0 µm3) called the confocal volume is created. To optimize the signal-to-noise ratio, the confocal volume should be occupied by a small number of fluorescent molecules at any given point in time. Temporal fluctuations in the measured fluorescence intensity are used to derive an autocorrelation curve. In the absence of any other processes which affect sample fluorescence, such as chemical reactions, the autocorrelation curve will be related to the translational diffusion of the fluorophore across the confocal volume. Diffusion times of the SRFA molecules are obtained from a best fit of the autocorrelation function (24) following the calibration of the size of the confocal volume using Rhodamine-6G (R6G), which has a diffusion coefficient of 2.8 × 10-10 m2 s-1 (25). The diffusion coefficient, D, of the SRFA was calculated from the following relationship
ω21 4τ1
(4)
where ω1 is the width of the confocal volume and τ1 is the characteristic diffusion time of the particle through the confocal volume. The method of histograms (26) was employed to determine distributions of diffusion times from the FCS autocorrelation function (27). In this case, the FCS diffusion time scale is divided into a finite number, n, of intervals, i. The corresponding fraction, ci, of particles in each interval is represented by a bar height and the corresponding FCS autocorrelation function is given by n
G(t) )
∑c
i
i)1
( )( ) 1+
t
τi
-1
1+
t
p2τi
i)1
The bar heights are varied in order to minimize the differences between the calculated and experimental correlation function. This approach is an ill-posed problem, which is overcome by introducing a regularization condition (27, 28). Pulsed-Field Gradient NMR (PFG-NMR). Proton PFGNMR spectra were acquired using the bipolar pulse longitudinal encode-decode (BPPLED) pulse sequence (29). The BPPLED spectra were acquired with a Bruker AM 360 NMR spectrometer using a 5 mm proton-optimized probe equipped with a shielded z-gradient coil. The gradient coil constant, 0.0531 T m-1 A-1, was determined by calibration with a 10 mM β-cyclodextrin solution. In the BPPLED experiment, the intensity of a resonance, I, is related to the diffusion coefficient of the molecule, D, by the equation
[ (
I ) Io exp -D ∆ -
Σinidi2 Polydispersity ) Σinidi Σini
D)
(6)
i
kT dH ) 3πηD
-1/2
(5)
where t is the delay time and p is the structural parameter or the ratio between the transversal and longitudinal dimensions of the confocal volume (p ) ω1/ω2). The normalizing condition is given by
δ τ 2 2 2 - Gγδ 3 2
)
]
(7)
where Io is the resonance intensity in the absence of a gradient pulse, ∆ is the time during which diffusion occurs, δ and G are the duration and amplitude of the bipolar pulse pair, respectively, τ is the delay following each gradient pulse, and γ is the gyromagnetic ratio. Following an initial 1.2 s relaxation delay, ∆, δ, and τ were held constant at 0.20 s, 1.2 ms, and 1.1 ms, respectively, while G was varied at regular intervals from 0.027 to 0.239 T m-1. An additional delay of 15 ms was employed after the last gradient pulse to eliminate the effects of residual eddy currents. All free induction decays (FIDs) were acquired at 298 K, using a spectral width of 6024 Hz and 16 384 data points. A minimum of 512 FIDs were coadded to obtain adequate signal-to-noise ratios in the final spectra. A total of 28 PFG-NMR spectra were measured for each experiment. The FIDs were transferred to a Silicon Graphics Indy workstation and processed using Felix 97.0 (Biosym). All FIDs were truncated at 4096 data points, apodized by multiplication with an exponential function equivalent to 10 Hz line broadening, and Fourier transformed. The spectra were baseline corrected by fitting selected baseline points to a fifth order polynomial. Four previously reported spectral regions were integrated: region 1: 0.8-1.9 ppm, region 2: 1.9-3.5 ppm, region 3: 3.5-4.3 ppm, and region 4: 6.3-8.1 ppm (12, 13, 30). Region 1 corresponds to protons on terminal methyl groups of methylene chains, aliphatic carbons bonded to other carbons, and protons on methyl groups of branched aliphatic structures. The resonances in region 2 result from protons on aliphatic carbons which are two or more carbons from an aromatic ring or polar functional groups. Region 3 corresponds to protons on carbons adjacent to aromatic rings or electronegative functional groups. The resonances in region 4 result from aromatic protons. The PFG-NMR spectral data were analyzed to determine diffusion coefficients using the computer program, CONTIN, which approximates a solution to the ill-posed problem of an inverse Laplace transform applied to the intensity decay by using assumed prior knowledge of the possible diffusion coefficients (28, 31, 32). A disadvantage of CONTIN analysis is that it tends to over-smooth the fit and broaden the diffusion coefficient distribution. However, CONTIN is attractive for the analysis of humic substances because it assumes a continuous distribution of diffusion coefficients. A more detailed discussion of the application of CONTIN analysis for the determination of humic substance diffusion coefficients from PFGNMR data has been reported elsewhere (12). To conserve spectrometer time, eight trials were performed for one sample to determine a relative standard deviation that was used to VOL. 34, NO. 16, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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calculate an experimental error for subsequent analyses. Measurements for each of the other samples were performed at least in duplicate and produced diffusion coefficients within the range predicted by the calculated experimental error. Flow Field-Flow Fractionation (FlFFF). The method of FlFFF has also been discussed in detail elsewhere (33-35). Briefly, it is a chromatography-like elution technique, where separation occurs in a thin, open channel. Unlike chromatography, the separation is based on the physical interactions of the sample with a field applied at right angles to the channel (in the FlFFF case, a fluid cross-flow). The field drives the sample toward an accumulation wall. Each sample component forms an ‘equilibrium cloud’ whose mean distance from the wall, l, is dependent on its field induced velocity, U, and its diffusion coefficient, D:
l)
D U
(8)
Separation occurs because the flow through the channel is laminar, with a parabolic cross sectional velocity profile. Thus, sample clouds with a center of mass further from the accumulation wall (lower D) will be eluted by faster vectors in the laminar flow stream. Diffusion coefficients can be determined directly for each component of a sample from their retention parameter, λ
D)
λVcw2
(9)
V0
where V0 is the channel void volume and λ is the retention parameter which is the ratio of the cloud thickness to the channel thickness, l/w. λ is calculated from the measured retention volume Vr using the general FFF retention equation
R)
V0 1 ) 6λ coth - 2λ Vr 2λ
(
)
(10)
where R is referred to as the retention ratio. The UV detector response, dm′/dVr, was converted to the diffusion coefficient based relative mass, dm′/dD, in arbitrary units using the following equation:
dm′ dm′ dVr ) ‚ dD dVr dD
(11)
Here m′ is the cumulative mass of the sample eluted up to a given point in the separation (35) and dVr/dD is the change in elution volume per change in the diffusion coefficient which is estimated from FlFFF theory using eqs 10 and 11. The FlFFF channel was cut into a Teflon sheet which was sandwiched between two Lucite blocks. Ceramic frits were mounted inside these blocks, allowing cross-flow of the carrier. To prevent sample loss, the lower frit (or accumulation wall) was covered with a cellulose-acetate membrane (28). The channel had a void volume of 1.142 mL and a channel thickness of 0.023 cm. The cross-flow and channel flow rates were maintained at approximately 3.9 and 0.8 mL min-1 respectively. Deionized water (Milli-Q, Millipore) was used as the carrier with the pH and ionic strength adjusted to that of the samples with NaOH, HCl, and NaCl. A sample injection loop of 20 µL was used, corresponding to an injected sample mass of 1 µg. The channel flow was stopped for 26 s following injection to allow for relaxation of the sample under the applied field. A UV detector (Spectra, 254 nm) was used to record the elution profile.
Results and Discussion When working with humic substances, one must be aware that they are not monodisperse model compounds but rather 3510
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FIGURE 1. Normalized distribution of diffusion coefficients determined by FCS at 5 and 50 mM ionic strength at pH 8.5. a distribution of a family of macromolecules with variable conformations and chemical compositions. For this reason, much attention must be paid to their distributions rather than simply average values. In this paper, diffusion coefficient distributions are determined allowing comparison of the most probable diffusion coefficient in addition to sample polydispersity. Fluorescence Correlation Spectroscopy (FCS). The fit for the FCS autocorrelation curve for the standard SRFA sample was excellent (r2 > 0.99), based on the assumption of a single fluorescent diffusing species. Although the use of two or three diffusion times were able to reduce the error compared to the use of a single diffusion time, the extracted parameters (diffusion time and fraction of each component present) were often physically unrealistic and poorly defined, indicating over-parametrization. The results indicated limited heterogeneity or polydispersity of the SRFA. The calculated distribution of diffusion coefficients is given in Figure 1 for the SRFA sample at pH 8.5. No significant differences were observed between average values obtained at 5 and 50 mM ionic strength. At 5 mM, the distribution of diffusion coefficients indicated only limited polydispersity, while at 50 mM, the apparent distribution was broader. Although these differences could be interpreted as an increased aggregation at the higher ionic strength, this result should be interpreted with caution since there is also some indication that the shape of the confocal volume may be modified at higher ionic strengths. Taking into account measured changes in the shape of the confocal volume, Lead et al. (10) concluded that there was no influence of ionic strength on the value of the Dp for the SRFA between 1 and 100 mM. At even higher ionic strengths, it was more difficult to obtain a precise distribution of D due to changes in the refractive index of the medium leading to an ill-defined confocal volume. A small but significant decrease in Dp was observed with decreasing pH (Table 1). This decrease could be attributed to the neutralization of charge on the SRFA, leading to the formation of small dimers and trimers at low pH (10). Pulsed Field Gradient-NMR (PFG-NMR). The PFG-NMR distributions of diffusion coefficients obtained for the SRFA are clearly non-Gaussian (Figure 2). Number averaged diffusion coefficients were greater than the most probable diffusion coefficients, reflecting the asymmetry of the distribution. As was observed for the FCS results, within experimental error, ionic strength did not affect the diffusion coefficients determined with PFG-NMR (Table 1). Diffusion coefficients were constant or increased slightly as a function of decreasing pH, although a pronounced change was not detected for each of the spectral regions analyzed (Table 1). One advantage of PFG-NMR is that differences in the diffusion coefficients can be observed as a function of
TABLE 1. Most Probablea Diffusion Coefficients (m2 s-1 × 1010) as a Function of pH and Ionic Strength as Measured by FCS, FlFFF, and PFG-NMRb ionic strength (mM) FCS FlFFF PFG-NMR region 1 region 2 region 3 region 4
4
pH (or pD) 5.5
7.0
5 50 500 5 50 500
2.21 (0.07) 2.52 (0.02) 2.71 (0.06) 2.05 (0.02) 2.40 (0.04) 2.61 (0.04) 2-3 2-3 2-3 3.0 (0.08) 2.9 (0.03) 1.9 (0.05) 2.2 (0.02)
low (8-27) 500 low (8-27) 500 low (8-27) 500 low (8-27) 500
3.6 (0.2) 3.6 (0.2) 3.4 (0.2) 3.2 (0.2) 2.7 (0.2) 2.8 (0.2) 2.8 (0.2) 2.6 (0.2)
3.7 (0.2) 3.7 (0.2) 3.4 (0.2) 3.2 (0.2) 2.5 (0.2) 2.6 (0.2) 2.7 (0.2) 2.7 (0.2)
3.5 (0.2) 3.5 (0.2) 3.1 (0.2) 3.2 (0.2) 2.6 (0.2) 2.7 (0.2) 2.4 (0.2) 2.5 (0.2)
a In FlFFF, this value corresponded to the peak maximum. b Standard deviations (FCS: n ) 3; PFG-NMR: n ) 8; FFF: n ) 3) are given in parentheses.
FIGURE 2. Normalized distribution of diffusion coefficients determined by PFG-NMR for each of the proton spectral regions. Data were obtained at an ionic strength of 27 mM at pD 8.5. chemical shift. For many humic substances, functional group and molecular weight heterogeneity produce significant variations in the average diffusion coefficient measured for different integrated regions of the NMR spectrum (12). However, SRFA diffusion coefficients are relatively constant over the 1H NMR chemical shift range. Comparison of the diffusion coefficients measured for different spectral regions indicates a small degree of heterogeneity with respect to molecular size. For instance, the measured diffusion coefficients indicate that the molecules responsible for the resonances in region 1, and to a lesser extent region 2, are on average distributed in a lower molecular weight range compared with those of regions 3 and 4, suggesting that the more aliphatic components of the sample are, on average, smaller in size. However these results should not be interpreted in terms of 4 different types of fulvic acid molecules giving rise to 4 distinct spectral regions. Most fulvic acid molecules probably contain protons that contribute to all four regions to some extent. For example, a fulvic acid molecule with some aliphatic carbon structures attached to an aromatic ring may contain protons contributing to all four spectral regions. Therefore the differences in diffusion coefficients determined for these chemical shift regions should be interpreted in terms of relative differences in functional group distribution. Flow Field-Flow Fractionation (FlFFF). Table 1 gives the diffusion coefficients obtained at the peak maximum mea-
FIGURE 3. Normalized distribution of diffusion coefficients determined by FlFFF at 5 and 50 mM ionic strength at pH 8.5. sured at different pH and ionic strength. For the FlFFF, the solution pH had a less significant effect on the distributions than did ionic strength, with the exception of the data at the highest ionic strength and lowest pH examined (I ) 50 mM NaCl and pH ) 5.5). For this sample, the peak was broadened and the area decreased compared to runs at the same ionic strength and higher pH values. For increasing values of ionic strength, peak area decreased. In fact, no peaks were observed at 500 mM ionic strength. This may be the result of aggregation induced by high ionic strength (not seen to any extent with FCS or NMR) or to membrane-humic interactions. Emergence of large peaks after termination of the field at the end of the run provides evidence for both explanations. Comparison of the distributions of the diffusion coefficients (Figure 3) and the calculated equivalent spherical hydrodynamic diameters of the SRFA at peak maxima suggests a slight increase in size from 1.5 to 2.1 nm by increasing the ionic strength from 5 to 50 mM. This corresponds to an increase in mass of 2.7 times which can be interpreted as aggregation of some of the humic components by formation of dimers and trimers. However, for the FlFFF results, one cannot disregard the possibility of membrane repulsion at low ionic strength, which might result in lower calculated hydrodynamic diameters. Nonetheless, previous studies using sedimentation FFF suggest that 5 mM ionic strength is high enough to effectively eliminate significant perturbations due to particle-wall and particleparticle repulsion (36). Molecular Sizes and Diffusion Coefficients. The three methods demonstrate clearly that, under the conditions examined here, the SRFA consists mainly of relatively small macromolecules (≈1.5-2.5 nm diameter) rather than molecular aggregates. This conclusion is also in agreement with results obtained from atomic force microscopy ((37, 38) Figure 4) for which relatively few macromolecular aggregates were observed. AFM observations indicated that individual SRFA particles were reasonably monodisperse (polydispersity ) weight average height/number average height ) 1.2) with adsorbed molecular heights which averaged 0.75 ( 0.3 nm (N ) 100). AFM height measurements are expected to give values that are smaller than measurements of hydrodynamic diameters due to tip-sample and sample-substrate interactions (38). Molar mass estimations of the SRFA based on the diffusion coefficients obtained here, under the assumption of a compact sphere, ranged from 530 to 1640 g mol-1 and are very similar to recent literature values (8, 13, 39). The values of D measured in this study are also in good agreement with the limited literature data available, despite uncertainties associated with some of the techniques previously used. Table 2 indicates that there are differences among the diffusion coefficients of aquatic, peat, and terrestrial natural organic matter (NOM). Nonetheless, with the excepVOL. 34, NO. 16, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 3. Most Probable, DP, and Number Average, DN, Diffusion Coefficients and Polydispersity Indices of SRFA Measured by FlFFF, PFG-NMR, and FCSa
FlFFF (5 mM) FlFFF (50 mM) FCS (5 mM) FCS (50 mM) NMR (region 1) NMR (region 2) NMR (region 3) NMR (region 4)
FIGURE 4. Hydrodynamic diameters of the SRFA calculated from the diffusion coefficients measured at pH 8.5 and low ionic strength (5-27 mM) using the Stoke’s-Einstein equation. Hydrodynamic diameters have been normalized to give an equivalent total signal intensity. The NMR results were calculated from the diffusion coefficient distribution for spectral region 4. Adsorbed heights of the SRFA as measured by AFM are presented as a histogram (N ) 100).
TABLE 2. Literature Data for the Values of Diffusion Coefficients of Natural Organic Mattera diffusion coeff (m2 s-1 × 1010)
technique
1.9-3.5 0.027-0.036 2.1-2.9 3.5-5.0 3.0-4.1 1.9-3.4 1-4.7 0.6-1.2
Aquatic NOM FCS/PFG-NMR/FlFFF PCS FCS PFG-NMR FlFFF FlFFF voltammetry voltammetry
0.005 0.05-0.2 0.2-0.9 0.023-0.12 0.05-0.4
material
ref
SRFA this study HA 5 NOM 10 SRFA 13 SRFA/SRHA 14 HA/FA 15 FA/HA 7 FA 44
Peat and Terrestrial NOM PCS peat HA voltammetry peat HA chromatography Aldrich HA PCS/voltammetry Fluka HA/ peat HA AUC soil HA
5 6 8 44 45
AUC - analytical ultracentrifugation, PCS - photon correlation spectroscopy. a
tion of ref 5, the values of aquatic NOM are all fairly consistent and in the range 0.6-5.0 × 10-10 m2 s-1. Small differences can be rationalized in terms of variable solution conditions and the use of both different types of NOM and different analytical techniques. For example, the data in ref 5 can be explained by the use of high concentrations, the bias of photon correlation spectroscopy (PCS) for larger molecules and the nature of the humic acids which were analyzed. Although, the PFG-NMR data presented here (and in the refs 12 and 13) were collected at comparable concentrations to those in ref 5, PFG-NMR values of diffusion coefficients are higher than the PCS values, most likely because PFG-NMR is less biased toward the larger fraction and because the SRFA has little tendency to aggregate at concentrations as high as 10 g L-1 (16). Furthermore, diffusion coefficients of the peat humics are consistently lower (larger size) than those of the aquatic NOM (Table 2), which is probably due to their greater hydrophobicity and larger molar mass. Polydispersity. Figure 4 shows the distributions of the calculated hydrodynamic diameters of SRFA at low ionic strength and neutral pH, calculated by transforming the diffusion coefficients using the Stokes-Einstein equation (eq 1). In general, only small differences can be observed among 3512
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DP (m2 s-1 × 1010)
DN (m2 s-1 × 1010)
polydispersity
3.0 2.2 2.7 2.8 3.3 2.7 2.4 2.4
2.9 3.3 2.4 2.4 3.5 3.1 2.9 2.7
1.2 1.3 1.3 1.5 1.9 1.9 1.8 1.8
a Data were collected at pH 8.5. PFG-NMR experiments were performed at pD ) 8.5 and 27 mM ionic strength.
the curve shapes and median values of the FCS, PFG-NMR, and FlFFF distributions. To quantify the polydispersity, diffusion coefficients for the SRFA at pH 8.5 are given as a most probable value (DP), a number average value (DN), and a polydispersity index (determined from eqs 2 and 3) in Table 3. Excellent agreement is obtained among the different techniques with a range of about 1 × 10-10 m2 s-1. Polydispersity values were similar among the different methods (Table 3) although somewhat higher values of polydispersity were obtained for PFG-NMR (Figure 4). For both PFG-NMR and FCS, polydispersity values may be exaggerated due to the fact that they are determined from a derived size distribution and small variations in the data may be raised to large powers (cf. eq 3). Given the dependency of the diameter on either the square or cube root of the molar mass (17), these values also correspond reasonably well to molar mass polydispersity values obtained for SRFA using size exclusion chromatography (40), i.e. Mw/ Mn ) 1.7, inferred dw/dn ) 1.2-1.3. Advantages/Limitations of the Techniques. The finding that each technique provides similar average values and similar distributions of the diffusion coefficients is encouraging, especially given the major differences in the techniques which are based on entirely different measurement and detection methods. Although extremely sensitive (down to ≈1 mg L-1 of SRFA), the FCS technique is limited to the measurement of the fluorescent moieties only. According to Senesi (41), these moieties make up only 1% of humic substances. However, the fluorescent components are likely to be representative of the overall humic substance (10). The PFG-NMR technique is likely to be the least perturbing of the techniques examined here and offers the advantage of some degree of resolution by chemical composition. In this respect, NMR results for the aromatic carbon (region 4), which are the most likely to be fluorescent, closely resembled the results obtained by FCS while D values for aliphatic carbon nuclei were generally larger. NMR is relatively insensitive and requires higher concentrations and longer experiment times than FCS, for which measurements may be acquired in
