Journal of Chromatography A, 1393 (2015) 115–121
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Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Factors affecting measurement of channel thickness in asymmetrical flow field-flow fractionation Haiyang Dou a,b,∗ , Euo Chang Jung c , Seungho Lee b,∗∗ a b c
College of Basic Medical Sciences, Hebei University, Baoding 071-002, China Department of Chemistry, Hannam University, Daejeon 305-811, South Korea Nuclear Chemistry Research Center, Korea Atomic Energy Research Institute, Daejeon 305-353, South Korea
a r t i c l e
i n f o
Article history: Received 13 October 2014 Received in revised form 24 February 2015 Accepted 9 March 2015 Available online 18 March 2015 Keywords: Asymmetrical flow field-flow fractionation Channel thickness determination Sample–membrane interaction Steric effect
a b s t r a c t Asymmetrical flow field-flow fractionation (AF4) has been considered to be a useful tool for simultaneous separation and characterization of polydisperse macromolecules or colloidal nanoparticles. AF4 analysis requires the knowledge of the channel thickness (w), which is usually measured by injecting a standard with known diffusion coefficient (D) or hydrodynamic diameter (dh ). An accurate w determination is a challenge due to its uncertainties arising from the membrane’s compressibility, which may vary with experimental condition. In the present study, influence of factors including the size and type of the standard on the measurement of w was systematically investigated. The results revealed that steric effect and the particles–membrane interaction by van der Waals or electrostatic force may result in an error in w measurement. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Field flow fractionation (FFF), a tool for the separation and characterization of particles and polymers, has attracted increasing interest in recent years owing to its broad dynamic range (approximately from 1 nm up to about 100 m) and the utilization of “open channel” which requires no stationary phase or packing materials [1]. The sample degradation or loss is minimized in FFF, and there are fewer problems of sample adsorption than in size exclusion chromatography (SEC). Since its introduction, various subtechniques of FFF have emerged depending on the type of the external field employed [2–6]. Among them, flow FFF (FlFFF) has been considered to be the most versatile subtechnique, because the displacement of sample by the external field (cross-flow) is universal. Asymmetrical FlFFF (AF4) has been extensively applied in various fields such as environmental study [7,8], food analysis [9,10], and life science [11,12]. In addition to separation, characterization of analytes by direct measurement of physicochemical parameters is one of the key features of FFF. Besides particle’s diffusion
∗ Corresponding author at: College of Basic Medical Sciences, Hebei University, Baoding 071-002, China. Tel.: +86 312 5075660; fax: +86 312 5937102. ∗∗ Corresponding author at: Department of Chemistry, Hannam University, Daejeon 305-811, South Korea. E-mail addresses: [email protected] (H. Dou), [email protected] (S. Lee). http://dx.doi.org/10.1016/j.chroma.2015.03.025 0021-9673/© 2015 Elsevier B.V. All rights reserved.
coefficient (D) and hydrodynamic diameter (dh ), the conformation of polymers can also be evaluated based on the ratio of radius of gyration (rg ) to hydrodynamic radius (rh ), which can be obtained simultaneously by coupling AF4 with multiple detectors including the multiangle light scattering detector [13–15]. In AF4, theory is well established for size determination of analytes [6,16]. Size determination in the lift-hyperlayer mode requires a calibration using a series of size standards. In the normal mode, dh can be directly calculated from measured retention time (tr ) and knowledge of experimental parameters such as the channel geometry and flow rates. Among the parameters, channel thickness (w) is one of critical parameters. According to AF4 theory, dh is inversely proportional to w (see below in Eq. (8b)). Thus accurate measurement of w is required for determination of dh . Also w affects the separation performance (e.g., resolution), as the separation efficiency (measured by the plate count N) increases with w when the cross-flow rate is held constant [17,18]. Usually w is smaller than the thickness of the channel spacer due to compressibility of porous ultrafiltration membrane used for the accumulation wall of the AF4 channel. The membrane is placed in the AF4 channel between the spacer and the frit that supports the membrane. The uncompressed portion of the membrane protrudes into the channel space resulting in the channel thickness w smaller than the spacer thickness as illustrated in Fig. 1. There have been a few methods suggested for w determination in AF4, which were summarized in a recent publication [19]. Among them, the method proposed by Litzén [20] is commonly
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where t0 and tr are ‘void time’ and ‘retention time’, respectively. In FFF theory, R is expressed by [6]: 6 R= w
w (−x/l)B(x) w (−x/l)B(x) 2 1 e xdx − w e x dx 0 0 , w (−x/l)B(x) e
0
(3)
dx
where B (x) = 1 −
used for w determination, which was established with some underlying assumptions such as strong retention and no steric effect [21]. Wahlund [19] had shown the reliability of Litzén’s method under certain experimental conditions. In practice, however, w measurement is not always straightforward since non-idealities may exist. Sometimes, experimental conditions do not allow the assumptions leading to the ‘simplified’ retention equation to be fulfilled, and thus the accuracy in sample characterization is impaired. Giddings [22] and Martin [23] have outlined systematically the factors which may give rise to departure from classical retention theory of FFF. Unfortunately, no systematic work has been reported to investigate the factors influencing the accuracy of w determination. Often w is determined using a standard sample with known D or dh without much attention to whether experimental conditions satisfy the underlying assumptions. Sometimes w measured at an experimental condition is used to determine dh from data obtained at different conditions without providing detailed information on how w was determined. Without knowledge on the influence of experimental conditions (such as the carrier liquid composition and flow rates), it may introduce an ambiguity into AF4 data treatment such as determination of dh [24,25]. It is thus important to understand the factors that limit accurate determination of w. In this work, the influence of factors on w determination was investigated systematically. The objective of this work is to study the influence of a variety of parameters affecting the w determination in AF4.
2. Theory In AF4, the field force F exerted on sample components is expressed by [16]: Vc wkT , V 0D
(1)
where Vc is the cross-flow rate, w is the channel thickness, k is the Boltzmann constant, T is the absolute temperature, and V0 is the void volume. Sample components are pushed toward the accumulation wall (membrane) by the field force. At the same time, the components diffuse away from the accumulation wall by Brownian motion, and eventually form an equilibrium layer between the two opposing transport processes. The mean layer thickness (l) equals to the distance from the accumulation wall to the center of gravity of the equilibrium layer as highly compressed analyte layer is close to the accumulation wall. In FFF experiments, retention ratio (R) is obtained by [6]: R=
t0 , tr
(4)
Due to the complexity of Eq. (3), R cannot be obtained in a closed form and therefore has to be evaluated numerically. In cases of high retention, B(x) could be assumed to be unity. Assuming B(x) = 1 and there is no steric effect, Eq. (3) is simplified to [17]:
Fig. 1. Schematic cross-section of AF4 channel.
F=
x2 x3 + w2 2w3
(2)
R = 6 coth
1 2
− 2 ,
(5)
where is the dimensionless retention parameter, which is expressed in AF4 by [26]: =
kTV 0 3Vc w2 dh
(6)
For highly retained components in AF4, meaning lw or → 0, Eq. (5) can be approximated to yield a so-called ‘simplified’ retention equation: R = 6
(7)
Retention equations can be used to determine from measured tr , then to determine dh . Using Eqs. (2), (6) and (7), dh can be determined directly from measured tr by: dh =
2kTV 0 tr Vc w2 t 0
(8a)
Substituting V0 = Aw (A is the area of the accumulation wall) into Eq. (8a) yields: dh =
2kTA tr Vc wt 0
(8b)
Eq. (8) is valid to within 1% when R ≤ 0.029, within 5% when R ≤ 0.17, and within 10% when R ≤ 0.44 [27]. Eq. (8) shows a linear relationship between dh and tr with the proportionality constant depending on the experimental conditions such as the channel geometry, flow rate, and the channel thickness w. In practice, w can be determined from Eq. (8) using a standard sample with known size (dh ) such as commercial polystyrene (PS) latex beads [28,29]. An alternative is to inject a standard sample with known D [20], where w is determined by:
w=
ln
1+
Vc Vout
6Dtr
1−
b0 −bL
b0 z −
2L
z 2 −y
,
(9)
A
where the Vout is the channel outlet flow rate, b0 and bL are the breadths of the trapezoid, z is the distance from tip of the channel inlet to the focusing point, L is the channel length, y is the area lost from the trapezoid by the tapered inlet and outlet ends. In both methods, a simplified retention equation (Eq. (7)) is employed, where it was assumed that the sample components are mass points and there is no inter-component interaction and component–membrane interaction [22]. Thus a finite component sizes and presence of component–membrane interaction may induce an error in w determination, and eventually in size determination.
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Williams et al. [30] modified the retention equation by introducing a semi-empirical parameter, ıw , which was defined by:
∞
ıw = 0
−Vw (ı) 1 − exp kT
dı,
(10)
where ı is the distance from the particle surface to the accumulation wall and Vw is the energy of interaction between the particles and the accumulation wall expressed as a function of ı. The ıw will be positive for a repulsive interaction and negative for a net attraction [31]. In AF4, the interaction mainly involves electrostatic force (Fel ) and the van der Waals force (FvdW ) [23,32]. The Fel can be described from the sphere-plate model by [33]: Fel = 32kTdH ∞ e(a0 +a)
−1
tan h
z e 1 1 4kT
tan h
z e 2 2 4kT
,
(11)
where ∞ is the density of media, is the thickness of the electrical double layer, e is the elementary charge, a0 is the adhesion distance, (a0 + a) is the distance between the two objects, z is the ion valence, and is the zeta potential. The attractive van der Waals force can be expressed from the same model by [32]: FvdW = −
various surfactants and salts. The carrier liquid flow was delivered by a P-6000 solvent delivery pump (Futecs Co., Ltd., Daejeon, Korea). PS samples were prepared by diluting a droplet of PS standard suspensions with 1 mL of AF4 carrier liquid, and named ‘PS20’, ‘PS40’, ‘PS80’, ‘PS100’, ‘PS150’, and ‘PS200’, respectively, where the numbers are the nominal diameters. Prior to injection into the AF4 channel, PS samples were sonicated in an FS60 ultrasonic cleaner (Fisher Scientific, Atlanta, USA) at a power of 100 W for 1 min to facilitate dispersion of the particles. The PS samples were injected by loading the 20 L loop of a Rheodyne injector (Cotati, CA, USA) with a microsyringe, and were introduced into the channel by a syringe pump (KD Scientific Inc., FL, USA) at the flow rate of 0.2 mL/min. After focusing and relaxation of the sample, particles were eluted, and the eluted particles were monitored by a SPD-20A UV/VIS detector with a 12 L flow cell (Shimadzu, Kyoto, Japan) at the operating wavelength of 254 nm. After each run, the channel was flushed with the cross-flow turned off for 20 min. All AF4 measurements were performed at room temperature. The temperature of carrier liquid was monitored by a thermometer and used for w determination. 4. Results and discussion
Hrh3 2 (2r + l lpm pm ) h
117
2
,
(12)
where H is the Hamaker constant for the solvent–particle– membrane interactions, rh is the hydrodynamic radius, and lpm is the surface distance between particle and membrane. It is noted that, as the particle size increases, the steric effect increasingly affects the retention behavior of the particle. Thus the so-called “full retention equation”, which includes correction for the steric exclusion effect [22,34], should be used instead of the simplified retention equation. 3. Experimental 3.1. Materials Suspensions of polystyrene (PS) latex beads having nominal diameters of 20, 40, 80, 100, 150, and 200 nm were purchased from Duke Scientific Corp. (Palo Alto, CA, USA). Deionized water was obtained from a Milli-Q Plus Ultra-Pure Water system (Millipore, MA, USA). All of the following chemicals were used without further purification. Ferritin (from horse spleen), sodium nitrate (NaNO3 ), and sodium dodecyl sulfate (SDS) were purchased from Sigma–Aldrich (St. Louis, MO, USA). FL-70, containing 3.8% triethanolamine oleate, 2.7% sodium carbonate, 1.8% ethoxylated C12–14 -secondary alcohols, 1.4% tetrasodium ethylenediamineteraacetate, 0.9% PEG, 0.5% sodium oleate, and 0.1% sodium bicarbonate in water, was purchased from Fisher Scientific (Fair Lawn, NJ, USA). Sodium hydroxide (NaOH) and hydrochloric acid (35.0–37.0% HCl) were purchased from Samchun Pure Chemical Co., Ltd. (Pyeongtaek, Korea) and used to adjust the pH value of the carrier liquid. 3.2. Asymmetrical flow field-flow fractionation (AF4) The AF4 system was equipped with an Eclipse channel (Wyatt Technology Europe, Dernbach, Germany), which was assembled with a 350 m-thick polyester spacer and a regenerated cellulose (RC) Millipore PLGC Membrane or polyethersulfone (PES) membrane (for Eclipse) with the same molecular weight cutoff of 10 kDa. The channel geometry was trapezoidal with the tip-to-tip length of 26.5 cm and the breadths at the inlet and outlet of 2.2 and 0.6 cm, respectively. The carrier liquid was deionized water containing
4.1. Effect of field strength (cross-flow rate, Vc ) and type of membrane In order to investigate the effect of retention level on the measured channel thickness (wmeasured ), the cross-flow rate Vc was varied while keeping Vout constant at 1.0 mL/min. Fig. 2 shows wmeasured and inverted retention ratio (1/R) measured for a series of PS latex beads (PS40, PS80, PS100, PS150, and PS200) at various Vc in a AF4 channel equipped with a RC membrane. The carrier liquid was deionized water containing 0.1% (w/v) FL-70. The wmeasured was obtained from measured tr using Eq. (8b) for each standard. 1/R was measured based on Eq. (2) where tr was retention time at the peak maximum of retained peak, and t0 was determined experimentally by measuring the elution time for an unretained peak. It was noted that the intensities of UV/VIS signal of void peak from PS standard runs are similar to those from control runs (data not shown), suggesting no significant sample components were eluted with void peak. All PS standards studied in this work are large enough to retain in the channel. The peak maxima were traced by using the Peakfit 4.12 software (Seasolve Software Inc., CA, USA). The error bars present one standard deviation (n = 3). Ideally wmeasured must be constant and independent of the size of the standard. As seen from Fig. 2(a), for Vc = 0.5 mL/min, the wmeasured continuously decreases with increasing size. The change in wmeasured with particle size can be explained by a combination of factors. One is the increasing influence of the steric effect with the particle size. As the particle size increases, the steric effect increases, and results in a departure from linearity of the 1/R vs. d plot as shown in Fig. 2(b). The presence of the steric effect will result in wmeasured decreasing with increasing particle size. The van der Waals attractive interaction may also present, which results in an increase in the retention of the particles, and thus yields an overestimation of wmeasured . The van der Waals interaction also increases with increasing particle size as shown in Eq. (12), and will result in the wmeasured increasing with the particle size. Results suggest, under the current operating conditions, the steric effect dominates over the van der Waals interaction, and results in the wmeasured decreasing with increasing particle size. As mentioned earlier, for accurate measurement of wmeasured , experimental conditions should fulfill requirements for the simplified retention equation to be valid (strong retention and no steric
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Fig. 2. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads at various cross-flow rates in AF4 channel with RC membrane. The channel outlet flow rate was fixed at 1 mL/min, and the carrier liquid was deionized water containing 0.1% (w/v) FL-70. Error bars represent one standard deviation (n = 3).
effect). In order to avoid the steric effect, smaller particles may be employed. In Fig. 2(b), 1/R = 5.8 for PS40 (the smallest among those tested) at Vc of 0.5 mL/min, which is too small for accurate measurement of the channel thickness. The use of higher Vc is thus needed. When Vc was increased to 1.0 mL/min, the wmeasured again decreases with increasing particle size initially. This time, however, wmeasured obtained with particles larger than about 100 nm stays almost constant at around 245 m with the relative error lower than 0.6%. The 1/R values measured for those larger than about 100 nm are larger than 20 as shown in Fig. 2(b). Similar trends were observed at Vc of 1.5 mL/min, where wmeasured obtained with particles larger than about 80 nm stays almost constant at around 238 m with the relative error lower than 0.9%. Again, the corresponding 1/R values are well larger than 20 for those larger than 80 nm. It seems 1/R > 20 is one of essential requirements for accurate w measurement. However, none of the wmeasured ’s presented in Fig. 2 can be taken as the accurate channel thickness as there still exists the steric effect (as shown in Fig. 2(b)) and the wmeasured ’s obtained at Vc of 1.0 and 1.5 mL/min are different. The wmeasured is expected to be either identical or slightly larger at higher Vc due to stronger compression of the membrane. In Fig. 2, wmeasured ’s obtained at Vc = 1.5 mL/min are smaller than those obtained at Vc = 1.0 mL/min. This rather anomalous behavior indicates that 1/R larger than 20 does not guarantee accurate w measurement. Fig. 3 shows the same plots as those shown in Fig. 2 obtained from the same AF4 system, except that the accumulation wall was
Fig. 3. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads at various cross-flow rates in AF4 channel with PES membrane. All other experimental conditions were the same as those in Fig. 2.
PES instead of RC. As with the PES membrane, there also exists the influence of the steric effect with the particle size as indicated by a decrease in the slope of the R vs. d curve as particle size increases (Fig. S1). In general, the steric effect should bend the curve of 1/R vs. d downward. However, a slight concave shape of the 1/R vs. d curve in Fig. 3(b) was observed. Meanwhile, a discontinuity in the 1/R vs. d curve between PS80 and PS100 was observed. This is probably due to the van der Waals interaction between PS particles and membrane, which is size-dependent as suggested by Eq. (12). The larger particle suffers from stronger van der Waals attraction, resulting in an increase in the retention time of analyte. Eventually, it leads to an overestimation in w determination along with a concave shape of the 1/R vs. d curve. Unlike with RC membrane, the wmeasured ’s obtained with PES membrane do not change much with the particle size, and do not show a trend of gradual change. Also the elution profiles of PS150 and PS200 showed tailings, especially at Vc = 1.0 mL/min (data not shown). These results suggest there may be stronger influence of attractive van der Waals interaction between PS particles and the PES membrane than with the RC membrane. As indicated by Eq. (12), the van der Waals attractive interaction depends not only on the surface properties but also on the particle size. As the particle size increases, the van der Waals attractive interaction becomes stronger. There may also exist electrostatic repulsive force in an AF4 channel, which counteracts the van der Waals attractive force. The electrostatic repulsive force
H. Dou et al. / J. Chromatogr. A 1393 (2015) 115–121
(a)
119
(a)
320 PES, 0.1% FL-70
wmeasured (μ μm)
300 PES, 0.05 % SD S RC, 0.05% SDS
280
260
RC, 0.1% FL-70
240 50
100
150
200
Diameter of PS latex bead (nm)
(b)
50
(b)
RC, 0.1% FL-70 RC, 0.05% SDS PES, 0.1% FL-70 PES, 0.05% SDS
40
1/R
30 20 10 0 50
100
150
200
Diameter of PS latex bead (nm) Fig. 4. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads in AF4 with various combinations of membranes and surfactants. Vc and Vout were 0.5 and 1.0 mL/min, respectively.
depends strongly on the composition of the carrier liquid [32], and an optimization of the composition of the carrier liquid is thus also required. 4.2. Effect of type of dispersing agent Fig. 4 shows wmeasured and 1/R measured for PS latex beads at various combinations of the types of the membrane (RC and PES) and the dispersing agent (FL-70 and SDS). Vc and Vout were 0.5 and 1.0 mL/min, respectively. It can be seen that the wmeasured ’s obtained with PES membrane are higher than those with RC membrane at the same operating condition. This may be explained by stronger influence of attractive van der Waals interaction between PS particles and the PES membrane than with the RC membrane. Also the PES membrane may protrude less than the RC membrane in the same AF4 channel [35]. With the same type of membrane, wmeasured ’s obtained with two different dispersing agents show similar trends. With the RC membrane, wmeasured ’s gradually decreases with increasing particle size, mainly due to the steric effect as explained earlier in Fig. 2(a). With the PES membrane, wmeasured ’s do not show a trend of gradual change with the particle size as shown in Fig. 3(a). Again the elution profiles obtained with the PES membrane showed some degree of tailing (data not shown) while those with the RC membrane did not show much tailing, which can be explained by stronger van der
Fig. 5. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads in AF4 channel with RC membrane. The carrier liquid was water containing 0.05% SDS and various concentrations of NaNO3 . Flow rates were the same as those in Fig. 4.
Waals attractive interaction of PS particles with the PES membrane together with a stronger retention with PES membrane (Fig. 4(b)) than with the RC membrane. In Fig. 4(a), with the same RC membrane, wmeasured ’s obtained with SDS are higher than those obtained with FL-70, whereas, with PES membrane, wmeasured ’s obtained with SDS are lower. Higher wmeasured ’s from the combination of the RC membrane with SDS than with FL-70 may be partly explained by lower protrusion of the RC membrane with SDS than with FL-70 [35]. Or there may be stronger van der Waals interaction between PS particles and RC membrane with SDS than with FL-70 [36], which may partly counteract the steric effect. Results presented in Fig. 4(a) indicate the degree and the pattern of the particle–membrane interaction vary with the type of the dispersing agent. 4.3. Effect of ionic strength As suggested by Eq. (11), the ionic strength of carrier liquid affects electrostatic interaction. The effects of the ionic strength on wmeasured and 1/R are shown in Fig. 5. As shown in Fig. 5(a), for a given particle size, the wmeasured increases with increasing ionic strength. With 5 mM NaNO3 added, wmeasured seems to be almost independent of the particle size with the relative error of 1.7%, which may be attributed to a counteraction of the steric effect and the van der Waals attractive interaction between
H. Dou et al. / J. Chromatogr. A 1393 (2015) 115–121
4.4. Effect of pH Fig. 6 shows wmeasured and 1/R obtained at various pH with the carrier liquid containing 0.05% SDS. It is shown that pH of the carrier
(a)
290 pH=2 7 12
wmeasured (μ μ m)
280
0.4 R
300
0.3
290 wmeasured
0.2
280 0.1
270 260
0.0 Ferritin
PS20
PS100
Type of standard Fig. 7. Channel thickness (square) and retention ratio (circle) measured in AF4 using various types of standards. The carrier liquid was water containing 0.05% SDS and 5 mM NaNO3 . All other experimental conditions were the same as those in Fig. 5.
liquid affects w measurement, as does the type of the surfactant or the ionic strength of the carrier liquid. The wmeasured ’s measured at pH 2 and 7 are similar in the size range tested, and both tends to decrease as the particle size increases. On the contrary, at a basic condition (pH 12), the wmeasured tends to increase with increasing particle size. This may be explained by an increase in the van der Waals attractive interaction between particles and membrane caused by an increase in the ionic strength of the carrier liquid, where 10 mM NaOH was added to adjust pH. Another possibility is that the thermodynamic force, which counteracts convective transport to the accumulation wall, is drastically increased when the particles become highly charged at basic conditions [37,38]. It seems more in-depth studies are needed for better understanding of this phenomenon.
270 4.5. Effect of the types of standard
260
250 50
(b)
310
Retention ratio, R
particles and the membrane. It can be seen in Fig. S2 that the slope of the plot decreases as particle size increases, suggesting there exists the steric effect at all conditions. It seems the influence of the steric effect on w determination is canceled out by adding 5 mM NaNO3 (Fig. 5(a)). When the concentration of NaNO3 was increased to 10 mM, wmeasured was slowly increased with increasing particle size, suggesting there exists stronger van der Waals attractive interaction between particles and the membrane. As the salt concentration was further increased to 30 mM, the wmeasured increases rather quickly with the particle size and the curve of 1/R vs. d is strongly bent upward (Fig. 5(b)). An increase in wmeasured with increasing ionic strength is expected from AF4 theory. An increase in the ionic strength leads to a reduction in the thickness of the electrostatic double layer [32], allowing particles approach closer to the accumulation wall, resulting in an increase in 1/R as shown in Fig. 5(b). In Fig. 5(a), high ionic strengths (10 or 30 mM NaNO3 ) led to strong van der Waals attractive interaction between particles and the membrane, resulting in an overestimation in wmeasured . Meanwhile, as mentioned above, the stronger van der Waals attraction could lead to a concave shape of the 1/R vs. d curve. It is noted that wmeasured obtained with PS150 is larger than the thickness of the spacer (350 m).
wmeasured (μ μm)
120
100
150
200
Diameter of PS latex bead (nm) 40 pH=2 7 12
1/R
30
20
Fig. 7 shows the wmeasured and R obtained with three different types of the standards (ferritin, PS20 and PS100). The carrier liquid was deionized water containing 0.05% SDS and 5 mM NaNO3 . Ferritin is commonly employed to measure AF4 channel thickness using Eq. (9). It can be seen that wmeasured obtained from ferritin are higher than those obtained with PS standards. The relative error of 5.7% was observed between wmeasured ’s obtained with ferritin and PS100, which would result in a large discrepancy in dh determination. A care must be taken when a protein standard (with known diffusion coefficient D) is used for w determination. First, D is temperature-dependent. And a protein standard may contain dimers and trimers, which could result in erroneous D. It has been reported that D measured by dynamic light scatting (DLS) was significantly affected by the presence of oligomers [19]. Use of a well-characterized spherical PS beads with uniform and narrow size distributions may be more reliable for w determination as dh is rather independent on the experimental conditions such as temperature.
10 5. Conclusions
0 50
100
150
200
Diameter of PS latex bead (nm) Fig. 6. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads at various pHs in AF4 channel with RC membrane. The carrier liquid was water containing 0.05% SDS. Flow rates were the same as those in Fig. 4.
In AF4 analysis, it is important to measure w accurately as w is needed to determine the diffusion coefficient D or dh of a sample from its retention data. Ideally w needs to be measured at the same condition as that used for sample analysis. The use of small proteins (e.g., ferritin) as a standard may not always be suitable as their retention levels may not be strong enough at operating conditions. Sometimes the interaction between particles and the
H. Dou et al. / J. Chromatogr. A 1393 (2015) 115–121
membrane may also come into play, which was not taken into consideration in the classical FFF theory, and, therefore can lead to departure from theory, and eventually, incorrect particle size analysis. Results showed that at relatively higher ionic strengths, attractive interactions may lead to an overestimation in w. It seems the ionic strength of the carrier liquid needs to be adjusted carefully so that the charges on the sample and the membrane would be screened effectively. The channel thickness w needs to be measured again whenever there is a change in the experimental conditions including the composition of the carrier liquid. And it is clear from the results that judicious selection of a standard must be made in order to extract accurate results. Acknowledgement The authors acknowledge the support provided by the National Research Foundation (NRF) of Korea (NRF-2014M2A8A5021929). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.chroma.2015.03.025. References [1] J.C. Giddings, Field-flow fractionation: analysis of macromolecular, colloidal, and particulate materials, Science 260 (1993) 1456–1465. [2] J.C. Giddings, A new separation concept based on a coupling of concentration and flow nonuniformities, Sep. Sci. 1 (1966) 123–125. [3] K.D. Caldwell, L.F. Kesner, M.N. Myers, J.C. Giddings, Electrical field-flow fractionation of proteins, Science 176 (1972) 296–298. [4] J.C. Giddings, F.J.F. Yang, M.N. Myers, Sedimentation field-flow fractionation, Anal. Chem. 46 (1974) 1917–1924. [5] J.C. Giddings, L.K. Smith, M.N. Myers, Thermal field-flow fractionation: extension to lower molecular weight separations by increasing the liquid temperature range using a pressurized system, Anal. Chem. 47 (1975) 2389–2394. [6] K.G. Wahlund, J.C. Giddings, Properties of an asymmetrical flow field-flow fractionation channel having one permeable wall, Anal. Chem. 59 (1987) 1332–1339. [7] M. Baalousha, J.R. Lead, Rationalizing nanomaterial sizes measured by atomic force microscopy, flow field-flow fractionation, and dynamic light scattering: sample preparation, polydispersity, and particle structure, Environ. Sci. Technol. 46 (2012) 6134–6142. [8] E. Alasonati, V.I. Slaveykova, H. Gallard, J.-P. Croué, M.F. Benedetti, Characterization of the colloidal organic matter from the Amazonian basin by asymmetrical flow field-flow fractionation and size exclusion chromatography, Water Res. 44 (2010) 223–231. [9] H. Dou, B. Zhou, H.-D. Jang, S. Lee, Study on antidiabetic activity of wheat and barley starch using asymmetrical flow field-flow fractionation coupled with multiangle light scattering, J. Chromatogr. A 1340 (2014) 115–120. [10] L. Nilsson, Separation and characterization of food macromolecules using fieldflow fractionation: a review, Food Hydrocoll. 30 (2013) 1–11. [11] J. Ashby, S. Schachermeyer, S. Pan, W. Zhong, Dissociation-based screening of nanoparticle–protein interaction via flow field-flow fractionation, Anal. Chem. 85 (2013) 7494–7501. [12] K. Rebolj, D. Pahovnik, E. Zˇ agar, Characterization of a protein conjugate using an asymmetrical-flow field-flow fractionation and a size-exclusion chromatography with multi-detection system, Anal. Chem. 84 (2012) 7374–7383. [13] S. Noskov, C. Scherer, M. Maskos, Determination of Hamaker constants of polymeric nanoparticles in organic solvents by asymmetrical flow field-flow fractionation, J. Chromatogr. A 1274 (2013) 151–158. [14] C.W. Isaacson, D. Bouchard, Asymmetric flow field flow fractionation of aqueous C60 nanoparticles with size determination by dynamic light scattering and quantification by liquid chromatography atmospheric pressure photoionization mass spectrometry, J. Chromatogr. A 1217 (2010) 1506–1512.
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[15] C.C. Rojas, K.G. Wahlund, B. Bergenståhl, L. Nilsson, Macromolecular geometries determined with field-flow fractionation and their impact on the overlap concentration, Biomacromolecules 9 (2008) 1684–1690. [16] M.E. Schimpf, K. Caldwell, J.C. Giddings, Field-Flow Fractionation Handbook, Wiley, New York, 2000. [17] K.G. Wahlund, H.S. Winegarner, K.D. Caldwell, J.C. Giddings, Improved flow field-flow fractionation system applied to water-soluble polymers: programming, outlet stream splitting, and flow optimization, Anal. Chem. 58 (1986) 573–578. [18] H. Dou, Y.-J. Lee, E.C. Jung, B.-C. Lee, S. Lee, Study on steric transition in asymmetrical flow field-flow fractionation and application to characterization of high-energy material, J. Chromatogr. A 1304 (2013) 211–219. [19] K.G. Wahlund, Flow field-flow fractionation: critical overview, J. Chromatogr. A 1287 (2013) 97–112. [20] A. Litzen, Separation speed, retention, and dispersion in asymmetrical flow field-flow fractionation as functions of channel dimensions and flow rates, Anal. Chem. 65 (1993) 461–470. [21] A. Håkansson, E. Magnusson, B. Bergenståhl, L. Nilsson, Hydrodynamic radius determination with asymmetrical flow field-flow fractionation using decaying cross-flows. Part I. A theoretical approach, J. Chromatogr. A 1253 (2012) 120–126. [22] J.C. Giddings, Factors influencing accuracy of colloidal and macromolecular properties measured by field-flow fractionation, Anal. Chem. 69 (1997) 552–557. [23] M. Martin, Deviations to classical retention theory of field-flow fractionation, J. Chromatogr. A 831 (1999) 73–87. [24] K. Lemke, C. Prietzel, J. Koetz, Fluorescent gold clusters synthesized in a poly(ethyleneimine) modified reverse microemulsion, J. Colloid Interface Sci. 394 (2013) 141–146. [25] H. Hagendorfer, R. Kaegi, J. Traber, S.F.L. Mertens, R. Scherrers, C. Ludwig, A. Ulrich, Application of an asymmetric flow field flow fractionation multidetector approach for metallic engineered nanoparticle characterization – prospects and limitations demonstrated on Au nanoparticles, Anal. Chim. Acta 706 (2011) 367–378. [26] M.E. Schimpf, K. Caldwell, J.C. Giddings, Field-flow fractionation handbook, in: B.N. Barman (Ed.), Latexes and Emulsions, Wiley, New York, 2000, pp. 348–350. [27] B. Wittgren, K.G. Wahlund, H. Dérand, B. Wesslén, Aggregation behavior of an amphiphilic graft copolymer in aqueous medium studied by asymmetrical flow field-flow fractionation, Macromolecules 29 (1996) 268–276. [28] K. Loeschner, J. Navratilova, S. Legros, S. Wagner, R. Grombe, J. Snell, F. von der Kammer, E.H. Larsen, Optimization and evaluation of asymmetric flow field-flow fractionation of silver nanoparticles, J. Chromatogr. A 1272 (2013) 116–125. [29] E. Magnusson, A. Håkansson, J. Janiak, B. Bergenståhl, L. Nilsson, Hydrodynamic radius determination with asymmetrical flow field-flow fractionation using decaying cross-flows. Part II. Experimental evaluation, J. Chromatogr. A 1253 (2012) 127–133. [30] P.S. Williams, Y. Xu, P. Reschiglian, J.C. Giddings, Colloid characterization by sedimentation field-flow fractionation: correction for particle–wall interaction, Anal. Chem. 69 (1997) 349–360. [31] Q. Du, M.E. Schimpf, Correction for particle–wall interactions in the separation of colloids by flow field-flow fractionation, Anal. Chem. 74 (2002) 2478–2485. [32] A. Ulrich, S. Losert, N. Bendixen, A. Al-Kattan, H. Hagendorfer, B. Nowack, C. Adlhart, J. Ebert, M. Lattuada, K. Hungerbuhler, Critical aspects of sample handling for direct nanoparticle analysis and analytical challenges using asymmetric field flow fractionation in a multi-detector approach, J. Anal. At. Spectrom. 27 (2012) 1120–1130. [33] G.M. Bell, S. Levine, L.N. McCartney, Approximate methods of determining the double-layer free energy of interaction between two charged colloidal spheres, J. Colloid Interface Sci. 33 (1970) 335–359. [34] M.N. Myers, J.C. Giddings, Properties of the transition from normal to steric field-flow fractionation, Anal. Chem. 54 (1982) 2284–2289. [35] M.E. Schimpf, K. Caldwell, J.C. Giddings, Field-flow fractionation handbook, in: M.A. Benincasa (Ed.), Synthetic Polymers-Water Soluble, Wiley, New York, 2000, pp. 428–430. [36] M. Madörin, P. van Hoogevest, R. Hilfiker, B. Langwost, G. Kresbach, M. Ehrat, H. Leuenberger, Analysis of drug/plasma protein interactions by means of asymmetrical flow field-flow fractionation, Pharm. Res. 14 (1997) 1706–1712. [37] A.-S. Jönsson, B. Jönsson, Ultrafiltration of colloidal dispersions – a theoretical model of the concentration polarization phenomena, J. Colloid Interface Sci. 180 (1996) 504–518. [38] A. Håkansson, M. Ulmius, L. Nilsson, Asymmetrical flow field-flow fractionation enables the characterization of molecular and supramolecular properties of cereal ˇ-glucan dispersions, Carbohydr. Polym. 87 (2012) 518–523.
Contents lists available at ScienceDirect
Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma
Factors affecting measurement of channel thickness in asymmetrical flow field-flow fractionation Haiyang Dou a,b,∗ , Euo Chang Jung c , Seungho Lee b,∗∗ a b c
College of Basic Medical Sciences, Hebei University, Baoding 071-002, China Department of Chemistry, Hannam University, Daejeon 305-811, South Korea Nuclear Chemistry Research Center, Korea Atomic Energy Research Institute, Daejeon 305-353, South Korea
a r t i c l e
i n f o
Article history: Received 13 October 2014 Received in revised form 24 February 2015 Accepted 9 March 2015 Available online 18 March 2015 Keywords: Asymmetrical flow field-flow fractionation Channel thickness determination Sample–membrane interaction Steric effect
a b s t r a c t Asymmetrical flow field-flow fractionation (AF4) has been considered to be a useful tool for simultaneous separation and characterization of polydisperse macromolecules or colloidal nanoparticles. AF4 analysis requires the knowledge of the channel thickness (w), which is usually measured by injecting a standard with known diffusion coefficient (D) or hydrodynamic diameter (dh ). An accurate w determination is a challenge due to its uncertainties arising from the membrane’s compressibility, which may vary with experimental condition. In the present study, influence of factors including the size and type of the standard on the measurement of w was systematically investigated. The results revealed that steric effect and the particles–membrane interaction by van der Waals or electrostatic force may result in an error in w measurement. © 2015 Elsevier B.V. All rights reserved.
1. Introduction Field flow fractionation (FFF), a tool for the separation and characterization of particles and polymers, has attracted increasing interest in recent years owing to its broad dynamic range (approximately from 1 nm up to about 100 m) and the utilization of “open channel” which requires no stationary phase or packing materials [1]. The sample degradation or loss is minimized in FFF, and there are fewer problems of sample adsorption than in size exclusion chromatography (SEC). Since its introduction, various subtechniques of FFF have emerged depending on the type of the external field employed [2–6]. Among them, flow FFF (FlFFF) has been considered to be the most versatile subtechnique, because the displacement of sample by the external field (cross-flow) is universal. Asymmetrical FlFFF (AF4) has been extensively applied in various fields such as environmental study [7,8], food analysis [9,10], and life science [11,12]. In addition to separation, characterization of analytes by direct measurement of physicochemical parameters is one of the key features of FFF. Besides particle’s diffusion
∗ Corresponding author at: College of Basic Medical Sciences, Hebei University, Baoding 071-002, China. Tel.: +86 312 5075660; fax: +86 312 5937102. ∗∗ Corresponding author at: Department of Chemistry, Hannam University, Daejeon 305-811, South Korea. E-mail addresses: [email protected] (H. Dou), [email protected] (S. Lee). http://dx.doi.org/10.1016/j.chroma.2015.03.025 0021-9673/© 2015 Elsevier B.V. All rights reserved.
coefficient (D) and hydrodynamic diameter (dh ), the conformation of polymers can also be evaluated based on the ratio of radius of gyration (rg ) to hydrodynamic radius (rh ), which can be obtained simultaneously by coupling AF4 with multiple detectors including the multiangle light scattering detector [13–15]. In AF4, theory is well established for size determination of analytes [6,16]. Size determination in the lift-hyperlayer mode requires a calibration using a series of size standards. In the normal mode, dh can be directly calculated from measured retention time (tr ) and knowledge of experimental parameters such as the channel geometry and flow rates. Among the parameters, channel thickness (w) is one of critical parameters. According to AF4 theory, dh is inversely proportional to w (see below in Eq. (8b)). Thus accurate measurement of w is required for determination of dh . Also w affects the separation performance (e.g., resolution), as the separation efficiency (measured by the plate count N) increases with w when the cross-flow rate is held constant [17,18]. Usually w is smaller than the thickness of the channel spacer due to compressibility of porous ultrafiltration membrane used for the accumulation wall of the AF4 channel. The membrane is placed in the AF4 channel between the spacer and the frit that supports the membrane. The uncompressed portion of the membrane protrudes into the channel space resulting in the channel thickness w smaller than the spacer thickness as illustrated in Fig. 1. There have been a few methods suggested for w determination in AF4, which were summarized in a recent publication [19]. Among them, the method proposed by Litzén [20] is commonly
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where t0 and tr are ‘void time’ and ‘retention time’, respectively. In FFF theory, R is expressed by [6]: 6 R= w
w (−x/l)B(x) w (−x/l)B(x) 2 1 e xdx − w e x dx 0 0 , w (−x/l)B(x) e
0
(3)
dx
where B (x) = 1 −
used for w determination, which was established with some underlying assumptions such as strong retention and no steric effect [21]. Wahlund [19] had shown the reliability of Litzén’s method under certain experimental conditions. In practice, however, w measurement is not always straightforward since non-idealities may exist. Sometimes, experimental conditions do not allow the assumptions leading to the ‘simplified’ retention equation to be fulfilled, and thus the accuracy in sample characterization is impaired. Giddings [22] and Martin [23] have outlined systematically the factors which may give rise to departure from classical retention theory of FFF. Unfortunately, no systematic work has been reported to investigate the factors influencing the accuracy of w determination. Often w is determined using a standard sample with known D or dh without much attention to whether experimental conditions satisfy the underlying assumptions. Sometimes w measured at an experimental condition is used to determine dh from data obtained at different conditions without providing detailed information on how w was determined. Without knowledge on the influence of experimental conditions (such as the carrier liquid composition and flow rates), it may introduce an ambiguity into AF4 data treatment such as determination of dh [24,25]. It is thus important to understand the factors that limit accurate determination of w. In this work, the influence of factors on w determination was investigated systematically. The objective of this work is to study the influence of a variety of parameters affecting the w determination in AF4.
2. Theory In AF4, the field force F exerted on sample components is expressed by [16]: Vc wkT , V 0D
(1)
where Vc is the cross-flow rate, w is the channel thickness, k is the Boltzmann constant, T is the absolute temperature, and V0 is the void volume. Sample components are pushed toward the accumulation wall (membrane) by the field force. At the same time, the components diffuse away from the accumulation wall by Brownian motion, and eventually form an equilibrium layer between the two opposing transport processes. The mean layer thickness (l) equals to the distance from the accumulation wall to the center of gravity of the equilibrium layer as highly compressed analyte layer is close to the accumulation wall. In FFF experiments, retention ratio (R) is obtained by [6]: R=
t0 , tr
(4)
Due to the complexity of Eq. (3), R cannot be obtained in a closed form and therefore has to be evaluated numerically. In cases of high retention, B(x) could be assumed to be unity. Assuming B(x) = 1 and there is no steric effect, Eq. (3) is simplified to [17]:
Fig. 1. Schematic cross-section of AF4 channel.
F=
x2 x3 + w2 2w3
(2)
R = 6 coth
1 2
− 2 ,
(5)
where is the dimensionless retention parameter, which is expressed in AF4 by [26]: =
kTV 0 3Vc w2 dh
(6)
For highly retained components in AF4, meaning lw or → 0, Eq. (5) can be approximated to yield a so-called ‘simplified’ retention equation: R = 6
(7)
Retention equations can be used to determine from measured tr , then to determine dh . Using Eqs. (2), (6) and (7), dh can be determined directly from measured tr by: dh =
2kTV 0 tr Vc w2 t 0
(8a)
Substituting V0 = Aw (A is the area of the accumulation wall) into Eq. (8a) yields: dh =
2kTA tr Vc wt 0
(8b)
Eq. (8) is valid to within 1% when R ≤ 0.029, within 5% when R ≤ 0.17, and within 10% when R ≤ 0.44 [27]. Eq. (8) shows a linear relationship between dh and tr with the proportionality constant depending on the experimental conditions such as the channel geometry, flow rate, and the channel thickness w. In practice, w can be determined from Eq. (8) using a standard sample with known size (dh ) such as commercial polystyrene (PS) latex beads [28,29]. An alternative is to inject a standard sample with known D [20], where w is determined by:
w=
ln
1+
Vc Vout
6Dtr
1−
b0 −bL
b0 z −
2L
z 2 −y
,
(9)
A
where the Vout is the channel outlet flow rate, b0 and bL are the breadths of the trapezoid, z is the distance from tip of the channel inlet to the focusing point, L is the channel length, y is the area lost from the trapezoid by the tapered inlet and outlet ends. In both methods, a simplified retention equation (Eq. (7)) is employed, where it was assumed that the sample components are mass points and there is no inter-component interaction and component–membrane interaction [22]. Thus a finite component sizes and presence of component–membrane interaction may induce an error in w determination, and eventually in size determination.
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Williams et al. [30] modified the retention equation by introducing a semi-empirical parameter, ıw , which was defined by:
∞
ıw = 0
−Vw (ı) 1 − exp kT
dı,
(10)
where ı is the distance from the particle surface to the accumulation wall and Vw is the energy of interaction between the particles and the accumulation wall expressed as a function of ı. The ıw will be positive for a repulsive interaction and negative for a net attraction [31]. In AF4, the interaction mainly involves electrostatic force (Fel ) and the van der Waals force (FvdW ) [23,32]. The Fel can be described from the sphere-plate model by [33]: Fel = 32kTdH ∞ e(a0 +a)
−1
tan h
z e 1 1 4kT
tan h
z e 2 2 4kT
,
(11)
where ∞ is the density of media, is the thickness of the electrical double layer, e is the elementary charge, a0 is the adhesion distance, (a0 + a) is the distance between the two objects, z is the ion valence, and is the zeta potential. The attractive van der Waals force can be expressed from the same model by [32]: FvdW = −
various surfactants and salts. The carrier liquid flow was delivered by a P-6000 solvent delivery pump (Futecs Co., Ltd., Daejeon, Korea). PS samples were prepared by diluting a droplet of PS standard suspensions with 1 mL of AF4 carrier liquid, and named ‘PS20’, ‘PS40’, ‘PS80’, ‘PS100’, ‘PS150’, and ‘PS200’, respectively, where the numbers are the nominal diameters. Prior to injection into the AF4 channel, PS samples were sonicated in an FS60 ultrasonic cleaner (Fisher Scientific, Atlanta, USA) at a power of 100 W for 1 min to facilitate dispersion of the particles. The PS samples were injected by loading the 20 L loop of a Rheodyne injector (Cotati, CA, USA) with a microsyringe, and were introduced into the channel by a syringe pump (KD Scientific Inc., FL, USA) at the flow rate of 0.2 mL/min. After focusing and relaxation of the sample, particles were eluted, and the eluted particles were monitored by a SPD-20A UV/VIS detector with a 12 L flow cell (Shimadzu, Kyoto, Japan) at the operating wavelength of 254 nm. After each run, the channel was flushed with the cross-flow turned off for 20 min. All AF4 measurements were performed at room temperature. The temperature of carrier liquid was monitored by a thermometer and used for w determination. 4. Results and discussion
Hrh3 2 (2r + l lpm pm ) h
117
2
,
(12)
where H is the Hamaker constant for the solvent–particle– membrane interactions, rh is the hydrodynamic radius, and lpm is the surface distance between particle and membrane. It is noted that, as the particle size increases, the steric effect increasingly affects the retention behavior of the particle. Thus the so-called “full retention equation”, which includes correction for the steric exclusion effect [22,34], should be used instead of the simplified retention equation. 3. Experimental 3.1. Materials Suspensions of polystyrene (PS) latex beads having nominal diameters of 20, 40, 80, 100, 150, and 200 nm were purchased from Duke Scientific Corp. (Palo Alto, CA, USA). Deionized water was obtained from a Milli-Q Plus Ultra-Pure Water system (Millipore, MA, USA). All of the following chemicals were used without further purification. Ferritin (from horse spleen), sodium nitrate (NaNO3 ), and sodium dodecyl sulfate (SDS) were purchased from Sigma–Aldrich (St. Louis, MO, USA). FL-70, containing 3.8% triethanolamine oleate, 2.7% sodium carbonate, 1.8% ethoxylated C12–14 -secondary alcohols, 1.4% tetrasodium ethylenediamineteraacetate, 0.9% PEG, 0.5% sodium oleate, and 0.1% sodium bicarbonate in water, was purchased from Fisher Scientific (Fair Lawn, NJ, USA). Sodium hydroxide (NaOH) and hydrochloric acid (35.0–37.0% HCl) were purchased from Samchun Pure Chemical Co., Ltd. (Pyeongtaek, Korea) and used to adjust the pH value of the carrier liquid. 3.2. Asymmetrical flow field-flow fractionation (AF4) The AF4 system was equipped with an Eclipse channel (Wyatt Technology Europe, Dernbach, Germany), which was assembled with a 350 m-thick polyester spacer and a regenerated cellulose (RC) Millipore PLGC Membrane or polyethersulfone (PES) membrane (for Eclipse) with the same molecular weight cutoff of 10 kDa. The channel geometry was trapezoidal with the tip-to-tip length of 26.5 cm and the breadths at the inlet and outlet of 2.2 and 0.6 cm, respectively. The carrier liquid was deionized water containing
4.1. Effect of field strength (cross-flow rate, Vc ) and type of membrane In order to investigate the effect of retention level on the measured channel thickness (wmeasured ), the cross-flow rate Vc was varied while keeping Vout constant at 1.0 mL/min. Fig. 2 shows wmeasured and inverted retention ratio (1/R) measured for a series of PS latex beads (PS40, PS80, PS100, PS150, and PS200) at various Vc in a AF4 channel equipped with a RC membrane. The carrier liquid was deionized water containing 0.1% (w/v) FL-70. The wmeasured was obtained from measured tr using Eq. (8b) for each standard. 1/R was measured based on Eq. (2) where tr was retention time at the peak maximum of retained peak, and t0 was determined experimentally by measuring the elution time for an unretained peak. It was noted that the intensities of UV/VIS signal of void peak from PS standard runs are similar to those from control runs (data not shown), suggesting no significant sample components were eluted with void peak. All PS standards studied in this work are large enough to retain in the channel. The peak maxima were traced by using the Peakfit 4.12 software (Seasolve Software Inc., CA, USA). The error bars present one standard deviation (n = 3). Ideally wmeasured must be constant and independent of the size of the standard. As seen from Fig. 2(a), for Vc = 0.5 mL/min, the wmeasured continuously decreases with increasing size. The change in wmeasured with particle size can be explained by a combination of factors. One is the increasing influence of the steric effect with the particle size. As the particle size increases, the steric effect increases, and results in a departure from linearity of the 1/R vs. d plot as shown in Fig. 2(b). The presence of the steric effect will result in wmeasured decreasing with increasing particle size. The van der Waals attractive interaction may also present, which results in an increase in the retention of the particles, and thus yields an overestimation of wmeasured . The van der Waals interaction also increases with increasing particle size as shown in Eq. (12), and will result in the wmeasured increasing with the particle size. Results suggest, under the current operating conditions, the steric effect dominates over the van der Waals interaction, and results in the wmeasured decreasing with increasing particle size. As mentioned earlier, for accurate measurement of wmeasured , experimental conditions should fulfill requirements for the simplified retention equation to be valid (strong retention and no steric
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Fig. 2. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads at various cross-flow rates in AF4 channel with RC membrane. The channel outlet flow rate was fixed at 1 mL/min, and the carrier liquid was deionized water containing 0.1% (w/v) FL-70. Error bars represent one standard deviation (n = 3).
effect). In order to avoid the steric effect, smaller particles may be employed. In Fig. 2(b), 1/R = 5.8 for PS40 (the smallest among those tested) at Vc of 0.5 mL/min, which is too small for accurate measurement of the channel thickness. The use of higher Vc is thus needed. When Vc was increased to 1.0 mL/min, the wmeasured again decreases with increasing particle size initially. This time, however, wmeasured obtained with particles larger than about 100 nm stays almost constant at around 245 m with the relative error lower than 0.6%. The 1/R values measured for those larger than about 100 nm are larger than 20 as shown in Fig. 2(b). Similar trends were observed at Vc of 1.5 mL/min, where wmeasured obtained with particles larger than about 80 nm stays almost constant at around 238 m with the relative error lower than 0.9%. Again, the corresponding 1/R values are well larger than 20 for those larger than 80 nm. It seems 1/R > 20 is one of essential requirements for accurate w measurement. However, none of the wmeasured ’s presented in Fig. 2 can be taken as the accurate channel thickness as there still exists the steric effect (as shown in Fig. 2(b)) and the wmeasured ’s obtained at Vc of 1.0 and 1.5 mL/min are different. The wmeasured is expected to be either identical or slightly larger at higher Vc due to stronger compression of the membrane. In Fig. 2, wmeasured ’s obtained at Vc = 1.5 mL/min are smaller than those obtained at Vc = 1.0 mL/min. This rather anomalous behavior indicates that 1/R larger than 20 does not guarantee accurate w measurement. Fig. 3 shows the same plots as those shown in Fig. 2 obtained from the same AF4 system, except that the accumulation wall was
Fig. 3. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads at various cross-flow rates in AF4 channel with PES membrane. All other experimental conditions were the same as those in Fig. 2.
PES instead of RC. As with the PES membrane, there also exists the influence of the steric effect with the particle size as indicated by a decrease in the slope of the R vs. d curve as particle size increases (Fig. S1). In general, the steric effect should bend the curve of 1/R vs. d downward. However, a slight concave shape of the 1/R vs. d curve in Fig. 3(b) was observed. Meanwhile, a discontinuity in the 1/R vs. d curve between PS80 and PS100 was observed. This is probably due to the van der Waals interaction between PS particles and membrane, which is size-dependent as suggested by Eq. (12). The larger particle suffers from stronger van der Waals attraction, resulting in an increase in the retention time of analyte. Eventually, it leads to an overestimation in w determination along with a concave shape of the 1/R vs. d curve. Unlike with RC membrane, the wmeasured ’s obtained with PES membrane do not change much with the particle size, and do not show a trend of gradual change. Also the elution profiles of PS150 and PS200 showed tailings, especially at Vc = 1.0 mL/min (data not shown). These results suggest there may be stronger influence of attractive van der Waals interaction between PS particles and the PES membrane than with the RC membrane. As indicated by Eq. (12), the van der Waals attractive interaction depends not only on the surface properties but also on the particle size. As the particle size increases, the van der Waals attractive interaction becomes stronger. There may also exist electrostatic repulsive force in an AF4 channel, which counteracts the van der Waals attractive force. The electrostatic repulsive force
H. Dou et al. / J. Chromatogr. A 1393 (2015) 115–121
(a)
119
(a)
320 PES, 0.1% FL-70
wmeasured (μ μm)
300 PES, 0.05 % SD S RC, 0.05% SDS
280
260
RC, 0.1% FL-70
240 50
100
150
200
Diameter of PS latex bead (nm)
(b)
50
(b)
RC, 0.1% FL-70 RC, 0.05% SDS PES, 0.1% FL-70 PES, 0.05% SDS
40
1/R
30 20 10 0 50
100
150
200
Diameter of PS latex bead (nm) Fig. 4. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads in AF4 with various combinations of membranes and surfactants. Vc and Vout were 0.5 and 1.0 mL/min, respectively.
depends strongly on the composition of the carrier liquid [32], and an optimization of the composition of the carrier liquid is thus also required. 4.2. Effect of type of dispersing agent Fig. 4 shows wmeasured and 1/R measured for PS latex beads at various combinations of the types of the membrane (RC and PES) and the dispersing agent (FL-70 and SDS). Vc and Vout were 0.5 and 1.0 mL/min, respectively. It can be seen that the wmeasured ’s obtained with PES membrane are higher than those with RC membrane at the same operating condition. This may be explained by stronger influence of attractive van der Waals interaction between PS particles and the PES membrane than with the RC membrane. Also the PES membrane may protrude less than the RC membrane in the same AF4 channel [35]. With the same type of membrane, wmeasured ’s obtained with two different dispersing agents show similar trends. With the RC membrane, wmeasured ’s gradually decreases with increasing particle size, mainly due to the steric effect as explained earlier in Fig. 2(a). With the PES membrane, wmeasured ’s do not show a trend of gradual change with the particle size as shown in Fig. 3(a). Again the elution profiles obtained with the PES membrane showed some degree of tailing (data not shown) while those with the RC membrane did not show much tailing, which can be explained by stronger van der
Fig. 5. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads in AF4 channel with RC membrane. The carrier liquid was water containing 0.05% SDS and various concentrations of NaNO3 . Flow rates were the same as those in Fig. 4.
Waals attractive interaction of PS particles with the PES membrane together with a stronger retention with PES membrane (Fig. 4(b)) than with the RC membrane. In Fig. 4(a), with the same RC membrane, wmeasured ’s obtained with SDS are higher than those obtained with FL-70, whereas, with PES membrane, wmeasured ’s obtained with SDS are lower. Higher wmeasured ’s from the combination of the RC membrane with SDS than with FL-70 may be partly explained by lower protrusion of the RC membrane with SDS than with FL-70 [35]. Or there may be stronger van der Waals interaction between PS particles and RC membrane with SDS than with FL-70 [36], which may partly counteract the steric effect. Results presented in Fig. 4(a) indicate the degree and the pattern of the particle–membrane interaction vary with the type of the dispersing agent. 4.3. Effect of ionic strength As suggested by Eq. (11), the ionic strength of carrier liquid affects electrostatic interaction. The effects of the ionic strength on wmeasured and 1/R are shown in Fig. 5. As shown in Fig. 5(a), for a given particle size, the wmeasured increases with increasing ionic strength. With 5 mM NaNO3 added, wmeasured seems to be almost independent of the particle size with the relative error of 1.7%, which may be attributed to a counteraction of the steric effect and the van der Waals attractive interaction between
H. Dou et al. / J. Chromatogr. A 1393 (2015) 115–121
4.4. Effect of pH Fig. 6 shows wmeasured and 1/R obtained at various pH with the carrier liquid containing 0.05% SDS. It is shown that pH of the carrier
(a)
290 pH=2 7 12
wmeasured (μ μ m)
280
0.4 R
300
0.3
290 wmeasured
0.2
280 0.1
270 260
0.0 Ferritin
PS20
PS100
Type of standard Fig. 7. Channel thickness (square) and retention ratio (circle) measured in AF4 using various types of standards. The carrier liquid was water containing 0.05% SDS and 5 mM NaNO3 . All other experimental conditions were the same as those in Fig. 5.
liquid affects w measurement, as does the type of the surfactant or the ionic strength of the carrier liquid. The wmeasured ’s measured at pH 2 and 7 are similar in the size range tested, and both tends to decrease as the particle size increases. On the contrary, at a basic condition (pH 12), the wmeasured tends to increase with increasing particle size. This may be explained by an increase in the van der Waals attractive interaction between particles and membrane caused by an increase in the ionic strength of the carrier liquid, where 10 mM NaOH was added to adjust pH. Another possibility is that the thermodynamic force, which counteracts convective transport to the accumulation wall, is drastically increased when the particles become highly charged at basic conditions [37,38]. It seems more in-depth studies are needed for better understanding of this phenomenon.
270 4.5. Effect of the types of standard
260
250 50
(b)
310
Retention ratio, R
particles and the membrane. It can be seen in Fig. S2 that the slope of the plot decreases as particle size increases, suggesting there exists the steric effect at all conditions. It seems the influence of the steric effect on w determination is canceled out by adding 5 mM NaNO3 (Fig. 5(a)). When the concentration of NaNO3 was increased to 10 mM, wmeasured was slowly increased with increasing particle size, suggesting there exists stronger van der Waals attractive interaction between particles and the membrane. As the salt concentration was further increased to 30 mM, the wmeasured increases rather quickly with the particle size and the curve of 1/R vs. d is strongly bent upward (Fig. 5(b)). An increase in wmeasured with increasing ionic strength is expected from AF4 theory. An increase in the ionic strength leads to a reduction in the thickness of the electrostatic double layer [32], allowing particles approach closer to the accumulation wall, resulting in an increase in 1/R as shown in Fig. 5(b). In Fig. 5(a), high ionic strengths (10 or 30 mM NaNO3 ) led to strong van der Waals attractive interaction between particles and the membrane, resulting in an overestimation in wmeasured . Meanwhile, as mentioned above, the stronger van der Waals attraction could lead to a concave shape of the 1/R vs. d curve. It is noted that wmeasured obtained with PS150 is larger than the thickness of the spacer (350 m).
wmeasured (μ μm)
120
100
150
200
Diameter of PS latex bead (nm) 40 pH=2 7 12
1/R
30
20
Fig. 7 shows the wmeasured and R obtained with three different types of the standards (ferritin, PS20 and PS100). The carrier liquid was deionized water containing 0.05% SDS and 5 mM NaNO3 . Ferritin is commonly employed to measure AF4 channel thickness using Eq. (9). It can be seen that wmeasured obtained from ferritin are higher than those obtained with PS standards. The relative error of 5.7% was observed between wmeasured ’s obtained with ferritin and PS100, which would result in a large discrepancy in dh determination. A care must be taken when a protein standard (with known diffusion coefficient D) is used for w determination. First, D is temperature-dependent. And a protein standard may contain dimers and trimers, which could result in erroneous D. It has been reported that D measured by dynamic light scatting (DLS) was significantly affected by the presence of oligomers [19]. Use of a well-characterized spherical PS beads with uniform and narrow size distributions may be more reliable for w determination as dh is rather independent on the experimental conditions such as temperature.
10 5. Conclusions
0 50
100
150
200
Diameter of PS latex bead (nm) Fig. 6. Channel thickness (a) and inverted retention ratio (b) measured for PS latex beads at various pHs in AF4 channel with RC membrane. The carrier liquid was water containing 0.05% SDS. Flow rates were the same as those in Fig. 4.
In AF4 analysis, it is important to measure w accurately as w is needed to determine the diffusion coefficient D or dh of a sample from its retention data. Ideally w needs to be measured at the same condition as that used for sample analysis. The use of small proteins (e.g., ferritin) as a standard may not always be suitable as their retention levels may not be strong enough at operating conditions. Sometimes the interaction between particles and the
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membrane may also come into play, which was not taken into consideration in the classical FFF theory, and, therefore can lead to departure from theory, and eventually, incorrect particle size analysis. Results showed that at relatively higher ionic strengths, attractive interactions may lead to an overestimation in w. It seems the ionic strength of the carrier liquid needs to be adjusted carefully so that the charges on the sample and the membrane would be screened effectively. The channel thickness w needs to be measured again whenever there is a change in the experimental conditions including the composition of the carrier liquid. And it is clear from the results that judicious selection of a standard must be made in order to extract accurate results. Acknowledgement The authors acknowledge the support provided by the National Research Foundation (NRF) of Korea (NRF-2014M2A8A5021929). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.chroma.2015.03.025. References [1] J.C. Giddings, Field-flow fractionation: analysis of macromolecular, colloidal, and particulate materials, Science 260 (1993) 1456–1465. [2] J.C. Giddings, A new separation concept based on a coupling of concentration and flow nonuniformities, Sep. Sci. 1 (1966) 123–125. [3] K.D. Caldwell, L.F. Kesner, M.N. Myers, J.C. Giddings, Electrical field-flow fractionation of proteins, Science 176 (1972) 296–298. [4] J.C. Giddings, F.J.F. Yang, M.N. Myers, Sedimentation field-flow fractionation, Anal. Chem. 46 (1974) 1917–1924. [5] J.C. Giddings, L.K. Smith, M.N. Myers, Thermal field-flow fractionation: extension to lower molecular weight separations by increasing the liquid temperature range using a pressurized system, Anal. Chem. 47 (1975) 2389–2394. [6] K.G. Wahlund, J.C. Giddings, Properties of an asymmetrical flow field-flow fractionation channel having one permeable wall, Anal. Chem. 59 (1987) 1332–1339. [7] M. Baalousha, J.R. Lead, Rationalizing nanomaterial sizes measured by atomic force microscopy, flow field-flow fractionation, and dynamic light scattering: sample preparation, polydispersity, and particle structure, Environ. Sci. Technol. 46 (2012) 6134–6142. [8] E. Alasonati, V.I. Slaveykova, H. Gallard, J.-P. Croué, M.F. Benedetti, Characterization of the colloidal organic matter from the Amazonian basin by asymmetrical flow field-flow fractionation and size exclusion chromatography, Water Res. 44 (2010) 223–231. [9] H. Dou, B. Zhou, H.-D. Jang, S. Lee, Study on antidiabetic activity of wheat and barley starch using asymmetrical flow field-flow fractionation coupled with multiangle light scattering, J. Chromatogr. A 1340 (2014) 115–120. [10] L. Nilsson, Separation and characterization of food macromolecules using fieldflow fractionation: a review, Food Hydrocoll. 30 (2013) 1–11. [11] J. Ashby, S. Schachermeyer, S. Pan, W. Zhong, Dissociation-based screening of nanoparticle–protein interaction via flow field-flow fractionation, Anal. Chem. 85 (2013) 7494–7501. [12] K. Rebolj, D. Pahovnik, E. Zˇ agar, Characterization of a protein conjugate using an asymmetrical-flow field-flow fractionation and a size-exclusion chromatography with multi-detection system, Anal. Chem. 84 (2012) 7374–7383. [13] S. Noskov, C. Scherer, M. Maskos, Determination of Hamaker constants of polymeric nanoparticles in organic solvents by asymmetrical flow field-flow fractionation, J. Chromatogr. A 1274 (2013) 151–158. [14] C.W. Isaacson, D. Bouchard, Asymmetric flow field flow fractionation of aqueous C60 nanoparticles with size determination by dynamic light scattering and quantification by liquid chromatography atmospheric pressure photoionization mass spectrometry, J. Chromatogr. A 1217 (2010) 1506–1512.
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