Anal. Chem. 2003, 75, 3666-3667
Comments on “A Microfabricated Thermal Field-Flow Fractionation System” A recently published article1 described the fabrication of a thermal field-flow fractionation (TFFF) channel by using some materials whose thermal conductivity is significantly lower in comparison with frequently used chromium-plated copper.2 As a result, the calculated temperature drop across the channel was as low as 4.8 K for a temperature difference ∆T ) 46 K measured outside the channel. In comparison with the microTFFF channel built up by using corrosion-resistant metal materials and described recently,3 it is not clear at all why the channel in which a high temperature difference has to be established to obtain a medium temperature should represent an advantage although a much higher temperature is necessary to fractionate small colloidal particles and macromolecules.2 In the Experimental Section, the authors1 described only one separation of two different size colloidal particles. As the dimensions of the channel are given only as lying within large limit values, it is difficult to understand some experimental data. The plate height was characterized as a function of average “channel velocity”, which probably means the average linear velocity of the carrier liquid.1 Figure 4 in this paper shows the elution time of roughly 64 s for an unretained solute while 117 s measured at a carrier liquid flow rate of 1.00 mL/min is the elution time mentioned in the text on page 1214.1 However, these values cannot be correct even if the channel has the maximal dimensions: width 27 µm, breadth 6 mm, and length 6 cm. The elution time of an unretained solute in such a channel whose volume is 9.72 µL should be roughly 0.6 s at the flow rate of 1.00 mL/min or roughly 36 s at the flow rate of 1.00 mL/h. With respect to the elution time of 31.2 s of an unretained solute in Figure 7 of ref 1 and the given flow rate of 1.25 mL/h, the only possible dimensions of the separation channel (within the limit values given in ref 1) are 27 µm × 6 mm × 6.5 cm. The length is slightly longer than the limit value given in ref 1; however, it can be due to the fact that the volume of the capillary connecting the channel with the detector is not taken into account. The elution time of an unretained solute given in Figure 6 of ref 1 is shorter and the temperature drop is lower compared with the values given in Figure 7. It might be due to an important thermal dilation of the channel under various experimental conditions, which is a serious drawback of its construction. The linear velocity 〈v〉 of the carrier liquid (which is the volumetric flow rate divided by the cross-sectional (1) Edwards, T. L.; Gale, B. K.; Frazier, A. B. Anal. Chem. 2002, 74, 12111216. (2) Jancˇa, J. Field-Flow Fractionation: Analysis of Macromolecules and Particles; Marcel Dekker: New York, 1988. (3) Jancˇa, J. J. Liq. Chromatogr., Relat. Technol., 2002, 25, 683-704.
3666 Analytical Chemistry, Vol. 75, No. 14, July 15, 2003
area of the channel) is 〈v〉 ) 0.214 cm/s for the experiment demonstrated in Figure 7. The plate height H calculated for the unretained peak from the fractogram in Figure 7 of ref 1 by using a well-known relationship
H ) L(σ/te)2
(1)
is H ) 0.93 cm. In eq 1, L is the length of the fractionation channel, te is the elution time of the concerned solute, and σ is standard deviation characterizing the width of the fractogram. On the other hand, the plate height corresponding to 〈v〉 ) 0.214 cm/s taken from Figure 5 of ref 1 is roughly H ) 1.2 cm. Although the origin of this difference is not clear, its magnitude is not dramatic, by supposing that the legend in Figure 5 is correct (even if contradictory to the caption under this figure). The fractogram in Figure 7 should represent a separation of two different size colloidal particles. The void volume peak in Figure 7, which corresponds to an unretained solute, is very broad and indicates an important zone spreading. On the other hand, two other peaks in Figure 7 are attributed by the authors to the separation of two retained colloidal particles of different sizes. This attribution seems to be unjustified because both peaks are substantially narrower than the void volume peak, but this is theoretically impossible and the known experimental FFF data2 confirmed the theory. The plate height in FFF is described by2
H)
χw2〈v〉 2D + + D R〈v〉
∑H
i
(2)
where D is the diffusion coefficient of the fractionated species, R is the retention ratio, w is the thickness of the channel, the sum of Hi represents the extrachannel contributions to the plate height, and χ is a dimensionless parameter, which is a complex function of the retention parameter λ ) l/w, where l is a distance between the accumulation wall and the center of gravity of the concentration distribution of the retained species across the channel. The experimental retention ratio R is simply the ratio of the retention time of the unretained solute to that of the retained one R ) to/te. The diffusion coefficient of the hard-sphere colloidal particles suspended in a liquid is given by the well-known Einstein-Stokes equation
D ) kBT/6πηr
(3)
where kB is Boltzmann constant, T is the temperature, η is the viscosity of the suspending liquid, and r is the particle radius. By neglecting the first and third terms on the right-hand side of the eq 1 and by taking into account the approximate relationship2 for χ
χ ) 24λ3 ) 24(R/6)3 10.1021/ac020738u CCC: $25.00
(4)
© 2003 American Chemical Society Published on Web 06/19/2003
the result is
H ) 2R3w2〈v〉πηr/3kBT
(5)
A simple calculation based on the theory of the zone broadening in FFF vas carried out by using eq 5 and the experimental data given in ref 1, namely, w ) 27 µm, 〈v〉 ) 0.214 cm/s, T ) 297 K (the cold wall temperature), and η ) 0.0094 P for water at 297 K, and the retention ratios R1 ) 0.441 and R2 ) 0.312, corresponding to the first and second peaks of the retained particles of diameters 204 and 272 nm, respectively, in Figure 7, ref 1. The resulting plate heights are H1,theor ) 0.654 cm and H2,theor ) 0.309 cm, respectively. On the other hand, the plate heights calculated from the experimental fractogram shown in Figure 7, ref 1, by using eq 1 are H1,exp ) 0.017 cm and
H2,exp ) 0.0021 cm, respectively. As a result, the retained peaks, measured by standard deviations, should be at least 6× and 12× larger, respectively, and thus unresolved. Consequently, it seems that the described separation system did not function correctly and thus the fractogram in Figure 7 of the ref 1 cannot represent the assumed separation. ACKNOWLEDGMENT This work was supported by Conseil Regional PoitouCharentes.
Josef Jancˇa
Universite´ de La Rochelle, Poˆ le Sciences et Technologie, Avenue Michel Cre´ peau, 17042 La Rochelle Cedex 01, France AC020738U
Analytical Chemistry, Vol. 75, No. 14, July 15, 2003
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