Anal. Chem. 2011, 83, 459
Reply to Comment on “Submicrometer Plate Heights for Capillaries Packed with Silica Colloidal Crystals” Douglas S. Malkin,† Bingchuan Wei,‡ and Mary J. Wirth*,‡ Department of Chemistry, University of Arizona, Tucson, Arizona 85721, United States, and Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States Dr. Neue’s comment regards our recent paper reporting 200 nm plates height for electrochromatography of a dye in a capillary packed with silica colloidal crystals. The paper showed that the plate height has no detectable contribution from inhomogeneous packing, i.e., there is no eddy diffusion to within ±20 nm. The comment is aside from the main conclusions of the paper, instead comparing the flow properties reported in the Supporting Information with flow properties through randomly packed particles. Dr. Neue calculated from Figure S2 in the Supporting Information that random packing would give the same flow rate. We need to correct a misunderstanding on his part: methanol was used as the solvent, and its viscosity at room temperature is 0.54 cP, lower than the viscosity of water that he used in his calculation. The KozenyCarman equation agrees with numerical solutions for monodisperse particles, hence we will assume it accurately reports porosity under these conditions.1 Using the correct viscosity, along with the slope of the linear regression for the graph in Figure S2 (0.015 nL/(min psi)), one calculates a dimensionless resistance to flow of 1900, which is f(ε) in Dr. Neue’s comment. This value of f(ε) corresponds to a porosity of 0.34, which is significantly lower than the 0.40 calculated by Dr. Neue, thus negating the idea that the particles are randomly packed. We need to correct some information in Dr. Neue’s comment in regards to the porosity measurement of Figure S3: the data were obtained by using bare silica particles that had been fully rehydroxylated, and the water spontaneously wicked into the capillary, i.e., no pressure was applied. The contact angle is nominally zero for the water/silica interface. The porosity of 0.25 from the wicking measurement is lower than that from the flow measurement, 0.34, yet both are reproducible. One cannot know why they disagree without embarking on a research project devoted to this topic. Dr. Neue suggests that the crystallinity shown in the SEM image of the paper is not indicative of the structure in the interior of the capillary. The suggestion is negated by the porosity being much lower than 0.40. In addition, photographs in the paper showed opalescence and blue color due to Bragg diffraction, indicative of bulk colloidal crystallization. To lend further insight, we present a new SEM image here in Figure 1, which shows a cross-section of a capillary packed the same way as that in the paper and then scored and broken at an arbitrary position in the middle. The loose particles are probably the result of the capillary being broken, but most of * To whom correspondence should be addressed. E-mail: mwirth@ purdue.edu. † University of Arizona. ‡ Purdue University. (1) Valdes-Parada, F. J.; Ochoa-Tapia, J. A.; Alvarez-Ramirez, J. Phys. A (Amsterdam, Neth.) 2009, 388, 789–798. 10.1021/ac102112m 2011 American Chemical Society Published on Web 12/02/2010
Figure 1. SEM image of a capillary that was packed with 300 nm particles and then fractured in the middle of the packed length. Despite apparent damage from the fracturing, the face-centered cubic structure is obvious. The red arrow points to one of the many examples of a vacancy defect.
the crystalline structure is intact. The SEM image is instructive because it offers a possible explanation for how a material might exhibit both Bragg diffraction and a porosity higher than 0.259: vacancy defects. Defects are always present in crystals, and if the defects were randomly positioned, they would allow Bragg diffraction to be combined with higher porosity and submicrometer plate heights in electrochromatography. Vacancy defects are thus consistent with all of the observations. To put this discussion about crystallinity back into the scope of the paper, reducing the contribution to the plate height from eddy diffusion was the goal. Eddy diffusion was demonstrated by Patel et al.2 to be due to radially heterogeneous packing, and we suggested in our paper that crystallization could be a tool for avoiding radially heterogeneous packing. The results in the paper support this idea. In short, we agree with Dr. Neue that the porosity is likely much higher than the theoretical minimum for face-centered cubic crystals, but we disagree with the notion that the materials used for the paper were comprised of randomly packed particles. We thank Dr. Neue for his carefully considered comment. Received for review August 10, 2010. Accepted November 19, 2010. AC102112M (2) Patel, K. D.; Jerkovich, A. D.; Link, J. C.; Jorgenson, J. W. Anal. Chem. 2004, 76, 5777–5786.
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