FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1450203416> ?p ?o ?g. }

• W1450203416 abstract "The plate heights of commercial LC columns have changed little over the last 20 years, following the trend of Hmin ~ 2dp, where dp is the particle diameter.1 Simulations have shown that Hmin~ dp is the limit for nonporous particles.2 With particle sizes dropping only a factor of about two over the last 20 years, plate heights have improved by the same factor over this time frame. The reason is not a lack of diligence or creativity; instead, it is because of the fundamental limits of mass transport, with the ultimate limit being the velocity spread of the mobile phase across the spaces between particles. We have recently employed a nanofluidic phenomenon called slip flow,3–8 which greatly reduces this velocity spread, thereby reducing the plate height dramatically. We demonstrated a plate height as low as 0.03dp, which was 15 nm.9 This opens a new horizon for efficiency in UHPLC.The concept of slip flow is illustrated in Figure 1. Imagine that the walls are the surfaces of two adjacent particles. The familiar Hagen-Poiseuille flow is depicted with its parabolic velocity profile, where the velocity goes to zero at the walls. This is the realm of chromatography today. The figure also depicts slip flow, where the velocity does not go to zero at the walls, thereby giving rise to a narrower distribution of velocities in the column. Slip flow occurs when the molecular interactions between fluid and the surface are weak, allowing the fluid at the interface to have a nonzero velocity. The existence of slip flow is common knowledge in the field of fluid dynamics, where it is typically a small correction factor when there are weak fluid-surface interactions, but it becomes big factor when the channel reaches the scale of tens of nanometers.3–8 Consequently, slip flow always occurs in reversed-phase liquid chromatography, but it is not distinguishable from Hagen-Poiseuille flow because the dimensions of chromatographic materials are relatively large. The nanoscale channel dimensions are achieved by using submicrometer particles.Figure 1Illustration of how slip flow gives a narrower velocity distribution compared to Hagen Poiseuille flow. The velocity is far from zero at the wall for slip flow.Experimentally, the parabolic flow profile cannot be directly viewed on the nanoscale, but it can be inferred because one can measure a companion to the narrower flow profile: a faster flow rate. Since slip flow gives a nonzero velocity at the wall, the volume flow rate, Q, is enhanced relative to that for Hagen-Poiseuille flow, QHP. In Equation 1, for a capillary of radius r, the term Ls is the slip length, which is defined as the ratio of the velocity to shear rate, each at the wall. Q/QHP=1+4·Ls/r(1)For water in contact with various hydrocarbon surfaces, the slip lengths are all under 100 nm,3,5,7–8 therefore, channel radii less than 100 nm will give noticeable slip flow. Having r in the denominator explains that the smaller the channel, the greater the enhancement from slip flow.Figure 2 shows experimental results for volume flow rates we have reported for a capillary packed with a 2-cm plug of 470 nm particles.9 These particles formed colloidal crystals inside the capillary.10–11 They were then chemically modified to have a mixed self-assembled monolayer of butyl groups and methyl groups.12 For varying mobile phase composition, the flow rates are normalized by mobile phase viscosity, after accounting for its small pressure dependence over this range.13 These lines would all coincide for Hagen-Poiseuille flow; instead, they are quite different from one another. Further, the slopes increase in order of immiscibility with alkanes, consistent with the idea that weaker interactions between the fluid and the surface give increased slip flow The data show that the slope for toluene coincides with the line calculated for Hagen-Poiseuille flow (dashed line), whereas the slope for water is five-fold higher. The reason is that slip flow is negligible for toluene because it interacts well with the hydrocarbon surface, whereas slip flow dominates for water because of its very weak interactions with hydrocarbons. The toluene data serve to confirm that the material does not have parasitic flow from cracks, wall gaps, or other defects that would enhance flow in an undesirable way.Figure 2Flow rate vs. pressure, normalized for viscosity, illustrating that slip flow increases with solvent immiscibility in hydrocarbon. The dashed line is calculated for Hagen-Poiseuille flow; other lines are linear fits to the flow data. L=2 cm. Graph is ...Chromatograms for a commercial monoclonal antibody are compared for A) a silica colloidal crystal like the one used for Figure 2, and B) a 5-cm long commercial wide-pore UHPLC column.9 The silica colloidal crystal can separate the antibody from its aggregates in 1/10 the time and at room temperature. It is the peak sharpness that enables use of low retention conditions to resolve these at room temperature. Since elevated temperature promotes antibody degradation and aggregation, slip flow allows operation under conditions that minimally alter the protein. Fluorescence imaging was used to sample the sharp peak of Figure 3A with high point density, revealing the plate height to be 70 nm for the monoclonal antibody peak.9 An example of fluorescence imaging is illustrated in Figure 3C for the lowest plate height we have observed, which is for bovine serum albumin (BSA). Over-labeling gives two peaks due to one vs. two dye labels on the protein. Figure 3C shows an image of the two BSA peaks as they approach the exit of a 2-cm long capillary. From Gaussian fitting of the peak profiles, shown in Figure 3D, the standard deviation of the earlier eluting peak is 16 µm, which corresponds to a plate height of 15 nm for the separation distance of 17.5 mm, thus approaching the diffusion limit.9 This plate height is a factor of 500 smaller than the plate height of a protein, chymotrypsin, measured for 1.5 µm nonporous silica particles in reversed phase UHPLC.14 The number of plates for this separation distance of 17.5 mm is 1.2×106 plates. The only other example of a plate number exceeding 1 million was a separation of aromatic compounds using silica monolith of L=8.5 m and P=340 bar, where the separation time was 1480 min (24 hr).15 This is more than 700 times longer than the 2 min separation time for the BSA sample for essentially the same pump pressure. This illustrates that the flattening of the Poiseuille flow profile under slip conditions has a very large effect on the column length needed to obtain a high separation efficiency.9Figure 3Chromatograms for monoclonal antibody using A) slip flow (isocratic 45:55 ACN/Water, 0.1% TFA, P=460 bar, L=1.45 cm) and B) UPHLC (Waters ACQUITY C4, 1.7mm, 10% to 70% ACN over 10 min, 1mL/min, C) Imaged peaks for BSA, with second peak due to double-labeling ...Something remarkable happens when separations approach the diffusion limit: length no longer contributes to resolution. Of course, for extremely short lengths other factors will eventually enter in, such as injected width. But for reasonable lengths, the equation for plate height, H, in the diffusion limit simplifies to just the B term in the van Deemter equation, as given in Equation 2. H=2eDv(2)In this case, only the diffusion coefficient, D, and the obstruction of diffusion by the limited column porosity, e, contribute to H for a given mobile phase velocity, v. The velocity is determined by the pressure, P, the mobile phase viscosity, η, and other factors described by the Kozeny-Carman relation of Equation 3, for which we added the flow enhancement factor, E. v=EP180·Ldp2η(e1−e)2(3)Since the number of plates, N, is L/H, it is straightforward to show that this maximum number of plates under the diffusion limit, Nmax, is dictated by pressure and is independent of length. Nmax=P·E360eDdp2η(e1−e)2(4)This situation is analogous to capillary electrophoresis, where the plate number is proportional to the applied voltage, but not length.16 Ultimately, injected width and heating impose an upper limit to N in capillary electrophoresis.16 For UHPLC, these limitations will not be reached as easily: injected width is minimized in chromatography by stacking at the head of the column, and heating is minimized because pumping brings in fresh fluid, and solids are better heat conductors than liquids. Radial homogeneity of the packing has been a problem in chromatography,17 but this is not the case for colloidal crystals.10–11 A method for rapid homogeneous packing with negligible eddy diffusion is the subject of a pending patent.18 The independence of plate height on separation length explains why it is possible to achieve such high plate numbers for such short separation distances of L< 2 cm.Using Eq. 4 to calculate the maximum possible plate number under the diffusion limit, for a typical medium sized protein, D=1.0×10−6 cm2/s, and for the separation parameters of dp=470 nm, e=0.28, a flow enhancement of 5, and Pmax= 800 bar, the result is Nmax= 1.5×106. It is important to note that when 1.5×106 plates are observed in 1-cm, for example, one cannot claim this corresponds to 1.5×108 plates per meter. The calculation also illustrates why the plate heights are so low for proteins: their diffusion coefficients are an order of magnitude or more lower than those of small molecules." @default.
• W1450203416 created "2016-06-24" @default.
• W1450203416 creator A5007042345 @default.
• W1450203416 creator A5064384011 @default.
• W1450203416 creator A5084639726 @default.
• W1450203416 date "2012-10-01" @default.
• W1450203416 modified "2023-09-27" @default.
• W1450203416 title "Ultra High Efficiency Protein Separations with Submicrometer Silica Using Slip Flow." @default.
• W1450203416 cites W1969270765 @default.
• W1450203416 cites W1976889007 @default.
• W1450203416 cites W1985067559 @default.
• W1450203416 cites W1994156659 @default.
• W1450203416 cites W1996789797 @default.
• W1450203416 cites W2023167709 @default.
• W1450203416 cites W2040092779 @default.
• W1450203416 cites W2040418788 @default.
• W1450203416 cites W2048391792 @default.
• W1450203416 cites W2057642130 @default.
• W1450203416 cites W2062388503 @default.
• W1450203416 cites W2080811282 @default.
• W1450203416 cites W2124339383 @default.
• W1450203416 cites W2334891630 @default.
• W1450203416 hasPubMedCentralId "https://www.ncbi.nlm.nih.gov/pmc/articles/4176710" @default.
• W1450203416 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/25267924" @default.
• W1450203416 hasPublicationYear "2012" @default.
• W1450203416 type Work @default.
• W1450203416 sameAs 1450203416 @default.
• W1450203416 citedByCount "2" @default.
• W1450203416 countsByYear W14502034162019 @default.
• W1450203416 countsByYear W14502034162021 @default.
• W1450203416 crossrefType "journal-article" @default.
• W1450203416 hasAuthorship W1450203416A5007042345 @default.
• W1450203416 hasAuthorship W1450203416A5064384011 @default.
• W1450203416 hasAuthorship W1450203416A5084639726 @default.
• W1450203416 hasConcept C121332964 @default.
• W1450203416 hasConcept C185592680 @default.
• W1450203416 hasConcept C195268267 @default.
• W1450203416 hasConcept C43617362 @default.
• W1450203416 hasConcept C97355855 @default.
• W1450203416 hasConceptScore W1450203416C121332964 @default.
• W1450203416 hasConceptScore W1450203416C185592680 @default.
• W1450203416 hasConceptScore W1450203416C195268267 @default.
• W1450203416 hasConceptScore W1450203416C43617362 @default.
• W1450203416 hasConceptScore W1450203416C97355855 @default.
• W1450203416 hasLocation W14502034161 @default.
• W1450203416 hasOpenAccess W1450203416 @default.
• W1450203416 hasPrimaryLocation W14502034161 @default.
• W1450203416 hasRelatedWork W1995282171 @default.
• W1450203416 hasRelatedWork W2001320270 @default.
• W1450203416 hasRelatedWork W2003274972 @default.
• W1450203416 hasRelatedWork W2024329988 @default.
• W1450203416 hasRelatedWork W2031469440 @default.
• W1450203416 hasRelatedWork W2031694227 @default.
• W1450203416 hasRelatedWork W2055085539 @default.
• W1450203416 hasRelatedWork W2059022937 @default.
• W1450203416 hasRelatedWork W2060204236 @default.
• W1450203416 hasRelatedWork W2067311536 @default.
• W1450203416 hasRelatedWork W2086076527 @default.
• W1450203416 hasRelatedWork W2125359258 @default.
• W1450203416 hasRelatedWork W2144503968 @default.
• W1450203416 hasRelatedWork W2152020389 @default.
• W1450203416 hasRelatedWork W2164195364 @default.
• W1450203416 hasRelatedWork W2499422207 @default.
• W1450203416 hasRelatedWork W2725526259 @default.
• W1450203416 hasRelatedWork W2736617651 @default.
• W1450203416 hasRelatedWork W3035129063 @default.
• W1450203416 hasRelatedWork W2589237245 @default.
• W1450203416 isParatext "false" @default.
• W1450203416 isRetracted "false" @default.
• W1450203416 magId "1450203416" @default.
• W1450203416 workType "article" @default.