Measuring porosities of chromatographic columns utilizing a mass-based total pore-blocking method: Superficially porous particles and pore-blocking critical pressure mechanism

Accepted Manuscript Title: Measuring porosities of chromatographic columns utilizing a mass-based total pore-blocking method: Superficially porous particles and pore-blocking critical pressure mechanism Authors: Nicole M. Devitt, Robert E. Moran, Justin M. Godinho, Brian M. Wagner, Mark R. Schure PII: DOI: Reference:

S0021-9673(19)30193-1 https://doi.org/10.1016/j.chroma.2019.02.045 CHROMA 360054

To appear in:

Journal of Chromatography A

Received date: Revised date: Accepted date:

15 November 2018 20 February 2019 20 February 2019

Please cite this article as: Devitt NM, Moran RE, Godinho JM, Wagner BM, Schure MR, Measuring porosities of chromatographic columns utilizing a mass-based total pore-blocking method: Superficially porous particles and poreblocking critical pressure mechanism, Journal of Chromatography A (2019), https://doi.org/10.1016/j.chroma.2019.02.045 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Measuring porosities of chromatographic columns utilizing a mass-based total poreblocking method: Superficially porous particles and pore-blocking critical pressure mechanism

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Nicole M. Devitt1,4, Robert E. Moran2, Justin M. Godinho2, Brian M. Wagner2, and, Mark R. Schure3,*

Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716

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Present address: Merck & Co., Inc., 126 E. Lincoln Ave. RY 119-200 Rahway, New Jersey, 07065

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Kroungold Analytical, Inc, 1299 Butler Pike, Blue Bell, Pennsylvania 19422

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Advanced Materials Technology, Inc, Suite 1-K, 3521 Silverside Rd, Wilmington, Delaware 19810

Author to whom correspondence should be addressed, e-mail: [email protected]

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*

Highlights

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a mass-based total pore blocking method is described for porosity measurements porosity measurements of superficially porous particles are performed the Young-Laplace equation is used to describe the pore blocking stability Calculations suggest that larger pores can be blocked at extremely low flow rates

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ABSTRACT Experimentally determined total, interstitial and intraparticle porosity values are necessary to equate theory, simulation and experimental column performance. This paper reports a study of a mass-based technique for determining total, interstitial and intraparticle porosity measurements based on the total pore-blocking (TPB) method. Commercially available superficially porous particle (SPP) columns, in a variety of small-pore and wide-pore materials, with both hydrophobic and hydrophilic surfaces, are utilized as samples. The results are compared with 1

previously determined literature values for a number of columns and contrasted with HPLCbased elution methods. This method uses only a high-precision balance and an HPLC pump.

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A simple theoretical analysis of the TPB method using the Young-Laplace equation shows the pressure bounds and flow rate constraints of the method which ensure pore blocking stability. The results suggest that particles with small-pore diameters can be analyzed over a range of solvent clearing pressures and flow rates. However, wide-pore materials, typically with pore diameters in excess of 400 Å, have very low critical pressures and are difficult to determine without losing the pore blocking component. Small mass differences between clearing solvents are shown to present a challenge for measuring the interstitial volume.

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keywords: porosity; total pore blocking; interstitial porosity; intraparticle porosity; HPLC

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1. Introduction

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The measurement of the total pore volume, also known as the void volume, V0, has been discussed in numerous publications and reviews [1-3]. This void volume is the total liquid volume accessible to low molecular weight solvents and solutes. This volume excludes solids, portions of the stationary phase and “inaccessible” pores. Accurate quantitation of the void volume is important for the development of new column packing materials, performing packing experiments and understanding column performance. Unfortunately, consensus has not been met on how best to identify this volume, either using elution chromatography or other methods such as mass-based measurements. This volume is not easily measured by elution chromatography due to the many interactions between the probe analyte, the chromatographic support and the stationary phase. In addition, solutes may not sample every particle pore and interstitial volume, due to limitations in mass transport, causing a statistical undersampling of the pore volume which may possibly be flow rate dependent. Other artefacts may be present in elution chromatography, such as Donnan exclusion, which is discussed below.

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In addition to the total pore volume, the interstitial volume, Vi, and the intraparticle volume, Vp, are of great importance. The interstitial volume is the volume between particles and the intraparticle or pore volume is the volume contained within particle pores. The corresponding porosities, εT, εi and εp are obtained by dividing the total pore (i.e. void) volume, the interstitial volume and the pore volume by the empty column volume, VT. These volumes have historically been determined by a number of methods, including using polymers (e.g. blue dextran), which are assumed to be excluded from the pores of the particle, to determine the interstitial volume. More complete pore size distributions may be obtained by inverse size exclusion chromatography (ISEC) [4-7]. 2

These methods are categorized as either dynamic methods, based on some form of elution measurement, or static methods, based on pycnometric (density) and/or mass measurements. The static measurement has a long history [8-12] and was one of the first methods used to probe the porosity of packed columns. In early studies it was determined that dynamic methods gave results that differed from the static measurements and a good deal of effort was made to explain these differences [1-3, 11]. Nonetheless, both types of measurements continue to be utilized.

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One of the most interesting methods for excluding solutes from intraparticle pores is to use the Donnan exclusion principle [3, 13-17], whereby the electrostatic repulsion of charged solutes from pores which possess some charge, can be utilized to measure the interstitial volume. This exclusion process requires that the pore chemistry be suitable and that the solvent conditions promote charge-charge repulsion interactions between test solutes and pores. This dynamic method works well when the conditions support the electrostatic mechanism but appears to fail under non-suitable conditions such as with wide-pore materials [17]. We operationally define wide-pore materials here as having pore sizes larger than 400 Å diameter.

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A recent addition to the dynamic methods is the “Total Pore Blocking” (TPB) method. This technique blocks solutes and solvents from entering pores with a fluid held in the pores. This experimental approach enables a measurement of the interstitial volume [18-21]. This technology has been applied to both hydrophobic materials (i.e. reversed-phase materials) [18, 19] and to hydrophilic materials (i.e. “normal phase” materials) [20]. Additional applications using the TPB method include determining interstitial porosity when studying the pressure drop characteristics of reversed-phase (RPLC) materials [21] and studying the differences between hydrophilic interaction chromatography (HILIC) and RPLC with the same packing [22]. The TPB methods can also be used as aids in studying mass transport effects [23,24] when it is desired to run experiments which probe both the interparticle transport and pore transport mechanisms of zone broadening by shutting off the particle porosity in situ. Note that all of the pore blocking studies described herein use the static mass-based method to determine the total column porosity. A review of previous work using the TPB method is shown here in Table 1.

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TPB methods require liquids that can be held in the particles’ pores due to a strong affinity for the pore surface chemistry, and be cleared out of the interstitial region because they are insoluble in a flushing or clearing solvent. Typical pairs of fluids include long-chain hydrocarbons and water, used as pore blocker and solvent respectively, for hydrophobic particle surface chemistries. One of the difficulties with the dynamic TPB experiment is that solutes used as void time markers can interact with the pore blocking fluid. Thus, the pore blocking fluid can act as a stationary phase and affect the accuracy of the measurement for Vi. Other problems exist for dynamic TPB methods such as a critical pressure above which the pore blocking fluid is displaced, and these will be discussed in detail below. In this paper we focus on a static measurement based on mass that implements the TPB method but does not require a transport determination of the void time through the interstitial volume. Although there is still an interaction between the interstitial solvent and pore blocking fluid, static measurements should minimize artifacts rooted in marker partitioning. We use a range of superficially porous particles (SPPs), from small-pore materials to wide-pore materials, both 3

with bare silica (HILIC) phases and reversed phase chemistries. These will be compared to previous literature measurements and an assessment made of the accuracy of determination. Comparison with HPLC elution times are made and differences noted for a few particles. An assessment of the generality of the TPB technology is made with respect to the pore sizes used in this study and contrasted with a theory of pore blocking stability based on the Young-Laplace equation.

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2. Experimental conditions

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2.1 Chemicals used in mass-based measurements. All of the chemicals used here were HPLC grade. Methanol was obtained from Honeywell (Morris Plains, NJ). Acetonitrile, methylene chloride, isopropyl alcohol, octane, n-propanol, cyclohexane, and ethyl acetate were obtained from MilliporeSigma (St. Louis, MO). Unstabilized tetrahydrofuran and additional methylene chloride were obtained from J.T. Baker (Avantor division, Center Valley, PA). The total pore volume is obtained using methanol, acetonitrile, methylene chloride and THF solvents for all particles. For experiments with C4 and C18 bonded phases, octane is used as the pore blocking solvent. For the HILIC phases, pure water is used as the pore blocking solvent. In both cases isopropanol (2-propanol) is used as the flushing solvent to clear pore blocker and interstitial solvents. The interstitial displacement solvents used for the hydrophobic bonded phase experiments include pure water, methanol and n-propanol. The last two are known to be slightly soluble in octane, yet show little difference in performance. The interstitial displacement solvents used for the HILIC phases include octane, methylene chloride, ethyl acetate and cyclohexane.

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2.2 Chemicals used in HPLC measurements. Uracil, naphthalene, potassium chloride and acetonitrile were obtained from MilliporeSigma. Carboxylate-modified polystyrene latex microspheres, 0.1 µm, were obtained from Bangs Laboratory (Fishers, IN) and used as exclusion markers. This particle size is clearly a compromise intended to minimize hydrodynamic effects with small size and yet large enough to be excluded by most of the pores.

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2.3 Columns. The columns used in this study were all from Advanced Materials Technology (Wilmington, DE) and are listed in Table 2. These columns are all packed with SPPs. Particles were packed into standard column hardware using a proprietary column packing process and stored in acetonitrile between experiments. Information regarding the average particle size, pore size, carbon load, surface area, endcapping status and pH and temperature limits is available on the company’s web site [25].

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2.4 HPLC equipment and measurement. Chromatographic void times were determined using a Shimadzu Nexera HPLC instrument (Columbia, MD). The mobile phase was 50/50 water/acetonitrile (v/v) and mixed in a 180 µL incorporated mixer. Instrument dwell volume was measured chromatographically to be 16.4 µL. This volume was subtracted from the chromatographically determined volumes. Uracil and naphthalene were used as total pore volume markers for hydrophobic and hydrophilic phases, respectively, and detected at 254 nm. Experiments with latex microspheres, used as exclusion markers to determine interstitial porosity, were detected at 210 nm and run at a flow rate of 0.5 mL min-1, except for a flow rate

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study described below. Data analysis was performed using integrated LabSolutions software (Shimadzu). 2.5 Mass measurement apparatus. All mass-based measurements were performed using a 5digit past the decimal point balance (Sartorius model CP225D, Bohemia, NY). An HPLC pump, Shimadzu model LC-30AD, was used for all filling and blocking experiments.

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2.6 Pore volume definitions. The procedures for determining the void volume, V0, the interstitial volume, Vi, and the particle pore (intraparticle) volume, Vp, are described below. These will then be converted to porosities. Let VT denote the empty column volume 𝑉𝑇 = 𝜋 𝑟 2 𝑙

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where l is the column length and r is the internal radius. VT can be broken down into two components: 𝑉𝑇 = 𝑉𝑆 + 𝑉0

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{2}

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where VS is the volume of solid material in the column and V0 represents the liquid volume of the column that is not composed of silica, bonded phase, or inaccessible pores. In this way, the total pore volume can be viewed as the empty space in the column that can be occupied by a wetting solvent. The total pore volume within a chromatographic column can be further broken down into the interstitial space, or space between the packed particles, and the intraparticle space associated with the pores of the particles. There is no clear delineation surface between the interstitial and intraparticle space, as one needs a model to describe that interface. In these terms

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𝑉0 = 𝑉𝑖 + 𝑉𝑝

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where Vi is the interstitial volume of the column and Vp is the intraparticle or pore volume.

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Once V0 is known and VT is calculated from the column specifications, VS (volume of solid material in the column) can be found by subtraction in Eq 2. The pore blocking experiments, detailed in the next section, seek to determine Vi and subsequently Vp by subtraction in Eq 3.

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2.7 Total pore volume method. To determine V0 experimentally, the chromatographic column was wetted with various solvents to provide a basis of comparison for their total masses. Because of the possibility of pore exclusion, the solvents used were chosen based on low molecular weights and their ability to fully wet the surfaces of the pores in the particles.

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V0 is determined using the following equation, adapted from Alhedai, Martire, and Scott [10]: V0 =

𝑚1 −𝑚2 𝜌1 −𝜌2

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where 𝑚1 and 𝑚2 are the mass of the column wetted with solvent 1, and 2, respectively. In addition, 𝜌1 and ρ2 are the density of solvent 1 and 2, respectively. Two potential sources of variation are the mass and density differences in Eq 4. The densities are taken from the solvent 5

manufacturer data. It is important to note the choice of solvents 1 and 2 used in calculating 𝑉0 . Due to the large value of error associated with small differences in solvent mass, solvent pairs for calculation of 𝑉0 from Eq 4 were chosen to maximize the difference in density between the two. Calculations made using Eq 4 determined that for two solvents with a density difference of about 0.01 g/cm3, as in the case of methanol and acetonitrile, the uncertainty associated with the calculation of 𝑉0 is greater than 𝑉0 itself, and therefore not a significant result.

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2.8 TPB method. The interstitial space, 𝑉𝑖 , and the pore volume of the particles, 𝑉𝑝 , are determined by the following procedure. Adapting the procedure for TPB used by Cabooter et al. [18] for an RPLC column, the steps are as follows: 1. Rinse the column with a solvent to dissolve both the hydrophilic and hydrophobic liquids it contains (Cabooter et. al.[18] used isopropanol at 0.2 mL min-1 for 60 min.).

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2. Fill the column pores with a hydrophobic solvent to replace the isopropanol – the hydrophobicity of this solvent will allow it to be retained in the intraparticle pores because of its affinity for the C4 or C18 layer bonded to the pore surface.

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3. Flush the column with a hydrophilic buffer to fill the interstitial space without displacing the hydrophobic solvent contained in the pores (the two substances are immiscible).

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4. Record the mass of the column and repeat the procedure for various hydrophilic interstitial displacement solvents.

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The conditions used here are similar to [18] with the exception of the pumping of the interstitial displacement solvent which we pump at 0.25 mL min-1 for 20 column volumes. This was determined empirically from repeated experiments and discussed further below.

Vi =

𝑚1 −𝑚2

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𝜌1 −𝜌2

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The volume of the interstitial space in the column, 𝑉𝑖 , is obtained as

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Data were collected for several hydrophilic interstitial displacement solvents to compute an average value for 𝑉𝑖 of each column. The same procedure is applied in reverse for a hydrophilic stationary phase and pore blocking solvent and a hydrophobic fluid to flush excess pore blocking fluid.

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The particle pore volume was determined by manipulating Eq 3 to yield an explicit expression for 𝑉𝑝 : 𝑉𝑃 = 𝑉0 − 𝑉𝑖 {6} The total porosity, εT, interstitial porosity, εi, and the intraparticle porosity, εp, are calculated from the total pore volume, interstitial pore volume and intraparticle pore volume by dividing these by the empty column volume respectively. Note that there are two interparticle porosity systems used in practice [26]. The system most often used in chromatography has the total porosity, εT, as the sum of the interstitial porosity, εi, and the intraparticle or particle porosity, εp. In some of the papers referenced here, the interparticle porosity is expressed as those used by 6

chemical engineers, εpCE, and is computed using the relationship εpCE=(εT-εi)/(1- εi). These particle porosities can be converted back to the additive intraparticle porosity used in chromatography through the relationship εp=(1-εi) εpCE. In this paper we use εT = εi + εp.

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To convert the void, interstitial and pore volumes to nondimensional porosity values, the empty column volume 𝑉𝑇 must be known. Two ways to do this include accepting the column dimensions from the tube manufacturer and to measure this volume experimentally. We have performed the column volume determination by measuring the mass of the empty column, filling the column with water using an HPLC pump, measuring the mass and then calculating the mass difference. Dividing this mass difference by the density of water at 294.3 °K, equal to 998.02 kg m-3, gives the volume of the column. The volumes measured here for columns with apparent bore of 2.1 mm and 4.6 mm are 0.1773 cm3 and 0.8414 cm3, respectively, and comprise measurements from three separate columns. The relative standard deviation of these measurements was 0.276% and 0.725% respectively. Assuming the columns are 50.0 mm in length and 2.10 mm and 4.60 mm in inner diameter, the error in volume was 2.40% and 1.26%, respectively. Using the measured volumes of these columns and assuming the length is 50.0 mm, the inner diameters were calculated to be 2.13 mm and 4.63 mm resulting in errors of apparent inner diameter of 1.19% and 0.63% respectively. Because the hardware used to pack these columns was readily known and available, it is feasible to measure the volume of an empty column without having to unpack and clean a packed column. Otherwise, the empty column volume would be estimated by its physical size.

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In all cases, 3 significant digits were utilized for the reported numbers. The pore volume (and porosity) is taken by difference of the total pore (void) volume and interstitial pore volume as given by Eq 6. The standard deviation of the pore porosity is obtained by the square root of the sum of variances of total pore porosity and interstitial porosities divided by the number of samples as is customary for estimating the variation of difference quantities.

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3. Results

3.1 TPB and total porosity experiments

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All data for these experiments is given in the Supplemental Information (SI). This includes Table S1, containing the total pore volume experiment data, Table S2, containing the mass measurements of the pore blocking experiments and Table S3, containing the total pore and interstitial volume error estimates. These data are combined to give the porosity results shown in Table 3. Also given in the SI is the propagation of error equations with values used to estimate the uncertainties of the process. These results indicate a number of important points. First, the total porosity numbers are very reproducible in each set of experiments; these are shown in the SI and are performed in duplicate or triplicate. The interstitial and particle porosities show larger variations in results. The numbers in Table 3 for columns 1 and 4, which are 90 Å SPPs with C18 and HILIC surfaces, can be contrasted with previous studies [27-33] where columns of these particles were also 7

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measured. In the case of the C18 particle, the total porosity average is in the range 0.498 [29] to 0.540 [31] with the exception of 0.45 [33]. This is in contrast to the average of 0.510 obtained here via the mass-based measurement, albeit they are not the same columns, but well within the literature values. The average interstitial porosity of the C18 material in the literature [27-33] is in the range of 0.38 [33] to 0.432 [31] as compared with the 0.375 average determined in this work. The interstitial porosity obtained by the elution measurement of the exclusion marker particle is within 3.2% of this average value and provides a useful comparison between the elution technique and the mass-based TPB method. For column 4, which contains the same basic particle as column 1 without the bonded phase, the average total porosity from mass-based measurements is 0.614, in complete agreement with 0.614 from other sources [28]. The interstitial porosity of the HILIC material is 0.583 from massbased measurements, as contrasted with 0.430 [28]. These values differ by 26% and suggests some systematic effect is driving this, as will be discussed below.

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It is surprising that the presence of a stationary phase makes a difference in the total porosities between the bonded and unbonded particle columns (columns 1 and 4). However, these columns are packed with a different solvent system and the packing protocol is different, so this may explain the difference between these values. The interstitial porosity quoted in the literature, 0.430 [28], is closer to the exclusion marker which gives a porosity of 0.388, however, this value is still in disagreement by ≈9.8%. The elution results of the exclusion particle will be presented below and will be shown to be flow rate dependent. However, the flow rate chosen for these measurements, 0.5 mL min-1, gives reasonable agreement for many of the results given here and is a simple and fast experiment.

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Columns 2 and 3, listed in Table 3, have C18 bonded phases with average pore diameters of 160 Å and 400 Å respectively. Again, the total porosities give reasonably good self-agreement, as judged by their standard deviations, and appear to be reasonable values. The literature value for the total porosity of the 160 Å particle column is 0.563 [29] compared with the value of 0.584 from Table 3, a 3.7% difference. The interstitial porosity from the literature [29] is 0.402 compared to 0.378 from Table 3, a difference of ≈6%. The exclusion marker for this column gives an interstitial porosity of 0.327, a value deviating from the mass-based TPB method by 13.5%.

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In the case of the 400 Å C18 column (column 3), both the total porosity and interstitial porosity (0.529 and 0.391) appear reasonable because this particle has a very thin shell and one would expect that the intraparticle porosity would be particularly small. Unfortunately, there are no literature values to compare these results to, however, the exclusion marker gives a value of 0.403, a difference of 3% with the TPB mass-based measurement showing consistency for these results. The 160 Å HILIC column (column 5) result has a higher total porosity than the bonded result, consistent with the 90 Å bonded and unbonded column values. However, the interstitial porosity for the unbonded column appears to be unreasonably high, noting there are no other literature

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values for this column. The exclusion marker for this column is 0.355, probably closer to the actual interstitial porosity but this is unfortunately hard to ascertain.

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In the case of column 6, the 1000 Å silica (HILIC) particle, the total porosity appears reasonable but the intraparticle porosity is very low. Although this particle type can be compared with the two C4 1000 Å particle columns (7 and 8 in Table 3) which have very similar total porosities, the 1000 Å HILIC column has almost no pore volume. Clearly, it appears that the pore blocking fluid has been displaced by the interstitial displacement fluid here. This is surprising, but may be explained by the sensitivity of pressure and flow velocity when clearing out the excess pore blocking solvent, as explained in the mechanism section below. Note that column 6 has a 4.6 mm inner diameter and columns 7 and 8 have 2.1 mm inner diameters but the total porosity shows little difference. As was mentioned above, our results show uncertain results for the HILIC columns.

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The columns listed as 7 and 8 in Table 3 are from the same lot. As can be seen, the total porosities are close, ≈3.6% different. The interstitial and intraparticle porosities are clearly different here, however, if one exceeded the critical pressure, as outlined in Section 3.3, one would expect the interstitial porosity to be closer to the total porosity, as was the case for column 6. Indeed, these two columns show less interstitial porosity than expected. One possibility is that the interstitial displacement solvent was not effective in clearing out excess pore blocking solvent; either not enough time was given for the clearing process or some physical instability unique to large pore materials occurred. This will be discussed more in the discussion in Section 4.

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Interestingly, the exclusion marker consistently gives an interstitial porosity of 0.371 and 0.367 between the two columns, within 1.1%. Realizing that the 1000 Å , C4 particle columns 7 and 8 did not give reproducible results for the TPB experiments, the TPB experiments were not run in duplicate or triplicate, as indicated in Table 3. The application of the TPB method to wide-pore materials is explained in detail in section 3.3.

3.2 Elution experiments

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As illustrated in Figure 1A and 1B, the injection of 1 μL of uracil as a void marker for column 1, the 90 Å C18 column, and column 7, the 1000 Å C4 column, shows a significant dependence on flow rate which was varied between 0.05 mL min-1 to 0.5 mL min-1. The dependence on flow rate suggests there are diffusion limitations and/or residual charge effects for these two columns. Although these flow variations are relatively small effects, they are present nonetheless and account for 4% variation in the 90 Å pore particle and 2% variation in the 1000 Å pore particle. Nonetheless, these void measurements show large differences with the total porosity determined by the mass-based methods. The total porosity was determined in Table 3 for column 1 by mass measurement as 0.510 and by elution as 0.66-0.687, a surprisingly large difference of ≈26%. The precision of the elution measurements are typically a few percent, so this is not the source of the discrepancy. 9

For the 1000 Å pore C4 particle, the total porosity was measured by mass as an average of 0.574; the elution experiment gave  0.844 at the lowest flow rate (0.05 mL min-1), 32% in disagreement shown in Figure 1B. The physical mechanism to explain this discrepancy may be due to solvent flow in the intraparticle pore space among other explanations; this is discussed further in the Discussion section. In the absence of salt it is shown that even at a much lower flow rate the elution method is in large disagreement with the mass-based measurement.

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Three studies, one simulation [34] and two experimental [35, 36], have explored the concept in detail of an enriched acetonitrile concentration at the bonded phase-solution interface. If uracil was excluded from this interfacial region, the porosity measured would be expected to decrease, not increase, as this exclusion process would favor a reduced retention volume compared to a fully accessible pore space. Comparing the total porosity results obtained by mass with the elution experiments shows that both uracil elution experiments in Figs 1a and 1b give higher total porosities. A more likely explanation is that these higher porosities are caused by retention of the uracil on accessible silanol groups of the silica packing material. This increase in retention volume would cause an increase in porosity and this explanation is probably the most likely cause of the disagreement between the elution study and the mass-based total porosity.

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The flow rate dependence of the colloidal particle, used as an exclusion marker, without salt in the buffer, is shown in Figure 1C for column 1. The retention volume and porosity increase with increasing flow over a range of 12.5%. If one extrapolates to zero flow, assuming a linear relationship, the resulting interstitial porosity would be 0.31 which would be in error compared to the TPB value obtained here. No attempt was made to correct for the finite size of the particle.

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The addition of salt for the experiment illustrated in Figure 1C showed a large increase in retention volume and hence interstitial porosity for the latex particle. This suggests that the carboxylic acid electrostabilization mechanism preventing aggregation of these particles was modified and the particles were possibly salted out and interacting more with the chromatographic particle or with themselves. This is one of the reasons that mass-based measurements provide an attractive alternative to elution measurements. In addition, any streaming potential, caused by solvent flow past a charged interface, are totally out of play with mass-based measurements as is any artefact from hydrodynamic interactions on the chromatographic particle’s surface. The data shown in Figure 1 are given in the Supplemental Information. 3.3 Critical pressure mechanism

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The fluid mechanics of the pore blocking method closely resembles the displacement and replacement of a wetting fluid by a non-wetting fluid in porous media [37-41]. Applications related to fluid replacement in a porous medium include soil remediation [42] and oil recovery with pumped fluids [43, 44]. The petrochemical applications of this displacement process are obviously of great importance. A closely related problem of chromatographic significance is the loss of retention when a pure water solvent is utilized with a reversed-phase column after depressurization [45].

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A nonwetting fluid can invade a pore filled with a wetting fluid when the driving pressure exceeds the capillary pressure pc, also called the “threshold pressure” [37-41, 46, 47]: pc = pnw - pw

{7}

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where pnw and pw are the pressures needed to drive the non-wetting and wetting fluids into a pore, respectively. The capillary pressure is a measure of the porous media’s ability to fill with the wetting fluid or to expel the non-wetting phase [37]. These two fluids are considered to be immiscible in this treatment. The capillary pressure may be expressed using the Young-Laplace equation [37, 39, 40, 44, 48, 49]: pc = γ (1/r1 + 1/r2)

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pc = 2 γ cos  rc-1

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where γ is the interfacial tension between wetting and non-wetting fluids and r1 and r2 are principle radii of curvature of the interface. Replacing the radii of curvature in Eq 8 with a mean radius of curvature, rc, [40] and assuming a spherical interface between two fluids with a finite contact angle gives the usual form of the capillary pressure:

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where  is the contact angle between immiscible fluids. Different forms of Eq 9 are available for different geometries, although these forms are more complicated. A more accurate geometry for this problem is that of intersecting and neighboring spheres [50], however this would greatly complicate the simple form of Eq 9.

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The contact angle for a wetting fluid is < 90°, and is 0° for a fully wetting fluid [51]. Spontaneous pore filling occurs with fully wetting fluids. A non-wetting fluid will reside in the pores above the capillary pressure. This is the case for pure water residing in hydrophobic pores bonded with C18 and well-known to chromatographers [45].

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Notice that cos  is positive for  < 90°. The pressure with which the pore blocking fluid will be displaced by the (immiscible) solvent is the capillary pressure. For a non-wetting fluid, the contact angle at the pore surface is typically > 90°, with extreme values being   120° for water contacting a fluorinated surface [52]. In this case cos  is negative. Note that pc can be positive or negative depending on the curvature of the interface.

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The two pertinent cases of interest here include the forced filling of a pure silica pore by hydrophobic alkane solvents for HILIC phases where water is used as the pore blocker and the wetting of alkyl chain bonded-phases with pure water when a hydrophobic species is used as the pore blocking fluid. The interfacial tension of an octane/water interface is reported as 51.16 mN m-1 [53] at 25.0 °C and 52.5 mN m-1 [54] at 22.0 °C. The values for the decane/water interfacial tension are similar within a few percent [53, 54]. The contact angles relevant for understanding water adsorbing on a hydrophobic surface include water on a paraffin surface of  = 110.6° [55] and water on an octadecyl trichlorosilane-modified Si wafer giving  = 109° [56], although a

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host of surfaces used in water adsorption studies [56] show a variety of contact angles with water that are highly dependent on the surface material.

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For a hydrophilic pore wall like bare silica, the wetting of the pore by hydrophobic fluids like octane is a somewhat different story. This is because for a freshly prepared silica, which has been cleaned by elevated temperature and outgassing, a hydrocarbon will adsorb on the surface [57] to some small degree. However, under chromatographic conditions, silica is well known to maintain a tightly held water layer at the surface [58-61], and this will cause a non-wetting surface to develop for medium to large alkanes under normal aqueous solvent conditions.

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Some examples using Eq 9 are shown in Figure 2 to illustrate the effect of pore diameter on the capillary pressure needed to replace the pore-wetting blocking fluid with the clearing solvent for both hydrophobic and hydrophilic cases discussed above. The interfacial tension mentioned above is held constant and the contact angle varied with  = 110° in the middle. In addition, contact angles of lower ( = 100°) and higher ( = 120°) hydrophobicity are shown. Two other curves are also shown with higher and lower interfacial tension.

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Figure 2 shows that substantially higher pressure needs to be applied to displace the pore blocking fluid with 90 Å particles than with larger pore size particles. This suggests that the TPB method is more reliable for small-pore materials; if larger pressures are utilized. With wide-pore particles the pore-blocking fluid may be displaced easily by a low pressure.

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An important and practical aspect of this plot is that the velocity of the clearing process, where a non-wetting fluid removes the excess pore blocking solvent, is critical because it determines the capillary pressure in the column given in Eq 9. Too high a velocity and the pore blocker will be displaced, thereby washing it out. The pressure is related to flow velocity (and flow rate) using Darcy’s law [37-40] for single-phase fluid transport: 𝑣̅ = - (k / μ) ∇p

{10}

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where k is the column permeability, μ is the viscosity, 𝑣̅ is the average velocity in the packed bed and ∇p is the pressure gradient driving force for fluid flow in the column. This equation shows that the fluid velocity and pressure gradient are linearly related so that higher velocity will require higher pressure. Conversely, Eq 10 can be rearranged to express the pressure as a function of the velocity. Hence, the pressure at the column head, which is measured by the pump pressure transducer, is adjustable through the flow rate (and average velocity). Thus, it should be possible with these equations to optimize the minimum velocity necessary to ensure the capillary pressure is not exceeded, although pressure is easily monitored and may be directly viewed so that it is not exceeded as flow rates are adjusted. Figure 2 also shows the critical nature of using larger pore materials with the TPB method. It doesn’t take much pressure with large pore materials to displace the pore blocking fluid. Hence, these must be run with the lowest pressures possible and consequently very small flow rates (and velocities). This will dictate the time necessary to clear the excess pore blocking solvent from a large pore particle; this can be very long as the pressure must be exceedingly small or else the 12

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method will fail due to disturbing the pore blocking fluid in the pore. Under the conditions run here for the large pore (1000 Å materials) the pressure was always near or above the critical pressure shown in Figure 2; reducing this pressure results in a very long time for flowing the clearing solvent. It must also be realized that the column pressure decreases through the length of the column and so the critical pressure may be exceeded at the column head but be below this pressure at some length down the column. Hence, some of the pore blocker fluid may be displaced at the head of the column but be held in place some distance along the column length. A discussion of the effective pressure along the column length and the applicable pressure for wettability is given in the Supplemental Information.

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These equations are simplistic for a number of reasons now discussed but overall show the magnitudes of numbers which should pertain to the TPB process. First, when a less viscous fluid displaces a more viscous fluid, such as when water displaces octane (the viscosity of octane is 5.195 x 10-5 Pa.s [62]) the liquid-liquid interfacial region becomes unstable and produces viscous fingering [63, 64]. In addition, “Haines jumps” [40, 41] occur due to kinetic effects where droplets are ejected in almost random collections as a result of interfacial instability and nonuniform pore effects. Furthermore, “snap off” effects [40] occur when a nonwetting fluid loses contact with the wall. These effects occur due to flow; using a mass-based approach to interstitial pore volume measurement can minimize these extra effects, but not eliminate them, since the pore filling occurs under flow. Hysteresis effects [37-41] are also known to occur where the repeated cycling between pore wetting and dewetting gives changing results. Hysteresis is thought to occur due to surface contamination, surface roughness and surface liquid immobility [40, 48]. Finally, all particles used in packed bed chromatography have pore size distributions; the pore diameters, which are not some ideal shape such as a cylinder, have a distribution and the average diameter is that which is usually reported.

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4. Discussion

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The use of TPB techniques for porosity measurements is wrought with difficulties but can return potentially valuable information if a number of variables are recognized and controlled. The results of the mechanism study show that wide-pore materials will be the most difficult because even a small pressure will purge the pore blocker out of the particle with the clearing solvent. The clearing process is the critical step in all of the samples that were run here. For pores in excess of 400 Å, the fluid pressure will probably be too high to leave the pore blocking fluid intact when clearing out the residual amount of pore blocking fluid. One way to access this is to utilize an extremely small flow rate (and accompanying pressure) for samples of this nature. Another way to do this is to monitor the effluent for any signs of the pore blocking fluid. In other TPB studies utilizing HPLC-based measurements, the detector signal indicated when the flushing step was complete, but does not indicate if the pore-blocking fluid remains in the pore. The results in this paper do not correct for the effects of liquid compressibility. Compressibility of the mobile and stationary phase has been discussed in liquid chromatography [65] and although liquids are generally thought of as incompressible, at pressures of less than 200 bar, which is well within the pressures used in these experiments, the change in volume from this pressure would be typically 2.4% for octane and 1% for water. Compensation for 13

compressibility in the TPB method was discussed in [23] where the authors show this effect does affect results by a few percent. However, as pointed out in [23] there is uncertainty in describing the location and geometry of the pore blocker-interstitial solvent interface. Therefore, we expect a small error from not compensating compressibility effects explicitly in the TPB method.

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The HPLC elution data show systematic variation, and it is well-known that this method is not a reliable method for determining total porosities. However, it is interesting to speculate that a large overestimation of the wide-pore material interstitial porosity may be due to flow through the particle [50] which has been calculated from models. Other problems with determining total, interstitial and intraparticle porosity for large pore particles are unique: the dividing surface between what is a pore and what is interstitial space is not defined for any porous particle [50]. The physical manifestation of a dividing surface in the TPB method is the meniscus at the interface between immiscible fluids, and the geometry of this is highly dependent on contact angle and the pore shape. This is an interesting area of research as characterization of wide-pore materials is a challenging area that still offers room for innovation. There is room for innovation with the TPB method, but its limitations become clear with the physical insight discussed above on the mechanism of pore filling with respect to pressure and pore size.

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The results from the HILIC columns reported here appear to have a systematic error. These are understandable for large pore materials, as discussed above, however, the smaller-pore HILIC materials did not appear to work with this method. This may be due to the wettability of the silica and any pretreatment of the surface, e.g. surface silanol activation. The TPB method was extended to hydrophylic (i.e. normal phase) particles [20], and used for small pore silica surfaces [28], however, this method has not been widely used. This is an area of further research in determining if the TPB method, with either the mass-based or HPLC-based method can explain these results.

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There are a few problems that are evident with any mass-based technique. The most dominant is that one is measuring small differences between large values and this can cause many accuracy and precision problems. Using a high resolution balance is absolutely mandatory for this type of method. Furthermore, precise handling of the column after filling is required and this procedure is one of the critical steps. The columns were always handled with gloves and connecting tubing was carefully attached in a jig to facilitate handling. Any loss of solvent before sealing the columns prior to weighing is critical and further innovation here is necessary. Some pressure variations are found depending on which end of the column is used as the filling end; we have marked the columns which show the filling end to consistently get the same pressures and this is the same column end as specified by the column manufacturer for use as the column head for elution chromatography. One interfacial instability mentioned previously, viscous fingering [63, 64], is usually found when a less viscous fluid displaces a more viscous fluid resulting in “finger-like” threads of solvent at the fluid-fluid interface. For the case of columns 7 and 8, the interstitial porosity was found to be lower than expected. The interstitial displacement fluid is water (more viscous than octane) and so the formation of viscous fingers is not expected. However, the wide-pore materials exhibit some intraparticle flow [50] and this could cause an instability if the interstitial 14

displacement flow of the water induces the octane to be driven out causing fingering in the interstitial space. Another and perhaps more likely possibility with these wide-pore materials is that they tend to interlock at the outer sol layers [50]. This may cause a continuum of pore blocking fluid around the particle-particle contact points and decrease the accessibility of the effective interstitial volume. This idea is speculative and requires a visualization technique to verify this possibility.

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The bonding density and character of the stationary phase are also important considerations in evaluating the suitability of the TPB method for porosity measurement. If the density of the bonded phase is lower than some critical density, one would expect significant amounts of a mixed surface. In this case the TPB method may give erroneous results. Mixed surface functionality, or so-called “mixed-mode” phases [66-68] which may include a mixture of hydrophobic and hydrophilic phases, could require more sophisticated TPB solvents to function properly.

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The method reported in this paper has the convenience of using only a high-accuracy balance and an HPLC pump. This method does not tie up a complete HPLC instrument for the time necessary for the TPB experiments. In most laboratories, HPLC instruments are utilized in an almost continuous manner through the use of autosamplers and work flow management software. Being entirely a static method, the implementation costs of this mass-based measurement are relatively low.

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The conditions used for determining the length of time for column filling were determined from literature values, with the exception of the time for pumping the interstitial displacement solvent. Using an HPLC detector for endpoint determination is an advantage in locating the time when excess pore blocking solvent is no longer pumped out. However, since these fluids typically don’t absorb in the UV, one is monitoring something related to the refractive index, not a true concentration. Our belief is that one would not expect these times to vary over a wide range of particle values. The choice of conditions was verified by the agreement with literature values and consistency, for at least the smaller pore particles and hydrophobic stationary phases. The ultimate reliability with all of these methods is perhaps determined by agreement with other methods such as microscopy. However, microscopy, perhaps the most accurate method, is a destructive method, hence our belief in further development of the TPB method as a reliable, non-destructive technique for the determination of interstitial and intraparticle porosity is justified.

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The exclusion marker results agree in most cases, but not all, with the interstitial porosities determined by the mass-based TPB method. This appears to be a good consistency check with the TPB method in general. However, the results for the wide-pore particle columns may be questionable because the pore size distribution is wide enough with these particles that some penetration of the microsphere is possible. The ISEC method, although time consuming and not free of problems, seems to be the most readily adopted to making accurate measurements of porosity. However, its use, although amenable to automation with an autosampler, may still have problems with wide-pore materials 15

because finding excluded materials may be difficult if not impossible; many high molecular weight solutes have non-ideal behavior in the vicinity of particles like hydrodynamic and slalom chromatographic modes [69] and these can complicate the ISEC data interpretation.

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As pore sizes of analytical chromatographic particles increases, it may be practical to utilize focused ion beam-scanning electron microscopy (FIB-SEM) [70-73] to determine the particle porosity directly through image slice analysis at the pore level. Both improved sample preparation methods and advances in software processing for FIB-SEM slice data will promote this development.

Acknowledgement

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The support of the National Institutes of Health under grant R44-GM108122-02 is gratefully acknowledged. This paper is in partial fulfillment of the Senior Thesis research of Nicole M. Devitt within the department of Chemical and Biomolecular Engineering at the University of Delaware. We thank Tom Waeghe (MAC-MOD Analytical, Chadds Ford, PA) for his literature database of SPP porosity measurements.

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References

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Figure 1. Void marker results using uracil for total porosity of A: column 1 B: Column 7 C: Exclusion marker results using 0.1 μm carboxylated latex particles for column 1.

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Figure 2. The effect of pore diameter on the capillary pressure needed to force the non-wetting fluid into the pore. The conditions for each curve are shown in the legend. The pore diameters of 90 Å, 160 Å, 400 Å and 1000 Å are delineated by dashed vertical lines.

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N U SC RI PT Solvent

Tracers

Pore Blockers

Thermo Hypersil

Hydrophilic buffer

Uracil Thiourea KI

Cyclohexane Octane Decane

A

Particle

C18, 175 Å

Hypersil Gold

C18, 175 Å, 5μm

NaNO3 Hydrophilic buffer

KI

A

CC E

PT

Liekens et. al.19

Column

ED

Author Cabooter et. al.18

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Table 1. Summary of TPB methods in the literature. The tracers and pore blockers listed are those tested and do not necessarily correspond to pairs. The surface phase, average particle size (in micrometers) and the average pore size (in Å) are given under the Particle column.

C9 C10 C12 C18,175 Å, 19μm

Hydrophilic buffer

KI

C10

Zorbax

C18, 80 Å, 5μm

Hydrophilic buffer

KI

C10

X Bridge

C18, 300 Å, 5μm Silica, 80 Å, 5μm Silica, 94 Å, 5μm C18, 175Å, 1.9μm

Hydrophilic buffer

KI

C10

See note

C10 Hydrophilic buffer

Zorbax Rx-SIL Sunfire Prep

Cabooter et al. 21

C8

Hypersil Gold

Liekens et. al. 20

C7

Hypersil Gold

C12 Hydrophilic buffer

Water KI

C10 24

Gritti et al. 23

Luna (Phenomenex) Jupiter (Phenomenex) Gemini (Phenomenex)

C18, 95 Å, 5μm (stripped particle) C18, 100 Å, 3 μm C18, 320 Å, 5 μm C18, 110 Å, 5 μm

Hydrophilic buffer

KI

C10

Hydrophilic buffer

KI

C10

Hydrophilic buffer

KI

C10

See note

C10 Hydrophilic buffer

Water

NaNO3

C9

Water

NaNO3

C9

Water

NaNO3

C9

ED

Gritti et al. 24

Zorbax Eclipse Plus

N U SC RI PT

Song et al.22

A

Zorbax

M

Acquity BEH

C18,135Å, 1.7 μm C18, 80 Å, 1.8 μm

A

CC E

PT

Sunfire (Waters) C18, 90 Å, 5 μm Water NaNO3 C9 Note: Refer to [18] for more information on the use of aromatic, cycloalkane, and aliphatic markers for tracer molecules. The hydrophilic buffer contains ammonium acetate as discussed in [19].

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ID

number

(mm)

(mm)

phase

Pore size (Å)

1

2.1

50

C18

90

2

2.1

50

C18

160

3

2.1

50

C18

400

4 5 6

2.1 4.6 4.6

50 50 50

HILIC HILIC HILIC

90 160 1000

7

2.1

50

8

2.1

50

ED

Length Bonded

M

Column

A

Table 2. Column specifications where the abbreviations ID and HILIC are inner diameter and hydrophilic interaction liquid chromatography, respectively.

1000

C4

1000

A

CC E

PT

C4

26

N U SC RI PT

Table 3. Total, interstitial and particle porosity measurements from pore blocking experiments. The interstitial porosities obtained by elution of the 0.1 μm exclusion marker particle are given in brackets [ ], except for column 6 which was not performed. Note that standard deviations for the porosities in this table were calculated from duplicate or triplicate measurements except for columns 7 and 8. Column 1 2

Type1 2.1x50 90A C18 2.1x50 160A C18

Total Porosity (εT) 0.510 ± 0.00530 0.584 ± 0.00359

3

2.1x50 400A C18

0.529 ± 0.00566

4

2.1x50 90A HILIC 4.6x50 160A HILIC 4.6x50 1000A HILIC 2.1x50 1000A C4 2.1x50 1000A C4

0.614 ± 0.0116 0.644 ± 0.00231

0.587 ± 0.000420 0.563 ± 0.0559 0.584 ± 0.0268

0.582 ± 0.00105 _ 0.252 [0.371] 0.329 [0.367]

0.00470 ± 0.000800 0.312 0.255

ED

M

A

Particle Porosity (εp) 0.135 ± 0.0582 0.206 ± 0.0964 0.138 ± 0.0446 0.0310 ± 0.0155 0.0475 ± 0.0112

A

CC E

6 7 8

PT

5

Interstitial Porosity (εi) 0.375 ± 0.100 [0.363] 0.378 ± 0.136 [0.327] 0.391 ± 0.0628 [0.403] 0.583 ± 0.0187 [0.388] 0.596 ± 0.0156 [0.355]

27