19 Table 1. Designed specifi cations of printed columns


Overlap Factor α


1.40 1.45 1.50 1.55


Design porosity ε


0.575 0.538 0.500 0.463


Design void volume VVOID


(ml)


1.150 1.076 1.000 0.926


Materials and Methods


CAD Models As shown in Figure 2a, CAD models comprising a full column including integrated end fi ttings, fl uid distributors and column walls were created in a single stereolithography (STL) fi le using SolidWorks 2012 (Dassault Systèmes). STL fi les defi ne the external surfaces of the CAD model as a set of adjacent triangles. It is worth noticing that fewer triangles are necessary to defi ne the external surface of an octahedron than a sphere, hence the computational challenges of producing a full column are dramatically reduced if octahedral elements are chosen instead of spherical beads. For example, a 20.6 ml column containing 106


octahedral beads would result in a 1.9 GB CAD fi le whereas a column containing an identical number of spherical beads would increase the fi le size by a factor of 252, i.e. around 500 GB, well beyond the processing capabilities of most 3D printing software. This observation is increasingly important for columns having larger volume. For this reason octahedral beads were chosen over the more intuitive spherical beads.


Specifi c Surface Area S-1


(mm-1


9.39 9.97


10.55 11.13


)


µm was found to be the lowest octahedron size that the printer could reliably create using a commercial acrylonitrile butadiene styrene (ABS) printing material (VisiJet®


X, 3D Systems,


Rock Hill, SC, USA). The printed columns thus contained beads with apothems of 115 µm. A minimum overlap factor of α = 1.40 was chosen because it was determined in initial experiments that this was the minimum required to ensure structural robustness in the packing structure (data not shown).


Residence Time Distribution Tests


To assess the fl ow properties of the printed columns, an ÄKTA Explorer10™ FPLC system equipped with an auto-sampler (GE Healthcare, Uppsala, Sweden) was used. Residence time distribution (RTD) tests were conducted by fi rst equilibrating the 3D printed columns with 10 column volumes (CVs) of pure water, followed by a 30 µl injection of 1 M NaCl. The concentration profi le was measured by monitoring the conductivity signal of the outlet stream. All tests were performed at a fl ow rate of 10 ml/min, corresponding to a superfi cial velocity of 298 cm.hr-1


. The mean residence volume, µ1, the variance, σ2 the skewness, ϒ1 , of the RTD profi les were calculated using the moment method:


where κ is the conductivity measurement and v is fl ow volume. The dimensionless residence volume, θr


exp, was calculated as follows: , and


(5) so their contribution to the fi rst moment (µ1


where VVOID is the designed void volume. Other volumes in the system were less than 4% exp


) was neglected. θr is an indicator of the


quality of the printed chromatography columns. In fact, a dimensionless residence time close to unity indicates both good control over particle shape at the printer’s limiting resolution, and good positional accuracy of the 3D packing elements in the lattice.θr


exp is


extremely valuable to assess the printing quality of packed bed columns, and is sensitive to subtle changes in the key geometrical parameters, including the overlap factor. For example, the differences in porosity across the four columns studied in the present work were relatively small, with a 7.5% change in porosity for each 0.05 increment in α. Even small errors in printing of the beads would make the four columns indistinguishable in their fl ow characteristics and chromatographic performance.


Results and Discussion Geometrical Analysis


Figure 2. (a) CAD model of chromatography column including end fi ttings, column walls, fl ow distributors and column packing. (b) An individual layer in simple cubic packing with a cylindrical cut.


In randomly packed chromatographic beds, the local porosity and local HETP along the column walls are not consistent with the bulk/overall properties of the column, particularly because of the physical constraints posed by the column walls on the arrangement of the packing elements. This problem was eliminated using 3D printing by creating partial beads with the same confi guration as the rest of the packing, as seen in Figure 2b. This means that the local porosity along the column walls was identical to that of the bulk packed bed. To measure the degree of overlap between two particles, an overlap factor, α, was introduced as a new geometrical parameter. This is simply defi ned as the ratio between the actual distance between the centres of two adjacent beads, Dact


, and the maximum


possible distance between their centres if their vertexes are just touching, Dmax (1)


Figure 3 shows the range of porosities that can be obtained by designing lattices characterised by different overlap factors. The overlap factor is a convenient parameter to control, as it directly infl uences the porosity, while maintaining the same packing confi guration, and consequently the same extent of radial and axial dispersion in the bed.


In this study, we compared four columns with overlaps factors of α = 1.40, 1.45, 1.50 and 1.55 (Table 1). The designed porosity for these packing is in the order of 0.6, namely the range of porosities usually found in randomly packed columns. The printed columns had an internal diameter and a wall thickness of 16 and 2 mm, respectively, and radial fl ow distributors and collectors were integrated at the inlets and outlets of the printed columns. The total column volume was kept constant at 2 ml (corresponding to a column height of 9.95 mm), meaning that void volume of each column varied with α.


Column Production and Post-Processing


The four columns were printed on a 3DS Projet HD 3500 printer (3D Systems, Rock Hill, SC, USA). In addition to the four whole columns, equivalent ‘cutaway’ pieces containing packings with the four tested overlap factors were printed for geometrical analysis. To support the overhanging features in the columns, paraffi n wax is used as a support material during the printing process. The supporting wax was removed using an alternating series of cyclohexane and water baths at 70o


C.


The nominal resolution of the 3D printer is 29 µm, however both the surface fi nish and positional accuracy of the 3D printer are dependent on several parameters, such as printing material, local temperature and relative humidity. A bead apothem of approximately 115


Figure 3. The effects of bead overlap on extra particle porosity in a simple cubic packing confi guration. The vertical bars identify the range of overlap factors investigated in the present study.


Figure 4 shows optical microscope images of the octahedral packings manufactured with different overlap factors. It is apparent that the beads are largely octahedral in shape and that the packing arrangements are highly ordered, similar to a range of packings we reported previously [7]. It is worth noting that features such as build size, orientation and materials could potentially result in imperfections in the printed part (as seen in the lower right hand side of Figure 4c, for example). Fine control of the lattice shape was confi rmed though geometrical analysis of the microscope images, as summarised in Table 2. The results from the geometrical analysis of these cutaway samples are consistent with design specifi cations of both bead and pore sizes, with a mean error of 2.4%, showing that 3D printing can create columns with only subtle differences in column packing parameters. It can reasonably be assumed that the whole columns printed would display similarly good fi delity with the CAD models.


Residence Time Distribution Profi les


Normalised residence time distribution curves of two printed columns are shown in Figure 5, where κ represents the normalised conductivity readings (i.e. conductivity data normalised to obtain a unit area under the curve). The peak maxima of the curves depend on the degree of overlap, consistent with expected extra-particle porosity. Figure 6 shows the comparison between theoretical (designed) and experimental residence times for the four columns tested, while Table 3 summarises the results obtained from the moment analysis.


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