We have designed and constructed a temperature-controllable shear flow cell for in-situ study on flow alignable systems. The device has been tested in the neutron diffraction and has the potential to be applied in the small angle neutron scattering configuration to characterize the nanostructures of the materials under flow. The required sample amount is as small as 1 ml. The shear rate on the sample is controlled by the flow rate produced by an external pump and can potentially vary from 0.11 to 3.8 × 105 s−1. Both unidirectional and oscillational flows are achievable by the setting of the pump. The instrument is validated by using a lipid bicellar mixture, which yields non-alignable nanodisc-like bicelles at low T and shear-alignable membranes at high T. Using the shear cell, the bicellar membranes can be aligned at 31 °C under the flow with a shear rate of 11.11 s−1. Multiple high-order Bragg peaks are observed and the full width at half maximum of the “rocking curve” around the Bragg’s condition is found to be 3.5°–4.1°. It is noteworthy that a portion of the membranes remains aligned even after the flow stops. Detailed and comprehensive intensity correction for the rocking curve has been derived based on the finite rectangular sample geometry and the absorption of the neutrons as a function of sample angle [See supplementary material at http://dx.doi.org/10.1063/1.4908165 for the detailed derivation of the absorption correction]. The device offers a new capability to study the conformational or orientational anisotropy of the solvated macromolecules or aggregates induced by the hydrodynamic interaction in a flow field.

Flow-induced deformation and orientational anisotropy of macromolecules (or aggregates) are important not only in fundamental physical science but also in many practical applications. A common example is the reduction of viscosity of a polymer solution under increased shear strain rate, known as “shear thinning.” The variation in rheological response thus provides a methodology for indirect measurement of molecular conformation under flow. In the past, microscopy was also commonly used for direct observation of deformation of micron-sized molecules (e.g., DNA2,3) or flow-induced anisotropy.4–9 

In regards to direct measurement of in-situ nanoscale structures in flow, neutron scattering turns out to be one of the most powerful methods. Several advantages of using neutrons as a probe are evident. First, neutrons can penetrate common materials except for few elements (such as H, B, Li, Cd, and Gd), thus allowing the construction of sample environment using metals like stainless steel, Al, Cu, and Si. The flexibility to vary contrast of a system presents another advantage in neutron scattering. Since the neutron scattering length of isotopes can be very different, e.g., −3.741 × 10−15 m and 6.671 × 10−15 m for H and D, respectively, we are able to enhance (or decrease) the scattering intensity by isotope substitution, without significantly varying the chemical properties of the systems.

The most common shear flow device employed in neutron scattering experiments is Couette flow cell,10–21 which adapts a concentric double-cylindrical configuration with the examined sample loaded in the gap between the cylinders. The shear flow is obtained by having one of the cylinders stationary and the other rotating and the shear rate can be determined by the distance of the gap and the rotating speed. The neutron beam can pass through the annulus either tangentially or radially. The scattering planes in the tangential and radial configurations are perpendicular to the flow direction and the shear gradient axis, respectively. It should be noted that the small angle neutron scattering (SANS) patterns of the samples tested in a Couette-type flow cell are usually smeared. The detected intensity is a combination of scattering from the sample subjected to the azimuthally misaligned flows. Moreover, in the radial configuration, the two scattering centers are apart by the average diameter of the two cylinders, while in the tangential configuration, the path length of the beam through the sample appears to be longer—both causing the smearing of the data. A recent development to mitigate such smearing effect is established with the incident beam going through the vorticity direction, where the SANS pattern is projected on the velocity (v)–velocity gradient (Δ v) plane.8,15,16,22–25 However, the application of Couette cells on high resolution diffraction studies remains a challenge.

It has also been reported that parallel-plate shear devices can be used in neutron or x-ray scattering or diffraction.23,24,26–31 Based on the concept, an in-situ, temperature-controlled continuous-flow device is designed and built for both in-plane and out-of-plane neutron scattering experiments. In this report, we mainly focused on the out-of-plane diffraction; the in-plane scattering can be achieved by rotating the device to 90°. The basic concept of design is to create a laminar flow between two parallel plates set apart by a narrow gap. The shear strain rate is proportional to the flow velocity and inversely proportional to the gap distance. The scattering signal is enhanced by using multiple adjacent parallel flow channels divided by single-crystal Si (111) wafers, while the flow is created by an external pump. The required sample amount is less than 1 ml including the exterior loop. To control the temperature, the device is sandwiched between two Al-jackets (at top and bottom), through which the thermostatic fluid (coolant) circulates continuously.

In this report, we validate the flow device using a lipid mixture, which has been reported for its alignability in solution under both magnetic32 and flow field33 previously. This mixture is composed of a long-chain dimyristoyl phosphatidylcholine (DMPC), a long-chain dimyristoyl phosphatidylglycerol (DMPG), and a short-chain dihexanoyl phosphatidylcholine (DHPC) with a DMPC:DMPG:DHPC molar ratio of 2.88:0.32:1.0 and a total lipid concentration of 20 wt. %. It has been reported that this mixture has a phase transition from non-alignable nanodiscs to alignable perforated lamellae as the sample temperature increases from low T [below the melting transition temperature of the long-chain lipid, TM (∼24 °C for DMPC)] to high T (e.g., above 30 °C). Diffraction curves at different temperatures, where nanodiscs or perforated lamellae exist and rocking curves at quiescence or under flow were collected. The results indicate that aligned lamellae (with a full width at half maximum of the alignment angle distribution, FWHM ∼4°) in the solution are achievable under a shear flow with a shear rate of ∼11.11 s−1, which is consistent with the previous report.33 This device enables in-situ nanostructural characterization under shear flows, thus allowing us to elucidate the structure-property relationship in solutions containing aggregates or polymers once the rheological parameters are measurable (currently under development). The knowledge will provide new insights to the fundamental understanding of hydrodynamic interaction in these systems.

Fig. 1 shows the design scheme of the shear flow cell, which is an I-shape Al block [yellow part in Figs. 1(a), 1(c), and 1(d)] of a dimension 40 mm × 16.5 mm × 25.4 mm with a centered rectangular opening of a dimension 40 mm × 2.1 mm × 10 mm. The interior faces of both 2.1 mm sides have four highly parallel, vertical trenches (each 0.3 mm wide and 0.5 mm deep) spaced equally by 0.3 mm, for the insertion of the rectangular Si (111) wafers (40 mm × 11 mm) as shown in Fig. 1(a). Si (111) wafers were carefully chosen and examined to show no low-q reflections prior to the study. As a result, three parallel channels are constructed in the gaps between wafers [Fig. 1(b) shows the top view from plane (1) at Fig. 1(a)]. Shear flow then happens as the sample is pumped through the vertical channels and the strain rate can be controlled by the flow rate. The incident neutron beam goes through from the planes (2) and (3) [Fig. 1(a)] (the enlarged images of planes (2) and (3) are illustrated at Figs. 1(c) and 1(d)) for the out-of-plane and in-plane configurations, respectively, where scattering plane is always perpendicular to the flow direction (see Fig. 2). To control the sample temperature, we use top and bottom Al blocks [green parts in Fig. 1(a) and blue parts in Figs. 1(c) and 1(d)] with internal channels for the circulating coolant, whose temperature is controlled by an external water bath, to sandwich the shear cell. O-rings between the T-controlling blocks and the shear cell ensure perfect sealing [Fig. 1(b)]. Sample enters and/or exits shear-flow cell through four identical injection ports aligned with the Si wafers inside [Figs. 1(a) and 1(c)] and follows to a small sample reservoir compartment (1 mm × 10 mm × 2.1 mm) to ensure an isotropic flow of sample through parallel channels and to improve its temperature equilibration. Outside the T-controlling blocks, each injection port connects through the tubing, which goes to a peristaltic pump (Masterflex L/S from Cole-Palmer) and then to the injection ports of the other block to form a closed loop. Sample can be pumped into the shear cell at a constant speed (from 0.001 to 3400 ml/min, equivalent to the range of shear rate for Newtonian fluids from 0.11 to 3.8 × 105 s−1 based on the sample geometry) unidirectionally or oscillationally (i.e., switching flow directions at a constant frequency). However, the strain rate of oscillatory flow also depends on the switch speed of the flow direction which is beyond the focus of this study.

FIG. 1.

The design of temperature controllable shear cell.

FIG. 1.

The design of temperature controllable shear cell.

Close modal
FIG. 2.

The designed mount for the shear cell to be installed on a neutron spectrometer.

FIG. 2.

The designed mount for the shear cell to be installed on a neutron spectrometer.

Close modal

Fig. 2 illustrates the designing scheme for mounting this unit on a rotating sample table at the sample stage of a neutron spectrometer, where the complete assembly of the shear cell is also shown at the left upper corner The unit is attached to the bottom of a disk (with a diameter of 50.8 cm), which is supported by four posts to provide a correct height with respect to incident neutron beam. The allowable rotating range of the sample angle is around 80° (i.e., ±40°) in both in-plane and out-of-plane configurations beyond which the posts would interfere with the incident neutron beam. Fig. 3 shows the photo of the whole unit as installed at the sample stage of the neutron spectrometer. The whole unit is then located on an X-Y-Z translation stage for a fine adjustment of the position of the shear cell.

FIG. 3.

Photographs of the device: (a) the side view of the shear cell as attached to the mount and (b) the top view of the whole unit (including the pump) installed at the sample stage of the N5 neutron spectrometer.

FIG. 3.

Photographs of the device: (a) the side view of the shear cell as attached to the mount and (b) the top view of the whole unit (including the pump) installed at the sample stage of the N5 neutron spectrometer.

Close modal

The neutron diffraction, ND experiment was conducted at N5 triple-axis neutron spectrometer adjunct to the National Research Universal (NRU) reactor located at Chalk River Laboratory (CRL). This neutron scattering facility is managed by the Canadian Neutron Beam Centre (CNBC). The neutrons from the NRU first passed through a sapphire filter to eliminate most of the fast neutrons. The wavelength of the neutrons, λ, was selected by a pyrolytic graphite (PG) crystal (50 mm × 89 mm × 1.6 mm) using (002) plane set at 20.69° to diffract neutrons with λ of 2.37 Å and its high-order harmonics (i.e., λ/2, λ/3, etc.). The selected neutrons were then collimated by a single channel collimator to yield a beam size of ∼4-mm at the sample location. A PG filter was also installed at the exit of the collimation channel to reduce the higher order harmonic neutrons. The sample stage was on a motor-controlled rotation table to manage sample angle (the angle between incident beam and Si wafer planes), θ with a precision of 0.01°. A 32-wire position-sensitive detector was used, while only the 4 central wires were integrated for enhanced resolution. It should be noted that another collimation channel was used on the detector side to ensure low scattering background.

A standard θ–2θ diffraction experiment was configured to measure the Bragg’s reflections of sample under the shear flow as shown in Fig. 4(a), a top view of the device. The flow direction was out of and perpendicular to the page (i.e., perpendicular to the scattering plane and parallel with the Si surface). The diffraction experiment allows us to identify the lattice parameters of the sample, thus deducing its possible structure (e.g., lamellae, hexagonal, or isotropic phases). In addition, the rocking curve was also collected as a function of θ at a constant detector angle satisfying the Bragg’s condition (i.e., 2θB). Briefly, rocking curves report the orientational distribution of the domain with a d-spacing satisfying the Bragg condition (i.e., θ = θB). Therefore, for an isotropic system, the rocking curve is shown as a flat line, while for a perfectly aligned system, it is a delta function at θ = θB. The width of the rocking curve reveals the angle distribution of the lattice structure with a d spacing of (λ/2)/sin θB. Fig. 4(b) also shows the potential use of such device for SANS application by rotating θ to 90°, i.e., a configuration with the incident beam perpendicular to Si wafer planes. SANS studies on polymer thin films deposited on Si wafers have validated this approach in the literatures.34,35

FIG. 4.

The schematics of scattering configurations of (a) neutron diffraction and (b) SANS. The Si (111) wafers are in grey and the flow direction is perpendicular to the page. The rocking curve was obtained at the fixed detector angle of 2θB as θ varied.

FIG. 4.

The schematics of scattering configurations of (a) neutron diffraction and (b) SANS. The Si (111) wafers are in grey and the flow direction is perpendicular to the page. The rocking curve was obtained at the fixed detector angle of 2θB as θ varied.

Close modal

All the lipids (DMPC, DMPG, and DHPC) were purchased from Avanti Polar Lipids, Inc. (Alabaster, AL). The molar composition of lipids remains constant, [DMPC]/[DMPG]/[DHPC] = 2.88/0.32/1.0, throughout the whole experiment. The lipid mixture was dissolved in D2O (99.99% acquired from CRL) to make a 20 wt. % solution. The final solution was transparent and liquid-like at low T (<15 °C) but turned into translucent and viscous (even gel-like) at high T (>20 °C). Therefore, the sample was loaded into the shear cell and the external tubing at low T (∼10 °C) when the viscosity is low.

For a laminar flow of Newtonian fluid through a rectangular channel with a gap of t and a width of w, the nominal strain rate close to the wall can be calculated as36 

γ ̇ = 6 Q t 2 w ,
(1)

where Q is the volumetric flow rate and is constant (=1.7 × 10−3 ml s−1) in this study. The t and w in the designed shear cell are 0.3 mm and 10 mm, respectively, yielding a nominal γ ̇ = 11 . 11 s−1. To verify the laminar flow, the Reynolds number (Re) was calculated for a rectangle channel as follows:37 

Re = ρ v D H μ ,
(2)

where ρ and μ are the density and the dynamic viscosity of the fluid, respectively, and DH is the hydraulic diameter of a rectangle tube defined as 4 A P , A and P being the cross sectional area and wetted perimeter, respectively, resulting in DH = 5.82 × 10−4 m. The density and viscosity were estimated from the literature report38 to be 0.97 g/ml and greater than 105 mPa s, respectively. Therefore, the calculated Re was 3.16 × 10−6, indicative of a laminar flow. It is estimated that the sample took more than 12 s to pass the preheating compartment at this flow rate, thus temperature equilibrium is expected to achieve at the scattering center. It should be noted that the bicellar mixture may be a non-Newtonian fluid, whose viscosity is a function of strain rate.

It has been previously reported that the DMPC/DHPC/DMPG mixtures form bicelles and perforated lamellae at low and high temperatures, respectively.39–41 The low-T bicelles are not alignable, while the high-T lamellae are alignable under a shear flow with their bilayer normal perpendicular to the confined surfaces.33 More interestingly, the aligned structure remains even several hours after the flow ceases. This mixture presents an ideal system for validating the designed flow device.

The ND experiment was conducted in the standard out-of-plane configuration (i.e., θ–2θ scans) where the incident neutron beam is nearly parallel with the surfaces of Si wafers. Fig. 5 shows the diffraction profiles of the DMPC/DHPC/DMPG mixture under a weak shear flow ( γ ̇ = 11 . 11 s−1) at three different temperatures, 10 °C, 22 °C, and 31 °C, respectively. The scattering vector, q, is defined as 4 π λ sin θ . The θ-2θ diffraction pattern of the sample at low T (10 °C) shows a monotonic decay, indicative of the isotropic (non-aligned) bicelles. At high T (31 °C), however, a sharp Bragg peak at 0.037 Å−1 and up to four of its higher orders are observed representing a highly ordered, smectic lamellar phase. The structural transition presumably starts to take place around 22 °C, where a broader peak appears at a q value of ∼0.05 Å−1, implicative of a smaller lamellar spacing (D). This is most likely a result of larger in-plane perforations at lower T leading to a smaller D value, consistent with the recent observation in literature.42 The bicelle-to-lamellae transition has also been reported elsewhere.39 

FIG. 5.

The diffraction data of a 20 wt. % DMPC/DHPC/DMPG mixture under a nominal strain rate of 11.11 s−1 at T = 10 (circles), 22 (squares), and 31 (triangles) °C.

FIG. 5.

The diffraction data of a 20 wt. % DMPC/DHPC/DMPG mixture under a nominal strain rate of 11.11 s−1 at T = 10 (circles), 22 (squares), and 31 (triangles) °C.

Close modal

To evaluate the degree of alignment of the sample under the shear flow, “rocking curve” measurement was performed by fixing the detector angle at the 1st order Bragg peak position (i.e., 2θB) and collecting the scattering intensity as a function of sample angle, θ. The attainable θ range was between −40° and 40° lest that the supporting posts might block the incident beam as descried in “Instrumental Design” section. Fig. 6 shows the raw data of the rocking curves of sample at 31 °C under a nominal shear flow of γ ̇ = 11 . 11 s−1 and at quiescent state after the flow, respectively. Both cases share a common pattern: a peak located exactly at the Bragg angle, θB (the inset of Fig. 6), and a valley followed by a broad shoulder found as θ extends outward on each side of θB. The two valleys are attributed to the strong absorption of the incident and diffracted neutrons at θ = 0 and 2θB, respectively (i.e., when the beams are parallel with sample plane). The shoulders represent the azimuthally misaligned population of bilayers. Similar patterns with less absorption were also observed in the cases of highly aligned lipid bilayers using a flat substrate.43,44 In the case of substrate-aligning membranes, there is only a small portion of the bilayers deviating from the Bragg condition within a reasonably narrow distribution (FWHM <0.5°).44 However, due to the higher mobility in the solution, the alignment of bilayers in our case is characterized by a broader distribution, resulting also in much broader shoulders.

FIG. 6.

The raw rocking curves of the DMPC/DHPC/DMPG mixture at T = 31 °C at γ ̇ = 11.11 s−1 (circles) and after the flow ceased (squares). The inset is a blowup figure illustrating the intensity around θB.

FIG. 6.

The raw rocking curves of the DMPC/DHPC/DMPG mixture at T = 31 °C at γ ̇ = 11.11 s−1 (circles) and after the flow ceased (squares). The inset is a blowup figure illustrating the intensity around θB.

Close modal

Before data analysis, we made several corrections for the incident flux (on the sample), the scattering volume (receivable by both the incident beam and detector), and the sample absorption, based on the finite size rectangular sample geometry rotating at different values of θ. Each aforementioned factor is discussed below.

The designed neutron beam width at the sample stage, wb, is 4 mm, which covers the whole sample for θ ranging from −20° to 20°. The incident beam in use is proportional to the sample length projected onto the beam, ws, which is the solid light brown line in Fig. 7. The portion of neutron beam “used” by the sample can be determined as ws/wb when it is less than 1 (in the current scenario). If ws/wb were larger than 1, i.e., the whole beam being utilized (not applicable here), no such correction for the incident flux would be required.

FIG. 7.

The schematic of scattering from the rectangular sample (top view).

FIG. 7.

The schematic of scattering from the rectangular sample (top view).

Close modal

Another correction is related to the scattering volume, which is defined as the intersection volume of the sample volume and the overlap region of the incident beam and the detector (the shaded rhomboid at Fig. 7). Currently, because the detecting angle is low (0.8°) and the sample rotation is restricted (−20° < θ < 20°), the whole sample area is always covered by the scattering volume. As a result, no correction is needed. However, if the rhomboid failed to cover the whole sample (i.e, only a portion of sample is contributing to the scattering intensity), correction due to the scattering volume would be required.

The last correction considered is due to sample absorption which can be calculated by Beer’s law as expressed in Eq. (3),

I I o = e μ Lk ,
(3)

where Io, I, μ, L, and k are the incident and transmitted intensities, absorption coefficient, the path length, and an adjustable parameter, respectively.43,44 The absorption coefficient can be calculated as

μ = N A N i σ i N i M i / ρ i ,
(4)

where NA is the Avogadro’s number, Ni is the molar ratio of i-th component, Mi is its molecular weight, σi is the total neutron cross section, and ρi is its the mass density. The value of L can be determined as a function of location (x, y) on the sample (the red line in Fig. 7). The average transmissivity (I/Io)ave can then be obtained through the integration over all (x, y) points within the possible scattering volume of sample and corresponding normalization.

( I I o ) ave = e μ L ( x , y ) k d x d y A .
(5)

For a finite-size sample, several geometrical scenarios have to be considered in various θ ranges.1 

In summary, the corrected intensity, IC, is expressed by Eq. (6) taking into account all the above-mentioned factors: (a) the portion of the beam “seen” by the sample yielding a normalization factor ws/wb, (b) the portion of the sample “viewed” by the detector (not applicable in the current case though), and (c) the correction due to the sample absorption (I/Io)ave.

I C = I 1 w s / w b 1 ( I / I o ) ave .
(6)

Fig. 8 shows the corrected rocking curves of the sample under the shear flow ( γ ̇ = 11 . 11 s−1) and the quiescent state after the flow ceased. The strong absorption at θ = 0 and θ = 2θB is successfully corrected. Both rocking curves were best fitted using Lorentz equation as follow:

y = y 0 + 2 B π b 4 ( x x c ) 2 + b 2 ,
(7)

where B is the area underneath the curve, b is the FWHM, and xc is the center on the x axis. The fitting results in FWHMs of 4.1° ± 0.045° and 3.5° ± 0.05° under shear flow and at quiescence, respectively. It is noteworthy that the FWHM only provides the information about the distribution of aligned membranes in the sample instead of their absolute aligned population. This result seems to suggest a slightly tighter alignment in the case of quiescent state, possibly attributed to the disturbance of the aligned bilayers near the surfaces due to the shear flow. Nevertheless, the indicated difference is well within the uncertainty expected for performed analysis of our experimental data. More interestingly, Fig. 8 also offers details on the relative amount of aligned bilayers versus those misaligned. Since the sample compositions and its amounts were the same for both (under the shear and at the quiescent conditions), the integrated area underneath the rocking curves over a given range provides a portion of bilayers aligned within that range, while integrals from −180° to 180° must be identical. This clearly indicates a significantly larger population of the bilayers aligned over the range of ±10° as induced by the shear flow compared to that at quiescence, suggesting that more membranes indeed align with their bilayer normal parallel with the velocity gradient. Moreover, larger background of the sample at higher θ in the case of quiescent sample is observed in corroboration of greater misalignment.

FIG. 8.

The corrected rocking curves of the raw data in Fig. 5 at γ ̇ = 11 . 11 s 1 (green) and after the flow ceased (yellow). The Lorentz fits of corrected data at γ ̇ = 11 . 11 s 1 (red) and after the flow ceased (blue). The R2 values of the best fitting results for quiescence and under shear flow are 0.976 and 0.986, respectively.

FIG. 8.

The corrected rocking curves of the raw data in Fig. 5 at γ ̇ = 11 . 11 s 1 (green) and after the flow ceased (yellow). The Lorentz fits of corrected data at γ ̇ = 11 . 11 s 1 (red) and after the flow ceased (blue). The R2 values of the best fitting results for quiescence and under shear flow are 0.976 and 0.986, respectively.

Close modal

The current results allow correct interpretation in the previous report based on SANS data, which interpreted the observation up to the forth-order Bragg peak in a quiescent sample after oscillating shear as a result of highly aligned membranes.33 Although the similar number of Bragg reflections can be observed in Fig. 5, the “rocking curves” obtained in the current shear flow device provide further insight to the degree of the alignment throughout the sample. It should be noted that the existence of higher-order Bragg peaks does not necessarily indicate highly aligned sample. In fact, randomly oriented samples may also result in higher order Bragg peaks as there is always a portion of the bilayers oriented in a way satisfying the Bragg’s condition and its higher order harmonics.

The potential application of this device is to perform SANS measurement at θ = 90° [as shown in Fig. 4(b)] to obtain the in-plane structure of the biomembranes, if highly aligned, using the experimental configuration reported previously.45 Here, due to the constraint of beam time and reconfiguration of the optical components, the SANS experiment was not performed on the sample. However, it is anticipated to be highly feasible.

We have shown that the newly designed T-controlled shear flow device is suitable for in-situ ND measurements. The shear strain rate can be easily adjusted through controlling the flow rate produced by the external pump. The required quantity of the sample under investigation is as low as 1 ml. The device allows the studies on the hydrodynamic effects on the nano-structures of materials and the conformational variations of molecules associated with aligned membranes under physiological conditions. The analysis of the scattered intensity corrected by the beam size, sample exposed volume, and absorption is also applicable to other rocking curve measurements on any rectangular samples of a finite size. We have also demonstrated that the “bicellar” sample can be aligned under a weak shear flow. In spite of the observation of many higher order Bragg peaks, the FWHM of the rocking curve is ∼4.1° much worse than the lipid bilayers aligned by flat substrates (normally with the FWHM <0.5°). After the shear flow stopped, a portion of the biomembranes remained aligned at the similar degree of alignment as under the shear flow, although the aligned population appeared to be smaller. The device provides a way to compare the alignability of samples under shear flows.

M.-P.N., Y.X., and M.L. would like to acknowledge the funding support from NSF (Nos. CMMI 1131587 and CBET 1433903) for this work. The neutron scattering facility was managed and the shear cell was constructed by CNBC at CRL.

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See supplementary material at http://dx.doi.org/10.1063/1.4908165 for the detailed derivation of the absorption correction.
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