REVIEW OF SCIENTIFIC INSTRUMENTS 86, 025112 (2015)

In-situ temperature-controllable shear flow device for neutron scatteringmeasurement—An example of aligned bicellar mixtures

Yan Xia,1 Ming Li,2 Norbert Kučerka,3,4,5 Shutao Li,3 and Mu-Ping Nieh1,2,61Department of Chemical and Biomolecular Engineering, University of Connecticut, Storrs,Connecticut 06269, USA2Polymer Program, Institute of Material Sciences, University of Connecticut, Storrs, Connecticut 06269, USA3Canadian Neutron Beam Centre, National Research Council Canada, Chalk River Laboratories, Chalk River,Ontario K0J 1J0, Canada4Department of Physical Chemistry of Drugs at Faculty of Pharmacy, Comenius University,832 32 Bratislava, Slovakia5Frank Laboratory of Neutron Physics at Joint Institute for Nuclear Research, 141980 Dubna,Moscow Region, Russia6Department of Biomedical Engineering, University of Connecticut, Storrs, Connecticut 06269, USA

(Received 14 August 2014; accepted 2 February 2015; published online 25 February 2015)

We have designed and constructed a temperature-controllable shear flow cell for in-situ study onflow alignable systems. The device has been tested in the neutron diffraction and has the potentialto be applied in the small angle neutron scattering configuration to characterize the nanostructuresof the materials under flow. The required sample amount is as small as 1 ml. The shear rate on thesample is controlled by the flow rate produced by an external pump and can potentially vary from0.11 to 3.8 × 105 s−1. Both unidirectional and oscillational flows are achievable by the setting ofthe pump. The instrument is validated by using a lipid bicellar mixture, which yields non-alignablenanodisc-like bicelles at low T and shear-alignable membranes at high T . Using the shear cell, thebicellar membranes can be aligned at 31 ◦C under the flow with a shear rate of 11.11 s−1. Multiplehigh-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 membranesremains aligned even after the flow stops. Detailed and comprehensive intensity correction for therocking curve has been derived based on the finite rectangular sample geometry and the absorptionof 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 newcapability to study the conformational or orientational anisotropy of the solvated macromoleculesor aggregates induced by the hydrodynamic interaction in a flow field. C 2015 AIP PublishingLLC. [http://dx.doi.org/10.1063/1.4908165]

INTRODUCTION

Flow-induced deformation and orientational anisotropyof macromolecules (or aggregates) are important not onlyin fundamental physical science but also in many practicalapplications. A common example is the reduction of viscosityof a polymer solution under increased shear strain rate, knownas “shear thinning.” The variation in rheological responsethus provides a methodology for indirect measurement ofmolecular conformation under flow. In the past, microscopywas also commonly used for direct observation of deformationof micron-sized molecules (e.g., DNA2,3) or flow-inducedanisotropy.4–9

In regards to direct measurement of in-situ nanoscalestructures in flow, neutron scattering turns out to be one of themost powerful methods. Several advantages of using neutronsas a probe are evident. First, neutrons can penetrate commonmaterials except for few elements (such as H, B, Li, Cd, andGd), thus allowing the construction of sample environmentusing metals like stainless steel, Al, Cu, and Si. The flexi-bility to vary contrast of a system presents another advantagein neutron scattering. Since the neutron scattering length of

isotopes can be very different, e.g., −3.741 × 10−15 m and6.671 × 10−15 m for H and D, respectively, we are able toenhance (or decrease) the scattering intensity by isotope sub-stitution, without significantly varying the chemical propertiesof the systems.

The most common shear flow device employed in neutronscattering experiments is Couette flow cell,10–21 which adapts aconcentric double-cylindrical configuration with the examinedsample loaded in the gap between the cylinders. The shearflow is obtained by having one of the cylinders stationary andthe other rotating and the shear rate can be determined bythe distance of the gap and the rotating speed. The neutronbeam can pass through the annulus either tangentially orradially. The scattering planes in the tangential and radialconfigurations are perpendicular to the flow direction andthe shear gradient axis, respectively. It should be noted thatthe small angle neutron scattering (SANS) patterns of thesamples tested in a Couette-type flow cell are usually smeared.The detected intensity is a combination of scattering fromthe sample subjected to the azimuthally misaligned flows.Moreover, in the radial configuration, the two scatteringcenters are apart by the average diameter of the two cylinders,

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while in the tangential configuration, the path length ofthe beam through the sample appears to be longer—bothcausing the smearing of the data. A recent development tomitigate such smearing effect is established with the incidentbeam going through the vorticity direction, where the SANSpattern is projected on the velocity (v)–velocity gradient (∆v)plane.8,15,16,22–25 However, the application of Couette cells onhigh resolution diffraction studies remains a challenge.

It has also been reported that parallel-plate shear devicescan be used in neutron or x-ray scattering or diffrac-tion.23,24,26–31 Based on the concept, an in-situ, temperature-controlled continuous-flow device is designed and built forboth in-plane and out-of-plane neutron scattering experi-ments. In this report, we mainly focused on the out-of-planediffraction; the in-plane scattering can be achieved by rotatingthe device to 90◦. The basic concept of design is to create alaminar flow between two parallel plates set apart by a narrowgap. The shear strain rate is proportional to the flow velocityand inversely proportional to the gap distance. The scatteringsignal is enhanced by using multiple adjacent parallel flowchannels divided by single-crystal Si (111) wafers, while theflow is created by an external pump. The required sampleamount is less than 1 ml including the exterior loop. To controlthe temperature, the device is sandwiched between two Al-jackets (at top and bottom), through which the thermostaticfluid (coolant) circulates continuously.

In this report, we validate the flow device using alipid mixture, which has been reported for its alignabilityin solution under both magnetic32 and flow field33 previ-ously. This mixture is composed of a long-chain dimyris-toyl phosphatidylcholine (DMPC), a long-chain dimyristoylphosphatidylglycerol (DMPG), and a short-chain dihexanoylphosphatidylcholine (DHPC) with a DMPC:DMPG:DHPCmolar ratio of 2.88:0.32:1.0 and a total lipid concentrationof 20 wt. %. It has been reported that this mixture has aphase transition from non-alignable nanodiscs to alignable

perforated lamellae as the sample temperature increases fromlow T [below the melting transition temperature of the long-chain lipid, TM (∼24 ◦C for DMPC)] to high T (e.g., above30 ◦C). Diffraction curves at different temperatures, wherenanodiscs or perforated lamellae exist and rocking curves atquiescence or under flow were collected. The results indicatethat aligned lamellae (with a full width at half maximum of thealignment angle distribution, FWHM ∼4◦) in the solution areachievable under a shear flow with a shear rate of ∼11.11 s−1,which is consistent with the previous report.33 This deviceenables in-situ nanostructural characterization under shearflows, thus allowing us to elucidate the structure-property rela-tionship in solutions containing aggregates or polymers oncethe rheological parameters are measurable (currently underdevelopment). The knowledge will provide new insights tothe fundamental understanding of hydrodynamic interactionin these systems.

INSTRUMENTAL DESIGN

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 mmwith a centered rectangular opening of a dimension 40 mm× 2.1 mm × 10 mm. The interior faces of both 2.1 mm sideshave four highly parallel, vertical trenches (each 0.3 mmwide and 0.5 mm deep) spaced equally by 0.3 mm, for theinsertion of the rectangular Si (111) wafers (40 mm × 11 mm)as shown in Fig. 1(a). Si (111) wafers were carefully chosenand examined to show no low-q reflections prior to thestudy. As a result, three parallel channels are constructedin the gaps between wafers [Fig. 1(b) shows the top viewfrom plane (1) at Fig. 1(a)]. Shear flow then happens asthe sample is pumped through the vertical channels andthe strain rate can be controlled by the flow rate. Theincident neutron beam goes through from the planes (2) and

FIG. 1. The design of temperature controllable shear cell. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:

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025112-3 Xia et al. Rev. Sci. Instrum. 86, 025112 (2015)

FIG. 2. The designed mount for the shear cell to be installed on a neutronspectrometer.

(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-planeand in-plane configurations, respectively, where scatteringplane is always perpendicular to the flow direction (seeFig. 2). To control the sample temperature, we use topand bottom Al blocks [green parts in Fig. 1(a) and blueparts in Figs. 1(c) and 1(d)] with internal channels for thecirculating coolant, whose temperature is controlled by anexternal water bath, to sandwich the shear cell. O-ringsbetween the T-controlling blocks and the shear cell ensureperfect sealing [Fig. 1(b)]. Sample enters and/or exits shear-flow cell through four identical injection ports aligned withthe Si wafers inside [Figs. 1(a) and 1(c)] and follows to a smallsample reservoir compartment (1 mm × 10 mm × 2.1 mm) toensure an isotropic flow of sample through parallel channelsand to improve its temperature equilibration. Outside the T-controlling blocks, each injection port connects through thetubing, which goes to a peristaltic pump (Masterflex L/S fromCole-Palmer) and then to the injection ports of the other block

to form a closed loop. Sample can be pumped into the shearcell at a constant speed (from 0.001 to 3400 ml/min, equivalentto the range of shear rate for Newtonian fluids from 0.11 to3.8 × 105 s−1 based on the sample geometry) unidirectionallyor oscillationally (i.e., switching flow directions at a constantfrequency). However, the strain rate of oscillatory flow alsodepends on the switch speed of the flow direction which isbeyond the focus of this study.

Fig. 2 illustrates the designing scheme for mounting thisunit on a rotating sample table at the sample stage of a neutronspectrometer, where the complete assembly of the shear cellis also shown at the left upper corner The unit is attached tothe bottom of a disk (with a diameter of 50.8 cm), which issupported by four posts to provide a correct height with respectto incident neutron beam. The allowable rotating range of thesample angle is around 80◦ (i.e., ±40◦) in both in-plane andout-of-plane configurations beyond which the posts wouldinterfere with the incident neutron beam. Fig. 3 shows thephoto of the whole unit as installed at the sample stage of theneutron spectrometer. The whole unit is then located on anX-Y-Z translation stage for a fine adjustment of the positionof the shear cell.

SPECTROMETER CONFIGURATION

The neutron diffraction, ND experiment was conductedat N5 triple-axis neutron spectrometer adjunct to the NationalResearch Universal (NRU) reactor located at Chalk River Lab-oratory (CRL). This neutron scattering facility is managedby the Canadian Neutron Beam Centre (CNBC). The neu-trons from the NRU first passed through a sapphire filter toeliminate most of the fast neutrons. The wavelength of theneutrons, λ, was selected by a pyrolytic graphite (PG) crystal(50 mm × 89 mm × 1.6 mm) using (002) plane set at 20.69◦ todiffract neutrons with λ of 2.37 Å and its high-order harmonics(i.e., λ/2, λ/3, etc.). The selected neutrons were then colli-mated by a single channel collimator to yield a beam size of∼4-mm at the sample location. A PG filter was also installedat the exit of the collimation channel to reduce the higher

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.

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FIG. 4. The schematics of scattering configurations of (a) neutron diffractionand (b) SANS. The Si (111) wafers are in grey and the flow directionis perpendicular to the page. The rocking curve was obtained at the fixeddetector angle of 2θB as θ varied.

order harmonic neutrons. The sample stage was on a motor-controlled rotation table to manage sample angle (the anglebetween incident beam and Si wafer planes), θ with a precisionof 0.01◦. A 32-wire position-sensitive detector was used, whileonly the 4 central wires were integrated for enhanced resolu-tion. It should be noted that another collimation channel wasused on the detector side to ensure low scattering background.

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

MATERIALS

All the lipids (DMPC, DMPG, and DHPC) were pur-chased from Avanti Polar Lipids, Inc. (Alabaster, AL). Themolar composition of lipids remains constant, [DMPC]/[DMPG]/[DHPC] = 2.88/0.32/1.0, throughout the wholeexperiment. The lipid mixture was dissolved in D2O (99.99%

acquired from CRL) to make a 20 wt. % solution. The finalsolution was transparent and liquid-like at low T (<15 ◦C)but turned into translucent and viscous (even gel-like) at highT (>20 ◦C). Therefore, the sample was loaded into the shearcell and the external tubing at low T (∼10 ◦C) when theviscosity is low.

RESULTS AND DISCUSSION

Nominal shear strain rate, γ

For a laminar flow of Newtonian fluid through a rectan-gular channel with a gap of t and a width of w, the nominalstrain rate close to the wall can be calculated as36

γ =6Q

t2 · 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 designedshear cell are 0.3 mm and 10 mm, respectively, yieldinga nominal γ = 11.11 s−1. To verify the laminar flow, theReynolds number (Re) was calculated for a rectangle channelas follows:37

Re =ρvDH

µ, (2)

where ρ and µ are the density and the dynamic viscosityof the fluid, respectively, and DH is the hydraulic diameterof a rectangle tube defined as 4A

P, A and P being the cross

sectional area and wetted perimeter, respectively, resultingin DH = 5.82 × 10−4 m. The density and viscosity wereestimated from the literature report38 to be 0.97 g/ml andgreater than 105 mPa s, respectively. Therefore, the calculatedRe was 3.16 × 10−6, indicative of a laminar flow. It is estimatedthat the sample took more than 12 s to pass the preheatingcompartment at this flow rate, thus temperature equilibriumis expected to achieve at the scattering center. It should benoted that the bicellar mixture may be a non-Newtonian fluid,whose viscosity is a function of strain rate.

Validation of the shear cell with a “bicellar” mixtureIt has been previously reported that the DMPC/DHPC/

DMPG mixtures form bicelles and perforated lamellae at lowand high temperatures, respectively.39–41 The low-T bicellesare not alignable, while the high-T lamellae are alignableunder a shear flow with their bilayer normal perpendicularto the confined surfaces.33 More interestingly, the alignedstructure remains even several hours after the flow ceases. Thismixture presents an ideal system for validating the designedflow device.

The ND experiment was conducted in the standard out-of-plane configuration (i.e., θ–2θ scans) where the inci-dent neutron beam is nearly parallel with the surfaces ofSi wafers. Fig. 5 shows the diffraction profiles of theDMPC/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 as4πλ

sin θ. The θ-2θ diffraction pattern of the sample at low T(10 ◦C) shows a monotonic decay, indicative of the isotropic

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025112-5 Xia et al. Rev. Sci. Instrum. 86, 025112 (2015)

FIG. 5. The diffraction data of a 20 wt. % DMPC/DHPC/DMPG mixtureunder a nominal strain rate of 11.11 s−1 at T = 10 (circles), 22 (squares), and31 (triangles) ◦C.

(non-aligned) bicelles. At high T (31 ◦C), however, a sharpBragg peak at 0.037 Å−1 and up to four of its higher ordersare observed representing a highly ordered, smectic lamellarphase. The structural transition presumably starts to take placearound 22 ◦C, where a broader peak appears at a q value of∼0.05 Å−1, implicative of a smaller lamellar spacing (D). Thisis most likely a result of larger in-plane perforations at lowerT leading to a smaller D value, consistent with the recentobservation in literature.42 The bicelle-to-lamellae transitionhas also been reported elsewhere.39

To evaluate the degree of alignment of the sample underthe shear flow, “rocking curve” measurement was performedby fixing the detector angle at the 1st order Bragg peak position(i.e., 2θB) and collecting the scattering intensity as a function ofsample angle, θ. The attainable θ range was between −40◦ and40◦ lest that the supporting posts might block the incident beamas descried in “Instrumental Design” section. Fig. 6 shows theraw data of the rocking curves of sample at 31 ◦C under anominal shear flow of γ = 11.11 s−1 and at quiescent state afterthe flow, respectively. Both cases share a common pattern: apeak located exactly at the Bragg angle, θB (the inset of Fig. 6),and a valley followed by a broad shoulder found as θ extends

FIG. 6. The raw rocking curves of the DMPC/DHPC/DMPG mixture atT = 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.

outward on each side of θB. The two valleys are attributed tothe strong absorption of the incident and diffracted neutrons atθ = 0 and 2θB, respectively (i.e., when the beams are parallelwith sample plane). The shoulders represent the azimuthallymisaligned population of bilayers. Similar patterns with lessabsorption were also observed in the cases of highly alignedlipid bilayers using a flat substrate.43,44 In the case of substrate-aligning membranes, there is only a small portion of the bila-yers deviating from the Bragg condition within a reasonablynarrow distribution (FWHM <0.5◦).44 However, due to thehigher mobility in the solution, the alignment of bilayers in ourcase is characterized by a broader distribution, resulting also inmuch broader shoulders.

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

The designed neutron beam width at the sample stage,wb, is 4 mm, which covers the whole sample for θ rangingfrom −20◦ to 20◦. The incident beam in use is proportionalto the sample length projected onto the beam, ws, which isthe solid light brown line in Fig. 7. The portion of neutronbeam “used” by the sample can be determined as ws/wb whenit is less than 1 (in the current scenario). If ws/wb were largerthan 1, i.e., the whole beam being utilized (not applicablehere), no such correction for the incident flux would be re-quired.

Another correction is related to the scattering volume,which is defined as the intersection volume of the samplevolume and the overlap region of the incident beam and thedetector (the shaded rhomboid at Fig. 7). Currently, becausethe detecting angle is low (0.8◦) and the sample rotation isrestricted (−20◦ < θ < 20◦), the whole sample area is alwayscovered by the scattering volume. As a result, no correctionis needed. However, if the rhomboid failed to cover the wholesample (i.e, only a portion of sample is contributing to thescattering intensity), correction due to the scattering volumewould be required.

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

IIo= e−µLk, (3)

where Io, I, µ, L, and k are the incident and transmittedintensities, absorption coefficient, the path length, and an ad-justable parameter, respectively.43,44 The absorption coeffi-cient can be calculated as

µ = NA

Niσi

NiMi/ρi, (4)

where NA is the Avogadro’s number, Ni is the molar ratio ofi-th component, Mi is its molecular weight, σi is the totalneutron cross section, and ρi is its the mass density. The valueof L can be determined as a function of location (x, y) onthe 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

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025112-6 Xia et al. Rev. Sci. Instrum. 86, 025112 (2015)

FIG. 7. The schematic of scattering from the rectangular sample (top view).

and corresponding normalization.

( IIo)ave =

e−µL(x, y)kdxdy

A. (5)

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

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

IC = I · 1(ws/wb) ·

1(I/Io)ave

. (6)

Fig. 8 shows the corrected rocking curves of the sampleunder the shear flow (γ = 11.11 s−1) and the quiescent stateafter the flow ceased. The strong absorption at θ = 0 andθ = 2θB is successfully corrected. Both rocking curves werebest fitted using Lorentz equation as follow:

y = y0 +2Bπ

b4(x − xc)2 + b2 , (7)

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 ofcorrected 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 0.976and 0.986, respectively.

where B is the area underneath the curve, b is the FWHM, andxc is the center on the x axis. The fitting results in FWHMs of4.1◦ ± 0.045◦ and 3.5◦ ± 0.05◦ under shear flow and at quies-cence, respectively. It is noteworthy that the FWHM only pro-vides the information about the distribution of aligned mem-branes in the sample instead of their absolute aligned popu-lation. This result seems to suggest a slightly tighter align-ment in the case of quiescent state, possibly attributed to thedisturbance of the aligned bilayers near the surfaces due tothe shear flow. Nevertheless, the indicated difference is wellwithin the uncertainty expected for performed analysis of ourexperimental data. More interestingly, Fig. 8 also offers de-tails on the relative amount of aligned bilayers versus thosemisaligned. Since the sample compositions and its amountswere the same for both (under the shear and at the quiescentconditions), the integrated area underneath the rocking curvesover a given range provides a portion of bilayers aligned withinthat range, while integrals from −180◦ to 180◦ must be iden-tical. This clearly indicates a significantly larger population ofthe bilayers aligned over the range of ±10◦ as induced by theshear flow compared to that at quiescence, suggesting that moremembranes indeed align with their bilayer normal parallelwith the velocity gradient. Moreover, larger background of thesample at higher θ in the case of quiescent sample is observedin corroboration of greater misalignment.

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

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025112-7 Xia et al. Rev. Sci. Instrum. 86, 025112 (2015)

The potential application of this device is to performSANS measurement at θ = 90◦ [as shown in Fig. 4(b)]to obtain the in-plane structure of the biomembranes, ifhighly aligned, using the experimental configuration reportedpreviously.45 Here, due to the constraint of beam timeand reconfiguration of the optical components, the SANSexperiment was not performed on the sample. However, it isanticipated to be highly feasible.

SUMMARY

We have shown that the newly designed T-controlledshear flow device is suitable for in-situ ND measurements.The shear strain rate can be easily adjusted through controllingthe flow rate produced by the external pump. The requiredquantity of the sample under investigation is as low as 1 ml.The device allows the studies on the hydrodynamic effectson the nano-structures of materials and the conformationalvariations of molecules associated with aligned membranesunder physiological conditions. The analysis of the scatteredintensity corrected by the beam size, sample exposed volume,and absorption is also applicable to other rocking curvemeasurements on any rectangular samples of a finite size.We have also demonstrated that the “bicellar” sample can bealigned under a weak shear flow. In spite of the observationof many higher order Bragg peaks, the FWHM of the rockingcurve is ∼4.1◦ much worse than the lipid bilayers aligned byflat substrates (normally with the FWHM <0.5◦). After theshear flow stopped, a portion of the biomembranes remainedaligned at the similar degree of alignment as under the shearflow, although the aligned population appeared to be smaller.The device provides a way to compare the alignability ofsamples under shear flows.

ACKNOWLEDGMENTS

M.-P.N., Y.X., and M.L. would like to acknowledge thefunding support from NSF (Nos. CMMI 1131587 and CBET1433903) for this work. The neutron scattering facility wasmanaged and the shear cell was constructed by CNBC at CRL.

1See supplementary material at http://dx.doi.org/10.1063/1.4908165 for thedetailed derivation of the absorption correction.

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