colloids 
and interfaces
Article
H2O/D2O Contrast Variation for Ultra-Small-Angle
Neutron Scattering to Minimize Multiple Scattering
Effects of Colloidal Particle Suspensions
Akira Otsuki 1,*, Liliana de Campo 2 , Christopher J. Garvey 2 and Christine Rehm 2,3
1 Ecole Nationale Supérieure de Géologie, GeoRessources UMR 7359 CNRS, University of Lorraine,
2 Rue du Doyen Marcel Roubault, BP 10162, 54505 Vandoeuvre-lès-Nancy, France
2 Australian Centre for Neutron Scattering, Australian Nuclear Science and Technology Organisation,
Lucas Heights, New South Wales 2234, Australia; liliana.decampo@ansto.gov.au (L.d.C.);
cjg@ansto.gov.au (C.J.G.); christine.rehm@gtiit.edu.cn (C.R.)
3 Guangdong Technion Israel Institute of Technology, 241 Da Xue Road,
Shantou 515063, Guangdong Province, China
* Correspondence: akira.otsuki@univ-lorraine.fr; Tel.: +33-372-744-543




Received: 20 August 2018; Accepted: 5 September 2018; Published: 7 September 2018 

Abstract: This study investigated the use of solvent contrast (H2O/D2O ratio) as a means to optimize the
ultra-small-angle neutron scattering (USANS) signal. By optimizing the signal, it was possible to reduce
the undesirable effects of coherent multiple scattering while still maintaining a measurable scattered
intensity. This result will further enable the use of USANS as a probe of the interactions between colloidal
particles and their structures within concentrated suspensions as well as particle dispersion/aggregation.
As a model system, we prepared silica colloidal particle suspensions at different solid concentrations.
USANS curves were measured using the classical Bonse–Hart double crystal diffractometer while varying
the scattering length density of the aqueous phase, thus varying the contrast to the silica particles. As a
means of assessing the impact of multiple scattering effects on different q-values, we analyzed the scattered
intensity at different contrasts at three different q values. The data were then used to determine the match
point of the silica particle suspensions from the expected square root dependence of the scattered intensity
with solvent composition, to analyze any differences associated with the solid concentration change,
and to determine the optimum H2O/D2O ratio in terms of high transmission (TSAS > 80%) and high
enough scattering intensity associated with the contrast of the system. Through this investigation series,
we confirmed that adjusting the contrast of the solvent (H2O/D2O) is a good methodology to reduce
multiple scattering while maintaining a strong enough scattering signal from a concentrated suspension
of silica particles for both USANS and rheometric USANS (rheo-USANS) experiments.
Keywords: silica; rheo-SANS; q-dependency; scattering length density; TSAS value; solid concentration
1. Introduction
Concentrated colloidal particle suspensions are found in a wide range of daily products
(e.g., milk, cosmetics) and industrial products/processes (e.g., mineral pulp, drug production).
Precise understanding and manipulation of interactions within such a particle suspension and its
resulting bulk behavior are thus of great interest and importance in both science and engineering.
In this work, our primary interest is submicron to micron size particle aqueous suspensions relevant
to the current and long-lasting challenges associated with colloidal particle processing/separation
(e.g., [1]) and their characterization methods (e.g., [2,3]).
The majority of characterization methods either requires some special sample preparation, or those
suitable for direct characterization of particle behavior in a solution require a very small volume fraction
Colloids Interfaces 2018, 2, 37; doi:10.3390/colloids2030037 www.mdpi.com/journal/colloids
Colloids Interfaces 2018, 2, 37 2 of 13
of particles (e.g., 1 × 10−5 vol % for dynamic light scattering [4]) due to the strength of the interaction
between light and the particle suspension [5]. Furthermore, when the linkage between microscopic
structure and bulk properties of a suspension is affected by an external field, such as a shear field,
techniques which can probe structure in situ are highly desirable. A related difficulty is to precisely
quantify the interactions in concentrated colloidal particle suspensions commonly prepared/processed
in actual plant operations (e.g., [6,7]) from the extrapolation of dilute solution studies.
Small-angle neutron scattering (SANS) methods have the potential to probe bulk average
structures in a concentrated colloidal particle suspension/dispersion and allow us to understand
and quantify the particle–particle interactions [8]. Scattering curves are interpreted in terms of the
angular or q-dependence of the scattered intensity [9](. )
4π θ
q = sin (1)
λ 2
where θ is the scattering angle and λ is the wavelength of the scattered radiation.
However, at high solid/particle concentrations, multiple scattering may hinder extracting the
desired structural information directly from the interpretation of SANS curves due to the consequential
q-dependent distortion of the measured scattered intensity [10]. If multiple scattering occurs for a
given particle/solvent system, it attenuates scattering of the incident beam that should be going in
a given (forward) direction and, therefore, distorts the signal which would have been recorded in
the limit of single scattering. It follows that the straightforward relationship between the differential
cross section and the pair correlation function, i.e., between the structure of the material and the
measured scattering signal, is lost [11]. While a typical approach to reduce multiple scattering is
either or both (a) reducing the particle concentration and/or (b) reducing the sample path length,
they have obvious limitations in (i) using the behavior of less concentrated suspension to understand
the more concentrated suspension; (ii) difficulty in proper feeding of a viscous suspension (in other
words, heterogeneity as well as the impact of the sample cell geometry on the structure could affect
the sample subjected to the beam and, thus, produce a misleading result); and (iii) the increasing
volumetric effect of the surface perturbation of two cell faces on the decreasing bulk of thinner samples.
On the other hand, for neutron scattering experiments, it is possible to optimize the scattering strength
of a sample by decreasing the contrast between the two phases, particulate, and solvent (water) in
a way that is analogous to the role of refractive index adjustment in light scattering [12]. In this
study, we adjusted the scattering length density of the solvent by varying the H2O/D2O composition,
i.e., by contrast variation (e.g., [13]). In other words, we utilized the difference between the neutron
scattering length densities (SLD) of H O (−0.50 × 10−6 Å−22 [14]) and D2O (6.37 × 10−6 Å−2 [14])
in order to adjust the scattering power of the sample, and thus to minimize the effects of multiple
scattering. To the best of the authors’ knowledge, systematic and extensive study of this approach
has been very limited. Apart from optimizing sample preparation, multiple scattering effects may
also be corrected for during data processing. For that, a variety of procedures is available such as
analytical approximations as discussed by, (e.g., [15–23]). The multiple scattering of neutrons has
also been studied using the technique of Monte Carlo simulation (e.g., [24–27]). Additionally, in the
case of thick samples, a partial correction for the effect of multiple scattering can be done using an
empirical approach (e.g., [28,29]), where various thicknesses of one sample are measured, the data
fitted—possibly using the equation described by Vineyard (1954) [15]—and multiple scattering from a
sample of known thickness accordingly corrected for.
In this article, we report our investigation on using a H2O/D2O contrast variation in conjunction
with ultra-small-angle neutron scattering (USANS) to limit the effects of coherent multiple scattering while
maintaining strong enough scattering that can be utilized to understand the particle–particle interactions
and particle dispersion/aggregation within highly concentrated colloidal suspensions. Multiple incoherent
scattering is out of our concern in this study since it contributes only to the background and can be
tolerated. Particle interactions and dispersions/aggregations will be separately reported in detail, and thus
Colllloiids Interffaces 2018,, 2,, 3x7 FOR PEER REVIEW  3 of 1132 
separately reported in detail, and thus are outside the scope of this article. The experiments were 
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aanndd eexxppllaaiinneeddi innt htheer eresusultlstsa nadndd idsicsucsussiosinosne sceticotnio. n. 
22.. MMaatteerriiaallss aanndd MMeetthhooddss 
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umsoen tioto mr tohneitionrt etnhsei tyinotefntshietyn oeuf ttrhoen nbeeuatmrotnr abnesammit tteradntshmroitutegdh tthhreosuagmhp tlhe,e insacmlupdlien,g inaclllundeiuntgro anlsl 
nsceautttreorends stocaltotwereadn gtole lsoawp aarntgflreosm aptharet qf-rvoamlu tehteh qa-tviaslrueefl tehcatet diso rnetfolecthteedm oanitno dthetee mctoari.n detector. 
 
FFiigguurree 11.. SSkkeettcchh ooff tthhee KKooookkaabbuurrrraa UUSSAANNSS iinnssttrruummeenntt llaayyoouutt.. 
IIn a ttypiicall USANS experiimentt rockiing curve proffiilles are measured by rottattiing tthe anallyzer 
crrysttall acrross tthe peak posiittiion and measurriing tthe neuttrron iinttensiitty as a ffuncttiion off tthe momenttum 
ttrransfferr ((orr scatttterriing vecttorr)) q att whiich datta arre collllectted att one vallue off q ((orr θ)) att a ttiime.. q iis rrellatted 
tto tthe rrottattiion orr scatttterriing anglle θ viiaa Equaattiioonn ((11)).. 
Notte tthhaattt hteheB oBnosne–sHe–aHrtaUrtS AUNSASNteSch tneicqhuneiqasuaep apsl ieadpponlieKdo okna bKuororakaisbounrlrya siesn sointilvye stoenscsaittitveeri ntog 
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wthaev peovsescitbolret rwanavsfevrse,cit.oe.r, tKroanoksfaebrusr, ria.em., Keaosoukreasbsucrartate mreedaisnutreenss istcyaftrtoemredth ientseanmspitlye fwroitmh  ethxcee sllaemntpalne gwuiltahr 
erexscoelluletinotn ahnogruizlaorn traellsyolouftaiofne whoarriczsoencotanldlys bouf taw fiethwa alarcrgsecaocncdeps tbanuct ewinitthh ea vlearrtgicea ladccireepcttaionnceo fina ftehwe 
vertical direction of a few degrees, which is described as ‘slit smearing’. The high angular resolution 
 
Colloids Interfaces 2018, 2, 37 4 of 13
degrees, which is described as ‘slit smearing’. The high angular resolution required for USANS experiments
is enhanced through multiple reflections of the neutron beam before and after the sample.
In this study, two different sample cell setups were used and a series of silica particle suspensions
were measured. The first one is an aluminum cell with a neutron path length of 0.5 mm and quartz
windows of 4 cm diameter, which was mounted onto a sample tumbler to avoid the effects of sample
sedimentation, and the beam was shaped by a Gadolinium aperture of 30 mm diameter. The second
one is a Couette quartz flow cell, outer diameter 54 mm, with the Anton-Paar MCR 500 rheometer
accepting the neutron beam in the normal (perpendicular) direction (Figure 1). A 25 mm circular Cd
aperture was mounted directly in front of the curved Couette cell, and its effective path length was
experimentally determined from a comparison of the scattering curves between the Couette and flat
cells. The Couette cell has a nominal gap of 0.5 mm, leading to a total beam path of 1 mm theoretically
(0.5 mm on each side). However, it should be noted that the effective path length can be slightly longer
because the Couette cell is curved, which is particularly important for the large apertures as used here.
Silica particles purchased from Sigma-Aldrich (St. Louis, MO, USA) with a size distribution
of 0.5–10 µm—with approximately 80% of particles between 1–5 µm—were used to create
sample/aqueous suspensions. Their physical properties are: D50 (average particle diameter measured
by laser diffraction) is 2.4 µm, BET surface area is 5.2 m2/g, and density is 2.6 g/cm3. The literature
value of the scattering length density of silica is 4.1 × 10−6 Å−2 [14]. USANS measurements were
conducted in the q-range from 3.5 × 10−5 to 0.01 Å−1. Silica particle suspensions were prepared in an
electrolyte solution of potassium nitrate (1 × 10−2 M) consisting of milli-Q water and D2O in different
volume ratios. Solid concentrations were adjusted to between 5 and 40 vol % in order to investigate
whether there is any influence on the optimization of the H2O/D2O ratio. Once a suspension was
evenly mixed, its pH value was adjusted to 10 using 1M and/or 0.1 M KOH in D2O. The suspension
was then mixed by magnetic stirring for 30 min. The suspension was then transferred to a flat cell
for USANS measurements or a cylindrical cell (Couette geometry) for rheo-USANS measurements.
Experimental rocking curves were reduced and normalized to absolute intensity scale using the
standard procedure [34] adapted to Kookaburra using Python scripts on the Gumtree platform [35].
3. Results and Discussion
Figures 2 and 3 show the results of contrast variation with 5 and 10 vol % SiO2 at pH 10,
respectively. Figure 2a shows the absolutely scaled slit-smeared intensity for a H2O/D2O contrast
variation series to investigate its effect on the scattering intensity and transmission of samples with
5 vol % silica. All the curves are fairly featureless which would be anticipated from the polydisperse
silica samples. Starting from a 30/70 H2O/D2O mixture, the signal increases with increasing H2O
content, and therefore contrast. It should be noted that the error bars are given in all the figures in this
article, but they are mostly smaller than experimental dot points.
The first step of this investigation was to determine q-dependence of the match point, i.e.,
the contrast, H2O/D2O ratio, where the scattered intensity is equal to 0. To extract the potentially
q-dependent match point from the data, the intensities at three q-values (1.0 × 10−4, 2.6 × 10−4,
6.7 × 10−4 Å−1) from each scattering pattern were plotted as a function of H2O vol % in H2O/D2O
ratio. As an approximation, the square root of the intensity is expected to give a linear relationship with
the H2O vol % [36,37], as plotted in Figure 2b. For a group of identical, randomly oriented particles,
the intensity of coherent, elastic scattering is dependent only on the magnitude of the scattering
momentum transfer q, and is defined as [11] ( )
I(q) = N ∆SLDV 2P(q)S(q) (2)
N is the number of particles per unit volume, V is the volume of the particles, P(q) is a form factor
that depends on the shape of the particles, S(q) is a structure factor that dictates the inter-particle
correlation structure, and ∆SLD is the scattering density difference between the scattering particles
Colloids Interfaces 2018, 2, 37 5 of 13
Colloids Interfaces 2018, 2, x FOR PEER REVIEW  5 of 12 
andansdo lsvoelvnet.ntT. hTuhsu,so, noenec acnand deedduuccee tthhee ccoorrrreellattiion beettweeeenn tthhee ssccaattteterirningg inintetnesnistyit yanadn dscsacttaetrtienrgin g
dendseintysitdyi fdfeifrfenrecnecaes as 
I(
±𝐼√(
q𝑞) ∝𝐼)( ∝
(
∆SL
𝑞)( ∝ΔSΔLD
)
D)2 (3)SLD (3) ± I(q) ∝ ∆SLD (4) (4)
ThTehEeq Euqautiaotnion(4 ()4i)s ius suesdedt otoc oconnstsrturuccttt thhoossee pplloottss iinn FFiigguurreess 22bb aanndd 33bb. .
(a)
5% Silica particles
107
q1 q2 q  
106 3      H2O/D2O
 70/30
105  60/40 50/50
 40/60
104  30/70
103
102
101
100
10-4 10-3 10-2
(b) Q (Å-1)
(c)
5% Silica particles 5% Silica particles
700 106
100
600      H2O/D2O
q  = 1.0x10-4Å-11 105  70/30
500 80  60/40
 50/50
400 104  40/60
300 60  30/70
3
q  = 2.6x10-4Å-1 10200 2
40
100 q3 = 6.7x10-4Å-1 102
0
20 101
-100
-200 0 100
20 30 40 50 60 70 10-4 10-3 10-2
% H2O in H2O/D2O Q (Å-1)  
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popionitn, tr,e rsepsepcetcivtievleyl.yR. Rigighht ta xaxisi:s:T TSAS,exp iinn 00..55 mmmm ppaatthh lleennggthth ((bbluluee sstatarsr)s )aass aa ffuunncctitoionn oof fvvool l%% HH2OO inin SAS,exp 2
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notmhaatvceh apnoyinqt ddeopeesn ndoent chya.vTeh aenvya lqu edeispceonndseinstceyn. tlTyhaer ovualnude 3i0s vcoonl s%isHtenOtly. T aorooubntadin 3a0 mvo2 olr e%q Hua2nOt.i tTatoi ve
meoabstuarien, aw me ofirtete qduaanst√𝐼 t
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√
s,g thIa=t 0fo, lwloewres obbetlaoiwne)d. Mata3tc0h.4 p±oi1n.2tsv, ol
% H  O = a0n, dwe3r1e.6 o±bta0i.n3evdo alt% 30H.4 ±O 1i.n2 vDolO %.  THh2Oe e asntidm 3a1t.e6d ±S 0L.3D voofl t%h eHp2Oar tiinc lDes2Ois. 4T.h2e8 e±sti0m.1a8te×d 1S0L−D6 oÅf −2
th2e particles is 4.28− ± 0.1−8 × 1
20−6 Å−2 a2nd 4.20 ± 0.18 × 10−6 −2and 4.20 ± 0.18 × 10 6 Å 2, respectively. This is in good Åagr,e reemspeencttiwveitlyh. tThheise xisp ienc tgeodomd aatgcrheepmoeinntt of
with the expected match point ×of sil−ic6a (l−it2erature value of SLD 4.1 × 10
−6 Å−2), corresponding to 32.4 
silivcaol( l%it eHraOtu.re2  Thvea lsuaemoef iSs LtrDue4 .f1or a1 s0ysteÅm w)i,thco 1r0re vsoplo %nd sionlgidt oco3n2t.e4nvt,o al s% shHo2wOn. Tinh Feisgaumree 3ibs,t rwuheefroer a
systtheem mwaittchh 1p0ovinotl w%asso dliedtecromnitneendt, wasitshh othw−6 −e 
nesintimFiagtuedre S3LbD, w ofh e4r.2e8t h±e 0m.06a t×c h10p−o6 iÅn−t2 wora 4s.d26e t±e r0m.0i7n ×ed 10w−6i th
theÅe−s2t. iTm
2 −6 −2
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upotno 1th0ev mola%tchS ipOo2intth. ere was no solid concentration dependen√cy on the match point.
IdeIdalelayl,lyth, ethreerseh sohuoludldb ebea ali nlineaearrr erelalatitoionnsshhiipp bbeettwweeeenn √𝐼I aanndd HH22OO vvool l%% fofro ra abibnianrayr ycocnotnratsrta st
sysstyesmte,mq,- dq-edpeepnednednetntd edveivaitaitoionnss frforomm ththisis ininddiiccaattee mmuullttiippllee ssccaatttteerriinngg eeffffeecctsts. .ThTehsee seeffeefcftesc tasrea re
ant icipated to increase with H2O vol % (i.e., contrast between solvent and particles) and be more
dΣ/dΩ -1smeared (cm )
T(sas)exp 5% in 0.5mm
dΣ/dΩ -1smeared (cm )
Colloids Interfaces 2018, 2, 37 6 of 13
Colloids Interfaces 2018, 2, x FOR PEER REVIEW  6 of 12 
proannotiucinpcaetdeda ttolo wincqrethasaen watithhi gHh2Oq. Tvholi s%e ff(ei.cet., iscoilnlutrsatsrta tbeedtwineeFnig suorlevse2nbt aanndd 3pba:rtai√ctltehse) hanigdh ebre qm-voarleu es
(q2parnondoqu3n)ctehde raet lioswa cql ethaarnl iante ahrigrhe lqa.t iTohniss heifpfe.cFt oisr itlhluestlroawteedr iqn- vFaiglueress( q21b) ,atnhde 3b:I actu trhvee hsiflghaettre qn- as
thevyalbueecso (mq2e ainndc rqe3)a sthinegrely isa aff eclcetaerd libnyeamr ureltliaptiloensschaitpte. rFionrg t.hAe tlo5wveorl q%-vsailluiceas s(qa1m), pthlee, √m𝐼u cltuiprvleess cflaatttteernin g
is vasis itbhleey fobrecqo1maet tihnecrheaigsihnegsltyc aofnfetrcatesdt  obfy7 0mvuoltlip%leH sc2aOtte(Fringgu.r eA2t b5) ,vaonl d%f osriltihcae s1a0m%pslea,m mpuleltitphlies is
alrsecaadttyerviinsgib ilse vfiosribql1e afotr6 q01 vaot lth%e Hhi2gOhe(sFt icgounrtera3sbt) o. fS 7c0a tvteorli %ng Hd2aOta (Fniogrumrea 2libz)e, dantod tfhoer tihnete 1n0s%it ysaamt apbleo ut
q2,tahiqs- irse galiroenadthya vt idsiobelse nfoort qa1p apt e6a0r vtol b%e Haf2fOec (tFeidgubryem 3bu)l.t Sipclaettsecrainttge rdiantga, naorermshaoliwzendi tno Fthigeu irnetsen2scitayn adt 3c.
It caabnoubte qs2e, ean qt-hreagtifoonr t5hvato ld%oes inliocta aspapmeparle to(F bigeu arfefe2ccte),dt hbey cmuurvlteips laef tsecratnteorimnga,l iazraet isohnowarne ivne rFyigsuimresil ar,
and2ct ahnuds 3mcu. Iltt icpalne bscea steteerni nthgaet fffoerc t5s vaorel %no stiloicbav siaomusp.lTe h(Feigcurrev e2ca)t, 4th0e/ c6u0ravpeps eaaftresr tnoobrme salliigzhattiloynh aigreh er
in ivnetreyn ssiimtyilaatrl,o awndq ,tahnuds mwuelatitptrlieb suctaetttehriisntgo esfmfeacltls vaarrei antoiot nosbivniosuasm. Tphleep cruerpvaer aatti o4n0/.6F0o arp1p0evaorsl %to sbieli ca
samslipglhet,lhy ohwigehveerr ,inth ientleonwsitqyp aat rltoswh oqw, asnad cwleea artdtreibpuetned tehnisc ytoo snmtahlel vcoarnitartaiosnt.sC inle saarmlyptlhee psraempapraletiaotnt. he
higFhoers 1t0c voonlt r%a sstil(i7ca0 svaoml p%leH, hoOw)ehvaesr,l othwee lrowin tqe pnasritty shaotwlosw a cqlethara ndetphendency on the2 ose with less co cnotnrtarsatst(.F Cigleuarrely2 c),
whtihceh siasma ptylep iacta tlhseig hnigohfemstu clotinptlreassct a(t7t0e rvinolg .%P Hlea2Ose) ahlasso lnoowteert hinattetnhseitsya amt plolews aqt t3h0a/n7 t0h,owseh iwchithar leesvse ry
clocsoenttoratsht e(Fmigautrceh 2pc)o, iwnth, iacph pise aa rtytopibcael ssliiggnh tolfy mlouwltieprlea tscloatwterqi.nSgi.n Pcleeatshei salcsaon nnootte btheaat tshigen saomf pmleusl taitp le
sca3t0te/7r0in, gw,hwicehs aurgeg veesrtyt hcalotsteh itso cthane mbeaatcthtr ipbouintetd, atpopheeatre troo gbeen seliigtihetslyin lothweerS LatD loowf t qh.e Spinacret itchleiss ,cpanonssoitb ly
be a sign of multiple scattering, we suggest that this can be attributed to heterogeneities in the SLD 
duoef ttohed epnasrtiticylevsa, rpiaotsisoibnlsy adruoeu ntod dtehnesiritya vvearraiagteiovnasl uareo,uwnhdi cthhecira navcearuagsee avnaluefef,e wcthtihchat ciasno cnaluysve iasnib le
vereyffecclot stehatto itsh oenmlya vticshibpleo ivnetr.y close to the match point. 
(a)
10% Silica particles
107
q  q  q       H2O/D O
106 1
2
2 3  70/30
 60/40
105  50/50
 40/60
104  30/70
103
102
101
100
10-4 10-3 10-2
(b) Q (Å-1) (c)
10% Silica particles 10% Silica particles
1,000 106
100
     H2O/D2O
800 q  = 1.0x10-4Å-1 10
5  70/30
1
80  60/40
4  50/50600 10  40/60
60  30/70
400 103
q2 = 2.6x10-4Å-1 40
200 102
q3 = 6.7x10-4Å-1
0 20 101
-200 0 100
20 30 40 50 60 70 10-4 10-3 10-2
% H2O in H2O/D2O Q (Å-1)  
FigFuigreur3e. 3C. oCnotnratrsatsvt avrairaitaitoinonw witihth1 100v vooll% % SSiiOO2 aatt ppHH 1100. .(a(a) )ScSacttering curves of samples with different 2 attering curves of samples with different
H HO2/OD/DO2Or raatitoioss; ;( (bb)) lleefftt aaxxiiss:: tthhee ssqquuaarree rroooott ooff tthhee ssccaattering intensity as a function of vol % H2O in 2 2 ttering intensity as a function of vol % H2O in
H HO2/OD/DO2Or raatitoioa anndd qq vvaalluuee ((bbrroowwnn,, rreedd,, aanndd oorraannggee ssyymmbboolsl sfofor rththe ethtrheree edidst2 2 isinticnt cqt-qv-avlualeuse).s T).hTeh fiettfeitdt ed
linleinceo rcroersrpeospnodnsdtos ttoh ethdea dtaatwa iwthitah pao psoitsiivteivsei gsnig(nd (adsahsehdedli nlien)ea) nadndn engeagtaivtieves isgingn(d (dotottetdedli lnine)e)s isgignnf oforrt he
firstthpe ofiinrstt, rpeospinetc, triveseplye.cRtiivgehltya. xRiisg: hTt axis: TiSnAS0,e.x5p minm 0.5p amthmle pnagtthh l(ebnlugeths t(abrlsu)ea sstaarfsu) nacst iao nfuonfcvtiooln of vol SAS,exp % H2O in
H %O /HD2OO inr aHti2oO; /(Dc)2aOp rlaottioo;f (tch) ea spclaottte orfin tghec uscravtetserfirnogm cu(ar)vneos rfmroamli z(ead) ntoortmhealsiazmede tvoa tlhuee saatmhieg vhaql.ue at 2high q2. 
 
dΣ/dΩsmeared (cm-1)
T(sas)exp 10% in 0.5mm
dΣ/dΩ -1smeared (cm )
Colloids Interfaces 2018, 2, 37 7 of 13
Another measure that can be used as a guide to evaluate the probability of multiple scattering,
is the so-called TSAS value. This corresponds to the fraction of the beam that passes through the
sample without being scattered [38,39]. The TSAS value of a sample is experimentally determined
as the ratio between the transmission of the direct beam (TRock, as measured on the main detector)
and the overall transmission of the direct beam and scattering pattern (TWide, as measured on the
transmission detector) and it can also be theoretically estimated. The definitions of these three values
are given in the Equations (5)–(7). Equation (8) was used for the theoretical estimation where Φ
is the volume fraction of particles, (∆SLD) is the neutron contrast between the particles, SLDparticle,
and the liquid, SLDsolvent, whose definition is given in the Equations (9) and (10); D is the diameter of
the particle, L is the sample thickness, ΦH2O is the volume fraction of H2O, and ΦD2O is the volume
fraction of D2O. As a guide, the ideal value for TSAS is above 0.9 (90%) [39]. A TSAS value well above
0.9 indicates that the scattering signal is rather weak for USANS with a reduced probability of multiple
scattering, while a decrease in a TSAS value below 0.9 indicates that there is an increased probability
of multiple scattering. The TSAS value can be a very useful tool as a guide to the expected degree of
multiple scattering [38–40]. Note however, that the effect of multiple scattering on scattering curves is
q-dependent (see discussion below), and a higher degree of multiple scattering can be tolerated if the
scattering curves do not show sharp features even in the single scattering regime.
In this study, we also used TSAS values to discuss the effect of multiple scattering in two different
geometries (i.e., flat cell, flow cell), and consequentially different path-lengths, under different solid
concentrations, and H2O/D2O ratios, coupling with changes in the scattering intensity.
T
T rockSAS,exp = (5)Twide
I
T sample(direct beam)Rock = (6)Iempty cell(direct beam)
I
T sample(direct beam plus scattering pattern)Wide = (7)Iempty cell(direct beam plus scattering pattern)
3 2 2
T −( λ Φ(1−Φ)(∆SAS,est = e 4 SLD) DL) (8)
∆SLD = SLDparticle − SLDsolvent (9)
SLDsolvent = ΦH2OSLDH2O + ΦD2OSLDD2O (10)
Table 1 shows the TSAS values with different H2O/D2O ratios for a system with 5 and 10 vol %
solid content in the tumbling cell with a thickness of 0.5 mm. Table 1 also shows the theoretically
estimated TSAS values for the same samples, based on Equation (8). The parameter in this Equation
that is not precisely known is the effective particle size D (it is a polydisperse system). This value
was manually adjusted to 2.25 µm to give very good agreement for the TSAS values at all investigated
contrasts for both the 5 vol % and 10 vol % silica sample. This value was also in good agreement with
the average particle size obtained for this sample from laser diffraction (2.4 µm). This good agreement
gave us confidence to use this formula to estimate the optimal H2O/D2O ratio for the Couette cell
(thickness = 1 mm) for rheo-SANS (see Table 1). The nominal/path-length thickness of the flow cell is
close to 1 mm, double of the tumbling cell thickness (0.5 mm).
Colloids Interfaces 2018, 2, 37 8 of 13
Table 1. Scattering length density (SLD) and TSAS values experimentally determined (TSAS,exp) at 5 vol % SiO2 and 10 vol % SiO2 at pH 10 with 0.5 mm path length,
respectively. Also shown are the corresponding calculated values TSAS, est for the thickness of 0.5 mm and 1 mm, using Equation (8) *.
Flat cell Flow cell
vol.%
SLD , Å−2
Tsas, exp Tsas,est T sas, exp
H O/D O (ave)2 2 5 vol.% SiO2 10 vol.% SiO2 5 vol.% SiO2 10 vol.% SiO2 5 vol.% SiO2 10 vol.% SiO2
in 0.5 mm in 0.5 mm in 0.5 mm in 0.5 mm in 1 mm in 1 mm 5 vol.% SiO2 10 vol.% SiO2
30/70 4.31 × 10−6 101% 100% 100% 99% 99% 99%
40/60 3.62 × 10−6 98% 92% 98% 96% 96% 92% 100% 92%
50/50 2.94 × 10−6 83% 74% 88% 79% 78% 63%
60/40 2.25 × 10−6 64% 57% 73% 56% 54% 31%
70/30 1.56 × 10−6 51% 33% 56% 33% 31% 11%
* The calculations are based on the literature value for the SLD of silica particles, and the particle size was used as an adjustable parameter to get good agreement between the experimental
and calculated values. It was fixed to 2.25 µm (close to the experimentally measured value of 2.4 µm by laser diffraction). The error in experimental TSAS values is estimated to be about 4%.
Colloids Interfaces 2018, 2, 37 9 of 13
 Colloids Interfaces 2018, 2, x FOR PEER REVIEW  9 of 12 
TThhee eexxppeerirmimeenntatalllyly ddeteetremrminiende dTsTass avsavluaelus ewsewree raelsaol spoloptltoedtt eind FinigFuirgeusr 2ebs a2nbda n3bd (3bblu(eb lsutaersst)a irns )
oirndoerr dteor itnoviensvtiegsattieg attheetihr eciorrcroerlaretiloanti ownitwhi tthhet hsecastctaetrtienrgin igntienntesnitsyi taysa as afufnucntciotino nofo fvvool l%% HH2O2O inin 
HH2O2O/D/2DO2.O I.t Ictacna nbeb enontoictiecde dthtahta tfofro rththe e5 5vvool l%% ssiliilcicaa ppaarrtticiclele ssuussppeennssioionnss TTsassa svvaaluluese saabboovvee 6600%% 
mmaainintatainineedd ggoooodd lilnineeaarirtiyty oonn ththe esqsquuaraer escsactattetreirning ginitnetnesnistyit yunutnilt i6l06 0vovlo %l % HH2O2 Oini nHH2O2/OD/2OD 2rOatiroa taito 
thate tlhoewleoswt qe srtaqngrae npgloetpteldot (t1e d× 1(10× A10)−, 4shAo−1−4 −1 w)in, sgh oonwlyin ag noengllyigaibnlee gelfifgeicbt loef emffueclttipolfem scualtttieprliensgc (aFtitgeruirneg 
2(bF)i.g Aurt e120 bv)o. lA %t  1s0ilivcoa lp%arstiiclilcea spuasprteicnlseiosnuss,p aebnosvioen 7s0,%ab Tosvase v7a0l%ueT msaasinvtaaluineedm athine tlaiinneeadrittyh,e ulipn etoa r5it0y ,
vuopl %to H502Ovo/Dl %2OH ra2Otio/ D(F2iOgurraet i3ob()F. iOgunr eth3eb o).thOenr thhaenodt,h feorrh tahned h, ifgohretrh eq hraignhgeers q(2ra.6n ×g e1s0(2 −4 −1−4 .A6 −×1, 61.07 × 1A0−4 ,
A6−.17),× th1e0r−e 4wAa−s 1n)o,  tdheevreiawtioans  nfroodme vthiaet iloinneafrroitmy ftohre tlhine ebaortihty 5f oarntdh 1e0b voothl %5  asnildic1a0 pvaortlic%les siluicsapepnasritoicnl,e 
insudsicpaetninsigo nth, aint dtihcea teinffgectth aotf tmheueltfifpeclet osfcamttuelrtiinpgle psrceastetenrti ning pthroesseen styisntethmoss eiss ymstinemimsails (mif inniomt aalb(siefnnto) t
waibtshe tnhte) swe iqth rathnegsees.q ranges.
BBaasseedd oonn ththeessee rreessuultltss, ,4400 vvool l%% HH2O2O wwasa ssesleelcetcetded fofor rththe erhrheoeo-s-esteutupp toto rerdeduucece mmuultlitpiplele scscaattteterriningg 
((TTSASAS,eSs,te =st 9=6%96 a%nda n9d2.59%2. 5a%t 1a mt 1mm pmathp laetnhgtlehn fgotrh thfoe r5 tvhoel 5%v aonld% 10a nvdol1 %0  vsaoml %ples,a smeep Tlea,bsleee 1T) awbhleile1 )
owpthiimleizoipntgi mthizei nsgcatthteerescda titnetreendsiitnyt.e Fnisgituyr.eF 4ig ushreow4 ss hthowe ssctahtetesrcinatgt ecruinrgvec ucrovmepcaormisponar ibseotnwbeeentw teheen 
mtheeasmuereamsuernetms eunstisngu sain fglaat cfleallt wceiltlhw tiuthmtbulimngb lmingotmioont iaonnda tnhde tChoeuCeottuee gtteeogmeeotmrye tfroyr frohreorh-UeoS-AUNSAS NatS 
aa sthaeasrh eraatre roaft e50o0f s5−01.0 Tsh−is1 .shTehairs rsahtee awr arsa tseelwecatseds ealse citt eisd waselilt aibsowvee ltlhaeb movineimthuemm riantiem tuhmat ernatseurtehda t
geonosdu rpeadrtgiocloed dpisaprteircsleiodni sdpuerrisniogn thdeu rminegasthueremeeanstu rfoemr ceonmt fpoarrciosomnp wariitsho nthwe ittuhmthbelitnugm fblalitn cgefllla. tTcheell .
vTishceovsiitsyc oosfi tthyeo sfuthspeesnussipoenn wsiaosn mweaassumreeads autr eindcaretainsicnrge acsoinnsgtacnont sshtaenatr srhaeteasr froart eas ffioxreda pfiexreidodp eorfi toidmoe f
(ptiemaek (hpoeladk tehsotl)d. Ttheset m). iTnhime mumin simheuamr rsahtee ator mraateinttoamin aai ncotanisntaancto vnisstcaonstitvyi wscaoss idtyetweramsidneetde ramndin heidghaenrd 
shhiegahre rrasteh etharanra ttheet hmainnitmheumi nwimasu tmestweda s(5t0es0t es−d1)(. 500 s−1).
 
FFigiguurree 44. .SSccaattteterirningg cucurvrvee cocommppaarirsiosonn bbeetwtweeeenn mmeeaasusureremmeenntsts uussiningg aa flflaat tcceelll lwwitihth tutummbblilningg mmootitoionn 
aanndd CCououetettet egegoemometerytr fyorf orrheroh-eUoS-UASNASN aSt 5a0t0 5s0−10 shs−ea1rs rhaetea.r (ara) t5e .vo(la %) 5 SivOo2l, %40 SvioOl %2,  H402Ov oinl  %H2OH/2DO2Oin 
rHat2ioO, /pDH21O0; r(abt)i o1,0p vHo1l 0%;  (Sbi)O120, 4v0o lv%ol S%iO H22,O40 inv oHl2%O/HD22O rinatHio2, OpH/D102.O ratio, pH10.
ItI tccaann bbee sseeenn ththaat tththeerree isis aa vveerryy ggoooodd aaggrreeemmeennt,t ,fofor rththee 55 vvool l%% ssiliilcicaa ssaammpplele (F(Figiguurere 44aa),) ,
bbeetwtweeenn ththee sshhaappee oof fththee ssccaatteterriningg ccuurrvveess oof fththee ssaammpplele inin ththee tutummbblilningg cceell laanndd inin ththee rrhheeoo-c-ceell laat t
55000 ss−1−, 1m, meaesausruerde dinidnedpeepnednednetnlytl.y T. hTeh ethtihcikcnkneses sofo tfhteh erhrheoe-oc-eclell dl duurirningg ddaatata rerdeduuctcitoionn, ,wwhhicichh imimppaacctsts 
oonn ththee oovveerraall linintetennssitiyty ssccaalele, ,wwaass cchhoosseenn toto bbee 11 mmmm aanndd ththee ggoooodd aaggrreeemmeennt tinin ththee inintetennssitiyty toto ththee 
ddaatata inin ttuummbblilningg mmooddee imimpplyly ththaat tththee ccuurrvvaatuturere oof fththee rrhheeoo-c-ceell lwwaass nnoot tssigignnifiificcaannt ttoto ininccrreeaassee ththee 
vvaaluluee ooff tthhee eefffeeccttivivee ssaammpplele tthhicickknneesss ssigignnifiificcaanntltyly. .AAt t1100 vvool l%% ((FFigiguurree 44bb),) ,wwee oobbsseerrvveedd ththaat tththee 
ssccaattteerriningg ccuurrvveess sslliigghhttllyy ddeevviiaattee aatt lloow qq bbeettween tthese ttwo scenarios. The experimental TSSAASS vvaalulueess 
foforr tthhee 55 vvooll % and 10 vol % silica sampllee,, TTaabblele1 1, ,c cleleaarlrylys hshoowwt hthatabt obtohthth tehseesesa smamplpeslesh sohuoludlndo ntobte 
bien ian raa rnagneg,ew, whehreerem muultlitpipleles csacattteterirninggi sisp prroonnoouunncceedd.. We therefore conclude thatt tthiiss ddiifffeerreennccee foforr 
ththee 1100 vvool l%% ssaammpplele isis aa rreeaal lssttrruuccttuurraal lcchhaannggee ththaat tisis ccaauusseedd bbyy ththee CCoouueettete sshheeaar.r .WWee ssuuggggeesst ttthhaat t
CCoouueettete sshheeaarr ggiviveess aa bbeetteterr ppaarrtticiclele ddisisppeerrssioionn ththaann ssimimpplele ttuummbblilningg mmootitoionn. .InIn ooththeerr wwoorrddss, ,ththeerree 
wweerree lleessss aaggggrreeggaatteess pprreesseenntt iinn tthhee rrheeomeetterr.  
Table 2 shows the TSAS values determined at different experimental conditions, such as 
solid/particle concentration, pH, and shear rate. Regardless of the experimental conditions varied, 
Colloids Interfaces 2018, 2, x; doi: FOR PEER REVIEW  www.mdpi.com/journal/colloids 
Colloids Interfaces 2018, 2, 37 10 of 13
Table 2 shows the TSAS values determined at different experimental conditions, such as
solid/particle concentration, pH, and shear rate. Regardless of the experimental conditions varied,
TSAS values were generally high enough (>90%) to reduce multiple scattering effects. For higher silica
concentration at 20 and 40 vol %, we anticipated even more multiple scattering than 5 and 10 vol % (if
we do not apply contrast variation). Thus, we selected slightly less H2O vol %—i.e., 37—compared
with the value suggested (40 vol % H2O) for less silica vol %. This yielded high TSAS values in general,
i.e., minimization of effects of multiple scattering.
There is a slight decrease in Tsas values with increasing the shear rate. It indicates the presence
of slightly more scattering that can be explained by the structural effects due to shear thickening
behavior of concentrated silica suspensions forming particle clustering [30]. Small degree of thickening
(i.e., small increase in viscosity) observed during the shear tests can explain the small change in Tsas
value. Thus, samples showing significant thickening behavior could largely reduce the Tsas value that
should be experimentally evaluated. Studying the effects of changes in particle/aggregate structure on
multiple scattering effects with the application of contrast variation can be a good future study topic in
this field.
Anovitz and Cole 2015 [11] reported that the thickness required for minimizing multiple scattering
effects and having TSAS value of higher than 90% is approximately below 0.15 mm without contrast
variation. In comparison, our sample thicknesses were 0.5 mm in a flat cell and 1 mm in a rheo-cell
that is up to the factor of 7 and still achieved minimizing multiple scattering effects, shown by TSAS
values higher than 90%.
Table 2. TSAS values experimentally determined from rheo-USANS measurements. The error in
experimental TSAS values is estimated to be about 4%.
SiO2 vol.% H2O% pH Shear rate (s−1) T(SAS)exp
250 102%
5 40 10 500 101%
1000 102%
250 94%
10 40 10 500 92%
1000 90%
500 98%
5 40 2 1000 99%
500 96%
10 40 2 1000 97%
500 98%
20 37 10 1000 97%
2000 94%
500 96%
20 37 2 1000 92%
2000 91%
5 94%
50 95%
40 37 2 500 95%
1000 77%
50 99%
500 99%
40 37 10 1000 100%
2000 99%
Colloids Interfaces 2018, 2, 37 11 of 13
4. Conclusions
The effect of H2O/D2O ratio was studied in terms of the scattering intensity and transmission
at different q values in order to further understand and reduce multiple scattering effects that can
be present in concentrated colloidal particle suspensions and maintain strong enough scattering
signals. We used two different sample geometries (i.e., flat cell√, rheo-cell) with different silica vol %,
and identified the changes in the square of scattering inte√nsity ( I) and transmission of silica particle
suspensions. In general, the deviations of the linearity of I, i.e., indication of multiple scattering only
observed at low q, well correlated with the decrease in the transmission that were evaluated by TSAS
values. The comparison between the experimentally determined and theoretically calculated TSAS
values showed good agreement. Thus, theoretical calculations were also applied to estimate the TSAS
values in different sample thickness and the selection of H2O/D2O ratio for rheo-USANS experiments.
It was found that H2O/D2O contrast variation is a good method to achieve the objectives of reducing
multiple scattering effects of colloidal particle suspensions for both ultra-small-angle neutron scattering
(USANS) and rheo-USANS experiments even for highly concentrated silica suspensions up to 40 vol %.
Author Contributions: Conceptualization, A.O. and C.J.G.; Formal analysis, A.O. and L.d.C.; Funding acquisition,
A.O.; Investigation, A.O. and L.d.C.; Methodology, A.O., L.d.C., C.J.G. and C.R.; Project administration, A.O.;
Resources, A.O.; Supervision, A.O.; Validation, A.O., L.d.C., C.J.G. and C.R.; Visualization, A.O. and L.d.C.;
Writing—original draft, A.O.; Writing–review & editing, A.O., L.d.C., C.J.G. and C.R.
Funding: Akira Otsuki would like to acknowledge the support for his travel to perform neutron scattering
experiments at ANSTO from the scientific mobility program between France and Australia as well as the
Observatoire Terre Environnement Lorraine (OTELo).
Acknowledgments: We acknowledge support of the Australian Centre for Neutron Scattering (ACNS) at the
Australian Nuclear Science and Technology Organisation (ANSTO), in providing the neutron research facilities
used in this work.
Conflicts of Interest: The authors declare no conflict of interest.
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