Fumed and Precipitated Hydrophilic Silica Suspension Gels in Mineral Oil: Stability and Rheological Properties

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Article Fumed and Precipitated Hydrophilic Silica Suspension Gels in Mineral Oil: Stability and Rheological Properties

Yoshiki Sugino and Masami Kawaguchi *

Laboratory of Colloid Rheology, Division of Chemistry for Materials, Graduate School of Engineering, Mie University, 1577 Kurimamachiya, Tsu 514-8507, Japan; [email protected] * Correspondence: [email protected]

Received: 26 June 2017; Accepted: 7 August 2017; Published: 9 August 2017

Abstract: Hydrophilic fumed silica (FS) and precipitated silica (PS) powders were suspended in mineral oil; increasing the silica volume fraction (ϕ in the suspension led to the formation of sol, pre-gel, and gel states. Gelation took place at lower ϕ values in the FS than the PS suspension because of the lower silanol density on the FS surface. The shear stresses and dynamic moduli of the FS and PS suspensions were measured as a function of ϕ. Plots of the apparent shear viscosity against shear rate depended on ϕ and the silica powder. The FS suspensions in the gel state exhibited shear thinning, followed by a weak shear thickening or by constant viscosity with an increasing shear rate. In contrast, the PS suspensions in the gel state showed shear thinning, irrespective of ϕ. The dynamic moduli of the pre-gel and gel states were dependent on the surface silanol density: at a ﬁxed ϕ, the storage modulus G0 in the linear viscoelasticity region was larger for the FS than for the PS suspension. Beyond the linear region, the G0 of the PS suspensions showed strain hardening and the loss modulus G” of the FS and PS suspensions exhibited weak strain overshoot.

Keywords: fumed silica suspension; precipitated silica suspension; mineral oil; surface silanol density; stability; rheological properties

1. Introduction Pristine fumed silica (FS) powders produced by hydrolysis of silicone tetrachloride in a flame, such as hydrophilic or native fumed silica powders, have a low tendency to aggregate and to form agglomerates because of their lower surface density of silanol groups; this results in a lower bulk density compared with precipitated hydrophilic silica (PS) powders, produced by acid precipitation of sodium silicate. The properties of FS powders suspended in polymer liquids, such as polydimethylsiloxane (PDMS) [1–10] have often been compared with those of PS powders [11,12], and the following differences were identified. The preparation of FS suspensions in PDMS requires lower amounts of powders compared with PS suspensions (1); FS suspensions show a higher bound rubber content, defined as the amount of non-extractable PDMS rubber (expressed as a percentage of the initial PDMS amount), than PS suspensions; this suggests that the silica/PDMS interaction is stronger in FS than PS suspensions, with larger adsorbed amounts of PDMS in the former (2); in the case of FS suspensions, the maximum loss modulus was observed at the end of the linear viscoelasticity region, whereas the loss modulus (G”) vs. strain curves of the PS suspensions showed no indications of strain-induced agglomeration (3). On the other hand, fewer studies have investigated PS suspensions in non-polar fluids such as mineral and paraffin oil, compared with several studies focused on FS suspensions. In the corresponding liquids, the FS particles interact through hydrogen bonds, which can result in the formation of a gel structure [13–17]. Khan and coworkers have thoroughly investigated the influence

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of the silica concentration on viscoelastic rheological properties [13–15] and static light scattering ofmeasurements the silica concentration [13] of FS suspensions on viscoelastic in mineral rheological oil, propertiesand they observed [13–15] andthe staticpresence light of scattering a gel-like measurementsnetwork. Yziquel [13 et] ofal. FShave suspensions studied the in non-linear mineral oil,viscoelastic and they behavior observed of theFS suspensions presence of in a gel-likeparaffin network.oil as a function Yziquel etof al.particle have studiedsize and the silica non-linear concentration viscoelastic [16]. behaviorThey found of FS that suspensions the reduced in paraffin storage oilmodulus as a function was independent of particle sizeof the and silica silica concentratio concentrationn and [16 that]. They the reduced found that loss the modulus reduced increased storage modulusmore rapidly was independentwith the strain of theamplitude silica concentration when the silica and concentration that the reduced was loss increased. modulus Chen increased et al. morereported rapidly the rheological with the strain properties amplitude of FS whensuspensions the silica in mineral concentration oil as a wasfunction increased. of particle Chen size et and al. reportedsilica concentration the rheological under properties steady and of FS oscillatory suspensions shear in mineral[17]. They oil found as a function that the of relative particle viscosities size and silicaof the concentration FS suspensions under were steady well and fitted oscillatory by the shearKrieger [17 and]. They Dougherty found that model the relative [18], which viscosities is often of theapplied FS suspensions to describe were the wellrelative fitted viscosities by the Krieger of concentrated and Dougherty hard modelsphere [ 18suspensions], which is oftenand plays applied an toimportant describe role the relativein understanding viscosities their of concentrated characteristics. hard sphere suspensions and plays an important role inAlthough understanding only few their studies characteristics. of PS suspensions in simple liquids, aimed at understanding their stabilityAlthough and rheological only few studies properties, of PS have suspensions been repo inrted, simple it can liquids, be expected aimed atthat understanding PS suspensions their in stabilitynon-polar and fluids rheological should be properties, stable at higher have silica been co reported,ncentrations it can because be expected of their thathigher PS surface suspensions silanol indensity non-polar compared fluids shouldwith the be FS stable powders. at higher Herein, silica we concentrations investigate changes because in of theirthe phase higher state surface and silanolrheological density properties compared of FS with and the PS FSsuspensions powders. in Herein, mineral we oil investigate where the PS changes suspensions in the should phase stateform andmore rheological compact aggregated properties microstructures of FS and PS suspensionsthan the FS insuspensions mineral oil due where to the the stronger PS suspensions hydrogen shouldbonding form between more compactthe higher aggregated surface microstructuressilanol groups, than associated the FS suspensions with variations due to in the the stronger silica hydrogenconcentration. bonding The results between are the discussed higher surfacein terms silanol of the groups,differentassociated surface silanol with density variations of the in two the silicamaterials. concentration. The results are discussed in terms of the different surface silanol density of the two materials. 2. Results and Discussion 2. Results and Discussion 2.1. Sample Classification 2.1. Sample Classification Based on visual inspection of the samples, the FS and PS suspensions were classified into sol, Based on visual inspection of the samples, the FS and PS suspensions were classified into sol, pre-gel, and gel states, irrespective of the silica powder type. The appearance of the silica suspensions pre-gel, and gel states, irrespective of the silica powder type. The appearance of the silica suspensions depended on the surface silanol density: the FS suspensions were found in the sol state (for φ ≤ 0.0083, depended on the surface silanol density: the FS suspensions were found in the sol state (for ϕ ≤ 0.0083, where φ is the volume fraction of silica in the suspensions), in the pre-gel state (for 0.0083 < φ ≤ 0.013), where ϕ is the volume fraction of silica in the suspensions), in the pre-gel state (for 0.0083 < ϕ ≤ 0.013), and in the gel state (for φ > 0.013); whereas the PS suspensions were in the sol state for φ ≤ 0.026, in and in the gel state (for ϕ > 0.013); whereas the PS suspensions were in the sol state for ϕ ≤ 0.026, in the pre-gel state for 0.026 < φ ≤ 0.030, and in the gel state for φ > 0.030. Figure 1 shows typical visual the pre-gel state for 0.026 < ϕ ≤ 0.030, and in the gel state for ϕ > 0.030. Figure1 shows typical visual appearances in the sol, pre-gel, and gel states of the FS suspensions. Gelation of the FS suspensions appearances in the sol, pre-gel, and gel states of the FS suspensions. Gelation of the FS suspensions took took place at lower silica concentrations compared with PS suspensions in mineral oil due to the less place at lower silica concentrations compared with PS suspensions in mineral oil due to the less surface surface silanol density and the less compact aggregated microstructures. A similar concentration silanol density and the less compact aggregated microstructures. A similar concentration dependence dependence of the gelation of PS suspensions in benzyl alcohol was observed by Hayashi and of the gelation of PS suspensions in benzyl alcohol was observed by Hayashi and Kawaguchi [19]. Kawaguchi [19].

Sol Pre-gel Gel Figure 1. Visual appearance of the fumed silica (FS) suspensions in the sol, pre-gel, and gel states. Figure 1. Visual appearance of the fumed silica (FS) suspensions in the sol, pre-gel, and gel states. 2.2. Transient Shear Stress 2.2. Transient Shear Stress Since a suspension is a complex dispersed system, it is important to understand its transient behaviorSince before a suspension examining is a its complex steady-state dispersed response system, for measuring it is important rheological to understand properties. its Figures transient 2– behavior4 show typical before transient examining shear its steady-state stress curves response of the FS for suspensions measuring rheological with φ = 0.013 properties. (pre-gel Figures state) 2and–4 show0.017 typical(gel state), transient and shearof the stress PS suspension curves of the with FS suspensionsφ = 0.030 (pre-gel with ϕ state),= 0.013 respectively. (pre-gel state) During and 0.017 the (gelpreshearing state), and period of the for PS suspensionthe pre-gel withstate,ϕ the= 0.030 shear (pre-gel stress state),of the respectively.FS suspensions During rapidly the preshearingreaches the periodplateau, for whereas the pre-gel the state, shear the stress shear of stress the PS of thesusp FSensions suspensions decreases rapidly with reaches increasing the plateau, time and whereas then gradually levels off to a plateau value. After the preshearing period, Figures 2 and 3 highlight a

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Gels 2017, 3, 32 3 of 12 Gels 2017, 3, 32 3 of 12 the shear stress of the PS suspensions decreases with increasing time and then gradually levels off sigmoid increase of the shear stress with increasing time, whereas the shear stress decreases sigmoidto a plateau increase value. of After the theshear preshearing stress with period, increasing Figures time,2 and 3whereas highlight the a sigmoidshear stress increase decreases of the sigmoidally with an increase in time in Figure 4, irrespective of the shear rate (). Similar changes in sigmoidallyshear stress with increasingan increase time, in time whereas in Figure the 4, shear irrespective stress decreases of the shear sigmoidally rate (). withSimilar an changes increase in in the measured shear stress after preshearing were. obtained for the FS and PS suspensions, irrespective thetime measured in Figure shear4, irrespective stress after of preshearing the shear rate were ( γ ).obta Similarined for changes the FS in and the PS measured suspensions, shear irrespective stress after of φ. At shear rates lower than 2 s−1, the shear stress in Figures 3 and 4 shows sustained oscillations, ofpreshearing φ. At shear were rates obtained lower than for the2 s− FS1, the and shear PS suspensions, stress in Figures irrespective 3 and 4 of showsϕ. At sustained shear rates oscillations, lower than whose−1 amplitude decreases with increasing shear rate. Moreover, sustained oscillations were whose2 s , theamplitude shear stress decreases in Figures with3 andincreasing4 shows shea sustainedr rate. oscillations, Moreover, whosesustained amplitude oscillations decreases were observed for the FS suspensions in the gel state and for the PS suspensions in the pre-gel and gel observedwith increasing for the shear FS suspensions rate. Moreover, in the sustained gel state oscillations and for the were PS suspensions observed for in the the FS pre-gel suspensions and gel in states. In contrast, no sustained shear stress oscillations were observed for the FS suspensions in the states.the gel In state contrast, and for no the sustained PS suspensions shear stress in the oscill pre-gelations and were gel observed states. In for contrast, the FS nosuspensions sustained in shear the pre-gel state, as shown in Figure 2. The difference in the FS and PS suspensions that exhibit sustained pre-gelstress oscillations state, as shown were in observed Figure 2. for The the difference FS suspensions in the inFS theand pre-gel PS suspensions state, as shown that exhibit in Figure sustained2. The oscillations is likely related to their different surface silanol density. Sustained oscillations in shear oscillationsdifference inis thelikely FS related and PS to suspensions their different that surf exhibitace silanol sustained density. oscillations Sustained is likely oscillations related in to shear their stress may reflect continuous repeated changes in buildup and breakdown of microstructures in the stressdifferent may surface reflect silanol continuous density. repeated Sustained changes oscillations in buildup in shear andstress breakdown may reﬂect of microstructures continuous repeated in the aggregated silica suspensions. aggregatedchanges in buildupsilica suspensions. and breakdown of microstructures in the aggregated silica suspensions. Similar sustained oscillations in the shear stress were observed for silica suspensions [20,21], SimilarSimilar sustained sustained oscillations oscillations in in the the shear shear stre stressss were were observed observed for for silica silica suspensions suspensions [20,21], [20,21], wormlike micelle solutions [22,23], as well as lamellar, onion, and sponge phases of surfactants wormlike micellemicelle solutionssolutions [ 22[22,23],,23], as as well well as lamellar,as lamellar, onion, onion, and spongeand sponge phases phases of surfactants of surfactants [24,25]. [24,25]. In these cases, the sustained oscillations were observed at specific shear rate ranges, beyond [24,25].In these In cases, these the cases, sustained the sustained oscillations oscillations were observed were observed at speciﬁc at specific shear rate shear ranges, rate ranges, beyond beyond which which steady-state shear thinning or thickening was observed. whichsteady-state steady-state shear thinningshear thinning or thickening or thickening was observed. was observed.

3 103 10 500 200500 50200 50 102 2 102 0.52 0.5

101 101 Shear stress (Pa) Shear stress (Pa) 100 00 1000 2000 3000 4000 5000 10 0 1000 2000 3000 4000 5000 Time (s) Time (s) Figure 2. Plots of the transient shear stress for the FS suspension at the volume fraction of silica φ = FigureFigure 2. 2. PlotsPlots of of the the transient transient shear shear stress stress for for the the FS FSsuspension suspension at the at thevolume volume fraction fraction of silica of silica φ = 0.013 at the shear rates of 0.5 s−1 (filled−1 orange circle), 2 s−1 (filled−1 purple circle), 50 s−1 (filled− 1blue circle), 0.013ϕ = 0.013 at theat shear the shear rates rates of 0.5 of s− 0.51 (filled s (filled orange orange circle), circle), 2 s−1 (filled 2 s purple(filled purple circle),circle), 50 s−1 (filled 50 s blue(filled circle), blue 200 s−1 (filled− green1 circle), and 500 s−1 (filled −red1 circle) as a function of time. 200circle), s−1 (filled 200 s green(filled circle), green and circle), 500 ands−1 (filled 500 s red(filled circle) red as circle)a function as a of function time. of time.

500 s-1 500 s-1 103 200 103 50200 1050 210 12 1 102 102

101 101 Shear stress (Pa) Shear stress (Pa) 100 1000 2000 4000 6000 8000 0 2000 4000 6000 8000 Time (s) Time (s) Figure 3. Plots of the transient shear stress for the FS suspension at φ = 0.017 at the shear rates of 1 s−1 Figure 3. Plots of the transient shear stress for the FS suspension at φ = 0.017 at the shear rates of 1 s−1 (filledFigure red 3. circle),Plots of 2 thes−1 (filled transient orange shear circle), stress 10 for s−1 the(filled FS purple suspension circle), at 50ϕ =s−1 0.017 (filled at blue the circle), shear rates 200 s of−1 (filled−1 red circle), 2 s−1 (filled−1 orange circle), 10 s−1 (filled−1 purple circle), 50 s−1 (filled− 1blue circle), 200 s−1 (filled1 s (filledgreen redcircle), circle), and 2 500 s s(filled−1 (filled orange black circle), circle) 10as sa function(filled purple of time. circle), 50 s (filled blue circle), −1 (filled200 s− green1 (filled circle), green and circle), 500 ands (filled 500 s −black1 (filled circle) black as circle)a function as a functionof time. of time.

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Gels 2017, 3, 32 3 4 of 12 10 500 s-1 Gels 2017, 3, 32 100 4 of 12 10 2 3 2 1 -1 10 500 s 0.5 100 10 2 2 101 1 0.5 Shear stress (Pa)

1 100 0 2000 4000 6000

Shear stress (Pa) Time (s) 100 Figure 4. Plots of the transient shear 0stress for 2000 the precipitated 4000 silica 6000 (PS) suspension at φ = 0.030 at the shear rates of 0.5 s−1 (filled red circle), 1 s−1 (filledTime orange (s) circle), 2 s−1 (filled purple circle), 10 s−1 (filled blue circle), 100 s−1 (filled green circle), and 500 s−1 (filled black circle) as a function of time. FigureFigure 4. Plots of thethe transienttransientshear shear stress stress for for the the precipitated precipitated silica silica (PS) (PS) suspension suspension at ϕat= φ 0.030 = 0.030 atthe at the shear rates of 0.5−1 s−1 (filled red circle), 1− 1s−1 (filled orange circle), 2− s1−1 (filled purple circle), 10 s−−1 2.3. Steady-Stateshear rates ofShear 0.5 sViscosity(filled red circle), 1 s (filled orange circle), 2 s (filled purple circle), 10 s (filled(filled blue circle), 100 s−1 1(filled(filled green green circle), circle), and and 500 500 s s−1− (filled1 (filled black black circle) circle) as as a function a function of of time. time.

Typical plots of the apparent steady-state shear viscosity (ηa) calculated from the ratio of the steady-state2.3.2.3. Steady-State Steady-State shear Shear Shear stress Viscosity Viscosity and , as a function of shear rate for FS and PS suspensions with different φ values,Typical are shown plots inof Figures the apparent 5 and 6, steady-state respectively. shear The steady-state viscosity (η shear) calculated stress was from regarded the ratio when of the Typical plots of the apparent steady-state shear viscosity (ηaa) calculated from the ratio of the transient shear stress was almost. independent of time for at least 5 min during the transient sweep. The steady-statesteady-state shear shear stress stress and and γ,, as a function of shear rate for FS and PSPS suspensionssuspensions with different φϕ plot for the FS suspension in the pre-gel state displays shear thinning behavior, while the FS suspension values, are shown in Figures Figures 55 andand6 6,, respectively. respectively. The The steady-state steady-state shear shear stress stress was was regarded regarded when when the the with φ = 0.017 in the gel state exhibits shear thinning behavior, followed by a small bump in η at the transienttransient shear shear stress stress was was almost almost independent independent of time time for at least 5 5 min during the transient sweep. a The The shearplot for rate the of FS FS 20 suspension suspension s−1, which seemsin in the the pre-gel pre-gelto be a kindstate state displaof displays weakys sheashear shearr thickening,thinning thinning behavior behavior, and the, while whileFS suspension the the FS FS suspension suspension with φ = 0.030 in the gel state shows shear thinning behavior, followed by constant and decreasing η with an with φϕ == 0.017 0.017 in in the the gel gel state state exhibits exhibits shear shear thinni thinningng behavior, behavior, followed followed by bya small a small bump bump ina η ina atη atheat −1 increasingshearthe shear rate rateofshear 20 of s rate.−1 20, which s In ,contrast, which seems seemsto the be PS a to kindsuspension be aof kind weaks of only shea weak exhibitr thickening, shear shear thickening, andthinning the andFS behavior, suspension the FS irrespective suspension with φ = ofwith theϕ specific= 0.030 state.in the The gel statedifference shows in shear η values thinning between behavior, the FS followed and PS by suspensions constant and depends decreasing on theηa 0.030 in the gel state shows shear thinninga behavior, followed by constant and decreasing ηa with an with an increasing shear rate. In contrast, the PS suspensions only exhibit shear thinning behavior, surfaceincreasing silanol shear density. rate. In On contrast, the other the hand, PS suspension when FS spowders only exhibit were shear dispersed thinning in polar behavior, organic irrespective solvents, irrespective of the specific state. The difference in η values between the FS and PS suspensions someof the interesting specific state. shear The thickening difference behaviors in η values were between observeda the and FS their and characteri PS suspensionsstics were depends discussed on theby depends on the surface silanol density. Ona the other hand, when FS powders were dispersed in polar thesurface interactions silanol density. between On silica the particother leshand, and when dispersants FS powders [14,15,26–28]. were dispersed in polar organic solvents, organic solvents, some interesting shear thickening behaviors were observed and their characteristics someA interesting useful parameter shear thickening to investigate behaviors the aggregated were observed structure and theirof particles characteri suspendedstics were in discusseda dispersing by liquidwere discussed is the relative by the viscosity interactions (η ) defined between as silica the ratio particles of η and to the dispersants viscosity [ 14of, 15the,26 dispersing–28]. liquid the interactions between silica particr les and dispersants [14,15,26–28].a A useful parameter to investigate the aggregated structure of particles suspended in a dispersing (ηo). ChenA useful et al. parameter reported to that investigate the ηr data the of aggregated hydrophilic structure and hydrop of particleshobic FS suspended suspensions in a dispersingin mineral liquid is the relative viscosity (ηr) defined as the ratio of ηa to the viscosity of the dispersing liquid (ηo). oilliquid [17] is were the wellrelative fitted viscosity by the Krieger(η ) defined and Doughertyas the ratio modelof η to [18], the whichviscosity is often of the applied dispersing to describe liquid Chen et al. reported that the ηr datar of hydrophilic and hydrophobica FS suspensions in mineral oil [17] the relative viscosities of concentrated hard sphere suspensions and plays an important role in (wereηo). Chen well fittedet al. byreported the Krieger that the and η Doughertyr data of hydrophilic model [18], and which hydrop is oftenhobic applied FS suspensions to describe thein mineral relative understanding their characteristics. Hayashi and Kawaguchi [19] also reported that the η values of oilviscosities [17] were of well concentrated fitted by the hard Krieger sphere and suspensions Dougherty and model plays [18], an which important is often role applied in understanding tor describe hydrophobicthetheir relative characteristics. viscosities PS suspensions Hayashi of concentrated andin benzyl Kawaguchi hardalcohol [sphere19] were also suspensions reported in good that agreement and the ηplaysr values with an ofimportantthe hydrophobic Krieger role and PSin Dougherty model [18]. understandingsuspensions in benzyltheir characteristics. alcohol were inHayashi good agreement and Kawaguchi with the [19] Krieger also reported and Dougherty that the modelηr values [18 ].of hydrophobic PS suspensions in benzyl alcohol were in good agreement with the Krieger and 102 Dougherty model [18]. 0.013 0.017 0.021 1012 0.013 0.017 0.021 (Pa s) (Pa

a 01

 10 (Pa s) (Pa

a -10

 1010 10-1 100 101 102 103 Shear rate (s-1) 10-1 -1 0 1 2 3 Figure 5. Double-logarithmic plots of10 the apparent10 10 steady-state10 10shear viscosities (η ) for the FS Figure 5. Double-logarithmic plots of the apparent steady-state shear viscosities (ηaa) for the FS Shear rate (s-1) suspensionssuspensions at at φϕ == 0.013 0.013 (open (open red red circle), circle), 0.017 0.017 (filled (ﬁlled red red ci circle),rcle), and and 0.021 0.021 (filled (ﬁlled blue blue square) square) as as a a functionfunction of of the the shear shear rate. rate. Figure 5. Double-logarithmic plots of the apparent steady-state shear viscosities (ηa) for the FS suspensions at φ = 0.013 (open red circle), 0.017 (filled red circle), and 0.021 (filled blue square) as a function of the shear rate.

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1 101 10 0.030 0.0300.035 0.035

0 100

(Pa s) (Pa 10 a (Pa s) (Pa  a 

10-1 10-110-1 100 101 102 103 10-1 100 101 102 103 -1 Shear rate (s-1 ) Shear rate (s ) Figure 6. Double-logarithmic plots of the apparent steady-state shear viscosities for the PS FigureFigure 6. Double-logarithmicDouble-logarithmic plots plots of theof apparentthe apparent steady-state steady-state shearviscosities shear viscosities for the PS for suspensions the PS suspensions at φ = 0.030 (open red circle) and 0.035 (filled red circle) as a function of the shear rate. suspensionsat ϕ = 0.030 at (open φ = 0.030 red circle) (open and red 0.035circle) (filled and 0.035 red circle) (filled as re ad functioncircle) as of a thefunction shear of rate. the shear rate. The Krieger and Dougherty model is described by the following equation: TheThe Krieger Krieger and and Dougherty Dougherty model model is is described described by by the the following following equation: equation: =(1− )[] (1) [] (1) =(1− ) −[η] ϕm ϕ ηr = 1 − (1) where φm is the maximum packing fraction and [] ϕism the intrinsic viscosity of the suspension. Figure where φm is the maximum packing fraction and [] is the intrinsic viscosity of the suspension. Figure 7 shows the fitting of the Krieger and Dougherty equation to the η vs. φ values measured for the FS where ϕ is the maximum packing fraction and [η] is the intrinsic viscosityr of the suspension. Figure7 7 shows them fitting of the Krieger and Dougherty equation to the ηr vs. φ values measured for the FS and PS suspensions at a shear rate of 1000 s−1; the fitting was performed by the least squares method andshows PS suspensions the fitting of theat a Kriegershear rate and of Dougherty 1000 s−1; the equation fitting towas the performedηr vs. ϕ values by the measured least squares for the method FS and −1 withPS suspensions two unknown at a shearparameters: rate of 1000φm and s ;[ the]. The fitting dashed was performed lines in the by thefigure, least corresponding squares method to withthe with two unknown parameters: φm and []. The dashed lines in the figure, corresponding to the Kriegertwo unknown and Dougherty parameters: equation,ϕm and show [η]. Thean excellent dashedlines fit to in the the experimental figure, corresponding data, with to resulting the Krieger φm Krieger and Dougherty equation, show an excellent fit to the experimental data, with resulting φm andand [ Dougherty] parameters equation, of 0.41 showand 48 an for excellent the FS fitsuspensions to the experimental and 0.51 and data, 34 with for resultingthe PS suspensions,ϕm and [η] and [] parameters of 0.41 and 48 for the FS suspensions and 0.51 and 34 for the PS suspensions, respectively.parameters of The 0.41 fitted and 48φ for values the FS are suspensions smaller than and the 0.51 theoretical and 34 for value the PS of suspensions, 0.74 for a close-packed respectively. respectively. The fitted φ m values are smaller than the theoretical value of 0.74 for a close-packed The fitted ϕm values are smallerm than the theoretical value of 0.74 for a close-packed array of spheres array of spheres of identical size, and the φm obtained for the FS suspensions is lower than that arrayof identical of spheres size, andof identical the ϕm obtainedsize, and for the the φm FS obtained suspensions for the islower FS suspen than thatsions corresponding is lower than tothat the corresponding to the PS suspensions. This indicates that the FS and PS suspensions have a relatively correspondingPS suspensions. to Thisthe PS indicates suspensions. that the This FS indicates and PS suspensions that the FS and have PS a relativelysuspensions more have open a relatively structure more open structure than the concentrated hard sphere suspensions, and the PS suspensions form morethan theopen concentrated structure than hard the sphere concentrated suspensions, hard and sphere the PS suspensions, suspensions and form the more PS suspensions tightly packed form and more tightly packed and agglomerated structures than the FS ones, owing to stronger hydrogen moreagglomerated tightly packed structures and than agglomerated the FS ones, structures owing to strongerthan thehydrogen FS ones, bondingowing to interactions stronger hydrogen [11,12,19]. bonding interactions [11,12,19]. In contrast, the [] value of the FS suspensions is larger than that of bondingIn contrast, interactions the [η] value [11,12,19]. of the In FS contrast, suspensions the [ is] largervalue thanof the that FS suspensions of the PS ones, is larger indicating than thatthat theof the PS ones, indicating that the former suspensions are less compact and form larger agglomerated theformer PS ones, suspensions indicating are that less the compact former and suspensi formons larger are agglomerated less compact structuresand form larger than the agglomerated latter. Thus, structures than the latter. Thus, larger [] values correspond to less compacted aggregates [29]. structureslarger [η] than values the correspond latter. Thus, to larger less compacted [] values aggregates correspond [29 to]. less compacted aggregates [29]. 5 5 FS FSPS 4 PS 4

r 3  r 3 

2 2

1 1 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05   Figure 7. The relative viscosity values of the FS (open blue circle) and PS suspensions (filled blue Figure 7. The relative viscosity values of the FS (open blue circle) and PS suspensions (filled blue circle)Figure at 7. theThe sh relativeear rate of viscosity 103 s−1 as values a function of the of FS φ. (open The dashed blue circle) lines andrepresent PS suspensions fit to the Krieger (ﬁlled blueand circle) at the shear rate of 1033 s−−1 as1 a function of φ. The dashed lines represent fit to the Krieger and Doughertycircle) at the equation. shear rate of 10 s as a function of ϕ. The dashed lines represent ﬁt to the Krieger and DoughertyDougherty equation. equation. 2.4. Dynamic Modulus 2.4. Dynamic Modulus Typical dynamic modulus vs. oscillatory shear strain curves of FS and PS suspensions with Typical dynamic modulus vs. oscillatory shear strain curves of FS and PS suspensions with various φ values are shown in Figures 8 and 9, respectively. The figures highlight that the linear various φ values are shown in Figures 8 and 9, respectively. The figures highlight that the linear

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2.4. Dynamic Modulus Typical dynamic modulus vs. oscillatory shear strain curves of FS and PS suspensions with Gels 20172017,, 33,, 3232 66 ofof 1212 various ϕ values are shown in Figures8 and9, respectively. The ﬁgures highlight that the linear region, region,region,in which inin the whichwhich dynamic thethe dynamicdynamic modulus modulusmodulus is independent isis independentindependent of the oscillatory ofof thethe oscillatoryoscillatory strain, spans strain,strain, a wider spansspans range aa widerwider for therangerange FS forforthan thethe the FSFS PS thanthan suspension; thethe PSPS suspension;suspension; moreover, themoreover,moreover, linear region thethe lilinear of the region FS suspension of the FS decreasessuspension with decreases increasing withϕ , increasingincreasingwhereas that φ,, whereaswhereas of the PS thatthat suspension ofof thethe PSPS shows suspensionsuspension the opposite showsshows thetheϕ dependence.oppositeopposite φ dependence.dependence. In addition, InIn at addition,addition,ϕ = 0.035, atat φ the == 0.035,dynamic the modulusdynamic ofmodulus the FS suspensionof the FS suspension in the linear in regionthe linear is larger region than is larger that of than the PSthat suspension. of the PS suspension.suspension.This suggests ThisThis that suggestssuggests the structure thatthat thethe of structurestructure the FS suspension ofof thethe FSFS suspensionsuspension is stronger isis and strongerstronger harder andand to harder breakharder up toto break thanbreak that upup thanthanof the thatthat PS suspension.ofof thethe PSPS suspension.suspension. The observed TheThe differences observedobserved indifferences the dynamic in the moduli dynamic and in moduli the corresponding and in the correspondingcorrespondingrange of their linear rangerange regions ofof theirtheir likely linearlinear derive regionsregions from likelylikely the somewhat derive from stronger the somewhat attractive interactions stronger attractive between interactionsinteractionsaggregated silicabetweenbetween particles aggregatedaggregated in mineral silicasilica oil particlesparticles with decreasing inin mineralmineral surface oiloil withwith silanol decreasingdecreasing density, surfacesurface as further silanolsilanol discussed density,density, asbelow. further Similar discussed results below. were Simila observedrr resultsresults for all werewereϕ values, observedobserved and forfor the allall dynamic φ values,values, moduli and the in dynamic the linear moduli region 0 ininincreased thethe linearlinear with regionregion increasing increasedincreasedϕ, irrespective withwith increasingincreasing of the silicaφ,, irrespectiveirrespective powder. Moreover, ofof thethe silicasilica the powder.powder. storage modulus Moreover,Moreover, (G the)the in storagestoragethe linear modulusmodulus region was((G′′)) largerinin thethe linear thanlinear the regionregion loss moduluswaswas largerlarger (G” thanthan), irrespective thethe lossloss modulusmodulus of ϕ. ((G″),), irrespectiveirrespective ofof φ..

5 10105 G' 0.017 G" 0.017 4 G' 0.035 10104 G' 0.035 G" 0.035

3 10103

2 G', G" (Pa) 10 2 G', G" (Pa) 10

1 1 1010 -2 -1 0 1 2 3 1010-2 1010-1 10100 10101 10102 10103 Strain (%) Strain (%) FigureFigure 8. Double-logarithmicDouble-logarithmic plotsplots plots of of the the storage storage modulus modulus ( (GG′′0,,, filledfilled ﬁlled circles)circles) circles) andand thethe loss loss modulus modulus ((G"G”,, openopen squares) squares) for for the the FS FS suspensions suspensions at at φϕ == 0.0170.017 0.017 (red)(red) (red) andand and 0.0350.035 (blue)(blue) asas aa functionfunction ofof strain.strain.

4 10104 0.0350.035 G'G' 0.0350.035 G''G'' 3 0.045 G' 10103 0.045 G' 0.0450.045 G''G''

2 10102

1 G', G" (Pa) 10 1 G', G" (Pa) 10

0 10 0 10 -2 -1 0 1 2 3 1010-2 1010-1 10100 10101 10102 10103 Strain (%) Strain (%) Figure 9. Double-logarithmic plots of G' (filled circles) and G" (open circles) for the PS suspensions at Figure 9. Double-logarithmicDouble-logarithmic plots of G'G0 (filled(ﬁlled circles) circles) and G"G” (open(open circles) circles) for the PS suspensions suspensions at φ = 0.035 (red) and 0.045 (blue) as a function of strain. φϕ == 0.035 0.035 (red) (red) and and 0.045 0.045 (blue) (blue) as as a a function function of of strain. strain.

The presence of the linear region in the oscillatory shear tests indicates that the FS and PS The presence of the linear region in the oscillatory shear tests indicates that the FS and PS suspensionssuspensions inin thethe gelgel statestate behavebehave asas aa gelgel network,network, formedformed uponupon coalescencecoalescence ofof aggregatesaggregates ofof silicasilica suspensions in the gel state behave as a gel network, formed upon coalescence of aggregates of silica particles (i.e., a floc). The latter process is promoted by bonding interactions between the silica particles (i.e., a ﬂoc). The latter process is promoted by bonding interactions between the silica particles, particles, which take place through the hydrogen bonds in the mineral oil. The formation of the gel which take place through the hydrogen bonds in the mineral oil. The formation of the gel network in network in the silica suspensions can be analyzed throughthrough thethe silicasilica concentrationconcentration dependencedependence ofof thethe the silica suspensions can be analyzed through the silica concentration dependence of the G0 value in G′′ valuevalue inin thethe linearlinear regionregion ((G′′0),), andand ofof thethe criticalcritical oscillatoryoscillatory shearshear strainstrain ((γc)) atat whichwhich thethe linearlinear the linear region (G0 ), and of the0 critical oscillatory shear strain (γ ) at which thec linear region ends, region ends, according0 to scaling models based on fractal analysisc [30–32]. This approach has been regionaccording ends, to according scaling models to scaling based models on fractal based analysis on fractal [30– analysis32]. This [30–32]. approach This has approach been successfully has been successfullysuccessfully appliedapplied toto severalseveral systems,systems, suchsuch asas FSFS suspensionssuspensions inin organicorganic solventssolvents [16,33–35][16,33–35] andand inin water [36–38], and PS suspensions in benzyl alcohol [19].

As shown in Figure 10, G′0 increases with increasing φ for both FS and PS suspensions; in As shown in Figure 10, G′0 increases with increasing φ for both FS and PS suspensions; in contrast, the magnitude of the γc value of the FS and PS suspensions decreases and increases with contrast, the magnitude of the γc value of the FS and PS suspensions decreases and increases with increasingincreasing φ,, respectively.respectively. SuchSuch φ dependencesdependences indicateindicate thatthat thethe FS and PS suspensions can be

Gels 2017, 3, 32 7 of 12 applied to several systems, such as FS suspensions in organic solvents [16,33–35] and in water [36–38], and PS suspensions in benzyl alcohol [19]. 0 As shown in Figure 10, G 0 increases with increasing ϕ for both FS and PS suspensions; in contrast, Gelsthe 2017 magnitude, 3, 32 of the γc value of the FS and PS suspensions decreases and increases with increasing7 of 12 ϕ, respectively. Such ϕ dependences indicate that the FS and PS suspensions can be classified as a classifiedstrong-link as and a strong-link a weak-link and gel, a respectivelyweak-link gel, [30 –respectively32]. In the case [30–32]. of a strong-link In the case gel, of thea strong-link links between gel, thedifferent links flocsbetween (interfloc different links) flocs have (interfloc a higher links) elastic have constant a higher than elastic those constant within the than same those floc within (intrafloc the samelinks), floc whereas (intrafloc in a links), weak-link whereas gel the in a interfloc weak-link links gel are the weaker interfloc than links the are intrafloc weaker ones than [the30– 32intrafloc]. This onesshows [30–32]. that the This PS shows suspensions that the form PS suspensions more compact form flocs more than compact the FS suspensions flocs than the due FS tosuspensions the higher duesurface to the silanol higher density. surface The silanol difference density. in theThe gel differe statence associated in the gel with state the associated FS and PS with silica the suspensions FS and PS silicaleads suspensions to their unique leads linear to their rheological unique responseslinear rheological described responses above. described above.

1 105 10 FS G' 0 PS G' 0 4 10  c (%) 0

(Pa) 10 0

G' 103 FS c PS c -1 102 10 10-2 10-1

 0 0 Figure 10. Double-logarithmicDouble-logarithmic plots plots of of the theG Gvalue′ value inthe in linearthe linear region region (G 0, filled(G'0, filled circles) circles) and the and critical the criticaloscillatory oscillatory shear strain shear (γ strainc, open (γ circles)c, open forcircles) the FS for (red) the FS and (red) PS (blue)and PS suspensions (blue) suspensions as a function as a function of ϕ. of φ. Although it is possible to estimate the fractal dimension of the FS and PS suspensions from the Although it is possible to estimate the0 fractal dimension of the FS and PS suspensions from the slope of the double logarithmic plots of G 0 and γc as a function of ϕ, we did not attempt to calculate it φ slopein this of case, the owingdouble tologarithmic the narrow plots ranges of G of′0ϕ andin theγc as pre-gel a function and gelof states,, we did as wellnot attempt as to the to somewhat calculate itscattered in this case, data owing (see Figure to the 10 narrow). ranges of φ in the pre-gel and gel states, as well as to the somewhat scatteredFurthermore, data (see fromFigure the 10). frequency dependence of the dynamic moduli, the linear region—observed for theFurthermore, FS and PS suspensions from the frequency in the pre-gel dependence and gel states of the (not dynamic shown)—indicates moduli, the that linear the Gregion—0 and G” observedvalues are for almost the FS independent and PS suspensions of the frequency, in the pre- irrespectivegel and gel of ϕstates, and (not the magnitudesshown)—indicates of the G that0 values the Gare′ and larger G″than values those are ofalmost the G” independentvalues. This of indicates the frequency, that these irrespective silica suspensions of φ, and arethein magnitudes the gel state. of the GThe′ values non-linear are larger trends than beyond those of the the linear G″ values. region This in the indicates dynamic that moduli these vs. silica strain suspensions plots, known are asin thelarge gel amplitude state. oscillatory shear (LAOS) responses, provide information on the interactions and on the shear-inducedThe non-linear formation trends beyond of microstructures the linear region in complex in the dynamic fluids, such moduli as polymer vs. strain solutions, plots, known polymer as largemelts, amplitude suspensions, oscillatory and emulsions. shear (LAOS) Hyun responses, et al. [39 –provide41] proposed information that the on LAOS the interactions responses and can on be theclassified shear-induced into four differentformation categories: of microstructures strain thinning, in complex strain hardening, fluids, such weak as strain polymer overshoot, solutions, and polymerstrong strain melts, overshoot. suspensions, Figures and8 emulsions. and9 highlight Hyun some et al. significant [39–41] proposed features that in the the LAOS LAOS responses responses canof the be FS classified and PS suspensions.into four different In the casecategories: of the FSstrain suspensions, thinning, thestrainG0 valueshardening, beyond weak the linearstrain overshoot,region decrease and strong with increasingstrain overshoot. strain, whereasFigures 8 the anG”d 9 valueshighlight show some a weak significant strain features overshoot; in the G”LAOSand responsesG0 curves of crossthe FS each and otherPS suspensions. at a given In strain, the case and of thenthe FS gradually suspensions, decrease the G with′ values increasing beyond thestrain. linear The region strain atdecrease which the withG” andincreasingG0 curves strain, cross whereas each other the decreases G″ values with show increasing a weakϕ, whichstrain overshoot;indicates that the theG″ and FS suspensionsG′ curves cross become each other more at brittle a given with strain, increasing and thenϕ. gradually An increase decrease in G” withjust increasing strain. The strain at which the G″ and G′ curves cross each other decreases with increasing φ, which indicates that the FS suspensions become more brittle with increasing φ. An increase in G″ just before decreasing in the non-linear region seems to correspond to a dissipative energy due to partial deformation of aggregated microstructures under shear. Similar results were obtained for several silica suspensions [14,15,19,33–35]. In contrast, the G′ values for the PS suspensions beyond the linear region decrease less steeply with increasing strain, compared with the FS suspensions. The G′ values show a clear peak, namely

Gels 2017, 3, 32 8 of 12 Gels 2017, 3, 32 8 of 12 before decreasing in the non-linear region seems to correspond to a dissipative energy due to partial φ straindeformation hardening of at aggregated a strain value microstructures that increases under with shear. increasing Similar results , and were the obtained G″ values for several also silicaexhibit a weaksuspensions strain overshoot: [14,15,19 in,33 particular,–35]. the PS suspensions exhibit a strong strain overshoot. The G″ and G′ curvesIn cross contrast, each the otherG0 values at a given for the strain, PS suspensions and then beyondgradually the decrease linear region with decrease increasing less steeplystrain. The strainwith values increasing corresponding strain, compared to the with strain the hardening FS suspensions. in the The GG′0 values showand ato clear the peak,crossover namely point betweenstrain the hardening G″ and at G a′ straincurves value increase that increases with increasing with increasing φ thisϕ ,indicates and the G” thatvalues the alsoPS exhibitsuspensions a possessweak stronger strain overshoot: structures in than particular, the FS the suspensions. PS suspensions exhibit a strong strain overshoot. The G” and 0 GThecurves different cross φ each dependence other at a givenof the strain, strain and value then at gradually which the decrease crossover with increasingoccurs in strain.the FS Theand PS 0 suspensionsstrain values and corresponding the presence to of the strain strain hardening hardening in in the theG valuesG′ values and toofthe the crossover PS suspensions point between seem to the G” and G0 curves increase with increasing ϕ this indicates that the PS suspensions possess stronger indicate that the PS suspensions form more rigid and less brittle aggregated microstructures than the structures than the FS suspensions. FS ones under the conditions corresponding to the LAOS responses. Moreover, the strains The different ϕ dependence of the strain value at which the crossover occurs in the FS and correspondingPS suspensions to the and thecrossover presence point of strain are hardening higher for in the theG 0 presentvalues of FS the PSsuspensions suspensions than seem for to FS 3 4 suspensionsindicate thatin benzyl the PS suspensionsalcohol [33], form for more which rigid the and G′ less0 values brittle range aggregated from microstructures4 × 10 to 2 × 10 than Pa, the and FS the correspondingones under strains the conditions are less corresponding than 1% in the to the gel LAOS states responses. with 0.095 Moreover, ≤ φ ≤ 0.115. the strains corresponding to the crossover point are higher for the present FS suspensions than for FS suspensions in benzyl Furthermore, the double logarithmic plots of the reduced moduli (G′/G′0 and G″/G″0, where G″0 alcohol [33], for which the G0 values range from 4 × 103 to 2 × 104 Pa, and the corresponding strains is the loss modulus in the linear0 region) vs. strain in the LAOS response region have often proven are less than 1% in the gel states with 0.095 ≤ ϕ ≤ 0.115. useful to understand the complicated behavior of complex fluids [39–41],0 as0 well as of FS [34,35] and Furthermore, the double logarithmic plots of the reduced moduli (G /G 0 and G”/G”0, where PS silica suspensions [19]. The reduced moduli G′/G′ and G″/G″ for the FS and PS suspensions are G”0 is the loss modulus in the linear region) vs. strain0 in the LAOS response0 region have often proven plotteduseful in toFigures understand 11 and the complicated12, respectively. behavior Both of complex reduced ﬂuids moduli [39–41 do], asnot well fully as of overlap FS [34,35 ]with and the PS silica suspensions [19]. The reduced moduli G0/G0 and G”/G” for the FS and PS suspensions are respective master curves: the G′/G′0 values show a negative0 deviation0 that increases with increasing plotted in Figures 11 and 12, respectively. Both reduced moduli do not fully overlap with the respective φ; this occurs at strain values higher than 5% for the FS suspensions and beyond the stain hardening master curves: the G0/G0 values show a negative deviation that increases with increasing ϕ; this for the PS suspensions, respectively.0 On the other hand, the G″/G″ values beyond the strain occurs at strain values higher than 5% for the FS suspensions and beyond the0 stain hardening for the PS overshootsuspensions, show a respectively. negative deviation On the other that hand, increases the G” with/G”0 increasingvalues beyond φ. Similar the strain negative overshoot deviations show a of 0 0 the reducednegative G deviation′/G′0 and that G″ increases/G″0 moduli with increasingwere observedϕ. Similar for negativeFS suspension deviations gels of in the benzyl reduced alcoholG /G 0 [33]. and G”/G”0 moduli were observed for FS suspension gels in benzyl alcohol [33]. In contrast, a positive In contrast, a positive deviation of the G″/G″0 values beyond the strain overshoot has often been deviation of the G”/G”0 values beyond the strain overshoot has often been observed for hydrophobic observedFS and for PS suspensionshydrophobic in organicFS and solvents PS suspensions [19,34,35], where in organic strong hydrophobicsolvents [19,34,35], interactions where between strong hydrophobichydrophobic interactions chains and between the dispersion hydrophobic medium ch areains present. and the dispersion medium are present.

101

0 100 G' 0.013 G" 0.013 -1 10 G' 0.017 , G"/G"

0 G" 0.017 G' 0.035 -2 10 G" 0.035 G'/G' G' 0.045 G" 0.045 10-3 10-3 10-2 10-1 100 101 102 103 Strain (%) 0 0 FigureFigure 11. Double-logarithmic 11. Double-logarithmic plots plots of of G'/G'G /G 00 (filled(ﬁlled circles)circles) and andG” G"/G”/G"0 (open0 (open circles) circles) for for the FSthe FS suspensions at ϕ = 0.013 (red), 0.017 (red), 0.035 (orange), and 0.045 (green) as a function of strain. G”0 suspensions at φ = 0.013 (red), 0.017 (red), 0.035 (orange), and 0.045 (green) as a function of strain. G″0 is the loss modulus in the linear region. is the loss modulus in the linear region.

Gels 2017, 3, 32 9 of 12 Gels 2017, 3, 32 9 of 12

101

0 0 10

10-1 G' 0.031 G" 0.031

, G"/G" G' 0.035 0 -2 10 G" 0.035 G' 0.040 -3 G" 0.040 G'/G' 10 G' 0.045 G" 0.045 10-4 10-3 10-2 10-1 100 101 102 103 Strain (%) Figure 12. Double-logarithmic plots of G'/G'0 0 (filled circles) and G"/G" (open circles) for the PS Figure 12. Double-logarithmic plots of G /G 00 (ﬁlled circles) and G”/G”00 (open circles) for the PS suspensionssuspensions at at φϕ == 0.031 0.031 (red), (red), 0.035 0.035 (red), (red), 0.040 0.040 (orange), (orange), an andd 0.045 0.045 (green) (green) as as a a function function of of strain. strain.

3.3. Experimental Experimental Procedures Procedures

3.1.3.1. Materials Materials FSFS and and PS PS powders powders were were kindly kindly supplied supplied from from Nippon Nippon Aerosil Aerosil Co. Co. Ltd.Ltd. (Yokkaichi, (Yokkaichi, Japan) Japan) and Tosohand Tosoh Silica SilicaCo. Ltd. Co. (Shunan, Ltd. (Shunan,Japan), respectively. Japan), respectively. The primary The silica primary particle silica size, particle Brunauer– size, Emmett–TellerBrunauer–Emmett–Teller (BET) specific (BET) surface specific area, surface and surface area, andsilanol surface density silanol of the density FS powders of the were FS powders 16 nm, 2 −2 130were ± 1625 nm,m2/g, 130 and± 252.2 m nm/g,−2, andrespectively. 2.2 nm ,On respectively. the other Onhand, the the other PS hand, powders the PS exhibited powders a exhibitedprimary 2 silicaa primary particle silica size particle of 19 nm, size a of BET 19 nm,specific a BET surface specific area surface of 155 area m2/g, of and 155 ma surface/g, and silanol a surface density silanol of −2 ca.density 4 nm of−2. ca. The 4nm above. The product above specifications product specifications were obtained were obtained from the from respective the respective suppliers. suppliers. The respectiveThe respective silica silica powders powders were were dried dried under under vacuum vacuum in inanan incubator incubator box box and and then then stored stored until until the the preparationpreparation of their suspensions. MineralMineral oil oil Cosmo Cosmo Pure Pure Safety Safety 46,46, supplied supplied from from Cosmo Cosmo Oil Lubricants Oil Lubricants Co. Ltd. Co. (Tokyo, Ltd. Japan), (Tokyo, wasJapan), used was as a used dispersant, as a dispersant, without further without purifica furthertion. purification. This mineral This oil has mineral a density oil has of a0.895 density g cm of−3 −3 ◦ 2 −1 ◦ at0.895 15 °C, g cm a kinematicat 15 C, viscosity a kinematic of 43.5 viscosity cSt (cm of2 s 43.5−1) at cSt40 °C, (cm ans average) at 40 molecularC, an average weight molecular of 403 g weightmol−1, − andof 403 paraffinic, g mol 1 ,naphthenic, and paraffinic, and naphthenic, aromatic hydrocarbon and aromatic contents hydrocarbon of 59.2, contents 30.2, ofand 59.2, 10.6 30.2, wt and%, respectively.10.6 wt %, respectively.

3.2.3.2. Preparation Preparation of of Silica Silica Suspensions Suspensions ToTo prepare a suspension, weighted amounts amounts of of th thee silica silica powder powder and and 30 30 mL mL mineral mineral oil oil were were mixedmixed in in a a 150 150 mL mL vessel. vessel. The The silica silica concentrations concentrations were were expressed expressed by by φϕ ofof silica silica in in the the suspensions. suspensions. TheThe resulting resulting suspensions suspensions were were agitated agitated for for 5 min 5 min with with a rotation a rotation of 800 of 800rpm rpmand a and revolution a revolution of 2000 of rpm,2000 and rpm, then and de-aerated then de-aerated for 3 min for with 3 min a withrotation a rotation of 60 rpm of 60and rpm a revolution and a revolution of 2200 rpm of 2200 using rpm a Keyenceusing a Keyence (Thinky (ThinkyCorporation, Corporation, Tokyo, Japan) Tokyo, HM-5 Japan)00 HM-500 hybrid hybridmixer—A mixer—A planetary planetary centrifugal centrifugal mixer thatmixer uses that a uses mechanism a mechanism in which in which the thecontainer container holding holding the the material material revolves revolves clockwise clockwise and and the the containercontainer itself itself rotates rotates counter-clockwise. counter-clockwise. The The suspensions suspensions were were placed placed in in a a Sanyo Sanyo MIR-153 MIR-153 incubator incubator ◦ (Sanyo(Sanyo Electric Electric Co., Co., Ltd., Ltd., Osaka, Osaka, Japan) Japan) at at 25 25 °CC fo forr 1 1 h h under under double double agitation, agitation, after after which which they they were were subjectedsubjected to to visual visual inspections inspections and and rheological rheological measurements. 3.3. Rheological Measurements 3.3. Rheological Measurements The FS and PS suspensions in the pre-gel and gel states were placed on a frosted glass plate of a The FS and PS suspensions in the pre-gel and gel states were placed on a frosted glass plate of a cone-plate ﬁxture with a diameter of 35 mm and an angle of 1◦ and then preconditioned by shearing cone-plate fixture with a diameter of 35 mm and an angle of 1° and then preconditioned by shearing at a rate of 1000 s−1 for 1500 s, 2000 s, or 3600 s. Longer preconditioning times were needed with at a rate of 1000 s−1 for 1500 s, 2000 s, or 3600 s. Longer preconditioning times were needed with increasing ϕ The serrated plate was used to suppress slippage of the suspension at the sample/plate increasing φ The serrated plate was used to suppress slippage of the suspension at the sample/plate interface. Transient stress measurements using a stress-controlled Rheoscope 1 rheometer (Thermo interface. Transient stress measurements using a stress-controlled Rheoscope 1 rheometer (Thermo Fisher Scientiﬁc, Waltham, MA, USA) at 25 ◦C were then performed. The time evolutions of the Fisher Scientific, Waltham, MA, USA) at 25 °C were then performed. The time evolutions of the transient shear stress of the suspensions were measured at shear rates ranging from 0.1 to 1000 s−1. transient shear stress of the suspensions were measured at shear rates ranging from 0.1 to 1000 s−1. This procedure was usually carried out over a period of less than 60 min at 25 °C. When the transient

Gels 2017, 3, 32 10 of 12

This procedure was usually carried out over a period of less than 60 min at 25 ◦C. When the transient shear stress did not reach a steady-state within the 30 min period, it took up to 90 min to measure the transient shear stress. On the other hand, for the measurements of the dynamic viscoelastic moduli, the FS and PS suspensions in the pre-gel and gel states were placed in a parallel plate fixture with a diameter of 35 mm and a gap of 1 mm and in the same cone-plate fixture described above, respectively. The dynamic viscoelastic moduli measurements were carried out under oscillatory strains increasing from 0.1 to 1000% at 25 ◦C and a fixed frequency of 5 rad/s, using the same stress-controlled Rheoscope 1 rheometer. Moreover, the frequency sweep measurements were performed in the linear viscoelastic region at a frequency ranging from 0.1 to 100 rad/s and with a fixed shear strain of 0.1%. The rheological measurements were repeated at least three times, and the corresponding experimental errors were within 5%.

4. Conclusions FS and PS powders were suspended in mineral oil, and the sol, pre-gel, and gel states of the resulting suspensions were investigated. The transient shear stress and steady-state shear viscosity of the silica suspensions in the pre-gel and gel states were investigated as a function of ϕ. At shear rates higher than 2 s−1, the silica suspensions almost approached a steady-state value within 30 min after the preshearing stage, irrespective of ϕ. At shear rates lower than 2 s−1, sustained oscillations in the shear stress were observed for the FS suspensions in the gel state and for the PS suspensions in the pre-gel and gel states. The ηr data of the FS and PS suspensions were well fitted by the Krieger and Dougherty model, and the fitted ϕm and [η] parameters indicate that the PS suspensions form more tightly packed and agglomerated structures than the FS suspensions. Based on dynamic modulus measurements in the linear region, the FS and PS suspensions could be classified as strong-link and weak-link gels, respectively, according to the fractal model. The LAOS responses highlighted a weak strain overshoot for the FS suspensions, whereas the PS suspensions showed strong strain overshoot. Therefore, an increase in the surface silanol density easily caused hydrogen bonding interactions between the surface silanol groups, formed more compact and smaller aggregated structures in the PS suspensions, and then the corresponding suspensions yielded lower shear stress and weaker dynamic moduli than the FS suspensions. Thus, the present study provides new data illustrating the influence of the surface silanol density on the shear stress and dynamic modulus data of silica suspension gels in mineral oil because the surface silanol density of the PS powders is twice as high as that of the FS powders.

Acknowledgments: The authors gratefully acknowledge the financially support from Nippon Aerosil Co. Ltd. (Yokkaichi, Japan) and Aqua Chemical Co. Ltd. (Izumi, Japan). Author Contributions: Yoshiki Sugino performed the experiments and analyzed the experimental data and Masami Kawaguchi analyzed the data and prepared the paper. Conflicts of Interest: The authors declare no conflict of interest.

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