An Optical Method for Quantitatively Determining the Surface FreeEnergy of Micro- and NanoparticlesZhenle Cao,† Shannon Nicole Tsai,† and Yi Y. Zuo*,†,‡

†Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, Hawaii 96822, United States‡Department of Pediatrics, John A. Burns School of Medicine, University of Hawaii, Honolulu, Hawaii 96826, United States

*S Supporting Information

ABSTRACT: Surface free energy (SFE) of micro- and nanoparticles playsa crucial role in determining the hydrophobicity and wettability of theparticles. To date, however, there are no easy-to-use methods fordetermining the SFE of particles. Here, with the application of severalinexpensive, easy-to-use, and commonly available lab procedures andfacilities, including particle dispersion, settling/centrifugation, pipetting,and visible-light spectroscopy, we developed a novel technique called themaximum particle dispersion (MPD) method for quantitatively determin-ing the SFE of micro- and nanoparticles. We demonstrated the versatilityand robustness of the MPD method by studying nine representativeparticles of various chemistries, sizes, dimensions, and morphologies. Theseare triethoxycaprylylsilane-coated zinc oxide nanoparticles, multiwalledcarbon nanotubes, graphene nanoplatelets, molybdenum(IV) sulfide flakes,neodymium(III) oxide nanoparticles, two sizes of zeolites, poly(vinylpolypyrrolidone), and polystyrene microparticles. The SFEof these micro- and nanoparticles was found to cover a range from 21 to 36 mJ/m2. These SFE values may find applications in abroad spectrum of scientific disciplines including the synthesis of these nanomaterials, such as in liquid-phase exfoliation. TheMPD method has the potential to be developed into a standard, low-cost, and easy-to-use method for quantitativelycharacterizing the SFE and hydrophobicity of particles at the micro- and nanoscale.

Surface free energy (SFE) is the excess energy per unitsurface area.1 It is a quantitative thermodynamic measure

of intermolecular and surface forces,2 thus also determining thehydrophobicity and wettability of a material. The SFE of aliquid−fluid interface, such as the air−liquid and liquid−liquidinterfaces, is equivalent to its surface/interfacial tension, whichcan be readily determined with an established method, such asthe Wilhelmy plate, drop weight method, maximum bubblepressure, or drop shape analysis.3 However, the SFE of a solidsurface cannot be determined directly. Despite extensivecontroversies in its theoretical interpretation,4,5 the contactangle method remains to be the only established method fordetermining the SFE of bulk materials.As compared to bulk materials, measuring the SFE of micro-

and nanoparticles is still a challenging task despite itsimportance in a variety of scientific and industrial applica-tions.6 The SFE of particulate matters determines thedispersion and aggregation states of the particles, thusinfluencing a variety of their physicochemical properties suchas melting point, glass transition temperature, elasticity,7,8

crystal structure,9 and toxicity of nanoparticles.10−12 The SFEof particles determines the stability of a colloidal suspension,which is crucial for applications that require controlledpartitioning, dispersion, and aggregation of the particles, suchas in composite materials,13 metallurgy,14 cosmetics, andpharmaceutical and food sciences.15 The SFE of particles also

determines their adhesion and adsorption to solid and liquidsurfaces, which is of utmost importance to the liquid-phaseexfoliation and synthesis of two-dimensional nanomateri-als16−19 as well as bacterial adhesion and biofilm formationof microorganisms.20 The SFE of particles can also be agoverning factor in applications where selective agglomerationand/or separation is desired such as in the flocculation ofmicroalgae for biofuel harvesting,21 recycling of nanocatalysts,wastewater treatment, and cell sorting.22

Because of its importance, multiple methodologies havebeen developed in the attempt to determine the SFE orhydrophobicity of particles.6 These methods can be separatedinto two general categories, qualitative approaches that areonly able to compare/rank the relative hydrophobicity ofparticles, and quantitative methods that are capable of directlydetermining the SFE of particles.The qualitative methods include dye partitioning methods,23

particle wettability at liquid−fluid interfaces,24 and the salting-out aggregation tests.25 These techniques have been developedto study the relative hydrophobicity and adhesion of particlesand are commonly used to study bacterial cells as well asabiotic particles. Using these methods, one can compare and

Received: May 31, 2019Accepted: September 5, 2019Published: September 5, 2019

Article

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© 2019 American Chemical Society 12819 DOI: 10.1021/acs.analchem.9b02507Anal. Chem. 2019, 91, 12819−12826

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rank the relative hydrophobicity of particles under the sameexperimental condition. However, it is difficult to directlycompare results reported across the literature.The quantitative methods include the contact angle

method,5 capillary penetration,26 sedimentation volume,27

and inverse gas chromatography.28,29 Among these methods,the contact angle measurement is the most established method.A typical contact angle measurement of micro- and nano-particles generally relies on compacting the particles into acake of equivalent bulk materials, measuring Young’s contactangle, and then determining the SFE using either one of thetwo available yet contradictory theories, that is, the surfacetension component theory4 or the Neumann’s equation ofstate.5 Hence, the controversy of contact angle measurementson bulk materials remains for particulate matter. In addition,this method introduces new uncertainties because thecompacted surface can hardly achieve an atomic smoothness,thus violating the fundamental assumption of measuringYoung’s contact angle. In fact, the procedure of compressingparticles into an equivalent bulk material may even modify theintrinsic SFE of the particles. Consequently, the SFE ofparticles determined with the contact angle method typicallyshows large discrepancies.Here, we report a novel method for determining the SFE of

micro- and nanoparticles. This method is termed the maximumparticle dispersion (MPD) method. It is an optical methodmodified from the classical sedimentation volume techniquethat relies on the Derjaguin−Landau−Vervey−Overbeek(DLVO) analysis of colloidal stability.2 The MPD methodwas used to determine the SFE of a range of micro- andnanoparticles of various chemistries, sizes, shapes, andmorphologies. We showed that the MPD method is a low-cost, easy-to-use, and versatile method for determining the SFEof various micro- and nanoparticles.

■ EXPERIMENTAL SECTIONMaterials. Particles and solvents were purchased from

commercial sources, summarized in Tables 1 and 2, and usedwithout further purification. Water used was Milli-Q ultrapure

water (Millipore, Billerica, MA) with a resistivity greater than18 MΩ cm at room temperature. Morphologies of the micro-and nanoparticles were characterized by scanning electronmicroscopy (Hitachi S-4800). Surface tensions of the solventswere determined with constrained drop surfactometry(CDS).30

Principles of the MPD Method. Principles of themaximum particle dispersion (MPD) method stem from theDLVO theory of colloidal stability. As shown in Figure 1, in anideal situation with a single type of particles suspended in aliquid, the particles can interact either with each other or withthe suspending liquid. Given such a system of liquidcomponent (1) and particles (2), the work of particle adhesionΔEadhesion is given by eq 1:

Δ = + −E E E E2adhesion 11 22 12 (1)

According to the DLVO theory, the predominant interactionsthat contribute to the colloidal stability of the particles are abalance between the repulsive electrostatic and attractive vander Waals forces. Contributions of the van der Waalsattractions can be described by the Hamaker interactionconstant A212:

= + −A A A A2212 11 22 12 (2)

Table 1. Summary of the Micro- and Nanoparticles Studied Herea

particlechemicalformula source

particledimension particle morphology and size

literature SFE(mJ/m2)

measured SFE(mJ/m2)

TCS-ZnO NPs C14H32O3Si JRC, EuropeanCommission

0D nanorods, 150 nm in length and 50 nmin diameter

20−23b,31 21.1 ± 0.1

MWCNTs Cn NanoLab, Waltham, MA 1D fibers, 30 nm in diameter and 1−5 μmin length

4,34 27.8,36 45.3,37

82.63525.3 ± 0.5

GNPs Cn Strem Chemicals,Newburyport, MA

2D sheets, 5 μm in diameter and 6−8 nmthick

46.738 30.3 ± 0.9

MSFs MoS2 Sigma-Aldrich, St. Louis,MO

2D flakes, 6 μm in diameter 46.539 28.6 ± 0.6

NO NPs Nd2O3 Sigma-Aldrich, St. Louis,MO

0D nanorods, 100 nm in length and 20 nmin diameter

n/a 30.4 ± 1.6

zeolite (L) AlnSinOn Sigma-Aldrich, St. Louis,MO

3D cubes, 4 μm in side length 34.4942 30.8 ± 0.1

zeolite (S) AlnSinOn Sigma-Aldrich, St. Louis,MO

3D cubes, 1 μm in side length 34.4942 31.7 ± 1.3

PVPP (C6H9NO)n Sigma-Aldrich, St. Louis,MO

0D porous spheroids, 5 μm in diameter 43.4b,45 34.2 ± 1.5

PS MPs (C8H8)n Thermo Scientific,Fremont, CA

0D monodisperse microspheres, 1 μm indiameter

30−43b,4 35.8 ± 0.4

aSFE, surface free energy; TCS-ZnO NP, triethoxycaprylylsilane-coated zinc oxide nanoparticle; JRC, joint research center repository ofrepresentative industrial nanomaterials; MWCNT, multiwalled carbon nanotube; GNP, graphene nanoplatelet; MSF, molybdenum(IV) sulfideflakes; NO, neodymium(III) oxide; L, large; S, small; PVPP, poly(vinylpolypyrrolidone); PS, polystyrene; MP, microparticle. bAvailable literaturevalues are for bulk, nonparticulate materials.

Table 2. Physicochemical Properties of the Probing Liquids

probing liquidschemicalformula CAS ref no.

boilingtemp(°C)

densityat 20°C

(g/cm3)

surfacetension at20 °C

(mJ/m2)

n-pentane C5H12 109-66-0 36.06 0.626 16.00n-hexane C6H14 110-54-3 68.73 0.659 18.43n-heptane C7H16 142-82-5 98.38 0.684 20.14n-octane C8H18 111-65-9 125.6 0.703 21.62n-decane C10H22 124-18-5 174.1 0.730 23.83n-hexadecane C16H34 544-76-3 286.5 0.773 27.47ethanol C2H6O 64-17-5 78.29 0.790 22.10water H2O 7732-18-5 99.97 1.000 72.80

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Assuming the liquid media is of low dielectric constant andthus dispersion forces dominate, the geometrical meancombining rule, = ·A A A12 11 22 , derived from the Lifshitztheory can be applied. Hence:

= −A A A( )212 11 222

(3)

Relating the Hamaker constant to the surface tension and SFE(γ) using A = 24πD2γ, where D is the minimum separationdistance between surfaces, we find:

π γ γ= −A D24 ( )2122

1 22

(4)

According to eq 4, when the surface tension of the suspendingliquid γ1 is equal to the SFE of the dispersed particles γ2, theinterparticle van der Waals attraction is minimized, thusresulting in the least agglomeration and the slowestprecipitation. The state of particle dispersion in a series ofsuspending liquids can be readily compared by measuring lightabsorbance. The surface tension of the liquid in which theparticles are maximumly dispersed, that is, with the highestoptical density, is expected to be equal to the SFE of thesuspending particles.Implementation of the MPD Method. Two sets of

probing liquids were used in the measurement of particle SFE.One set was composed of 16 binary mixtures of ethanol andwater with surface tensions ranging from 22 mJ/m2 (for pureethanol) to 72 mJ/m2 (for pure water). Another set consistedof six pure alkanes ranging from C5 to C16, with a surfacetension range of 16−27 mJ/m2. Surface tensions of theseprobing liquids were determined at room temperature usingCDS.A trace amount of the particle stock solution was added to

the series of probing liquids, each at 0.5 mL, vortexed, and leftundisturbed for 10−30 min to allow natural sedimentation.When the natural sedimentation was too slow, centrifugationwas used to accelerate the process. After effective sedimenta-

tion, 160 μL of the supernatant from each probing liquid wascarefully transferred from the centrifuge tubes to a 96-wellmicroplate. Optical densities (ODs) of these supernatants weremeasured using a microplate reader (Epoch, BioTek,Winooski, VT). A characteristic wavelength of 400 nm wasdetermined prior to the measurements. The OD400 was plottedagainst the surface tensions of the probing liquids. A maximumOD value was determined by peak fitting experimental pointswith data smoothing followed by third-order polynomial fittingusing OriginPro (Northampton, MA). Each measurement wasrepeated at least three times. Results were shown as mean ±standard deviation.

■ RESULTSMorphology of the Micro- and Nanoparticles. Figure 2

shows the electron micrographs of nine representative micro-

and nanoparticles that cover a range of chemistries, sizes,dimensions, and morphologies. These are (a) triethoxycapry-lylsilane-coated zinc oxide nanoparticles (TCS-ZnO NPs), (b)multiwalled carbon nanotubes (MWCNTs), (c) graphenenanoplatelets (GNPs), (d) molybdenum(IV) sulfide flakes(MSFs), (e) neodymium(III) oxide (NO) NPs, (f) largezeolite microparticles (MPs), (g) small zeolite MPs, (h)poly(vinylpolypyrrolidone) (PVPP) MPs, and (i) polystyrene(PS) MPs. The chemical formula, source, morphology, size,and literature SFE value, if available, of these particles aresummarized in Table 1.

Proof of Feasibility of the MPD Method. We showedthe feasibility of the MPD method in determining the SFE ofTCS-ZnO NPs and MWCNTs using two sets of probingliquids, each with three repetitions. One was a polar liquid setcomposed of binary mixtures of water and ethanol, which

Figure 1. Measurement principle of the maximum particle dispersion(MPD) method. The classical DLVO theory predicts that thecolloidal stability of a particle suspension is determined by the balancebetween the electrostatic repulsion and van der Waals attraction.Dispersing particles in a liquid of surface tension similar to the surfacefree energy (SFE) of the particles minimizes the van der Waalsattraction between particles across the suspending liquid, thusresulting in maximum particle dispersion. Hence, it is expected thatthe surface tension of the liquid (γlv) resulting in a maximum lightabsorbance should be close to the SFE of the particles (γpv). The lightabsorbance of the particle suspension in a series of liquids can beeasily measured with the optical density (OD) and compared using aregular microplate reader.

Figure 2. Scanning electron microscopy (SEM) micrographs showingthe morphology of the studied micro- and nanoparticles: (a)Triethoxycaprylylsilane-coated zinc oxide nanoparticles (TCS-ZnONPs); (b) multiwalled carbon nanotubes (MWCNTs); (c) graphenenanoplatelets (GNPs); (d) molybdenum(IV) sulfide flakes (MSFs);(e) neodymium(III) oxide (NO) NPs; (f) zeolite (large); (g) zeolite(small); (h) poly(vinylpolypyrrolidone) (PVPP); and (i) polystyrenemicroparticles (PS MPs).

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provides a large surface tension range from 22 to 72 mJ/m2.The second one was a nonpolar liquid set comprised of sixpure alkanes of varying lengths, from C5 to C16, which covers asurface tension range from 16 to 27 mJ/m2. (Characterizationof the polar and nonpolar liquid sets can be found in FiguresS1 and S2.) The nonpolar liquid set overlaps the surfacetension range of the polar liquid set on the low surface tensionend, and extends the surface tension range of the polar liquidset by 6 mJ/m2 toward the lower end. Physicochemicalproperties of the probing liquids can be found in Table 2.As shown in Figure 3a, when measured in the polar liquid

set, no peak in the optical density (OD) value can be found forthe TCS-ZnO NPs. Rather, the OD value quickly increasedwhen the surface tension is lower than 30 mJ/m2 andmaximizes in pure ethanol. When measured in the nonpolarliquid set, as shown in Figure 3b, an OD peak appears at 21.1mJ/m2, indicating the maximum particle dispersion. Figure 3cshows the superimposed measurements with the polar andnonpolar liquid sets. It is clear that the OD value transitssmoothly between the two sets of probing liquids, indicatingthat the MPD method is nonspecific to the probing liquids

used in measurements. Within the combined surface tensionrange from 16 to 72 mJ/m2, a single peak of the OD valueappears at 21.1 mJ/m2, indicating the SFE of the siloxane-coated ZnO NPs. This value is in good agreement with theliterature SFE value of similar silanes and siloxanes.31

Figure 4a−c shows the measurements of MWCNTs in bothpolar and nonpolar sets of the probing liquids. Opposite toTCS-ZnO NPs, the OD peak of MWCNTs appears at 25.3mJ/m2 when measured in the polar liquid set, while the ODvalue in the nonpolar liquid set monotonically increases withincreasing surface tension. Consequently, only a single ODpeak appears in the combined surface tension range of 16−72mJ/m2, indicating a unique SFE value at 25.3 mJ/m2.

SFE of Micro- and Nanoparticles. Figure 5 shows theSFE measurements of all nine micro- and nanoparticles, eachwith three repetitions. Among these particles, TCS-ZnO NPs,MWCNTs, and GNPs were measured with both polar andnonpolar probing liquids, while the rest of the particles weremeasured with only the polar probing liquids that provide asufficiently large surface tension range to cover the SFEs ofthese particles. It is clear that the MPD method was able to

Figure 3. Determination of the surface free energy (SFE) of triethoxycaprylylsilane-coated zinc oxide nanoparticles (TCS-ZnO NPs) using themaximum particle dispersion (MPD) method. Each panel shows the optical density at 400 nm (OD400) as a function of the surface tension of theprobing liquids. Three runs of each measurement are presented to show reproducibility. (a) OD curves obtained with the polar liquid set, that is,water/ethanol mixtures. The OD curves show no local peak values but monotonically increase with reducing surface tension, indicating that theSFE of the TCS-ZnO NPs is lower than the minimum surface tension of the polar probing liquids. (b) OD curves obtained with the nonpolarliquid set, that is, single alkanes of varying carbon chains. The OD curves show a local peak value at 21.1 ± 0.1 mJ/m2, indicating the SFE of theTCS-ZnO NPs. (c) Superimposed OD curves obtained with the polar and nonpolar liquid sets. A single peak appears in the large surface tensionrange from 16 to 72 mJ/m2, indicating uniqueness of the SFE measurement.

Figure 4. Determination of the surface free energy (SFE) of multiwalled carbon nanotubes (MWCNTs) using the maximum particle dispersion(MPD) method. Each panel shows the optical density at 400 nm (OD400) as a function of the surface tension of the probing liquids. Three runs ofeach measurement are presented to show reproducibility. (a) OD curves obtained with the polar liquid set, that is, water/ethanol mixtures. The ODcurves show a local peak value at 25.3 ± 0.5 mJ/m2, indicating the SFE of the MWCNTs. (b) OD curves obtained with the nonpolar liquid set, thatis, single alkanes of varying carbon chains. The OD curves show no local peak values but monotonically increase with increasing surface tension,indicating that the SFE of the MWCNTs is higher than the maximum surface tension of the nonpolar probing liquids. (c) Superimposed OD curvesobtained with the polar and nonpolar liquid sets. A single peak appears in the large surface tension range from 16 to 72 mJ/m2, indicatinguniqueness of the SFE measurement.

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determine the SFEs of all tested particles as indicated byreproducible single OD peaks appearing in all measurements.The SFE of these micro- and nanoparticles are summarized inTable 1, and compared to the literature SFE values, if available.

■ DISCUSSIONDespite its importance in many scientific and industrialapplications, literature values for the SFE of micro- andnanoparticles are not only scarce but also highly contentious,which highlights the urgency of developing an easy-to-usemethod in determining the SFE of particulate matters. Theinvention of the maximum particle dispersion (MPD) methodfor quantitatively determining the SFE of micro- andnanoparticles aids in accomplishing this task. Nine representa-

tive particles studied here cover a large range of chemistries(silanes, carbon, rare-earth element, and polymers), sizes (from∼50 nm to ∼5 μm), dimensions (0D, 1D, 2D, and 3D), andmorphologies (spheres, rods, fibers, plates, and cubes),demonstrating the versatility and robustness of this method.Understanding the SFE of these micro- and nanoparticlesprovides novel insights into many surface science and materialapplications.

Triethoxycaprylylsilane-Coated ZnO NPs. Triethoxy-caprylylsilane (TCS) is a silane/siloxane commonly found incosmetics and personal care products. It has also been used inhydrophobic coatings and Pickering emulsions. To the best ofour knowledge, the exact SFE of silane/siloxane materials hasnot been reported, although the SFE of one commonly used

Figure 5. Determination of the surface free energy (SFE) of various micro- and nanoparticles using the maximum particle dispersion (MPD)method. Three runs of each measurement are presented to show reproducibility. (a) Triethoxycaprylylsilane-coated zinc oxide nanoparticles (TCS-ZnO NPs); (b) multiwalled carbon nanotubes (MWCNTs); (c) graphene nanoplatelets (GNPs); (d) molybdenum(IV) sulfide flakes (MSFs); (e)neodymium(III) oxide (NO) NPs; (f) zeolite (large); (g) zeolite (small); (h) poly(vinylpolypyrrolidone) (PVPP); and (i) polystyrenemicroparticles (PS MPs). Among these particles, TCS-ZnO NPs, MWCNTs, and GNPs (a−c) were measured with both polar (hollow symbols)and nonpolar (solid symbols) liquid sets, while the rest of the particles (d−i) were measured with only the polar probing liquids. The determinedSFE values are summarized in Table 1.

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polymeric siloxane, polydimethylsiloxane (PDMS), is typicallyestimated to be around 20−23 mJ/m2.31 Here, the SFE ofTCS-ZnO NPs was determined at 21.1 ± 0.1 mJ/m2, which isconsistent with previous estimations.Multiwalled Carbon Nanotubes (MWCNTs): 1D (Fi-

brous) Nanomaterials. The SFE of CNTs plays an essentialrole in determining their dispersibility and aggregation states incomposite materials, as well as their surface interactions withpolymer matrix.32,33 MWCNT is one of the most studiedparticulate matters in term of its SFE. However, availableliterature values showed large variations from as low as 4 mJ/m2,34 to as high as 82.6 mJ/m2.35 Two methods have beendeveloped to specifically measure the SFE of CNTs, bothtaking advantage of the fibrous shape of the CNTs. Barber etal. modified a single MWCNT to simulate the Wilhelmy platetechnique.36 A single MWCNT was attached to an atomicforce microscopy (AFM) tip and dipped into various testliquids. The SFE of the MWCNT was calculated from differentcapillary forces measured during the advancing and recedingprocesses. Using this method, these workers estimated the SFEof MWCNTs to be 27.8 mJ/m2.36 Nuriel et al. calculated theSFE of fibrous nanomaterials by using various polymer melts asprobing materials and measuring their contact angles onMWCNTs via scanning electron microscopy (SEM).37 Thismethod estimated the SFE of MWCNTs to be 45.3 mJ/m2.37

It should be noted that both of these methods are based on themeasurement of single MWCNTs. Hence, both methods sufferfrom errors due to variations among individual MWCNTs. Incontrast, our MPD method determines the SFE of MWCNTsas an averaged thermodynamic property. Here, we report theSFE of MWCNTs to be 25.3 ± 0.5 mJ/m2, which is near theSFE value reported by Barber et al.36

Graphene Nanoplatelets and MoS2 Flakes: 2D(Planar) Nanomaterials. Graphene nanoplatelets and MoS2flakes are two widely used 2D nanomaterials, especially in theenergy and semiconductor industry. The plane shape of thesenanomaterials facilitates their fabrication into relatively smoothsurfaces that permit SFE measurements using the traditionalcontact angle method. Available literature values of SFE forthese two 2D nanomaterials, obtained with the contact anglemethod, are almost identical, 46.7 mJ/m2 for graphene38 and46.5 mJ/m2 for MoS2.

39

Here, we determined the SFEs of graphene and MoS2 to be30.3 ± 0.9 and 28.6 ± 0.6 mJ/m2, respectively, significantlylower than previously expected. These differences in SFE maybe explained by the so-called wetting transparency effect.40

When determining the SFE of 2D nanomaterials using thecontact angle method, one needs to immobilize a thin film, ifnot a single layer, of these nanomaterials onto a macroscopicsubstrate, usually made of hydrophilic materials such as micaor glass. Consequently, the contact angle phenomenon of the2D nanomaterials, as well as the resultant SFE, would beinfluenced by that of the hydrophilic substrate, thus resultingin a relatively higher SFE estimation.The SFE of 2D nanomaterials determined here could be

useful in a range of applications. For example, one recent andincreasingly popular method of synthesizing 2D nanomaterialsis their exfoliation in the liquid phase.41 The solid precursor forthe 2D nanomaterial, for example, graphite for graphene, isadded into a selected liquid and ultrasonically agitated, whichexfoliates the monolayered nanomaterial from its bulkprecursor. Recent studies showed that the efficiency ofexfoliation was largely affected by the selection of the liquid

phase.16 The optimal performance was found in a liquid phasewhose surface tension matches the SFE of the exfoliated 2Dnanomaterials.18,19 This is not unexpected as the exfoliated 2Dnanomaterials would be maximumly dispersed in the liquidwith matching surface energies.

Neodymium(III) Oxide NPs. Neodymium(III) oxide is arare-earth oxide that shows increasing applications in catalysisand additive manufacturing of ceramics and magnets. Under-standing its SFE allows more accurate and efficient tuning ofmanufacturing processes such as the sintering dynamics ofpowder into solid ceramics and glass. To the best of ourknowledge, the SFE of neodymium(III) oxide NPs has not yetbeen reported. Here, we have determined their SFE to be 30.4± 1.6 mJ/m2 using the MPD method.

Zeolites: 3D (Cubic) Porous MPs. Aluminosilicates andclays are another important category of materials often used atthe micro- and nanoscale. In particular, zeolites, which arehydrated aluminosilicates with microporous structures, areoften used as molecular sieves for purification in the form ofmicroparticles as well as for the fluid catalytic cracking of highmolecular weight hydrocarbons. In their use as adsorbents andcatalysts, their efficiencies are largely dependent on their SFE.However, the SFE of zeolites are very difficult to measure dueto their inherent porosity, which prohibits the use of thetraditional contact angle method. In the present work, wedetermined the SFEs of two zeolite-A cubic MPs with differentsizes (4 vs 1 μm). Because both particles are of micrometersize, their SFEs do not differ significantly, with 30.8 ± 0.1 mJ/m2 for the larger zeolite MPs and 31.7 ± 1.3 mJ/m2 for thesmaller zeolite MPs. Our measurements are slightly lower thanthe SFE of zeolites determined with the capillary penetrationmethod, that is, 34.49 mJ/m2.42

PVPP and Polystyrene: Polymeric MPs. PVPP is acommon polymeric material used in pharmaceutical excipients,as well as filtration/binding agents used in the production ofalcoholic beverages. Polystyrene is commonly used as modelparticles for studying nanotoxicology, drug delivery, and self-assembly. Because of their importance, there are many studiesthat report the SFE of polymeric particles and bulk polymers.The SFE of these polymeric materials is commonly reported inthe range of 30−43 mJ/m2.43−45

Here, the SFEs of PVPP and polystyrene MPs aredetermined to be 34.2 ± 1.5 and 35.8 ± 0.4 mJ/m2,respectively. These measurements fall into the lower end ofthe literature values. Understanding the SFE of polymericparticles plays an important role not only in their applicationsbut also in their syntheses. It has been long known thatselecting a correct synthesis liquid is paramount for controllingthe polydispersity of polystyrene nano- and microspheres.46 Inthis case, it is most likely that the surface tension of thesynthesis liquid and the SFE of the polystyrene particles have asynergistic effect in determining the final size distribution ofthe nano- and microspheres.

Advantages and Limitations of the MPD Method. TheMPD method has three key advantages that make it superb toexisting methods in determining the SFE of particles. First, theMPD method is versatile and applicable to various particles. Asdemonstrated by the SFE measurements of nine representativemicro- and nanoparticles, the MPD method is not limited bythe chemistry, size, dimension, or morphology of the particles.This method is successful in determining the SFE of particlesencompassing 3 orders of magnitude from ∼50 nm to 5 μm insize. Second, the MPD method is simple in principle and thus

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requires no complicated theoretical interpretations. This isparticularly advantageous over the classical contact anglemethod in which theoretical interpretations are a necessity forthe SFE measurements. Third, the MPD method is easy-to-use,fast, and inexpensive. The only specialized facility needed forthe measurement is a microplate reader that is low-cost andreadily available in many research laboratories. Once theprobing liquids are prepared, calibrated, and stored, the entireSFE measurements, including particle dispersion, sedimenta-tion, and optical analysis, can be completed usually within anhour. In addition, because the MPD method replies on thecomparison of OD values in various probing liquids, neitherthe actual particle concentration of the stock solution, nor theactual sedimentation time or the centrifugation settings, affectthe location of the OD peak, that is, the SFE measurements.Despite its numerous advantages, the MPD method also has

one theoretical limitation and one practical limitation. Thetheoretical limitation is inherent from the DLVO theory, whichis most applicable to colloidal systems where the competitionbetween van der Waals attractions and electrostatic repulsionsdominates the colloidal stability.2 For very hydrophilicparticles, that is, high SFE particles, however, additionalintermolecular and surface forces such as the hydration forcesbecome predominant, at which the MPD method inevitablyexperiences difficulties. The practical limitation of the methodis that it obviously cannot measure particles soluble in theprobing liquids, or particles of which the refractive index (n) isvery close to that of the probing liquids. For example, whenattempting to measure the SFE of Teflon microparticles of n ≈1.35 with water/ethanol mixtures of n ≈ 1.33−1.36, theparticles do not significantly refract light and would appeartransparent. This limitation may be mitigated either byswitching probing liquids with different refractive index or bytagging particles with a small amount of fluorescent dyes.

■ CONCLUSIONS

With the application and combination of several inexpensive,easy-to-use, and commonly available lab procedures andfacilities, such as particle dispersion, settling/centrifugation,pipetting, and visible-light spectroscopy, a new technique forquantitatively determining the surface free energy (SFE) ofmicro- and nanoparticles was developed. This technique istermed the maximum particle dispersion (MPD) method.From the measurements of nine representative particles ofvarious chemistries, sizes, dimensions, and morphologies, theMPD method demonstrated its versatility and robustness. TheSFE of the nine micro- and nanoparticles studied here covers arange of 21−36 mJ/m2. These SFE values may findapplications in a broad spectrum of scientific disciplinesincluding the synthesis of these nanomaterials, such as byexfoliation or liquid-phase polymerization. The MPD methodhas the potential to be developed into a standard, low-cost, andeasy-to-use method for quantitatively characterizing the surfacefree energy and hydrophobicity of particles at the micro- andnanoscale.

■ ASSOCIATED CONTENT

*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.anal-chem.9b02507.

Characterization of the polar and nonpolar liquid sets(PDF)

■ AUTHOR INFORMATIONCorresponding Author*Tel.: (808) 956-9650. Fax: (808) 956-2373. E-mail: yzuo@hawaii.edu.ORCIDYi Y. Zuo: 0000-0002-3992-3238NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThis research was supported by the National ScienceFoundation Grant nos. CBET-1254795 and CBET-1604119(Y.Y.Z.).

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