An Optical Method for Quantitatively Determining the Surface

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An Optical Method for Quantitatively Determining the Surface Free Energy of Micro- and Nanoparticles Zhenle Cao, Shannon Nicole Tsai, and Yi Y. Zuo Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.9b02507 • Publication Date (Web): 05 Sep 2019 Downloaded from pubs.acs.org on September 6, 2019

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Analytical Chemistry

An Optical Method for Quantitatively Determining the Surface Free Energy of Micro- and Nanoparticles Zhenle Cao,1 Shannon Nicole Tsai,1 and Yi Y. Zuo1,2*

1. Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, Hawaii 96822, USA

2. Department of Pediatrics, John A. Burns School of Medicine, University of Hawaii, Honolulu, Hawaii, 96826, USA

*corresponding author: Yi Y. Zuo

Department of Mechanical Engineering, University of Hawaii at Manoa 2540 Dole St, Holmes Hall 302, Honolulu, Hawaii, 96822, United States Email: [email protected]; Tel: 808-956-9650; Fax: 808-956-2373

1 ACS Paragon Plus Environment

Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Surface free energy (SFE) of micro- and nanoparticles plays a crucial role in determining the hydrophobicity and wettability of the particles. To date, however, there are no easy-to-use methods for determining the SFE of particles. Here, with the application of several inexpensive, easy-touse and commonly available lab procedures and facilities, including particle dispersion, settling/centrifugation, pipetting, and visible-light spectroscopy, we developed a novel technique called the maximum particle dispersion (MPD) method for quantitatively determining the SFE of micro- and nanoparticles. We demonstrated the versatility and robustness of the MPD method by studying nine representative particles of various chemistries, sizes, dimensions, and morphologies. These are triethoxycaprylylsilane coated zinc oxide nanoparticles, multiwalled carbon nanotubes, graphene nanoplatelets, molybdenum(IV) sulfide flakes, neodymium(III) oxide nanoparticles, two sizes of zeolites, poly(vinylpolypyrrolidone) and polystyrene microparticles. The SFE of these micro- and nanoparticles was found to cover a range from 21 to 36 mJ/m2. These SFE values may find applications in a broad spectrum of scientific disciplines including the synthesis of these nanomaterials, such as in liquid-phase exfoliation. The MPD method has the potential to be developed into a standard, low-cost, and easy-to-use method for quantitatively characterizing the SFE and hydrophobicity of particles at the micro- and nanoscale.

Keywords: surface free energy; surface tension; hydrophobicity; particle; spectrophotometry; maximum particle dispersion method


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Surface free energy (SFE) is the excess energy per unit surface area.1 It is a quantitative thermodynamic measure of intermolecular and surface forces,2 thus also determining the hydrophobicity and wettability of a material. The SFE of a liquid-fluid interface, such as the airliquid and liquid-liquid interfaces, is equivalent to its surface/interfacial tension, which can be readily determined with an established method, such as the Wilhelmy plate, drop weight method, maximum bubble pressure, or drop shape analysis.3 However, the SFE of a solid surface cannot be determined directly. Despite extensive controversies in its theoretical interpretation,4,

5

the

contact angle method remains to be the only established method for determining the SFE of bulk materials. Compared to bulk materials, measuring the SFE of micro- and nanoparticles is still a challenging task in spite of its importance in a variety of scientific and industrial applications.6 The SFE of particulate matters determines the dispersion and aggregation states of the particles, thus influencing a variety of their physicochemical properties such as melting point, glass transition temperature, elasticity,7, 8 crystal structure,9 and toxicity of nanoparticles.10-12 The SFE of particles determines the stability of a colloidal suspension, which is crucial for applications that require controlled partitioning, dispersion, and aggregation of the particles, such as in composite materials,13, metallurgy,14 cosmetics, pharmaceutical and food sciences.15 The SFE of particles also determines their adhesion and adsorption to solid and liquid surfaces, which is of utmost importance to the liquid-phase exfoliation and synthesis of two-dimensional nanomaterials 16-19 as well as bacterial adhesion and biofilm formation of microorganisms.20 The SFE of particles can also be a governing factor in applications where selective agglomeration and/or separation is desired such as in the flocculation of microalgae for biofuel harvesting,21 recycling of nanocatalysts, wastewater treatment, and cell sorting.22



Because of its importance, multiple methodologies have been developed in the attempt to determine the SFE or hydrophobicity of particles.6 These methods can be separated into two general categories, qualitative approaches that are only able to compare/rank the relative hydrophobicity of particles, and quantitative methods that are capable of directly determining 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 developed to study the relative hydrophobicity and adhesion of particles and are commonly used to study bacterial cells as well as abiotic particles. Using these methods, one can compare and rank the relative hydrophobicity of particles under the same experimental condition. However, it is difficult to directly compare results reported across 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 microand nanoparticles generally relies on compacting the particles into a cake of equivalent bulk materials, measuring Young’s contact angle, and then determining the SFE using either one of the two available yet contradictory theories, i.e., the surface tension component theory4 or the Neumann’s equation of state5. Hence, the controversy of contact angle measurements on bulk materials remains for particulate matter. In addition, this method introduces new uncertainties since the compacted surface can hardly achieve an atomic smoothness, thus violating the fundamental assumption of measuring Young’s contact angle. In fact, the procedure of compressing particles into an equivalent bulk material may even modify the intrinsic SFE of the


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particles. Consequently, the SFE of particles determined with the contact angle method typically shows large discrepancies. Here, we report a novel method for determining the SFE of micro- and nanoparticles. This method is termed the maximum particle dispersion (MPD) method. It is an optical method modified from the classical sedimentation volume technique that relies on the Derjaguin-LandauVervey-Overbeek (DLVO) analysis of colloidal stability.2 The MPD method was used to determine the SFE of a range of micro- and nanoparticles of various chemistries, sizes, shapes, and morphologies. We showed that the MPD method is a low-cost, easy-to-use, and versatile method for determining the SFE of various micro- and nanoparticles.

Experimental Section Materials. Particles and solvents were purchased from commercial sources, summarized in Tables 1 and 2, and used without further purification. Water used was Milli-Q ultrapure water (Millipore, Billerica, MA) with a resistivity greater than 18 MΩcm at room temperature. Morphologies of the micro- and nanoparticles were characterized by scanning electron microscopy (Hitachi S-4800). Surface tensions of the solvents were determined with constrained drop surfactometry (CDS).30 Principles of the MPD method. Principles of the maximum particle dispersion (MPD) method stem from the DLVO theory of colloidal stability. As shown in Figure 1, in an ideal situation with a single type of particles suspended in a liquid, the particles can either interact with each other or with the suspending liquid. Given such a system of liquid component (1) and particles (2), the work of particle adhesion ΔEadhesion is given by Eq. 1, ∆𝐸𝑎𝑑ℎ𝑒𝑠𝑖𝑜𝑛 = 𝐸11 + 𝐸22 ― 2𝐸12

(1)

According to the DLVO theory, the predominant interactions that contribute to the colloidal stability of the particles is a balance between the repulsive electrostatic and attractive van der 5 ACS Paragon Plus Environment


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Waals forces. Contributions of the van der Waals attractions can be described by the Hamaker interaction constant 𝐴212, 𝐴212 = 𝐴11 + 𝐴22 ― 2𝐴12

(2)

Assuming the liquid media is of low dielectric constant and thus dispersion forces dominate, the geometrical mean combining rule, 𝐴12 =

𝐴11 ∙ 𝐴22, derived from the Lifshitz theory can be

applied. Hence, 𝐴22)2

𝐴212 = ( 𝐴11 ―

(3)

Relating the Hamaker constant to the surface tension and SFE (γ) using 𝐴 = 24𝜋𝐷2γ, where D is the minimum separation distance between surfaces. 𝐴212 = 24𝜋𝐷2( γ1 ―

γ2)2

(4)

According to Eq. 4, when the surface tension of the suspending liquid γ1 is equal to the SFE of the dispersed particles γ2, the interparticle van der Waals attraction is minimized, thus resulting in the least agglomeration and the slowest precipitation. The state of particle dispersion in a series of suspending liquids can be readily compared by measuring light absorbance. The surface tension of the liquid in which the particles are maximumly dispersed, i.e., with the highest optical density, is expected to be equal to the SFE of the suspending particles. Implementation of the MPD method. Two sets of probing liquids were used in the measurement of particle SFE. One set was composed of sixteen binary mixtures of ethanol and water with surface tensions ranging from 22 mJ/m2 (for pure ethanol) to 72 mJ/m2 (for pure water). Another set consisted of six pure alkanes ranging from C5 to C16, with a surface tension range of 16-27 mJ/m2. Surface tensions of these probing liquids were determined at room temperature using CDS. A trace amount of the particle stock solution was added to the series of probing liquids, each at 0.5 mL, vortexed, and left undisturbed for 10-30 min to allow natural sedimentation. When the 6 ACS Paragon Plus Environment

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natural sedimentation was too slow, centrifugation was used to accelerate the process. After effective sedimentation, 160 μL of the supernatant from each probing liquid was carefully transferred from the centrifuge tubes to a 96-well microplate. Optical densities (ODs) of these supernatants were measured using a microplate reader (Epoch, BioTek, Winooski, VT). A characteristic wavelength of 400 nm was determined prior to the measurements. The OD400 was plotted against the surface tensions of the probing liquids. A maximum OD value was determined by peak fitting experimental points with data smoothing followed by 3rd order polynomial fitting using OriginPro (Northampton, MA). Each measurement was repeated for at least three times. Results were shown as mean ± standard deviation.

Figure 1. Measurement principle of the maximum particle dispersion (MPD) method. The classical DLVO theory predicts that the colloidal stability of a particle suspension is determined by the balance between the electrostatic repulsion and van der Waals attraction. Dispersing particles in a liquid of surface tension similar to the surface free energy (SFE) of the particles minimizes the van der Waals attraction between particles across the suspending liquid, thus resulting in maximum particle dispersion. Hence, it is expected that the surface tension of the liquid (γlv) resulting in a maximum light absorbance should be close to the SFE of the particles



(γpv). The light absorbance of the particle suspension in a series of liquids can be easily measured with the optical density (OD) and compared using a regular microplate reader.

Results Morphology 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) 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) large zeolite 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 are summarized in Table 1.


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TCS-ZnO NPs

MWCNTs

(a)

(b)

100 nm

200 nm

MSFs

(d)

)

NO NPs

(e)

)

(g)

)

2 µm

Zeolite (L)

(f)

)

4 µm

100 nm

4 µm

Zeolite (S)

(c)

)

)

)

GNPs

PVPP

(h)

)

PS MPs

(i)

)

2 µm

4 µm

1 µm

Figure 2. Scanning electron microscopy (SEM) micrographs showing the morphology of the studied micro- and nanoparticles. (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) Polystyrene microparticles (PS MPs).


Analytical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

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Table 1. Summary of the micro- and nanoparticles studied here. Particle

Chemical formula

TCS-ZnO NPs

Source

Particle Particle morphology and dimension size

Literature SFE (mJ/m2)

Measured SFE (mJ/m2)

C14H32O3Si JRC, European Commission

0D

Nanorods, 150 nm in length and 50 nm in diameter

20-23* 31

21.1 ± 0.1

MWCNTs

Cn

NanoLab, Waltham, MA

1D

Fibers, 30 nm in diameter and 1-5 µm in length

4 34, 27.8 36, 45.3 37 82.6 35

25.3 ± 0.5

GNPs

Cn

Strem Chemicals, Newburyport, MA

2D

Sheets, 5 μm in diameter and 46.7 38 6-8 nm thick

30.3 ± 0.9

MSFs

MoS2

Sigma Aldrich, St. Louis, MO

2D

Flakes, 6 μm in diameter

46.5 39

28.6 ± 0.6

NO NPs

Nd2O3


0D

Nanorods, 100 nm in length and 20 nm in diameter

n/a

30.4 ± 1.6

Zeolite (L)

AlnSinOn


3D

Cubes, 4 µm in side length

34.49 42

30.8 ± 0.1

Zeolite (S)

AlnSinOn


3D

Cubes, 1 µm in side length

34.49 42

31.7 ± 1.3

PVPP

(C6H9NO)n


0D

Porous spheroids, 5 µm in diameter

43.4* 45

34.2 ± 1.5

PS MPs

(C8H8)n

Thermo Scientific, Fremont, CA

0D

Monodisperse microspheres, 1 µm in diameter

30-43* 4

35.8 ± 0.4

SFE: surface free energy; TCS-ZnO NP: triethoxycaprylylsilane coated zinc oxide nanoparticle; JRC: joint research centre repository of representative industrial nanomaterials; MWCNT: multiwalled carbon nanotube; GNP: graphene nanoplatelet; MSF: molybdenum(IV) sulfide flakes; NO: neodymium(III) oxide; L: large; S: small; PVPP: poly(vinylpolypyrrolidone); PS: polystyrene; MP: microparticle. * Available literature values are for bulk, non-particulate materials. 10 ACS Paragon Plus Environment

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Table 2. Physicochemical properties of the probing liquids used here. Probing liquids

Chemical formula

CAS Ref. No.

Boiling temp. (°C)

Density at Surface tension 3 20°C (g/cm ) at 20 °C (mJ/m2)

n-Pentane n-Hexane n-Heptane n-Octane n-Decane n-Hexadecane Ethanol Water

C5H12 C6H14 C7H16 C8H18 C10H22 C16H34 C2H6O H2O

109-66-0 110-54-3 142-82-5 111-65-9 124-18-5 544-76-3 64-17-5 7732-18-5

36.06 68.73 98.38 125.6 174.1 286.5 78.29 99.97

0.626 0.659 0.684 0.703 0.730 0.773 0.790 1.000

16.00 18.43 20.14 21.62 23.83 27.47 22.10 72.80

Proof of feasibility of the MPD method. We showed the feasibility of the MPD method in determining the SFE of TCS-ZnO NPs and MWCNTs using two sets of probing liquids, each with three repetitions. One was a polar liquid set composed of binary mixtures of water and ethanol, which provides a large surface tension range from 22 to 72 mJ/m2. The second one was a nonpolar liquid set comprised of six pure alkanes of varying lengths, from C5 to C16, which covers a surface tension range from 16 to 27 mJ/m2. (Characterization of the polar and nonpolar liquid sets can be found in Figures S1 and S2 of the Supporting Information.) The nonpolar liquid set overlaps the surface tension range of the polar liquid set on the low surface tension end, and extends the surface tension range of the polar liquid set by 6 mJ/m2 towards the lower end. Physicochemical properties 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 for the TCS-ZnO NPs. Rather, the OD value quickly increased when the surface tension is lower than 30 mJ/m2 and maximizes in pure ethanol. When measured in the nonpolar liquid set, as shown in Figure 3b, an OD peak appears at 21.1 mJ/m2, indicating the maximum particle dispersion. Figure 3c shows the superimposed measurements with the polar and nonpolar liquid sets. It is clear that the OD value transits smoothly between the two sets of

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probing liquids, indicating that the MPD method is nonspecific to the probing liquids used in measurements. Within the combined surface tension range from 16 to 72 mJ/m2, a single peak of the OD value appears at 21.1 mJ/m2, indicating the SFE of the siloxane coated ZnO NPs. This value is in good agreement with the literature SFE value of similar silanes and siloxanes.31 Figure 4a-c shows the measurements of MWCNTs in both polar and nonpolar sets of the probing liquids. Opposite to TCS-ZnO NPs, the OD peak of MWCNTs appears at 25.3 mJ/m2 when measured in the polar liquid set; while the OD value in the nonpolar liquid set monotonically increases with increasing surface tension. Consequently, only a single OD peak appears in the combined surface tension range of 16-72 mJ/m2, indicating a unique SFE value at 25.3 mJ/m2. 1.6

1.6

Run 1 Run 2 Run 3

1.4

1.6

Run 1 Run 2 Run 3

1.4

1.2

1.0

1.0

OD400

1.2

1.0 0.8

0.8

0.8

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.6

0.0

(a) 20

)

30

40

50

60

2

Surface Tension (mJ/m )

70

80

0.2

(b)

0.0 15

)

0.0

20

25

30 2


Polar Nonpolar

1.4

1.2

OD400

OD400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(c) 20

)

30

40

50

60

2


70

80

Figure 3. Determination of the surface free energy (SFE) of triethoxycaprylylsilane coated zinc oxide nanoparticles (TCS-ZnO NPs) 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 of each measurement are presented to show reproducibility. (a) OD curves obtained with the polar liquid set, i.e., water/ethanol mixtures. The OD curves show no local peak values but monotonically increases with reducing surface tension, indicating that the SFE of the TCS-ZnO NPs is lower than the minimum surface tension of the polar probing liquids. (b) OD curves obtained with the nonpolar liquid set, i.e., 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 the TCS-ZnO

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NPs. (c) Superimposed OD curves obtained with the polar and nonpolar liquid sets. A single peak appears in the large surface tension range from 16 to 72 mJ/m2, indicating uniqueness of the SFE measurement.

0.4 Run 1 Run 2 Run 3

(a) 0.3

0.7

0.7

(b)

0.6

0.6

0.5

0.5

)

0.4

OD400

0.2

)

OD400

OD400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.3 0.2

0.1

0.0

20

30

40

50

60

2


70

80

Polar Nonpolar

)

0.3 0.2

Run 1 Run 2 Run 3

0.1

0.0

0.4

(c)

15

20

25

2


0.1 0.0 30

20

30

40

50

60

2

70

80


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 of each measurement are presented to show reproducibility. (a) OD curves obtained with the polar liquid set, i.e., water/ethanol mixtures. The OD curves 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, i.e., single alkanes of varying carbon chains. The OD curves show no local peak values but monotonically increases 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 curves obtained with the polar and nonpolar liquid sets. A single peak appears in the large surface tension range from 16 to 72 mJ/m2, indicating uniqueness of the SFE measurement.

SFE of micro- and nanoparticles. Figure 5 shows the SFE measurements of all nine micro- and nanoparticles, each with three repetitions. Among these particles, TCS-ZnO NPs, MWCNTs and GNPs were measured with both polar and nonpolar probing liquids, while the rest of the particles 13



were measured with only the polar probing liquids that provide a sufficiently large surface tension range to cover the SFEs of these particles. It is clear that the MPD method was able to determine the SFEs of all tested particles as indicated by reproducible single OD peaks appearing in all measurements. The SFE of these micro- and nanoparticles are summarized in Table 1, and compared to the literature SFE values, if available. 1.2 1.6

0.7

TCS-ZnO NPs (a)

1.4 1.2

0.8 0.6

0.3

0.2

0.1

0.0

0.0 20

30

40

50

60

2

70

80

0.7

0.2 0.0

30

40

50

60

2


70

OD400

0.2

0.40

0.1

0.35

40

50

60

2

70

60

2

70

80

Zeolite (L) (f)

0.16

0.12

0.45

30

50

0.14

0.50

0.3

20

(e)

0.55

0.4

40

Surface Tension (mJ/m ) 0.18

NO NPs

0.60

)

0.5

30

OD400

0.6

(d)

20

80

0.65

MSFs

0.6 0.4

20


(c)

)

0.8

0.4

0.2

0.4

GNPs

1.0

OD400

OD400

OD400

(b)

0.5

1.0

OD400

MWCNTs

0.6

0.10 0.08

20

80

30

40

50

60

2

70

20

80

30

40

50

60

2

70

80



Surface Tension (mJ/m ) 0.18

Zeolite (S) (g)

0.7

PVPP

0.16

0.6

0.40

(h)

PS MPs

0.35

(i)

0.30

OD400

0.4 0.3

0.14

0.25

OD400

)

0.5

OD400

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.12

0.20 0.15 0.10

0.10

0.05

0.2 0.08

20

30

40

50

60

2


70

80

20

30

40

50

60

2

70


80

0.00 20

30

40

50

60

2

70

80


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

14


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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) Polystyrene microparticles (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 determined SFE values are summarized in Table 1.

Discussion Despite its importance in many scientific and industrial applications, literature values for the SFE of micro- and nanoparticles are not only scarce but also highly contentious, which highlights the urgency of developing an easy-to-use method in determining the SFE of particulate matters. The invention of the maximum particle dispersion (MPD) method for quantitatively determining the SFE of micro- and nanoparticles aids in accomplishing this task. Nine representative 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), and morphologies (spheres, rods, fibers, plates, and cubes), demonstrating the versatility and robustness of this method. Understanding the SFE of these micro- and nanoparticles provides novel insights into many surface science and material applications. Triethoxycaprylylsilane coated ZnO NPs. Triethoxycaprylylsilane (TCS) is a silane/siloxane commonly found in cosmetics and personal care products. It has also been used in hydrophobic coatings and Pickering emulsions. To the best of our knowledge, the exact SFE of silane/siloxane

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materials has not been reported, although the SFE of one commonly used polymeric siloxane, polydimethylsiloxane (PDMS), is typically estimated to be around 20-23 mJ/m2.31 Here the SFE of TCS-ZnO NPs was determined at 21.1±0.1 mJ/m2, which is consistent with previous estimations. Multiwalled carbon nanotubes (MWCNTs): 1D (fibrous) nanomaterials. The SFE of CNTs plays an essential role in determining their dispersibility and aggregation states in composite materials, as well as their surface interactions with polymer matrix.32, 33 MWCNT is one of the most studied particulate matters in term of its SFE. However, available literature values showed large variations from as low as 4 mJ/m2,34 to as high as 82.6 mJ/m2.35 Two methods have been developed to specifically measure the SFE of CNTs, both taking advantage of the fibrous shape of the CNTs. Barber et al. modified a single MWCNT to simulate the Wilhelmy plate technique.36 A single MWCNT was attached to an atomic force microscopy (AFM) tip and dipped into various test liquids. The SFE of the MWCNT was calculated from different capillary forces measured during the advancing and receding processes. Using this method, these workers estimated the SFE of MWCNTs to be 27.8 mJ/m2.36 Nuriel et al. calculated the SFE of fibrous nanomaterials by using various polymer melts as probing materials and measuring their contact angles on MWCNTs via scanning electron microscopy (SEM).37 This method estimated the SFE of MWCNTs to be 45.3 mJ/m2.37 It should be noted that both of these methods are based on the measurement of single MWCNTs. Hence, both methods suffer from errors due to variations among individual MWCNTs. In contrast, our MPD method determines the SFE of MWCNTs as an averaged thermodynamic property. Here we report the SFE of MWCNTs to be 25.3±0.5 mJ/m2, which is near the SFE value reported by Barber et al.36 Graphene nanoplatelets and MoS2 flakes: 2D (planar) nanomaterials. Graphene nanoplatelets and MoS2 flakes are two widely used 2D nanomaterials, especially in the energy and semiconductor

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industry. The plane shape of these nanomaterials facilitates their fabrication into relatively smooth surfaces that permit SFE measurements using the traditional contact angle method. Available literature values of SFE for these two 2D nanomaterials, obtained with the contact angle method, are almost identical, 46.7 mJ/m2 for graphene38 and 46.5 mJ/m2 for MoS239. Here we determined the SFEs of graphene and MoS2 to be 30.3±0.9 and 28.6±0.6 mJ/m2, respectively, significantly lower than previously expected. These differences in SFE may be explained by the so-called wetting transparency effect.40 When determining the SFE of 2D nanomaterials using the contact angle method, one needs to immobilize a thin film, if not a single layer, of these nanomaterials onto a macroscopic substrate, usually made of hydrophilic materials such as mica or glass. Consequently, the contact angle phenomenon of the 2D nanomaterials, as well as the resultant SFE, would be influenced by that of the hydrophilic substrate, thus resulting in a relatively higher SFE estimation. The SFE of 2D nanomaterials determined here could be useful in a range of applications. For example, one recent and increasingly popular method of synthesizing 2D nanomaterials is their exfoliation in the liquid phase.41 The solid precursor for the 2D nanomaterial, e.g., graphite for graphene, is added into a selected liquid and ultrasonically agitated, which exfoliates the monolayered nanomaterial from its bulk precursor. Recent studies showed that the efficiency of exfoliation was largely affected by the selection of the liquid phase.16 The optimal performance was found in a liquid phase whose surface tension matches the SFE of the exfoliated 2D nanomaterials.18,

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This is not unexpected as the exfoliated 2D nanomaterials would be

maximumly dispersed in the liquid with matching surface energies. Neodymium(III) oxide NPs. Neodymium(III) oxide is a rare-earth oxide that shows increasing applications in catalysis and additive manufacturing of ceramics and magnets. Understanding its

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SFE allows more accurate and efficient tuning of manufacturing processes such as the sintering dynamics of powder into solid ceramics and glass. To the best of our knowledge, the SFE of neodymium(III) oxide NPs has not yet been 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 and clays are another important category of materials often used at the micro- and nanoscale. In particular, zeolites, which are hydrated aluminosilicates with microporous structures, are often used as molecular sieves for purification in the form of microparticles as well as for the fluid catalytic cracking of high molecular weight hydrocarbons. In their use as adsorbents and catalysts, their efficiencies are largely dependent on their SFE. However, the SFE of zeolites are very difficult to measure due to their inherent porosity which prohibits the use of the traditional contact angle method. In the present work, we determined the SFEs of two zeolite-A cubic MPs with different sizes (4 vs. 1 µm). Since both particles are in micrometer size, 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 the smaller zeolite MPs. Our measurements are slightly lower than the SFE of zeolites determined with the capillary penetration method, i.e., 34.49 mJ/m2.42 PVPP and polystyrene: Polymeric MPs. PVPP is a common polymeric material used in pharmaceutical excipients, as well as filtration/binding agents used in the production of alcoholic beverages. Polystyrene is commonly used as model particles for studying nanotoxicology, drug delivery, and self-assembly. Due to their importance, there are many studies that report the SFE of polymeric particles and bulk polymers. The SFE of these polymeric materials is commonly reported in the range of 30-43 mJ/m2.43-45 Here, the SFEs of PVPP and polystyrene MPs are determined to be 34.2±1.5 and 35.8±0.4 mJ/m2, respectively. These measurements fall into the lower-end of the literature values.

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Understanding the SFE of polymeric particles plays an important role not only in their applications but also in their syntheses. It has been long known that selecting a correct synthesis liquid is paramount for controlling the polydispersity of polystyrene nano- and microspheres.46 In this case, it is most likely that the surface tension of the synthesis liquid and the SFE of the polystyrene particles have a synergistic effect in determining the final size distribution of the nano- and microspheres. Advantages and limitations of the MPD method. The MPD method has three key advantages that make it superb to existing methods in determining the SFE of particles. First, the MPD method is versatile and applicable to various particles. As demonstrated by the SFE measurements of nine representative micro- and nanoparticles, the MPD method is not limited by the chemistry, size, dimension, or morphology of the particles. This method is successful in determining the SFE of particles encompassing three orders of magnitude from ~50 nm to 5 µm in size. Second, the MPD method is simple in principle and thus requires no complicated theoretical interpretations. This is particularly advantageous over the classical contact angle method in which theoretical interpretations are a necessity for the SFE measurements. Third, the MPD method is easy-to-use, fast, and inexpensive. The only specialized facility needed for the measurement is a microplate reader that is low-cost and readily available in many research labs. Once the probing liquids are prepared, calibrated, and stored, the entire SFE measurements, including particle dispersion, sedimentation, and optical analysis can be completed usually within an hour. In addition, since the MPD method replies on the comparison of OD values in various probing liquids, neither the actual particle concentration of the stock solution, nor the actual sedimentation time or the centrifugation settings affect the location of the OD peak, i.e., the SFE measurements.

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Despite its numerous advantages, the MPD method also has one theoretical limitation and one practical limitation. The theoretical limitation is inherent from the DLVO theory which is most applicable to colloidal systems where the competition between van der Waals attractions and electrostatic repulsions dominates the colloidal stability.2 For very hydrophilic particles, i.e., high SFE particles, however, additional intermolecular and surface forces such as the hydration forces become predominant, at which the MPD method inevitably experiences difficulties. The practical limitation of the method is that it obviously cannot measure particles soluble in the probing liquids, or particles of which the refractive index (n) is very close to that of the probing liquids. For example, when attempting to measure the SFE of Teflon microparticles of n≈1.35 with water/ethanol mixtures of n≈1.33-1.36, the particles do not significantly refract light and would appear transparent. This limitation may be mitigated either by switching probing liquids with different refractive index or by tagging particles with a small amount of fluorescent dyes.47

Conclusions With the application and combination of several inexpensive, easy-to-use and commonly available lab procedures and facilities, such as particle dispersion, settling/centrifugation, pipetting, and visible-light spectroscopy, a new technique for quantitatively determining the surface free energy (SFE) of micro- and nanoparticles was developed. This technique is termed the maximum particle dispersion (MPD) method. From the measurements of nine representative particles of various chemistries, sizes, dimensions, and morphologies, the MPD method demonstrated its versatility and robustness. The SFE of the nine micro- and nanoparticles studied here covers a range of 21 to 36 mJ/m2. These SFE values may find applications in a broad spectrum of scientific disciplines including the synthesis of these nanomaterials, such as by exfoliation or liquid phase

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polymerization. The MPD method has the potential to be developed into a standard, low-cost, and easy-to-use method for quantitatively characterizing the surface free energy and hydrophobicity of particles at the micro- and nanoscale.

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ASSOCIATED CONTENT

AUTHOR INFORMATION

Corresponding Author *Email: [email protected]

Notes The authors declare no competing financial interests. ACKNOWLEDGEMENT

This research was supported by the National Science Foundation Grant Nos. CBET-1254795 and CBET-1604119 (Y.Y.Z.).

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website. 

Characterization of the polar and nonpolar liquid sets (PDF)

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Graphical Table of Contents

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An Optical Method for Quantitatively Determining the Surface

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