Thermodynamic Driving Force in the Spontaneous Formation of

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Thermodynamic Driving Force in the Spontaneous Formation of Inorganic Nanoparticle Solutions Lance M. Wheeler, Nicolaas Johannes Kramer, and Uwe R. Kortshagen Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b05187 • Publication Date (Web): 26 Feb 2018 Downloaded from http://pubs.acs.org on February 27, 2018

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Thermodynamic Driving Force in the Spontaneous Formation of Inorganic Nanoparticle Solutions Lance M. Wheeler,∗,†,‡ Nicolaas J. Kramer,† and Uwe R. Kortshagen∗,† †Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota, USA ‡Current address: Chemistry and Nanoscience Center, National Renewable Energy Laboratory, Golden, CO 80401, USA E-mail: [email protected]; [email protected]

Abstract Nanoparticles are the bridge between the molecular and the macroscopic worlds. The growing number of commercial applications for nanoparticles spans from consumer products to new frontiers of medicine and next-generation optoelectronic technology. They are most commonly deployed in the form of a colloid, or “ink," which are formulated with solvents, surfactants, and electrolytes to kinetically prevent the solid particulate phase from reaching the thermodynamically-favored state of separate solid and liquid phases. In this work, we theoretically determine the thermodynamic requirements for forming a single-phase solution of spherical particles and engineer a model system to experimentally demonstrate the spontaneous formation of solutions composed of only solvent and bare inorganic nanoparticles. We show molecular interactions at the nanoparticle interface are the driving force in high-concentration nanoparticle solutions. The work establishes a regime where inorganic nanoparticles behave as molecular solutes as opposed to kinetically stable colloids, which has far-reaching implications for the future design and deployment of nanomaterial technologies.

Keywords: silicon, ligand-free, quantum dot, semiconductor nanocrystal, colloidal stability

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Bare inorganic particles are typically observed to form a metastable two-phase dispersion after the addition of mechanical energy to transfer the particles from the thermodynamically favored agglomerated state into the liquid phase. Particles remain isolated in the liquid phase for a finite time due to a kinetic barrier in the form of an electrostatic double layer 1 or steric repulsions due to long-chain organic molecules. 2 In contrast, lyophilic colloids spontaneously form a single-phase solution (not dispersion) when solute is brought into contact with solvent. In the absence of changes to chemistry or temperature, a solution is stable indefinitely. 3 Beyond typical molecular systems, this behavior has only been observed for organic systems such as polymers, 4 proteins, 5 and microemulsions. 6 Recent reports of spontaneous solution formation of carbon nanotubes 7–10 and graphene 11 has demonstrated true thermodynamic solution behavior from exciting new organic nanomaterials. The possibility of thermodynamic solutions of bare inorganic particles is often reflexively ignored, but there is no a priori reason to argue against their existence. 12–14 Thermodynamic behavior of ligand-functionalized nanoparticles (NPs) has been recognized, but the thermodynamics are dominated by the ligand interactions with solvent molecules. 15 Transfer of NPs from a non-polar solvent to a polar one has been shown for a number of materials, including metallic, 16–18 metal oxide, 17 and semiconducting 16–20 NPs following ionic ligand functionalization. The exchange of long-chain ligands for short, labile ones that are typically balanced with a counterion in solution has led many researchers to believe kinetic models like DLVO theory 1 describes these systems, in which an electrical double layer is a kinetic barrier to NP agglomeration. However, there are two main issues with this evaluation: (i) DLVO describes lyophobic particles – An underlying assumption is solvent molecules do not favorably interact with the particle surface. The solvent is considered a continuous dielectric medium. (ii) Even with extensions to the DLVO model that incorporate molecular interactions, 21 the theory describes kinetic stability after colloid formation – Formation is not spontaneous; it requires the addition of energy well above kT to the system (typically sonication) to drive the solid phase temporarily into the liquid phase. Here we show thermodynamically stable

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solutions of Si NPs with engineered surfaces spontaneously form and develop a model that shows molecular interactions at the NP surface are the driving force for solution formation. Figure 1a shows still-frame images extracted from the Supplementary Movie S1 of dimethylsulfoxide (DMSO) being added to 7 nm (±20%) silicon NP powder to spontaneously form a single phase. The process resembles solvating a molecular solid into a liquid (e.g. sugar in water). Shaking the vial expedites solution formation, especially for high concentrations (>20 mg ml−1 ), but it is not necessary. It is clear from the transmission electron microscopy (TEM) image in Fig. 1b, the NPs have gone from an agglomerated solid phase of NPs to a solution of singly isolated NPs exhibiting a solvodynamic diameter of 7 to 10 nm observed by dynamic light scattering (DLS) in Fig. 1c. These solutions have remained as a single-phase for over three years. Different behavior is observed for other solvents. The still-frame images in Fig. 1d shows Si NPs remain in an isolated second phase after H2 O addition. Evidence in previous work suggests NP solution formation is strongly dependent on NP surface chemistry and choice of solvent. 20,22–27 Here we control NP surface chemistry using a nonthermal plasma reactor. 28 Silane (SiH4 ) is decomposed in the presence of diborane (B2 H6 ) to produce silicon NPs with boron terminating the surface (see Experimental Section for details). NPs produced without (B2 H6 ) do not spontaneously form solutions. 23 Figure 2a is a diagram illustrating the structure of boronated Si NP that we determined using X-ray photoelectron (XPS) and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy. Fig. 2b shows the B1s core-level XPS spectrum of the assynthesized Si NPs. The spectrum is deconvolved into four peaks wherein the broad peak centered at 188 eV (cyan) is Lewis acidic three-coordinate boron 29 that resides at the Si NP surface with a 2pz orbital available for bonding (Fig. 2a). Peak integration of the XPS spectrum reveals ∼60% of the boron is on the Si NP surface. First principles calculations show B atoms to energetically favor surface segregation in a trivalent coordination as opposed to substitutional incorporation. 30,31 High-energy X-ray diffraction measurements coupled to atomic pair distribution function analysis and reverse Monte Carlo simulations have also

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Figure 1: Spontaneous NP solution formation. a. Still-frame images from Supplementary Movie S1 showing the spontaneous formation of a NP solution after the addition of DMSO to yield a ∼10 mg ml−1 solution. b. TEM image shows the initial agglomerated state of Si NPs before the addition of solvent. The scale bar is 10 nm. c, DLS spectrum showing Si NPs form a solution of individually-isolated particles after the addition of DMSO. d, Still-frame images from Supplementary Movie S1 showing water added to Si NPs to yield a 2-phase system. shown B to reside at the Si NP surface. 32 The orange peak at 185 eV corresponds to fourcoordinate boron that is incorporated into the core of the NP, and the two smaller high binding energy peaks (magenta) are four-coordinate B bonded to oxygen atoms at the Si NP surface. 29 The diamond cubic crystalline core and the disordered acidic B surface are observed in the transmission electron microscope (TEM) image of Fig. 2c. Our previous work showed donor-acceptor (Lewis acid-base) solvent interaction were critical in achieving solutions of Si NPs with chloronated surfaces. 23 Interactions with the acidic B surface of the NPs is demonstrated using ATR-FTIR. In Figure 2d, n-methylpyrrolidone (NMP), which features a spectrally-isolated carbonyl stretch vibration at 1684 cm−1 , is added to Si NPs residing on an ATR crystal and allowed to evaporate over the course of

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Figure 2: Boronated Si NP surface. a. Diagram illustrating the structure of boronated Si NPs. b. XPS B1s spectrum of Si NPs as they are produced from the plasma reaction. Surface B (cyan) accounts for ∼60% of the boron in the sample. c, TEM image of a Si NP with a crystalline core and acidic surface. The scale bar is 3 nm. d, FTIR spectra of an Si NP solution in NMP as NMP evaporates to form a Si NP film, which clearly illustrates strong donor-acceptor bonds formed between the carbonyl group of NMP and the acidic B sites at the NP surface. Spectra are taken continuously over the course of 60 minutes. Spectra are chosen at varied intervals to show the evolution. ∼ 60 minutes. At early times, the spectrum is dominated by features corresponding to free NMP molecules in solution (purple spectrum). As the solution evaporates, and the relative Si NP concentration increases, the carbonyl group of NMP shifts from 1684 cm−1 to reach a final state (red spectrum) with a broader peak centered at 1647 cm−1 , which is an indication of electron density transfer from the Lewis basic C=O group to a Lewis acidic B group of the Si NP surface to form a donor-acceptor complex. 33 A peak emerges at 1329 cm−1 that we assign to the *Si3 B-O vibration of the carbonyl group interacting with B at the Si NP surface. However, boron may also exist on the surface with a terminal hydride (*Si2 B-H). Boron in this state also serves as a Lewis acidic surface site that will interact with carbonyl group. Spontaneous solution formation is a thermodynamic effect. Here we derive a thermodynamic model that predicts the observed NP solution behavior by extending the thermodynamic process considered for molecular solvation 34 to a statistical mechanical system

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composed of two adjacent phases of hard spheres (Fig. 3a). The solvent phase is composed of hard spheres of diameter σs (blue), and the NP phase is composed of hard spheres of diameter σN P (red). The transfer of a NP from the NP phase into the solvent phase is described by the Gibb’s energy of solvation, ∆Gsolv , and must be less than, or equal to, zero for a single-phase solution to spontaneously form:

∆Gsolv =

   ≤ 0, spontaneous solution

(1)

  > 0, two phases Fig. 3a shows the three thermodynamic steps considered to determine ∆Gsolv : (I) A cavity the diameter of a NP, σN P , is formed in the solvent phase, which gives rise to two unfavorable processes – The Gibb’s energy of cavity formation, ∆Gcav,s , and loss of interaction between solvent molecules, ∆Gs-s . (II) A cavity the diameter of a NP, σN P , is formed in the NP phase. The Gibb’s energy of cavity formation in the NP phase, ∆Gcav,NP , and loss of cohesion between particles, ∆GN P -N P , are energetically unfavorable processes. (III) The NP is transferred to the solvent phase, which is described by the Gibb’s energy of mixing, ∆Gmix , and the new interactions between NP-solvent and solvent-NP, ∆GN P -s and ∆Gs-N P , respectively, to yield an expression for ∆Gsolv analogous to regular solution theory and similar to those used to effectively model micelle formation 35 and fullerene solvation: 36

∆Gsolv = ∆Gmix + ∆Gcav,N P + ∆Gcav,s + ∆Gs-s + ∆GN P -N P + ∆Gs-N P + ∆GN P -s

(2)

where ∆Gmix = ∆Gideal + ∆Gex . ∆Gideal is the conventional ideal term, ∆Gideal = xi ln xi + xj ln xj , and ∆Gex is the excess Gibb’s energy based on the Boublik-MansooriCarnahan-Starling-Leland equation of state (BMCSL EoS). 37 We describe the Gibb’s energy of cavity formation in both phases, ∆Gcav,i (where i is the solvent, s, or nanoparticle, N P ), with a derivative of Scaled Particle Theory 38,39 developed by Matyushov and Ladanyi, 40

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Figure 3: Thermodynamics of NP solution formation. a. Thermodynamic process describing ∆Gsolv for NP solution formation. Two phases are considered: the solvent phase composed of hard spheres of diameter σs (blue) and the NP phase composed of hard spheres of diameter σN P (red). b. ∆Gsolv as a function of the number fraction of NPs in solution, xN P . Each set of lines represents sphere diameter ratios, σN P /σs = 2000 (red), 1000 (orange), 200 (yellow), 100 (green), 20 (blue). Each line is calculated by varying ∆gs-N P from 10kT (leftmost thick line) to -25kT (rightmost thick line) in increments of 5kT (thin lines). c, d. Each component of the thermodynamic process is plotted as a function of diameter ratio, σN P /σs for xN P = 1 × 10−6 (c) and xN P = 1 × 10−4 (d). Positive contributions are red, whereas negative contributions are shown in blue (∆Gs-N P ) and green (∆Gmix ) and corresponds to the steps labeled in a. ∆Gs-NP (blue) is evaluated at ∆gs-N P = −25kT . The black curves are ∆Gsolv with labels that correspond to ∆gs-N P values. Unlabeled black curves are calculated in 5kT increments. In all calculations (b-d), ∆Gs-s is evaluated at ∆gs-s = 10kT , ∆Gcav = ∆Gcav,s +∆Gcav,N P , and ∆GNP-NP is evaluated at ∆gN P -N P = 10kT , and the sphere number density is η = 0.48.

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which is based on the BMCSL EoS. The interaction terms, ∆Gi-j (where i and j are the solvent, s, or nanoparticle, N P ), are defined as the number of interactions at the cavity interface in hard sphere system i, zi , times the strength of molecular interaction, ∆gi-j , between species i at the j interface: ∆Gi-j /N kT = xi zj

∆gi-j , kT

where N = Ni + Nj is the total

number of spheres, xi is the number fraction of i, and zi is determined by integrating over the radial distribution function at contact over a spherical shell volume at the cavity interface (Fig. S1). Details on the mathematical framework developed to describe this process are included in the Supporting Information. ∆Gsolv is plotted as a function of the number fraction of NPs in solution, xN P , in Fig. 3b. Each series of curves are for a particular diameter ratio (σN P /σs = 20 (blue), 100 (green), 200 (yellow), 1000 (orange), and 2000 (red)). Each curve increases ∆gs-N P from -25kT to 10kT, keeping ∆gs-s constant. It is clear the maximum theoretical concentration and thermodynamic driving force (magnitude of −∆Gsolv ) are strongly dependent on NP size. At large sizes (σN P /σs > 200), small, but finite, solubilities are predicted but with a driving force only slightly above the thermal energy (∼ 2kT ). The Gibb’s energy of mixing, ∆Gmix , is the dominant contributor in these systems. This is clear from Fig. 3c, which plots each thermodynamic contribution as a function of diameter ratio at a concentration of xN P = 1 × 10−6 . Higher concentrations are limited to smaller diameter solutes (NPs). At high absolute values of ∆gs-N P (∆gs-N P < −15kT ), NPs are even “miscible” for all xN P . Rather than an entropic driving force, there is a shift to molecular interactions as the dominant driving force for small diameter NPs. This is illustrated in Fig. 3d, which shows the individual contributions to ∆Gsolv at high concentration (xN P = 1 × 10−4 ). In this regime, Eq. 2 is reduced to: ∆Gsolv ∆Gmix ∆Gcav,s ∆g + ∆gs-N P ≈ + + xN P zs s-s N kT N kT N kT kT

(3)

Equation 3 shows the Gibb’s energy of solvation is determined by the Gibb’s energy of 8


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10

-3

Saturated xNP

xNP 10

-4

10

-5

10

-6

10

x10

1

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-7

0 -20

1 2

Gsolv

(

gs

NP

,

NP

/

s

)=0

345

6 10 8 1112 13 14 15 16 18 17 15 19 20 21

-10

7

9

20

25

22,23

0

24-27

10

Gvap + Gd-a (kT)

Figure 4: Evaluation of NP solubility. a, Saturated NP concentration as a function of ∆Gvap + ∆Gd-a for a number of solvents. Bubble diameter reflects relative solvent diameter. Red curves are δxδN P ∆Gsolv (∆gs-N P , σN P /σs) = 0 as a function of ∆gs-N P for diameter ratios of 15, 20, and 25 (red text). White and gray number labels indicate solvent, which correspond to data in Table . mixing, the Gibb’s energy of cavity formation in the solvent, and competitive intermolecular interactions: The energy cost of removing interactions from the cavity interface, ∆Gs-s , is in direct competition with the favorable interactions at the cavity interface after the NP is transferred to the solvent, ∆Gs-N P . ∆gs-N P must be negative and greater than ∆gs-s in order for spontaneous solution formation to occur. The importance of competitive molecular interactions has been similarly described in theories of polymer solvation. 41 We evaluate Eq. 3 by adding solvents to B-terminated Si NPs and experimentally measureing the saturated NP concentration (xN P ). Experimentally-determined xN P is plotted as a function of ∆Gvap + ∆Gd-a , where ∆Gvap is the Gibb’s energy of vaporization, and ∆Gd-a is the Gibb’s energy of donor-acceptor bond formation. In principle, the NPs in9


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teract with solvent molecules through van der Waals forces (ion-dipole, dipole-dipole or dipole-induced dipole) as well as donor-acceptor (Lewis acid-base) interactions. However, we assume donor-acceptor interactions dominate, and Gibb’s energy of donor-acceptor formation (∆gs-N P ≈ ∆Gd-a ) because we experimentally observe these interactions, and are typically significantly stronger than other non-covalent interactions. We apply a = SbCl5 as the standard acceptor due to the extensive data available. 42 ∆gs-s is approximated as Gibb’s energy of vaporization (∆gs-s ≈ ∆Gvap ), which is a measure of the strength of intermolecular interactions. We identify a number of solvents that provide high NP concentrations. For 7 nm (±20%) NPs, xN P = 1 × 10−4 is equivalent to ∼ 4% volume fraction or 100 mg ml−1 without any stabilizing ligand or additive. The maximum number fraction presented in Fig. 4 where each solvent is represented by a blue bubble and a number that corresponds to the solvent listed in Table . The derivative of the Gibb’s energy of solvation with respect to xN P is set to zero ( δxδN P ∆Gsolv = 0) to determine theoretically predicted saturated xN P values. This function is superposed onto the experimental data in Fig. 3 as red curves. Diameter ratios of 15, 20, and 25 are shown to accommodate the spread of data. For reference, the diameter ratio of a 8 nm NP in DMSO (σs ≈ 0.4 nm) is 20. The simple hard sphere model is nicely correlated to the experimental data and validates molecular interactions as the thermodynamic driving force for spontaneous solution formation in this size regime. Discrepancies observed are easily rationalized due to the oversimplifying assumptions to the complex system. Considering the long-standing difficulty with predicting solubility of even molecular systems, the model is surprisingly effective at reproducing the experimental data.

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Table 1: Solvent data compiled for Figure 4.

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

Solvent Dimethyl Sulfoxide Dimethyacetamide N,N-Dimethylformamide N-methylformamide N-Methyl-2-pyrrolidone Cyclohexanone Acetophenone 2-Pentanone Benzonitrile 2-Butanone Acetone Methanol Formamide n-Butanol Butanenitrile Propionitrile Isobutyl Ketone Ethanol Water 1,4-Dioxane Acetonitrile Phosphorus Oxychloride Chloroform Nitromethane 1,2-Dichlorobenzene Hexane Toluene

∆Hvap ⊥ ∆Svap ? ∆Gvap ± ∆Hd-a ∆Gd-a k (∆Gvap + ∆Gd-a ) kJ mol−1 J K−1 mol−1 kJ mol−1 kJ mol−1 kJ mol−1 kJ mol−1

52.9 50.2 46.9 54.4 55.3 45.1 55.4 36.1 49.1 34.4 29.0 37.5 60.2 52.4 39.2 35.3 37.7 42.4 40.7 38.6 33.0 35.1 31.4 38.3 48.5 31.0 38.1

114.4 114.6 110.1 119.4 116.4 105.1 116.6 96.6 106.5 97.5 88.1 110.8 124.6 134.0 100.5 95.6 96.6 120.5 108.9 103.3 92.9 92.6 93.9 102.6 107.0 90.9 99.2

19.3 16.6 14.6 19.4 21.2 14.3 21.2 7.8 17.9 5.8 3.2 5.0 23.7 13.1 9.7 7.3 9.4 7.0 8.7 8.4 5.8 7.9 3.9 8.2 17.1 4.4 9.0

-124.7 -116.3 -111.3 -113.0 -114.2 -75.3 -62.8 -62.8 -49.8 -72.8 -71.1 -79.5 -100.4 -81.6 -69.5 -67.4 -66.9 -80.3 -75.3 -61.9 -59.0 -49.0 -16.7 -11.3 -12.6 0.0 -0.4

-63.4‡ ‡

-59.9 -51.2 -52.1 -52.8 -31.7 -24.9 -24.9 -12.2‡ -30.3 -27.7‡ -34.0 -45.3 -35.1 -28.5 -27.4 -27.1 -34.4 -30.0‡ -24.4 -22.8 -4.0‡ 0.1 3.1 2.4 9.2 9.0

-44.0 -43.3 -36.6 -32.7 -31.6 -17.4 -3.6 -17.0 5.7 -24.5 -24.5 -29.0 -21.6 -22.0 -18.8 -20.1 -17.8 -27.4 -21.3 -16.0 -17.1 3.9 4.0 11.3 19.5 13.6 18.0

kT

-17.8 -17.5 -14.8 -13.2 -12.8 -7.0 -1.5 -6.9 2.3 -9.9 -9.9 -11.7 -8.7 -8.9 -7.6 -8.1 -7.2 -11.1 -8.6 -6.5 -6.9 1.6 1.6 4.6 7.9 5.5 7.3

Numbers correspond to labels in Figure 4 Data compiled from Ref. 43 ∆Hvap ? , where Tboil is the boiling point of the solvent Calculated using the relation: ∆Svap = Tboil This data is for SbCl5 is the reference acceptor (∆Hd-SbCl5 ). This value is traditionally known as the donor number, DN. 44 ∓ ∆Gvap = ∆Hvap − T ∆Svap where T = 20◦ C is assumed. k Due to the scarcity of experimental data, most ∆Gd-a values are obtained from a linear fit to ∆Gd-a vs. ∆Hd-a of available data in Ref. 45: ∆Gd-a = −0.54 × Hd-a + 9.23. ‡ Indicates experimental data is used. ⊥

It is interesting to consider the physics captured by our thermodynamic model may be interpreted in a number of ways. Models describing the thermodynamics of micelle and microemulsion systems consider similar contributions to the Gibb’s energy of the colloidal system. 46 Entropy drives the system into a thermodynamic solution when the interaction of surfactant molecules sufficiently reduces interfacial tension (surface energy) at the oil/water interface. Decreasing interface energy is analogous to the solvent-NP interactions; this may be viewed as reduction in surface tension. Implicit solvation models are also heavily em11


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ployed to describe the solvation of complex biomolecules like proteins. 47 In these models, one considers the Gibb’s energy change to transfer a solute from the gas phase to the solvent phase. The solvent is treated as a structureless continuum dielectric medium described by the dielectric constant. The solute is treated as a collection of partial charges in a cavity and is also described by a dielectric constant. In our work, the dielectric constant of bulk silicon (11.7) may be reduced due to the size of the crystal 48,49 as well as the charge at the NP surface. The addition of electron density to the NP by the formation of donor-acceptor bonds with solvent molecules at the NP surface increases charge in the NP, thus reducing the dielectric constant. This would increase the magnitude of the Gibb’s energy of transfer and make solvation more thermodynamically favorable. Similar to our model, this insight suggests conductive materials, such as metals, or materials with acidic surface sites, such as metal oxides and chalcogenides, should display similar behavior NP solution behavior to the Si NPs studied here. The observed solvent-specific solubility of Si NPs limits the number solvents that can be practically applied. However, we are able to formulate an array of cosolvent mixtures that produce NP solutions in solvents that do not yield solubility alone. This is a strategy often used in molecular systems 50 to, for instance, enhance aqueous solubility of drugs 51 or better solubilize proteins. 52 Supplementary Movie S1 shows Si NPs can be diluted in water after being solubilized in DMSO to yield a biocompatible solution of Si NPs. Figure 4a is a photograph of four additional cosolvent solutions of NPs prepared in the same way: H2 O is added to NPs solvated in NMP, nitromethane (NM) is added to NPs solvated in acetophenone (APh), 1,2-dichlorobenzene (DCB) is added to NPs solvated in dimethylacetamide (DMA), and acetonitrile (ACN) is added to NPs solvated in DMSO at 50% by volume to yield stable NP solutions. A similar observation was briefly reported previously by Dong et al. who noticed a variety of metallic and semiconducting NPs will solubilize in water only if DMF is included as well. 17 We believe cosolvent NP solutions are enabled by selective NP solvation and a decrease

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Figure 5: Cosolvent formulations of Si NP solutions. a, Various solution mixtures formed by adding the solvent listed on top to the Si NPs and diluting 50% by volume with the cosolvent listed below. NMP = n-methylpyrollidone, NM = nitromethane, APh = acetophenone, DCB = 1,2-dichlorobenzene, DMA = dimethylacetamide, ACN = acetonitrile, and DMSO = dimethylsulfoxide b, FTIR spectra for films of Si NPs cast from NMP/H2 O mixture of varying volume fractions. Spectra are normalized and offset for clarity. in ∆gs-s . Moreover, it is likely a large driving force is needed to overcome any kinetic effects in the system. A smaller driving force is needed to mix additional solvents after the NP solution is formed. Evidence for selective solvation is provided in Fig. 5. Si NPs in NMP that are diluted with water from 0% up to 94% by volume and left at ambient conditions for two weeks. These solutions were cast onto an ATR crystal and allowed to evaporate. The hydrocarbon (ν(C-Hx )=1684 cm−1 ) and carbonyl (ν(C=O)=1684 cm−1 ) stretching modes of NMP, highlighted with dashed lines, are observed even at high volume fractions of water. Note the ν(C=O) stretch is obscured by the bending vibration of water at ∼1644 cm−1 at

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volume fractions of 50% and 94%. Interestingly, the surface of the Si NPs remain unoxidized at 10% water by volume indicated by the lack of ν(Si-O-Si) stretch (centered at 1190 cm−1 ). Though the ν(O-H) stretch of water is observed in all samples (red highlight), it appears the B surface, in addition to the NMP molecules preferentially bound to the surface through a donor-acceptor complex, actually protect the NPs from oxidation. In this work, we demonstrate the formation of high concentration solutions of bare inorganic NPs and show this behavior is consistent with a statistical thermodynamic model. Bare inorganic NPs behave as molecular solutes to form a single thermodynamic phase with solvents rather than a kinetically-stable colloid. The results suggest our observations go beyond the current Si NP system explored here. For instance, a boronated Si NC surface can be produced using post-synthetic solution chemistry 53 instead of relying on surface segregation during plasma growth. Other group IV NPs (Ge and SiGe) produced in a plasma with diborane have also been shown to have boronated surfaces. 54 We find strong surface interactions are the driving force for spontaneous solution formation. In this context, NP systems with vastly different chemistry may behave similar to the observations here, and metals and metal-based insulators or semiconductors already show spontaneous phase transfer from one solvent to another. 16–20 In these systems, the thermodynamics governing molecular interactions with ionic species on the NP surface as well as the counterion in solution likely play a significant role. 55 Ultimately, this work provides a new framework in the design of nanoparticle solutions and deepens our understanding in the regime that transitions the molecular world to the macroscopic one.

Experimental methods Si NP synthesis. Si NPs are synthesized in a continuous-flow nonthermal plasma reactor from gas mixture of argon, silane, and diborane. Gas flows through a borosilicate glass tube with a pair of copper ring electrodes secured to it. Typical flow rates are 30–50 standard

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Nano Letters

cubic centimetres per minute (sccm) of argon, 0.4–0.6 sccm of silane, 0–2 sccm of diborane diluted in hydrogen (10%). 13.56 MHz radiofrequency power at 110 to 130 W is supplied to the ring electrodes to strike a plasma and yield crystalline Si NPs. A rectangular nozzle controls the gas pressure in the plasma region by restricting the flow. Adjusting the width of the nozzle opening allows for the pressure to change independently of the gas flow. This method is used to produce nanocrystals at reactor pressures ranging from 90 to 150 Pa. As a result, the nanoparticle size can be precisely controlled between 5 and 15 nm. 7.5 nm Si NPs are used throughout this study.

Si NP collection and solution formation. Powder samples of silicon nanocrystals are collected directly from the gas-phase by impacting them onto a substrate mounted onto a manual feed-through located inside the reactor. A rectangular nozzle is placed in between the deposition and plasma region to accelerate the particles and impact them directly onto the substrate. The substrate is then retracted into a portable loadlock and transferred airfree to a N2 -purged glovebox for further processing. Si NPs are weighed and solvated in various solvents.

XPS. XPS spectra are acquired on a Surface Science Laboratories, Inc. SSX-100 XPS with a monochromatic Al Kα X-ray source. A X-ray power of 200 W with a 1×1 mm2 spot size was used. Si NP samples are prepared by directly impacting a

Thermodynamic Driving Force in the Spontaneous Formation of

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