Thermochemical Measurements of Cation Exchange in CdSe

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Thermochemical Measurements of Cation Exchange in CdSe Nanocrystals using Isothermal Titration Calorimetry Suprita Jharimune, Ajay Sathe, and Robert M. Rioux Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b02661 • Publication Date (Web): 30 Aug 2018 Downloaded from http://pubs.acs.org on September 1, 2018

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Thermochemical Measurements of Cation Exchange in CdSe Nanocrystals using Isothermal Titration Calorimetry Suprita Jharimuneǂ, Ajay A Satheǂ, Robert M Rioux§,ǂ,* ǂ

§

Department of Chemistry

Department of Chemical Engineering The Pennsylvania State University University Park, PA 16801 *

email: [email protected]

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ABSTRACT

Among the various reported post synthetic modifications of colloidal nanocrystals, cation exchange (CE) is one of the most promising and versatile approaches for the synthesis of nanostructures that cannot be directly synthesized from their constitutive precursors. Numerous studies have reported on the qualitative analysis of these reactions, but rigorous quantitative study of the thermodynamics of CE in colloidal nanoparticles is still lacking. We demonstrate using isothermal titration calorimetry (ITC), the thermodynamics of the CE between cadmium selenide (CdSe) nanocrystals and silver in solution can be quantified. We survey the influence of CdSe nanocrystal diameter, capping ligands and temperature on the thermodynamics of the exchange reaction.

Results obtained from ITC provide a detailed description of overall

thermodynamic parameters — equilibrium constant (Keq), enthalpy (∆H), entropy (∆S) and stoichiometry (n) — of the exchange reaction. We compared the free energy change of reaction (∆G) between CdSe and Ag+ obtained directly from ITC for both CdSe bulk and nanoparticles with values calculated from previously reported methods. While the calculated value is closer to the experimentally obtained ∆Grxn for bulk particles, nanocrystals show an additional Gibbs free energy stabilization of ~ -14 kJ/mol Se. We discuss a thermochemical cycle elucidating the steps involved in the overall cation exchange process. This work demonstrates the application of ITC to probe the thermochemistry of nanoscale transformations under relevant solution conditions. KEYWORDS: CdSe nanocrystals, cation exchange, thermodynamics, isothermal titration calorimetry, nanocrystal size, capping ligands


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INTRODUCTION Cation exchange (CE) in nanocrystals has emerged as a powerful post-synthetic modification tool during the last decade largely due to the efforts of developing complex nanostructures with materials and morphologies inaccessible by direct colloidal synthesis.1-6 CE in nanocrystals, much similar to those in bulk phases, involves replacement of cations in a well-defined nanocrystal template with foreign cations while preserving the anionic framework. Rates of CE in nanocrystals are orders of magnitude faster compared to bulk due to the faster diffusion of cations in nanocrystal systems.7 Additionally, preservation of the anion framework during CE allows a wide range of synthesis design goals to be achieved.8-10 Currently, the mechanism for CE in nanocrystals is mostly debated to be diffusion controlled and depends on a number of factors including cation diffusivity through interstitial sites11, 12 and the presence of vacancies.13,

14

Recent studies by Jain and co-workers indicate CE of CdSe

nanocrystals by Ag+ follows a co-operative transformation behavior rather than a diffusionlimited cation-by-cation exchange.15

While limited fundamental quantitative study of CE

reaction kinetics exist16, quantification of exchange thermodynamics under realistic conditions is completely lacking. The probability of a CE reaction is usually estimated based on differences in lattice energies of reactant and product crystals or bond dissociation energies of the compounds.1 Qualitative thermodynamic approaches include free energy change (∆Grxn) calculations from association and dissociation energies of crystal lattices and solvation and desolvation energies of the exchanging cations as discussed in details in publications by the Jain and Alivisatos groups.5, 17

However, this method is applicable for bulk materials, provides only an approximation of

∆Grxn for nanocrystals. Formation energy calculations by this method neglect several factors such as size, shape, and ligands on the surface of nanocrystals which may contribute differently 2 ACS Paragon Plus Environment

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to the final state of the reactant and product phases. Furthermore, the reduction potential values used for estimating free energy changes are dependent on the surrounding solvent environment and presence of any ligands.18 Jeong et. al. utilized the equilibrium solubility constant of the reactant and the product phase to calculate their respective free energy changes and hence predict if a particular CE transformation is thermodynamically favorable.19 While solubility data for a number of compounds is readily available in water, extension to other solvent systems which are most typically used in CE reactions is difficult due a lack of compiled data. With the unavailability of any quantitative thermodynamic data on nanocrystal CE under relevant solvent conditions, we applied calorimetry to accurately measure the thermodynamic parameters of CE reaction in nanocrystals. In this paper we demonstrate isothermal titration calorimetry (ITC) can be employed to measure the thermodynamics of CE in nanocrystals. ITC directly measures the enthalpy of exchange reaction and provides a more realistic estimate, taking into consideration all the factors (viz. particle size, capping ligands, solvent, temperature, etc.) that impact exchange. To the best of our knowledge, this is the first absolute quantitative study of the thermodynamics of CE in nanocrystals. Titration calorimetry, first described in the 1960s as a technique for the simultaneous determination of the equilibrium constant (Keq) and heat of reaction (∆H),

20, 21

was originally

used to study acid base equilibria and formation of metal complexes.21-23 ITC has since been routinely utilized in the determination of thermodynamic properties of biochemically relevant ligand-receptor binding.24-26 Previous work from our group extended the use of this technique to systems relevant to organometallic catalysis such as ligand exchange reactions in palladium complexes,27,

28

oxidative addition of amines at phosphorous centers,29 and the influence of

precursor binding on catalyst support.30,

31

Recently, ITC is being increasingly employed to


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study binding characteristics of ligands on the surface of nanoparticles.32-35 Analogous to ligand exchange studies in ITC, CE in nanocrystals can be thought of as a ligand binding (incoming cation) to the nanocrystals, with subsequent release of a different ligand (outgoing cation). With ITC, we investigated the CE process between CdSe nanocrystals and Ag+ cations. The CdSeAg+ system was selected since it is one of the most commonly studied CE system in literature.7, 12, 16

Moreover, synthesis of CdSe nanoparticles with tunable size and capping ligands is well-

known and straightforward.36,

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We studied the influence of three variables — size of the

nanoparticles, capping ligands and temperature — on the CE thermodynamics of CdSe nanoparticles. An advantage of ITC is it allows for measurement of the equilibrium constant (Keq), change in enthalpy (∆H) and stoichiometry (n) in a single experiment as opposed to the traditional approaches such as the Van’t Hoff analysis, which require multiple experiments over a range of temperature.21,

38

Utilizing a model based evaluation of the incremental heat flow

data, temperature-dependent thermodynamic variables can be reported.32


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MATERIALS AND METHODS Chemicals. Cadmium oxide (≥99.99%), octadecene (90%), oleic acid (90%), Se powder (99.99%), trioctylphosphine (98%), anhydrous toluene and acetonitrile (99.8%), silver triflate (≥99%), silver nitrate (≥99%), and technical grade (~90%) hexadecylamine (HDA), trioctylphophine oxide (TOPO), octanethiol, and octanoic acid were obtained from SigmaAldrich. 2.5 nm CdSe nanoparticles were purchased from Sigma-Aldrich while other sizes — 3.4, 5.5, 6.2 and 7.2 nm were synthesized following literature procedures.39, 40 Synthesis of cadmium selenide particles. In a typical synthesis, cadmium oxide (CdO) is used as the cadmium precursor and a mixture of oleic acid (OA) and octadecene (ODE) as the capping ligand and reaction solvent, respectively. The selenium precursor is prepared from selenium powder (Se) dissolved in trioctylphosphine (TOP) and ODE. In a three-neck round-bottom flask (100 mL), CdO (51.36 mg, 0.4 mmol), OA (3.15 mL, 10 mmol) and ODE (20 mL) were degassed under vacuum for 30 mins and then heated under argon to the reaction temperature of 300ºC. At this temperature, a mixture of Se powder (157.94 mg, 2 mmol), TOP (5 mL) and ODE (8.5 mL) was rapidly injected into the solution. The mixture was stirred for 1 min (3.4 nm), 8 min (5.5 nm), 10 min (6.2 nm) and 13 min (7.2 nm) and then removed from the heating mantle. The reaction mixture was cooled to 60°C and equally distributed into 3-4 40 mL plastic centrifugation tubes.

Excess methanol was added to each tube to precipitate out the

nanoparticles. The gel-like mixture is centrifuged at 6000 rpm and the supernatant is removed. Toluene and methanol (1:4) are added followed by centrifugation. This process is repeated 4-8 times, until a gel-free solution is obtained. The final precipitate of CdSe nanoparticles were collected and dispersed in toluene and stored in refrigerator for further use. The particles are stable for 6-8 months. 5 ACS Paragon Plus Environment

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Ligand exchange of as-synthesized CdSe nanoparticles. The as-synthesized CdSe nanoparticles were capped with OA and TOP/TOPO.

To obtain CdSe nanoparticles with

different capping ligands, the as-synthesized nanoparticles obtained from one batch of synthesis were exchanged with ~20 mmol of the desired ligand.37

In a typical ligand exchange

experiment, CdSe nanoparticles suspended in toluene and the ligands in toluene were mixed together and degassed for 30 min. The mixture was then allowed to reflux overnight at 110°C. The exchange solution was then cooled and precipitated with excess methanol. To remove the excess ligands, nanoparticles were re-dispersed in toluene and methanol (1:4) and centrifuged at 6000 rpm. This step was repeated three times to ensure removal of excess ligands. Cation exchange experiments in ITC. ITC experiments were performed using a NanoITC calorimeter (TA instruments) equipped with gold reference and sample cells (V = 1.014 mL). All titrations were carried out using a 100 µL syringe at 298.15 K (or stated temperature) with a stirring rate of 250 rpm. In ITC experiments to examine the influence of nanoparticle diameter, capping ligands and temperature, solutions of 0.129 mM (concentration of Cd, determined by ICP-OES) CdSe nanoparticles in toluene was titrated with 5 mM solution of silver triflate dispersed in the same solvent. Injections with a volume of 4 µL were made every 15 mins to allow for the heat flow to return to the baseline following each injection. For exchange of bulk CdSe particles, a suspension of 1 mM bulk CdSe in acetonitrile was titrated with 30 mM AgNO3 solution at 298.15 K. Injections with a volume of 3.2 µL were made every 60 mins. For comparison of bulk CdSe with the nanoparticles, 0.129 mM, 2.5 nm CdSe nanoparticles were exchanged with 5 mM AgNO3 in acetonitrile at 298.15 K. Experiments were repeated in triplicates and all reported data are the mean of three trials. Error bars represent standard deviation of the mean over three measurements.

Data analysis was performed using the 6

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NanoAnalyze software from TA instruments and all data were fitted to an independent singlesite model. CdSe nanocrystals likely have different cation binding sites in the crystal—cation sites on the surface or in the bulk. However, each site is considered thermodynamically identical or independent of each other with similar affinity for the Ag+ ions based on reasonably good fit we obtained from singlesite binding model. The stoichiometry obtained for each fit is ~2 as expected during CdSe exchange with Ag+. Details of ITC theory are found in the Supporting Information.

Characterization. Optical characterization was performed on 3.4 nm CdSe nanocrystals and the exchanged product nanocrystals after dissolving them in hexane. UV-Vis absorption spectra were acquired on a Shimadzu UV-3600 UV-VIS-NIR spectrophotometer.

Powder X-ray

diffraction (XRD) were collected in PANalytical XPert Pro MPD - diffractometer using Cu Kα (λ = 1.5406 Å) radiation at 45 kV and 40 mA are shown in Figure 2. The nanoparticles were concentrated by removing most of the solvent (toluene) and then drop-cast into the cavity of a silicon zero background holder and allowed to dry completely. The MPD is equipped with a PIXcel 1D detector using scanning line mode detection, and the incident beam optics were configured with a 0.5° anti-scatter slit, 10 mm beam mask, 0.25° fixed divergence slit, and 0.25° receiving slit. Diffraction patterns were collected with step size 0.026 2 over the range of 2070° 2. Experimental XRD patterns were compared with those published in the Inorganic Crystal Structure Database (ICSD) PDF database. Rietveld refinement were performed on the bulk CdSe exchanged with AgNO3 in acetonitrile, using Los Alamos General Structure Analysis System (GSAS)41 and its graphical interface, EXPGUI.42 TEM images of the nanocrystals were acquired on a FEI Talos™ microscope operating at 200 kV. Dilute solutions of the nanocrystals in hexane were dropped onto 50 Å thick carbon coated


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copper grids (400 mesh) and the excess solution dried under vacuum. The average size of the particles was determined by analyzing the TEM images using ImageJ software (Figure S2-S3). The concentration of the CdSe nanoparticles were determined using Agilent 700 Series ICPOES. The standards for calibration (0.5 ppm, 2 ppm, 4 ppm, 8 ppm, 16 ppm) were prepared by serial dilution of the commercial stock solution (100 µg/mL) of Cd and Se obtained in 2% HNO3 (High-purity Standards, Charleston, SC) to make 10 mL solution of each. CdSe samples were prepared by dissolving 50 µL of solution in 1 mL of aqua regia and digested by heating. Once all of the aqua regia was evaporated, 10 mL of 2% HNO3 is added to prepare the final solution. 1

H and 31P NMR experiments were carried out on an 11.75 T Bruker Avance-III-HD-500- MHz

instrument operating at a 1H frequency of 500.203 MHz and a

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P frequency of 202.493 MHz,

using a 5-mm CPPBBO BB-1H/19F/D Z-GRD LN2 cryoprobe. Samples were dissolved in CDCl3 containing TMS as internal standard and analyzed at 298.15 K. NMR samples of CdSe nanoparticles were prepared by diluting 0.05 mmol (based on Cd conc.) nanoparticles in 0.5 mL CDCl3. 1H experiments were performed with 1 s relaxation delay, flip angle of 30o (the 90o pulse was 10.05 µs at 20 W), acquisition time of 3.3 s, and a spectral width of 10 kHz. 31P experiments were performed with 2 s relaxation delay, 90o angle (the 90o pulse was 11.25 µs at 53 W), acquisition time of 0.4 s, and a spectral width of 21.3 kHz.


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RESULTS AND DISCUSSION Influence of particle size on cation exchange thermodynamics. CE of CdSe nanoparticles with Ag+ is much faster compared to bulk phases16, 17, 43 owing to their smaller size and hence increased surface-to-volume ratio which likely lowers the activation barrier for the diffusion of ions.17 We studied CE of CdSe with four different nanocrystal sizes (with an average diameter of 3.4, 5.5, 6.2 and 7.2 nm). All CdSe nanocrystals capped with hexadecylamine (HDA) dispersed in toluene were exchanged with AgOTf at 298.15 K. Figure (1A-B) represents the thermogram and corresponding isotherm obtained for 6.2 nm HDA-capped CdSe nanocrystals. Thermograms and isotherms for other sizes are presented in Figure S5. The resulting isotherm (Figure 1B) can be divided into three distinct regions: the section prior to the point of inflection represents the exchange of Cd2+ with Ag+, followed by the non-linear portion of the sigmoid near the point of inflection where exchange of final few Cd2+ ions in the parent crystal occurs. The final section corresponds to the heat of mixing/dilution of the silver salt solution where minimal solid-state exchange occurs. It is apparent from Figure 1A, the heat of mixing of excess Ag+ and triflate ions into the reaction mixture after completion of CE is endothermic, while the exchange reaction itself is exothermic. Formation of Ag2Se nanocrystals from the exchange of CdSe nanoparticles with Ag+ is confirmed by complementary techniques — optical absorption spectra and X-ray diffraction (XRD). UV-Vis absorption spectra (Figure S1) indicates a characteristic absorption maximum at 561 nm for 3.4 nm particles which disappears upon the formation of Ag2Se nanoparticles after CE.44 Powder XRD of the synthesized 5.5 nm CdSe nanocrystals shows a cubic phase (Figure 2A) while the exchanged Ag2Se nanoparticles contain a mixture of cubic and orthorhombic phases (Figure 2B).


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Table 1 shows the best-fit parameters obtained for the CE reactions with different nanoparticle diameter measured in the ITC. The stoichiometry (n) of the Ag2Se nanoparticles obtained directly from ITC was found to be 2.0 ± 0.2 which agrees with the expected stoichiometry of CdSe exchange with Ag+. The enthalpy, entropy and overall free energy changes do not vary significantly from each other with nanoparticle sizes. However, it is interesting to note that the free energy change follows a decreasing trend (becomes more negative) with decreasing nanoparticle diameter (Figure 3). The observed trend of free energy change with size could be an interplay of several factors.

It is well-known from literature the surface energy of

nanocrystals can vary with size and especially in the lower size regime where large surface-tovolume ratio leads to a greater number of atoms residing on the surface of the particle compared to its bulk.45,

46

Huxter et. al. reported that colloidal CdSe nanoparticles capped with

trioctylphosphine oxide (TOPO) ligands, dispersed in toluene show a size-dependent surface energy.47 Surface energy of these particles scales inversely with size until a maximum is reached at a particle diameter of 2.8 nm, where the surface energy is found to be ~ -8.6 J/m2. More recently, Xu et. al. reported calorimetrically measured surface energy of wurtzite CdSe nanoparticles.48 Using high-temperature oxide melt solution calorimetry and water adsorption calorimetry they determined the surface energy of CdSe nanocrystals in size range of 20-60 nm equals to 1.65 ± 0.27 J/m2. Therefore, CdSe nanoparticles with different diameters may have varying surface energy contributions that could alter the free energy difference between the parent and product crystal. However, contribution of nanoparticle surface energy to the ∆Grxn of CE in CdSe nanoparticles could be nearly negligible owing to their lower magnitude.47,

48

A

more significant contributing factor is perhaps the energy of vacancy formation in nanocrystals. While the mechanism of CE is still debated, most reports indicate the exchange occurs via


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diffusion of guest cations in the host lattice through vacancy formation or interstitials.13, 49 The energy of vacancy formation increases with increase in nanoparticle size.50-52 Banin et. al., in a recent publication demonstrated that doping of Cu2S nanoparticles through a vacancy formation reaction is size-dependent.51 They observed, for particle size varying from 3 to 14 nm in diameter, the doping reaction efficiency increases with increase in particle size. They concluded that this result is a combined consequence of vacancy formation energy and surface effect, the latter predominating in their case. The process of nanocrystal doping is comparable to nanocrystal CE in terms of formation of vacancies, except that there is no foreign cation substitution during doping. In our case, we observe that the ∆Grxn is comparable for nanoparticle sizes 3.4, 5.5, and 6.2 nm, whereas a jump is observed for the 7.2 nm nanoparticles (Figure 3). The formation of vacancies involve bond breaking between an atom and its surrounding atoms. At lower nanoparticle size range, a larger number of atoms reside on the surface and may have multiple broken bonds, making vacancy formation easier compared to larger nanoparticles where most of the atoms approach bulk, requiring larger number of bonds to be broken in order to form vacancies. Therefore, the thermodynamic effect of vacancy formation energy could be attributed to be the dominating factor in our current study. As the size decreases, vacancy formation become more favorable, leading to a decrease in ∆Grxn of CE.


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(A)

(C)

(B)

(D)

Figure 1. Real-time ITC thermograms for cation exchange of 6.2 nm CdSe nanoparticles capped by (A) HDA, and (C) octanethiol with AgOTf in toluene at 298.15 K. (B) and (D) represent their corresponding integrated heat data with single-site model fitting.


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(A)

(B)

Figure 2. X-ray powder diffraction pattern for (A) 5.5 nm HDA-capped CdSe nanoparticles (experimental data shown in red), (B) product after exchange with Ag+ (experimental data shown in blue). Simulated patterns refer to CdSe cubic phase (PDF #01-088-2346), Ag2Se cubic phase (PDF #01-076-0135), and Ag2Se orthorhombic phase (PDF #01-071-2410).


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Figure 3. Size dependence of overall free energy change (∆G) of cation exchange between HDA-capped CdSe nanocrystals of average diameters 3.4, 5.5, 6.2, and 7.2 nm with AgOTf in toluene at 298.15 K.


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Table 1. Influence of HDA-capped CdSe nanoparticle diameter on the thermodynamics of cation exchange. The equilibrium constant (K), Gibbs free energy change (∆G), enthalpy change (∆H), and entropy change (T∆S) calculated per mole of Se for CdSe exchange with AgOTf in toluene at 298.15 K.

Size (nm)

K (×106 M-1)

∆G (kJ/mol)

∆H (kJ/mol)

T∆S (kJ/mol)

n

3.4

4.3 ± 0.3

-37.9 ± 0.2

-54.8 ± 2.8

-16.9 ± 2.9

2.2 ± 0.1

5.5

2.2 ± 0.6

-36.1 ± 0.8

-50.4 ± 2.1

-14.3 ± 1.4

2.1 ± 0.0

6.2

1.6 ± 0.2

-35.4 ± 0.3

-49.9 ± 0.2

-14.5 ± 0.4

2.1 ± 0.1

7.2

0.3 ± 0.0

-31.2 ± 0.7

-51.2 ± 2.2

-20.0 ± 1.6

1.9 ± 0.1


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Influence of capping ligands on cation exchange thermodynamics. Capping ligands are used to stabilize nanoparticle in solution and prevent their aggregation.53 They are also known to influence nucleation and growth kinetics of nanocrystals during synthesis.54 The influence of capping ligands on the synthesized nanocrystals can be two-fold. Through stabilization of certain specific facets, capping ligands can dictate a particular morphology or crystallographic form.55 Moreover, depending on the chain length of the organic ligand, steric effect can impact the diffusion of

monomers to the growing surface leading to differences in the size of

synthesized nanocrystals.56

Several CE reactions in nanocrystals which are otherwise

thermodynamically unfavorable, can be driven in presence of particular ligands.57 In order to verify if capping ligands on CdSe surface could also influence the thermodynamics of CE, we investigated CE of CdSe nanoparticles capped with different ligands. Four commonly utilized capping ligands for the synthesis of chalcogenide nanocrystals including diverse functional groups — amine, carboxylic acid, thiol and phosphine oxide — were chosen for our study.58 CdSe nanocrystals capped with hexadecylamine (HDA), trioctylphosphine oxide (TOPO), octanethiol, and octanoic acid were obtained by ligand exchange of the initially synthesized CdSe nanocrystals (details in Experimental section). In order to confirm ligand exchange, we performed

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P and 1H NMR on the CdSe nanoparticles.

Figure S4 summarizes the NMR

spectrum obtained for TOP-Se, pure TOPO, as-synthesized CdSe nanoparticles, and HDA and TOPO-capped CdSe nanoparticles. Figure S4A-B shows peak at 48.51 ppm which may be assigned to free TOPO.59,

60

This peak is seen in the as-synthesized and TOPO-capped

nanoparticles but shifted downfield to 49.66 ppm and 49.08 ppm respectively, indicating the ligands present are bound to the surface of the nanoparticle.35, 60 The TOP-Se peak (36.35 ppm) is shifted slightly upfield to 36.38 ppm in both cases.59 The presence of 31P NMR peaks in the


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as-synthesized nanoparticles are due to the selenium precursor (TOP-Se) used during synthesis. The intensity of

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P NMR peaks in TOPO-capped CdSe nanoparticles is higher than the as-

synthesized nanoparticles, while it is absent in HDA-capped nanoparticles (Figure S4-D), indicating successful exchange of the initial TOPO/TOP ligands. Furthermore, 1H NMR spectra (Figure S4-F) was collected from TOPO-capped CdSe nanoparticles to confirm exchange of oleic acid ligands. The spectrum shows very small peaks in δ = 5.8-5.9 ppm region which could be attributed to oleic acid ligands.59, 61-65 However, unlike bound oleic acid ligands which are present as a very broad peak,57, 59-63 these peaks are sharp and indicate the presence of a small amount of residual free oleic acid ligands in the solution after ligand exchange. Additionally, to ensure complete exchange, 2-3 times excess exchange ligand was added in order to thermodynamically drive the ligand exchange equilibrium. The best-fit parameters for the observed integrated heat data for CE of CdSe nanoparticles capped with different ligands are presented in Table 2. Figure 1 represents the real-time ITC thermograms and their integrated heat data with fitted model for CdSe nanoparticles capped with HDA (Figure 1A-B) and octanethiol (Figure 1C-D) exchanged with AgOTf in toluene at 298.15 K. Thermograms of other capping ligands are shown in Figure S6. The results obtained from ITC do not show any significant variation in the thermodynamic parameter values for the different capping ligands. The enthalpy of reaction and entropy values for HDA capped CdSe nanocrystals were found to be slightly less negative compared to those capped with TOPO, octanoic acid and octanethiol. The change in enthalpy for different capping ligands is matched by a proportional change in the entropy of the reaction leading to very little variation in the free energy change of reaction. The plot of observed change in enthalpy versus change in entropy yields a linear enthalpy-entropy compensation relationship (Figure 4).66 While the origin and


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physical significance of the compensation effect is unknown, it has been observed in many chemical systems such as coordination chemistry, solvation, molecular recognition, heterogeneous catalysis, etc.67-70 The stoichiometry (n) obtained from ITC results also matches the expected stoichiometric value, regardless of the bound ligand.

Nearly similar

thermodynamic parameters for CE suggests that ligands bound to the nanocrystal surfaces have minimal influence on the CE thermodynamics. A common strategy to thermodynamically drive CE reactions is based on Pearson hard-soft acid base principle (HSAB) that involves addition of external ligands (bases) that have greater affinity towards the outgoing cations (acids).71 Alivisatos group reported CE of Cu2S to PbS3 or Ag2Se to CdSe7 occurs only when tributylphosphine (TBP) ligands are added to the reaction mixture. Similarly, Gui et. al. utilized a number of phosphine ligands to mediate CE of N2E (N= Ag, Cu; E=S, Se, Te) to ME (Cd, Zn, Pb).57 In both cases despite the presence of oleic acid and/or alkyl phosphines ligands as capping ligands on the surface of the starting nanoparticles, CE reactions occur only when external ligands are added to the reaction medium. This observation could be attributed to lower ligand coverages on nanocrystal surfaces, where ligands are only bound to the surface atoms, leaving most of the bulk atoms bare and hence insufficient to influence the CE thermodynamics. Lower surface ligand coverages are also commonly reported in literature. Bochmann et. al.72 reported 2 nm CdSe nanoparticles had carboxylic acid (oleic acid) and thiol (dodecanthiol) ligand density of 1.8 and 1.9-2.8 ligands per nm-2, while Bawendi73 reported TOPO density to be ~3.7 ligands per nm-2 for CdSe nanoparticles with 3.7 nm diameter. On the other hand, in order to thermodynamically drive a CE reaction by ligands, an excess (at least 10 times more concentrated compared to the nanoparticle concentration in solution) of ligands are added. Additionally, several literature studies also indicate that the reaction enthalpy (∆H) of


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ligands binding to CdSe nanoparticle surfaces could be borderline exothermic/endothermic or almost negligible. In a very recent publication, Hens et. al. using van’t Hoff analysis determined the binding enthalpy of common amine ligands — tetramethylethylene-1,2-diamine (TMEDA), n-butylamine (BuNH2), and benzylamine (BnNH2) on CdSe nanoparticles.61 They reported ∆H values of −16 ± 2 kJ/mol for BuNH2, −7 ± 2 kJ/mol for BnNH2, and 0 ± 2 kJ/mol for TMEDA on CdSe nanoparticles. Previously, Dempsey et. al. reported ∆H = +8.45 ± 0.1 kJ/mol for binding of undec-10-enoic acid (UDA) to CdSe nanocrystal surface from a van’t Hoff analysis.62 Our study further corroborates all these observations and reports in literature that capping ligands have very small to no influence on CE thermodynamics of nanoparticles.


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Table 2. Influence of capping ligands on thermodynamics of CdSe cation exchange reaction. The equilibrium constant (K), Gibbs free energy change (∆G), enthalpy change (∆H), and entropy change (T∆S) calculated per mole of Se for 6.2 nm CdSe exchange with AgOTf in toluene at 298.15 K. Capping Ligand

K (×106 M-1)

∆G (kJ/mol)

∆H (kJ/mol)

T∆S (kJ/mol)

n

Hexadecylamine

1.6 ± 0.2

-35.4 ± 0.3

-49.9 ± 0.2

-14.5 ± 0.4

2.1 ± 0.1

TOPO

1.1 ± 0.6

-33.8 ± 2.0

-51.8 ± 1.0

-18.0 ± 1.0

1.8 ± 0.1

Octanethiol

0.8 ± 0.1

-33.5 ± 0.5

-52.3 ± 0.5

-18.8 ± 0.6

2.0 ± 0.2

Octanoic Acid

0.7 ± 0.6

-32.9 ± 1.9

-53.6 ± 0.8

-20.7 ± 2.0

2.0 ± 0.1


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Figure 4. Compensation plot for the enthalpy and entropy of cation exchange of 6.2 nm CdSe nanocrystals capped with hexadecylamine (HDA), trioctylphophine oxide (TOPO), octanethiol, and octanoic acid with AgOTf in toluene at 298.15 K. The ∆H (kJ/mol) and ∆S (J/mol.K) values are average of triplicate ITC measurements and the error bars represent the standard deviation over the mean of ∆H (kJ/mol).


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Influence of temperature on cation exchange thermodynamics. The influence of temperature on the CE of CdSe with Ag+ was examined by ITC. Three different temperature — 288.15 K, 298.15 K and 308.15 K — were examined and 5.5 nm HDA-capped CdSe nanoparticles were exchanged with AgOTf in toluene. We observed the equilibrium constant reduces with an increase in temperature, consistent with the Le Chatelier’s principle for exothermic reactions. Significant differences in thermodynamic parameters were not observed as a result of the change in temperature. The best fitting parameters obtained from the ITC for different temperatures are presented in Table 3. Thermograms with integrated heat data are presented in Figure S7.


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Table 3. Influence of temperature on cation exchange thermodynamics of HDA-capped CdSe nanoparticles. The equilibrium constant (K), Gibbs free energy change (∆G), enthalpy change (∆H), and entropy change (T∆S) calculated per mole of Se for CdSe exchange with AgOTf in toluene. Temperature (K) 288.15

K (×106 M-1)

∆G (kJ/mol)

∆H (kJ/mol)

T∆S (kJ/mol)

n

0.7 ± 0.5

-31.9 ± 1.6

-47.6 ± 1.6

-15.7 ± 2.8

2.1 ± 0.1

298.15

0.6 ± 0.0

-32.8 ± 0.3

-49.9 ± 2.1

-17.1 ± 1.9

1.9 ± 0.1

308.15

0.5 ± 0.0

-33.6 ± 0.3

-49.9 ± 0.4

-16.3 ± 0.6

1.9 ± 0.1


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Comparison between the calculated and observed heat of reaction between cadmium selenide and silver ions. Using the method proposed by Alivisatos et. al.,5 the overall CE reaction (1) between CdSe and Ag+ can be divided into two electrochemical half reactions (2a-b) Ag+ (sol) + CdSe (crystal) ⇌ Cd2+ (sol) + Ag2Se (crystal)

(1)

CdSe ⇌ Cd2+ + 2e- + Se0

(2a)

2Ag+ + 2e- + Se0 ⇌ Ag2Se

(2b)

The two half reactions can be further simplified in terms of the free energies of formation (∆G°) and standard reduction potentials (E°) in a given solvent (acetonitrile in our case) for the respective species. CdSe ⇌ Cd 0 + Se0

−∆

Cd 0 ⇌ Cd2+ + 2e-

−( )

(4)

2Ag0 + Se0 ⇌ Ag2Se

(∆ )

(5)

2Ag+ + 2e- ⇌ 2Ag0

( )

(6)

(3)

By adding the resulting terms, the overall ∆Grxn for the process in the given solvent can be calculated as (7) ∆ rxn = (∆ ) − (∆ ) − 2F [( ) − ( ) ]

(7)

Using the standard free energy of formation of cadmium selenide,74 silver selenide,75 and the reduction potentials of Ag+ and Cd2+ in acetonitrile,18 we calculate the value of free energy change for CE to be ~ -21 kJ/mol.

To compare this value with experimental results we

conducted CE of bulk CdSe particles. Commercial bulk CdSe of particle size (crystal) + mHDA (sol. ) (e) Cd1,< Ag ; Se4 (HDA)7,> (crystal) + mHDA (sol. ) → Cd1,< Ag ; Se4 (HDA)7 (crystal) (f) Cd;* (sol. ) + 2OTf , (sol. ) ↔ Cd(OTf); (sol. ) (g) Cd1 Se4 (HDA)7 (crystal) + 2AgOTf (sol. ) ↔ Cd1,< Ag ; Se4 (HDA)7 (crystal) + Cd(OTf); (sol. )


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CONCLUSION ITC is shown to be a robust method, capable of directly measuring thermodynamics of CE in nanocrystals. We measured the thermodynamic parameters of CE to examine the impact of nanocrystal size, capping ligands, and temperature on the apparent exchange thermodynamics. While we have focused mainly on CdSe exchange with Ag+, this protocol can be extended to other nanocrystal CE systems. A systematic study of the effect of size, capping ligands and temperature as described here for different nanocrystal systems spanning over the periodic table could expand our understanding of the subtle effect of these variables on exchange thermodynamics. Additionally, ITC could also be used to study effects of other variables such as solvents and/or presence of anions accompanying the incoming exchanging cations. We believe from the work described within, ITC has the potential to become a truly powerful technique, in combination with other structural characterization like X-ray diffraction, liquid state transmission electron microscopy, x-ray absorption spectroscopy and X-ray photoelectron spectroscopy can pave the way to understanding subtle roles of different parameters in controlling the overall mechanism of cation exchange reactions.


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ASSOCIATED CONTENT Supporting Information. ITC theory, UV-Vis absorption spectra, TEM micrographs, particle size distribution, 31P NMR spectra, SEM and XRD of bulk CdSe, Rietveld refinement of bulk CdSe exchange, elemental analysis of CdSe nanoparticles, and additional ITC thermograms and thermodynamic parameters. AUTHOR INFORMATION Corresponding Author * Email: [email protected] Note The authors declare no competing financial interest. ACKNOWLEDGMENTS S. J. and R. M. R. acknowledge funding from the Department of Energy, Office of Basic Energy Sciences, Materials Science Division, grant number DE-FG02-07ER46414. We acknowledge Dr. Carlos Pacheco of the Pennsylvania State University, Department of Chemistry NMR facility for assistance with the

31

P NMR experiments.

Anish Dasgupta is acknowledged for his

assistance with the Rietveld refinement of the XRD data for the bulk CdSe samples. XRD and TEM experiments were performed at the Materials Characterization Lab in Penn State Materials Research Institute. SEM imaging was performed at the Penn State Microscopy and Cytometry and facility.


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ΔH = -ve

Table of Contents Graphic


Thermochemical Measurements of Cation Exchange in CdSe

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