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The Dynamics of Nanoparticle Growth and Phase Change During Synthesis of #-NaYF

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Paul B. May, John D Suter, Paul Stanley May, and Mary T. Berry J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b01365 • Publication Date (Web): 15 Apr 2016 Downloaded from http://pubs.acs.org on April 19, 2016

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The Journal of Physical Chemistry

The Dynamics of Nanoparticle Growth and Phase Change During Synthesis of β-NaYF4

Paul B. May, John D. Suter II, P. Stanley May, and Mary T. Berry* Department of Chemistry, University of South Dakota Email: [email protected]

Abstract: We implement a model for nanocrystal growth and crystallographic phase transition during the synthesis of β-NaYF4. In this model, the size of the α-phase nanoparticles, formed during the heating of the precursor materials, grows slightly in mean diameter and broadens in distribution width until some particles reach a size at which the β phase is thermodynamically favored. Individual particles crossing this threshold convert to the β phase, and then, being less soluble than the α phase, grow at the expense of dissolving α-phase particles. Implementing a straightforward kinetic formalism for individual particle growth and a variable phase definition depending on particle size, the model reproduces in a quantitative fashion, the experimentally observed growth dynamics of β- NaYF4:Yb,Er. This work supports a hypothesis that the β-particle seeds arise from a phase transition in individual α-phase particles. The model also suggests that the great variability observed in the duration of the stage during which the α particle ripen, before β particles begin to appear, may be attributed to rather small differences in the size distribution of the α particles formed during the heating of precursor material.

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Introduction: Hexagonal-phase β-NaYF4 doped with lanthanides is one of the most commonly employed upconversion (UC) phosphors. With appropriate choice of dopants, the materials show exceptional quantum efficiency,1,2 excellent red, green, or blue color purity,3,4 and, in the form of nanoparticles, good dispersibility in a wide range of polar and non-polar matrices.5,6 Many applications of UC nanoparticles require narrow particle-size distributions. Among the various co-precipitation methods of synthesis, the so-called “heat up” method reliably produces narrow size distributions of the β-phase material and has rapidly increased in popularity since its introduction by Zhang et al.7,8 Here, all precursors are combined in a high-boiling-point solvent mixture prior to heat-up, as opposed to injecting the lanthanide precursors into an already hot solution containing the fluoride reactant. After heat-up, the mixture is maintained at a temperature close to 300 oC for approximately one hour, and then allowed to cool. An initial amorphous precipitate is formed from the combination of precursors in the cold solvent mixture. During the heat-up, small cubic α-phase particles appear, followed by the later appearance of larger β-phase particles. For a given set of synthesis conditions, the resulting β-phase particles exhibit very reproducible sizes with remarkably narrow size distributions. There have been several revealing studies that shed light on the mechanism for this reaction including early work by Lifshitz, Slyozov, and Wagner, (LSW)9,10 and by Talapin et al.11 Two later studies by Voss et al. demonstrated rather convincingly that the “size focusing” of the β-phase product particles occurs due to their growth in the presence of the α-phase particles formed in the initial stages of synthesis.12,13 The higher solubility of the α-phase relative to the β-phase provides a condition of super-saturation for β-phase particle growth, which leads to the size focusing that is 2 ACS Paragon Plus Environment

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expected in the diffusion-limited growth regime. Van Veggel, et al. have exploited this effect to produce size-focused, β-phase, core-shell nanocrystals by ripening β-phase cores in the presence of sacrificial nanoparticles of α-phase shell material.14 In contrast, β-phase particles growing in isolation, in the absence of sacrificial α-phase particles, exhibit the size broadening expected for normal Ostwald ripening. Suter et al., by monitoring the NIR-to-visible UC emission signal from the ‘heat-up’ synthesis of NaYF4:Yb,Er upconversion particles in real-time, obtained detailed kinetic information regarding the progression of the reaction through its various stages.15 A significant finding of this study was that there is a large synthesis-to-synthesis variation in total reaction time, and that the variation in reaction time is due almost entirely to the variation in the delay between the initial formation of the small α-phase nanoparticles and the start of the phase transition to form the larger β-phase product particles. Interestingly, the final size distribution of the β-phase nanoparticles was quite reproducible, and showed no correlation with reaction time. Referring to Figures 1 and 2 and data from reference 15, weak UC luminescence is evident even prior to heat-up, but no crystalline material can be isolated. During heat-up (Stage I), small αphase particles begin to form and, by the time the temperature reaches 300oC (end of Stage I) , all detectable solid in the mixture is in the form of small (~4-5 nm) α particles. Stage II is characterized by a period of relative stasis of widely variable duration (63 ± 22 min), during which the spectroscopic signature remains nearly constant, corresponding to only minor changes in the initial α-particle population (in the form of slight particle growth and modest increase in the width of the size-distribution). Subsequently, a rapid α→β phase transition (Stage III) is signaled by a steep increase in UC intensity and corresponding increase in the green-to-red intensity ratio. The duration of this phase-change stage was fairly reproducible from synthesis to synthesis (10 ± 2 3 ACS Paragon Plus Environment


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min). The UC intensity plateaus after the phase change is complete (Stage IV) and the reaction is terminated shortly thereafter to avoid further Ostwald ripening of the phase-pure β product.

Figure 1. (Left) Schematic illustration of the spectroscopic signature of green and red upconversion corresponding to the four stages identified in the synthesis of NaYF4 nanoparticles. (Right) TEM of a typical product distribution from synthesis as described in references 15 and 16.

Based on the work of Voss et al. discussed above, it is clear that the tightly focused size distribution for the final β-phase product produced by the heat-up method is a result of the β-phase particles growing in the presence of sacrificial α-phase particles in Stage III. The more soluble α-phase particles maintain a condition of super-saturation in the dispersion, so that the β-phase particles grow in the diffusion limit, illustrated schematically in Figure 3. What is not clear is the reason for the high variability in the duration of the ripening of α-phase particles (Stage II) leading up to the phase change (Stage III). Moreover, the origin of the βparticle seeds that appear at the beginning of Stage III is not established. Also interesting, yet unexplained, is the observation that there appears to be no correlation between size distribution of


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the final product and the duration of the α-particle ripening (Stage II). In addition we make note of the observation that although the duration of the β growth period (Period III) was very consistent for a given set of reaction conditions, it was quite sensitive to the solvent make-up, specifically, that is, to the relative amounts of oleic acid and octadecene.16

Figure 2. Particle size distribution during synthesis of β-NaYF4:Er,Yb. Aliquots were withdrawn and analyzed by TEM during real-time monitoring of upconversion luminescence (inset). The relative number of α particles as compared to the number of β particles is not represented, 100 particles from any phase present were used to calculate the distribution. The t = 0 on the time scale is set at the beginning of heating for Stage I. (data from reference 16)

In this study, we present a kinetic model for the reaction mechanism for the synthesis of β-NaYF4 nanoparticles via the heat-up method. The model quantitatively accounts for the evolution of the



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reaction mixture, starting after the initial formation of the intermediate α-phase particles through to completion of the α→β phase transformation that results in the final β-phase products. The model assumes that β-phase seed particles are formed through the phase transformation of individual α-phase particles that reach a critical size, where a phase transition from α to β is thermodynamically favored. The variation in observed reaction times is well explained in terms of slight differences in size distributions of the α-phase particles as they are initially formed during the heat up to reaction temperature. The model simulations are also consistent with the observation that consistent final β-particle sizes are obtained, independent of the total reaction time.

Figure 3. Schematic of representation of β-particle growth during Stage III of the reaction. During Stage III, the β-particles grow at the expense of the more soluble α-phase by consuming the dissolved components, referred to as “dissolved monomer” for historical reasons.


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Methods: Mathematical Model The critical size for thermodynamically-favored α→β phase transition, , is determined by the differences in the bulk lattice energies (lower for β-phase) and the surface energies (lower for αphase) for the two phases.

∆

= = ∆

(1)

Where, Vm represents the molar volume of the crystal, ∆ is the change in surface energy, and ∆

is the change in molar lattice energy, using the approximation that the molar volume is similar for the two phases. (See SI for derivation if equation 1) The surface energies may be quite sensitive to surfactant coverage and therefore the critical size for phase conversion may also depend on surfactant coverage. There is no direct experimental evidence to indicate whether the growing α particles do indeed become the seeds for the final β-phase crystals or whether, alternatively, the β seeds form de novo from solution. However the assumption in our model is consistent with the relative size-dependent thermodynamic stability of the two phases. A similar size-dependent phase transformation has been previously observed for nanoparticulate zirconia.17 The purpose of this study then is to test the model as proposed here for agreement with the observations made during real-time monitoring of the growth dynamics of β-NaYF4 and, in future, to use the model to create testable predictions. Here we develop the model for nanoparticle growth in any single phase. The nanoparticles are approximated as spherical so that their size is defined by a single variable, r, and their mass by m



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= 4πr3ρ/3, where ρ is the density of the material.

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This treatment parallels that of Talapin and

details may be found in supporting information.10 For a given nanoparticle,

= !"# $%&'$( ' − !# $%&'

(2)

Where m is the mass of the nanoparticle, SA is the surface area, and CS is the concentration of precursor material in solution. The kinetic rate constants, !"# and !# control nanoparticle growth and dissolution, respectively. The “np” designation is given to the rate constants because they are expected to be size dependent and differ from the bulk values. A further consideration arises in that, under diffusion-limited growth, the concentration of precursor in solution at the surface of the nanoparticles $( ' may be different that the concentration in the bulk solution ((* '. Taking these factors into consideration, we have:

=

6 7

+, $-.'/0 +1 $-.'234 5 8 234 5

6 89 $+, /;' 7

,

(3)

where k1 and k2 are rate constants for the bulk material, D is an effective diffusion coefficient for the precursor material, and < =

=

. The quantity, L, is often referred to as a “capillary length”

and relates to a size below which the nanoparticle solubility is greatly accelerated. It is different than the transition radius, rT , which defines a size at which the α and β phases are in thermodynamic equilibrium. In the denominator of Equation (3), the term, A

B ǂ

exp 5 8 = exp 5 = 8


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describes the effect of any increase in the free energy of the activated complex for solution/dissolution in the nanomaterials as compared to the bulk. These quantities are illustrated in Figure 4.

µŧ

µŧ(np) Δŧµ1

Δŧµ2

Figure 4. Arrhenius diagrams for the growth and dissolution of bulk solid (left) and nanoparticles (right). The KL G4 activation energy for growth in the nanoparticles, Δŧ μ" , is shown with an increase of I ǂ = J M relative to the N

G4

bulk solid, resulting in a net decrease in the activation energy for dissolution, Δŧ μ , KL KL $1 − J' M = b M . In this work we have employed a = b = ½. N

by

N

Equation (3) can describe the growth of either the α or β phase particles. Starting with an initial Gaussian distribution of approximately 6000 α particles, the particles grow according to equation (3) until those in the leading edge of the distribution reach the transition radius, given in Equation (1). As particles cross this transition radius, the particles’ identity is reassigned as β and those β-particles continue to grow as described by equation (3), but now grow with the newly assigned rate constants, ki and capillary length, L, appropriate to their new β-phase identity. These β-particles, having a lower solubility that the α-particles, consume precursor material from solution, in response to which, the remaining α-particles begin to dissolve. A derivation of equation (3) is given in SI.



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Fitting Methods To compare the model growth dynamics to the experimental results from the real-time monitoring experiments, we have treated several of the characteristic physical constants for the materials as variable parameters and determined the values, through a simplex algorithm, that give the best fit to specific experimental observables. Tables 1 and 2 give a summary of the parameters and observables, respectively, used in the fit. The observables include average values for Stage duration and particle size distributions. The parameters include bulk rate constants, capillary lengths, diffusion coefficients, and transition radius, as defined for equations (1) and (3). The mean radius $μ0 = 〈 S 〉U ' and standard deviation (σ0) of the starting size distribution are also included among the parameters. The starting distribution is created by distributing 6000 particles, in appropriate proportion for a normal distribution, among 60 bins of equal width, in the range µ 0 ± 3σ0. The particles within each bin are then evenly distributed in size across the bin, such that no particles have exactly the same size. Because we don’t include particles that lie further than 3 standard deviations from the mean, the total number of initial particles in the simulation is 5951. An additional strategy for creating a skew-normal starting distribution is discussed toward the end of the next section. Results and Discussion: Using a fourth-order Runge-Kutta method18 to propagate the growth of an initial α-particle distribution, and a simplex19 routine to choose the parameters which best reproduced the observables, we obtained the parameter values given under “Fit A” in Table 1. The values in the column under “Fit B” are derived from a skewed starting distribution and will be discussed later. Initial fits, under “A” included the observables for Stage II and III duration and for final β-particle 10 ACS Paragon Plus Environment

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size distribution as averages from the six syntheses reported in reference 15. Also included was the early Stage II, average size for the α-particle distribution, 〈 S 〉 . This latter data point was from a single measurement reported in Reference 15 but is consistent with other samples we have previously measured. The relevant observables are given in Table 2.

Table 1: Physical constants serving as free parameters in a simplex fit of simulation results to observables given in Table 2. Parameters !"S !S V

!"

V

!

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