Insight into Fast Nucleation and Growth of Zeolitic Imidazolate

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Insight into Fast Nucleation and Growth of Zeolitic Imidazolate Framework-71 by In Situ Static Light Scattering at Variable Temperature and Kinetic Modeling Sanjib Saha, Michael Wiebcke, and Klaus Huber Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.8b00626 • Publication Date (Web): 12 Jun 2018 Downloaded from http://pubs.acs.org on June 18, 2018

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Crystal Growth & Design

COVER PAGE

Insight into Fast Nucleation and Growth of Zeolitic Imidazolate Framework-71 by In Situ Static Light Scattering at Variable Temperature and Kinetic Modeling Sanjib Saha,† Michael Wiebcke,‡ Klaus Huber*,† †

Department Chemie, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany. Institut für Anorganische Chemie, Leibniz Universität Hannover, Callinstr. 9, 30167 Hannover, Germany.

‡

ABSTRACT. Zeolitic imidazolate frameworks (ZIFs) represent an important subclass of porous metal organic frameworks (MOFs). The present work extends a previous study on ZIF-71 nanocrystal formation at room temperature (Cryst. Growth Des. 2016, 16, 2002-2010), which proposed a four-step formation process. It introduces a kinetic nucleation and growth model, which satisfactorily reproduces in situ time-resolved static light scattering data measured at room temperature in the previous work and at variable temperatures in the present work. Successful fitting can only be achieved with a precursor reaction being put before particle nucleation. The kinetic analysis provides rate constants for the precursor reaction, for particle nucleation, and for particle growth via monomer addition, and the equilibrium concentration of non-consumed matter at the end of reaction. The rate constants of the precursor reaction and the nucleation process increase with temperature, which is counterintuitive if compared to classical nucleation theory as it suggests a decrease of the nucleation rate with temperature. In fact, ZIF-71 formation deviates from classical nucleation in that a precursor reaction to produce active “monomers” precedes the formation of amorphous particles that subsequently transform into the crystalline ZIF phase.

Klaus Huber Universität Paderborn, Dept. Chem. Warburger Str. 100, 33098 Paderborn, Germany Phone: 0049 5251 60 2125 Fax: 0049 5251 60 4208 e-mail: [email protected] web: http://chemie.uni-paderborn.de/arbeitskreise/physikalische-chemie/huber/

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Insight into Fast Nucleation and Growth of Zeolitic Imidazolate Framework-71 by In Situ Static Light Scattering at Variable Temperature and Kinetic Modeling

Sanjib Saha,† Michael Wiebcke,‡ Klaus Huber*,† †

Department Chemie, Universität Paderborn, Warburger Str. 100, 33098 Paderborn, Germany.

‡

Institut für Anorganische Chemie, Leibniz Universität Hannover, Callinstr. 9, 30167 Hannover,

Germany.


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ABSTRACT. Zeolitic imidazolate frameworks (ZIFs) represent an important subclass of porous metal organic frameworks (MOFs). The present work extends a previous study on ZIF-71 nanocrystal formation at room temperature (Cryst. Growth & Design 2016, 16, 2002-2010), which proposed a four-step formation process. It introduces for the first time a kinetic nucleation and growth model, which satisfactorily reproduces in situ time-resolved static light scattering data measured at room temperature in the previous work and at variable temperatures in the present work. Successful fitting can only be achieved with a precursor reaction being put before particle nucleation. The kinetic analysis provides rate constants for the precursor reaction, for particle nucleation, and for particle growth via monomer addition, and the equilibrium concentration of non-consumed matter at the end of reaction. The rate constants of the precursor reaction and the nucleation process increase with temperature, which is counterintuitive if compared to classical nucleation theory as it suggests a decrease of the nucleation rate with temperature. In fact, ZIF-71 formation deviates from classical nucleation in that a precursor reaction to produce active “monomers” precedes the formation of amorphous particles that subsequently transform into the crystalline ZIF phase.


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INTRODUCTION Zeolitic imidazolate frameworks (ZIFs) are a distinctive subclass of metal-organic framework (MOF) materials.1 They are composed of divalent metal cations and linking imidazolate anions.24

As ZIFs combine porous zeolite-related framework structures with functional variability at the

imidazolate moiety, they are very attractive materials for many potential applications, for instance, in separation, catalysis, and drug delivery.5 A number of in situ studies6,7 on ZIF formation from solution have so far been performed using scattering/diffraction,8-13 total scattering/pair distribution function,14 electron microcopy,15 and mass spectrometry16 methods, yet the crystallization mechanisms remain still poorly understood. Improving that understanding could promote considerably the synthesis of new ZIF phases and the control of morphology.8,12,17,18 In a preceding work,19 based on in situ studies at room temperature using time-resolved static and dynamic light scattering (TR-SLS/DLS) and time-resolved small-angle and wide-angle X-ray scattering (TR-SAXS/WAXS) experiments, we have proposed a mechanism for the fast formation of crystalline ZIF-71 in 1-propanol (1-PrOH), which proceeds along four steps and which henceforth will be denoted as four-step-process (FSP). In a first step, small amorphous clusters are formed via a coagulation mechanism. The clusters, which do not get larger than a few nm, are consumed in the following step, where a population of amorphous nanoparticles (aNP) grows via a monomer-addition process. The “monomers” may correspond to the small amorphous clusters from the first step and/or to smaller building units. In a third step, partly overlaying the second step, the growing aNP undergo transformation to crystalline nanoparticles (cNP) with RHO topology (ZIF-71). The cNP aggregate randomly in a fourth step. This preceding work complemented earlier in situ studies8,9 on the formation of cNP with SOD


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topology (ZIF-8) suggesting that the FSP is more generally valid for ZIF cNP formation from alcoholic solutions. Further insight into the details of the FSP can be expected from an interpretation of kinetic data by mathematical modeling, and an investigation of the impact of temperature. In experimental in situ ZIF formation studies, kinetic analyses have so far been exclusively based on data derived from X-ray diffraction (XRD) and WAXS experiments applying Avrami-Erofe´ev20 and/or Gualtieri21 models and considering only the formation of the crystalline ZIF phase.10,11,13,19 Whereas the models20,21 are in fact designed to describe phase transformation in bulk, they are less adequate to model the formation of a new phase from diluted solution with supersaturation as the driving force. Therefore, we here present a detailed in situ TR-SLS investigation of the ZIF-71 cNP formation at variable temperature, which focuses on the growth of both aNP and cNP (steps 2 and 3 of the FSP), but in addition points indirectly (via mathematical modeling) to the importance of a preceding precursor reaction (e.g., formation of clusters, step 1of the FSP). Although, light scattering is not able to discriminate between the nucleation of an amorphous phase and a crystalline phase, it is able to characterize nanoparticles once they differ in their scattering contrast from the surrounding medium. Apart from that, a time resolved analysis of a full angular dependency becomes possible due to the use of a multi-angle light scattering set-up. The evolution of the weight-averaged particle mass, which is based on the second moment of the mass distribution22 and which is directly accessible with a high resolution in time by means of TR-SLS, can serve as an excellent set of data highly suitable for kinetic analysis. Accordingly, a simple nucleation and growth (NG) model is applied, which was developed in a recent study in order to describe the formation of amorphous silica particles from supersaturated solutions. Application of this model became possible because we succeeded to derive a numerical recipe to


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calculate the evolution of the first three moments of the corresponding mass distribution over time.23 The results of the present work are presented as follows. We first introduce and install a kinetic NG model with its application to experimental TR-SLS data recorded in our preceding work19 at T = 25 °C at variable ratios of Zn(NO3)2·6H2O/dichloroimidazole (Hdcim)/1-PrOH. Subsequently, we analyze in detail the impact of temperature (10°C < T < 32°C) on the formation of particles using new TR-SLS data generated at four different compositions. Finally, we interpret this impact of temperature at a selected composition with the established kinetic NG model.

EXPERIMENTAL SECTION Materials and General Synthetic Method. Zinc nitrate (Zn(NO3)2.6H2O; Sigma-Aldrich, > 99%), 4,5-dichloroimidazole (Hdcim; Sigma-Aldrich, > 98%), and 1-propanol (1-PrOH; SigmaAldrich, > 99.5%) served as Zn2+ source , linker, and solvent, respectively. All chemicals were used as received. The ZIF-71 cNP synthesis studied here closely followed the protocol reported elsewhere.24 Generally, a solution of the zinc salt in 1-PrOH was combined with a solution of the linker in 1PrOH. The formation of ZIF-71 proceeds according to the following overall reaction.

ZnNO + 2 C H Cl N → ZnC HCl N + 2HNO

(1)


6

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Time-Resolved Static Light Scattering (TR-SLS). Solutions of Zn(NO3)2·6H2O and Hdcim were prepared by dissolving the solid chemicals in appropriate amounts of 1-PrOH and were allowed to reach the anticipated reaction temperature, corresponding to either 10, 17, 25, or 32 °C. The solutions had a concentration twice as large as required for the respective experiment. At first, 3 mL of the Zn(NO3)2·6H2O solution were filtered into a pre-cleaned LS cuvette using a 0.2 µm syringe filter. The cuvette was placed inside the LS goniometer and held at constant temperature for around 30 minutes. Successively, 3 mL of the thermally equilibrated linker solution in 1-PrOH were filtered into the same cuvette making the overall compositions Zn2+/Hdcim/1-PrOH = 1 : X : 4000 with X = 1, 2, and 3, and Zn2+/Hdcim/1-PrOH = 1 : 2 : 3000. All filtrations were performed with 0.2 µm PET filters from Macherey-Nagel (Germany). Addition of the linker solution triggered the clock for recording the time, t, of the particle formation process. The time period between mixing of the component solutions (t=0) and the onset of data collection varied between 20-30 s. The LS cuvette was maintained at the required temperature throughout the duration of data collection. A home-built multi-angle goniometer was used for all TR-SLS measurements. A He-Ne-Laser from Melles Griot, operating at a wavelength of λ = 632.8 nm, provided the primary beam. The 2 times 19 detectors, pairwise symmetrically arranged around the primary beam, detected simultaneously the scattered light over an angular range of 26° < θ < 143°. Details of the setup are given elsewhere.25 The time required to record a single scattering curve was 2 ms. The time resolution of a given kinetic run depended on exactly how many of such single scattering curves had to be averaged in order to get an acceptable statistics. The time resolution varied between 3 s – 5 s for most of the experiments, and was 30 s in case of the composition Zn2+/Hdcim/1-PrOH = 1 : 1 : 4000 at T = 10 °C. The scattering signal was transformed into absolute scattering cross


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sections per volume (Rayleigh ratio R(q)) by means of the Rayleigh ratio of toluene (Rt), which was used as standard. The temperature dependence of the Rayleigh ratio was taken into account by using the following values for Rt of toluene: 1.3138.10-3 m-1 (10°C), 1.33866.10-3 m-1 (17°C), 1.3603.10-3 m-1(25°C) and1.39185.10-3 m-1(32°C). Lag times, τ, were determined by comparing the evolution of the count rate with time recorded at the observation angle θ = 26° with the corresponding count rate observed for the pure solvent. Once first NP were formed, the signal surpassed that of the solvent and defined the lag time τ. Evaluation of Light Scattering Data. The TR-SLS data were evaluated with Guinier's approximation26 ln

= ln +

(2)

valid in the low-q regime, where q is the magnitude of the scattering vector determined by the scattering angle θ,

=

4 × & sin % ' !" 2

(3)

c is the concentration of scattering species in g⋅mL–1 and Mw and Rg2 are, respectively, the weight-average molar mass and z-average of the squared radius of gyration. R(q) is the excess absolute scattering intensity at q. In eq 3, λ0=632.8 nm is the vacuum wavelength of the primary laser beam and n = 1.385 is the refractive index of the solvent. The contrast factor, K, introduced on the left hand side of eq 2, is given by


8

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4 )= ×% *+ × !,"

. ' - × ./

(4)

It includes the Avogadro number NA, the refractive index of the toluene bath, nt = 1.496, and the refractive index increment, dn/dc, of ZIF-71 in 1-PrOH. Lack of a proper dn/dc value for ZIF-71 forced us to use dn/dc = 0.1 mL/g as a default value. Temperature dependent variations of n and nt kept within 0.5% in the regime of 10 °C < T < 32 °C and were neglected. The scattering species in the present experiments comprise all entities with a composition of Zn(dcim)2. For all compositions of Zn2+/Hdcim/1-PrOH = 1 : X : 4000 with X > 2, the concentration was calculated assuming a complete stoichiometric reaction according to eq 1 with all Zn2+ ions initially present in the respective solutions. For the solution with a composition of Zn2+/Hdcim/1-PrOH = 1 : 1 : 4000, where Hdcim was present in sub-stoichiometric amount, c was calculated by taking into account that only half of the initial Zn2+ ions were available for forming the particles. Values for transmissions turned out to be close to one, and the derived MW values did therefore not require any corrections for transmission losses.19

THE NUCLEATION AND GROWTH (NG) MODEL A NG model is used in the present work to interpret the evolution of ZIF-71 NP with time. The NG model is related to a model introduced by Tsapatsis and coworkers to describe crystal growth by aggregation of metastable precursor NP.27 It comprises three reactions 12

0 34 5 1>

5 34 ? 1A

?@ + 5 34 ?@B

Precursor reaction Nucleation

(5)

Growth via monomer addition


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where in the first reaction precursors A transform into reactive ”monomers” B. In the second reaction, monomers nucleate to NP of degree of polymerization one (C1). In subsequent reactions establishing reaction 3, NP denoted Ci add further monomers, thereby increasing their degree of polymerization by one (i i+1), respectively. The reaction scheme of eq 5 is translated into five coupled differential equations (see Section S1 of the Supporting Information for further details of the NG model). IJ+K

IIJRK IIV IIW IIX I-

= −MN OJ0K − J0KP Q

= MN OJ0K − J0KP Q − MS J5K − MT J5KU"

= MS J5K

(6)

= MS J5K + MT J5KU"

= MS J5K + MT J5KU" + 2MT U

where the appearance of a solubility limit was taken into account by an equilibrium concentration of precursor [A]eq. Those equations describe the evolution of the precursor concentration [A], the monomer concentration [B], the concentrations of NP [Ci], and the first three moments of the particle mass distribution M0 , M1 , and M2 U1 = ∑@[ Z 1 J?@ K , M = 0 , 1 , 2 . . .

(7)

with time. Numerical solution of the coupled differential equations leads to the weight-averaged molar mass of the whole ensemble of reactants including precursor, monomers and polymers/particles of any degree of polymerization i U_ ` =

aV J+KBJRKBX J+KV

(8)


10

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where m0 is the molar mass of the monomer (and precursor) and [A]0 is the initial concentration of precursor. It is Mw(t), which can be compared directly with a TR-SLS experiment. However, the model certainly oversimplifies the nature of any real chemical species and of the reaction specifying the transformation of precursors into monomers or to describe the formation and growth of small clusters, proposed as the first step of the FSP leading to cNP of ZIF-71.19 The model is also not capable of adequately considering the variation of the size of critical nuclei as monomers are consumed. The latter feature is an important characteristic of the classical nucleation theory (CNT),28-30 which predicts an increase of the critical size at which species in solution turn into a nucleus as the supersaturation decreases with the progress of reaction. Finally, the rate constant of growth in the present model is independent of the size of the NP. This may not fully account for real processes because the rate constant may depend on the diffusion coefficient and/or the size of the (reactive) surface area of the growing NP. Therefore, care has to be taken in adequately discussing the physical meaning of any trend observed with the parameters resulting from fits of the NG model to the experimentally determined weight averaged mass values. Those fit parameters comprise the three rate constants kp, kn, and kg as defined in eq 5, and the equilibrium precursor concentration [A]eq reached after completion of reaction. Details of the fitting procedure are given in Section S1 and S2 of the Supporting Information. Fits to Experimental Data Based on the NG Model. The experimental data were analyzed with the kinetic NG model, which is described above, and in full detail in Section S1 of the Supporting Information. For solving the set of differential equations eq 6 (eq 8 of the Supporting Information), an inbuilt function in MATLAB programming language (version MATLAB 2014a) denoted ‘ode45’ was used. For the fitting process, a minimization algorithm in


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MATLAB named ‘fminsearch’ was used. ‘fminsearch’ uses a simplex algorithm to find the minimum of a function, which in the present case was n

m bcde = ∑d[oOfg,hijh d − fg,klm dQ

p

(9)

where Mw,calc.(i) is the molar mass calculated according to eq 8 (corresponding to eq 7 of the Supporting Information), and Mw,exp.(i) is the experimental molar mass measured by TR-SLS and established by eq 2. The quality of the fits is represented as χ2 calculated by normalization of fmin with the number of data points Np available for the respective fits.

qp =

nm fg,hijh drfg,klm d fg,klm d

∑dso

p

nm

(10)

As the MATLAB-routine did not reveal uncertainties of the fitted parameters we established a realistic guess of the uncertainties by varying one parameter at a time, starting from the respective best fit and recording the resulting increase of χ in eq 10. Admitting an increase by a 100 %, [A]eq varied between 1 % and 2 %, depending on the specific experiment and the rate constants revealed variations in the range of 5 % - 20 %.

RESULTS AND DISCUSSION Application of the NG Model to Room Temperature Data. In a preceding work,19 TR-SLS data have been recorded on the formation of cNP of ZIF-71 in solutions of 1-PrOH with compositions of Zn2+/Hdcim/1-PrOH = 1:X:4000 (1 ≤ X ≤ 8) at T = 25 °C. The data are


12

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insensitive to any crystallization event, i.e., both aNP (formed first in step 2 of the FSP) and cNP (formed later in step 3 of the FSP) cannot be discriminated by SLS and are therefore termed NP hereafter.19 Data from all investigated compositions revealed a power law relation between the radius of gyration and the mass for the growing NP of T ~U_u

(11)

with a = 1/6. This exponent, which is exactly half of 1/3, indicates a growth of compact NP of spherical or cubic shape obeying a monomer-addition mechanism.31,32 Another characteristic feature of the experiments was the decrease in final size of the NP as the Hdcim linker concentration increased. Such a trend is compatible with an amplification of nucleation, which leads to an increasing number of NP forced to share a distinct amount of matter fixed by the weighed in amount of Zn2+ cations. Taken together, those results suggest to be interpreted with a NG model, which incorporates a monomer-addition step for particle growth and which has to be simple enough to give access to weight averaged particle mass values measured with TR-SLS. Such a NG model could recently be applied with success to the formation of silica aNP,23 where the growing aNP obey the same power law as observed for the growth of ZIF-71 NP. It is this model which will now be applied to the data generated in a preceding study19 at variable compositions of Zn2+/Hdcim/1-PrOH = 1 : X : 4000 at T = 25 °C. As is demonstrated in Figure 1 by means of a selection of three compositions, the NG model satisfactorily reproduces the evolution of NP mass with time in the period within which growth proceeded according to a monomer-addition mechanism. Fortunately, this time period can unambiguously be identified by the correlation of Rg versus Mw obeying a power law (see eq 11)


13


with an exponent of 1/6. This power law behavior is limited by a further growth, where NP aggregate and where turbidity starts to interfere with a proper analysis of light scattering data. The onset of this last step of the FSP is clearly discernible by an upturn of the trend of Rg versus Mw. As is demonstrated by the Figures 3A and 3B in Section S3 of the Supporting Information, which presents a full account of all investigated compositions, the deviation from the power law behavior with a = 1/6 first appears at a ratio of Zn2+/Hdcim/1-PrOH = 1 : 5 : 4000 and becomes increasingly significant with increasing linker concentration X. Importantly, our kinetic modeling clearly demonstrates that ZIF-71 NP do not directly nucleate from solvated Zn2+ cations and Hdcim linker molecules, as kinetic models that did not include any precursor reaction could not reproduce the experimental data adequately (Figure S3C of the Supporting Information), in full agreement with our previous SAXS studies.19 Depending on the specific solution composition, the active monomers might be small clusters as observed by SAXS (for

-1

two solution compositions)19 and/or polynuclear Zn-Hdcim/dcim complexes (oligomers).16

15

10

5

Mw / 10 kg mol

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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5

0 0

2

4

6

8 2

10

12

14

16

t / 10 s

Figure 1. Evolution of particle mass (MW) with time (t) recorded at T = 25 °C for the compositions Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000 (), 1 : 4 : 4000 (), and 1 : 6 : 4000 (∆). The green curves indicate fits to the experimental data based on the NG model. Parameters of the fits are summarized in Table 1 and Figures 3 and 4. Experimental data were taken from Ref 19.


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It is worth having a closer look on how the concentration of monomers [B] and the zeroth moment M0 corresponding to the number of particles is going to vary with time, since both quantities are revealed automatically in addition to Mw during a fitting process. As expected, monomers are formed and consumed, which generates a concentration maximum in the case of each reaction (see Figure 2 for Zn2+/Hdcim/1-PrOH = 1:4:4000 as an example). That maximum is shifted to longer times as the linker concentration is decreased, in accordance with a decreasing transformation of matter into NP (Figure S4A of the Supporting Information). Further insight is provided by the evolution of the zeroth moment, M0. As the linker concentration rises, M0 is increasing, which indicates that the larger the linker concentration gets, the more NP are nucleated (Figure S4B of the Supporting Information). Hence, the kinetic model properly attributes the decreasing NP size observed with increasing linker concentration19 to an enhanced nucleation rate.

3.50

5

3.25 4

2.75

3

2.50 0.08

2

0.06 0.04

-11

M

3.00

M0 / 10

[B],[A] / mM

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


1

0.02 0.00

0

2

4

2

6

8

0

t / 10 s Figure 2. Precursor concentration [A], monomer concentration [B] (left ordinate) and zeroth moment M0 (right ordinate) as a function of time, obtained by fitting experimental Mw with the kinetic model for the solution composition Zn2+/Hdcim/1-PrOH = 1:4:4000 shown in Figure S3A. Calculations are only extended over the time period where data in Figure S3B are following the power law of Rg ~ Mw1/6.


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An overview on the entire set of the resulting fit parameters for the experiments with Zn2+/Hdcim/1-PrOH = 1 : X : 4000 is given in Figures 3 and 4 and in Table 1. The equilibrium concentration of precursors [A]eq approached at the end of the process decreases as the linker concentration increases (Figure 3), which can be nicely reconciled with a shift in equilibrium toward NP formation. With the exception of the fit to data from the experiment with a substoichiometric amount of Hdcim (X = 1), the precursor rate constant kp as well as the rate constant of the monomer addition process kg are independent of the applied concentration of the linker (Figures 4 and in Table 1). This result is particularly valuable for a proper validation of the NG model in reproducing the formation of ZIF-71 NP for the following reason. Constancy of kp and kg justifies the simplifications adopted for the precursor and growth reactions in Section “Nucleation and Growth Model” and clearly demonstrates that application of a precursor reaction and a growth via monomer addition capture essential physical features of the formation process. In case of a unique rate constant capable of reproducing properly a time dependent growth of NP, that growth rate constant, kg, represents a value averaged over all size values of NP passed during the growth. With increasing X, the initial supersaturation of the respective reaction solution increases. The NG model, in spite of its oversimplified physics, can respond to this increase in supersaturation with an increase in the nucleation rate constant kn, in accordance with our expectation.


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3.5 3.0

Aeq / mM

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


2.5 2.0 1.5 1.0 0.5 0.0

0

1

2

3

4

5

6

7

8

9

X Figure 3. Equilibrium concentration of precursors ([A]eq) at variable content of linker (X) for the compositions Zn2+/Hdcim/1-PrOH = 1 : X : 4000 as obtained by fitting the NG model to experimental data determined at 25 °C in Ref. 19. The blue dashed line indicates the initial concentration of the Zn-cations.

Table 1. Fit parameters received from fitting the NG model to experimental data19 recorded at T = 25°C with TR-SLS on solutions with compositions of Zn2+/Hdcim/1-PrOH = 1 : X : 4000 at variable linker content X. [A]eq

kp

kn

kg

χ2

M

10-3 s-1

10-7 s-1

109 M-1s-1

kg/mol

1

0.00323

3.92

8.7*10-5

34

2

0.00306

1.68

3.7*10-3

6.5

3

0.00283

2.12

1.07*10-2

2.8

4

0.0025

2.32

2.9*10-2

1.89

5

0.00223

1.98

4.8*10-2

2.1

6

0.00189

2.09

1.37*10-1

1.18

8

0.00132

1.96

1.15*10-1

3.4

X

1)

1)

58496 2782 293 619 597 296 124

χ2 characterizes the fit quality is defined by eq 10.


17


-1

5

-3

kp / 10 s

4 3 2 1 0

-7

kn / 10 s

-1

0.1 0.01

-1 -1

1E-3 1E-4 35 30 25 20 15 10 5 0

9

kg / 10 M s

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

Page 18 of 36

0

1

2

3

4

5

6

7

8

9

X Figure 4. Rate constants from fits with the NG model (eq 5) to experimental data determined at 25 °C at variable content of linker (X) with compositions Zn2+/Hdcim/1-PrOH = 1 : X : 4000. Experimental data were taken from Ref. 19. From top to bottom: rate constant of the precursor reaction (kp), rate constant of nucleation (kn), rate constant of growth (kg).

Having available a simple but useful kinetic model that is capable of revealing some of the essential physical aspects of the ZIF-71 cNP formation, we are now ready to analyze the impact of temperature on this formation process and to recover potential trends with the set of rate constants and the final equilibrium concentration [A]eq.

Impact of Temperature on the Formation of ZIF-71 Nanocrystals. In the present study, the growth of ZIF-71 NP was followed by TR-SLS at four different temperatures, T = 10, 17, 25 and


18

Page 19 of 36

32 °C, with four different compositions of Zn2+/Hdcim/1-PrOH = 1 : 1 : 4000, 1 : 2 : 4000, 1 : 3 : 4000, and 1 : 2 : 3000, respectively. As all four compositions show the same qualitative behavior upon variation of temperature, we shall restrict detailed discussion to the results of the analysis at the composition of Zn2+/Hdcim/1-PrOH = 1 : 2: 4000, and summarize the data on the other three

1.0

Mw / 10 kgmol

-1

compositions in Section S4 of the Supporting Information.

0.8

6

0.6 0.4 0.2 0.0

200

Rg / nm

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


150 100 50 0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

3

t / 10 s

Figure 5. Evolution of the particle mass (Mw) and radius of gyration (Rg) with time (t) determined at a composition of Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000 at four different temperatures: T = 10 °C (), T = 17 °C (), T = 25 °C () and T = 32 °C ().

Figure 5 outlines the evolution of the weight-averaged molecular weight Mw of the NP and their size values measured as the radius of gyration Rg with time. At all four temperatures, values for the final NP size reach a plateau close to Rg ~ 150 – 200 nm and the corresponding NP mass approaches values of 106 kg/mol. The only variation observed is an increasing lag time,


19


corresponding to the time period until the appearance of first NP, as the temperature was lowered. Plots of Rg versus Mw in Figure 6 reveal a power law according to eq 11, all having the same exponent of 1/6, in full agreement with our preceding work carried out at T = 25 °C.19 This confirms that independent of temperature, the formation of NP in the second and third steps of the FSP follows a monomer-addition process.31,32

100

Rg / nm

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

Page 20 of 36

10 2 10

10

3

4

10

10

5

6

-1

Mw / 10 kg mol

Figure 6. Correlation of the radius of gyration (Rg) with the molar particle mass (Mw) determined at a composition of Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000 at four different temperatures: T = 10 °C (), T = 17 °C (), T = 25 °C () and T = 32 °C (). Data are the same as shown in Figure 5. All data obey a power law according to eq 11 with an exponent of 1/6 as indicated by the black line.

The temperature dependent experiments carried out at all compositions revealed essentially the same trends, i. e. the nucleation rate is amplified with increasing temperature and, at least over a certain period of time, the correlation of Rg versus Mw obeys a power law with an exponent of a = 1/6 (Figures S5 in the Supporting Information). The experiment with the highest concentration of Zn2+/Hdcim/1-PrOH = 1 : 2 : 3000 shows an upturn of Rg versus Mw, as has also been observed with the highest linker concentrations in the series of experiments at T = 25 °C


20

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(Zn2+/Hdcim/1-PrOH = 1 : X : 4000 with X = 8).19 This upturn can again be attributed to the onset of the fourth step of the FSP corresponding to an aggregation of NP emerging from the preceding steps. Only at the lowest concentration of linker with Zn2+/Hdcim/1-PrOH = 1 : 1 : 4000, deviations from the simple power law behavior of Rg versus Mw are slightly more prominent (Figure S5A in the Supporting Information). In this case, at all four temperatures, the power laws seem to be limited by two different trends, which extend with decreasing temperature. At low mass values, a steeper increase of Rg with Mw can be discerned during an initial period of time, and at high mass values, i.e., at the end of the reactions, the trend turns into a plateau where NP mass is still increasing while NP size keeps constant. Accordingly, the power law is best noticeable at the two highest temperatures and turns into a rather continuously bended curve with decreasing temperature. These two deviations from the power law suggest a slower nucleation rate, where the number of nucleated NP is increasing throughout the entire NP growth process. At the end of the process measurements indicate a number of NP increasing with T, however with the same final size, which corresponds to an increase of the mass fraction of matter being transformed to NP. This still affects the weight-averaged mass based on the second moment, but scarcely increases the z-averaged squared radius of gyration based on the third moment as the next higher moment. Hence, the square root of the z-averaged squared radius of gyration reaches its final value at Rg ~ 250 nm already at an earlier time. In conclusion, the most striking effect observed with varying temperature is the decrease in lag time τ as the temperature is increased (see Figure 7). Given that the lag time correlates with the initial steps captured as precursor reaction and nucleation by the NG model, such a trend suggests an Arrhenius type of behavior for those initial steps. Accordingly, we expect further


21


insight into the mechanism of ZIF-71 NP formation by interpreting the temperature dependent measurements with the NG model. This shall be done with the experiments carried out at the composition Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000, since the monomer-addition feature is best pronounced at this composition.

10000

1000

τ/s

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

Page 22 of 36

100

10

280

285

290

295

300

305

310

T/K

Figure 7. Lag time (τ) as a function of temperature (T) at four different compositions of Zn2+/Hdcim/1-PrOH = 1 : X : 4000 with X = 1 (), X = 2 (), and X = 3 (), and Zn2+/Hdcim/1-PrOH = 1 : 2 : 3000 (). Data at T = 25 °C (red data points) were taken from Ref. 19.

The fits of the NG model to the experimental data at all four temperatures reveal satisfactory agreement. An overview is presented in Figures S6 of the Supporting Information. The resulting fit parameters are summarized in Figures 8 and 9 and Table 2. As can be seen in Figure 8, the NG model reveals a final equilibrium concentration of precursors [A]eq decreasing with increasing temperature. From the point of view of the formation of the ZIF-71 framework it indicates that the equilibrium is shifted to the ZIF-71 product side with rise of temperature. Interestingly, the rate constants kp and kn, which take care of the initiation of NP growth (nucleation within CNT) increase with temperature with the actual variations covering more than an order of magnitude. This is in contrast to the prediction of CNT, because a decrease of


22

Page 23 of 36

temperature usually increases the degree of supersaturation and thereby increases the rate of nucleation.28,29,33 From the Arrhenius plots in Figure 9, the activation energies for the precursor and the nucleation reactions are estimated as Ep = 9 kJmol-1 and En = 22 kJmol-1, respectively. On the other hand, the growth constant kg remains in the order of magnitude of 109 M-1s-1 and seems to slightly decrease with increasing temperature.

3.5 3.0

[A]eq/ mM

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


2.5 2.0 1.5 1.0 0.5 0.0 280

290

300

310

T/K Figure 8. Final equilibrium concentration of precursors ([A]eq) from fits with the NG model (eq 5) to the experimentally determined particle mass values (Mw) shown in Figure 5, which were evaluated at variable temperature. The composition at all temperatures is Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000. The blue dashed line indicates the initial concentration of the Zn-cations.

Table 2. Fit parameters received from fitting the NG model to experimental data recorded from solutions with a composition of Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000 at variable temperature. [A]eq

kp

kn

kg

χ2

M

10-3 s-1

10-7 s-1

109 M-1s-1

kg/mol

10

0.00321

0.802

3.7*10-4

4.2

17

0.00316

1.25

1.06*10-3

4.0

25

0.00308

2.32

7.4*10-3

3.8

32

0.0028

3.49

1.43*10-2

1.03

T / °C

1)

1)

4764 1628 2219 1398

χ2 characterizes the fit quality is defined by eq 10.


23

-3

kp / 10 s

1

0.1

-9

kn / 10 s

-1

1

0.1

-1 -1

4

9

0.01 5

2

kg / 10 M s

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

Page 24 of 36

-1


3

1 0

3.3

3.4

3.5

-3

-1

1/T / 10 K

Figure 9. Rate constants from fits with the NG model (eq 5) to the experimentally determined molar particle mass values (Mw) shown in Figure 5, which were evaluated at variable temperature. The composition at all temperatures is Zn2+/Hdcim/1-PrOH = 1 : 2 : 4000. From top to bottom: rate constant of the precursor reaction (kp), rate constant of nucleation (kn), rate constant of growth (kg).

In accordance with the initiation reactions accelerated by a rise in temperature, the evolution of the number density of NP given by the zeroth moment of the NP size distribution increases with increasing temperature (Figure S7B). As a consequence of this, the monomer consumption is accelerated with the point in time of largest intermediate monomer concentration being shifted to shorter times as the temperature increases (Figure S7A).


24

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The result of our kinetic modeling, which suggests that nucleation of the NP does not follow CNT is in line with the clusters observed in our preceding SAXS study19 (step 1 of the FSP), as the latter also indicated an alternative nucleation pathway to the NP. It must be stressed that this nucleation, which we followed here by TR-SLS, primarily refers to the nucleation of the aNP (step 2 of the FSP). From this we have to distinguish the second nucleation process, namely that of the cNP in step 3 of FSP, for which we have tentatively proposed an intra-particle reconstruction process on the basis of a kinetic analysis of WAXS data.19 We note that an increase of nucleation rate with temperature was previously observed also by Vekilov et al.34,35 for protein crystallization in a particular temperature regime and discussed by means of a two-step mechanism, where dense liquid clusters/droplets, unlike CNT, are formed first, which in a second step transform into crystalline solids. This model process interpreted the maximum in the rate of nucleation as a function of temperature as follows: The increase of the rate of nucleation of crystals with decreasing temperature is caused by the increasing degree of supersaturation of the crystal phase. The branch where the nucleation rate decreases with further decreasing temperature was attributed to a strong decrease in viscosity occurring in the liquid clusters/droplets, where nucleation of the crystals takes place and by the decreasing number of liquid clusters/droplets, whose formation free energy is positive with respect to the solution state.33-35 In case of the formation of the ZIF-71 framework, it must be the activation energies accompanied with the precursor reaction and the nucleation of aNP, which are responsible for the branch where the “nucleation rate” decreases with decreasing temperature. Initiation of ZIF71 particle formation corresponds to a process where formation of coordinative bonds plays a significant role. In line with observations made for the Zeolite beta formation from clear sols36,


25


Page 26 of 36

this bond formation occurs during the first three steps of the FSP of ZIF-71 NP formation. Involvement of bond formation, which is absent in CNT, causes deviations of the kinetics as well as of the thermodynamics of ZIF-71-particle formation from that of CNT. In situ studies that are in particular sensitive to the atomic structures of the species involved in the early stages (i.e., solvated mono- and multinuclear metal complexes, amorphous clusters, aNP), using for example mass spectrometry16 and total scattering methods,14 could provide further insight into the mechanism of ZIF-71 crystallization.

CONCLUSIONS The present study has extended a previous work19 on the formation of ZIF-71 cNP from supersaturated solutions, which postulated a four step process. Two main issues were addressed, the introduction of a kinetic model on the evolution of mass data during the first two steps and an investigation of the effect of temperature variation on these two steps. A kinetic NG model was introduced and successfully applied to time-resolved static light scattering data measured at 25 °C in a previous work19. Application provided the first three moments of the particle mass distribution and revealed four parameters: the rate constants for a precursor reaction, for particle nucleation, and for particle growth, and the equilibrium concentration of non-consumed starting material at the end of reaction. The experimental data could only be described satisfactorily if a precursor reaction generating active “monomers” was put before the nucleation of particles, which in turn initiate particle growth via a monomeraddition process. Validity of the model was supported by the fact that the rate constant of the


26

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nucleation process depended on the degree of supersaturation but not the rate constant of particle growth. Further time-resolved static light scattering data, measured in the same way as in the previous work19 were recorded at four different temperatures in the regime of 10° C < T < 32 °C. Analysis with the kinetic NG model revealed that the rate constants of the precursor reaction and the nucleation process increased with temperature. Such an increase with temperature is counterintuitive if compared to classical nucleation theory as it suggests an increase of the nucleation rate with temperature. In fact, the formation of ZIF-71 cNP deviates from classical nucleation with respect to several aspects. A precursor reaction only provides the active “monomers” and the formation of an amorphous phase precedes crystallization, which most likely occurs within the amorphous particles.19


27


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ASSOCIATED CONTENT Supporting Information. Description of the kinetic NG model, estimation of an equilibrium concentration of “monomers” at T = 25°C, fits with the NG model to TR-SLS data recorded at T = 25 °C, detailed outline of the temperature dependent TR-SLS experiments, fits with the NG model to TR-SLS data recorded at variable T.

AUTHOR INFORMATION Corresponding Author *(K.H.) E-mail: [email protected]. Present Addresses †If an author’s address is different than the one given in the affiliation line, this information may be included here. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources DFG grants WI 1156/3-2 and HU 807/14-2. Notes The authors declare no competing financial interest.


28

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ACKNOWLEDGMENT This work was supported by grants from the DFG Priority Program SPP1415 “Crystalline NonEquilibrium Phases” (WI 1156/3-2, HU 807/14-2).


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7 Walton, R. I.; Millange, F. In Situ Studies of the Crystallization of Metal-Organic Frameworks. In The Chemistry of Metal-Organic Frameworks: Synthesis, Characterization, and Application; Kaskel, S.; Wiley-VCH, 2016, 1th Ed., pp. 729-764. 8 Cravillon, J.; Nayuk, R.; Springer, S.; Feldhoff, A.; Huber, K.; Wiebcke, M. Controlling Zeolitic Imidazolate Framework Nano- and Microcrystal Formation: Insight into Crystal Growth by Time-Resolved In Situ Static Light Scattering. Chem. Mater. 2011, 23, 2130-2141. 9 Cravillon, J.; Schröder, C. A.; Nayuk, R.; Gummel, J.; Huber, K.; Wiebcke, M. Fast Nucleation and Growth of ZIF‐8 Nanocrystals Monitored by Time‐Resolved In Situ Small‐Angle and Wide‐Angle X‐Ray Scattering. Angew. Chem., Int. Ed. 2011, 50, 8067-8071. 10 Cravillon, J.; Schröder, C. A.; Bux, H.; Rothkirch, A.; Caro, J.; Wiebcke, M. Formate modulated solvothermal synthesis of ZIF-8 investigated using time-resolved in situ X-ray diffraction and scanning electron microscopy. CrystEngComm 2012, 14, 492-498. 11 Goesten, M.; Stavitski, E.; Pidko, E. A.; Gücüyener, C.; Boshuizen, B.; Ehrlich, S. N.; Hensen, E. J. M.; Kapteijn, F.; Gascon, J. The Molecular Pathway to ZIF-7 Microrods Revealed by In Situ Time-Resolved Small- and Wide-Angle X-Ray Scattering, Quick-Scanning Extended X-Ray Absorption Spectroscopy, and DFT Calculations. Chem. – Eur. J. 2013, 19, 7809-7816. 12 Springer, S.; Heidenreich, N,; Stock, N,; van Wüllen, L.; Huber, K.; Leoni, S.; Wiebcke, M. The ZIF system zinc(II) 4,5-dichoroimidazolate: theoretical and experimental investigations of the polymorphism and crystallization mechanisms. Z. Kristallogr. 2017, 232, 77-90.


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27 Drews, T. O.; Katsoulakis, M. A.; Tsapatsis, M. A Mathematical Model for Crystal Growth by Aggregation of Precursor Metastable Nanoparticles. J. Phys. Chem. B 2005, 109, 23879– 23887. 28 Volmer, M.; Weber, A. Keimbildung in Ubersattigten Gebilden. Z. Phys. Chem. 1926, 119, 277–301. 29 Becker, R.; Döring, W. Kinetische Behandlung der Keimbildung in übersättigten Dämpfen. Ann. Phys. 1935, 24, 719–752. 30 Robb, D. T.; Privman, V. Model of nanocrystal formation in solution by burst nucleation and diffusional growth. Langmuir 2008, 24, 26–35. 31 Liu, J.; Rieger, J.; Huber, K. Analysis of the Nucleation and Growth of Amorphous CaCO3 by Means of Time-Resolved Static Light Scattering. Langmuir 2008, 24, 8262–8271. 32 Liu, J.; Pancera, S.; Boyko, V.; Shukla, A.; Narayanan, T.; Huber, K. Evaluation of the Particle Growth of Amorphous Calcium Carbonate in Water by means of the Porod Invariant from SAXS. Langmuir 2010, 26, 17405–17412. 33 Vekilov, P. G. Nucleation. Cryst. Growth & Design 2010, 10, 5007-5019. 34 Pan, W.; Kolomeisky, A. B.; Vekilov P. G. Nucleation of ordered solid phases of proteins via a disordered high-density state: Phenomenological approach. J. Chem. Phys. 2005, 122, 174905. 35 Galkin, O.; Vekilov, P. G. Control of protein crystal nucleation around the metastable liquid– liquid phase boundary. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 6277–6281.


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36 Castro, M.; Haouas, M.; Lim, I.; Bongard, H. J.; Schüth, F.; Taulelle F.; Karlsson, G.; Alfredsson, V.; Breyneart, E.; Kirschhock, C. E. A.; Schmidt W. Zeolite Beta Formation from Clear Sols: Silicate Speciation, Particle Formation and Crystallization Monitored by Complementary Analysis Methods. Chemistry Eur. J. 2016, 22, 15307 – 15319.


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For Table of Contents Use Only

Insight into Fast Nucleation and Growth of Zeolitic Imidazolate Framework-71 by In Situ Static Light Scattering at Variable Temperature and Kinetic Modeling

Sanjib Saha, Michael Wiebcke, Klaus Huber

Time-resolved light scattering is applied to follow the evolution of ZIF-71 nanoparticles from supersaturated solutions at variable temperature. Interpretation of the resulting particle mass and size values with a nucleation and growth model requires consideration of a precursor reaction. The rate constants of the precursor reaction and nucleation increase with temperature indicating deviations from the classical nucleation theory.


36

Insight into Fast Nucleation and Growth of Zeolitic Imidazolate

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