# Synthesis of Gold Clusters and Nanoparticles Using Cinnamon Extract—A Mechanism and Kinetics Study

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{1}= 70.6 kJ, E

_{2}= 19.6 kJ, ΔH

_{1}= 67.9 kJ/mol, ΔH

_{2}= 17 kJ/mol, ΔS

_{1}= −76.2 J/(K·mol), ΔS

_{2}= −204.2 J/(K·mol), respectively. In this work the limitation of each technique (spectrophotometry vs. HRSTEM) as a complex tool to understand the dynamic of the colloidal system was discussed.

## 1. Introduction

_{4}leads to “burst” nucleation [11], protecting against further particle growth. However, sodium borohydride is dangerous and toxic [12]; therefore, the application of other efficient and “green” reductants is desirable from the point of view of medical applications or syntheses using harmless reagents.

_{n}in Equation (1), Ir(0)

_{n}

_{+1}—product of reaction (2), k

_{1}—rate constant of nucleation, k

_{2}—rate constant of autocatalytic growth.

_{L}—large particles, k

_{3}—rate constant of bimolecular aggregation.

_{L}) particles was considered. In this work, the W—F model in its basic form, Equations (3) and (4) was used. To rule out the problem of separating the nucleation and growth steps over time in the graph obtained after the sigmoidal curve linearization process, the Bentea et al. [20] approach to facilitating the determination of kinetic rate constants using the tools available in the Origin Pro 8.5 software was applied.

## 2. Results and Discussion

#### 2.1. Experimental Conditions

#### 2.2. Preview of the Course of the Reaction

_{4}]

^{−}complex (Figure 2a), whereas an aqueous solution of the cinnamon extract absorbs light below 400 nm. When diluting the cinnamon extract to concentration 0.2 g/L, the spectrum exhibits two characteristic maxima, with the first one registering at 200 nm and the second one at 282 nm (sample C, Figure 1a).

#### 2.3. Determination of Slow Continuous Nucleation and Growth Rate Constants

_{1}and k

_{2}, which are the constants of the reaction rate. Knowing them, we can write the formula for the total reaction rate (6):

_{0}= 0, so the sum of [A]

_{t}+ [B]

_{t}= [A]

_{0}for the entire duration of the process. Performing the differentiation of the kinetic Equation (6) we obtain the expression for [A]

_{t}and [B]

_{t}, which are given as:

_{t}= f (t), see Figure 3b). The key condition is the assumption that k

_{1}≪ k

_{2}[A]

_{0}, which allows for the separation of nucleation and growth processes. Bentea et al. [20] summarized the mathematical operation and equations which are needed for determination of rate constants of nucleation and particle growth determination from sigmoidal kinetic curves. Most important parameters, i.e., t

_{max}, ${[B]}_{{t}_{\mathrm{max}}}$, t

_{in}

_{(jerk)}and corresponding formulas are summarized in Table 1.

_{max}. This time value can be determined by calculating the derivative of the function [B]

_{t}(Figure S4a, Supplementary Materials). The obtained graph exhibits the maximum corresponding to the time (t

_{max}) for which the process rate is the highest (Figure S4a, Supplementary Materials). The value of t

_{max}corresponds to the value of ${[B]}_{{t}_{\mathrm{max}}}$ and is equal to ~2.5 (a.u.). These values are needed for the determination of observed rate constants and the value of [A]

_{0}(Equations (10)–(12)), respectively. The determination of successive derivatives, including the third-order derivative, allows for the determination of the t

_{in}

_{(jerk)}(this time representing a zero point in the jerk curve of the third derivative of B [20], Figure S4c, Supporting Materials) and thus needs a third equation allowing for the solution of Equations (10)–(12). The second derivative allows for t

_{in}(time of induction period) determination [20] (Figure S4b, Supplementary Materials).

_{in}

_{(jerk)}value and is 4.44 min at 40 °C (Figure S4c, Supporting Materials). The determined value of t

_{in}

_{(jerk)}allows us to calculate the value of k

_{2}, which is 0.165 (a.u.)

^{−1}min

^{−1}. The value of the rate constant for the nucleation process (k

_{1}) was determined from the formula described by Equation (10) and equals 0.0056 min

^{−1}. The corresponding rate constants at other temperatures were determined in an analogous manner, and the calculated values of the rate constants for the nucleation process and the autocatalytic growth of gold nanoparticles, as well as t

_{max}and t

_{in}

_{(jerk)}, are summarized in Table 2.

#### 2.4. Thermodynamic Parameters Determination for Nucleation and Growth of Gold Nanoparticles

_{max}, t

_{in}

_{(jerk)}were determined from the first and third derivatives (examples shown in Figure S4a,c, Supporting Materials), and calculated values of k

_{1}and k

_{2}from Equations (10) and (12) (see, Table 2) were obtained.

_{1}) and autocatalytic growth (k

_{2}), respectively, T—temperature in Kelvin; R—gas constant (8.314 J/(mol·K)); k

_{B}—Boltzmann constant; h—Planck’s constant, ΔS—activation entropy of nucleation (ΔS

_{1}) and autocatalytic growth (ΔS

_{2}), respectively; ΔH—activation enthalpy of nucleation (ΔH

_{1}) and autocatalytic growth (ΔH

_{2}), respectively.

_{1}) and autocatalytic growth (k

_{2}), respectively, T—temperature in Kelvin; R—gas constant (8.314 J/(mol·K)); A—pre-exponential factor; E

_{a}—activation energy, J.

#### 2.5. High Resolution Scanning Transmission Microscope for Gold Nanoparticles Characterization

#### 2.6. The Role of Eugenol and Cinnamaldehyde in the Process of Gold Nanoparticles Formation

_{R1}—kinetic rates constant of Au(III) to Au(I) ions reduction; k

_{R2}—kinetic rates constant of Au(I) reduction to Au(0); k

_{R3}—kinetic rates constant of autocatalytic growth.

#### 2.7. The Possible Mechanism of Metastable Clusters, Cluster Aggregates and Ultra-Small Particles Formation—HRSTEM vs. Spectrophotometry Analysis

_{C}

_{1}—kinetic rate constant of metastable cluster formation; k

_{C}

_{2}—kinetic rate constant of autocatalytic cluster growth, k

_{C}

_{3}—kinetic rate constant of USP nucleation; k

_{P}

_{1}—kinetic rate constant of USP growth and NPs formation (D > 2 nm); k

_{P}

_{2}—kinetic rate constant of autocatalytic growth of nanoparticles; Au(0)—gold atoms; Au(0)

_{n}—gold clusters; Au(0)

_{n}

_{+1}—gold clusters with the core; USP—ultra-small particles; AuNPs—gold nanoparticles; AuNPs

_{n}—larger gold nanoparticles.

#### 2.8. The Impact of the Beam Irradiation on Gold Cluster Transformation—Single and Multi-Core Formation

## 3. Materials and Methods

#### 3.1. Chemicals

_{4}(pH = 1, 0.1 M HCl as a solvent (preventing gold hydrolysis) was used. Cinnamon extract was used as an Au(III) ion bio reductant and particle stabilizer. For this purpose, 2 g of cinnamon powder (bark powder commercially available in the market, Prymat, Koszalin, Poland) was dispersed in 100 mL of deionized water (concentration—20 g/L). The solution was mixed (360 rpm, T = 20 °C) for 24 h according to procedure described by Siemieniec and Kruk [21]. Investigations were performed at a constant temperature in the range of 20–60 °C. Afterward, the solution underwent a two-stage filtration process with middle pore sized paper and a syringe filter (0.2 µm). After this process, the solution had an intense yellow color and was ready to use.

#### 3.2. Gold Nanoparticles Synthesis

#### 3.3. Methods of Analysis

## 4. Conclusions

_{1}= 70.6 kJ, E

_{2}= 19.6 kJ, ΔH

_{1}= 67.9 kJ/mol, ΔH

_{2}= 17 kJ/mol, ΔS

_{1}= −76.2 J/(K·mol), ΔS

_{2}= −204.2 J/(K·mol) were determined. A HRSTEM analysis showed that, depending on the temperature of the synthesis process, the transformation of the Au cluster into nanoparticles can be observed. Densely packed clusters with core undergoes coalescence, which leads to formation of nanoparticles with size D > 2 nm. At 60 °C, particles that were ultra-small in size, i.e., 1–2 nm (in diameter), and spherical in shape were observed (Figure 7c). Then, the USP growth occurred because of Ostwald ripening.

## Supplementary Materials

_{max}, t

_{in}and t

_{in(jerk)}. S4—HRSTEM analysis. S5. HRSTEM movie animation description and movie. Figures: Figure S1: Statistic data: the numbers of papers (number of publications by topic: Fluorescence; Metal Clusters; Icosahedron) published within 10 years (a), Publication share by subject area (b). Source: Scopus database (SciVial); Figure S2: The deconvolution of the cinnamon extract spectrum, 100,000 dissolutions of base solution in H

_{2}O, T = 20 °C; Figure S3: The spectrum of cinnamaldehyde (CA) and eugenol (Eug) after 100,000 dissolutions of base solutions (CA, >98%, Fluka; Eug, 99%, p.a., Thermo Scientific) in H

_{2}O; Figure S4: The first (a), second (b) and third-order (c) derivative of B in time function. The kinetic curve registered at 538 nm (d) with highlighted points on the time scale. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 40 °C; Figure S5: The HRSTEM analysis showing a gold cluster structure. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 20 °C; Figure S6: The HRSTEM analysis showing a fragment of the larger gold crystal with a marked l5 nm thick layer (A) of gold nanoclusters aggregates and/or MCC (a); the fragment of the larger gold crystal with marked (B) ultra-small gold particles (b); gold nanoparticles with irregular shapes (c) and exemplary particles with a gray border around the particle (black circles); magnification of cluster aggregates (d). Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 60 °C (a,b). T = 20 °C (c,d); Figure S7: The HRSTEM analysis showing the coalescence of cores within gold nanoclusters aggregates at a beginning (a) and after irradiation (b). A–A’—coalescence of two cores, B–B’—coalescence gold clusters and/or aggregated gold clusters leading to a new core formation. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 20 °C (a,b). Figure S8: Fluorescence spectrum obtained at different excitation wavelengths. Sample notation: A_0—colloidal solution after one year; A_1—colloidal solution after 10-times dissolution. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 60 °C. Figure S9: A: HRSTEM image with selected analyzed area, B: FFT analysis with selected spots (1-1, 2-2, 3-3), C1–C2: Mask used to select certain spots for IFFT, D1–D2: IFFT image using indices chosen by C1–C2 mask, E1–E2: lattice parameter measurement through measuring the distance of white fringes on IFFT (D1–D2) images. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 20 °C. Reference [39] is cited in the Supplementary Materials.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Spectra of reagents, i.e., an aqueous solution of Au(III) ions and cinnamon extract (Cex). Conditions: C

_{0, Au(III)}= 0.2 mM (A); C

_{0, Au(III)}= 1.0 mM (B); C

_{0,Cex}= 20 g/L (diluted 100 times in deionized water, C), T = 20 °C (

**a**); Spectra evolution after reagents mixing, i.e., Au(III) ions and cinnamon extract (

**b**). Samples notation: A—1 min, B—5 min; C—10 min and D—15 min later. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 20 °C (

**b**).

**Figure 3.**Spectra evolution and change of solution color (A—1 min later, B—6 min later, C—25 min later) after reagents mixing, i.e., Au(III) ions and cinnamon extract (

**a**); Kinetic curve registered at 538 nm (

**b**). Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 40 °C.

**Figure 4.**Kinetic curves for slow continuous nucleation and fast autocatalytic growth of gold nanoparticles obtained through Au(III) ion reduction using cinnamon extract. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L.

**Figure 5.**The Arrhenius (

**a**) and Eyring (

**b**) dependencies. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 20–60 °C.

**Figure 6.**HRSTEM results registered at different magnification (

**a**–

**c**). Conditions: C

_{0, Au(III}) = 0.01 M, C

_{0,Cex}= 18 g/L, T = 20 °C.

**Figure 7.**HRSTEM results registered at different magnification (

**a**–

**c**). Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 60 °C.

**Figure 8.**(

**A**) HRTEM image with selected analyzed area, (

**B**) FFT analysis with selected spots (1–1, 2–2, 3–3), (

**C1**–

**C3**) Mask used to select certain spots for IFFT, (

**D1**–

**D3**) IFFT image using indices chosen by (

**C1**–

**C3**) mask, (

**E1**–

**E3**) lattice parameter measurement through measuring the distance of white fringes on IFFT (

**D1**–

**D3**) images. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 60 °C.

**Figure 9.**HRSTEM analysis of AuNC synthesized at 20 °C (

**a**); 60 °C (

**b**). Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L. A—small Au cluster (few atoms), B—fragment of dense packed cluster (DPC), C—Au cluster aggregates; USP—ultra- small particles, MCC—metastable cluster clouds.

**Figure 10.**The proposed mechanism of Au nanoparticles formation based on HRSTEM results with the highlighted range of available techniques used in this work. Notation (from left): Au(III) ions (yellow—gold; green—chloride); Au(I) ions; free gold atoms; metastable clusters; dense packed cluster aggregates with core; small particles, D < 2 nm (only HRSTEM), nanoparticles with size D > 2 nm (UV-Vis and HRSTEM), crystal growth (D < 100 nm); crystal further growth, D > 100 nm (turbidity on UV-Vis spectrum). EQ

_{1–6}—dynamic equilibria. UV—wavelength below 400 nm, Vis—wavelength in the range 400–900 nm.

**Table 1.**Most important parameters, i.e., t

_{max}, ${[B]}_{{t}_{\mathrm{max}}}$, t

_{in}

_{(jerk)}and formulas needed for kinetics rate constants of nucleation and particles growth determination.

Parameter | Formula | Equation No. |
---|---|---|

t_{max} | ${t}_{\mathrm{max}}=\frac{\mathrm{ln}(\frac{{k}_{2}{[A]}_{0}}{{k}_{1}})}{{k}_{2}{[A]}_{0}}$ | (10) |

${[B]}_{{t}_{\mathrm{max}}}$ | ${[B]}_{{t}_{\mathrm{max}}}=\frac{{[A]}_{0}}{2}$ | (11) |

t_{in}_{(jerk)} | ${t}_{in(jerk)}={t}_{\mathrm{max}}-\frac{1.3}{{k}_{2}{[A]}_{0}}$ | (12) |

**Table 2.**The values of obtained rate constants for slow continuous nucleation and fast autocatalytic growth *. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L.

T, °C | t_{max}, min | t_{in}_{(jerk)}, min | k_{1}·10^{3}, min^{−1} | k_{2}·10^{2}, (a.u.) ^{−1}min^{−1} |
---|---|---|---|---|

20 | 12 | 9.87 | 0.4 | 12.11 |

30 | 8 | 6.40 | 1.2 | 16.11 |

40 | 6 | 4.44 | 5.6 | 16.53 |

50 | 4 | 3.00 | 7.2 | 25.79 |

60 | 3 | 2.20 | 12.4 | 32.24 |

_{0}= 5.04 (a.u).

**Table 3.**The values of obtained rate constants for slow continuous nucleation and fast autocatalytic growth. Conditions: C

_{0, Au(III)}= 0.01 M, C

_{0,Cex}= 18 g/L, T = 20–60 °C.

Process | A, dm^{3}mol^{−1}min^{−1} | E_{a}, kJ | $\u2206\mathit{S}$, JK^{−1}mol^{−1} | $\u2206\mathit{H}$, kJ mol^{−1} |
---|---|---|---|---|

nucleation | 1.3 × 10^{9} | 70.6 | −76.2 | 67.9 |

growth | 4.0 × 10^{2} | 19.6 | −204.2 | 17.0 |

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## Share and Cite

**MDPI and ACS Style**

Luty-Błocho, M.; Cyndrowska, J.; Rutkowski, B.; Hessel, V.
Synthesis of Gold Clusters and Nanoparticles Using Cinnamon Extract—A Mechanism and Kinetics Study. *Molecules* **2024**, *29*, 1426.
https://doi.org/10.3390/molecules29071426

**AMA Style**

Luty-Błocho M, Cyndrowska J, Rutkowski B, Hessel V.
Synthesis of Gold Clusters and Nanoparticles Using Cinnamon Extract—A Mechanism and Kinetics Study. *Molecules*. 2024; 29(7):1426.
https://doi.org/10.3390/molecules29071426

**Chicago/Turabian Style**

Luty-Błocho, Magdalena, Jowita Cyndrowska, Bogdan Rutkowski, and Volker Hessel.
2024. "Synthesis of Gold Clusters and Nanoparticles Using Cinnamon Extract—A Mechanism and Kinetics Study" *Molecules* 29, no. 7: 1426.
https://doi.org/10.3390/molecules29071426