Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

DOI: 10.1039/C9NA00636B
(Paper)
Nanoscale Adv., 2020, Advance Article

Prakash Natarajan‡
^{a},
Awad Shalabny‡^{a},
Sumesh Sadhujan^{a},
Ahmad Idilbi^{a} and
Muhammad Y. Bashouti*^{ab}
^{a}Department of Solar Energy and Environmental Physics, Swiss Institute for Dryland Environmental and Energy Research, J. Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Midreshet Ben-Gurion 8499000, Israel. E-mail: bashouti@bgu.ac.il
^{b}The IlSe-Katz Institute for Nanoscale Science & Technology, Ben-Gurion University of the Negev, Beersheba, 8410501, Israel

Received
8th October 2019
, Accepted 3rd December 2019

First published on 4th December 2019

The solution-based growth mechanism is a common process for nanomaterials. The Maxwell-Garnett theory (for light–matter interactions) describes the solution growth in an effective medium, homogenized by a mean electromagnetic field, which applies when materials are in a stationary phase. However, the charge transitions (inter- and intra-transitions) during the growth of nanomaterials lead to a non-stationary phase and are associated with time-dependent permittivity constant transitions (for nanomaterials). Therefore, time-independence in the standard Maxwell-Garnett theory is lost, resulting in time dependence, ε_{i}(t). This becomes important when the optical spectrum of a solution needs to be deconvoluted at different reaction times since each peak represents a specific charge/energy transfer with a specific permittivity constant. Based on this, we developed a time-resolved deconvolution approach, f(t) ∝ ε_{i}(t), which led us to identify the transitions (inter- and intra-transitions) with their dominated growth regimes. Two gold ion peaks were precisely measured (322 nm and 367 nm) for the inter-transition, and three different polyaniline oxidation states (PAOS) for the intra-transition, including A (372 nm), B (680 nm), and C (530 nm). In the initial reaction time regime (0–90 min), the permittivity constant of gold was found to be highly dependent on time, i.e. f_{E} ∝ ε_{i}(t), since charge transfer takes place from the PAOS to gold ions (i.e. inter-transition leads to a reduction reaction). In the second time regime (90–180 min), the permittivity constant of gold changes as the material deforms from 3D to 2D (f_{S} ∝ ε_{3D–2D}), i.e. intra-transition (combined with thermal reduction). Our approach provides a new framework for the time-dependent modelling of (an)isotropic solutions of other nanomaterials and their syntheses.

In our case, we are interested in the time period for gold nucleation towards 2D gold formation, which is a dynamically changing process, during which the permittivity of the different elements of the mixture changes with time as the charge transfer (i.e. inter-transition for nucleation) and energy (i.e. intra-transition for 2D formation) continue. Thus, light as an external probe, was illuminated during the formation time to measure the transitions.^{21,22} Accordingly, we unraveled the inter- and intra-transitions by introducing the time-dependent Maxwell-Garnett permittivity (MGt) effective parameter, which to the best of our knowledge has never been done before. Based on this, we performed deconvolution based on the time-dependence model (MGt) at the different stages of the chemical reaction until the formation of the final state. Two main regimes were identified: (i) the first time regime (0–90 min), where the permittivity constant of gold was found to be highly dependent on time, i.e., f_{E} ∝ ε_{i}(t) as charge transfer from the polyaniline oxidation states (PAOS) to gold ions (i.e. inter-transitions leads to a reduction reaction) takes place, and (ii) the second time regime (90–180 min), where the permittivity constant of gold changes as the material deforms from 3D to 2D (f_{S} ∝ ε_{3D–2D}), i.e. intra-transition.

After performing the deconvolution, we correlated the data analysis with the material, chemical kinetics and electronic properties of the 2D gold flakes. The data was cross-checked with data from SEM and AFM to follow the morphology, EBSD and XRD to follow the material crystallinity, KPFM to follow the electronic properties, and absorbance to follow the transitions and kinetics. Materially, we showed the formation of high-quality 2D gold flakes (monocrystalline) with ultra-sharpness (roughness below 1 nm) and a low level of residual impurities, regardless of the time, temperature and concentration. The formation of 2D monocrystalline gold flakes is particularly appealing as a basis for precise plasmonic nanostructures for the transport of both optical signals without grain boundaries or defects and for associated strongly enhanced local fields with marginal ohmic losses.^{23} Thus, these 2D structures combine the superior technical advantages of both photonics and electronics on the same chip.^{24} Chemically, we tuned the lateral area dimension of the flake from the nanoscale (250 nm^{2}) to sub-millimetre area size, 0.006 mm^{2}, while keeping the thickness always at the nanoscale (below 60 nm). Electronically, the KPFM studies revealed the electronic grade surface quality of the 2D flake (with work-function of 5.17 eV) as in a bulk. Optically, we identified three states with intra-transitions for the PAOS, A (372 nm),^{25} B (680 nm),^{26} and C (530 nm),^{27} and two states for the gold (322 nm and 367 nm) for inter-transitions.^{28} The presented model, i.e. MG (t), is simple and allows a time-resolved deconvolution and follows the evolution of the nanomaterial growth with its permittivity constant in the solution process. The model can be justified based on experimental data that already has been published by other researchers as well as by our group for different materials.

(1) |

(2) |

This is supported by the marginal shift in the absorbance spectrum of the different states. For example, state A shows a shift of 3 nm, while that of states B and C is about 10 nm. This holds even in the non-stationary phase when the total mass reserved. However, we distinguished between the two transitions, (i) inter charge transition, where the charges are transferred between PAOS (from state A to gold ions, as will be explained later); and (ii) when the gold nuclei are transferred from 3D to 2D gold flakes (shown later). Therefore, the time independence in the standard MG is lost and we have a time dependent ε_{i}(t), and in turn, ε_{MG} also becomes time dependent: ε_{MG} = ε_{MG}(t). Since dε_{PAOS}/dt = 0, we propose the following:

ε_{MG}(t) = f_{E}[1 − θ(t − t_{1})] + f_{S}[1 + θ(t_{1} − t)]
| (3) |

(4) |

ε_{MG}(t) = ε_{MG} × [[e^{−rt}θ(t_{1} − t) + e^{−rt1}[θ(t − t_{1}) − θ(t − t_{2})]] + [e^{−rt1} + f_{S,2D}(t − t_{2})]θ(t − t_{2})]
| (5) |

The theoretical foundations on which the construction of the last equation are based on are as follows. The polymer will definitely have certain PAOS. In general, some of these states will start transferring charges and energy to the host medium and to other PAOS, as will be shown in the chemistry and kinetics parts. In the initial period, (t < t_{1}), and the host medium will not undergo major changes in its structure other than starting to form gold nuclei. Thus, we assumed that until a certain time t_{1}, the main change in the permittivity comes solely from the inter transitions (from ions), while some of the PAOS may transform between their own states. Thus, we get a contribution to ε_{MG}(t) only from the first term (in our case t_{1} = 60 min), i.e. after this time no charge will be supported to the gold ions. The first term in eqn (5) results from a solution of a first order differential equation with the initial condition: ε_{MG}(t = 0) = ε_{MG}. This gives an exponential decay, as discussed above and as will be shown later. Subsequently, it is expected to have a short period of time, which can be considered as a semi-relaxation time, where the remaining PAOS organize themselves energetically while the gold nuclei aggregate. At this intermediate stage, the shape of the gold nuclei is still unchanged (basically spherical) and the permittivity is constant (60 min < t < t_{2}). This is depicted in the second term in eqn (5). At a later time, 2D gold flakes will form (thus creating the nano gold flakes) and all the decay rates will become constant with time, and thus the total effect on the time changing ε_{MG}(t) comes from the shape deformation of the 3D to 2D transition and described by f_{S,2D}. This is the contribution of the third and last term in our formula, where we assumed a linear time-dependence while considering the shape deformation through the parameter f_{S,2D}. In our case, we t_{2} = 90 min. The above formula is valid until the reaction has stopped at t_{final} = 180 min. It should be mentioned that our formula for ε_{MG}(t) is a continuous function of time (t), while not differentiable at t_{1} and t_{2}. The second term describes the shape deformation at the second stage of the reaction, where we averaged the initial dielectric constant ε_{MG} (t = t_{1}) and the final value (t_{1} ≪ t).

However, the as the charge transferred from the PAOS to gold ions and formed gold nuclei, the permittivity parameter of the gold ions/nanoparticle was not constant and is time dependent (see the Model section, eqn (5)). Visually, the charge transfer can be followed by the color of the reaction (see Fig. 1). For example, at t = 0 min, and before aniline was added, the solution color was yellow. When the solution was heated to 80 °C, it remained green (#8A8871) for less than 30 min, after which its color slowly changed to “blue” dove gray (#696363) (t = 45–75 min). As the reaction proceeded, the solution color again changed, becoming a “red” Chico color (#A0645C) at time exceeding 90 min and until the end of the reaction (t = 180 min, see Fig. 1).

Fig. 3 Subtracted deconvolution of the UV/Vis spectra, showing an example of the deconvoluted spectra for t = 20 min. |

Since all the PAOS have the same permittivities then a great simplification in calculating ε_{MG} is obtained. Therefore, we posited the full width at half-maximum (fwhm) to be similar for all the PAOS and constant over the reaction course (57 ± 8 nm).^{25} In contrast, the Au spectra showed a varying fwhm, which become larger (∼50%) with the reaction time (from 12.4 nm to 21.6 nm). The observed differences in the fwhm values of the components of the Au spectra are attributed to the charge transfer and to the gradual permittivity constant transition (from ions to metal). Note that we subtracted the “ground absorbance” values of the Au particles and of the solvent (ethylene glycol) to obtain the absorbance of only the PAOS and gold ions. Accordingly, we deconvoluted the optical spectra at different reaction times in Fig. 1. Thus, all the positive spectra represent the PAOS (intra transitions), while the negative spectra represent the Au ions (inter transition). When combining the two sets of spectra, we obtained excellent agreement between our model-based theoretical spectra with that recorded in the experiments (Fig. 3–6). Consequently, our subtracted deconvolution model based on the time-dependent permittivity constant works sufficiently well.

Fig. 4 depicts the normalized intensity values of the PAOS peaks (I_{PAOS}) and the Au peaks (I_{Au}) versus the reaction time, as determined by the fitted data. The rates of the three PAOS states A, B and C [K_{PAOS} = ΔI_{PAOS}/Δt], and the gold ions, [K_{Au} = ΔI_{Au}/Δt] show two main reaction time regimes: (i) 0–90 min, and (ii) 90–180 min (Fig. 4). For the PAOS, in the first regime, we can define two phases (0–60 min and 60–90 min). In first phase, an inter-transition is observed, where state A is transferred equally to B and C, i.e.: −[K_{A}]_{0–60min} = [K_{B}]_{0–60min} + [K_{C}]_{0–60min}, with the rate of [K_{A}]_{0–60min} = −2.0 × 10^{−3} min^{−1}, where [K_{B}]_{0–60min} = 1.1 × 10^{−3} min^{−1} and [K_{C}]_{0–60min} = 0.9 × 10^{−3} min^{−1}. Based on the model, the kinetics of A, [K_{A}], follows the first pseudo-order reaction. This experimental observation is depicted in our model by the existence of only one decay rate parameter, r, rather than a multiple of decay rates and represents the decay rate of state A (Fig. 4a). This is also a result of solving the first order differential equation, resulting in the exponential factor in the model. In the second phase, the inter-transition stops (no more oxidation of gold ions), and an intra-transition starts, where state B oxidizes to state C, but at an inversed rate, −[K_{B}]_{60–90min} > [K_{C}]_{60–90min}. However, in the second regime (90–180 min), state C is constant with time, i.e., [K_{C}]_{90–180min} = 0, while state B continues to lose its weight, but decomposes thermally by the rate of [K_{B}]_{90–180min} = −0.8 × 10^{−3} min^{−1} (Fig. 4a).

Thus, we can define the two regimes based the PAOS kinetic analysis where the first regime (0–90 min) is controlled by the oxidation process of PA (i.e. inter-transition), while the second regime (90–180 min) is controlled by the thermal decomposition process (no more inter-transition). It is worth pausing and clarifying the agreement of the above kinetic analysis with the third term in our master formula (eqn (5)). At the period of time: 90 < t < 180 min, all the intra-transitions have stopped, states A and B become irrelevant and state C becomes constant. The only remaining dynamic factor is the formation of 2-D gold flakes. This shape deformation is exactly the origin of the linear third term in eqn (5). The difference between the intra-transition rates in the two regimes indicates further the existence of two different mechanisms, protonation in the first regime (oxidation of PA) and thermal decomposition in the second regime. Similar kinetic behavior was observed in the inter-transition rates in the case of gold ions, i.e., K_{Au} = ΔI_{Au}/Δt, which shows the same two regimes. In the first regime, [K_{Au}]_{0–90min} = 6 × 10^{−3} min^{−1} was higher by three times relative to the second regime of [K_{Au}]_{90–180min} = 2 × 10^{−3} min^{−1} (Fig. 4b). The different rates (triple rate factor) indicate that [K_{Au}] is affected by the two mechanisms in the first regime and only by the thermal reduction in the second regime via the ethylene glycol solvent (since there is no more state A in the second regime).^{33}

Considering these results, we suggest the following scenario for the inter- and intra-transitions: state A undergoes rapid oxidation (factor of 2) to produce states B and C until it is completely eliminated (t = 60 min). The oxidation process consists of consuming protons by converting the benzoid groups to quinoid groups.^{25} This is followed by the appearance of a peak at 440 nm (Fig. 4c), which represents the protonated quinoid groups. Subsequently, there is a short interval, from 60 min to 90 min, as a transition state, during which we observed a rapid intermediate transition from state B to state C via the deprotonation of B. During this short period of time, the effective MG is constant since the B and C states are almost identical in structure and the transition of gold from 3-D to 2-D flakes has marginally started. This is depicted in our master formula (eqn (5)) by the second term in the square brackets. However, after 90 min, the deprotonation stopped and state B began to decompose thermally (Fig. 4a), and therefore, the concentration of state C became constant (the suggested reaction pathway is schematically drawn in ESI-3†). This scenario is supported not only by the fact that no further deprotonation was possible (after 90 min), but also by the mass conservation law. The total mass (M_{tot} = A + B + C) remains constant until B starts to decompose, where the mass becomes lower than M_{tot} in the second regime, and therefore, dε_{PAOS}/dt will be ≈ 0 (see ESI-4†). In the second regime along the time axis, state C reached a saturation level, i.e., [K_{C}]_{90–180min} = 0, and therefore, the oxidation ceased (Fig. 4a). Additional support for the intra-transition is apparent in the reduction mechanism of the gold ions (inter transition). Accordingly, we followed the concentration of the gold ions, as explained earlier (Fig. 4b). After 90 min, the protonated quinoid became constant, indicating the termination of the polyaniline-driven reduction of AuCl_{4}^{−}. Therefore, the reduction rate of the gold ions became thermal only in the second regime. This is also found to be in good agreement with the non-constant ratio between the gold peaks (322 nm and 367 nm) in the two regimes since the permittivity constant became different in the two regimes and f_{E} ≠ f_{S}. The last inequality is obvious since the two functions have two completely different physical origins. The above experimental observations and the physical insight behind the existence of the two distinct regimes were the basis for constructing our master formula for ε_{MG}(t), in which the two theta functions distinguish between regime (i) and regime (ii), where two different mechanisms (charge transfer in the first part with mass conservation) intact and shape deformation in the second part, and the mass lost due to thermal decomposition of state B affects the effective time-changing permittivity parameter.

Additional information based on AFM can be found in ESI-5.† Fig. 5a represents the first phase (0–60 min) in regime (i) and shows faceted nuclei with sizes ranging from 50 nm to 300 nm. Note that the growth of Au nuclei can be minimized by adding additional surfactant (CTAB) and by replacing ethylene glycol with water as the solvent (shown in ESI-6†). Since state A was completely converted to states B and C, the oxidizing capability of polyaniline reached the minimum and the Au reduction decreased (second phase in regime (i)), and hence the Au seeds aggregated to reduce the energy of the system (three examples are marked in blue in Fig. 5b). This tendency can also be understood in terms of Le Chatelier's principle. As the seeds are formed, the Gibbs energy of the system increases. The seeds are brought closer together to reduce this increase in energy (state B rate of oxidation induces aggregation), and therefore acts to counteract the perturbation. In this phase (60–90 min), the seeds undergo aggregation and begin to form nano-flakes in regime (ii). Therefore, the permittivity constant is not time dependent in this regime, as supported by eqn (5). This indicates that the internal migration to produce 2D flakes with uniform thickness in regime (ii) is cause due to state C. The anisotropic growth in the second regime starts to generate gold flakes with lateral edge lengths of several microns. However, the horizontal lengths remain in the nanoscale due to the capping effect of state C on the (111) plane direction, which emphasizes the role of state C in this regime.^{34,35} After 90 min of reaction, the aggregated structures are replaced with more regular Au microplates, indicating that the Au seeds coalesce into 2D flakes (Fig. 5c). According to the comparison of the different stages of the reaction (Fig. 3 and 5), it can be concluded that the 2D flakes grow at the expense of the 3D particles, which is known as the “crystal nucleation and growth” model. Therefore, we can explain the transformation of 3D aggregates to 2D flakes by the differences in the growth rates of the various crystallographic facets. Briefly, once the nucleation starts, the seeds coalesce to reduce the surface energy. Since the {111} facet has a lower surface energy compared to the other facets such as {110} and {100}, the oxidized aniline adsorbs on the {111} plane and acts as a capping agent. This process facilitates the addition of the gold atoms to the high energy facets ({110} and {100}) to release the maximum energy. The Au seeds fuse through the {110} and {100} facets to form thin 2D flakes (Fig. 5b). After the formation of the 2D flakes, the growth continues very fast at the edges, i.e. lateral direction due to the high surface energy of {110} and {100} facets and slow growth taking place in the vertical {111} direction. Therefore, the converted 2D flakes can expand to micrometre flakes but with nanometre thickness.^{35–39} Actually, the differences in the growth rates of the different facets are the main source for the changes in the permittivity constant in the second regime.

Accordingly, we conclude that controlling the concentration of state C in the second regime enables control of the generated 2-D Au flakes. Indeed, as shown in Fig. 6, the 2-D flakes can be tuned from the nanoscale to the microscale by adjusting the concentration of state C (factor scale, Fig. 6a).

We found that by increasing the state concentration by a factor of 10, it resulted in an increase in flake area by 10^{6} orders of magnitude (from an area of nanometer size, 250 nm^{2}, to one of millimeter area size, 0.006 mm^{2}, Fig. 6a and b). These results are based on the SEM analysis of 10^{6} particles, as shown in Fig. 6c. The solution color darkened as a function of the factor scale (see inset in Fig. 6). The differences in color are due to the higher concentration of state C that was produced over the course of the reaction.

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## Footnotes |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c9na00636b |

‡ PN and AS are equally contributed. |

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