Au Nanoparticle Synthesis Via Femtosecond Laser-Induced Photochemical Reduction of [AuCl4]−

Laser-assisted metallic nanoparticle synthesis is a versatile “green” method that has become a topic of active research. This chapter discusses the photochemical reaction mechanisms driving AuCl4 1⁄2 reduction using femtosecond-laser irradiation, and reviews recent advances in Au nanoparticle size-control. We begin by describing the physical processes underlying the interactions between laser pulses and the condensed media, including optical breakdown and supercontinuum emission. These processes produce a highly reactive plasma containing free electrons, which reduce AuCl4 1⁄2 , and radical species producing H2O2 that cause autocatalytic growth of Au nanoparticles. Then, we discuss the reduction kinetics of AuCl4 1⁄2 , which follow an autocatalytic rate law in which the firstand second-order rate constants depend on free electrons and H2O2 availability. Finally, we explain strategies to control the size of gold nanoparticles as they are synthesized; including modifications of laser parameters and solution compositions.


Introduction
The unique chemical and physical qualities of metallic nanoparticles have attracted the attention of researchers. Their size-and shape-dependent optical properties make them especially appealing due to the potential technological applications [1][2][3][4]. In particular, gold nanoparticles (AuNPs) have strong absorptions in the visible spectrum that come from the collective oscillations of surface conduction-band electrons as they interact with light, which is called the surface plasmon resonance (SPR). The dependence of the SPR absorption on particle size and shape opens a range of application possibilities for AuNPs, including surface enhanced Raman spectroscopy [5]; non-invasive diagnostic imaging [2]; photothermal cancer therapy [3,6]; plasmonenabled photochemistry; and catalytic reactions such as water-splitting [7,8]. It is necessary to these ends that the NP sizes and shapes are controllable during synthesis [9,10]. Control can be achieved chemically, by modifying experimental conditions like temperature, reaction time, metal-ion concentration, and the absence or presence of reducing agents and surfactants [2]. Laser-assisted approaches to AuNP fabrication allow the manufacture of "pure" NPs which lack chemical reducing agents or surfactants, making this synthesis method ideal for NPs intended to be used in catalysis, and other electronic, biological or medical applications [11,12].
There are two common approaches to colloidal AuNP synthesis using laser-assisted methods. The first is bulk-metal ablation, in which metal atoms are ejected from the target material and form nanoparticles in solution [13]. The second is by irradiating a metal-salt solution to produce reducing agents via solvent-molecule photolysis [14][15][16]. Controlling nucleation and growth of the nanoparticles during metal-salt reduction by changing laser parameters (focusing conditions, pulse duration, pulse energy, irradiation time), and chemical parameters (metal-ion concentration, solvent composition, presence of capping agents), determines the size, shape, and stability of the colloidal products [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Laser-assisted AuNP fabrication requires a simple setup, which facilitates experimentation [12]. Section 2 of this chapter examines AuCl 4 ½ À reduction under femtosecond-laser irradiation, specifically the microplasma formation that arises from optical breakdown (OB) and super continuum emission (SCE). We review both theoretical models for OB and SCE, and provide experimental measurements of both OB and SCE to show which dominates each set of experimental conditions. In Section 3, we describe the chemical reactions that cause photochemical AuCl 4 ½ À reduction and AuNP formation, and compare them with the observed autocatalytic reduction kinetics. We relate observed first-and second-order autocatalytic rate constants to the availability of reducing species in the microplasma. Lastly, in Section 4, we review recent literature that describes control over AuNP size-and shape-control through manipulation of laser conditions and chemical composition of the solution.

Background: interactions of ultrashort laser pulses with condensed media
In a dielectric medium with a band gap that exceeds the laser photon-energy, ultrashort laser pulses can produce quasi-free electrons in the conduction band by two processes: (1) nonlinear multiphoton ionization and tunneling photoionization [31], and (2) high-kinetic-energy free electron collisions with neutral molecules, causing cascade ionization, also called avalanche ionization [32]. The formation of free electrons initially generates a localized, weakly-ionized plasma [32][33][34], which can initiate optical breakdown (OB), supercontinuum emission (SCE), or both [35][36][37]. This section provides an overview of the theory behind both processes, and some experimental measurements.

Optical breakdown
Optical breakdown (OB) of a transparent dielectric medium occurs when the free-electron density r e in plasma exceeds a critical value, and depends on the peak intensity I of the excitation pulse [32][33][34]. Recent experiments in water have quantified the critical value for r e as the threshold for cavitation-bubble formation at r e ¼ 1:8 Â 10 20 cm À3 [38]. In order to calculate the electron density resulting from the laser-medium interaction, media such as water and other solvents are typically modeled as a dielectric, with band gap Δ. For water, the band gap is usually specified as Δ ¼ 6:5 eV [33,34], although some recent experiments have placed the effective band gap as high as 9.5 eV for direct excitation into the conduction band [39,40].
Conventionally, the laser pulse propagates in the z direction with a time-dependent Gaussian intensity envelope based on the focusing conditions [41], where P t; z ð Þ is the time-dependent power density, A z ð Þ the cross-sectional area, E p the pulse energy, τ p the pulse duration, c the speed of light, w 0 the beam waist at the focus, and z R the Rayleigh range.
The time evolution of the free-electron density r e produced by the laser-water interaction is governed by the differential equation [33] ∂r e ∂t ¼ W photo þ W casc r e À W diff r e À W rec r 2 e : Free electrons are produced according to the photoionization rate W photo and cascade ionization rate W casc , while electrons are lost from the focal volume at diffusion rate W diff , and recombination rate W rec . The specific formulas describing each rate are reviewed elsewhere [33,34].
At a given laser wavelength, the peak-intensity needed to reach critical electron density for OB is highly dependent on pulse duration, due to the interplay between the photoionization and cascade ionization rates [33,34]. To illustrate this effect over a wide range of pulse durations used in recent AuCl 4 ½ À photochemical reduction studies [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], Eq.(2) coupled to the appropriate formulas for each rate [33,34] was solved using the Runge-Kutta integrator ode45 incorporated into MATLAB, as in our previous work [16]. The critical electron density threshold was taken to be the recently reported experimental value r e ¼ 1:8 Â 10 20 cm À3 [38]. Figure 1(a) shows the calculated time-dependent electron density r e t ð Þ for pulses at intensity I ¼ 10 13 W cm À2 with durations of 30 fs (dark blue), 100 fs (light blue), 200 fs (green), 1.5 ps (orange), and 36 ps (red). The value of zero on the abscissa corresponds to the center of the pulse, and the time is normalized to the respective pulse durations. The dashed line at r e ¼ 1:8 Â 10 20 cm À3 indicates the OB threshold. The rise in peak electron density with pulse duration results from the increased contribution of cascade ionization to the formation of free electrons as the pulse lengthens [33,34]. As a result, the threshold intensity to achieve OB decreases by two orders of magnitude as the pulse duration is increased from 30 fs to 36 ps (inset, Figure 1(a)).
The high pulse-energies of up to 5 mJ and tight-focusing conditions often used in AuCl 4 ½ À reduction experiments [14][15][16][17][18][19][20][21] produce peak intensities that significantly exceed the OB threshold. For instance, irradiation with 1 mJ pulses under the conditions described above results in a peak electron-density that surpasses the OB threshold by at least factor of 50 and even exceeds the maximum electron-density of 4 Â 10 22 cm À3 achievable in liquid water [42] for shorter pulses (dotted line, Figure 1(b)). Thus, to model the availability of electrons for AuCl 4 ½ À reduction, it is of primary importance to estimate the plasma volume in which the electron-density exceeds the OB threshold. The plasma volume may be estimated by calculating the critical distance z crit in front of the focus where the OB threshold is exceeded. The value of z crit for a given pulse energy, duration, and focusing-geometry may be calculated by solving Eq. (2) for a Gaussian beam in Eq. (1) at a series of propagation distances z < 0 cm (i.e., before the focal spot at z ¼ 0 cm) in order to determine the highest electron density achieved. The resulting peak electron-density as a function of z is shown for the series of 1 mJ pulses from Figure 1 Figure 1(c). As the pulse duration decreases, OB begins farther from the focus, with z crit increasing from 0.1 cm for 36 ps pulses to 0.3 cm for 30 fs pulses. This result shows that the plasma volume, which is proportional to z 3 crit , depends strongly on both pulse energy and duration in a given experiment. Our earlier simulations have shown that for a series of pulse durations with the same focusing-geometry, z crit grows with peak-intensity as z crit ∝ I 1=2 , meaning that the plasma volume grows as I 3=2 [16]. As discussed below, the growth of plasma volume is directly proportional to the AuCl 4 ½ À reduction rate.

Supercontinuum emission and filamentation
The filamentation process leading to SCE arises from self-focusing of the laser pulse in a nonlinear Kerr medium. A full discussion of the details of nonlinear light propagation leading self-focusing is beyond the scope of this work and may be found in Refs. [35][36][37]. Briefly, filamentation depends on the laser power P and is initiated when P exceeds the critical power P crit [37,43] where λ is the laser's wavelength, n 0 is the refractive index of the medium, and n 2 characterizes the intensity-dependent refractive index n ¼ n 0 þ n 2 I. In water, P crit has been measured at 4:2 Â 10 6 W for 800 nm pulses [44], which translates into very modest pulse energies of 0.13 and 0.42 μJ at 30 and 100 fs. Filamentation causes spectral broadening to both the red and blue of the laser wavelength. A red-shift is caused by rotational and vibrational motion of the molecules in the medium, and a blue-shift happens when the power P is high enough to form a shockwave at the trailing temporal edge of each pulse [36]. Blue-shifts produce a broad pedestal as far as 400 nm in the output-spectrum for pulses shorter than 100 fs [16,27,28,[35][36][37]45] (see also Figure 2). Because SCE depends on power instead of peak intensity, filamentation may occur at intensities below the OB threshold; especially when the laser beam is weakly-focused or collimated [35][36][37][45][46][47][48][49]. For laser beams with peak-intensities on the order of 10 12 W cm À2 , the filament electron-density has been measured at 1 À 3 Â 10 18 cm À3 [48,49]. Such weaklyionized SCE plasmas can drive AuCl 4 ½ À reduction even in the absence of OB [26][27][28], while the white light from the SCE has been shown to induce AuNP-fragmentation by resonant absorption and Coulomb explosion [45][46][47].

Experimental measurement of OB and SCE
The presence of OB and SCE may be measured with a spectrometer arranged as shown in Figure 2(a) [35,36]. To detect OB from light that has scattered off of the OB plasma, the fiber mount is placed at a 90 ∘ angle to the laser beam (geometry (i) in Figure 2(a)) and a series of lenses focuses the light into the fiber mount. For SCE detection, the fiber mount is placed along the beam path, behind the sample (geometry (ii) in Figure 2(a)). A diffuser is attached to the fiber mount to avoid saturating the spectrometer. For tightly focused beams, OB is expected at any pulse duration, and SCE may also be present if the pulse is short. When the beam is loosely-focused or collimated, only SCE is expected.
To illustrate the conditions in which OB, SCE, or both are present, tightly focused pulses [16] and unfocused, collimated pulses [28] were measured using the setup in Figure 2(a). Figure 2 shows spectra obtained at detector (i) for tightly focused 30 and 1500 fs pulses at 0.3 and 0.03 mJ pulse energy. The broadened spectrum for 30 fs pulses indicates the presence of SCE along with OB, while the narrow spectrum with 1500 fs pulses indicates that no SCE occurs. Figure 2(c) and (d) show SCE spectra obtained for 30 fs pulses at a series of pulse energies for tightly focused and collimated pulses. Under both conditions, asymmetric broadening towards the visible region of the spectrum grows with increasing pulse energy. The spectral broadening saturates for tightly focused pulses at energies above 1.2 mJ (Figure 2(c)), while greater pulseenergies would be needed to saturate the spectral width for unfocused pulses (Figure 2(d)). No OB is observed when the beam is collimated, indicating that a low-density plasma (LDP) with r e $ 10 18 cm À3 is present in the filaments [48,49]. LDP conditions have been used by research groups to control the synthesis of AuNPs [26,28,45,50].

Reactions of water
The key role that water photolysis plays, in the photochemical reduction of AuCl 4 ½ À and other metal salts, is well-established [14-22, 26, 27], and supported by the presence of H 2 , O 2 , and H 2 O 2 as water is irradiated with high-intensity femtosecond laser pulses [14,19,51]. Two common mechanisms proposed to explain the reduction of aqueous AuCl 4 ½ À under highintensity laser irradiation are (a) direct homolysis of the Au-Cl bond by multiphoton absorption to form Au(II) and Au(I) intermediates, and (b) chemical reduction of Au(III) ions by the reactive species formed from water photolysis [15][16][17][18][19]26]. Since the number of water molecules far surpasses the number of AuCl 4 ½ À molecules in solution, the second proposed mechanism is more likely for AuCl 4 ½ À reduction to Au(0) in aqueous solutions. The photolysis reactions involved include [27,[52][53][54][55] Although both hydrated-electrons and hydrogen radicals are capable of reducing AuCl 4 ½ À , the fast consumption of H. via Eq. (9) observed in water photolysis using picosecond pulses [53] suggests an inconsequential contribution by H. to AuCl 4 ½ À reduction. In contrast, hydrated electrons may be formed from both the free electrons generated in OB plasma via Eq. (5) within several hundred femtoseconds [54,55], and from the reaction of water with H. via Eq. (9). Hydrated electrons have lifetimes of up to hundreds of nanoseconds in pure water [56] and react with AuCl 4 ½ À with a diffusion-controlled rate constant of 6:1 Â 10 10 M À1 s À1 [57]. Therefore, hydrated electrons are the dominant AuCl 4 ½ À reducing agent through the reaction [27] Another product of water photolysis, H 2 O 2 , is generated from the recombination of two hydroxyl radicals via Eq. (8) and drives AuCl 4 ½ À reduction and AuNP formation [15,16,19,20]. Tangeysh et al. explored the role that H 2 O 2 played in AuCl 4 ½ À reduction by monitoring the UV-vis absorbance of AuCl 4 ½ À samples after laser-irradiation termination, but before all of the AuCl 4 ½ À had been consumed [19]. They explained the post-irradiation AuCl 4 ½ À reduction and SPR absorbance-peak growth by proposing that the H 2 O 2 produced during irradiation reduced the remaining AuCl 4 ½ À , in the presence of the existing AuNPs [19]. This hypothesis was developed further by Tibbetts et al. [15] where the existing AuNPs act as a catalyst for AuCl 4 ½ À reduction. This process underlies the observed autocatalytic reduction kinetics of AuCl 4 ½ À .

Kinetics
Controlling the sizes and shapes of AuNPs starts with kinetic control of their nucleation and growth. LaMer's nucleation theory, developed in 1950 [60], was used to describe AuNP formation first [4,9,61], but Turkevich's studies [62] on reduction of HAuCl 4 using sodium citrate yielded more appropriate AuNP formation-mechanisms, including autocatalysis [62][63][64] and aggregative growth [65,66]. In 1997, Watzky and Finke described the reduction of transition metal salts using H 2 , undergoing slow, continuous nucleation accompanied by fast, autocatalytic surface growth to form nanoparticles. They described this mechanism using a quantitative, two-step rate law [67], where [A] is the precursor (metal salt) concentration, [B] is the metal nanoparticle concentration, k 1 is the rate constant of metal-cluster nucleation (slow) and k 2 is the rate constant of autocatalytic growth of the nanoparticles (fast) [67,68]. Integration of Eq. (12)   where [A(0)] is the initial precursor concentration. The rate law in Eq. (13) has been used to describe AuNP formation from reducing ionic precursors via wet chemical routes [67][68][69] and for femtosecond laser-induced AuCl 4 ½ À reduction under a variety of laser conditions and solution compositions [15,16,26,28]. Eq. (14) follows if it is assumed that the conversion of Au(III) to Au(0) is fast enough that no significant concentration of intermediate species like Au(I) builds up.
The time-dependent concentrations of AuCl 4 ½ À and AuNPs needed to determine the reaction kinetics may be obtained from in situ UV-vis spectra recorded during laser irradiation [15]. Figure 3(a) displays representative absorbance spectra of AuCl 4 ½ À after different irradiation times. The arrow labeled 250 nm corresponds to the decrease in the LMCT band of AuCl 4 ½ À , while the arrow labeled 450 nm corresponds to the growth of AuNPs [15,16,70]. To obtain the time-dependent AuCl 4 ½ À concentration in Eq. (13), the absorbance of AuCl 4 ½ À is monitored at λ = 250 nm. Because AuNPs also absorb across the UV range, the absorbance at 250 nm corresponds to the absorbance contributions from both the AuCl 4 ½ À precursor and AuNP product species. The AuCl 4 ½ À contribution can be isolated from the 250 nm absorbance by subtracting off the AuNP contribution, as described in previous work [15,16]. Alternatively, monitoring the absorbance at λ ¼ 450 nm where only the AuNPs absorb [70] [16]. The dots denote the experimental data, and the solid lines are fits to Eq. (13) (Figure 3(b)) or Eq. (14) (Figure 3(c)). The disappearance rate of AuCl 4 ½ À and growth rate of AuNPs mirror each other, showing that the rate constants may be extracted from fitting either spectral absorbance. In practice, small amounts of intermediate species such as Au(I) are present during photochemical reduction [15], so the rate constants extracted from fitting the normalized 450 nm absorbance to Eq. (14) are 20 À 50% lower than those from fitting the normalized 250 nm absorbance to Eq. (13).
The third rate constant, k 3 , is zeroth order with respect to the AuCl 4 ½ À concentration, and was suggested arise due to limited availability of reducing species from photolysis of the solvent [15]. This rate equation more accurately fits the reduction kinetics when the laser beam is collimated such that LDP conditions are present [28], as shown in Figure 3(d). When the pulse energy is sufficiently low (2.4 mJ), the AuNP growth was significantly slower due to agglomeration of the formed nanoparticles; therefore, only the first portion of the experimental data was fit to Eq. (16). Similar agglomeration has been observed in other experiments conducted under LDP conditions, in which the initial portion of experimental data was fit to Finke-Watsky kinetics [26].
Extracting the rate constants at a series of experimental conditions (e.g., solution pH [15], pulse energy [16,28]) provides significant insight into the roles that the reactions in Eqs. (4)-(9) play in the conversion of AuCl 4 ½ À to AuNPs. Figure 4(a) and (b) show the rate constants k 1 and k 2 extracted from fits to Eqs. (13) and (16), respectively, for tightly focused and collimated 30 fs pulses, as a function of pulse energy (proportional to peak intensity I) [16,28]. In the log-log plots, the slopes of the least squares fit lines denote the power law dependence of each rate constant on the peak intensity. For the tight focusing geometry in Figure 4(a), the nucleation rate constant grows as k 1 $ I 1:6AE0:2 ð Þ , a factor of three faster than the growth of the autocatalytic rate constant k 2 $ I 0:56AE0:02 ð Þ . In contrast, under LDP conditions, k 1 , k 2 , and k 3 all grow approximately as I 4 (Figure 4(b)).
The power law dependence of k 1 under tight-focusing conditions corresponds to the growth of the OB plasma volume V with peak-intensity I as V $ I 1:5 calculated via Eq. (2) (c.f., Section 2.1) [16]. Figure 4(c) shows that k 1 $ V for pulse durations ranging from 30 to 1500 fs under tight-focusing conditions. This result demonstrates the that the production of hydrated electrons an OB plasma controls the rate of nucleation of AuCl 4 ½ À . The higher sensitivity of k 1 $ I 4 under LDP conditions [28] is consistent with the electron density in LDP conditions being proportional to the multiphoton order required for ionization of the medium [37], where 5 photons at 800 nm are needed to ionize water [34]. The importance of hydrated electrons to AuCl 4 ½ À reduction has been demonstrated in two other works [15,26]. The addition of N 2 O as a hydrated electron scavenger to aqueous AuCl 4 ½ À significantly lowers the value of k 1 in Eq. (14) with respect to k 2 , thereby isolating the contribution of hydrated electrons to AuCl 4 ½ À nucleation [26]. Increasing the solution pH of aqueous AuCl 4 ½ À through addition of KOH significantly increases k 1 [15], which is consistent with previous findings that the lifetimes of hydrated electrons are suppressed in acidic solution [55].
Under both tight-focusing and LDP conditions, the power law dependence of k 2 corresponds to the formation rate of H 2 [28]. Both correlations between H 2 O 2 ½ and k 2 are shown in Figure 4(d). These results are consistent with other work in which the addition of the OH. scavenger 2-propanol [26] resulted in increased k 1 values relative to k 2 values and slower growth of AuNPs.
The kinetics results quantifying the dependence of both nucleation and autocatalytic growth rate constants demonstrate the importance of both short and long-lived reducing species to control the formation of AuNPs via photochemical reduction of aqueous AuCl 4 ½ À . The reactive species produced during water photolysis can be controlled by changing both the laser irradiation conditions [16,28] and the chemical composition of the AuCl 4 ½ À solution [15,26]. The following section will review how changing both of these reaction conditions can control the size and shape of the synthesized AuNPs.

Controlling Au nanoparticle sizes
Several recent articles have reported some degree of control over the size of AuNPs synthesized by photochemical reduction of AuCl 4 ½ À through the manipulation of experimental conditions: broadly, the laser parameters and solution composition. The focusing-geometry, pulse energy, and pulse duration determine the generation of OB and SCE, which direct AuNP growth [16,20,28]. Adding scavengers and modifying the solution pH also change the AuCl 4 ½ À reduction kinetics, and therefore, particle size [15,26]. Finally, adding capping can produce smaller AuNPs [14,19,20,29,30].

Focusing-geometry
Focusing-geometries influence the nature of the nonlinear interactions between the laser and solution (c.f., Section 2). Without strong-focusing, SCE yields a LDP environment containing electron-densities on the order of r e $ 10 18 cm À3 . This setup has been used for photochemical AuCl 4 ½ À reduction [26,28] experiments and Au ablation [45,50] experiments. LDP conditions seem well-suited to applications like AuNP synthesis, because second-order reactions are suppressed, including those that yield H 2 O 2 [26,50]. Without abundant reducing species, AuCl 4 ½ À to AuNP conversion is slow. Many research groups opt to use a focused-geometry [14][15][16][17][18][19][20], which yield electron densities that exceed the OB threshold, $ 10 20 cm À3 . Low numerical aperture (NA) geometries produce SCE through self-focusing and filamentation processes. These processes can cause intensity-clamping, which stops the intensity from exceeding I $ 10 13 W cm À2 [37], and limits the number of reactive species available for reduction [20]. In contrast, tight-focusing (high-NA) geometries, simultaneous spatial and temporal focusing (SSTF) [71], or spatial beam-shaping [72] can avoid excessive filamentation and intensity clamping. In Au nanoparticle synthesis, tight-focusing [14,16,18] and SSTF [15,19,20], where the frequency components of the laser pulse are spatially separated prior to focusing, have both been used for this purpose. Figure 5 shows schematic diagrams (top) and photographs (bottom) of fs-laser irradiation of water using (a) collimated beam geometry [28], (b) low-NA focusing [20], (c) high-NA focusing [16], and (d) SSTF [19]. The absence of visible filaments in panels (c) and (d), compared to (b), suggest less intensity-clamping, and so a higher peakintensity at the focal spot.
Another phenomenon to consider when experimenting with focusing-conditions is cavitation bubble formation, which happens when the OB electron-density threshold is exceeded [38].
The generated cavitation bubbles are sensitive to the shape of the laser-plasma [20,72]. Under low-NA focusing-conditions with filamentation and SCE, the bubbles are ejected from the focus with low kinetic energy, seen as a small stream of bubbles rising from the center of the cuvette in Figure 5(b). This condition results in inefficient and asymmetrical mixing-dynamics of the reactive species throughout the solution, but can be improved with the addition of a magnetic stir-bar [20]. Similarly, a stir bar is needed when operating under LDP conditions to ensure that the solution is being mixed [26,28]. Both high-NA focusing and SSTF produce more spherical plasmas, which eject high kinetic energy bubbles into solution radially [72], causing turbulent mixing of the reactive species into the solution (evident in Figure 5(c)) and removing the need for stirring [16,20]. The complex interactions between high-intensity fs laser pulses and aqueous solution result in the particle size being sensitive to different focusing-conditions. Table 1 summarizes the results of AuNP syntheses prepared in aqueous solutions without capping agents across focusing conditions. Of the reported sizes, the largest AuNPs resulted from the LDP conditions [26,28], which limits production of the reducing species, driving AuNP formation through aggregative growth and agglomeration. Smaller AuNPs were formed with the high-NA focusing conditions [16,18], which produces high electron-densities because of tight laser-focus; filamentation is suppressed, and the reducing species (electrons and H 2 O 2 ) are thoroughly mixed throughout the solution by the OB plasma. In combination, these conditions generate many Au(0) seeds but limit Au(III) ions. SSTF and low-NA focusing-geometries create intermediate AuNP sizes. The SSTF focusing-geometry improves size-distribution because it mixes the reactive species well with its spherical plasma [20]. Adjusting the laser's focus-geometry has a strong influence on both the production rate and spatial distribution of the reducing species required for AuNP formation, and yields another dimension of control over particle sizes.

Pulse energy and duration
Several studies on focusing-conditions have demonstrated that increasing the pulse energy reduces AuNP size [16,20,28]. When tight-focusing geometry was used, increasing the energy of a 30 fs pulse from 0.15 mJ to 2.4 mJ decreased AuNP size from 6:4 AE 5:6 nm to 3:5 AE 1:9 nm [16] (Figure 6(a) and (b)). This trend was also seen when LDP conditions were used: increasing the energy of 30 fs pulses from 2.7 to 3.3 mJ reduced AuNP size from 27 AE 7 to 14 AE 6 nm [28] ( Figure 6(c) and (d)). These results are consistent with earlier reports using SSTF with 36 ps pulses to irradiate solutions of AuCl 4 ½ À and polyethylene glycol (PEG), a capping agent. Increasing the pulse energy from 0.45 mJ to 1.8 mJ reduced the average particle size from 9:6 AE 2:7 to 5:8 AE 1:1 nm [20].
While the pulse energy strongly influences the size of the AuNPs from photochemical reduction of AuCl 4 ½ À , the pulse duration, or linear frequency chirp, has at most a modest effect on the AuNP size at a fixed pulse energy and focusing condition [16,20]. Under tight focusing conditions, stretching the pulse duration was stretched from 30 to 1500 fs (negatively chirped) at a 0.15 mJ pulse energy slightly decreased the AuNP sizes from 6:4 AE 5:6 to 4:4 AE 4:0 nm [16]. When the experiment was repeated at a high pulse energy (2.4 mJ), the AuNP size increased from 3:5 AE 1:9 nm for 30 fs pulses to 6:3 AE 2:4 nm for 1500 fs pulses [16]. In a separate experiment using low-NA focusing conditions, 1.8 mJ pulses with chirp coefficients of þ20; 000 fs 2 , 0 fs 2 , and À20; 000 fs 2 (corresponding to 35 fs unchirped pulses and 2 ps chirped pulses) produced 8:2 AE 3:5, 8:1 AE 3:4, and 8:1 AE 6:5 nm AuNPs, respectively [20]. Collectively, these results suggest that that for sufficiently high peak intensities generating OB conditions, the pulse duration does not significantly affect the size of AuNPs produced by photochemical reduction of AuCl 4 ½ À .

Scavengers
Water photolysis produces reactive species, which govern AuCl 4 ½ À reduction and therefore AuNP formation. To manage particle growth, radical scavengers can be added to solution. As summarized in Section 3, it is primarily the hydrated electrons that reduce AuCl 4 ½ À (Eq. (10)). H 2 O 2 (formed by the recombination of two hydroxyl radicals (Eq. (8)), facilitates autocatalytic particle growth (Eq. (11)). Scavengers can selectively hinder the production of water photolysis byproducts such as H 2 O 2 [73], so they have been used to control reduction kinetics [26].
The hydrated-electron scavenger N 2 O, and hydroxyl radical scavengers 2-propanol and ammonia, were originally studied in water radiolysis using X-rays and γ rays [74]. More recently, they have been used to control the photochemical synthesis of Au and Ag nanoparticles in femtosecond-laser plasmas [21,26,73,75]. The addition of N 2 O to aqueous AuCl 4 ½ À is expected to limit the availability of hydrated electrons and slow the AuCl 4 ½ À reduction rate, forming fewer Au(0) nuclei in solution. This situation would result in a significant number of Au(III) ions being reduced on the surface of the Au(0) nuclei in the presence of H 2 O 2 , promoting the surface- mediated autocatalytic growth into larger AuNPs. In contrast, the addition of a hydroxyl radical scavenger such as 2-propanol should not only limit the production of H 2 O 2 via Eq. (8), but also prevent the quenching of hydrated electrons via Eq. (6). As a result, AuCl 4 ½ À reduction should be fast and autocatalytic AuNP growth should be limited, resulting in smaller AuNPs. These predictions have been laid out in recent literature [21,26].
Belmouaddine et al. [26] investigated the effect of adding N 2 O or 2-propanol to aqueous AuCl 4 ½ À solutions they irradiated with 1.35 mJ, 112 fs pulses. They monitored the reduction kinetics to determine the k 1 and k 2 rate constants in Eq. (13). By comparing the k 2 /k 1 ratios obtained in the two scavenger experiments, they were able to relate each scavenger to its role in the reduction and autocatalytic growth processes. In the presence of the hydrated-electron scavenger N 2 O, the k 2 /k 1 ratio was two orders of magnitude higher than it was when the radical scavenger 2-propanol was used. This is consistent with the dependence of k 1 and k 2 on hydrated-electrons and H 2 O 2 , discussed in Section 3. The resulting AuNPs synthesized in the presence of N 2 O and 2-propanol were 54:4 AE 9:8 nm, and 28:5 AE 5:9 nm. These results are consistent with the predictions that (1) slow nucleation and significant autocatalytic growth in the presence of N 2 O will produce large AuNPs, and (2) fast nucleation and limited autocatalytic growth in the presence of 2-propanol will produce small AuNPs.
In another study, Uwada et al. [21] investigated the effects of alcohols (1-propanol, 2-propanol, ethanol) on aqueous AuCl 4 ½ À solutions irradiated with 120 fs pulses, using a series of pulse energies from 1 to 50 μJ. At low pulse energies, with intensity below 7Â10 15 W cm À2 , no AuNPs formed if there were no alcohols. AuNP size-dependence on the pulse energy followed the opposite trend to that observed in Refs. [16,20] and discussed in Section 4.1.2: the AuNPs formed in solutions containing 1-propanol increased in diameter from 24 to 37 nm when the intensity increased from 2 Â 10 15 to 7 Â 10 15 W cm À2 [21]. The authors proposed that the alcohol radicals formed from the OH. scavenging reaction act as the primary reducing agents of AuCl 4 ½ À at low laser intensities where few hydrated electrons are formed. These results suggest that radical scavengers not only manage the AuNP size, but also boost photochemical reduction of AuCl 4 ½ À into AuNPs at lower laser intensities by providing an additional free-radical reducing agent.

pH
Changing the pH of irradiated aqueous AuCl 4 ½ À solutions by adding either HCl or KOH affects both the reduction kinetics and the resulting AuNP sizes [15]. Solution pH is well known to affect Au(III) complex speciation: AuCl 4 ½ À dominates under acidic conditions, Au OH ð Þ 4 Â Ã À dominates under basic conditions, and mixtures of AuCl species exist under neutral conditions [76,77]. Different complex stabilities were thought to be the driving force for Au(III) reduction with chemical reducing agents, where Au OH ð Þ 4 Â Ã À was less reactive because of stronger Au-OH bonds, compared to Au-Cl bonds [76,77]. With increasing pH, as solution was irradiated with 36 ps, 2.5 mJ pulses under SSTF focusing conditions, the reverse trend occurred, and higher AuCl 4 ½ À reduction rates formed smaller AuNPs [15]. At low pH, the hydrated-electron lifetime is reduced [55] and H 2 O 2 oxidizes AuNPs [78], causing a slow AuCl 4 ½ À reduction rate that produced large, polydisperse 19:4 AE 7:1 nm AuNPs (at pH 2.5). When pH was higher (pH 5.4), the hydrated-electron lifetime is longer [55] and the oxidation potential of H 2 O 2 increases as it is deprotonated to HO 2 À [59], leading to faster reduction of AuCl 4 ½ À and small AuNPs with size distributions of 4:8 AE 1:9 nm. Slightly larger 6:6 AE 3:1 nm AuNPs were formed at pH 8.4 due to the acceleration of the autocatalytic growth rate constant k 2 in Eq. (13).
For comparison with the results in Ref. [15], experiments performed in our laboratory using the tight-focusing conditions in Ref. [16] also showed that the AuNP size depends on solution pH. Aqueous solutions (0.1 mM KAuCl 4 ) with varying amounts of KOH (up to 0.75 mM, pH 4.0-9.3) were irradiated with 50 μJ, 30 fs pulses for 10-33 min, sufficient to convert all AuCl 4 ½ À to AuNPs. The UV-vis spectra recorded when the conversions of AuCl 4 ½ À to AuNPs were completed are shown in Figure 7(a). As the solution pH increases, the SPR feature blueshifts and decreases in intensity, indicating the production of smaller AuNPs [70]. TEM analysis of the AuNPs synthesized at pH 4.0, 5.2, and 9.3 (Figure 7(b)-(d)) agreed. At pH 4.0, there is a distinct bimodal size-distribution, with a number of small (< 4 nm) AuNPs and a broad distribution of particles to as large as 65 nm. As a result, a meaningless statistical sizedistribution of 8:6 AE 12:4 nm is obtained. At pH 5.2, there is a bimodal distribution centered at 3 and 18 nm, with a size-distribution of 8:6 AE 6:7 nm. The most monodisperse AuNPs are seen at pH 9.3, with a size-distribution of 9:2 AE 4:5 nm. The slightly larger average AuNP size is because there are very few < 4 nm particles compared to what had been seen at lower pH. This absence of extremely small particles is likely due to the high concentration of H 2 O 2 produced in the plasma, as discussed in Ref. [15].

Capping agents
One of the most widely used strategies for controlling AuNP size during chemical synthesis is the addition of capping agents, including polymers and surfactants, to stop particle growth [2]. Increasing the molar ratio of a capping agent to Au(III) salt typically results in smaller AuNPs in chemical syntheses [79]. A similar trend is observed for femtosecond laser-based syntheses of AuNPs, as shown in Table 2. Nakamura et al. [14] found that addition of polyvinylpyrrolidone (PVP) to aqueous HAuCl 4 decreased AuNP size and gave a tighter size-distribution, Figure 7. UV-vis spectra (a) and TEM images with size distributions (b)-(d) of AuNPs synthesized at different solution pH using the experimental setup in ref. [16]. up to a 0.1:1 PVP:Au ratio. Tangeysh et al. [19] used poly(ethylene glycol) (PEG 45 , n ¼ 45) and found an optimal PEG 45 :Au ratio of 0.25:1. The same trend is observed when femtosecond pulses are used to ablate an Au target [45], where the smallest particles made from irradiating AuNPs in solutions of varied dextran concentrations were optimized at a dextran:Au ratio of 0.05:1.
In addition to controlling AuNP size in femtosecond laser-based syntheses, capping agents like PEG 45 [19], chitosan (a cationic polysaccharide) [29], and (2-hydroxyethyl) trimethylammonium glycinate ([HETMA][Gly], an ionic liquid) [30] accelerate the conversion of AuCl 4 ½ À to AuNPs. It was proposed that fragmentation of PEG 45 in the laser-generated plasma produces alcohol radicals (analogous to Eq. (17)) that can reduce AuCl 4 ½ À and accelerate AuNP formation [19]. The formation of AuNPs in the presence of chitosan correlates with the oxidation of hydroxyl groups on the chitosan [29], indicating that the chitosan contributes to AuCl 4 ½ À reduction. The [HETMA][Gly] forms a complex with AuCl 4 ½ À , which facilitated its reduction under OB conditions with tight-focusing [30]. These results suggest the potential of selective control over both AuCl 4 ½ À reduction kinetics and AuNP size through careful choice of capping agents and their concentrations.

Conclusion
Photochemical reduction of AuCl 4 ½ À using femtosecond laser irradiation is a simple, green method for controlling the growth of AuNPs. This chapter presented a review of the physical and chemical mechanisms of aqueous AuCl 4 ½ À transformation to AuNPs, from the physical  processes occurring in plasma to AuNP size-control through selective tailoring of the solution composition. In Section 2, we discussed the physical processes of OB and SCE that occur because of ultrafast laser irradiation of water. The time-dependent electron density generated in OB plasma was modeled in relation to laser intensity, and the role that electrons play in AuCl 4 ½ À reduction were explained in Section 3. Reactive species produced in OB plasma were identified, and their roles in the kinetically controlled photochemical reduction of AuCl 4 ½ À (electrons ∝ k 1 ) and surface-mediated autocatalytic growth into AuNPs (H 2 O 2 production ∝ k 2 ) were quantified and discussed. Finally, in Section 4, these approaches to control the size of AuNPs were reviewed. Both laser parameters (focusing-geometry, pulse energy, and duration) and solution modifications (pH, adding scavengers or capping agents) were discussed in how they affected the chemical system and reaction mechanism, allowing for size-control of AuNPs. Laser parameters and solution composition both play significant roles in the formation and resulting size of AuNPs, and this chapter highlights these considerations to direct future research.