Understanding the Seed-Mediated Growth of Gold Nanorods through

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Understanding the Seed-Mediated Growth of Gold Nanorods through a Fractional Factorial Design of Experiments Nathan D. Burrows,* Samantha Harvey, Fred A. Idesis, and Catherine J. Murphy* Department of Chemistry, 600 S. Mathews Avenue, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States

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S Supporting Information *

ABSTRACT: Since the development of simple, aqueous protocols for the synthesis of anisotropic metal nanoparticles, research into many promising, valuable applications of gold nanorods has grown considerably, but a number of challenges remain, including goldparticle yield, robustness to minor impurities, and precise control of gold nanorod surface chemistry. Herein we present the results of a composite fractional factorial series of experiments designed to screen seven additional potential avenues of control and to understand the seed-mediated silver-assisted synthesis of gold nanorods. These synthesis variables are the amount of sodium borohydride used and the rate of stirring when producing seed nanoparticles, the age of and the amount of seeds added, the reaction temperature, the amounts of silver nitrate and ascorbic acid added, and the age of the reduced growth solution before seed nanoparticles are added to initiate rod formation. This statistical experimental design and analysis method, besides determining which experimental variables are important and which are not when synthesizing gold nanorods (and quantifying their effects), gives further insight into the mechanism of growth by measuring the degree to which variables interact with each other by mapping out their mechanistic connections. This work demonstrates that when forming gold nanorods by the reduction of auric ions by ascorbic acid onto seed nanoparticles, ascorbic acid determines how much gold is reduced, and the amount of seeds determine how it is divided, yet both influence the intrinsic growth rates, in both width and length, of the forming nanorods. Furthermore, this work shows that the reduction of gold proceeds via direct reduction on the surface of seeds and not through a disproportionation reaction. Further control over the length of gold nanorods can be achieved by tuning the amount of silver nitrate or the reaction temperature. This work shows that silver does not directly influence rod length or width, and a new primary role for silver is proposed as a catalyst promoting the reduction of gold on the ends of forming nanorods. Furthermore, this silver catalyst is removed from the reaction by adsorption onto the surface of the growing nanorod. This work also demonstrates the importance of freshly prepared silver nitrate and ascorbic acid solutions, free from even a few hours of photodegradation, in preparing gold nanorods with high shape purity and gold yield.

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INTRODUCTION

optical extinction spectrum for a suspension of gold nanorods is strongly influenced by the aspect ratio of the gold nanorods. Gold nanorods were initially prepared using electrochemical methods in a hard template of porous alumina or polycarbonate membranes.30,31 This was followed by the development of a more accessible three-step seeded growth synthesis that results in rods with aspect ratios (length/width) of between 8 and 20 with absolute dimensions of (150−1800 nm) × 25 nm.13−15 In the decade following this development, the method of seeded growth has been extended to other anisotropic shapes and materials and has been improved upon, resulting in many modifications.32−35 These include the development of one-step silver-assisted seeded growth,3,36,37 the addition of small organic additives,38−40 a seedless version,38,41,42 cosurfactants,43 alternative reducing agents, 44−46 and several gram-scale

Research has exponentially exploded in the past two decades concerning the study of gold nanoparticles. Over 17 000 published research articles on gold nanorods alone have appeared since 2005. This level of research activity can be attributed to two primary developments. First is the development of simple, aqueous protocols for anisotropic metal nanoparticle synthesis that have enabled unprecedented access to these nanomaterials for research.1−15 Second is the promise of valuable applications in sensing and plasmon-enhanced spectroscopies,9,16 biomedical imaging,8,17,18 drug/gene delivery,8,16,18−20 and photothermal therapy8,16,18,19,21,22 due to their shape-dependent optical and physical properties. Gold nanorods are also applied in nonbiological applications including optical power limiters,23 solar cells,24,25 light-emitting diodes,26 stress/strain sensors,27,28 and catalysis.29 It is the tunability of these properties through changes in particle dimensions that makes these potential applications possible; for example, the © 2016 American Chemical Society

Received: October 3, 2016 Revised: December 2, 2016 Published: December 5, 2016 1891

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Langmuir syntheses of gold nanorods.38,39,47−49 A more detailed accounting of the history of gold nanorod synthesis and recent developments can be found in numerous review articles.5,7,9,10 The result of this decade of intense research is that the seeded growth approach to synthesizing many inorganic nanomaterials dominates the literature.50−57 Yet, a number of challenges remain. These include an improved gold-particle yield, robustness to minor impurities, and precise control over gold nanorod surface chemistry. Herein we present the results of a composite fractional factorial series of experiments designed to screen seven potential avenues of controlling gold nanorod synthesis. Besides determining which factors are important and which are not when synthesizing gold nanorods, these experiments also give further insight into the mechanism of growth by measuring the degree to which variables interact with each other.

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RESULTS AND DISCUSSION This work focuses on the one-step silver-assisted seeded growth synthesis of gold nanorods.36 The current standard protocol in the Murphy group for preparing cetyltrimethylammonium bromide (CTAB)-capped gold nanoparticle seeds and their subsequent growth into CTAB-capped gold nanorods on a 10 mL scale resulting in approximately 1 mg of nanoparticles (assuming 100% yield) is as follows. First, 250 μL of 0.0100 M chloroauric acid is diluted with 9.75 mL of 0.100 M CTAB and stirred with a magnetic bar. Second, a fresh, cold solution of 0.0100 M sodium borohydride is prepared by dissolving 0.0378 g of sodium borohydride in 10 mL of ice-cold nanopure water and diluting 1 mL of this solution to 10 mL with ice-cold nanopure water. This solution (600 μL) is then immediately injected into the stirring gold solution and stirred for 10 min. This results in a honey-colored suspension of gold nanoparticle seeds that is aged for 1 h so that any excess sodium borohydride may decompose. Third, a nanorod growth solution is prepared by adding varying amounts of 0.0100 M silver nitrate (20−150 μL) to 9.5 mL of 0.100 M CTAB followed by 500 μL of 0.0100 M chloroauric acid and 55 μL of 0.100 M ascorbic acid. At these concentrations, the weak reducing agent ascorbic acid is the limiting reagent. To this growth solution, 12 μL of the prepared seed suspension is added. The formation of color is observed after about 10 min, which grows in intensity over the next hour as gold nanorods form. The product is then collected by centrifugation at 11 000 rcf for 15 min and formed into a pellet, the supernatant is siphoned off, and the pellet is resuspended in nanopure water. This suspension of gold nanorods is typically characterized by optical absorption/ scattering techniques (e.g., ultraviolet−visible−infrared spectroscopy (UV−vis−NIR) and dynamic and phase analysis light scattering techniques) and microscopy (e.g., optical, transmission electron, and scanning electron microscopy). Figure 1 presents a typical set of shape-controlled gold nanorod suspensions produced in an afternoon and characterized by vis−NIR spectroscopy following the standard Murphy protocol. An analysis of the longitudinal localized surface plasmon resonance (LSPR) extinction band as a function of silver nitrate concentration (Figure 1B), from experiments done by one experienced person, shows that although there is a positive correlation between the amount of silver nitrate and the resultant longitudinal LSPR peak wavelength (black fitted line) small incremental increases in silver nitrate do not always correspond to an increase in the peak wavelength and suggest that additional, unintentionally

Figure 1. Vis−NIR spectroscopic analysis of gold nanorods produced via the standard Murphy protocol. (A) Vis−NIR extinction spectra as a function of silver nitrate concentration used in the synthesis of a series of gold nanorod suspensions, with all other synthesis variables being held constant. Inset images are of the corresponding nanorod suspensions. (B) Plot of the longitudinal surface plasmon resonance extinction peak wavelength as a function of silver nitrate concentration employed for the same set of suspensions presented in part A, for experiments done by one experienced person. (C) Plot similar to that in part B showing the synthesis variation by different individuals produced in the Murphy group over the last half-decade when attempting to control the longitudinal absorption peak wavelength by varying only the concentration of silver nitrate. The blue line in part C is the best-fitting power equation by least squares, and the horizontal red line is at 785 nm for illustrative purposes. (See the text for details.)

varied factors influence the longitudinal LSPR peak wavelength. Comparing many product suspensions from over 10 different researchers within our group over the last five years (Figure 1C), including students with different degrees of experience, shows a large degree of variability but still displays a trend of increasing longitudinal LSPR as a function of silver nitrate concentration (blue fitted line). However, the red horizontal line illustrates the difficulty of preparing rods that have an extinction at 785 nm, a typical laser wavelength used in 1892

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one factor influences how another factor affects a response on top of its primary effect, then a factorial design can detect, identify, and estimate this nonadditive, synergistic secondary interaction effect. Table 1 presents the factors studied here,

biomedical research due to the low absorption coefficient of water in this region of the electromagnetic spectrum allowing for deep tissue penetration. For example, an individual researcher could find that a wide range of silver nitrate concentrations, 50 to about 200 μM, would lead to gold nanorods that exhibited a longitudinal plasmon band maximum at 785 nm, with all other concentrations being the same. Many possible sources of variation across researchers were found to occur when executing the standard protocol (in addition to intentionally varying the silver nitrate concentration) that theoretically could contribute to the observed scatter in LSPR wavelength as a function of silver nitrate concentration (Figure 1C). Variation involving the preparation of seed nanoparticles includes (1) the accuracy of the mass of sodium borohydride used because of the adsorption of atmospheric water vapor, (2) the rate of stirring during sodium borohydride addition, and (3) the age of the seed suspension unintentionally varied anywhere from 1 to 48 h when used to prepare gold nanorods. When growing the gold nanorods from seeds, plausible sources of variation include (1) the amount of seeds added, (2) the temperature in the laboratory, (3) the amount/concentration of ascorbic acid added, and (4) the amount of time that passed between adding the ascorbic acid to reduce the auric ions to aurous ions and adding the seed nanoparticles to initiate rod growth that was unintentionally varied over a 30 min period (i.e., the age of the reduced growth solution). Other possible sources of variation also include changes in vendors and lots of reagents used and the experience of the scientist conducting the synthesis; however, the variation in LSPR peak wavelength can also be observed when conducted by the same person 3 days in a row using the same chemical stock. Many of these variables have been systematically studied though not simultaneously, including [AgNO 3 ], 3 8 , 4 1 , 4 2 , 4 5 , 4 6 , 5 8 − 6 1 [reductant], 3 6 , 4 5 , 4 6 , 5 8 , 6 0 [seeds],36,38,41,45,46,60−62 and temperature.38,46,60 Presented with all of these possible variables to test, an efficient experimental design of minimal effort (and resources) to screen these variables can be found in a factorial design of experiments. Such a design consists of a set number of levels or versions for each factor (i.e., variable) to be studied, and experiments are conducted for each possible combination. Although this statistical method of experimentation and analysis was developed in the 1920s and brought into the chemical sciences after World War II,63 a search of the literature finds few examples of factorial experimental design that involves nanoparticles. This method has been applied in optimizing analytical methods involving nanoparticles 64−66 and in preparing pharmaceutical nanoparticle therapies,67−71 nanoparticle composites,72,73 and nanoparticles of various compositions.74−78 Changing one factor at a time while the remaining factors are held constant, the one-factor-at-a-time method of experimentation, is standard practice in chemistry. However, the one-factor-at-a-time experimental design provides only an estimate of an effect for a single factor at selected and fixed levels for all other factors. It is then necessary to assume that the effect would behave similarly at all other levels of the remaining factors to have more general relevance; in other words, there is an assumption that these remaining factors affect only the response additively. Factorial experiments have a 2-fold advantage over the one-factor-at-a-time method. First, if factors do act additively, then a factorial design can measure this primary effect for each factor, but with much more precision and fewer experiments per factor studied. Second, if

Table 1. Experimental Levels Used for Each Factor of Study Compared to the Standard Protocol on a 10 mL Synthesis Scalea factors A B C D L M N O

amount of NaBH4 rate of stiring seed solution age of seed solution amount of seeds temperature amount of silver (0.0100 M) amount of ascorbic acid (0.100 M) age of reduced solution

standard protocol 0.0378 g 1h 12 μL room variable 55 μL

low (−)

high (+)

0.0378 g 260 rpm 1h 12 μL 26 °C 40 μL 55 μL

0.0450 g 750 rpm 5h 60 μL 50 °C 90 μL 70 μL

1 min

30 min

a

Reagent concentrations at the beginning of rod growth for the standard protocol: 94.0 mM CTAB, 0.495 mM HAuCl4, 0.544 mM ascorbic acid, 0.040 mM AgNO3, 0.672 μM NaBH4, and [seeds]syn × 0.00119.

their level in the standard synthesis protocol, and the levels used for each factor in these factorial experiments. Further details on the selection of these levels can be found in Materials and Methods. The results and discussion presented here are focused on the presentation and discussion of the best-fitting, refined responsesurface models that explain trends in the experimental response data. These models are summarized and presented as perspective plots; however, topographic versions of the perspective plots are available in the Supporting Information along with the results of a t test and tabulated and graphical ANOVAs (SI section 7). For each synthesis run, the product was characterized by vis−NIR extinction, TEM, and ICP−MS (with details described in Materials and Methods). An example of this raw data for an experimental run is presented in Figure 2. Additional plots of vis−NIR extinction spectra, rod width as a function of rod length, and aspect ratio distribution are available for each of the 42 synthesis runs conducted in SI sections 3 and 4. This raw characterization data has been analyzed, as described in Materials and Methods, resulting in the longitudinal LSPR peak wavelength, extinction, yield, purity, and descriptive statistics of nanoparticle distributions for each run. These results are tabulated in SI section 5. By themselves, these data do not offer insight easily as to where trends are located and to which factors are important in influencing these trends. Their value comes from the composite fractional factorial experimental design and its analysis. The screening response-surface models considering all eight factors and their two-factor interactions for each response are tabulated in SI section 6 with the results of a t test, tabulated and graphical ANOVAs (i.e., residual analysis), a Daniel plot, and a Bayes plot for each response. Further details on the statistical methods employed here may be found in Materials and Methods. Longitudinal Peak Wavelength. It is known that the amount of trace silver ion in gold nanorod synthesis influences the aspect ratio and hence their longitudinal surface plasmon resonance extinction peak wavelength.59 However, the best refined response-surface model shows four active factors, and 1893

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Figure 3. Graphical summary of the significant primary and secondary interaction effects on the longitudinal surface plasmon resonance extinction peak wavelength. See Table 1 for the code for each letter condition. Black spectra illustrate the average extinction peak wavelength response. Blue|red spectra illustrate the average blue|red shift in the extinction peak wavelength response. Effects are reported as a response to increasing factor levels as reported in Table 1. P values: (***) < 0.001 < (**) < 0.01 < (*) < 0.05 < (.) < 0.1 < () < 1.

are approximately the same order of magnitude, namely, red or blue shifts ranging from about 20 to 50 nm when increasing from the low to high factor level. In order of decreasing absolute average shift, increasing the amount of seeds produces a red shift of 50 ± 12 nm, whereas increasing the temperature or the amount of ascorbic acid results in a blue shift of 37 ± 12 or 20 ± 12 nm, respectively. These quantified primary effects agree with previously published qualitative observations regarding the influence of the silver nitrate concentration;36,45,46,59 the amount of seeds;36,45,46,62 the temperature;46 and the amount of reducing agent, whether ascorbic acid,36 dopamine,46 or hydroquinone.45 Similar qualitative results in the seedless or in situ seed-generated synthesis of gold nanorods have been observed when increasing the silver nitrate concentration,38,60,61 the amount of seeds generated by increasing the amount of strong reductant,38,60,61 the temperature,38 and the amount of weak reducing agent.60 To our knowledge, no one has previously studied the nonadditive, secondary interaction effects of the amount of silver nitrate added, the amount of seeds added, the temperature, and the amount of reducing agent added either qualitatively or quantitatively. Increasing the ascorbic acid when increasing the amount of silver nitrate produces a blue shift of 28 ± 12 nm whereas increasing the temperature with increased ascorbic acid produces a red shift of 43 ± 12 nm. Increasing the amount of silver nitrate and the temperature results in a red shift of 24 ± 12 nm, and increasing the amount of ascorbic acid and the amount of seeds added produces a red shift of 21 ± 12 nm. Increasing the amount of silver nitrate and the amount of seeds added results in a red shift of 27 ± 12 nm. If all four of these primary effects had been independent, then nothing new would have been gained through these experiments because these four variables have been previously studied independently. However, the existence of these secondary interaction effects shows that these factors are connected mechanistically. (See Mechanistic Implications of Secondary Effects for discussion.) What is surprising is the sheer number of secondary effects on the LSPR peak wavelength and that the

Figure 2. Example of the raw data collected for 1 of 42 synthesis runs including (A) a vis−NIR extinction spectrum, (B) transmission electron microscopy images and graphical representations of the distribution of the nanoparticles’ (C) lengths, widths, and (D) aspect ratios.

their significant primary and secondary interaction effects tune the longitudinal peak wavelength (Figure 3). In addition to the amount of silver nitrate added, the amount of seeds added, the temperature, and the amount of ascorbic acid added have significant primary effects on the longitudinal peak wavelength as seen in the tabulated results of the t tests (SI section 7.A.i). Also, five of the six possible secondary interaction effects appear to be significant as well. Perspective plots of the refined model are presented in Figure 4. Tabulated and graphical ANOVA and a lack-of-fit test (SI section 7.A.i) show that the model has an excellent fit with an adjusted R2 value of 0.7238. From these figures, it is quite apparent that changing the amount of silver nitrate added produces the largest effect, specifically red-shifting the longitudinal peak by an average of 85 ± 12 nm when increasing the silver nitrate added from 40 to 90 μL. The remaining primary and secondary interaction effects 1894

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Figure 4. Perspective plots showing the longitudinal extinction peak wavelength in response to changing the amount of seeds, temperature, amount of silver nitrate, and amount of ascorbic acid. Each plot shows a slice of the longitudinal peak wavelength response with one of the possible pairs of factors on each axis with the other two factors at the center point. (A) Slice at 65 μL of AgNO3 and 62.5 μL of ascorbic acid, (B) slice at 38 °C and 62.5 μL of ascorbic acid, (C) slice at 38 °C and 65 μL of AgNO3, (D) slice at 36 μL of seeds and 62.5 μL of ascorbic acid, (E) slice at 36 μL of seeds and 65 μL of AgNO3, and (F) slice at 36 μL of seeds and 38 °C.

amount of silver nitrate connects with all three of the other active factors. Metallic Gold Yield. The best, refined response-surface model describing metallic gold yield, based on ICP-MS measurements has two factors and their significant primary and secondary interaction effects are summarized in Figure 5. The temperature and amount of ascorbic acid have significant primary effects and a secondary interaction effect as seen in the tabulated results of the t tests (SI section 7.B). Increasing the temperature results in a metallic yield decrease of about 7.3 ± 2.1% on average, and increasing the amount of ascorbic acid results in a metallic yield increase of about 6.2 ± 2.1% on average. Blocking effects also appear to be significant and indicate that freshly prepared ascorbic acid solutions are ideal for higher yields. In the statistical theory of the design of experiments, blocking is the arranging of experiments in groups (i.e., blocks) that are similar to one another. Usually a block of experiments is conducted together to minimize unintentional differences within a block and allows for the statistical accounting of both intentional (e.g., stock reagent solution age) and unintentional (e.g., new reagent lots) differences between blocks. Tabulated and graphical ANOVA and lack-offit tests (SI section 7.B) show that the model has an adequate fit with an adjusted R2 value of 0.4277. An alternative and experimentally expeditious way to approximate a semiquantitative metallic gold yield is to use the extinction at the longitudinal peak wavelength as a proxy measurement for yield, assuming that the particles produced are of similar size with similar absorption coefficients and scattering cross sections and are suspended in similar volumes. Spectroscopic methods have previously been employed to measure the metallic gold yield with semiquantitative success, although when compared to ICP measurements of digested

Figure 5. Graphical summary of the significant primary and secondary interaction effects on the percent yield of gold. See Table 1 for the code for each letter condition. Each pie represents the 100% metallic gold yield, where the gold wedge illustrates the average gold yield and the green|red wedge represents an average increase|decrease of the reported percentage. Effects are reported as a response to increasing factor levels as reported in Table 1. P values: (***) < 0.001 < (**) < 0.01 < (*) < 0.05 < (.) < 0.1 < () < 1 s.

gold nanorods, spectroscopic methods can have a 20−30% error.58,79 Perspective plots of both models are presented in Figure 6. The best, refined response-surface model of extinction also has only temperature and the amount of ascorbic acid added as active factors and similarly shows that increasing only 1895

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the surfactant micelles and is unavailable for aurous reduction to metallic gold on the surface of the seeds. In support of this notion is the fact that although nearly 100% metallic gold yield can be achieved with a significant stoichiometric excess of ascorbic acid,58 hydroquinone45 and other phenols,60 or dopamine46 as the reducing agent, a greater stoichiometric excess is needed in the case of phenols and dopamine to achieve that yield. These reducing agents are expected to have a higher hydrophobic partition coefficient than ascorbic acid because of their aromatic rings. Furthermore, increasing the temperature appears to negate any benefit from increasing the amount of ascorbic acid and may be due to changes in the hydrophobic partition coefficient of the reducing agent. Shape Purity. Shape purity (i.e., the fraction of nanoparticles that have the desired shape) is an important parameter to control because it is the morphology of the nanoparticles that leads to their interesting and useful properties. And although morphological impurities can be removed,80−84 this is done at considerable effort and expense. The shape purity can be semiquantitatively measured by determining the extinction ratio of the longitudinal and transverse LSPR peaks due to the overlap of the transverse LSPR of rods with the LSPR of spheres.62 However, a more quantitative measure of purity is the fraction of particles that have rodlike morphology as determined by counting particles in TEM micrographs, which is the method of measuring purity employed here. The best refined response-surface model describing the fraction of rods has two active factors (Figure 7). Increasing either the temperature or the amount of silver or both results in a decrease of 3.6 ± 2.1, 7.9 ± 2.1, or 7.3 ± 2.1%, respectively, in the fraction of rods. Tabulated t tests demonstrate the significance of temperature and the amount of silver nitrate (SI section 7.C.i). Blocking effects also appear to be significant and may be more important than these factors because their effect, an increased rod yield of about 17 ± 12.7%, is 2 to 3 times larger. The active blocking effect suggests that freshly prepared silver nitrate is needed to ensure a low shape impurity and that even solutions wrapped in aluminum foil to prevent photodegradation are no longer ideal after a few hours. Tabulated and graphical ANOVA and a lack-of-fit test (SI section 7.C.i) show that the model has an adequate fit for identifying active factors with an adjusted R2 value of 0.4719. Frequently in the published literature, the yield has been mistakenly synonymous with shape purity,36,38,42,62 which has been characterized both qualitatively38,45,46,60,62,85 and quantitatively.36,42,62 The primary effects observed here agree with previously published results on the effects of silver nitrate38,45,46 and temperature.38 Similar results have also been observed with the seedless in situ seed-generated synthesis of gold nanorods.38,42,60 Though some have noted a much lower fraction of nanorods than reported in this work due to increased silver nitrate or temperature, this lower purity may actually be due to the age of their silver nitrate stock solution that has not been previously monitored or reported before this work. Also, to the best of our knowledge, no one has previously reported the synergistic effect of increasing both silver nitrate and temperature on the decreasing shape purity. Rod Length and Width. Measurements of the individual members of a population of nanoparticles will have a distribution where there are multiple statistical measurements to describe that distribution. Three descriptions of rod length include the mode (the most common length), the median (the middle length when sorted by size), and the mean (the average

Figure 6. Perspective plots showing (A) the percent Au yield and (B) the extinction, at the longitudinal LSPR peak wavelength, in response to changing the temperature and amount of ascorbic acid added.

the ascorbic acid and keeping a lower temperature can achieve a higher yield or extinction. Significant primary and secondary interaction effects are seen in the tabulated t tests (SI section 7.A.ii). Tabulated and graphical ANOVA and the lack-of-fit test (SI section 7.A.ii) show that the model has an adequate fit with an adjusted R2 value of 0.7832. Very few published studies have examined the metallic gold yield when preparing gold nanorods.45,46,58,59 Historically59 (and in this work), the gold yield has always been low in an absolute sense; however, nearly quantitative conversion of gold ions to metallic gold can be achieved by using a large stoichiometric excess of reducing agent.45,46,58 Under both experimental conditions in this work (i.e., 55 vs 70 μL of 0.100 M), ascorbic acid is the stoichiometrically limiting reagent in the reduction of auric ions with 20 and 80% theoretical gold yields, respectively, therefore allowing for the identification of additional factors that influence metallic yield. Operating in an experimental space where theoretical gold yields are less than 100% permits the discovery of additional factors that improve the reduction of aurous ions, not only through a primary effect but even through a secondary effect that operates only at the higher ascorbic acid concentration. However, the model shows that actual gold yields tend to be about 5 and 20% at the standard temperature condition of 26 °C (Figure 6). One idea for the cause of this large discrepancy between stoichiometric and actual yields is that the reaction is limited by the number of available nucleation points for growth (i.e., seeds). However, this work demonstrates that this is not the case because the amount of seeds added does not appear to play an active role in determining the gold yield. Systematically, it appears that yields tend to be about 25% of the theoretical yield, and we propose that a portion of the ascorbic acid is sequestered within the hydrophobic phase of 1896

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Figure 8. Graphical summary of the significant primary and secondary interaction effects on the median nanorod length. See Table 1 for the code for each letter condition. The black nanorods illustrate the average median dimensions of the nanorods, where red|green represents the average decrease|increase in median nanorod length. Effects are reported as a response to increasing factor levels as reported in Table 1. P values: (***) < 0.001 < (**) < 0.01 < (*) < 0.05 < (.) < 0.1 < () < 1.

same two active factors that have similar effects (SI sections 7.E.i-iii). Using the median again for illustration, increasing the amount of ascorbic acid results in thicker rods (increase of 4.07 ± 0.63 nm), and increasing the amount of seeds added results in thinner rods (decrease of 7.07 ± 0.66 nm, Figure 10). Increasing both the amount of ascorbic acid and the seeds results in an additional average decrease of 2.66 ± 0.62 nm in width. Tabulated t tests demonstrate the significance of the amount of ascorbic acid and the amount of seeds added (SI section 7.E.ii). Blocking effects appear to be significant and suggest that fresher ascorbic acid solutions result in rods thinner by 4.19 ± 1.62 nm on average. Tabulated and graphical ANOVA and the lack-of-fit test (SI section 7.E.ii) show that the model has an excellent fit with an adjusted R2 value of 0.7827. As the amount of seeds was increased 5-fold, it produced the largest effect on rod length and width. The dominant role of the amount of seeds is easier to understand because the amount of seeds does not play a determining role in the amount of gold that is reduced in forming particles. By increasing the amount of seeds, there is less gold being added to each seed on average. This results in shorter, thinner rods (Figures 8 and 10) as the amount of seeds added increases. We see the combined effect of this in the LSPR peak wavelength, which according to Gans theory1,86−88 is dominated by the particle aspect ratio and changes in the local medium dielectric constant. Because the decrease in nanorod width is a larger percent change (48%) in that dimension compared to the decreasing length (33%), this results in an increase in the particle’s aspect ratio and a corresponding red shift of the LSPR peak wavelength (Figure 3). Similar results have been observed previously regarding rod dimensions, the longitudinal LSPR peak wavelength, and the amount of seeds added.36,45,46,62 Comparatively, increasing the amount of sodium borohydride in the seedless in situ seedgenerated synthesis of gold nanorods produces more nucleation points (i.e., in situ seeds) and has a similar effect on rod dimensions and the LSPR peak wavelength.41,60,61 Because increasing the amount of ascorbic acid increases the yield of metallic gold, there is more gold available for each growing seed particle. This results in longer, thicker rods as the amount of ascorbic acid is increased (Figures 8 and 10). The LSPR peak blue shifts when the amount of ascorbic acid is

Figure 7. (A) Perspective plot showing the fraction of rods in response to changing the temperature and amount of silver nitrate added. (B) Graphical summary of the significant primary and secondary interaction effects on the fraction of rods. See Table 1 for the code for each letter condition. Each pie represents 100% purity, where the gold wedge illustrates the average fraction of rods, the blue wedge illustrates the average fraction of shape impurities (usually spheres), and the red wedge represents the average decrease in the reported percentage. Effects are reported as a response to increasing factor levels as reported in Table 1. P value: (***) < 0.001 < (**) < 0.01 < (*) < 0.05 < (.) < 0.1 < () < 1.

length). The best, refined response-surface model for each of these responses has the same four active factors and presents similar trends (SI sections 7.D.i-iii). Using the median rod length for illustration, significant primary and secondary interaction effects are summarized in Figure 8. Tabulated t tests demonstrate the significance of the amount of seeds, temperature, the amount of silver nitrate, and the amount of ascorbic acid (SI section 7.D.ii). Perspective plots of the refined model are presented in Figure 9 in which it is apparent that changing the amount of seeds produced the largest effect, an average median length decrease of 11.2 ± 1.3 nm. Interestingly, there are only three primary and two secondary interaction effects. Increasing the amount of ascorbic acid results in an average median length increase of 5.3 ± 1.3 nm, whereas increasing the temperature results in an average median length decrease of 3.2 ± 1.3 nm. The amount of silver nitrate has only a secondary, synergistic effect on the amount of ascorbic acid further increasing the average median length by 2.8 ± 1.2 nm and no primary effect. Tabulated and graphical ANOVA and the lack-of-fit test (SI section 7.D.ii) show that the model has an excellent fit with an adjusted R2 value of 0.8241. The mode, median, and mean of the rod width are similar to the length in that all three response-surface models have the 1897

DOI: 10.1021/acs.langmuir.6b03606 Langmuir 2017, 33, 1891−1907

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Figure 9. Perspective plots showing the median rod length in response to changing the amount of seeds, temperature, amount of silver nitrate, and amount of ascorbic acid. Each plot shows a slice of the average median rod length response with one of the possible pairs of factors on each axis with the other two factors at the center point. Panels A−-F have the same meaning as those in Figure 4.

appear to be affected by the amount of seeds and ascorbic acid, the amount of seeds, and the amount of sodium borohydride, respectively. Aspect Ratio and Multivariate Dimensional Characterization. The aspect ratio is a difficult response to model as a linear relationship between the primary and secondary interaction effects. The models for the mode, median, and mean aspect ratio suggest that the amount of seeds and the amount of silver nitrate influence the aspect ratio (SI section 7.G.i-iii). Despite significant P values, adjusted R2 values are below 0.4 for the mode, median, and mean aspect ratio. Changing the amount of ascorbic acid does not show an appreciable effect on the aspect ratio despite being important in influencing both the length and width. This may be due to the proportional influence of ascorbic acid between the length and width maintaining a nearly constant average aspect ratio within statistical error over the range studied and therefore does not measure as a major influential factor. Models for the standard deviation and skewness of the aspect ratio also have low R2 values but show significant effects from changing the amount of seeds and the temperature, respectively (SI section 7.G.iv-v). The model for aspect ratio kurtosis, a measure of the distribution spread, shows significant primary effects in the amount of seeds added and the amount of silver nitrate causing a decrease or increase, respectively, with an adjusted R2 value of greater than 0.50 (SI section 7.G.vi). An alternative approach to considering both the length and width simultaneously is to use multivariate descriptive statistics. The coordinate-wise mean is identical to the mean obtained when considering the length and width simultaneously and is susceptible to outliers. Alternatively, the median is resistant to outliers, and the multivariate median employed here is a spatial median that minimizes the sum of the Euclidean distances between the spatial median and the data. The best, refined

increased because the aspect ratio is decreasing (Figure 3). This decrease occurs because the percent increase in the width (28%) is larger than that in the length (16%) when increasing the ascorbic acid. Analogous results have been observed when increasing the amount of reductant, regardless of the specific reductant (e.g., ascorbic acid,36 hydroquinone,45 dopamine,46 or other phenol derivatives60). Both temperature and the amount of silver nitrate seem to have an influence on only the nanorod length and not the width. Increasing the temperature results in shorter nanorods (Figure 8), decreased aspect ratios, and therefore a blue-shifted LSPR peak wavelength (Figure 3). In contrast to this, increasing the silver nitrate contributes to longer rods and therefore an increased aspect ratio and a red-shifted LSPR peak wavelength. These results are consistent with previously published results regarding the effects of silver nitrate42,45,46,59−61 and temperature.46,60 Other statistical descriptors of rod length and width describing the dispersion, such as the standard deviation, skewness, and kurtosis, are poorly modeled by these responsesurface models with adjusted R2 values typically well below 0.5 but still have significant P values. This shows that these responses are not well modeled as a linear relationship between the primary and secondary interaction effects of these factors but that the models do capture all of the linear information in the data that exists (albeit that is not much). Furthermore, this suggests that there are additional unknown and uncontrolled factors (in these experiments) that influence the dispersion of rod dimensions. This data suggests that the amount of seeds plays a role in the standard deviation and kurtosis of rod length (SI sections 7.D.iv and 7.D.vi) and that the temperature and amount of silver nitrate influence the skewness of the rod length (SI section 7.D.iv). However, the standard deviation, skewness, and kurtosis of rod width (SI section 7.E.iv−vi) 1898

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error in the models for determining which secondary interaction effects are significant. In the case of the LSPR peak, the standard error is about 11 nm and corresponds to an exceedingly small change in the aspect ratio. In the case of length and especially width, the standard errors are about 1.2 and 0.7 nm, respectively, and are larger percent errors than observed for the LSPR peak wavelength (SI sections 7.A.i, 7.D.i-iii, and 7.E.i-iii). Therefore, a factor has to be of greater importance to be significant in the nanoparticle dimensional data; conversely, the LSPR data is better at measuring smaller yet still significant effects. Secondary interaction effects that appear in the dimensional data show a mechanistic connection between these factors. Auric Reduction. The net redox reaction for the reduction of AuIII to Au0 in this synthesis is presented in Scheme 1A. AuBr4− 1 has been identified as the main gold species present in a solution of CTAB micelles,58,89 and under the acidic conditions of the synthesis, L-ascorbic acid is mostly in the form of Lascorbate 2.90,91 The reduction of AuIII, however, occurs in two steps: reduction to AuI when ascorbic acid is added (Scheme 1B), followed by reduction to Au0 once the seeds are added (Scheme 1C or D) because ascorbate is not a strong enough reductant to reduce AuI to Au0 without a gold surface. The twoelectron oxidation of L-ascorbic acid 7 is presented in Scheme 1E with the dominant secondary reducing species, radical anionic ascorbate 6, which is the strongest reductant of the possible radical ascorbates.91 Because L-ascorbate 2 is the limiting reagent in Scheme 1B and complete reduction to AuI is observed, the product radical anionic ascorbate 6 must also participate in the reduction of AuIII (Scheme 1B). Two mechanisms for the second reduction of AuI to Au0 have been proposed, namely, the disproportionation of AuI to Au0 and AuIII (Scheme 1C) and the direct reduction of AuI (Scheme 1D). It has been observed that the production of metallic gold as a function of time has a sigmoidal shape consistent with an autocatalytic reaction;58 however, this cannot distinguish between the two mechanisms because both mechanisms are catalyzed by metallic gold and would be autocatalytic as metallic gold is produced. In the results presented here, the amount of seeds and the amount of ascorbic acid added have an additional secondary interaction effect that when both are increased rods are shorter and thinner (Figures 8 and 10) than the sum of either factor alone. Because the decrease in width is a larger percent change (8 vs 18%), the aspect ratio increases, resulting in a red shift of the LSPR peak wavelength (Figure 3). The existence of this secondary effect suggests that the seeds and the ascorbic acid are physically interacting and supports the direct reduction of aurous ions on the surface of the seed by ascorbic acid (Scheme 1D) over a disproportionation reaction of three aurous ions on the seed (Scheme 1C). Furthermore, with the range of concentrations employed, there is only one or two AuBr4− 1 solubilized with the surface of each micelle,58 and this reduces the likelihood of three aurous ions meeting for disproportionation. Only at temperatures higher than employed here (100 °C) can the two-electron oxidized product of ascorbic acid, dehydroascorbic acid 3, and its easily hydrolyzed form 2,3diketo-1-gulonic acid reduce gold ions as a result of the presence of mild reducing alcohol groups.92 However, the results presented here on the effects of temperature on metallic gold yield (Figure 5) indicate that increasing the temperature results in a deceased yield and that 50 °C is insufficient to cause

Figure 10. (A) Perspective plot showing the median rod width in response to changing the amount of seeds and the amount of ascorbic acid added. (B) Graphical summary of the significant primary and secondary interaction effects on the median rod width. See Table 1 for the code for each letter condition. The black nanorods illustrate the average median dimensions of the nanorods, and red|green represents the average decrease|increase in the median nanorod width. Effects are reported as a response to increasing factor levels as reported in Table 1. P values: (***) < 0.001 < (**) < 0.01 < (*) < 0.05 < (.) < 0.1 < () < 1.

response-surface models for the spatial median length and width have the same active factors and trends as their coordinate-wise counterparts with an equally adequate model fit and adjusted R2 values (SI section 7.F.i-ii). Multivariate descriptive statistics can also be used to describe the dispersion in the data (i.e., multivariate mean and median deviation, total variation) as well as the shape (i.e., multivariate skewness and kurtosis). Like the coordinate-wise dispersion statistics, multivariate dispersion statistics are poorly modeled as a linear relationship between the primary and secondary interaction effects of these factors, but the data does suggest that the amount of seeds and temperature may play roles in the dispersion of their dimensions (SI section 7.F.iii-vii). With more data at additional factor levels, fully quadratic models may be better able to determine significant dispersion effects for these factors, or the larger data set could suggest appropriate transformations so that it may be more easily modeled. Mechanistic Implications of Secondary Effects. Secondary effects are manifested when one factor synergistically influences how another factor affects a response in addition to their primary effect. Interestingly, more significant secondary effects are observed in the LSPR data than in either the length or width data. This is most likely due to the increased sensitivity of the LSPR peak wavelength with respect to changes in the aspect ratio or local medium dielectric and the level of 1899

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Langmuir Scheme 1. Various Reactions Involved in the Reduction of AuIII to Au0a

a

(A) Net reaction, (B) primary reduction of AuIII to AuI, (C) disproportionation reaction of AuI to AuIII and Au0, (D) direct reduction of AuI to Au0, and (E) oxidation of L-ascorbic acid to L-dehydroascorbic acid. Note that only Au is shown balanced; bromide ions are not shown.

complexes blocking gold addition to these side facets.7,10 The third mechanism is a soft template mechanism based on the rodlike micelle structure that CTAB forms above its critical micelle concentration (∼1 mM).10,38,96 The addition of silver to CTAB micelles may alter their shape and subsequently the nanorods.38,97 There is evidence that silver is incorporated into the gold nanorods (2.5 to 9%) and that it is preferentially at or near the surface using a combination of XPS, SERS, and ICP−MS.59,98 Furthermore, ICP−AES and XPS studies on a variety of gold nanoparticle shapes (i.e., octahedral, rhombic dodecahedra, truncated ditetragonal prisms, and concave cubes) produced by varying the trace silver concentration show a correlation

an appreciable reduction of gold by dehydroascorbic acid or 2,3-diketo-1-gulonic acid. At the temperatures employed here, ascorbic acid is limited to providing two electrons per molecule for the reduction of gold. Role of Silver. Three differing mechanisms have been proposed for the role of silver in the growth of gold nanorods. The first mechanism is that silver is selectively reduced from Ag+ to Ag0 on specific faces as a result of the reduction potential of the growth solution, blocking isotropic growth and resulting in nanorods.7,10,33,93 The underpotential deposition of silver on gold is expected to prefer the high-energy side facets of gold nanorods. 33,93−95 A second, similar alternative mechanism is the preferential deposition of silver bromide 1900

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concentrations of silver nitrate are needed when producing gold mininanorods62 or larger nanorods via reduction with hydroquinone45 or a sodium oleate cosurfactant.109 Because of an increased production of surface area, which serves as a larger silver sink, higher concentrations of silver nitrate are needed to compensate for the increase in silver lost to a larger silver sink. Silver nitrate playing a relatively minor role in determining the absolute dimensions of the nanorods (Figure 8 and 10) begs the question as to why changes in silver nitrate produce the largest effect on the longitudinal LSPR wavelength (Figure 3). According to extended Mie theory by Gans,1,86−88 the longitudinal LSPR wavelength is mainly dependent on two properties: (1) the dimensions of the nanorod (specifically its aspect ratio), which effect the polarizability of the LSPR, and (2) the effective medium dielectric surrounding the nanorod, which includes adsorbed species. Therefore, we propose, if silver is not the dominating factor controlling the dimensions of the nanorods, that it must be influencing the effective medium dielectric that the nanorod experiences through the adsorption of silver complexing with bromide on the surface. Inactive Factors. Four of the eight factors studied here (age of seeds, increasing borohydride concentration for seed formation, rate of stirring during growth, and age of growth solution) do not appear to have any appreciable effect on any of the responses; however, when taken to an extreme value outside these experimental ranges, an effect would be expected for all factors. For example, using seed particles that are weeks old that may have ripened into much larger particles or dissolved into a colorless solution would not be expected to successfully produce nanorods. However, the lack of difference between 1 h old seeds and 5 h old seeds indicates that the structure, surface chemistry, and reactivity of the seeds are relatively stable over this time frame and that any excess sodium borohydride has sufficiently decomposed within 1 h and does not appreciably affect the nanorod synthesis. The lack of an effect when increasing the amount of sodium borohydride used in the synthesis of the seeds demonstrates that the byproducts of borohydride oxidation do not influence the subsequent nanorod synthesis. It shows that it is an increase in the number of seed particles that is responsible for the observed effects of increasing the volume of the seed suspension added and not borohydride oxidation byproducts. The rate of stirring when preparing the seed nanoparticles does not have any appreciable effect, despite laboratory lore to the contrary. And finally, the lack of an effect when varying the age of the reduced growth solution shows that the reduction of auric ions to aurous ions is a thermodynamically controlled process and is not kinetically controlled under these conditions, where equilibrium is rapidly reached. This includes the distribution of remaining ascorbic acid molecules that are available (or not available, i.e., sequestered) for the subsequent reduction of aurous ions to metallic gold.

between silver coverage on gold facets and what was predicted if silver serves as a blocking agent.99 However, it is unclear if a similar mechanism is at play in nanorods because the shapes studied in these experiments did not included nanorods. Further evidence also shows the presence of bromide at the surface of gold nanorods. The bromide ion is an important synthesis component because the replacement of bromide completely with chloride does not result in nanorods; however, with bromide still on the seeds it can be replaced with sodium oleate in the growth solution.100 Au−Br and Ag−Br species have been identified by XPS and SERS, and the disappearance of the Au−Br stretch has been observed by Raman spectroscopy upon addition of thiols.42,98,101 Furthermore, multiple groups have identified the presence of AgBr2− and AuBr2− by mass spectrometry.102,103 However, recent work employing HR-TEM and STEM− EDS elemental maps suggests that silver is present on all surfaces of gold nanorods, contradicting these first two mechanisms.104 Little experimental evidence exists besides the correlation between elongated CTAB micelles and nanorod shape in support of the third mechanism.38,105 The preferential adsorption of CTAB to specific facets of the growing nanorod is usually invoked as thermodynamic arguments for the anisotropic growth. However, the adsorption of CTA+ on different crystallographic planes of flat gold, in electrochemical experiments, demonstrates little thermodynamic preference between crystal faces.106,107 These electrochemical experiments do show differing levels of bromide adsorption on different crystallographic planes. This suggests that there may be a sufficiently different electronic state between crystal facets so that the diffusion of charged species (i.e., reagents) to these faces would be different in impacting their reactivity and rate of growth.97 The surfactant still may be critical in the symmetrybreaking event required to go from a symmetrical seed to an anisotropic nanorod. In this work, the amount of silver does not show a primary effect in either length or width but does have a secondary interaction effect with the amount of ascorbic acid resulting in longer rods (Figure 8), an increased aspect ratio, and a redshifted LSPR peak (Figure 3). Because there is not a primary effect in length or width, the corollary is that silver does not directly influence the length or width despite being eventually deposited on the surface of the growing nanorod. We propose that the deposition of silver on the gold surface is not the driving force for an anisotropic particle, and we propose, as others have before, that the high levels of bromide are responsible for promoting and stabilizing the nanoparticle anisotropy.106−108 Our current results suggest that the primary role of silver is to modify the rate of reduction of aurous ions by a radical ascorbate anion. This reduction is kinetically suppressed by CTA+ compared to the synthesis of CTA+-free gold spheres, and this work shows that the growth is finely tuned further to a slightly faster rate on the ends of the rods as a result of silver synergistically assisting ascorbic acid in the reduction of gold. This may be achieved mechanistically by the silver cation shielding the aurous bromide anion or the radical ascorbate anion allowing it to more readily approach the negatively charged, bromide-coated gold surface. Furthermore, we propose that the loss of silver to the surface of the nanorod operates as a sink for silver, removing it from the reaction. This silver sink is responsible for the cessation of growth once the silver cations are no longer available in sufficient quantities to shield anionic reagents. This notion agrees with why higher

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CONCLUSIONS Combined, these results show that the basic process of forming gold nanorods is the reduction of auric ions by ascorbic acid onto seed nanoparticles. The amount of ascorbic acid mainly influences how much metallic gold will be produced, and the amount of seeds determines how it is divided. The particles grow with intrinsic yet different rates of growth on the ends vs the sides, forming rods, where the growth in these directions is either decreased or increased as a function of increasing the amount of seeds or ascorbic acid, respectively. Furthermore, the 1901

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controlled for between blocks, which occurred over a 6 month period. The following chemicals were employed in this research: cetyltrimethylammonium bromide (Sigma), chloroauric acid (Sigma-Aldrich), silver nitrate (Sigma-Aldrich), ascorbic acid (Acros and Sigma), and sodium borohydride (Aldrich). A table of lot designators is available in the Supporting Information. Chemicals were used as received without further purification, but some specific care was taken in handling certain reagents. Fresh silver nitrate and ascorbic acid solutions were prepared and wrapped in aluminum foil to minimize photodegradation. These were prepared fresh every 3 days (block 1) or every day (blocks 2−4). Sodium borohydride was opened, weighed, and stored under dry nitrogen in a glovebag and desiccator until use. This was done to minimize the adsorption of atmospheric water and the associated decomposition to ensure accurate masses. The nitrogen gas was dried using Drierite and a laboratory gas-drying unit (W. A. Hammond Drierite Company). For consistent stirring, all stir bars were a Teflon coated 1/2 in. × 1/8 in. polygon stir bar. Sample Characterization and Analysis. In addition to controlling the longitudinal plasmon peak wavelength, there are a few additional parameters that are useful to control when synthesizing gold nanorods. These include the particle dimensions and their distributions (i.e., length, width, and aspect ratio), metallic gold yield, and particle shape purity. Quite often in the scientific literature, the yield is used interchangeably to describe how much of the starting material is recovered in the final nanoparticles or how many of the final nanoparticles adopt a specific morphology (e.g., spheres vs rods). Here, yield is used to describe the former (i.e., the percent of gold added that is recovered as nanoparticles), and purity, the later (i.e., the percent of particles with rod morphology). Visible−Near-Infrared Extinction Spectroscopy. To determine the longitudinal plasmon peak wavelength as well as its extinction (i.e., a proxy for yield), the visible−near-infrared (vis−NIR) extinction spectrum was measured from 400 to 1100 nm using a Cary 5000 series UV−vis−NIR spectrophotometer (Agilent Technologies). Spectra were recorded using a 1 cm quartz cuvette with nanopure water background subtraction and a scan interval of 1 nm at a rate of 30 nm per second. Inductively Coupled Plasma Mass Spectrometry. To determine the gold yield, samples from each run were digested with freshly prepared metal-free aqua regia (3:1 v/v neat HCl/HNO3) and quantitatively diluted to between 10 and 80 ppb Au. These were then submitted to the UIUC School of Chemical Science’s Microanalysis Laboratory for elemental analysis by inductively coupled plasma−mass spectrometry (ICP-MS). Samples were analyzed in triplicate on a SCIEX ELAN DRCe ICP-MS against appropriate standards to determine yields with standard errors. An alternative spectroscopic method (absorbance at 400 nm, which is indicative of elemental gold) has recently been developed using spherical particles that show both a size and a surface functionalization dependence causing up to 30% uncertainty.79 At the outset of these experiments, ICP−MS was selected as the means employed here to determine gold yield due to established analysis protocols within the research group and the potential of a size dependence (and need for optimization with nanorods); however, since the completion of this work, this method has been demonstrated with nanorods,110 achieving similar levels of uncertainty as ICP−MS, and was found to have little size dependence most likely due to the small size range in nanorod width observed. Transmission Electron Microscopy. Transmission electron microscopy (TEM) was employed to characterize the dimensions of the nanoparticles as well as their purity. TEM samples were prepared by drop casting sample suspensions on 200 mesh copper grids that were coated with a holey, amorphous carbon support film (SPI, inc.) and allowed to air dry. Images were collected on two TEM instruments in the UIUC Materials Research Laboratory’s Center for the Microanalysis of Materials. Specifically, either a JEOL 2100 cryo-TEM or a JEOL 2010 LaB6 TEM was employed at 200 kV to collect images on either a Gatan UltraScan 2k × 2k CCD or a Gatan MatScan1k × 1k progressive scan CCD with 1 s exposure, respectively. For each sample, >350 particles were counted and measured under two conditions, namely, that every particle in an image must be

proportional changes in length and width can result in an increased or decreased aspect ratio, respectively, and a corresponding shift in the LSPR peak wavelength. The growth on the ends of the rods can be further tuned by changing the amount of silver nitrate or the temperature, providing the main methods of control over the optical properties of the nanoparticles. Careful and intentional control of the amount of ascorbic acid, the temperature, and especially the amount of seeds added leads to the most reproducible and robust nanorod syntheses. Furthermore, a slight photodegradation of silver nitrate and ascorbic acid reagents can negatively impact the nanoparticle purity and gold yield, respectively. Future work expanding on the ranges examined here in the active factors will allow for better modeling of the data through canonical analysis, error reduction, and the use of fully quadratic models. This will lead to better synthesis control at higher yields where multiple responses could be simultaneously controlled and optimized. Furthermore, having a larger data matrix will potentially allow for an improved understanding of the effects of these factors on the aspect ratio, as directly measured, and measures of particle dispersion. Has the problem presented in Figure 1C of less than satisfactory precision and reproducibility, when averaged over many people over a long time, been completely solved? No. The chemical community is still struggling to achieve this goal in syntheses. The example of general chemistry laboratory experiments comes to mind: even with explicitly detailed instructions, when thousands of people do an experiment, they do not all achieve the same result. One experienced person can produce the beautiful data of Figure 1B. However, this article represents progress toward the goal of robust precision and reproducibility, especially for these kinetically controlled crystal growth processes, and validates this experimental approach in general when studying nanomaterial synthesis. However, more research needs to be done even on just this synthesis. One set of synthesis parameters was studied here. At the outset of these experiments, some were known to be important ([Ag+] and [reductant]) and some were thought unlikely to be important (rate of stirring), serving as a negative control. Still many possibly important factors and more importantly their interactions with each other remain to be studied in quantitative detail including pH, the time required for halide ligand exchange between HAuCl4 and CTAB, alternative and mixtures of reducing agents, and various cosurfactants. Even the nitrate counterions and oxygen in the air have redox chemistry that has not been explored and might be important in reducing the variability in the synthesis. There are commercial sources of gold nanorods that, as far as we are aware, are prepared in batches not dissimilar to our method. Improved production will likely be done via a programmed and automated system, perhaps similar to our own millifluidic reactor,48 to achieve improved precision and reproducibility. Achieving that goal requires that all of the important synthesis parameters to control be identified, including how they influence each other.

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MATERIALS AND METHODS

Materials. Reagent solutions were prepared with nanopure water (Barnstead NANOpure II) in volumetric flasks that had been cleaned with fresh aqua regia and rinsed five times with nanopure water (as was all equipment used here). The pH of nanopure water can vary, especially over half a decade, and may have contributed to the variability observed in Figure 1C. However, it is not likely to vary significantly over the 3 days of experiments within each block and is 1902

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Table 2. Composite Fractional Factorial Design of Experiments Conducted Consisting of a 28−4 IV Fractional Factorial Design with a Center Point, Multiple-Column Foldover (A, C, D, L, and M) Factorial Design, and Additional Runs Selected through Bayesian Screening Analysis Listed in Randomized Order of Experimentation NaBH4

speed

seed age

seed amount

temperature

silver

ascorbic

reduced age

exp

A

B

C

D

L

M

N

O

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

− − + + − − − − + + + + + + − − 0 + − + + − − − − + 0 + − + + − + − + − − − − − − −

− − + + + + − − + + − − − − + + 0 − + − − − − + + + 0 + + + + − − − − + − − − − − −

− − − − − − + + + + − − + + + + 0 + + − + + − − − − 0 + + − + + − − − + + − + + − −

− + − + − + − + − + − + − + − + 0 + − − − + + − + + 0 − + − + − + − − − − + − − + +

− − − − + + + + + + + + − − − − 0 + + − + − + − − + 0 − + + − − − + − − − + − + − −

− + − + + − − + − + + − + − + − 0 + − − − − − − + − 0 + + + − + + + + + − + + + − +

− + + − − + + − − + + − − + + − 0 − − − + + − + − + 0 + + − − − + + − − − − + + − +

− + + − + − + − − + − + + − − + 0 − − − + − + + − − 0 − + + + + + − − − + + + + + −

counted and measured and that once 350 particles had been measured the final image had to be finished. This was done to avoid sampling bias in describing the population distribution. Image analysis was performed using ImageJ.111−114 Statistical descriptions of the particle distributions (i.e., mode, median, mean, standard deviation, skewness, and kurtosis) for the length, width, and aspect ratio for each run were calculated using Mathematica.115 Furthermore, multivariate characterization (i.e., spatial median, mean deviation, median deviation, skewness, kurtosis, and total variation) was also performed by considering both the length and width simultaneously. Calculating the standard error of many of these descriptive statistics is not a trivial matter; however, they can be computationally approximated using a bootstrap method.116,117 Assuming each sampling of >350 measurements is representative of the entire TEM sample, 1000 virtual data sets were created by random selection with replacement for which each of the aforementioned descriptive statistics was determined. The

standard deviations of these statistics over the virtual data sets are estimates of the standard errors for the statistics determined from the original sample population. Composite Fractional Factorial Design of Experiments. A composite fractional factorial design of experiments is a sequentialexperimentation process to optimize a response-surface model in determining which factors are active and which are essentially inert. A principal reference in the application of statistical methods, as applied to experimental design, is Statistics for Experimenters: Design, Innovation, and Discovery, to which the interested reader is directed for through instruction in the application of these methods.63 The factors employed and their variable levels are presented in Table 1. These levels are carefully selected, and their selection is of utmost importance in designing successful factorial experiments.63 The experimental design employed here is presented in Table 2. Blocking was employed to account for differences between stages of sequential 1903

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Langmuir experimentation, both intentional differences (i.e., the age of silver nitrate and ascorbic acid solutions) and unintentional differences (i.e., changes between reagent lots). In these experiments, a full 28 factorial design consisting of the aforementioned 8 factors each with 2 experimental levels results in 256 possible different experimental sets of conditions to run. Because this number of experiments is prohibitively costly and time-consuming, a specific subset of these 256 experiments was selected plus a center point that would still allow the unconfounded approximation of the primary effects of these factors to determine their importance.63,118,119 Further details on the experimental design can be found in SI section 1. Fractional Factorial Analysis. The composite fractional factorial design employed here was analyzed through response-surface methods using the rsm package120 and BsMD package121 for R,122,123 with 30 response variables produced from sample characterization and analysis. For each response variable, a response surface was modeled on the basis of all eight factors and their two-factor interactions through a weighted least-squares approach, where the weights were the inverse of the standard error squared for each data point. An adjusted R2, F statistic, and P value for each model were calculated. Along with these values, the fit of the model was evaluated through a tabulated and graphical analysis of variance (ANOVA) by plotting the standardized residuals against a normal distribution, order of experimentation, and modeled values. This was done to check for large irregularities (i.e., the lack of independent, normal, and identically distributed random errors, model additively, and constant variance) that would suggest a nonrandom nature of the residuals and the need for data transformation (e.g., scaling), new models, or correction for systematic errors.63 On the basis of these analyses, the top 10 candidates out of 256 possible models for each response variable were then fit to the data, without essentially inert factors, to find the best refined model. The removal of essentially inert factors from the design analysis causes some runs to essentially be replicates.63 This is because the inert factors were the only experimental differences between runs, and these differences were determined to produce no significant effect on the response parameter. If there are enough inert factors, then this results in a fractional factorial design collapsing into a complete factorial design of the active factors as a result of the projectivity of fractional factorial designs. This means that the data can be more accurately modeled without confounding interaction effects and smaller standard errors. The best of these models uses the most factors without additional, unnecessary factors, resulting in a large adjusted R2 value and a small P value for the model as a whole. Models with a P value of less than 0.05 for the lack-of-fit test are considered to inadequately describe the response data and are therefore rejected as possible models. Furthermore, each factor in a refined model needs to have a significant (i.e., P value < 0.05) primary effect, two-term interaction effect, or both. If a factor does not have a significant effect, then it is only aiding the model in fitting the experimental error (i.e., noise) and is therefore eliminated as a suitable model. In some cases, multiple models remain statistically viable after this selection process, and these models were ranked using a Bayesian information criterion to determine the best refined model. The remaining alternative refined models do not describe the experimental data as well as the best refined model; however, they describe the data sufficiently to suggest possible additional active factors that require further experiments to conclude if those factors are actually active. Further details on the fractional factorial analysis can be found in SI sections 6 and 8.

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Design of the experiment, reagent lots, vis−NIR characterization, TEM characterization, data from characterization analysis, fractional factorial screening models, best refined surface-response models and analysis, alternative refined surface-response models and analysis, and references (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Nathan D. Burrows: 0000-0002-3973-1017 Catherine J. Murphy: 0000-0001-7066-5575 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out in part in the Frederick Seitz Materials Research Laboratory Central Research Facilities, University of Illinois at Urbana−Champaign. We acknowledge the National Science Foundation for the financial support of this work through grants CHE-1306596 and CBET-1336411. S.H. thanks the UIUC Department of Chemistry for the opportunity to participate in the Research Experience for Undergraduates program funded by the National Science Foundation and the 3M Foundation. We thank Dr. Rudiger Laufhutte at the UIUC School of Chemical Science’s Microanalysis Laboratory for conducting elemental analysis by ICP−MS. We thank the rest of the Murphy group for thoughtful discussions of synthesis protocols and laboratory practices.

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REFERENCES

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DOI: 10.1021/acs.langmuir.6b03606 Langmuir 2017, 33, 1891−1907