CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of U.S. Patent Application No. 62/750,615, entitled“PHOTOCHEMICAL SYNTHESIS OF DENDRITIC SILVER PARTICLES,” and filed on October 25, 2018, which is incorporated herein by reference in its entirety.

TECHNICAL FIELD

[0002] This invention relates to photochemical synthesis of dendritic silver particles.

BACKGROUND

[0003] Over the last several years, the global value of counterfeit goods has exceeded half a trillion dollars. In addition to direct economic losses to manufacturers, counterfeit materials, parts and assemblies typically provide inferior performance and poor reliability, which can cause security issues, such as security risks for national defense. There is an increasing demand for high trust, high reliability tagging methodologies, in which genuine articles manufactured in a legitimate facility carry“trust elements” incapable of being cloned.

Current physical tagging technologies include holograms, coded tags, DNA signatures, mechanical deformation, and fabricated nanostructures. However, such techniques have several disadvantages, including difficulties in manufacture, lack of structural stability and reliability, and complicated readout procedures.

[0004] Fractal structures, such as synthetic dendritic silver particles, are promising candidates for physical identifiers to combat counterfeiting. For example, dendritic silver particles can be applied to an item and decoded to yield a large exclusive integer, which can be mapped to the item in a secure database. Traditionally, dendritic silver particles are prepared using organic reducing agents, ultrasonically assisted templated synthesis, direct replacement reactions, photoreduction, plating, g-irradiation, magnetic field assisted growth, or pulsed sonoelectro-chemical methods. These methods, however, typically require a long preparation time and/or precisely controlled environmental conditions that are not conducive to mass manufacturing. In addition, the morphology of dendritic silver particles obtained by these methods can lack natural diversity.

SUMMARY

[0005] Dendritic silver particles are synthesized by a photochemical process of irradiating an aqueous precursor solution containing silver ions, a conjugate base of a weak acid, and a polymer comprising amine groups. This process yields dendritic silver particles after 20 minutes or less of UV irradiation under ambient conditions. The size and shape of the particles can be altered by varying experimental parameters, such as length of irradiation and local chemical environment. Unique dendritic structures obtained by this process have distinctive morphological characteristics suitable for tagging and securing manufactured items. The dendritic silver particles synthesized by this process can reach sizes of up to about 100 pm, which allows structural information about the particles to be quickly read and analyzed by optical microscopy, thereby facilitating the use of the particles as anti counterfeiting labels in supply chains.

[0006] In a general aspect, dendritic silver particles are formed by combining silver ions, a reducing agent, and a polymer comprising amine groups in an aqueous solution to yield a precursor solution, and irradiating the precursor solution with ultraviolet radiation to form a multiplicity of dendritic silver particles.

[0007] Implementations may include one or more of the following features.

[0008] The reducing agent may include an organic acid (e.g., citric acid or ascorbic acid). A molar ratio of silver ions to the conjugate base of the weak acid in the precursor solution is typically in a range of about 3 to about 3.5. In one example, the polymer is poly(allylamine). A pH of the precursor solution is in a range of about 12 to about 13. A molar ratio of amine groups to silver in the precursor solution is between about 6 and about 12. Irradiating the precursor solution occurs under ambient conditions. The precursor solution is typically irradiated with ultraviolet radiation for at least 3 minutes, up to 20 minutes, or both. The wavelength of the ultraviolet radiation is typically in a range of about 320 nm to about 400 nm. The ultraviolet radiation has an output power in a range of about 1.5 W/cm ² to about 4 W/cm ² .

[0009] The dendritic silver particles typically have a linear dimension up to about 100 microns. In some cases, the dendritic silver particles are dendritic silver nanoparticles. The dendritic silver particles comprise at least 95 wt% silver. A branch density of the dendritic silver particles is in a range of about 0.1 x 10 ⁵ branch/mm ² to about 11 x 10 ⁵ branch/mm ² . A junction density of the dendritic silver particles is in a range of about 1 x 10 ⁴ junction/mm ² to about 36 x 10 ⁴ junction/mm ² . A fractal dimension of the dendritic silver particles is in a range of about 1.4 to about 1.9. Each dendritic silver particle of the multiplicity has a unique structure. In some cases, selecting a molar ratio of amine groups to silver, a length of time of the irradiating, or both is selected to achieve a desired morphology of the multiplicity of dendritic silver particles. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. 1 depicts an exemplary scheme for synthesis of dendritic silver particles.

[0011] FIGS. 2A- 2B show samples of precursor solution before and after the solution is subjected to UV irradiation, respectively.

[0012] FIGS. 3A- 3C show electron microscopy images of the structure of dendritic silver particles.

[0013] FIG. 4 shows the energy-dispersive X-ray spectrometry spectrum for an exemplary branch of a dendritic silver particle.

[0014] FIGS. 5A- 5C show transmission electron microscopy images of dendritic silver particles at 30 seconds, 60 seconds, and 3 minutes of ultraviolet (UV) irradiation, respectively.

[0015] FIG. 6A depicts the growth mechanism of dendritic silver particles. FIG. 6B depicts a proposed structure of a silver particle- poly(allylamine) ((AgNP)-PAAm) complex that enables the formation of dendritic particles.

[0016] FIG. 7 shows dendritic silver particles synthesized from precursor solutions containing various amine/silver ratios. The scale bars represent 500 nm.

[0017] FIGS. 8A- 8E show patterns of dendritic silver particles formed after 20 minutes of UV irradiation.

[0018] FIG. 9 depicts an exemplary skeleton analysis for identification of dendritic branch levels.

[0019] FIGS. 10A- 10E show branch length distribution plots for five types of dendritic silver particle patterns.

[0020] FIG. 11 shows a plot of dendritic silver particle branch densities as a function of fractal dimension.

[0021] FIG. 12 shows molecular structures of silver particles during the synthesis of dendritic silver particles using a precursor solution containing allylamine (AAm).

[0022] FIG. 13 depicts molecular structural changes that occur during synthesis of dendritic silver particles.

[0023] FIG. 14 shows a plot of the average branch length of dendritic silver particles as a function of the amine/silver ratio of the precursor solution.

[0024] FIGS. 15A- 15E show distributions of the weighted number of branches of a specific length (w) as a function of branch length (/.) for five types of dendritic silver particle patterns. DETAILED DESCRIPTION

[0025] A method for synthesizing dendritic silver particles is described. This method includes steps of combining silver ions, a reducing agent, and a polymer comprising amine groups in an aqueous solution to yield a precursor solution, and irradiating the precursor solution with ultraviolet radiation to form a multiplicity of dendritic silver particles.

Examples of suitable reducing agents for the precursor solution include organic acids, such as citric acid and ascorbic acid. An example of a suitable polymer comprising amine groups in the precursor solution is poly(allylamine) (PAAm). The pH of the precursor solution is typically in a range of about 12 to about 13. The molar ratio of silver ions to weak acid in the precursor solution is typically in a range of about 3 to about 3.5. The molar ratio of amine groups to silver in the precursor solution is typically in a range of about 6 to about 12. The described method of synthesizing dendritic silver particles may be conducted under ambient conditions. As used herein,“ambient conditions” generally refers to a combination of common or prevailing temperature, pressure, and relative humidity found in a laboratory or manufacturing setting.

[0026] Irradiation of the precursor solution to synthesize dendritic silver particles is performed using ultraviolet (ETV) radiation. The precursor solution may be irradiated for a length of time between about 3 minutes and about 20 minutes or more to achieve a desired variation in the size and patterns of the dendritic silver particles. A wavelength of the UV radiation is typically from about 320 nm to about 400 nm (e.g., ETV A), and the output power of the UV radiation is in typically in a range of about 1.5 W/cm ² to about 4 W/cm ² .

[0027] The dendritic silver particles synthesized by the described method have defined geometric features, including a core and dendritic branches that extend from the core. The dendritic silver particles also include junctions (or nodes) at which the dendritic branches meet. These geometric features, or minutiae, of the dendritic silver particles create unique patterns and structures that enable individual particles to be identified out of the multiplicity of particles. The branch density of the dendritic silver particles synthesized by the described method ranges from about 0.23 x 10 ⁵ branch/mm ² to about 10.4 x 10 ⁵ branch/mm ² . The junction density of the dendritic silver particles synthesized by the described method ranges from about 1.0 x 10 ⁴ junction/mm ² to about 35.8 x 10 ⁴ junction/mm ² . Individual particles may be distinguished from the multiplicity of particles by determining the fractal dimension of the particle. The fractal dimension of the dendritic silver particles synthesized by the described method ranges from about 1.4 to about 1.8.

[0028] The dendritic silver particles synthesized by the described method can have a size of up to about 100 microns. As used herein,“particle size” refers to the linear dimension from the end of one dendrite (i.e., branch) of the particle to the end of an opposing dendrite of the particle. In some implementations, the dendritic silver particles created by the described method are nanoparticles. As used herein,“nanoparticle” refers to particles with a dimension in a range of about 20 nm to about 1000 nm. The dendritic silver particles created by the described process are substantially pure silver (e.g., at least 95 wt% silver).

[0029] FIG. 1 depicts an exemplary setup 100 for synthesis of dendritic silver particles using a process of polymer-assisted photolysis. A precursor solution 102 for synthesis of dendritic silver particles may be obtained by combining silver nitrate, sodium citrate, and a poly(allylamine) (PAAm) solution. In one example, a precursor solution was prepared by combining silver nitrate and sodium citrate at a 2: 1 molar ratio with a poly(allylamine) (PAAm) solution containing a ~l M amine group. A photo-reduction of nitrate and a polymeric ligand was selected for the precursor solution to achieve synthesis of dendritic silver particles under ambient conditions. The precursor solution was exposed to UV radiation. In one example, the precursor solution was irradiated by a 365 nm UV light for 3 minutes. As a result of UV radiation, small dendritic silver particles were formed. A change in color of the precursor solution 200 and 202 in FIGS. 2A and 2B, respectively, was observed as a result of the UV radiation, indicating the presence of dendritic silver particles. The dendritic silver particles bound to the PAAm and served as seeds for further growth. The bounded particles connected via crystal growth under the presence of citrate and free amine groups. Following irradiation, polymeric ligands formed a polymer backbone to create a chain tethering together the particles. Some amine groups fixed the relative positions of dendritic silver particles by forming N-Ag coordination bonds. Free amine groups served as a reducing agent that facilitated Ag growth, especially inter-particle growth.

[0030] As shown in FIGS. 3A and 3B, presence of dendritic silver particles 300 was confirmed using transmission electron microscopy (TEM). The dendritic silver particles 300 contained a dense core 302 and extended branches 304. Each branch was composed of silver particles approximately 50 nm in size. The composition of the dendritic silver particles 300 was further analyzed using scanning electron microscope (SEM) (as shown in FIG. 3C). As shown in FIG. 4, energy-dispersive X-ray spectrometry of the particles revealed a high abundance of Ag (39.14%), indicating that the particles obtained from the precursor solution were substantially pure silver. The remaining elements are believed to be from the substrate (e.g., carbon coated copper TEM grid). Silver distribution matched the morphology of the observed dendritic particles. [0031] As shown in FIGS. 5A and 5B, as radiation time increased to 60 seconds, a densely packed Ag core 500 emerged, with newly formed particles 502 extending from the edges. As shown in FIG. 5C, further increasing the UV exposure time to 3 min resulted in the formation of dendritic particles 504. As indicated by FIGS. 5A-5C and 6A, the formation of dendrites, rather than simple isotropic growth, is preferred due to the local chemical gradient created by PAAm. The chemical concentration gradient around the growth front of crystals is vital in the formation of dendritic particles. As shown in FIG. 6A, the presence of PAAm provides a nanoscale chemical gradient for formation of dendritic silver particles. Fixation of a portion of the silver particles by PAAm creates a steric effect that results in the fixed silver particles having improved accessibility to reagents compared to non-fixed silver particles, creating a first chemical gradient. In addition, the distribution of free amine groups on PAAm is anisotropic with regard to individual silver particles, resulting in a second degree of chemical gradient.

[0032] The dendritic AgNPs are believed to grow in a two-step process. First, during nucleation, small AgNPs form after UV illumination through the photoreduction of silver nitrate with sodium citrate as the reducing agent, and further bind PAAm to yield clusters. Next, during growth, the clusters serve as seeds to guide the further growth of Ag crystals under the presence of reducing agents (e.g., citrate and PAAm). FIG. 6B depicts a proposed structure of a silver particle (AgNP)-PAAm complex 600 that enables the formation of dendritic particles. The amine group between AgNPs 602 indicated by dashed curves 604 facilitates the anisotropic growth of silver.

[0033] Alteration of the local chemical environment changes the relative reaction rate of Ag nucleation and seeded growth, which results in significant changes in the morphology of the silver particles. The amine/ Ag ⁺ ratio (N/Ag) can be adjusted to alter the local chemical environment. In one example, precursor solutions with N/Ag ratios of 1, 2, 4, 6, 10, 12, and 20 were tested and the corresponding products obtained after 3 minutes of UV irradiation were analyzed. As shown in FIG. 7, five distinctive dendritic morphologies 700, 702, 704, 706, and 708 were observed. For precursor solutions with N/Ag < 6, only random silver particle aggregates formed as a result of insufficient amine groups. Dendritic silver particles possessing long major branches and short sub-branches started to form at N/Ag ratios equal to 6. Some individual silver particles that did not have a chance to grow can be observed. For precursor solutions with N/Ag ratios equal to 6-8 (700 and 702), the sub-branches were longer, and a well-branched dendritic structure was observed. Further increasing the N/Ag ratio to 8-10 (704 and 706) led to the formation of medium and long sub-branches, and the apparent number of branches started to reduce. When the N/Ag ratio of the precursor solution was equal to 10 (706), a further reduction in branch number was observed and the as-formed dendritic structures featured very long branches and sub-branches. Increasing the N/Ag ratio to 12 (708) led to formation of small particles with very thick branches. Only individual silver particles were observed when the N/Ag ratio of the precursor was above 12.

[0034] The size of dendritic particles can be adjusted by increasing or decreasing the irradiation time. In one example, the irradiation time was increased to 20 minutes. As shown in FIGS. 8A-8E, the size of the Ag particles (type I-type V, or 800, 802, 804, 806, and 808, respectively) increased by approximately 1-2 orders of magnitude when the irradiation time was increased from 3 minutes to about 20 minutes. Dendritic patterns as large as 50-100 pm can be formed by adjusting irradiation times to about 20 minutes.

[0035] Mathematical analysis of the dendritic Ag patterns may be performed to reveal their unique structures, as well as their potential as information carriers. The type and position of minutiae, geometric features of the particles, confer uniqueness on a dendritic pattern and distinguish one pattern from all others. For dendritic silver particles, the junctions (or nodes) of the dendrites are the relevant minutiae. A measurable parameter in each of the nodes may be used to represent a value of modulus B such that the total number of possible patterns is given by B ^no , where n ₀ is the number of junctions measured. For example, if the position of each junction was read as being in either an even (0) or odd (1) numbered location in a Cartesian grid overlay, then 5 = 2. When the junction density is 10 ⁵ per mm ² and the reading resolution is 3 pm, the total number of possible patterns in a 50 pmx 50 pm dendrite area is in the order of 10 ⁷⁵ , which is more than enough to tag every manufactured item. Considering the junction density and the branch length distributions shown in Table 1 below, type III patterns may be most suitable for tagging purposes as they possesses a high junction density and a greater portion of branches over 3 pm in length.

Table 1. Exemplary branch and junction densities for five pattern types of dendritic silver particles

Pattern type

Branches per ₂ .7 0.50xl ₍ fi 3.9±0.09xl0 ⁵ 2.0±0.78xl0 ⁵ 0.35±0.12xl0 ⁵ 8.0±2.4xl0 ⁵ mm ²

Junctions per 9 _7±2 9xl0 ⁴ 15.7±0.5 ^c 10 ⁴ 8.1±3.6xl0 ⁴ 1.5±0.5xl0 ⁴ 26.2±9.6xl0 ⁴ [0036] In one example, image analysis was performed using Image! Skeleton analysis of a dendrite may be conducted to reveal branch and junction information, such as first, seocnd, and third branches 900 and junctions 902 depicted in FIG. 9. FIGS. 10A-10E show changes in the N/Ag ratio of the precursor solution resulted in variations in branch/junction densities and distinctive branch length distributions. As shown in Table 1, when N/Ag ratio of the precursor solution increased, the branch/junction density also increased (type II), and then dropped until the N/Ag ratio of the precursor solution reached 10. Type V pahems possessed the highest branch/junction density. This trend was verified using optical imaging (FIGS. 8A - 8E). When the N/Ag ratio of the precursor solution was relatively low, increasing the N/Ag ratio resulted in increased branching. As N/Ag ratio of the precursor solution further increased, longer but fewer branches were favored. At very high N/Ag ratios, small and highly dense branches were formed.

[0037] As shown in Table 2, essentially all of the dendritic silver particle pahems were found to be perfect dendritic structures and were distinguishable according to their fractal dimension (FD). As shown in FIG. 11, formation of fractal structure is driven by reaction dynamics. Branch density increased as a power of FD.

Table 2. Exemplary fractal dimension of five pattern types of dendritic silver particles

Pattern

II III IV V type

FD 1.716±0.013 1.671±0.017 l.57l±0.046 l.4l±0.058 1.821±0.015

2

R 0.998 0.999 0.999 0.998 0.999

EXAMPLE

[0038] Silver nitrate (ACS reagent, >99.0%), sodium citrate dehydrate (>99.0%), allylamine (>99.0%) and poly(allylamine) solution (Mw -17,000, 20 wt. % in H20) were purchased from Sigma- Aldrich. 400 mesh ultra-thin carbon coated TEM grids were purchased from Ted Pella.

[0039] Dendritic silver particles were synthesized via polymer-assisted photolysis. A precursor solution for silver particle synthesis was obtained by first combining 204 mg silver nitrate and 134 mg sodium citrate dehydrate in 200 mL DI water. A poly (allylamine) (PAAm) solution containing - 1 M amine group was obtained by diluting 20% PAAm solution. 1 mL of the silver nitrate/sodium citrate solution was mixed with the PAAm solution, with the final precursor solution having an equivalent molar ratio of amine group and Ag ⁺ ions (N/Ag) of 10: 1. For samples with different N/Ag values, the amount of PAAm solution added was adjusted accordingly to mix with 1 mL silver nitrate/sodium citrate solution to achieve a final precursor solution having an equivalent molar ratio of amine group and Ag ⁺ ions (N/Ag) of 10: 1. For the purpose of comparison, the synthetic process was also repeated by replacing PAAm with allylamine (AAm).

[0040] The final precursor solution was subjected to UV radiation. UV radiation was applied using a BlueWave® 200 UV curing spot lamp. The output power of the UVA band was adjusted to 3.0 W/cm ² . The wavelength of the UV radiation was about 365 nm.

[0041] The reaction products were deposited on a TEM grid following irradiation for TEM and SEM analysis. TEM images were captured using a Philips CM 12 TEM. SEM and energy-dispersive X-ray spectrometry (EDX) data was obtained using a Hitachi S4700 FESEM.

[0042] Microscopic images of the reaction products were obtained using an Olympus BX53 microscope. For optical imaging, reaction products were drop-casted onto a glass slide cleaned with Harrick plasma cleaner. The reaction products were allowed to dry in air overnight before imaging.

[0043] As shown in FIG. 12, for mixtures containing AAm, rather than PAAm, as the ligand and reducing agent, no dendritic particles were formed. In mixtures containing AAm, silver particles 1200 were bound to the small molecule ligands and remained subject to random movement in the aqueous solution. As a result, particles could not be connected efficiently through crystal growth. By comparison, in mixtures containing PAAm, the polymeric ligand was able to fix the relative positions of adjacent silver particles, so that inter-particle Ag growth could occur. As depicted in FIG. 13, the relative position of the initially formed silver particles 1300 was fixed by PAAm chains 1302 through chelation, which resulted in variation of the accessibility of individual silver particles to citrate ions 1304. For example, silver particles 1300 located at the edge of polymer chains 1302 had a greater chance to continue growing under the presence of a reducing agent. In addition, the local distribution of free amine groups varied for individual silver particles 1300, leading to an anisotropic growth of Ag under continuous UV irradiation.

[0044] Optical images of dendritic silver patterns were analyzed using ImageJ (Fiji version). Fractal box analysis was conducted by converting images to 8 bit and using the “fractal box count” function. The box size was chosen to be 2, 3, 4, 6, 8, 12, 16, 32 and 64. The number of boxes containing a fraction of the image was counted. All of the patterns observed were perfect dendritic structures, demonstrated by the high R values in linear regression shown in Table 2. The FD value for various pattern types varied from 1.41 to 1.82 (Table 2). The standard deviation of FD for a specific type of pattern was much smaller than the difference in FD between the various pattern types, making it possible to readily distinguish pattern types according to FD.

[0045] In order to count the number of branches and junctions of the dendritic silver particles, the 8 bit image was first skeletonized and then analyzed using the“analyze skeleton” function. The skeletonization function classified the distance between two adjacent junctions (or one junction and one end) as a branch. The junction/end was defined as a voxel that had more than two neighbors or only one neighbor, respectively. The shortest branch method was used to prune the ends to eliminate loops and end-points. For accuracy, at least three images were analyzed for each type of pattern.

[0046] As shown in FIG. 9, different levels of branches may be observed in dendritic patterns corresponding to the order of silver growth, with the smallest n ^th level branch the result of Ag particles that attached to the Ag nanowire network. The number of branches increased as the order of silver growth increased. Branch density increased following a near exponential trend as the FD increased, as shown in FIG. 11. This is explained by the fact that FD is a measurement of surface coverage and follows a scaling rule:

N = e ^~FD

where the variable N stands for the number of segments, and e is the scaling factor. The only deviation from the scaling rule observed was in type I patterns, which may be the result of increased branch thickness compared to the other pattern types.

[0047] Changes in the N/Ag ratio resulted in an alteration in the reaction rate, which lead to variations in branch/junction densities and distinctive branch length distributions (FIGS. 10A - 10E). For type I and type II patterns, the branch length distribution was fitted by a single Gaussian function with peak centers located at 1.3 pm and 1.5 pm, respectively.

Compared with type I patterns, the branches in the type II pattern had a narrower distribution. Additional Gaussian peaks were observed in type III patterns at 4.2 pm and type IV patterns at 5.4 pm, which corresponds to longer branches and indicates that the growth speed of the Ag crystals exceeded the seeding speed under those conditions. The longest branches only exist as first level branches due to steric effects (FIG. 9). As a result, the major portion of branches still featured a shorter length. The average branch length dropped to 0.8 pm for type V patterns. The drop in branch length may be due to the insufficiency of free silver ions, as most silver ions were chelated by the amine groups on PAAm, which hindered crystal growth.

[0048] As shown in FIG. 14, the average branch length (L) generally reflected the same findings. To analyze the branching characters in dendritic Ag patterns, a parameter w was defined as the weighted number of branches at a specific length. The value of w represents the total length of Ag that grows into a specific type of branch. By definition, w = N _L x L, where NL is the number of branches with length L. Each type of dendritic pattern can be distinguished by the distribution of w as a function of branch length (FIGS. 15A - 15E). In the w-L plot, several linear trends can be observed for each type of dendritic structure. The slope of the linear trends represents NL, and for each linear trend NL is the same. In addition, the linear trend with the lower slope typically possesses a greater average length. Each linear trend represents one level of branching. The trend with the smallest slope comes from level 1 branching, which is the major branch that first forms in the solution. Similarly, the trend with the second, third, ... , m ^th smallest slope will be level 2, 3, ... , m branches. The number of distinguishable linear trends indicates the number of times the structure has copied itself. For type II, III and IV patterns, four levels of branches are identified, demonstrating a significant complexity for these pattern types. For type I and V, three levels are observed, indicating a lower complexity for these pattern types.

[0049] Application. Two tags were made using the dendrites, and a series of tests were performed to verify if it is possible to discriminate features from different tags. Two rectangular regions of 90 pm x 50 pm were located under the microscope, and denoted as tag I and tag II. The microscopic features of them were recorded to establish a database. Tag I was assumed to be the label of an authentic or wanted object, while tag II was a control. Five square regions 25 pm x 25 pm were randomly chosen from tag I and tag II, which were set as keys to be identified. A scale-invariant feature transform (SIFT) analysis was performed to identify those keys via comparing feature points. It was found that all the keys selected from tag I could be readily identified. Tens to hundreds of matching feature points were found between tag I and key 1-4, the positions of which accurately matched the regions that the keys were selected from. On the other hand, key 5 selected from tag II didn’t show any match to tag I, although both tags were generated from the same batch of Ag dendrites. The results showed that the dendritic features possessed great ability to form unique taggants. Moreover, the information contained in a tiny region was already sufficient for identification, which has several advantages. First, the cost for a single tag could be readily reduced. For example, tags with a dimension of 100 pm x 100 pm would be sufficiently large for encryption, which only cost 2 nL of the Ag dendrite suspension. Second, it is possible to produce a vast number of tags from a single batch of product (5 x 10 ⁵ tags per mL). Third, a tag could still be accurately identified even if most of it were damaged, which makes the tag highly durable and reliable.

[0050] In summary, a photochemical method to synthesize various types of dendritic AgNPs has been demonstrated. Experimental parameters (e.g., N/Ag ratio and illumination time) were found to affect the morphologies of the dendrite AgNPs. Moreover, the size and morphology of those particles can be uniquely generated and readily tuned by choosing appropriate growth parameters (e.g., N/Ag and illumination time). Optical imaging and mathematical analysis revealed that dendritic particles grown under the different conditions could be well distinguished based on their branch/junction densities and branch lengths. Further, the superior ability of the as-prepared dendrites to produce vast numbers of unique patterns makes it perfectly suitable for physical tagging for anti-counterfeiting and security purposes.

[0051] A number of embodiments have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other embodiments are within the scope of the following claims.