Ultra-small, size-controlled Ni(OH) 2 nanoparticles: elucidating the relationship between particle size and electrochemical performance for advanced energy storage devices

Nanosizing is the fashionable method to obtain a desirable electrode material for energy storage applications, and thus, a question arises: do smaller electrode materials exhibit better electrochemical performance? In this context, theoretical analyses on the particle size, band gap and conductivity of nano-electrode materials were performed; it was determined that a critical size exist between particle size and electrochemical performance. To verify this determination, for the first time, a scalable formation and disassociation of nickel-citrate complex approach was performed to synthesize ultra-small Ni(OH)2 nanoparticles with different average sizes (3.3, 3.7, 4.4, 6.0, 6.3, 7.9, 9.4, 10.0 and 12.2 nm). The best electrochemical performance was observed with a specific capacity of 406 C g−1, an excellent rate capability was achieved at a critical size of 7.9 nm and a rapid decrease in the specific capacity was observed when the particle size was <7.9 nm. This result is because of the quantum confinement effect, which decreased the electrical conductivity and the sluggish charge and proton transfer. The results presented here provide a new insight into the nanosize effect on the electrochemical performance to help design advanced energy storage devices. There is acritical size for nanoparticles that maximizes their electrochemical performance in energy storage devices, show a team in China. This finding goes against the conventional wisdom that smaller is better for the electrode material of such devices. Electrochemical energy storage devices such as batteries and supercapacitors are attractive power sources. One way to boost their performance has been to reduce the size of their electrode materials. Xingbin Yan and co-workers at the Lanzhou Institute of Chemical Physics prepared nine sets of Ni(OH)2 nanoparticles having various average sizes in the range 3.3 to 12.2 nanometers. They found that the best electrochemical performance was obtained at a size of 7.9 nanometers. Below that size, the specific capacity dropped off rapidly due to the quantum confinement effect and slower charge and proton transfer. Ultra-small Ni(OH)2 nanoparticles with different average sizes are prepared in large scale, and the best electrochemical performance is obtained at the critical size rather than the smallest size, which provides a new insight on nanosize effect on electrode materials in energy storage.


INTRODUCTION
Recently, electrochemical energy storage devices, such as batteries and supercapacitors, have attracted great attention because of their many advantages compared with other power-source technologies. However, these devices could realize further gains in energy and power densities if the electrochemical performance of electrode materials is largely improved. 1,2 Reducing the dimensions of electrode materials down to the nanoscale level is an effective strategy to promote their electrochemical performance, which primarily benefits from the nanosize effect, that is, achieving a higher surface area and a shorter ion diffusion length. 3,4 In this context, various nanosize electrode materials with greatly improved electrochemical performance have been synthesized. [5][6][7][8][9] Thereupon a fundamental question arises: do smaller electrode materials exhibit better electrochemical performance?
According to the relationship between the band gap (E g ) and the size (a) of a nanoparticle (for semiconductor) defined by [Equation (1)] 10-12 (where E bulk is the bulk band gap, ΔE is related to the quantum confinement effect, m e * is the effective mass of an electron, m h * is the effective mass of a hole and h is Plank's constant), the band gap increases as the particle size reduces. It should be noted that the quantum confinement effect, a sort of nanosize effect, inevitably arises as the particle size reduces to the nanoscale, particularly when o10 nm. [10][11][12] Furthermore, we deduced the relationships between particle size, conductivity (σ) and ΔE (Equation (2) and Equation (3)) (σ o represents the conductivity of the bulk-state semiconductor, k B is the Boltzmann constant, q is a constant related to m e * and m h *), which are plotted in Figure 1 (additional details regarding this deduction are shown in Supplementary Information). The widening of the band gap is closely related to the quantum confinement effect, which decreases σ (Figure 1a), and a dramatic decrease in σ occurs as the particle size reduces to an extent (shadow region in Figure 1b). Importantly, most works have proved that σ is closely related to the ion diffusional limitation and the polarization loss for electrode materials, where a decrease in σ causes an inferior electrochemical performance of electrode materials. 10,[13][14][15][16] Inspired by the above analyses, we hypothesize that minimizing the particle size may have a negative effect on the electrochemical performance, such that a critical size should exist for electrode materials. In addition, while many nanomaterials used in electrochemical energy storage devices have been synthesized by various methods, a precisely size-controlled synthesis and a systematic study of size-dependent electrochemical performance for the electrode materials are rarely performed due to the difficulty in controlling the size, particularly when o10 nm. These reasons have strongly motivated us to explore size-controlled electrode materials to elucidate the nanosize effect on the electrochemical properties for sub-10-nm materials for energy storage applications. Ni(OH) 2 , a typical lamellar-type hydroxide, is an important electrode material with a high theoretical capacity and has recently attracted great attention for use in designing high-performance battery and supercapacitor systems. 3,9,14,15,17 Herein, for the first time, a series of ultra-small Ni(OH) 2 nanoparticles with tunable sizes ranging from 3.3 to 12.2 nm are prepared via a scalable formation and disassociation of a nickel-citrate complex. These size-controlled Ni(OH) 2 nanoparticles overcome the previous size limitation and could be a desirable platform to reveal the nanosize effect on the electrochemical performance of sub-10-nm electrode materials.

EXPERIMENTAL PROCEDURE
Synthesis of size-controlled Ni(OH) 2

nanoparticles
In a typical synthesis, 0.172 mM of Ni(NO 3 ) 2 ·6H 2 O and 1.16 mM of C 6 H 5 Na 3 O 7 ·2H 2 O were first dissolved in 20 ml of distilled water under magnetic stirring. Then, 10 ml of a NaBH 4 aqueous solution (0.1 M) was rapidly injected into this mixture with vigorous stirring, which created a black solution. The entire solution was stirred for 10 h at 35°C to promote the complete oxidation of Ni particles and form stable nickel-citrate species, as observed by the color change of the solution from black to clear green. More details regarding the role of sodium citrate are given in our previous work. 18,19 Afterwards, 5 ml of NaOH aqueous solution (4 M) was added to the mixture immediately. The reaction mixture was continuously stirred for 5 min, then transferred into an autoclave and heated at a given reaction temperature (20,40, 60, 80, 100, 120, 140, 160 or 180°C) for 24 h. Finally, a green sediment was obtained, which indicates the formation of Ni(OH) 2 . The sediment was collected, washed with distilled water by centrifugation at 10 000 r.p.m. and re-dispersed in distilled water for further study.

Structural characterization
A transmission electron microscope (TEM, JEOL 2100 FEG, Tokyo, Japan) was employed to investigate the microstructure of the as-prepared Ni(OH) 2 nanoparticles. Powder X-ray diffraction (XRD, Rigaku D/Max-2400, Tokyo, Japan) was performed using Cu-Kα radiation to investigate the structure and composition of the samples. The zeta potential of the Ni(OH) 2 nanoparticles dispersed in distilled water was measured with a Zetasizernano 3600 instrument. The Raman spectra of Ni(OH) 2 nanoparticles were recorded by using a micro-Raman spectroscope (JY-HR800, Paris, France, excitation wavelength of 532 nm). The UV-vis absorption spectra of Ni(OH) 2 nanoparticles in water were recorded on a UV-vis spectrophotometer (Hitachi U-3010, Tokyo, Japan).

Electrode preparation and electrochemical measurements
The working electrodes were prepared as follows: the glassy carbon electrode (gas chromatography, 5 mm in diameter) was polished mechanically to become mirror-like by successively using 50-nm alumina powder, cleaned in an ultrasonic water bath and dried in an oven at 45°C. Five milliliter of the Ni(OH) 2 suspension (2.0 mg ml − 1 ) was ultrasonically mixed with 2 ml of ethanol, 3 ml of distilled water and 0.5 mg of conductive carbon black (XC-72, Cabot, Shanghai, China) to form a homogeneous ink. 10 μl of this ink was deposited onto the surface of the gas chromatography electrode and then dried naturally. Afterwards, 8 μl of diluted Nafion solution (5 wt%) was deposited to fix the active material onto the electrode. For all working electrodes, the same mass loading of~50 μg cm − 2 was used to reduce the effect of the electrode thickness on the electrochemical properties.
Electrochemical measurements were first performed using an electrochemical working station (CHI660D, Shanghai, China) in a three-electrode system in a 2-M KOH aqueous electrolyte at room temperature. A platinum wire electrode and a saturated calomel electrode served as the counter electrode and reference electrode, respectively.
Cyclic voltammetry was applied to study the electrochemical properties and measure the proton diffusion coefficient according to the Randles-Sevcik equation: 20 where I p is the peak current, n is the electron number of the reaction (approximately 1 for Ni(OH) 2 ), F is Faraday's constant, S is the real surface area of the electrode, R is the ideal gas constant, T is the temperature, D is the diffusion coefficient, v is the scanning rate and c 0 is the initial concentration of the reactant.  Figure S1 show that ultra-small, crystalline Ni(OH) 2 nanoparticles were synthesized on a large scale via the formation and disassociation of a nickel-citrate complex process with high yields (exceeding 92%, more details in Supplementary Information). The lattice fringes of the Ni(OH) 2 nanoparticles with an average spacing of~0.24 nm can be indexed as the (101) plane ( Figure 2b). The merit of this approach is the ability to synthesize sizecontrolled Ni(OH) 2 nanoparticles by adjusting the reaction temperature from 20 to 180°C, which was confirmed by TEM images ( Figure S3). It should be noted that several bar-like particles exist in larger sized Ni(OH) 2 synthesized at a higher reaction temperature. The difference in morphology of the Ni(OH) 2 nanoparticles may be due to the placing of particles in different directions, where the platelet-like morphology is related to an upward (100) facet of Ni(OH) 2 and the bar-like morphology is related to an upward (001) facet of Ni(OH) 2 (more details are given in Supplementary Figure S3). Figure 3a shows the XRD patterns of the Ni(OH) 2 nanoparticles of different sizes. All XRD diffraction peaks can be indexed as a hexagonal phase β-Ni(OH) 2 (space group P-3m1(164), a = b = 0.313 respectively. An almost linear relation between the particle size of Ni(OH) 2 and the reaction temperature is observed (Figure 3c), which indicates that the particle size of Ni(OH) 2 could be well controlled by the reaction temperature. Note that there is a difference in particle size values estimated from XRD and TEM, as shown in Supplementary Table S1, which can be ascribed to the hexagonal lamellar structures of Ni(OH) 2 (more details given in Supplementary Figure S3). Figure 3d and Supplementary Figure S4 show selected regions of the Raman spectra for nanocrystalline Ni(OH) 2 with different sizes, ranging from 3.3 to 12.2 nm. Three identified Raman peaks at 310,~450 and~3580 cm − 1 are observed, which can be assigned to the E-type vibration of the Ni-OH lattice, Ni-O stretching (vNi-O) and symmetric stretching of the hydroxyl groups (vOH), respectively. 21 The full-width at the half-maximum values of these peaks, particularly at 3580 cm − 1 , increase as the particle size decreases (Figure 3e). This phenomenon is also observed in other works on Ni (OH) 2 , 22 LiCoO 2 23 and MoS 2 24 with different particle sizes. Moreover, no clear peak appears at~3680 cm − 1 , which is generally assigned to free -OH groups on the surface, impurities, crystal defects and OH stretching for a new crystal phase, which indicates the good crystallized structure of the as-prepared Ni(OH) 2 nanoparticles. 21 This result is consistent with the aforementioned TEM results. Interestingly, high concentrations of the Ni(OH) 2 dispersion (reaction temperature at 20°C) turned into a transparent green gel (Figure 3f Figure S6). The Ni(OH) 2 colloids (reaction temperature o100°C) can be stable for over half a year because of their negative zeta potential (Supplementary Figure S7) or ultra-small particle sizes. Figure 3h shows the UV-visible spectra of Ni(OH) 2 nanoparticles dispersed in water. The steep absorption in the UV spectra below 350 nm is attributed to the band gap absorption of the Size-controlled Ni(OH) 2 nanoparticles R Wang et al Ni(OH) 2 nanoparticles. As seen in inset of Figure 3h, smaller Ni(OH) 2 nanoparticles have larger band gap values. Such a size-dependent blue shift in the band gap energy of the Ni(OH) 2 nanoparticles can be attributed to the quantum confinement effect, 10-12 which also has been observed in various semiconductor quantum dots or nanofilms, which include ZnO, 11 CdS, 25 CdSe 26 and InAs. 27

Electrochemical characterization
The electrochemical response of these different sized Ni(OH) 2 was characterized using cyclic voltammetry and galvanostatic discharge/ charge in 2 M KOH. For all of the Ni(OH) 2 electrodes, one pair of redox peaks is located on their cyclic voltammetry curves, as shown in Figure 4a, which indicates that the capacity response is primarily due to the Faradaic redox reaction of Ni 2+ to Ni 3+ . A larger potential difference between the oxygen-evolution-reaction potential (E o ) and anodic peak (E a ) and a smaller potential difference between E a and the cathodic peak (E c ) can be observed in the smaller Ni(OH) 2 nanoparticles (Supplementary Table S2), which indicate better reversibility and a higher charge efficiency. 28 Figure 4b shows the discharge curves for Ni(OH) 2 nanoparticles at 1 A g − 1 . Each discharge profile is composed of two sloping potential regions (greater than 0.22 V and less than 0.15 V) and a battery-type potential plateau between 0.15 and 0.22 V. The sloping regions can be ascribed to the pseudocapacitive contribution from surface or near-surface layer charge storage. 23 The battery-type potential plateau in all discharge curves is greatly related to the redox action between the Ni(OH) 2 and NiOOH phase. Notably, the proportion of the sloping region increased as the size of the Ni(OH) 2 nanoparticles decreased, which became clearer at the high discharge current density of 20 A g − 1 (Figure 4c and Supplementary Figure S8). To a certain extent, the proportion of the sloping region increases with a decrease in size, which indicates the increased pseudocapacitive behavior due to the nanosize effect on the surface reaction. 23,29 Such a nanosize effect on the electrochemical property of Ni(OH) 2 nanoparticles is also indicated by the lower redox voltage of Ni 2+ to Ni 3+ (Figure 4a and Supplementary Table S2) and steeper charge curves for smaller Ni(OH) 2 nanoparticles (Supplementary Figure S9). Figure 4d shows the specific capacity of these different sized Ni(OH) 2 nanoparticles as a function of discharge current density. The traditional concept of how particle size affects the specific capacity of electrode materials is that smaller particles exhibit better electrochemical performance. Therefore, it is expected that 3.3-nm Ni(OH) 2 Size-controlled Ni(OH) 2 nanoparticles R Wang et al nanoparticles will exhibit the highest electrochemical performance. Indeed, decreasing the average size from 12.2 to 7.9 nm causes a gradual increase in the capacity value (from 243 to 406 C g − 1 at 1 A g − 1 ), as expected. However, the opposite trend is observed in the specific capacity as the particle size continues to decrease. With a decrease in the particle size from 7.9 to 3.3 nm, the specific capacity decreases rapidly from 406 to 224 C g − 1 at 1 A g − 1 . When the discharge current density further increases to 20 A g − 1 , the same trend is observed. Accordingly, the optimal electrochemical performance is obtained at a critical size of 7.9 nm, not at 3.3 nm, which cannot be explained by the traditional understanding. These results are particularly interesting; however, it is still unclear what causes this reverse trend and how it affects the electrochemical performance. To make this clear, we first investigate the relationship between the conductivity, band gap and particle size of the Ni(OH) 2 nanoparticles. UV spectroscopy (Figure 3h inset) shows that smaller Ni(OH) 2 nanoparticles have a larger blue shift of the band gap (ΔE) due to the quantum confinement effect. According to the relationship in Figure 1a, with a decrease in the particle size from 12.2 to 7.9 nm, the band gap increases~0.08 eV, which leads to the conductivity decreasing by~4.75 times. As the particle size decreases from 7.9 to 3.3 nm, the band gap shifts~0.27 eV, resulting in a decrease in conductivity by~166 times. Weidner et al. suggested that the rapid decrease in conductivity causes a significant polarization loss via the theoretical simulation of the discharge character of Ni(OH) 2 . [30][31][32] In our study, at a particle size that is less than the critical value (7.9 nm), there is a decrease in capacity as the particle size decreases, which corresponds to a rapid decrease in conductivity; this result demonstrates the role of conductivity in the electrochemical performance. Moreover, many works have proven that the conductivity of electrode materials is closely related to the diffusion of protons through the nanoparticle and the redox reaction rate on the surface. 10,13,[30][31][32][33][34][35] This result leads us to hypothesize that the charge transfer resistance (R ct ) and proton diffusion coefficient (D) in the electrodes and electrolytes could change and differ from the traditional understanding because the particle size of Ni(OH) 2 is less than the critical size.
To prove this, the R ct and D of these size-tunable Ni(OH) 2 nanoparticles were tested. As shown in Figure 5a, the diameter of the semi-circle in the high-frequency region of the electrical impedance spectra is ascribed to R ct . An equivalent circuit was used to simulate the electrical impedance spectra curves, and the corresponding parameters are summarized in Supplementary Figure S10 and Supplementary Table S3. There is a trend of decreasing R ct values when the particle size decreases from 12.2 to 7.9 nm (Figure 5b). However, at a particle size of less than a critical value (7.9 nm), the trend reverses, and there is a rapid increase in R ct , which indicates the slow kinetics of the redox reaction of Ni(OH) 2 . In addition, the redox reaction for Ni(OH) 2 is widely recognized as a typical proton (H) controlled diffusion; thus, the proton diffusion coefficient (D) can be calculated from the Randles-Sevcik equation (Supplementary Figure   Figure 4  Size-controlled Ni(OH) 2 nanoparticles R Wang et al S11). 36,37 Figure 5c shows that the trend of D manifests the inverse behavior with R ct . There is an increase in D as the particle size decreases from 12.2 to 7.9 nm; however, a sharp decrease in D is observed when the particle size is less than 4.4 nm. The decrease of D in small electrode materials for a Li-ion battery, such as Li 4 Ti 5 O 12 and TiO 2 , was also reported recently. 38,39 As we know, the enlarged proton diffusion limitation and increased charge transfer resistance will lead to a great degree-of-discharge at the surface, and a larger overpotential is required to maintain a constant-current discharge. 23 Therefore, a small D and a large R ct value will decrease the use of active materials, resulting in an inferior electrochemical performance. In our study, decreasing the particle size from 12.2 to 7.9 nm caused a slight increase in D and a decrease in R ct , which is identical to the traditional nanosize concept, where nanosizing is used to increase the active surface area and reduce the diffusion path of protons and electrolyte ions. As expected, an increase in capacity is observed. In contrast, a reverse trend in R ct and D is observed as the size of the Ni(OH) 2 nanoparticles further decreases below 7.9 nm, and a decrease in the capacity occurs. It should be noted that this reverse trend in R ct and D is synchronized with the rapidly decreasing trend in σ caused by the quantum confinement effect, which is consistent with other reports 10,13,[30][31][32][33][34][35] and confirms the underlying relationship between σ, R ct and D. As a result, 3.3-nm Ni(OH) 2 nanoparticles have a minimum capacity value because of their low conductivity, large charge transfer resistance and small proton diffusion coefficient.
Generally speaking, three steps are involved in the redox reaction of Ni(OH) 2 in an alkaline solution: the diffusion of the electrolyte to the electrode surface, the intercalation/deintercalation of protons and the electron transfer in/out of the Ni(OH) 2 electrode. [35][36][37] Accordingly, a simple model that considers the relationship between the above stated parameters (σ, R ct and D) and electrochemical performance is proposed to explain the nanosize effect on these Ni(OH) 2 nanoparticles with tunable sizes, as shown in Figure 5d. Extreme reductions in the particle size to less than 7.9 nm decreases the electrochemical performance of Ni(OH) 2 , which can be ascribed to the quantum confinement effect for the decreased electrical conductivity and the sluggish charge and proton transfer. When the particle size is greater than 7.9 nm, the decreased electrochemical performance of Ni(OH) 2 nanoparticles is observed due to the increasing charge and proton transfer resistance. A critical size (7.9 nm), which is where the best electrochemical performance is obtained, exists for Ni(OH) 2 nanoparticles, which would largely account for the synergistic effect from the low charge and proton resistance as well as the acceptable electrical conductivity.

CONCLUSIONS
In summary, size-controlled Ni(OH) 2 nanoparticles overcome the previous limitation in synthesizing size-controlled electrode materials less than 10 nm in size and are a desirable platform to study the nanosize effect on electrochemical performance. The maximum capacity value can be obtained at the critical size of~7.9 nm, and a rapid decrease in the specific capacity is observed when the extremely reduced size is less than the critical size. Clearly, the nanosize effect on Ni(OH) 2 nanoparticles presented here is different from the popular concept, that is, that below the critical size, smaller Ni(OH) 2 nanoparticles have a lower capacity due to the quantum confinement effect from the decreased conductivity and sluggish charge and proton transfer. Thus, this work helps in understanding the nanosize effect on electrochemical behaviors and provides valuable information for Size-controlled Ni(OH) 2 nanoparticles R Wang et al selecting appropriately sized electrode materials to design highperformance energy storage devices.