Influence of polyvinylpyrrolidone (PVP) capping layer on silver nanowire networks: theoretical and experimental studies

Abstract

This study conducts an experimental and theoretical investigation of the influence of a polyvinylpyrrolidone (PVP) capping layer on silver nanowire (AgNWs) networks. Through a washing method, a PVP layer on AgNWs was removed and the contact resistance (R_C) between AgNWs was reduced, thereby obtaining a reduced sheet resistance (R_S) of AgNW film. During the washing process, the thickness of the PVP layer decreased to 1 nm with an increasing number of washes, as demonstrated by a molecular dynamics simulation. In addition, the size of the change in R_S resulting from the reduction in R_C by the removal of PVP decreased as the areal coverage of NWs increased. In order to explain the results, Monte Carlo simulations were performed and the results show that the reduction in R_C by the removal of PVP apparently reduces the value of R_S more as the areal coverage of NWs decreases and the initial value of R_C of the network increases. Saturation of the reduction in R_S also occurs when the inherent resistance of AgNW (R_NW) becomes dominant. Along with the electrical properties, improved transmittance and a reduction in haze were observed with the removal of PVP, and the results prove that R_S can be reduced by reducing R_C without impairing the optical properties of transparent conducting electrodes.

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1. Introduction

Silver nanowire (AgNW) films have been extensively investigated as promising candidates for transparent conducting electrodes (TCEs) as a substitute for tin-doped indium oxide (ITO) that provides low sheet resistance (R_S) (<10² Ω sq⁻¹), high transmittance (>90%), mechanical flexibility, and a highly scalable wet process.^1–5 However, AgNW films exhibit strong absorption and scattering, in particular, in the wavelength range of 300–500 nm, due to localized surface plasmonic resonance (LSPR).⁶ Therefore, an appreciable haze and yellowness were observed in AgNW electrodes compared with other types of flexible TCEs such as those made from graphene, carbon nanotubes, and conducting polymers.⁵ These optical characteristics of AgNWs limit the areal coverage of a AgNW network for TCE applications and, as a result, other factors need to be manipulated in order to reduce the value of R_S further without causing a deterioration in the optical properties of TCEs.

At a constant areal coverage of wires, the value of R_S of a percolating network has been known to depend primarily on the contact resistance (R_C) between the wires. In the case of AgNW networks, the R_C between the AgNWs is mainly produced by the insulating polyvinylpyrrolidone (PVP) capping layer of the AgNWs, which is an inherent residue of the polyol process used to synthesize the AgNWs with PVP as a polymeric capping reagent.⁷ The outer polymer layer forms a metal–insulator–metal contact at the AgNW junction and therefore conducted electrons pass through the junction by means of tunneling. Therefore, the value of R_C at the junction could be reduced by adjusting the tunneling barrier that arises from the insulating layer.

Several approaches have attempted to reduce the value of R_C between AgNWs such as thermal annealing,^8,9 Joule heating,¹⁰ plasmonic welding,¹¹ mechanical pressing,¹² electroless deposition,¹³ and solvent washing.^14–16 The solvent washing approach is possibly the most suitable for practical applications, owing to it being a scalable wet process. Although several researchers have examined solvent washing methods for reducing the value of R_C on AgNWs,^14–16 there have been few theoretical interpretations of the relationship between the removal of PVP from AgNWs and their electrical/optical properties. This paper investigates the influence of the PVP capping layer on silver nanowire networks. By adjusting the thickness of the PVP capping layer on AgNWs, improved electrical and optical properties were obtained, which was confirmed both experimentally and theoretically. In addition, this study shows that the thickness of the PVP layer after washing was reduced to 1 nm as the number of washes increased, which was supported by molecular dynamics simulation results. Also, the size of the reduction in R_S resulting from the removal of PVP is studied in terms of the areal coverage of NWs and the initial value of R_C of AgNW networks using a Monte Carlo simulation.

2. Experimental

A dispersion of AgNWs (diameter 20 nm and length 15 μm) in deionized (DI) water was purchased from Aiden. To reduce the thickness of the PVP layer on the AgNWs, the as-received AgNWs were washed with deionized (DI) water several times. After washing, the precipitate was redispersed in DI water. The morphology of the treated AgNWs was characterized by transmission electron microscopy (TEM: Tecnai G2, 200 kV). Along with the TEM characterization, TGA (Mettler Toledo) was used to investigate the effect of washing by measuring the weight of the residual PVP. Samples of approximately 7 mg of each AgNW were placed in an alumina pan and tested at a ramping speed of 10 °C min⁻¹ from 20 to 600 °C under a flow of N₂. The value of R_S of a AgNW network was measured using a four-point probe system (Loresta-GP, MCP-T610, Mitsubishi Chemical). To minimize dependence on the dispersion, the value of R_S of a percolating network of each AgNW (as-received and washed) was directly measured on a filter paper (Whatman) after a vacuum filtration process. In parallel, for TCE applications, AgNWs and hydroxypropylmethylcellulose (HPMC) were mixed and dispersed in DI water, and then were coated on a polycarbonate (PC) substrate. The transmittance and haze were measured using a haze meter (NDH 7000SP, Nippon Denshoku). For each sample, five points were measured to obtain average values.

A molecular dynamics simulation was performed using DL_POLY software.¹⁷ The simulation cell comprised 256 N-vinylpyrrolidone oligomers and 1200 TIP3P water molecules¹⁸ confined to silver plates. The silver plates were modeled as four rigid, flat layers with dimensions of 3.24 × 3.24 nm. For convenience, we employed a Cartesian coordinate system, in which the surface of the silver plates was located at z = 0 and its normal defined the z-direction. A polarizable CHARMM-based force field was used to describe the Ag (100) surface¹⁹ and the force fields of PVP and water were taken from previous studies.^18,20 All simulation instances were carried out in a canonical ensemble with a Nose–Hoover thermostat at 298 K. Periodic boundary conditions were imposed. Long-range electrostatic interactions were computed via the standard Ewald method with a correction for the slab geometry, which resulted in essentially no truncation of these interactions.²¹ The trajectories were integrated via the Verlet leapfrog algorithm using a time step of 0.5 fs. Five independent equilibrium simulations were carried out with equilibration times of 2 ns, followed by a production run of 1 ns, from which the ensemble averages were computed.

A Monte Carlo simulation was performed to calculate the value of R_S of a AgNW network in terms of R_C and the areal coverage of NWs. The AgNW network was obtained by placing multiple random instances of a rigid rectangular rod in a square domain (200 μm by 200 μm). To generate a single random instance, a two-dimensional center point and angle of a rigid rectangular rod with a width of 20 nm and a length of 15 μm were sampled uniformly at random. The connectivity of two rods was tested by calculating the distance between two lines that corresponded to the cylindrical axes of the rods. The two rods were considered to be in contact if this distance was less than the width of the rods (20 nm).

The connectivity information was used to explore the percolating paths, traversing from one end to the other end of the simulation domain, and all rods were classified into separate groups according to the paths that they belonged to.²² If any conducting paths existed, a system of linear equations was constructed by applying Kirchhoff's current law (KCL) at every junction in the path.²³ In this simulation, both components that arose from the inherent resistance of the AgNW, namely, the resistance of the nanowire (R_NW) and R_C between two NWs, were considered when KCL was applied to every node in the network, as illustrated in Fig. 1. The value of R_NW between two neighboring junctions, i and j, on the same NW is approximated by using a simple resistance equation, R_NWij = ρ_AgNW (πr²_NW/L_ij), where r_NW is the radius of the NW, L_ij is the distance between the junctions i and j, and ρ_AgNW is the resistivity of the AgNW.^24,25 In addition, the value of R_C between AgNWs was approximated by using a generalized formula for the tunnel resistivity of a thin insulating film between similar electrodes:²⁶

where h is the Planck constant, m is the mass of an electron, e is the elementary charge, d is the thickness of the film, and λ is the effective height of the tunneling barrier. Finally, the total current that flows through the network under an applied voltage of 1 V was calculated by using a linear algebra software package to solve the system of equations numerically, and the reciprocal of the total current calculated from the solution corresponds to the value of R_S of the network. The estimated value of R_S was calculated by taking the ensemble average of 1000 independently generated random instances of the AgNW network. The MC simulation in this work is of a static configuration based on random sampling of the center positions of rods, where a new sample does not depend on previous samples, instead of a dynamic configuration where the initial configuration may be in a transition state, thereby requiring careful treatment of equilibration and sampling. Therefore, the initial configurations in the simulation were also considered to be valid and were included for calculating the sheet resistance.

Fig. 1 Conceptual illustration of R_C and R_NW and the equivalent circuit of a Ag NW network used for a Monte Carlo simulation instance.

3. Results and discussion

A change in the value of R_C between AgNWs was achieved by reducing the thickness of the PVP layer on AgNWs by using washing methods.^14–16 PVP-reduced AgNWs were obtained by washing as-synthesized AgNWs with deionized (DI) water several times. Fig. 2(a) and (b) show images obtained via TEM and the average thickness of the as-synthesized AgNWs can be seen to decrease from 3 nm to 1 nm after washing 20 times with DI water. In addition to the TEM characterization, TGA was carried out to investigate the reduction in the thickness of PVP due to washing. As shown in Fig. 3(a), weight loss began to appear at about 350 °C for both AgNWs when the PVP layer began to decompose.²⁷ However, the percentage weight loss of the washed AgNWs became 2.6% less than that of the as-synthesized AgNWs, which indicates that the PVP capping layer on the washed AgNWs was thinner. It is noted that the PVP capping layer over the AgNWs cannot be removed completely by washing with DI water or solvents, as was inferred from the reduction in the weight of the washed AgNW at 350 °C in the TGA experiment, as well as observed in previous studies.^14–16 Also, according to the results of repeated analyses of TEM images shown in Fig. 3(b), the thickness of the PVP converged to 1 nm as the number of washes increased.

Fig. 2 (a) TEM image of an as-synthesized PVP-capped AgNW and (b) the same NW after washing 20 times with DI water.

Fig. 3 (a) Percentage of residual weight of as-synthesized AgNW (black solid line) and NW after washing 20 times with DI water (red solid line), as measured via thermogravimetric analysis. (b) Average thickness measured for the PVP capping layer on the AgNWs with different numbers of repetitions of the washing process.

To gain further insight into the limits to the thickness of the PVP layers, the molecular dynamics simulation on the PVP layers that form an interface with the Ag (100) surface in water was performed [Fig. 4(a)]. The number distribution n_α(z) of the center of mass for atom species α was calculated such that:

where N_α(z) is the total number of atoms α in a simulation box with a length of z perpendicular to the surface. The results for the average number distribution n_α(z) are shown in Fig. 4(b).

Fig. 4 (a) Snapshot of the PVP layer on the Ag (100) surface in water obtained at 298 K. The gray balls at the bottom represent the Ag atoms that form an interface with the PVP layers. Carbon and nitrogen are illustrated in cyan and blue colors. Oxygen and hydrogen atoms in water molecules are depicted by red and gray colors, respectively. (b) Number distribution functions n_α(z) as functions of the distance from the Ag surface, z, for nitrogen, carbon, and oxygen atoms in PVP, averaged over five independent trajectories of 1 ns at 298 K. (c) Snapshots representing the equilibrium state of the PVP layer (carbon, nitrogen, and oxygen in the PVP molecules are drawn in cyan, blue, and red colors, respectively) in water with a width of 1 nm adjacent to the Ag surface (purple balls). (Left) Side view and (Right) top view.

The oxygen atom of the carbonyl group in PVP produces a strong peak structure at z = 0.3 nm from the Ag surface, followed by a second peak at z = 0.7 nm, which indicates that pyrrolidone rings form a layered structure on the surface. This result can be attributed to strong bonding between the oxygen atom in the carbonyl group and silver atoms in the first layer, which thereby prevents the removal of the PVP layer adjacent to the Ag surface by washing. The snapshots in Fig. 4(c) depict the interfacial structure of the bilayered PVP with a thickness of about 1 nm, which corresponds to that in the TEM image in Fig. 2(b).

The change in R_C that was attributed to washing the PVP layer was studied regarding its effect on the electrical properties of the AgNW percolating network by conducting experiments and Monte Carlo simulations with variations in the areal coverage of NWs.^22,23 Fig. 5(a) shows the results of a Monte Carlo simulation as a function of the areal coverage of NWs for AgNWs with PVP layers of 3 nm and 1 nm, respectively. The value of R_S decreased as the thickness of PVP was reduced, which indicates that a reduction in the value of R_C is obviously advantageous for a decrease in R_S. This is consistent with the experimental results for the value of R_S of networks fabricated with as-synthesized AgNWs and AgNWs washed 20 times, as shown in Fig. 5(b). In this experiment, the weight of AgNWs could be quantitatively converted into the areal coverage of their network by considering the weight and geometry of AgNWs.

Fig. 5 (a) R_S calculated for the values of R_C of PVP layers with thicknesses of 3 nm and 1 nm. (b) Measured values of R_S with error bars for a random AgNW network made of AgNWs with PVP capping layers of 3 nm and 1 nm. (c) Relationship between R_S and R_C calculated for various areal coverages when the internal resistance of the NW was ignored (dashed line) and considered (solid line) in a Monte Carlo simulation. (d) R_S calculated when R_C is 10⁵ Ω and ρ_NW is ρ_AgNW of a AgNW with a diameter of 20 nm (black solid line), when R_C is 10⁵ Ω and ρ_NW is 0.5ρ_AgNW (reduction in R_NW, blue dashed line), and when R_C is 10³ Ω and ρ_NW is ρ_AgNW (reduction in R_C, red solid line). (e) R_S calculated when R_C is 10³ Ω and ρ_NW is ρ_AgNW (black solid line), when R_C is 10³ Ω and ρ_NW is 0.5ρ_AgNW (reduction in R_NW, blue dashed line), and when R_C is 10¹ Ω and ρ_NW is ρ_AgNW (reduction in R_C, red solid line).

However, for the results in both Fig. 5(a) and (b), the size of the change in R_S with respect to a given value of R_S (ΔR_{S(washed NW−original NW)}/R_{S0(original NW)}, which can be inferred from the gap, Δy₁, between the black and red solid lines in Fig. 5(a) and (b)) steadily decreases as the areal coverage of NWs increases. In order to explain the decrease in the reduction rate (ΔR_{S(washed NW−original NW)}/R_{S0(original NW)}), two different cases of the Monte Carlo simulation were performed as a function of R_C. As shown in Fig. 5(c), one set was calculated with the value of R_NW of a AgNW with a diameter of 20 nm (solid lines), and the other set was calculated with R_NW = 0 (dashed lines). According to the results of the simulation with R_NW = 0, at a certain change in R_C the reduction rate (ΔR_{S(washed NW−original NW)}/R_{S0(original NW)}, which can be inferred from the size of Δy₂ in Fig. 5(c)) will be almost constant for all values of areal coverage regardless of the initial value of R_C of the AgNW network, because all the dashed lines are parallel. This is at variance with the results in Fig. 5(a) and (b). In contrast, the value of R_S calculated with the finite value of R_NW deviates gradually from that of R_S without R_NW (R_NW = 0) as R_C decreases. Both sets of simulation results almost coincide in the range of R_C > ∼10⁴ Ω [blue shaded area in Fig. 5(c)] when the value of R_S is determined predominantly by that of R_C. However, as R_C decreases further to the region of R_C < ∼10² Ω [red shaded area in Fig. 5(c)], R_S with the finite value of R_NW converges to a specific value because, in this case, the value of R_S of the AgNW network is determined predominantly by R_NW. In addition, the value of R_C where R_S starts to become saturated increases as the areal coverage of the AgNWs increases. Therefore, for this set of results (solid lines in Fig. 5(c)), at a certain change in R_C the reduction rate (ΔR_{S(washed NW−original NW)}/R_{S0(original NW)}, which can be inferred from the size of Δy₃ in Fig. 5(c)) decreases as the areal coverage of AgNWs increases and as the initial value of R_C of the network decreases. In other words, the reduction in R_C by the washing of PVP will provide an apparent reduction in R_S when the initial R_S of the AgNW network is dominated by R_C (low areal coverage of NWs or high initial value of R_C), whereas the change in R_S due to the removal of PVP will be subtle when the initial R_S of the AgNW network is dominated by R_NW (high areal coverage of NWs or low initial value of R_C).

To extend the results, two different behaviors of R_S can be expressed as a function of the areal coverage of NWs according to changes in R_C. As shown in Fig. 5(d), if R_C dominates the initial R_S of the network (black solid line), a change in the value of R_C will reduce R_S (red solid line) decisively, whereas the change in the value of R_S due to a change in R_NW is negligible (blue dashed line). Also, in the case where the value of R_S is reduced due to a change in R_C, the reduction rate of R_S (ΔR_S/R_S0) will decrease as the areal coverage of the network increases. On the other hand, Fig. 5(e) shows that if the initial R_S of the network is dominated by R_NW, a change in R_NW will reduce the value of R_S decisively, whereas the change in the value of R_S due to a change in R_C can be practically ignored. In the case where the value of R_S is reduced by a change in R_NW, the reduction rate of R_S (ΔR_S/R_S0) will increase as the areal coverage of the network increases.

Furthermore, improvements in optical properties such as transmittance and haze due to the removal of PVP are shown in Fig. 6(a) and (c), respectively. Optical measurements were performed with percolating networks of as-synthesized AgNWs and AgNWs washed 20 times, which were coated on a polycarbonate (PC) substrate by a machine-controlled wire-wound rod. The areal coverage of the AgNW network was controlled by adjusting the size of the rod, i.e., the bar number,²⁸ while the concentration of AgNWs was fixed.

Fig. 6 (a) Transmittance versus bar number of a Mayer rod with error bars (in order to avoid an overlap in the plots of transmittance and R_S, the left y-axis (transmittance) is in reverse order). (b) Absorption cross-section of Ag nanoparticles with PVP capping layers of 3 nm and 1 nm. (c) Haze versus bar number of a Mayer rod with error bars (the values of R_S of the corresponding samples are plotted together in order to indicate the different areal coverages of the AgNW networks that were coated with different bar numbers of the Mayer rod). (d) Scattering cross-section of Ag nanoparticles with PVP capping layers of 3 nm and 1 nm.

According to Fig. 6(a), a AgNW network with a thinner PVP layer (∼1 nm) provides a higher transmittance than a network with a thicker PVP later (∼3 nm) for all values of areal coverage. Similarly, the haze measured for a network with a PVP layer of 1 nm is always less than that for a network with a PVP layer of 3 nm, as shown in Fig. 6(c). The improvements in transmittance and haze due to the removal of the PVP can be explained via the extinction cross-section of the metal nanoparticles:²⁹

where C_abs and C_sca are the absorption and scattering cross-sections, respectively. Also, a is the radius of the nanoparticles, ε and ε_m are the optical permittivities of the metal nanoparticles and medium, respectively, k = 2πε_m^1/2/λ is the wavenumber in the medium, and α is the electrostatic polarizability, which was calculated by:

The principle of dipole equivalence³⁰ was used to modify α and ε in eqn (4) via the following equations:

where β_Ag–PVP = (ε_Ag − ε_PVP)/(ε_Ag + 2ε_PVP) and f = r_Ag²/(r_Ag + d_PVP).² With the modified equations, the values of C_abs and C_sca of Ag nanoparticles (diameter 20 nm) with PVP capping layers of 3 nm and 1 nm were calculated and the corresponding spectra in the visible range (wavelength 300–800 nm) are depicted in Fig. 6(b) and (d), respectively. The calculated results indicate that the removal of 2 nm of PVP resulted in decreases of 39% and 58% in C_abs and C_sca, respectively. This demonstrates the improvement in transmittance and haze in the AgNW network. In addition, the blue shift and reduction in intensity of the peak at 400 nm in both spectra in Fig. 6(b) and (d) suggest that less yellowness will be observed in AgNW network TCEs with a thinner PVP layer.

4. Conclusions

In summary, a reduction in the value of R_S of a AgNW network due to a change in R_C by the removal of PVP is shown by experiment and Monte Carlo simulations. Both results show that the size of the reduction in R_S decreases as the areal coverage of NWs increases. This tendency is explained based on the Monte Carlo simulations, and the results indicate that the reduction in R_C by the washing of PVP will lead to an apparent reduction in R_S at a low areal coverage of NWs or a high initial value of R_C, whereas the change in R_S will be subtle at a high areal coverage of NWs or a low initial value of R_C. In addition, an improvement in optical properties, i.e., transmittance and haze, is demonstrated by reducing the thickness of the PVP. The results confirm that the value of R_S can be reduced via a change in R_C without a deterioration in the optical properties of TCEs.

Acknowledgements

The authors declare no competing financial interests.

References and notes

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