A New Method for Controlling the Quantized Growth of Dendritic

Dec 8, 2014 - The goal of this study was to produce dendrite-type point contacts with ...... In Spectroscopy of Emerging Materials; Faulques , E. C. ;...
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A New Method for Controlling the Quantized Growth of Dendritic Nanoscale Point Contacts via Switchover and Shell Effects A. P. Pospelov,† A. I. Pilipenko,† G. V. Kamarchuk,‡ V. V. Fisun,‡ I. K. Yanson,‡ and E. Faulques*,§ †

National Technical University “Kharkov Polytechnic Institute”, 21 Frunze Str., Kharkov, 61002, Ukraine B. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., Kharkov, 61103, Ukraine § Institut des Matériaux Jean Rouxel, University of Nantes, CNRS, UMR 6502, 2 rue de la Houssinière, BP 32229, 44322 Nantes Cedex 3, France ‡

ABSTRACT: We report on quantum electrical characteristics of dendritic copper point contacts (PCs) formed through an electrochemical process via a new cyclic switchover effect that is demonstrated by the occurrence of steps in the time dependence of the dendritic-PCs conductance. We show that this quantization of the electrical conductance is due to an electronic shell effect governing the dendrite growth. The cyclic variations of conductance during dendritic PCs electrosynthesis offer the possibility for forming nanostructures of preassigned sizes controlled through their electrical resistance.

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filled with metal11 and connecting bulk metallic bankselectrodes. The spatial parameters that influence the fundamental properties of PCs are of primary importance. In accordance to the theory of point-contact spectroscopy by Kulik, Omelyanchuk, and Shekhter,15 the main criterion that determines the PCs behavior is the relation between their dimensions and the electron mean free path. This relation means also that the PC sizes can span nanometer to angstrom scales up to the size of molecules.7,11 The most functional electron transit through a PC sample is known as the ballistic regime, which occurs when the mean free path of charge carriers exceeds significantly the PC length and diameterthe so-called pure limit. At room temperature, this regime can be found in high-conductivity metals (e.g., copper and gold or carbon nanotubes).17−20 Otherwise, when the electronic mean free path is shorter, a current flow in the thermal regime develops in the PC that behaves like a bulk material. Under this condition, a PC can hardly avoid degradation at high current density. In contrast, pristine nanosized PCs are invulnerable at room temperatures up to a current density of 107 A/cm2 (in this case, bulk samples will be structurally degraded even at a

INTRODUCTION Recently, much research interest in nanosciences has focused on novel approaches in the design of functional nanodimensional objects presenting modified physical or chemical properties with respect to the bulk. In this context, electrochemical methods proved to be very efficient because they allow an easy control of shaping processes through fine current and potential tuning. Samples with preassigned shapes and sizes can be gently prepared at controllable electrical rates. These methods were extensively employed to make nanowires for nanoelectronics.1−6 Electrochemical processes are used both at preparatory stages like electrode treatment and in the formation of samples for point contact (PC) investigations, especially for room temperature researches.7−12 Since it has been found recently that, owing to their specific nature, PCs can be suitable as nanoscale sensing elements for detecting gas media, highquality dimensional and electronic characteristics are also a prerequisite for their applications at room temperature.13,14 A point contact is usually defined as a contact of small size that is created between two bulk metallic electrodes touching each other on a small area.7,11 There are several theoretical models that describe adequately the nature of the physical phenomena in real point contacts. The most widely used are the model of the orifice in the dielectric partition dividing two metallic half-spaces and the model involving a long channel © XXXX American Chemical Society

Received: July 3, 2014 Revised: December 6, 2014

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The Journal of Physical Chemistry C density as low as 102 A/cm2).13 Therefore, external factors only consequent to a considerable current rise can induce PC degradation in the thermal regime. As a result, a PC working in the ballistic regime instead of the thermal regime of current flow is more suitable for many applications. The probability to reach the pure limit can be augmented by a proper selection of the geometric and structural characteristics of PCs.21 On the one hand, the geometry-based approach allows tailoring PCs as small as single-atom sizes. In practical terms, it also permits a fine control of PC lengths and diameters in the long-channel model.7,11 On the other hand, the structure-based approach is dependent on possible defects in the materials that decrease the electron mean free path in the contact. Therefore, a good geometry-structure compromise can bring both charge carrier mean free path and PC sizes to correlated values favorable for reaching the ballistic limit. In this paper, we describe the formation and quantized physical properties of nanoscale dendrite PCs obtained by approaching an electrochemically grown nanosized copper tip electrode near a flat counter-electrode surface. Generally, electrochemical processes proceed in nonuniform electric f ield distribution over electrode surfaces inducing density gradients in the electrolysis current. The field line nonuniformity can be rather significant depending on the correlation between the surface irregularities on the electrodes and the electrode spacing. When electrodes are immersed parallel to each other in an electrolyte, the bulging areas at their surfaces have higher current densities; i.e., the electrochemical processes are faster there. In an electrolyte containing metal ions extended crystalline formations, the so-called dendrites, appear on these parts of electrodes.22 When a dendrite grows, it will ultimately touch the counter-electrode surface to form a direct contact between the electrodes, provoking a short circuit. Here, we investigate a short-circuited PC system in an electric field. The goal of this study was to produce dendritetype point contacts with definite diameters in suitable electrochemistry conditions and to investigate their quantum electrical characteristics. We reveal a novel electrochemically stimulated effect producing a cyclic switchover of dendrite growth and dissolution. The cycles are caused by periodic nanodimensional transformations of the sample structure leading to an electronic shell effect observed in time-dependent conductance measurements. By taking advantage of this cyclic effect, it is possible to control accurately the growth parameters of PCs.

Figure 1. General scheme of the needle−anvil dendrite PC preparation. 1: needle; 2: a drop of electrolyte; 3: anvil; 4: dendrite.

current determining the rate of the electrochemical process was within 1−1000 μA. Direct (d.c.) and alternative currents were used to grow dendrites and for electrical measurements, respectively. We investigated the time dependence of the electrical resistance R(t) of the electrode system and the point contacts using an original point-contact spectrometer developed at B. Verkin Institute for Low Temperature Physics and Engineering. A four-probe arrangement was used to cancel the influence of current-feeding leads. The electrical resistance of the sample (i.e., the needle−electrolyte−anvil system) was measured in alternating current (477 Hz, 1−3 μA) with a lock-in amplifier (SR 830 DSP) whose signal range corresponded to the resistance region of a PC with direct conductivity (0−12.9 kΩ).7,11 The setup prohibited the influence of possible parasitic electromagnetic fields. Because of its low level, the measuring current had a negligible effect both on the nanostructure formation and on additional electrochemical processes. Resistance was not registered when the metallic needle−anvil contact was absent because, in this case, the resistance is far beyond the specified interval. During dendrite growth, the resistance of the system varies with time, entailing corresponding changes in the current or the voltage that depend on the operating regime of the electric circuit. Since a PC consists of a small number of atoms, a slight enhancement of the current in the circuit can immediately affect the size of the growing nanoobject or even cause its thermal destruction. The high-rate process of PC dimensional change reduces the lifetime of the system and hampers the measurement of its resistance. To avoid this problem, we provided an automatic control of the current in the circuit by stabilizing the voltage drop in the electrode system when the circuit is operated in the voltage source regime. In this case, the increasing resistance suppresses the current in the PC circuit and decreases the deposition rate of Cu atoms. Since the circuit measuring the PC resistance operated in the current-source mode and the feed circuit of the electrochemical process was connected to the voltage source, it was necessary to exclude their interaction. For this purpose, a special electronic feedback circuit was designed, which permitted the electric circuits to operate independently. In the voltage-source mode, the current passing through low-resistive PCs can destroy the system even at low stabilized voltage. The problem can be remedied by transferring the system into the current-source regime. Taking into account these features, we provided automatic monitoring of the current regimes during sample growth. In PCs with electrical resistance below 1 kΩ, the electrochemical process proceeds in the d.c. current-source mode. Above 1 kΩ, the circuit changes to the d.c. voltagesource mode. The regime switching provides an automatic

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EXPERIMENTAL SECTION Dendrite-type point contacts were formed in the needle−anvil geometry. Copper electrodes were placed in a special device, affording a fine and smooth control of the interelectrode distance.23 In this way, metallic dendrites were grown as depicted below under electrochemical conditions at room temperature. Initially, an electrochemically sharpened needle electrode was fixed on a spring damper above a flat electrode perpendicular to its surface at a distance ≤ 5 μm (Figure 1). The interelectrode spacing was controlled by the absence of conductivity in the circuit. A CuSO4 electrolyte droplet was placed in the interelectrode gap to form an electrolytic needle− anvil contact. Electrolyte concentration c was varied in the range of 10−6 to 7.5 × 10−1 mol/dm3. The system was connected to a circuit operating as a current/voltage source. The negative pole of the source was connected to the needle electrode and the positive one to the flat anvil electrode. The B

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Figure 2. (a) Scanning electron micrograph (SEM) of a Cu needle tip after passing the current through the needle−electrolyte−anvil system. Distinct areas of growing dendrites are seen. The arrow points to the most developed dendrite that will form a PC. The white deposits at the surface are the remains of the electrolyte salts. (b) SEM picture of another dendrite.

control of the electrochemical process. An original cyclic switchover effect takes place. The metallic dendrite grows electrochemically until direct contact with the counterelectrode occurs. At this stage, the growth is stopped and dendrite dissolution begins until contact breakage; thereon, the dissolution stops and allows another growth cycle to begin. This repeatedly occurring cyclic switchover is allowed by the electrochemical nature of the system and operates under both d.c. current-source and d.c. voltage-source conditions. Because of the original potential distribution in the point contact7,11,13,15 the potential drop is concentrated in the region of contact constriction when the current is flowing in the contact channel. Therefore, a point-contact channel immersed into the electrolyte transforms into an elongated electrochemical component16 and can operate as a nanostructured tool to govern chemical processes on the nanoscale.

Figure 3. Point-contact resistance R versus time t. (a) General view of the dependence R(t). 1: examples of peaks in the R(t) dependence corresponding to small diameter contacts; 2: examples of the local minima in the R(t) dependence corresponding to PCs with large diameters. (b) Magnification of R(t) in the area delimited with a rectangle. Dashed lines show conductance steps and metastable states of the contact. The concentration of the aqueous CuSO4·5H2O solution is 5 × 10−1 mol/dm3. I = 20 μA.

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RESULTS AND DISCUSSION When current flows through the needle−electrolyte−anvil system (the needle is the cathode and the anvil is the anode), dendrites start to grow in the electrode-active areas of the needle surface having the highest density of electric field lines (Figure 2). Dendrites may have different linear rates of growth, and sometimes one of them will grow to touch the surface of the counter-electrode. We have found that the formed contact is a point contact with direct conductivity. If current continues to flow, a cyclic process develops in the system after fractions of a second to several minutes: the PC resistance varies with time when going through the stages of growth, reduction, and stabilization. The stages are repeated many times, accounting for the cyclic changes in the physical and chemical properties of the object. The cyclic changes recurrence is automatic with no external influence. The duration of the process is dependent first of all on the electrolyte stability, and in certain situations, it can last for several hours. The typical time-dependent resistance R(t) of a copper dendritic PC is illustrated in Figure 3. When there is no direct electrical needle−anvil contact, the interelectrode space is filled with electrolyte. Since the electric field is higher at the needle tip, one can evaluate the electrical resistance of the “electrode−electrolyte−electrode” system in the absence of direct conductivity between the needle and the anvil. In this case, the current loss at the side surface of the needle and the current spreading around the contact area at the anode are negligible. The current channel through electrolyte can be modeled as a cylinder with a diameter equal to that of the needle tip or the dendrite. The ionic current maintaining

dendrite growth and connection successively flows through the dendrite-electrolyte boundary, the electrolyte, and the electrolyte−counter-electrode (anvil) interface. According to calculation, the resistance of the whole system is determined by the polarization resistance, which, at the “dendrite−electrolyte” boundary, is over an order of magnitude higher than that of the electrolyte, the distance between the dendrite tip and the counter-electrode size ranging from several tens of angstroms to several micrometers. Assuming that the specific conductivity of the electrolyte CuSO4·5H2O (c = 0.5 mol/dm3) is σ = 3 Ω−1m−1,24 the polarization resistivity at the “copper−CuSO4” boundary is22 ∼10−3 Ω m2 and the effective diameter of the active surface on the cathode (dendrite tip) is 0.1 μm, we can estimate the total resistance of the ionic portion of the circuit to be about ∼40 MΩ. This estimate shows that the resistance levels of the electrolyte and the interfaces exceed considerably 2 −1 the resistance of a single atomic PC given by G−1 0 = ((2e )/h) = 12.9 kΩ, where G0 is the conductance quantum in the PC, e is the electron charge, and h is the Planck constant.25,26 This allows a resistometric control of the nanostructure formation in the configuration used. As the dendrite approaches the anvil, the diameter of its tip decreases, which further enhances the polarization resistance at the interface and increases the difference between the electrical resistances in the electrolyte gap and the single atomic PC. This makes the shunting effect of C

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The Journal of Physical Chemistry C the current flowing through the side surface of the needle insignificant. Besides, the lifetime of the sample state in which the direct electrical needle−anvil contact is broken during the cyclic growth of dendritic PCs is rather short, as seen, for example, by sharp changes of the R(t) dependence in Figure 3 at high resistance values. Since PC breakage or formation of atomicsized contacts is very fast, special techniques and devices for selective signal amplification with finite time constant of detection are necessary to measure the parameters of the growing system. We chose a measurement range of the lock-in amplifier that corresponded to the resistance interval of directconductivity PCs, i.e., 0−12.9 kΩ, and only these sample states were fixed. When a direct needle−anvil contact is formed, the sample resistance drops to a level marked by the local minimum in the corresponding part of the R(t) dependence in Figure 3. According to the theory of PC spectroscopy, there is a correlation between the PC resistance and the PC diameter. In the pure limit of current flow near zero voltage bias, the PC resistance is described by the Sharvin equation both in the orifice and long channel models27

R0 =

16ρl 3πd 2

shell effect in metal PC nanochannels were revealed by Yanson et al. and studied in detail.29,34 An artist’s depiction of atomic positions in the normal cross section of the wire demonstrating the shell effect is sketched in Figure 3.22 of Yanson’s thesis.34 He et al. have also published different atomic configurations of ultrathin Cu nanowires.35 It was found that metallic nanowires formed at low temperatures by the break-junction technique should satisfy definite dimensions (amounting the diameters of conductance channel) corresponding to stable states of the nanostructure; i.e., alkali-metal PCs exhibited conductance maxima corresponding to a strictly definite number of atoms forming a contact. During the break-junction cycles, nanowires are characterized by diameters spanning from a single atom to a few tens of atoms in size with a definite quantized conductance. Such dimensions are observed with the highest probability and correspond to the states of longest lived PCs. A similar correlation was detected in noble metals at room temperature.36 Other nanowire atomic configurations in which values of quantized conductance differ from those of the most observable states are not completely forbidden.37 They can be observed in a lesser extent and reflect quasi-stable states of nanowires with short lifetimes. The conductance of cylindrical nanowires is related to their cross-sectional radii by34

(1)

where ρl is the product of the metal resistivity and the electron mean free path. This quantity is a constant for each metal. The inverse R0−d relation persists in the intermediate and diffusive current limits. This means that a decrease or an increase in the resistance is caused by the corresponding increase or decrease in the PC diameter. Thus, the maxima in the R(t) dependence of Figure 3 correspond to contacts having small cross sections close to the PCs’ atomic size. The variations of the interelectrode voltage during selfoscillations of the resistance show up as clearly visible steps in the dependence R(t) attributed to electron conductance quantization of dendritic PCs and the electronic shell effect.28−30 The staircase shape of the curve along with the starting conditions of the experiment and the cyclic character of the process point to the formation of a PC nanostructure whose size can be easily obtained through conductance measurement. The shell effect has already long been described for different quantum physical objects. It manifests itself as a periodic dependence of the measured physical quantities along linear dimensions of the sample under investigation. In this case, values that are observed more frequently testify about stable quantum states of the system and evidence for the existence of a shell structure. In fact, the shell effect is due to energy distribution of particles in a quantum system. Quantized particles in a quantum system have energies that group into bunches of degenerate or close-lying levels, called shells. The case of a shell with a definite set of completely filled energy states corresponds to a local minimum in the total energy of the system and characterizes the ground state with highest stability. Cross-sectional diameters of metallic nanowires that are produced as point contacts in the long channel model have also direct correlation to their electrical transport properties.25,31 The dependence of the electronic free energy on the nanowire radius contains minima that represent stable nanowire configurations due to shell filling.32 Steps in electrical resistance of the point contact connected with variation of point-contact diameter were observed for the first time by Akimenko et al.33 Quantum character of electrical transport and

⎡⎛ k r ⎞ 2 ⎤ kr 1 G = gG0 = G0⎢⎜ F ⎟ − F + + ...⎥ ⎢⎣⎝ 2 ⎠ ⎥⎦ 2 6

(2)

which, in the case of ballistic electron transport, is

⎛ kFr ⎞2 G = G0⎜ ⎟ ⎝ 2 ⎠

(3)

where r is the cross-sectional radius of the conductor, and kF is the Fermi wave vector. Time-dependence G(t) of dendritic PCs obtained by inverse transformation of the experimental curves R(t) is shown in Figure 4.

Figure 4. Time variations of the conductance G of dendritic copper PCs demonstrating enhanced stability states. The currents of PC formation (μA) are 10(1), 20(2), 50(3).

The conductance variations in a dendritic PC structure account for the states of enhanced stability corresponding to certain PC diameters. The plateaus in the stepped dependence G(t) correspond to the metastable states of the contact. Each stable state changes to another by jumps of resistance (conductance), which produces stepped regions in the curve. The minima and the maxima in the conductance of a growing D

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The Journal of Physical Chemistry C dendritic PC are reproduced in many cycles of the selfoscillatory process. Many conductance steps repeatedly occur in the ascending and descending regions of the curve G(t). However, sometimes these steps appear only at one side of the cycle but are absent at the other side. Obviously, an individual cycle of dendrite growth or dissolution is insufficient to form a dendritic PC with a complete set of stable shells inherent to the metal involved. A similar effect was also observed in an individual cycle of PC formation and breakage by the breakjunction method.34 It is found experimentally that the dendrite growth and dissolution can proceed smoothly, without breaking the contact. This can be achieved by tuning the voltage bias in the needle−anvil contact. In this case, both sides of the R(t) curve have steps generated by quantization of the contact conductance due to the shell effect (e.g., see Figure 4, curve 3). This behavior may be attributed to a shunt of the needle and anvil by the gas molecules or molecular clusters formed in the electrolyte that are adsorbed between the end atoms of the electrode surfaces and form a conducting bridge. A similar situation was observed in the conductance of gold PCs in which the electrodes came into contact through a bridge of adsorbed CO molecules38 and for Au, Ag, Cu, and Pt atomic contacts in hydrogen and nitrogen environments.39,40 Simultaneous growth of several approximately equal dendrites must not be ruled out. In this case, superposition of the processes involving several dendrites can be viewed as a missing information on complete PC breaking in G(t). From the above observations, the cyclic switchover effect in electrochemical formation of point-contact dendrite structures manifests itself as clear steps in the time dependence of the dendritic-PCs conductance, which is completely distinctive from the behavior of samples formed for break junctions.34,36 Indeed, in nanowires formed by the mechanically controlled break-junction method, the lifetime of a metastable PC state is rather short (less than a second) due to the continuous application of a pulling force during PC formation.41 In the enhanced-stability state, our PC lives much longer (several seconds) and allows direct observation of the conductance steps in the dependence G(t). This agrees with the data for nanowires formed by the traditional technique of electrochemical dissolution or deposition of electrodes.4,10,37 Additionally, PCs of a particular resistance range can be formed by varying the electrolyte concentration and current. For example, nanostructures of smaller cross sections can be obtained with dilute electrolyte solution by using our cyclic process for dendritic PC growth and dissolution. As the concentration of the electrolyte increases, the cyclic process shifts into the region of PCs with relatively large diameters. Figure 5 shows the conductivities of dendritic PCs growth in the cyclic process as a function of the electrolyte concentration c for a series of special experiments designed to reveal the effect of c on the formation and the size of copper PCs. Each solution was investigated in five experiments under identical conditions, and five dependences R(t) were measured. Histograms were then derived to characterize the distribution of the PCs’ conductance. The histogram maximum corresponds to the most probable PC under the conditions of the experiment. The highest values of conductance in five histograms for electrolytes of identical concentrations were used to estimate a credible interval of conductance with 95% probability. Since c correlates with the density of the exchange current, any decrease of c leads to an enhanced polarizability of

Figure 5. Conductance G of copper PCs as a function of the concentration c of the aqueous electrolyte solution CuSO4·5H2O.

electrodes.22 In the potentiostatic regime, this effect slows down the electrochemical process at invariant electrode polarization. However, as c decreases, the frequency of connections somewhat increases; i.e., the linear rate of dendrite growth becomes higher. Owing to the property of selforganization of the system during the dendrite growth, the effective current density remains essentially constant. Therefore, the decrease of c is related to a decrease in the effective diameters of the growing dendrites. Experimentally, this appears as a rise of dendritic PC resistance at a decreasing electrolyte concentration. The conductance steps appearing in a large number of successive cycles of dendritic PC transformations were used to obtain conductance histograms of the growing PCs. The histograms for different electrolyte concentrations are illustrated in Figure 6.

Figure 6. Conductance histograms of copper PCs. Curve 1: copper break junction.36 Curve 2: dendritic PCs (950 conductance steps in the dependence G(t) were processed). The CuSO4·5H2O concentration c is 10−6 mol/dm3. Curve 3: dendritic PCs (1500 conductance steps in the dependence G(t) were processed). The CuSO4·5H2O concentration is 5.0 × 10−3 mol/dm3. Curve 4: dendritic PCs (2100 conductance steps in the dependence G(t) were processed). The CuSO4·5H2O concentration is 2.5 × 10−1 mol/dm3. The labels at the top (3 → 9 → 21) represent the number of maxima occurring in curves 2−4.

The positions of the conductance maxima in the histograms, which correspond to the most probable metastable states related to specific cross sections of dendritic PCs grown in the self-oscillatory process (Figure 6, curves 2−4), agree with those obtained for copper nanowires (curve 1, Figure 6).36 The conductance histograms based on the dependences R(t) registered during the cyclic formation of dendritic PCs at particular c values have a bell-like shape presumably because the E

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The Journal of Physical Chemistry C size of a dendritic point contact is dependent on its formation rate. The higher is c, the faster is the electrochemical process at invariant polarization in the general case. Thus, for each concentration, there is a most probable size distribution of the PC conductivity channel. The probability of structures having other sizes is determined by the classical Gauss distribution. According to eq 2, a linear relation between the square root of the relative PC conductance and the PC diameter in kFr units is a strong hint for the occurrence of the shell effect. To check this, the maxima in conductance histograms 2−4 (Figure 6) corresponding to the most probable conductance steps in the dependences G(t) were numbered according to Yanson et al. and Mares et al.34,36 There is a satisfactory linear dependence of G versus the conductance peak number n in Figure 7, which

Figure 8. Stabilization of dendritic PC size in electrolytes of different concentrations after switching off the current in the system. The switch-off time is indicated by the vertical line. The electrolyte is an aqueous CuSO4·5H2O solution with the concentrations 10−6 mol/dm3 (a) and 5 × 10−3 mol/dm3 (b).

Figure 7. Relative PC conductance dependence on the conductancepeak number in the histograms of Figure 6.

can be fitted according to eq 2. This relationship is a clear manifestation of the shell effect in our experiments.29,36 The dependence has two linear regions with different slope values of 0.52 and 0.28. They are most likely due to the crossover from the electronic to the atomic shell effect.29,42 In this case, two series of PC dendrites with stable diameters result from electronic and atomic shell filling. The slight deviations of some points from the linear dependence can be the consequence of incomplete formation of all stable shells within one cycle of PCs growth or dissolution. The detection of long-lived stable states of definite diameters in dendritic copper structures formed at room temperature is one of the key results of this study. The long lifetime of a PC in these states can be connected with chemical stability due to a reduced reactivity toward O2.43 Previously, good mechanical stability of nanowires was also observed in experimental investigations of electrochemical dissolution and deposition of electrodes.4,10,37 The detected effect of cyclic variations of electrical conductance during dendritic PCs electrosynthesis offers possibilities for forming nanostructures of preassigned sizes controlled through their electrical resistance. The rate of a dendrite growth and dissolution can be monitored accurately by varying the electrolyte concentration and the current in the system. Accordingly, the PC size can be varied with atomic resolution due to the detection of the conductivity steps in R(t). Each step corresponds to the conductivity of a definite number of atomic-sized conducting channels measured in G0 units. Since G0 is the conductance quantum of a single atomic PC, NG0 roughly corresponds to approximately N atoms in the cross section.34,36 A contact of the required size is readily obtainable by switching off the current in the circuit at the corresponding point of the dependence R(t). Figure 8 demonstrates the formation of PCs with diameters of approximately 14 (curve (a)) and 32 Cu atoms (curve (b))

after switching off the current, corresponding to sizes of 36 and 83 Å for a Cu atomic size of 2.6 Å, respectively. Thus, the time dependence of the resistance R of a dendritic copper PC recorded during the cyclic process evidences a shell effect in the system. The cyclic variations of R during dendritic PC transformations can be used to enhance the point-contact formation process. This offers new possibilities for formations of solid nanostructures within a liquid-phase electrolyte.

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CONCLUSION In summary, a cyclic switchover effect in electrochemical formation of dendritic PCs has been observed in this study for the first time. We have found that growth of dendritic PCs is governed by the shell effect, which exists only in conductors having a perfect crystalline structure without impurities or defects. The electrosynthesized PCs are, therefore, samples of high quality with preassigned properties. Such contacts can be used in sensory investigations at room temperatures and for developing novel sensing elements proposed by Kamarchuk et al.14 According to PC spectroscopic principles,7,11 high-quality spectra are obtained with contacts free of structural defects, impurities, all kinds of inhomogeneities, tunnel barriers, etc., i.e., contacts allowing a spectroscopic regime of current flow with a maximal electronic mean free path. In the view of the present results and those reported by Kamarchuk et al.,13,14 we can expect that dendritic PCs comply with the above requirements. Preliminary experiments show that these new objects are gas-sensitive, which is a sequel of the gas-sensory effect, discovered recently in point contacts. Further ongoing investigations in this line will provide additional information about the phenomenon discussed here. F

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (E.F.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge Dr. O. I. Shklyarevskii for helpful discussions and expert comments and V.A. Gudimenko for assistance in the treatment of results.

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DOI: 10.1021/jp506649u J. Phys. Chem. C XXXX, XXX, XXX−XXX