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Atomistic Simulation of “Drop-on-Demand” Inkjet Dynamics Francesca Lugli and Francesco Zerbetto* Dipartimento di Chimica “G. Ciamician”, UniVersita` di Bologna, V. F. Selmi 2, 40126 Bologna, Italy ReceiVed: July 13, 2007; ReVised Manuscript ReceiVed: March 31, 2008
The atomistic simulation of the inkjet printing process starts with a burst of heat applied at the bottom of a cell of liquid. Bubbles develop, form jets, and fragment into droplets. All the observations at the atomistic level are understood in terms of classical physics, with parameters obtained by the calculations. The efficiency, critical for the deposition of fragile materials, ranges from 0.05 to 0.42%. The calculated quantities agree with those of real life devices. Introduction In the past few years, the familiar inkjet printing has developed into a new technique to print electrical and optical devices with organic components. Inkjet printers can also be used to produce arrays of proteins and nucleic acids. The drive for a potentially versatile inkjet technology for the fabrication of multilayer devices from molecular systems via self-assembly raises a number of practical problems that need to be addressed.1 One of them is the molecular mechanism at the basis of the process. The two main operating modes of inkjet printers exploit the formation of droplets from a stretched liquid stream,2 a phenomenon first described by Lord Rayleigh.3 In the continuous mechanism, the drop forms by the application of a wave pressure to the liquid that is then forced through a nozzle. The droplet is subsequently charged and deflected by an electric field. Variation of the number of droplets deposited controls the gray scale. In 1979, Canon invented the “drop-on-demand” inkjet technology, where ink drops are ejected from a nozzle via the growth and collapse of a bubble that is formed on the top surface of a small heater located near the nozzle.4,5 Canon called this technology “bubble-jet”. In 1984, Hewlett-Packard commercialized the thermal inkjets that have now come to dominate the market of color printers.6 The core of a thermal inkjet printer consists of an ink chamber with a nozzle close to the heater. Its functioning can be divided in several steps, see Figure 1: (i) a pulse of current with a duration of a few microseconds or less passes through the heater; (ii) heat is transferred from the surface of the heater to the liquid; (iii) the liquid is superheated to the critical temperature of the bubble nucleation; (iv) a bubble instantaneously expands to force the ink out of the nozzle; (v) after the heat received by the liquid is used, the bubble collapses on the surface of the heater; (vi) the retreating liquid pinches off the droplet, which breaks off and proceeds toward the surface of the paper. The whole process of bubble formation, collapse, and drop ejection takes place in less than 10 microseconds. Several variables affect the quality of inkjet printing. They are the heating temperature, the heating rate, the printing pressure, and the viscosity of the liquid. Crucial to the formulation and the optimization of the printing process is the * Corresponding author e-mail:
[email protected].
fast heating of the silicon chip that must avoid formation of multiple bubbles. Recently, measurements of the temperature of inkjet printer heads have found values of 570 K.7 The liquid must reach the high temperature with a rate of surface heating higher than 100 million degrees per second. The dimension of the head is about 60 µm2 and the volume of the liquid ejected is on the order of a few picoliters. Much insight into the process that drives the ejection of liquid can be directly obtained in a macroscopic framework, such as that offered by the Rayleigh-Plesset equation, which describes bubbles dynamics for Newtonian fluids, that is fluids with welldefined viscosity. The equation reads,
(
3 1 R˘ 2γ RR¨ + R˘ 2 ) pg - P0 - P(t) - 4µ 2 F R R
)
(1)
where R, R˙ and R¨ are the bubble radius and its time derivatives, γ is the surface tension, µ is the viscosity, and pg, P0, and P(t) are the pressures of the gas inside the bubble, on the liquid, and of an acoustic wave (absent in inkjet printers), respectively. If only the inertia of the liquid matters, that is, in the case of the collapse of an empty cavity, eq 1 becomes eq 2,
3 RR¨ + R˘ 2 ) 0 2 and its integration gives eq 3,
( )
Rcav(t) ) R0 1 -
t tc
(2)
2⁄5
(3)
where R0 is the initial radius, and tc is the time the collapse requires to reach completion. We have recently proposed to study the process of collapsing bubbles by molecular dynamics.8–10 We found that the Rayleigh-Plesset and the molecular dynamics approaches provide the same description of the collapse at all temperatures of liquid water and heavily salted water. No adjustable parameters were required to make the two approaches coincide. Apart from the generalized Rayleigh-Plesset and molecular dynamics (MD) approaches, several studies were carried out to investigate bubble nucleation in liquids.11–13 This stage of the inkjet mechanism could also be analyzed by the model of bubble growth that was used in the case of bubble growth in carbonated beverages.14 Chen and Groll15 simulated the bubble growing dynamics on a heating surface by numerical solution of the Young-Laplace equation. Nagayama et al.16 performed MD simulations to examine bubble nucleation in a nanochannel. Some preliminary simulations showed that the second stage, that is the
10.1021/jp075482g CCC: $40.75 2008 American Chemical Society Published on Web 06/26/2008
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Figure 1. Drop formation during thermal inkjet printing. Left: Schematic representation in two snapshots; Right: Variation of some physical quantities during the drop formation.
TABLE 1: Summary of the Calculationsa system δz (Å) z1 z2 z3 z4 z5 z6 z7 z8 z9 z10 z11 z12 z13 system
Figure 2. Representation of the heating system: the heated molecules are in a layer (left) or in a semispherical envelope (right).
ejection of liquid, has a flow with a highly oscillatory behavior.17 Huang pointed out that also the breakup of the inkjet may be caused by the highly oscillatory nature of the flow, at least initially.17 The purpose of this work is to simulate the inkjet printing process by MD in order to study bubble formation and the consequent collapse at the molecular level. As an initial system, we use water, although one should be aware that other molecular, colloidal, and polymeric systems will require investigation in the future. Computational Methods The calculations were performed with NAMD 2.6 Molecular Dynamics Software,18 and water molecules were described by the TIP3P model.19 The procedure followed in this work to heat the liquid is similar, although different in the details, to that used by others20 where the simulations heated the central 80 atoms of a box of Lennard-Jones particles and the dynamics was performed and analyzed in reduced variables. A box of 8000 iso-oriented water molecules was created with a side length of 62.54 Å. The first two layers of molecules along the z-axis, for a total of 800 molecules, were frozen to force the movement of the remaining molecules only toward positive z-values. The system was first optimized; the z-axis of the box was then increased by 100 Å to create a liquid/vapor interface. The liquid was equilibrated for 50 ps at 300 K. A variable number of water molecules, Nh, was then instantaneously heated from 300 K to Theat by rescaling their velocities, and the
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11
10 10 10 10 10 10 15 15 15 20 20 20 20 Rdrop (Å) 15 15 20 20 20 20 20 25 25 25 25
Nh 1359 1359 1359 1359 1359 1359 2018 2018 2018 2673 2673 2673 2673 Nh 392 392 824 824 824 824 824 1530 1530 1530 1530
Th (K) 1200 1400 1500 1600 1700 1800 1000 1200 1300 800 1000 1100 1200 Th (K) 2000 2200 2200 2500 3000 3300 3700 1000 1500 2000 2200
T0b (K) 476 514 533 553 572 591 500 556 585 491 566 604 642
cavity no yes, yes, yes, yes no no yes no yes, yes yes no
jet and droplets
no small no small no small yes, small yes yes no no yes small unclear no yes yes
T0b (K) cavity
jet and droplets
362 369 456 480 521 545 577 413 490 570 601
no no no no no no yes no no traces yes
no no yes yes yes yes yes no yes yes yes
a The systems are divided according to the heating scheme of Figure 2; Nh is the number of heated molecules, Th is the temperature at which the heated molecules are instantaneously brought; T0 is the effective temperature of the whole system. Formation of either cavity or jet is in the last two columns. b The effective initial temperature (T0) is evaluated as NtotT0 ) NhTh + (Ntot - Nh)Teq, where N is the number of molecules.
simulation was carried out for 100 ps at constant energy. The heated molecules form either a layer, characterized by a thickness, δz, or a semispherical envelope/drop characterized by a radius, Rdrop (see Figure 2). Results and Discussion Table 1 summarizes 24 cases that were explored by MD with the heating procedures of Figure 2. In practice, one can vary the size of the heated region and the amount of heat provided and then visually inspect the result. When a flat layer of water molecules is heated, the cavity consistently forms a rather flat and far from spherical region of vacuum. The liquid simply surges upward and the picture is very far from that of the process exploited in inkjet printing. For this reason, the following
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Figure 3. (a) Maximum bubble radius Rmax; (b) bubble collapse time tc, as a function of the amount of heat provided divided by the surface area, JQ. The lines are present only to assist the eye.
TABLE 2: Details of the Simulations Reported in Figure 3a system T0 (K) Tmin (K) JQ (J m-2) Rmax (Å) tmax (ps) tc (ps) tlife (ps) R3 R4 R5 R6 R9
456 480 521 545 490
335 342 535 361 346
0.908 1.051 1.290 1.434 0.714
22.0 26.5 28.0 38.0 21.5
12.7 14.1 21.5 30.0 13.4
11.8 17.6 28.0 47.8 12.0
24.5 31.7 49.5 77.8 25.4
a T0 is the effective nonequilibrium temperature, Tmin is minimal temperature reached during bubble formation (see Figure 4). JQ is the amount of heat provided divided by the surface of the heated area, Rmax is the maximum radius that the cavity reaches at time tmax, tc is the time that the cavity takes to collapse after reaching its greatest dimension, and tlife is the lifetime of the bubble.
discussion will consider only the semispherical heating where the formation of globular cavities is observed although a brief summary of the results produced by heating a flat region is shown. Table 1 shows under which conditions a bubble, or a bubble plus a jet, is formed. It also gives the effective nonequilibrium temperature (T0), which is the average of the temperatures of the heated and nonheated regions. Interestingly, jets occur when T0 is greater than 570 K, that is, the critical temperature determined experimentally in the printing process
of inkjets.7 The stability and robustness of the results was checked by performing a set of eight simulations with cubic boxes of 4096 water molecules (not shown). Also in these cases, liquid jets occur when T0 is greater than 570 K. The results with the larger box presented here are therefore at convergence with the size of the system. Further, 11 additional simulations were performed with the SPC/E water model. The results are consistent with those reported in Table 1, although the liquid has to reach a higher temperature to form the jet (∼640 K). The higher temperature is readily explained if one considers that the self-diffusion coefficient of TIP3P ranges, as a function of temperature, from 5.2 × 10-9 to 7.0 × 10-9 m2 s-1, whereas for SPC/E it ranges from 2.2 × 10-9 to 4.4 × 10-9 m2 s-1. Two tables with the additional calculations are reported in the Supporting Information. To understand the relationship between quantity of heat provided by the sudden burst and bubble dynamics, we examined the systems where bubbles nucleate, but no liquid jets, and hence drops, are formed, namely R3, R4, R5, R6, and R9. We define JQ as the ratio of the amount of heat given to the system (Qh) and the contact area (S) of the heated semidrop. The maximum bubble radius and the bubble collapse time are
Figure 4. The R9 system (see Table 1): (a) temperature of the liquid vs time; (b) displacement of the center of mass vs time. The R7 system (see Table 1): (c) temperature of the liquid vs time; (d) displacement of the center of mass vs time.
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Figure 5. Snapshots of the cavity nucleation for the R9 system at different times: (a) t ) 2.5 ps; (b) t ) 7.5 ps; (c) t ) 10.0 ps; (d) t ) 13.8 ps. The beads are located at the grid points used to estimate the presence of vacuum and should only help the eye to perceive the formation of the empty volume.
Figure 6. Cavity probability maps for (a) R3, (b) R4, (c) R5, and (d) R6. The blue points show the more probable vacuum area, whereas the red are less probable.
Figure 7. Normalized liquid density for each shell as a function of time in R9. The innermost shells drain first.
a function of JQ (Figure 3, details in Table 2), which has the dimensions of a surface tension. In practice, the larger this quantity JQ, the greater the surface it can create in the liquid and the longer the liquid can sustain it. Analysis of the continuum model simulations of Asai21 shows similar trends for much larger values of several hundreds of J m-2.21 The temperature of the systems can be monitored in time. Figure 4 shows its variation for the R9 system that we elected as a reference for much of the discussion, although other systems are
also discussed in detail. In this case, the radius of the heated spherical envelope is 25 Å, for a total of 1530 water molecules, and the temperature of heating is 1500 K. After the heat burst, the effective initial temperature of the system temperature is 491 K and rapidly drops to ∼350 K to equilibrate at ∼360 K. Figure 4 also shows the motion of the center of mass of the system. The liquid rapidly rises and reaches the maximum displacement in ∼10 ps, then it returns to equilibrium in less than 30 ps. The motion of the center of mass is oscillatory, in agreement with the results of Huang.17 In general, bubble nucleation can occur at an effective temperature (T0) lower than 570 K, but formation of a liquid jet, and drops, takes place only when T0 is above this critical value. The nonoscillatory results of R7 (see Figure 4, panels c and d), where the initial temperature of the liquid is 577 K, gives a fast-moving liquid jet. To visualize the cavity formation and its dynamics, the first 50 ps were analyzed in detail by dividing the space into a threedimensional (3D) grid of cubes of 8 Å3 of volume. The cubes were considered empty when there was no molecule within 1.2 times the contact length between two oxygen atoms, σO ) 3.16 Å, of the Lennard-Jones potential.11 Some snapshots of the cavity nucleation from the reference simulation R9 are shown in Figure 5. Initially, several nucleation
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Figure 8. Cavity radius of R9 as a function of time: (a) entire dynamics; (b) collapse region (dots) and its comparison to the violent solution of the Rayleigh equation (continuous line).
Figure 9. Bubble radius in time (dots) and Rayleigh violent collapse equation (line) for four different runs: (a) R4, (b) R5, (c) R6, and (d) R7.
Figure 10. Evolution of the classical stress caused by the cavity collapse in the five cases where no pinch off is observed in the MD simulations.
TABLE 3: Work and Efficiency of the Nano-inkjet Printers of This Work system R9 R3 R4 R5 R6
Qh (kcal mol-1)
Wc (kcal mol-1)
η (%)/6
8077 6569 7607 9337 10375
21.54 52.98 72.88 178.33 256.68
0.05 0.13 0.15 0.32 0.42
sites appear; the small cavities then join each other, and a single larger cavity forms and grows until it reaches its maximum radius. Snapshots of the cavities formed in systems R3, R4, R5, and R6 are shown in Figure 6 in the form of probability maps. The pictures are averages in time and show the grid points where the probability to find a vacuum, averaged on the first 50 ps of the simulation, is greater than 10%. The cavity is almost
spherical in the case of small values of JQ (R3 and R4), whereas it is elliptical in the case of larger values of JQ (R5 and R6). Figure 7 shows the density in time for a series of concentric shells of 2.0 Å of thickness on the top of the heated region for the R9 system. When a curve reaches a value of 0, the shell is empty. The innermost shells are the first to deplete and do not immediately drain. Figure 8 shows that the growth process takes place in four steps: (i) a cavity of 5 Å of radius forms rapidly and reaches a plateau in ∼2.5 ps. Comparison of Figures 7 and 8 shows that, in this regime, water is compressed since the density in the innermost region where the cavity is contained remains constant. (ii) between 2.5 and 5 ps, the radius of the cavity remains constant, but the density of water in the innermost shells starts decreasing, which implies that now the liquid is stretching. (iii) after 5 ps, the cavity steadily augments to reach a maximum value of 21.5 Å after 13.4 ps and then collapses. (iv) finally, the bubble collapse reaches completion in 12 ps. One can compare the data of the collapse with the Rayleigh solution for the violent regime given by eq 3. Using the collapse time calculated in the simulation, the agreement between the function and the calculations is satisfactory and confirms previous results8–10 that were obtained with an idealized initial spherical arrangement of the cavity and not in a dynamical setup of growth and collapse such as the present one. Notice that no adjustable parameters are used and that in Figure 8b the temperature of the system when the bubble begins to collapse is 355 K, which implies that the growth of the cavity has dissipated a substantial amount of heat. The bubbles radii in time for the other four systems that show bubble nucleation (but no jets) are plotted in Figure 9, together with the theoretical curve of the violent Rayleigh-Plesset collapse. The robustness of the results was checked by additional calculations, see Figures 1-3 and Tables 3 and 4 of the Supporting Information, where the heating was carried out in steps over a time of 100-200 ps. Cavity nucleation occurs when the liquid temperature rises above 430 K, but the bubble dynamics requires temperatures above 500 K. Although some differences are observed, the shape of the curve of Figure 8a also appears with the slower heating procedure. When larger values of JQ are used, the agreement between the MD simulations and the curves in eq 3 is only approximate. The extra heat keeps the cavity open, and the effect of viscosity and surface tension should perhaps be considered for a better description of the bubble dynamics.22,23 However, the amount of liquid retracting and its speed can still be calculated using eq 3. It is this reflux that causes pinching off of the drop during
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inkjet printing. In the five examples of Figures 8 and 9, there is no droplet formation. Equation 4 evaluates the stress (τ) the cavity collapse exerts on the liquid. It is obtained by combining Newton’s second law with the second time derivative of eq 3;
( )( )
F 1 ¨ 2 R0 ) FRR ) - F S 3 25 tc
τ)
2
1-
t tc
-6/5
(4)
where S is the surface area of the cavity cross-section, F is the density of water, R0 is the maximum radius of the cavity, and tc is the time of collapse calculated by the simulations. Figure 10 shows how the stress varies in time for R3, R4, R5, R6, and R9 before reaching the discontinuity at time tc and compares the results with the tensile strength of water. For safety, the lower estimate of tensile strength of water as 500 bar is taken.24 It is readily perceived that for these five simulations pinch off would occur only when the bubble has completely collapsed so that there is no liquid available to form droplets. Although tc and R0 are obtained by the atomistic simulations, eq 4 is completely classical. Both approaches concur that in the five cases examined no drops should form. The simulations also afford insight into the production of mechanical work during inkjet printing. The process converts heat into mechanical work, and it is possible to estimate the overall efficiency. The more efficient the printing the less likely it is to damage ejected material, a feature that becomes important for functionally active biosystems that may denaturate.25,26 The work done arises from the change of volume of the liquid when the cavity expands and travels upward. The thermal efficiency (η) is the ratio of the work (Wc) produced during the expansion of the cavity divided by the input thermal energy (Qh). We assume that the heat flux from the heater to the liquid is instantaneously turned on and off at t ) 0. From homogeneous nucleation theory,27,28 one can derive the amount of work done by the bubble, which is equal to the energy necessary to create the bubble in the liquid. This consists of two parts: (i) the work done to create the surface of the bubble of that amount is 4πR2γ, with γ the surface tension, and (ii) the work done to displace the liquid outward in order to create the cavity, which is the volume of the bubble multiplied by the pressure. The total work done by the growing cavity in the liquid is given by eq 5,
Wc )
∫0t
max
(4πRc(t)2γ dt) +
∫0t
max
( 34 πR (t) P (t) dt) 3
c
l
(5)
where tmax is the time required by the bubble to reach its maximum radius, Pl is the time-dependent pressure of the liquid (obtained from the simulation), and γ is the experimental value at the simulation temperature. The work produced according to eq 5 is not entirely available to the jet since the cavity expands in three directions and only half of the z-direction is actually exploited in the device. The results are summarized in Table 3, where the ratio Wc/Qh is divided by six to bring it in line with the functioning of real inkjet printers. The estimated efficiency for an inkjet printer is ∼0.04%29 and is slightly less than what found here. When a slower heating schedule was used—see Supporting Information—the efficiency of the process was slightly lower, and, as a rule, faster heating produced higher efficiency. Conclusion In conclusion, inkjet printing has the potential to become a major technology for organic deposition.30–33 In reality, a large number
of practical difficulties remain. Molecular dynamics simulations can provide insight into the processes that drive ejection of liquid from a confined environment after a heat burst. The efficiency and the operating temperature are well simulated by atomistic simulations that prove that classical physics can be used also at this nanoscale level and provide details of the growth and collapse of the real machine behind inkjet printing, namely the bubble. Acknowledgment. Support from EU programs and MUIR projects is gratefully acknowledged. Supporting Information Available: Tables and figures with additional calculations to check the robustness of the results with respect to (i) size of the system, (ii) water model, and (iii) heating schedule. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) (2) (3) (4)
Calvert, P. Chem. Mater. 2001, 13, 3299. Le, H. P. J. Imaging Sci. Tech. 1998, 42, 1. Rayleigh, F. R. S. Proc. London Math. Soc. 1878, 10, 4. Hara, T.; Endo, I. J. Inst. Image Electron Engrs. Jpn. 1982, 11,
66. (5) Endo, I.; Sato, Y.; Saito, S.; Nakagiri, T.; Ohno, S. Great Britain Patent 2007162, 1979. (6) Vaught, J. L.; Clautier, F. L.; Donald, D. K.; Meyer, J. D.; Tacklind, C. A.; Taub, H. H. U.S. Patent 4490728, 1984. (7) Avedisian, C. T.; Osborne, W. S.; McLeod, F. D.; Curley, C. M. Proc. Roy. Soc. Lond. 1999, 455, 3875. (8) Lugli, F.; Hoefinger, S.; Zerbetto, F. J. Am. Chem. Soc. 2005, 127, 8020. (9) Lugli, F.; Zerbetto, F. ChemPhysChem 2007, 8, 47. (10) Lugli, F.; Zerbetto, F. Phys. Chem. Chem. Phys. 2007, 9, 2447. (11) Kimura, T.; Maruyama, S. Int. J. Heat Tech. 2000, 18, 69. (12) Kenjio, T.; Matsumoto, M. Fluid Phase Equilib. 1998, 144, 343. (13) Wu, Y. W.; Pan, C. Micro. Therm. Eng. 2003, 7, 137. (14) Uzel, S.; Chappell, M. A.; Payne, S. J. J. Phys. Chem. B 2006, 110, 7579. (15) Chen, Y.; Groll, M. Int. J. Heat Mass Transfer 2006, 49, 1115. (16) Nagayama, G.; Tsuruta, T.; Keng, P. Int. J. Heat Mass. Trans. 2006, 49, 4437. (17) Huang, H. Proceeding of the Fourty-fifth European Study Group with Industry; Pik, D., Rottschäfer, V., Eds., Technology Foundation STW: Leiden, The Netherlands, 2003; chapter 3, pp 45-56. (18) Phillips, J. C.; Braun, R.; Wang, W.; Gumbart, J.; Tajkhorshid, E.; Villa, E.; Chipot, C.; Skeel, R. D.; Kale, L.; Schulten, K. J. Comput. Chem. 2005, 26, 1781. (19) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926. (20) Okumura, H.; Ito, N. Phys. ReV. E 2003, 67, 045301. (21) Asai, A. J. Heat Transfer 1991, 113, 973. (22) Dzubiella, J. J. Chem. Phys. 2007, 126, 194504. (23) Bogoyavlenskiy, V. A. Phys. ReV. E 2000, 62, 2158. (24) Temperley, H. N. V. Proc. Phys. Soc. 1947, 59, 199. (25) Nishioka, G. M.; Markey, A.; Holloway, C. K. J. Am. Chem. Soc. 2004, 126, 16320. (26) Fletcher, B. L.; Hullander, E. D.; Melechko, A. V.; McKnight, T. E.; Klein, K. L.; Hensley, D. K.; Morrell, J. L.; Simpson, M. L.; Doktycz, M. J. Nano Lett. 2004, 4, 1809. (27) Skripov, V. P. Metastable Liquids; J. Wiley: New York, 1974. (28) Brennen, C. E. CaVitation and Bubble Dyanmics; Oxford University Press: New York, 1995. (29) Nayve, R.; Fujii, M.; Fukugawa, A.; Takeuchi, T.; Murata, M.; Yamada, Y.; Koyanagi, M. J. Microelectromech. Sys. 2004, 13, 814. (30) de Gans, B. J.; Duineveld, P. C.; Schubert, U. S. AdV. Mater. 2004, 16, 203. (31) Bharathan, J.; Yang, Y. Appl. Phys. Lett. 1998, 72, 2660. (32) Hebner, T. R.; Wu, C. C.; Marcy, D.; Lu, M. H.; Sturm, J. C. Appl. Phys. Lett. 1998, 72, 519–521. (33) Mehta, A.; Kumar, P.; Dadmun, M. D.; Zheng, J.; Dickson, R. M.; Thundat, T.; Sumpter, B. G.; Barnes, M. D. Nano Lett. 2003, 3, 603.
JP075482G
