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Understanding the Dynamics of Signal Transduction for Adsorption of Gases and Vapors on Carbon Nanotube Sensors Chang Young Lee and Michael S. Strano* Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 Received December 17, 2004. In Final Form: March 6, 2005 Adsorption dynamics and their influence on signal transduction for carbon nanotube-based chemical sensors are explored using continuum site balance equations and a mass action model. These sensors are shown to possess both reversible and irreversible binding sites that can be modeled independently. For the case of irreversible adsorption, it is shown that the characteristic response time scales inversely with analyte concentration. It is inappropriate to report a detection limit for this type of sensor since any nonzero analyte concentration can be detected in theory but at a cost of increasing transduction time with decreasing concentration. The response curve should examine the initial rate of signal change as a function of analyte concentration. Conversely, a reversible sensor has a predefined detection limit, independent of the detector geometry with a characteristic time scaling that becomes constant in the zero analyte concentration limit. A simple analytical test is presented to distinguish between these two mechanisms from the transient response of a nanotube sensor array. Two systems appearing in the literature are shown to have an irreversible component, and regressed surface rate constants for this component are similar across different sensor geometries and analytes.
1. Introduction Single walled carbon nanotubes (SWNTs) have several advantages as sensor elements, including large surfaceto-volume ratios, one-dimensional electronic structure, and a molecular composition consisting of only surface atoms.1-6 Carbon nanotube gas sensors are among the only materials to electrically transduce molecules binding to their surface directly at analyte concentrations well below the ppb level.1,7 Recent versions utilize a change in dielectric constant,6 but typically the change in conductivity of a single or array of nanotubes is used for such applications. Undoped, metallic nanotubes have a lower density of states at and around the Fermi level compared to the valance band edge of the semiconductors.8,9 Hence, the latter are assumed to play a larger role in the sensing mechanism.3,4 Both individual-SWNT10,11 and multiple-SWNT-array1,7 transistors have been utilized as sensor elements, and polymer coatings have been used to enhance the sensitivity and selectivity of the gas sensing.1,7 Different methods for * Author to whom correspondence should be addressed. (1) Qi, P.; Vermesh, O.; Grecu, M.; Javey, A.; Wang, O.; Dai, H. J.; Peng, S.; Cho, K. J. Nano Lett. 2003, 3, 347-351. (2) Barone, P. W.; Baik, S.; Heller, D. A.; Strano, M. S. Nat. Mater. 2005, 4, 86-92. (3) Peng, S.; Cho, K. J. Nano Lett. 2003, 3, 513-517. (4) Peng, S.; Cho, K. J.; Qi, P. F.; Dai, H. J. Chem. Phys. Lett. 2004, 387, 271-276. (5) Collins, P. G.; Bradley, K.; Ishigami, M.; Zettl, A. Science 2000, 287, 1801-1804. (6) Chopra, S.; McGuire, K.; Gothard, N.; Rao, A. M.; Pham, A. Appl. Phys. Lett. 2003, 83, 2280-2282. (7) Novak, J. P.; Snow, E. S.; Houser, E. J.; Park, D.; Stepnowski, J. L.; McGill, R. A. Appl. Phys. Lett. 2003, 83, 4026-4028. (8) Dresselhaus, M. S.; Dresselhaus, G.; Eklund, P. C. Science of fullerenes and carbon nanotubes; Academic Press: San Diego, 1996. (9) Saito, R.; Dresselhaus, G.; Dresselhaus, M. S. Physical Properties of Carbon Nanotubes; Imperial College Press: London, 1998. (10) Shim, M.; Javey, A.; Kam, N. W. S.; Dai, H. J. J. Am. Chem. Soc. 2001, 123, 11512-11513. (11) Kong, J.; Franklin, N. R.; Zhou, C. W.; Chapline, M. G.; Peng, S.; Cho, K. J.; Dai, H. J. Science 2000, 287, 622-625.
sensor regeneration also have been studied: venting under ambient conditions,11 heating to high temperature,11 applying bias to the Si gate,7 and exposing to UV light.1,12 Different analytes have been utilized to benchmark performance. Detection of oxygen,5 nitrogen dioxide,11 ammonia,11 methane13 for environmental purposes, and a nerve agent simulant dimethyl methylphosphonate (DMMP)7 has been studied with sub-ppm detection. For the detection of molecules which do not have any electrondonating or -withdrawing properties, SWNTs loaded with transition metal nanoparticles are used.13 Peng and Cho,3 in their ab initio study, show the possibility of detecting molecules which do not bind to a nanotube such as CO and H2O. Substitutional doping of impurity atoms (boron, nitrogen, etc.) into SWNTs or the use of composite BxCyNz nanotubes are what they suggested, and these techniques are realized by Han and co-workers.14 However, there exists some confusion as to the appropriate way to benchmark sensor responses or how to compare the behavior of different device types. Reversible gas sensors produce signals where, at steady state, the magnitude is related to the analyte concentration. Conversely, molecular binding to carbon nanotube sensing arrays is at least partially irreversible for a wide range of analytes of interest. It is precisely this property that yields the ability to detect increasingly small analyte concentrations by integral trapping at the surface. The presence of irreversible binding sites, however, changes the dynamics of such a sensor and introduces a tradeoff between analyte detection and total transduction time. In this work, we develop a highly simplified model of signal transduction in SWNT sensors with the objective of defining parameters that benchmark the performance (12) Tans, S. J.; Devoret, M. H.; Dai, H. J.; Thess, A.; Smalley, R. E.; Geerligs, L. J.; Dekker, C. Nature 1997, 386, 474-477. (13) Lu, Y. J.; Li, J.; Han, J.; Ng, H. T.; Binder, C.; Partridge, C.; Meyyappan, M. Chem. Phys. Lett. 2004, 391, 344-348. (14) Han, W. Q.; Cumings, J.; Huang, X. S.; Bradley, K.; Zettl, A. Chem. Phys. Lett. 2001, 346, 368-372.
10.1021/la046867i CCC: $30.25 © 2005 American Chemical Society Published on Web 04/28/2005
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d2S )0 d(Aθ)2 This is true in the case of where the analyte primarily dopes the semiconducting nanotubes in the array causing a constant shift of the sub-threshold slope to either higher or lower bias voltages. It is also true for devices where metallic nanotubes dominate the baseline conductance and the analyte introduces carrier scattering via its adsorption that can be linearized. The proportionality constant changes its sign and magnitude depending on the type of nanotube detector (n-type, p-type) and the overall electronegativity of analyte molecules. The rate of the sensor response is found by mass action using eq 1 Figure 1. Schematic of a prototypical nanotube gas sensor array. Gas-phase analyte molecules (A) adsorb and occupy (Aθ) sites on the nanotube surface, leaving (θ) empty. The total available sites for sensing (Tθ), which is a constant for a given array, is proportional to the accessible nanotube surface area.
of different geometries or array types. We restrict the discussion to sensors that involve direct transduction of the binding event via electrical modulation of the sensor surface. We also present a straightforward analytical test that can distinguish between reversible and irreversible binding of the analyte from transient response curves. Literature data are examined within the context of the model, and agreement is demonstrated for seemingly diverse sensing platforms and analytes. 2. Model Development 2.1. Case I: Irreversible Adsorption. Evidence in the literature1,5,7 indicates that molecular binding to most carbon nanotube sensing arrays is either partially or completely irreversible. Removing the chemical potential of the analyte above the sensor does not regenerate the surface on a time scale less than many times the original transduction time scale. In practice, various regeneration methods introduced are sufficient to restore the sensor, but our focus in this work is on the molecular binding event itself. Thus, irreversible adsorption shows a response which cannot be restored completely on the time scale of the initial transduction by simply removing the gas-phase analyte from the sensor. We consider a general sensing array as depicted in Figure 1. The accessible nanotube surface is divided into Tθ total sites for molecular adsorption, with θ and Aθ being the concentration of unoccupied and occupied sites of the analyte, respectively. The analyte molecule, A, having some constant gas-phase concentration, Ca, reacts with an unoccupied site according to the surface reaction:
θ(sur) + A(g) f Aθ(sur)
(1)
Here, the forward rate constant is k, and g and sur denote gas phase and surface bound species, respectively. The number of sites on the sensor surface is conserved.
θ(sur) + Aθ(sur) ) Tθ(sur)
(2)
By definition, Tθ is a constant property of the array, proportional to the accessible surface area. The signal one measures, S, is the conductance change (∆G) normalized by the baseline conductance (Go) of the detector. We consider the case where S is directly proportional to Aθ.
dAθ ) kθCa dt
(3)
In the simplest case, the gas phase species A reacts directly with the unoccupied site in a variation of an Eley-Ridealtype mechanism.15 For an uncoated array (i.e., no polymer overlayer), the assumption of no pre-adsorption isotherm is reasonable. Using the site balance in eq 2
dAθ ) k[Tθ - Aθ]Ca dt
(4)
Solving eq 4 for the case of an initially clean array at t ) 0:
Aθ(t) ) (Tθ)(1 - exp[-kCat]) S(t) ) Smax (1 - exp[-kCat])
(5)
Smax is the maximum conductance change when the detector is saturated. Note that it is not appropriate to report a detection limit for this kind of sensor. Upon exposure to a stream of any concentration of analyte, the sensor will ultimately respond and eventually saturate. The figure of merit is rather the response time, which scales as τ ) 1/(kCa). The appropriate benchmark to report is the surface reaction rate constant, k, since this parameter communicates the ability to transduce a given concentration, Ca, within a predefined time. The lack of a detection limit for these sensors is the reason carbon nanotube arrays electrically transduce molecular binding far below the ppb level, where most sensor elements become equilibrium limited.15 There is also no need to examine the response as t f ∞ since it will always saturate at a value proportional to Tθ independent of the analyte concentration. One can instead examine and report the slope of the transient response near the initial introduction of the analyte at t ) 0. The response rate is actually:
dAθ(t) ) (Tθ)kcaexp[-kCat] dt dS ) Smax kcaexp[-kCat] dt
(6)
Correlating the initial response rate with analyte concentration is the appropriate way to report the response curve. The response can be examined long enough to obtain this slope, and the system can be regenerated thereafter. From eq 6, we find that there are three principal means of increasing the signal transduction rate. One is increasing the number of nanotubes in the array, thereby (15) Masel, R. I. Principles of adsorption and reaction on solid surfaces; Wiley: New York, 1996.
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increasing (Tθ). Another is increasing the surface reaction rate constant, k. This can be accomplished through controlled doping of the array. The third is partitioning the analyte into a matrix above the array where its solubility is higher.1,7 This has the effect of increasing the effective concentration at the sensor boundary. 2.2. Case II: Reversible Adsorption. If the binding to the sensor surface is readily reversible such that there is a constant exchange with the gas phase, the dynamics will be inherently different. In this case, the surface is regenerated simply by flowing analyte-free gas across the surface. We can again model the binding as an adsorption of gas-phase analyte, A, with an unoccupied adsorption site on the nanotube surface.
θ(sur) + A(g) T Aθ(sur)
(7)
The forward rate constant is still k, but the reverse rate constant is k/K, where K is the binding equilibrium constant. The site balance in eq 2 still applies, but the mass action law is
k dAθ ) k[Tθ - Aθ]Ca - [Aθ] dt K
(8)
Solving eq 8 for the case of a partially occupied sensor element with a surface concentration of Aθ(0) yields
[
](
1 + CaK kt K Aθ(0) + CaKAθ(0) 1 + CaK 1 + CaK kt CaK(Tθ) 1 - exp K
exp Aθ(t) )
[
(
]))
with the case of an initially clean array at t ) 0 simplifying to
Aθ(t) )
[
(
]) ])
CaK(Tθ) 1 + CaK kt 1 - exp 1 + CaK K
[
(
1 + CaK CaK kt S(t) ) Smax 1 - exp 1 + CaK K
(9)
) )
1 + CaK dAθ(t) ) k(Tθ)Caexp kt dt K 1 + CaK dS(t) ) Smax kCaexp kt dt K
Note that the properties of this type of sensor are very different. The characteristic time of the response becomes independent of concentration in the infinite dilution limit.
lim τ ) lim
Caf0
(
1
Caf0k
min
min
One consequence is that for any nonzero heat of adsorption ∆H,
K ) exp
∆G ) exp(- ) (∆SR) exp(-∆H RT ) RT
Here, ∆S and ∆G are the change in entropy and Gibbs free energy, respectively, upon binding to the nanotube surface. The detection limit must become poorer with an increase in temperature as the equilibrium constant decreases. In the reversible case, it is appropriate to report a measured detection limit, which is essentially independent of detector geometry. The steady-state signal after exposure to the analyte also carries some meaning and, as Ca becomes small, can be correlated as the familiar linear response. Some researchers1,7 examine various functional coatings on the surface of the sensor to impart additional sensitivity and selectivity to particular analytes. In this case, if adsorption into the coating is a linear function of concentration, both the irreversible and reversible cases can be modified to replace Ca with the product of a Henry’s law factor (Ha) and bulk concentration (HaCa). This product reflects a preferential enhancement or diminution of the analyte in the over-coating layer. If the matrix has a particularly high partitioning coefficient such that the dissolved gas concentration is large, a nonlinear solubility relation must be considered. Additionally, the rate constant k may also change for different functional coatings because of an apparent increase or decrease of the sticking coefficient, S(θ). The forward rate of adsorption, ra, and k are related to the sticking coefficient by
ra ) S(θ)Iˆz ) kθCa
In this case, the response rate is
( (
Climit
Aθ ( Tθ) ) Aθ K(1 - ( ) ) Tθ
)
K K ) 1 + CaK k
Examining the scaling of the response time as the analyte concentration tends to zero is a straightforward way of determining which process dominates: reversible or irreversible binding. Note that when the concentration of the analyte is large, the binding can be modeled as irreversible. The reversible sensor also has a well-defined detection limit, Climit. This limit is set by the minimum occupancy ratio (Aθ/Tθ)min that can be resolved above the noise level.
where, Iˆz is the total flux of analyte molecules.15 For instance, k for the adsorption of electron-withdrawing molecules will increase if nanotubes are coated with electron-rich polymers. Sticking coefficients for NO2 adsorption are reported both for electron-rich polyethyleneimine (PEI)-coated nanotubes and for as-grown ones, and the former has 2 orders of magnitude higher value than that of the latter.1 3. Application to Literature Data Qi et al. examine NO2 detection using arrays of electrodes with PEI-functionalized CVD-grown nanotubes. The signal recovery time from NO2 detection at roomtemperature air was 12 h for a single as-grown semiconducting nanotube.11 This time will be longer for a multitube device coated with electron-rich PEI because of the enhanced binding affinity and sticking coefficient for the electron-withdrawing NO2.1 The transient conductance change parametric in NO2 concentration is shown in Figure 2a. None reach a steady state, and at the end of an arbitrary exposure period, the surface is regenerated using UV irradiation for approximately 5 min.16 The maximum response, Smax, is approximately 0.43. Equation 5 suggests a useful scaling for these data assuming a completely irreversible response. Plotting the responses (16) Chen, R. J.; Franklin, N. R.; Kong, J.; Cao, J.; Tombler, T. W.; Zhang, Y. G.; Dai, H. J. Appl. Phys. Lett. 2001, 79, 2258-2260.
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Figure 2. (a) Conductance change of PEI-coated carbon nanotubes by an irreversible adsorption of NO2 (data from ref 2). The responses do not reach steady state and are regenerated via UV irradiation after an arbitrary period.16 (b) When these data are plotted as a function of (Cat), the points collapse to a single model curve (red dotted) described by eq 5 (k ) 1.64 × 10-6 (ppt‚s)-1, Smax ) 0.43). (c) Alternatively, a predicted reversible response17 simulated by eq 9 shows parametric behavior in concentration. The data converge to one curve as the concentration increases. (d) Plotting the initial rate of conductance change versus concentration yields a more useful response function. At low concentrations, experimental data (diamond) fit accurately to a model line (red dotted) plotted by eq 6.
against the product, Cat, collapses the curves to one (Figure 2b) for this case. This behavior is a signature of irreversible adsorption and a plot of response versus Cat for different analyte concentrations can be used to distinguish irreversible adsorption from reversible adsorption. The NO2 surface rate constant on the carbon nanotube array (k ) 1.64 × 10-6 (ppt‚s)-1) is regressed. This rate constant should be independent of detector geometry and the number of nanotubes in the array. In contrast, the sensor response for reversible adsorption is predicted to be parametric in concentrations when plotted in this manner via eq 9, as demonstrated17 in Figure 2c. Note that at high concentrations, where binding becomes irreversible, the data collapse to a single curve. Equation 6 suggests a correlation of the slope of the initial signal response with concentration (Figure 2d). Here, the first 120 s of the response was used to calculate the initial rate. For all but the largest concentration,18 the initial slope of the conductance change with time appears to increase with analyte concentration, and the model predicts the response curve accurately using the two previously regressed parameters. Qi et al.1 and Peng et al.4 modeled the NO2 vapor sensor response using a Langmuir adsorption model based upon the reversible adsorption limit. The conductance change is plotted as a function of analyte pressure parametric in sticking coefficient. From this, an experimental sticking coefficient was determined. However, for this system, NO2 adsorption is reported as partially irreversible because of a strong binding of the NO3 co-adsorbate and stabilization (17) In Figure 2c, the parameters Smax ) 0.43, k ) 3.02 × 10-6 (ppt‚s)-1, and K ) 8.2 × 10-3 ppt-1 were used as an illustration. (18) All but one of the responses in Figure 2a (from ref 2) show systematic changes with analyte concentration. Curiously, the 10 ppb response is virtually identical to the 5 ppb case. The data are shown to overlap in Figure 2a, and this causes unexplained discontinuities in the response function (Figure 2b) and its derivative (Figure 2d). For this reason, we limit the discussion to the reported behavior below 10 ppb.
of NO2 by electron-rich polymer coatings. This irreversibility means that the sensor only reaches steady state at saturation when all sites are occupied. Additional insight may be gained by examining the irreversible surface rate constant, k, and how it varies for different analytes. A similar analysis can be performed for other systems in the literature. Novak and co-workers7 use a modified geometry consisting of a tubular chemiresistor with a grown monolayer of nanotubes on the interior surface. They consider the analyte DMMP (a chemical weapons simulant) but apply a positive bias to the Si gate to desorb the analyte from the surface. The sensor shows only partial reversibility of the response when the saturated element is flushed using DMMP-free carrier gas. Figure 3a plots the experimental response for their system. The electrondonating DMMP, when adsorbed on a bare p-type nanotube device, is less stable than electron-withdrawing NO2 on electron-rich PEI-coated nanotubes. This may explain why DMMP adsorption shows both reversible and irreversible site dependence. Irreversible adsorption suggests strong binding sites, while reversible adsorption corresponds to weaker sites. Therefore, the ratio of irreversible and reversible sites is expected to depend on the properties of sensor and the analyte molecules. The simplest model results when one assumes that these two sites contribute to the sensor response independently. Taking a linear combination of the two models above (labeled the additive model), the data can be fit to extract reversible and irreversible components. The best-fit surface reaction rate constant of irreversible component in this case is 1.98 × 10-6 (ppt‚s)-1, with approximately half (50%) of the total sensor response coming from the irreversible component. Figure 3b shows the conductance change of the same sensor array for NH3 detection.7 The analyte concentration in this case is unknown.19 Since NH3 is a weaker electrondonating molecule than DMMP, it should be more stable on a hole-rich p-type nanotube array. The contribution of
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Figure 3. Sensor response for the nanotubes grown in a tubular chemiresistor (data from ref 7). The response here has both irreversible (yellow) and reversible (green) components. Additive models are shown for detection (red) and regeneration (blue) (a) Conductance change for the exposure to 1 ppb DMMP. 50% of the total response is from an irreversible component. k(irrev) ) 1.98 × 10-6 (ppt‚s)-1, k(rev) ) 3.02 × 10-6 (ppt‚s)-1, K ) 8.24 × 10-3 ppt-1 are regressed. (b) Conductance change and response model for a different sensor array exposed to NH3. A value of 100 ppb was assumed. In this case, the contribution of the irreversible component is apparently higher at 74%. Regressed rate constants are k(irrev) ) 1.56 × 10-6 (ppt‚s)-1, k(rev) ) 6.32 × 10-3 (ppt‚s)-1, K ) 2.59 × 10-2 ppt-1.
the irreversible component in this case is found to be higher (74%). Future work will correlate the forward surface rate constant, k, and the analyte binding energy. This binding energy for NO2 is -0.42 eV, whereas -0.18 eV is reported for NH3.20 The corresponding surface rate constants show a similar trend with a larger value for the former. 4. Conclusions The dynamics of signal transduction have been modeled for the case of both irreversible and reversible binding to a carbon nanotube sensor surface. In the irreversible case, there is no limiting detection concentration. Rather, total (19) The authors of ref 7 are unsure of the NH3 concentration dosed for the data reproduced in Figure 3b. Using parameters for the DMMP case, one can estimate a value of 100 ppb. This value was used to generate the model curves for comparison. (20) Chang, H.; Lee, J. D.; Lee, S. M.; Lee, Y. H. Appl. Phys. Lett. 2001, 79, 3863-3865.
transduction time becomes longer as the analyte becomes more dilute. Conversely, a reversible sensor has a predefined detection limit, independent of the detector geometry. Carbon nanotube sensing arrays are shown to generally be combinations of both types of sensors, with the former component responsible for the very high sensitivities that have been reported. Several aspects of this analysis are shown to describe systems in the literature very well. Acknowledgment. The authors acknowledge R. Masel and M. Shannon for useful discussions. This work was supported by DARPA/MTO and a grant from the National Science Foundation CTS-0330350. Funding from the Dupont Co. molecular electronics group is also appreciated. LA046867I
