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Fast piezoelectric actuation of an elastomeric micropore
Measurement 46 (2013) 3560–3567
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Fast piezoelectric actuation of an elastomeric micropore Murray L. Jansen a, Geoff R. Willmott a,b,⇑, Ingrid Hoek a, W. Mike Arnold a,b,⇑ a b
Industrial Research Ltd., PO Box 31-310, Lower Hutt 5040, New Zealand The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
a r t i c l e
i n f o
Article history: Received 20 November 2012 Received in revised form 2 May 2013 Accepted 16 May 2013 Available online 7 June 2013 Keywords: Tunable pore Micropore Piezo-actuator Viscoelastic Membrane
a b s t r a c t A viscoelastic membrane unit fabricated from thermoplastic polyurethane, with a formed single micropore, was interfaced to a piezoelectric actuator to demonstrate rapid actuation of the pore. Changes in through-pore conductance were measured as a function of the voltage applied to the actuator. The pore was opened and closed either in a stepwise fashion, or else made to oscillate between more and less open positions at up to 200 Hz. The step-driven response exhibited both a fast (<100 ms) majority component and a slow (1 s) minority component. The oscillatory method indicated that the majority component reached 95% of the low frequency (5 Hz) conductance amplitude in 5 ms, fast enough for a pore to close upon a particle driven by a 50 Pa pressure head. This advance in the rapid control of very small pores was achieved by reducing the amount of viscoelastic material between the pore and the source of actuation. This technique has potential for measurement and manipulation of micro- and nano-particles. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In recent years there has been increasing interest in the use of individual micro- and nanopores in thin membranes for sensing of small particles dispersed in aqueous electrolyte, using the resistive pulse technique. This technique could find applications in high growth areas as such as biosecurity, medical diagnostics and water quality monitoring, although research has been mostly driven by the promise of sensing single molecules, particularly DNA [1–3]. Molecular-scale nanopores can be made from solidstate [1] or biological materials [2], while larger-scale pores have been fabricated from carbon nanotubes [4], polymers [5] and glass [6,7]. Tunable pores (TPs) are one emerging type of pore which can be used to sense and interrogate micro- and nano-particles [3,8–21]. TPs are particularly interesting be-
⇑ Corresponding authors. Present address: Callaghan Innovation, PO Box 31-310, Lower Hutt 5040, New Zealand. Tel.: +64 4 9313000; fax: +64 4 9313754. E-mail addresses: [email protected] (G.R. Willmott), [email protected] (W.M. Arnold). 0263-2241/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2013.05.023
cause they are formed in an elastomeric membrane, and can be reversibly increased or decreased in size (geometrically ‘tuned’) on the micro- to nano-scale by macroscopic stretching of the surrounding elastomeric material [3,8– 12]. Like some other nanopore types [5–7], TPs are conical in shape. TPs, including mechanical and electronic hardware as well as data-processing software, are available commercially from Izon Science (Christchurch, New Zealand) in the form of the qNano apparatus [22]. Similar stretchable channels and valves have been reported in the wider fields of microfluidics and nanofluidics [23–27]. Here, we report on a method for fast actuation of elastomeric micropores similar to commercial TPs, including high-frequency oscillatory opening and closing. Previously, the ‘tuning’ functionality of TPs has been studied in terms of measured [8–12], imaged [8–13] and modelled [10,11,14] behaviour, while active use of tuning has been limited to in situ optimisation of experimental resolution and apparent gating of DNA plasmids [3]. ‘Fast’ actuation, not previously reported for TPs, is characterized by application of strains in excess of 10% over time scales approaching the dwell time for particles near or within a pore. This represents an important step towards automation of resistive
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pulse sensing, and could also be applied for functions in which pores mechanically interact with fluid and particles. Perhaps the most obvious is particle trapping, in which a pore closes upon and holds a single particle. Particles could be gated, perhaps discriminating between particles in a mixture. In microfluidics, droplet throughput can now reach the kilohertz range [28], and a fast TP might be programmed to sense, analyse, and manipulate droplets according to real-time feedback. A fast submicron TP could dramatically improve our mechanical understanding of ‘soft’ nanoparticles in emulsions, drug delivery agents, and similar systems. New apparatus has been developed to achieve fast actuation. Preliminary work in this laboratory identified two key practical considerations: the basic response time of the actuation mechanism, and the mass of elastomeric material surrounding the nanopore and to which the actuating element is attached [29]. It was determined that piezo-actuation should be used and that the rigid attachment of the actuating element should be brought as close as possible to the pore. Thermoplastic polyurethane (TPU) has been the material of choice for constructing TPs, because it combines excellent elasticity with toughness. As with any elastomer, TPU is viscoelastic, and for TP actuation three important consequences of viscoelasticity have been established [10]. Firstly, the stress–strain characteristic is near-reproducible following cyclical stress-softening up to some maximum strain (the Mullins effect [30]). Secondly, the material will slightly creep over very long time scales (h). Finally, material immediately adjacent to pores will have been highly inelastically deformed during pore formation. By bringing the actuation element close to the pore, the importance of these viscoelastic complications can be reduced. Our actuation unit actuates a pore membrane in one dimension (1D), with the orthogonal direction held clamped, in contrast with the 2D actuation applied to commercial TPs. Actuation can be usefully quantified by relating the applied 1D strain (er) to the ionic resistance of the pore (R), which can be measured precisely and relatively easily in real time. We use two semi-empirical relations
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to model 1D near-pore actuation. The first, a power law of the form
R ¼ Aen r ;
ð1Þ
has provided a reasonable fit to the resistance–strain relation in previous 2D actuation experiments and modelling [10–12,14], where A and n are constants. Physically, the power law represents a pore of zero radius with no strain applied, and radius extending linearly with strain. We also use an exponential model, which has the advantage of finite resistance at zero strain, and takes the form
R ¼ Bexpper ;
ð2Þ
where B and p are constants. 2. Material and methods 2.1. Membrane unit and pore fabrication As illustrated in Fig. 1, glass fibre bundles were incorporated into a TPU membrane so that the ends of these bundles were separated by 500 lm across a central area of 50 lm thick TPU membrane. For fabrication, 200 lm wide bundles of glass fibres were first lightly soaked in a 2% solution of polyurethane in tetrahydrofuran (THF) to hold the fibres together. Two lengths (25 mm) of these bundles were laid crossed at right angles, on top of a smooth polytetrafluorethylene (PTFE) plate. A square (side length 20 mm) of 130 lm thick TPU elastomer was placed over these crossed bundles, then another PTFE plate was clamped in place to lightly press the glass and polyurethane together, before the assembly was oven heated at 164 °C for 10 min. After cooling, the membrane was released and a 500 lm hole was punched where the glass bundles crossed using a truncated and sharpened syringe needle. A further square (side length 20 mm) of 50 lm thick TPU elastomer was then laid over the punctured membrane, pressed between clamped PTFE plates as before and reheated to 164 °C for 10 min. At this temperature the TPU membranes welded together with little distortion. A final step involved placing a small drop of THF (2 lL)
Fig. 1. Schematic diagrams showing the structure of the thermally welded TPU membranes enclosing glass fibre bundles, and in which a micropore is formed. (a) Plan view. (b) Cross sectional view.
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within the 500 lm well to seal in the exposed glass fibres adjacent to the well. The completed membrane was sandwiched between two 6–8 mm long tubes of TPU (outside diameter 6 mm, inside diameter 4 mm), with the well concentric with respect to both of them. THF was used to solvent weld the membrane in place: the final membrane unit is shown in Fig. 2. A piece of polyurethane membrane was attached over the lower end of the bottom tube. The lower cavity could be filled with a solution using a syringe via a perforation in this lower membrane. This method for introducing solution minimised trapped air bubbles while allowing reliable electrolytic contact with an electrode placed within the lower cavity. A micropore was formed by pressing a fine tungsten needle into the 50 lm membrane within the central 500 lm area. Needles were made electrolytically from 0.5 mm tungsten rod by adapting the procedures described elsewhere [31,32]. Tip radii of about 1 lm could be formed in this way. Pores were made under a microscope by first lowering the tungsten tip close to the membrane surface, then pressing gently to puncture the membrane with a KCl solution contained on the other side of the membrane. The solution appeared to limit distension of the membrane as the tip pressed onto the surface, and probably also enhanced wetting of the pore channel. The solutions used in measurements were 0.1 and 1 M KCl containing Triton X-100 wetting agent (0.01 vol%). Ag/AgCl electrodes were dipped directly into these solutions.
Fig. 3. Schematic diagram of the TPU elastomer unit mounted in the piezo-actuator apparatus. Ag/AgCl electrodes (red) make contact with KCl electrolyte in tubes above and below the membrane. The two glass fibre bundles oriented along the non-actuated axis (in and out of the diagram’s plane) were clamped to a frame (not shown) that encircled the device. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2.2. Actuation equipment Figs. 3 and 4 show how the membrane unit was mounted to undergo changes in pore size, utilizing a piezo-actuator bearing on a moveable arm. This arm and a fixed arm to which it was hinged were attached to small jaws that gripped the glass fibre bundles extending outside
Fig. 2. Completed membrane unit showing the membrane, with crossed glass fibre bundles, solvent welded between upper and lower TPU tubes. A perforated TPU membrane (blue) has been welded over the base of the lower tube to provide better retention of electrolyte. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Schematic diagram of the piezo-actuation and through-pore resistance measurement system for the initial stepped-voltage experiments. The two metal clamps press directly across the glass fibre bundles embedded in the TPU membrane. In this diagram, the piezo-actuator is shown positioned on the moving arm about half way between the pivot point and the pore, giving a theoretical 2:1 mechanical advantage over an actuator placed at the right-hand end of the moving arm.
the tubes. By means of separate adjusting screws some manual setting of the starting position of the jaws was possible before commencing an experiment: e.g., to establish a prestressed state in either tension or compression. Jaws orthogonal to the actuation direction were permanently fixed to reduce narrowing of the pore during actuation. The actuation unit (PAZ 100, Piezo Actuator with Feedback, Thor Labs Ltd., Newtown, NJ) was fixed to a baseboard on one side of the moveable arm via a steel ball and magnetic coupling. This coupling could be positioned to give mechanical advantage settings from 1:1 to 1:10. The apparatus was physically arranged to allow an optical microscope to focus on the pore area of the membrane – viewed through the upper electrolyte solution. The PAZ 100 device was under computer control, utilising Thor Labs APT user software and via a Piezo Controller BPC202 (Thor Labs). The maximum stroke for this actuator was 100 lm.
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Small (micron) step changes could be programmed as required. 2.3. Actuation experiments In a first series of measurements the piezo controller was operated manually. A constant DC voltage was applied between the Ag/AgCl electrodes, and for stepwise changes in the actuator position, pore resistances were logged by LabView software receiving data at 10 Hz from a high precision multimeter (HP 34401A, Hewlett Packard). In a second series of measurements, designed to more closely characterise the response times of the TPU membrane units, AC actuation was carried out at different frequencies, driven by a tunable sine wave generator. The piezo-actuator was then driven to give a constant-amplitude sinusoidally-varying displacement over this frequency range. Variations in ionic current resulting from changes in pore geometry were applied to a resistive bridge which had been balanced before application of the sine-wave. The out-of-balance voltage was measured on one channel of a
digital oscilloscope (Tektronix TDS 3012C) and the sinewave drive on another channel. In this way, the driving and response signals could be compared in phase and amplitude over the frequency range of interest. 3. Results and discussion 3.1. Transfer of piezo-actuation to the membrane Calibrated microscope observations revealed that, within measurement uncertainty, the displacement of the jaws was as expected (accounting for mechanical advantage), indicating no significant mechanical losses in the membrane-jaw connections. The size of the central well in the polyurethane membrane was measured in a similar way, by focussing on opposing glass fibre bundles. As the piezo-actuator was stepped from 0 to 100 lm with 2:1 mechanical advantage, the width of the central well area increased by about half (90 ± 6 lm) of the 200 lm jaw displacement, indicating that about half of the applied displacement is lost. It is most likely that this loss occurs
(a)
(b)
(c) Fig. 5. (a) Through-pore ionic resistance of the polyurethane membrane unit, as one-dimensional changes were applied by the piezo-actuator in 5 lm steps from 100-0-100 lm. More detailed data (b) and (c) show step changes as the pore undergoes stretching and relaxation respectively. Between actuation steps, the resistance data are in close, discrete bands, indicating the resolution of the logging apparatus (0.2 kX).
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within the membrane between the glass fibres and the well, because other elements are more rigid. Actuation of 100 lm represents 20% of the initial well diameter (500 lm). Similar strains have been recorded when TPs have been used for conventional resistive pulse sensing of particles [9,13,15,16], suggesting that the piezoelectrically-driven jaws could be used for similar work. In such experiments, mechanical tuning is important for optimising the experimental signal, for studying and understanding the sensing process, and for removing pore blockages. Actuation need not be carried out in real time – stretching typically takes several seconds, and is carried out a few minutes (or longer) before measurements. The applied strain is held constant thereafter, and during any measurements.
3.2. Changes in electrical resistance in response to stepped actuation Piezo-actuation, triggered manually in set steps, produced changes in through-pore resistance as shown in Fig. 5. Here, the pore was filled and surrounded by 0.1 M KCl electrolyte. The jaws were initially adjusted so that the resistance was as close to the maximum as possible without closing the pore. The orthogonal pore dimension was held fixed (Fig. 3 caption). Fig. 5a shows steps in resistance as membrane tension is progressively increased then reduced. Given that most steps show no intermediate resistance data points, most of each step change in pore size must occur within the logging interval (100 ms). However, Fig. 5b and c indicates that the resistance does not immediately settle to a new value after the pore diameter changes. Residual viscoelastic behaviour prevents immediate change to a new equilibrium state of pore closure. Following the initial step change, a closing pore takes an additional 0.5 s to reach an equilibrium value of resistance, and it takes a few seconds longer for pore opening. Fig. 5 also shows that fluctu-
Fig. 6. Change in through-pore resistance as the piezo-actuator opens the pore, with experimental data derived from Fig. 5. The power law fit (Eq. (1)), which excludes the data point at er = 0, has values of A = 0.055 and n = 0.656, with R2 = 0.98. The exponential fit (Eq. (2)) has values of B = 0.481 and p = 4.57, with R2 = 0.79.
ations in measured resistance were typically ±0.1–0.2% in these experiments. An obvious feature of Fig. 5 is the progressively smaller changes in resistance as the pore is opened. This is explored in Fig. 6, which shows the change in through-pore resistance as the pore area changes with piezo-actuation. Here, we quantify the actuation using an applied strain,
er ¼
x x0 ; x0
ð3Þ
where x is the separation between the ends of glass fibres on opposite sides of the pore, and x0 is the value of x with no stretch applied (500 lm). A complete model of TP actuation must account for viscoelastic material properties, including the full actuation history of membrane. One of the most important aspects of this history is the formation of the pore itself, which is likely to induce elevated stresses in the material immediately adjacent to the pore. First steps towards such a model are addressed elsewhere [10,11,14]. To obtain relevant experimental data using easily measurable quantities (er and pore ionic resistance R), it is most useful to explore semi-empirical relationships such as Eqs. (1) and (2), on the basis that ionic resistance is given by
R¼q
Z
dz ; Across ðzÞ
ð4Þ
where resistivity q is a constant, Across(z) is the cross sectional area of the pore (constant if the pore is cylindrical) and the integral is over the length of the pore in the zdirection, which is normal to the membrane surface. For example, when the pore resistance is most sensitive to actuation in Fig. 5a, the ionic resistance is approximately 0.5 MX. This value corresponds to a pore radius of 5.0 lm, assuming a cylindrical pore in a 50 lm thick membrane and 0.1 M KCl electrolyte (q = 0.776 Xm at 25 °C [33]). Eqs. (1) and (2) owe their physical origin to simple elastic models for material deformation [10,12]. As an intuitive starting point, one can consider ‘affine’ material stretching, in which the pore area in plane of the membrane increases proportionally to (1 + er)2. Unfortunately, this relation is not useful for describing measured TP resistances [12]. The power law expression (Eq. (1)) arises from an assumption that pore dimensions within the membrane plane (perpendicular to the the z-direction) scale linearly with er. This expression has proved most useful for other TP experiments [11,12], but has the feature that resistance is infinite at zero stretch. To address this shortcoming, the exponential expression (Eq. (2)) is also used. The data in Fig. 6 provide further evidence for the utility of Eq. (1), although the data point at zero stretch is excluded from the fit. The applied strain is 1D, with clamps applied in the unstretched direction. Actuation is likely to generate a nearelliptical pore (even if it was initially circular) [10], forming a progressively longer slit of approximately constant width with increasing applied strain. For comparison with 2D actuation, we can approximate that predicted changes in Across(z) scale as if one linear dimension of the pore moves, with the other stationary. This approximation is consistent
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with the observed difference in power laws (n = 1.2 for strains between 0.05 and 0.25 in [11], n = 0.656 in Fig. 6). A key advantage of the present experiments is that, because the far-field strain is applied more directly to the pore, one can assume with some confidence that near-pore actuation is proportional to applied stretch er. One important lesson arising from the comparison of fits is that it is difficult to predict the measured resistance at the onset of stretching. This observation reflects that wrinkling can occur adjacent to mechanically formed holes at low strains, resulting in some ‘slack’ to be taken up before the pore geometry is altered. Some experiments were more consistent with the power law than Fig. 6, because the through-pore resistance was observed to suddenly increase many orders of magnitude when the pore was closed in a small (2 lm) step. It is likely that such a step pushed the pore walls together, causing the pore to dewet, possibly under the influence of surface forces in the TPU polymer.
3.3. Changes in electrical conductance in response to sinusoidal actuation
These results refine the step-change measurements (Fig. 6) which indicated that the majority of the response occurred in less than 100 ms. A physical interpretation is that, in addition to the viscoelasticity in the TPU membrane and attached TPU tubes already discussed in relation to Fig. 6, above 50 Hz another factor comes into play. This could be inertia due to the mass of the arm attached to the moving jaw. The analogy can be made between this damped mechanical system and an electrical low-pass filter. The response of such a circuit is characterised by frequency fc giving a 3 dB drop in response (0.707 of the low frequency amplitude) - in this case, at 100 Hz. On this basis the time constant, given by s = 1/(2pfc), is estimated to be s = 1.6 ms. It is of interest to estimate whether the response time of the elastomer is sufficiently fast for applications. The obvious model system is that of a particle passing through a cylindrical pore in pressure-driven flow, where the pore is required to close within the time that the particle is within the pore. Assuming Hagen–Poiseuille flow due to a pressure DP applied across the ends of a pore of radius r and length d, the dwell time within the pore is 2
In order to better resolve the activation response, the piezo driving voltage and the resulting pore conductance were displayed on an oscilloscope. A sine-wave drive of constant amplitude was applied over a frequency range between 5 Hz and 200 Hz. Results in Fig. 7a show that up to about 50 Hz, the amplitude of pore actuation is not greatly affected compared to low-frequency values. However at higher frequencies the pore appears unable to respond, as evidenced by the drop in measured amplitude. Moreover, over the entire frequency range there is an increasing phase shift between the response and the driving signal. An example of this phase shift is seen in Fig. 7b.
(a)
t¼
8ld ; r 2 DP
ð5Þ
where l is the fluid viscosity (1 mPa s for water at room temperature). Using indicative values for the specific pores in our experiments (d = 50 lm, r = 5 lm) and DP = 50 Pa, equivalent to a 5 mm gravitational pressure head, we find a dwell time of 16 ms. This value is greater than s and comparable to the oscillation period at fc (10 ms), indicating both that particle trapping with our device should be possible, and that the limitations of material response could be an important consideration. Particle detection and triggering of the actuation can be carried out electronically, so it
(b)
Fig. 7. Sinusoidal piezo-actuation of a micropore. (a) Results of an experiment in which the piezo-actuator is driven over a range of frequencies. At the same time a constant voltage is applied across the pore and the resultant through-pore current (and therefore conductance) is measured. (b) Example of data at 100 Hz: through-pore conductance (lower, blue trace) lags a 100 Hz voltage (upper, yellow trace) applied to drive the piezo-actuator, which controls pore opening and closing. In this record the current trace is displayed inverted: the phase shift between actuator voltage and through-pore conductance is about 76°. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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likely that the material or the inertia of the transmission link would provide the response time bottleneck if still faster actuation were required. As Eq. (5) shows, t is strongly dependent on pore geometry, and pressure-driven flows through thinner, longer cylinders will provide much greater dwell times, with the trade-off that fewer particles will pass through the pore in any given time (with particle concentration held constant). The applied pressure can be controlled to increase the dwell time or otherwise manipulate the particle, and indeed control and understanding of transport mechanisms (pressure-driven, electrokinetic, magnetic, etc.) has been an important consideration in recent TP research [17,18]. When using conical pores (such as TPs [9,13], which are also mechanically formed) rather than cylindrical pores, particle trapping is likely to be more difficult. When a particle is far from the constriction of a conical pore, resistive pulses are less prominent and mechanical interactions between the pore and the particle may be hindered. At smaller length scales, surface chemistry also becomes more important. Finally, we note that particles which are significantly longer than the pore (such as rods, fibres and chains) will have an extended dwell time.
4. Conclusions Results of the step-change work (Figs. 5 and 6) indicated that the majority of the mechanical response of an elastomeric micropore to piezo-actuation occurred faster than the sampling rate (100 ms). After each step change, there was a subsequent (smaller) response of up to several seconds as the pore settled into a new equilibrium conformation. For faster, oscillatory actuation, the response could be explained by a single time-constant model with a 3 dB drop at about 100 Hz, indicating a time constant of 1.6 ms. On this basis, 95% (3 time constants) of the actuation seen at low frequencies will be attained within 5 ms. This represents a significantly more rapid response than previously achieved using tunable pores in elastomeric membranes. Conventionally [3,8–12], actuation steps have been applied over 1 s or more, and attempts at faster actuation have been frustrated by slow pore response due to the amount of elastomer between the pore and the point of actuation. Rapid actuation has been achieved by using piezo-actuation and by greatly reducing the amount of viscoelastic material between the pore area and the point of rigid actuation. The site of rigid actuation was located 250 lm from the pore by embedding bundles of glass fibres in the TPU elastomer, and attaching these bundles to the actuator jaws. Furthermore, by virtue of the rigidity of the glass fibres, this actuation was effective in both the opening and closing directions. In this work actuation was carried out in 1D, with the membrane held stationary in the orthogonal direction. Notwithstanding the interesting elliptical geometry, this configuration probably represents an initial step towards practical applications in which 2D actuation is achieved by replacing the clamps with a second, identical actuating unit. This capability, while more technically complicated,
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Contents lists available at SciVerse ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Fast piezoelectric actuation of an elastomeric micropore Murray L. Jansen a, Geoff R. Willmott a,b,⇑, Ingrid Hoek a, W. Mike Arnold a,b,⇑ a b
Industrial Research Ltd., PO Box 31-310, Lower Hutt 5040, New Zealand The MacDiarmid Institute for Advanced Materials and Nanotechnology, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
a r t i c l e
i n f o
Article history: Received 20 November 2012 Received in revised form 2 May 2013 Accepted 16 May 2013 Available online 7 June 2013 Keywords: Tunable pore Micropore Piezo-actuator Viscoelastic Membrane
a b s t r a c t A viscoelastic membrane unit fabricated from thermoplastic polyurethane, with a formed single micropore, was interfaced to a piezoelectric actuator to demonstrate rapid actuation of the pore. Changes in through-pore conductance were measured as a function of the voltage applied to the actuator. The pore was opened and closed either in a stepwise fashion, or else made to oscillate between more and less open positions at up to 200 Hz. The step-driven response exhibited both a fast (<100 ms) majority component and a slow (1 s) minority component. The oscillatory method indicated that the majority component reached 95% of the low frequency (5 Hz) conductance amplitude in 5 ms, fast enough for a pore to close upon a particle driven by a 50 Pa pressure head. This advance in the rapid control of very small pores was achieved by reducing the amount of viscoelastic material between the pore and the source of actuation. This technique has potential for measurement and manipulation of micro- and nano-particles. Ó 2013 Elsevier Ltd. All rights reserved.
1. Introduction In recent years there has been increasing interest in the use of individual micro- and nanopores in thin membranes for sensing of small particles dispersed in aqueous electrolyte, using the resistive pulse technique. This technique could find applications in high growth areas as such as biosecurity, medical diagnostics and water quality monitoring, although research has been mostly driven by the promise of sensing single molecules, particularly DNA [1–3]. Molecular-scale nanopores can be made from solidstate [1] or biological materials [2], while larger-scale pores have been fabricated from carbon nanotubes [4], polymers [5] and glass [6,7]. Tunable pores (TPs) are one emerging type of pore which can be used to sense and interrogate micro- and nano-particles [3,8–21]. TPs are particularly interesting be-
⇑ Corresponding authors. Present address: Callaghan Innovation, PO Box 31-310, Lower Hutt 5040, New Zealand. Tel.: +64 4 9313000; fax: +64 4 9313754. E-mail addresses: [email protected] (G.R. Willmott), [email protected] (W.M. Arnold). 0263-2241/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.measurement.2013.05.023
cause they are formed in an elastomeric membrane, and can be reversibly increased or decreased in size (geometrically ‘tuned’) on the micro- to nano-scale by macroscopic stretching of the surrounding elastomeric material [3,8– 12]. Like some other nanopore types [5–7], TPs are conical in shape. TPs, including mechanical and electronic hardware as well as data-processing software, are available commercially from Izon Science (Christchurch, New Zealand) in the form of the qNano apparatus [22]. Similar stretchable channels and valves have been reported in the wider fields of microfluidics and nanofluidics [23–27]. Here, we report on a method for fast actuation of elastomeric micropores similar to commercial TPs, including high-frequency oscillatory opening and closing. Previously, the ‘tuning’ functionality of TPs has been studied in terms of measured [8–12], imaged [8–13] and modelled [10,11,14] behaviour, while active use of tuning has been limited to in situ optimisation of experimental resolution and apparent gating of DNA plasmids [3]. ‘Fast’ actuation, not previously reported for TPs, is characterized by application of strains in excess of 10% over time scales approaching the dwell time for particles near or within a pore. This represents an important step towards automation of resistive
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pulse sensing, and could also be applied for functions in which pores mechanically interact with fluid and particles. Perhaps the most obvious is particle trapping, in which a pore closes upon and holds a single particle. Particles could be gated, perhaps discriminating between particles in a mixture. In microfluidics, droplet throughput can now reach the kilohertz range [28], and a fast TP might be programmed to sense, analyse, and manipulate droplets according to real-time feedback. A fast submicron TP could dramatically improve our mechanical understanding of ‘soft’ nanoparticles in emulsions, drug delivery agents, and similar systems. New apparatus has been developed to achieve fast actuation. Preliminary work in this laboratory identified two key practical considerations: the basic response time of the actuation mechanism, and the mass of elastomeric material surrounding the nanopore and to which the actuating element is attached [29]. It was determined that piezo-actuation should be used and that the rigid attachment of the actuating element should be brought as close as possible to the pore. Thermoplastic polyurethane (TPU) has been the material of choice for constructing TPs, because it combines excellent elasticity with toughness. As with any elastomer, TPU is viscoelastic, and for TP actuation three important consequences of viscoelasticity have been established [10]. Firstly, the stress–strain characteristic is near-reproducible following cyclical stress-softening up to some maximum strain (the Mullins effect [30]). Secondly, the material will slightly creep over very long time scales (h). Finally, material immediately adjacent to pores will have been highly inelastically deformed during pore formation. By bringing the actuation element close to the pore, the importance of these viscoelastic complications can be reduced. Our actuation unit actuates a pore membrane in one dimension (1D), with the orthogonal direction held clamped, in contrast with the 2D actuation applied to commercial TPs. Actuation can be usefully quantified by relating the applied 1D strain (er) to the ionic resistance of the pore (R), which can be measured precisely and relatively easily in real time. We use two semi-empirical relations
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to model 1D near-pore actuation. The first, a power law of the form
R ¼ Aen r ;
ð1Þ
has provided a reasonable fit to the resistance–strain relation in previous 2D actuation experiments and modelling [10–12,14], where A and n are constants. Physically, the power law represents a pore of zero radius with no strain applied, and radius extending linearly with strain. We also use an exponential model, which has the advantage of finite resistance at zero strain, and takes the form
R ¼ Bexpper ;
ð2Þ
where B and p are constants. 2. Material and methods 2.1. Membrane unit and pore fabrication As illustrated in Fig. 1, glass fibre bundles were incorporated into a TPU membrane so that the ends of these bundles were separated by 500 lm across a central area of 50 lm thick TPU membrane. For fabrication, 200 lm wide bundles of glass fibres were first lightly soaked in a 2% solution of polyurethane in tetrahydrofuran (THF) to hold the fibres together. Two lengths (25 mm) of these bundles were laid crossed at right angles, on top of a smooth polytetrafluorethylene (PTFE) plate. A square (side length 20 mm) of 130 lm thick TPU elastomer was placed over these crossed bundles, then another PTFE plate was clamped in place to lightly press the glass and polyurethane together, before the assembly was oven heated at 164 °C for 10 min. After cooling, the membrane was released and a 500 lm hole was punched where the glass bundles crossed using a truncated and sharpened syringe needle. A further square (side length 20 mm) of 50 lm thick TPU elastomer was then laid over the punctured membrane, pressed between clamped PTFE plates as before and reheated to 164 °C for 10 min. At this temperature the TPU membranes welded together with little distortion. A final step involved placing a small drop of THF (2 lL)
Fig. 1. Schematic diagrams showing the structure of the thermally welded TPU membranes enclosing glass fibre bundles, and in which a micropore is formed. (a) Plan view. (b) Cross sectional view.
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within the 500 lm well to seal in the exposed glass fibres adjacent to the well. The completed membrane was sandwiched between two 6–8 mm long tubes of TPU (outside diameter 6 mm, inside diameter 4 mm), with the well concentric with respect to both of them. THF was used to solvent weld the membrane in place: the final membrane unit is shown in Fig. 2. A piece of polyurethane membrane was attached over the lower end of the bottom tube. The lower cavity could be filled with a solution using a syringe via a perforation in this lower membrane. This method for introducing solution minimised trapped air bubbles while allowing reliable electrolytic contact with an electrode placed within the lower cavity. A micropore was formed by pressing a fine tungsten needle into the 50 lm membrane within the central 500 lm area. Needles were made electrolytically from 0.5 mm tungsten rod by adapting the procedures described elsewhere [31,32]. Tip radii of about 1 lm could be formed in this way. Pores were made under a microscope by first lowering the tungsten tip close to the membrane surface, then pressing gently to puncture the membrane with a KCl solution contained on the other side of the membrane. The solution appeared to limit distension of the membrane as the tip pressed onto the surface, and probably also enhanced wetting of the pore channel. The solutions used in measurements were 0.1 and 1 M KCl containing Triton X-100 wetting agent (0.01 vol%). Ag/AgCl electrodes were dipped directly into these solutions.
Fig. 3. Schematic diagram of the TPU elastomer unit mounted in the piezo-actuator apparatus. Ag/AgCl electrodes (red) make contact with KCl electrolyte in tubes above and below the membrane. The two glass fibre bundles oriented along the non-actuated axis (in and out of the diagram’s plane) were clamped to a frame (not shown) that encircled the device. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
2.2. Actuation equipment Figs. 3 and 4 show how the membrane unit was mounted to undergo changes in pore size, utilizing a piezo-actuator bearing on a moveable arm. This arm and a fixed arm to which it was hinged were attached to small jaws that gripped the glass fibre bundles extending outside
Fig. 2. Completed membrane unit showing the membrane, with crossed glass fibre bundles, solvent welded between upper and lower TPU tubes. A perforated TPU membrane (blue) has been welded over the base of the lower tube to provide better retention of electrolyte. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Schematic diagram of the piezo-actuation and through-pore resistance measurement system for the initial stepped-voltage experiments. The two metal clamps press directly across the glass fibre bundles embedded in the TPU membrane. In this diagram, the piezo-actuator is shown positioned on the moving arm about half way between the pivot point and the pore, giving a theoretical 2:1 mechanical advantage over an actuator placed at the right-hand end of the moving arm.
the tubes. By means of separate adjusting screws some manual setting of the starting position of the jaws was possible before commencing an experiment: e.g., to establish a prestressed state in either tension or compression. Jaws orthogonal to the actuation direction were permanently fixed to reduce narrowing of the pore during actuation. The actuation unit (PAZ 100, Piezo Actuator with Feedback, Thor Labs Ltd., Newtown, NJ) was fixed to a baseboard on one side of the moveable arm via a steel ball and magnetic coupling. This coupling could be positioned to give mechanical advantage settings from 1:1 to 1:10. The apparatus was physically arranged to allow an optical microscope to focus on the pore area of the membrane – viewed through the upper electrolyte solution. The PAZ 100 device was under computer control, utilising Thor Labs APT user software and via a Piezo Controller BPC202 (Thor Labs). The maximum stroke for this actuator was 100 lm.
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Small (micron) step changes could be programmed as required. 2.3. Actuation experiments In a first series of measurements the piezo controller was operated manually. A constant DC voltage was applied between the Ag/AgCl electrodes, and for stepwise changes in the actuator position, pore resistances were logged by LabView software receiving data at 10 Hz from a high precision multimeter (HP 34401A, Hewlett Packard). In a second series of measurements, designed to more closely characterise the response times of the TPU membrane units, AC actuation was carried out at different frequencies, driven by a tunable sine wave generator. The piezo-actuator was then driven to give a constant-amplitude sinusoidally-varying displacement over this frequency range. Variations in ionic current resulting from changes in pore geometry were applied to a resistive bridge which had been balanced before application of the sine-wave. The out-of-balance voltage was measured on one channel of a
digital oscilloscope (Tektronix TDS 3012C) and the sinewave drive on another channel. In this way, the driving and response signals could be compared in phase and amplitude over the frequency range of interest. 3. Results and discussion 3.1. Transfer of piezo-actuation to the membrane Calibrated microscope observations revealed that, within measurement uncertainty, the displacement of the jaws was as expected (accounting for mechanical advantage), indicating no significant mechanical losses in the membrane-jaw connections. The size of the central well in the polyurethane membrane was measured in a similar way, by focussing on opposing glass fibre bundles. As the piezo-actuator was stepped from 0 to 100 lm with 2:1 mechanical advantage, the width of the central well area increased by about half (90 ± 6 lm) of the 200 lm jaw displacement, indicating that about half of the applied displacement is lost. It is most likely that this loss occurs
(a)
(b)
(c) Fig. 5. (a) Through-pore ionic resistance of the polyurethane membrane unit, as one-dimensional changes were applied by the piezo-actuator in 5 lm steps from 100-0-100 lm. More detailed data (b) and (c) show step changes as the pore undergoes stretching and relaxation respectively. Between actuation steps, the resistance data are in close, discrete bands, indicating the resolution of the logging apparatus (0.2 kX).
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within the membrane between the glass fibres and the well, because other elements are more rigid. Actuation of 100 lm represents 20% of the initial well diameter (500 lm). Similar strains have been recorded when TPs have been used for conventional resistive pulse sensing of particles [9,13,15,16], suggesting that the piezoelectrically-driven jaws could be used for similar work. In such experiments, mechanical tuning is important for optimising the experimental signal, for studying and understanding the sensing process, and for removing pore blockages. Actuation need not be carried out in real time – stretching typically takes several seconds, and is carried out a few minutes (or longer) before measurements. The applied strain is held constant thereafter, and during any measurements.
3.2. Changes in electrical resistance in response to stepped actuation Piezo-actuation, triggered manually in set steps, produced changes in through-pore resistance as shown in Fig. 5. Here, the pore was filled and surrounded by 0.1 M KCl electrolyte. The jaws were initially adjusted so that the resistance was as close to the maximum as possible without closing the pore. The orthogonal pore dimension was held fixed (Fig. 3 caption). Fig. 5a shows steps in resistance as membrane tension is progressively increased then reduced. Given that most steps show no intermediate resistance data points, most of each step change in pore size must occur within the logging interval (100 ms). However, Fig. 5b and c indicates that the resistance does not immediately settle to a new value after the pore diameter changes. Residual viscoelastic behaviour prevents immediate change to a new equilibrium state of pore closure. Following the initial step change, a closing pore takes an additional 0.5 s to reach an equilibrium value of resistance, and it takes a few seconds longer for pore opening. Fig. 5 also shows that fluctu-
Fig. 6. Change in through-pore resistance as the piezo-actuator opens the pore, with experimental data derived from Fig. 5. The power law fit (Eq. (1)), which excludes the data point at er = 0, has values of A = 0.055 and n = 0.656, with R2 = 0.98. The exponential fit (Eq. (2)) has values of B = 0.481 and p = 4.57, with R2 = 0.79.
ations in measured resistance were typically ±0.1–0.2% in these experiments. An obvious feature of Fig. 5 is the progressively smaller changes in resistance as the pore is opened. This is explored in Fig. 6, which shows the change in through-pore resistance as the pore area changes with piezo-actuation. Here, we quantify the actuation using an applied strain,
er ¼
x x0 ; x0
ð3Þ
where x is the separation between the ends of glass fibres on opposite sides of the pore, and x0 is the value of x with no stretch applied (500 lm). A complete model of TP actuation must account for viscoelastic material properties, including the full actuation history of membrane. One of the most important aspects of this history is the formation of the pore itself, which is likely to induce elevated stresses in the material immediately adjacent to the pore. First steps towards such a model are addressed elsewhere [10,11,14]. To obtain relevant experimental data using easily measurable quantities (er and pore ionic resistance R), it is most useful to explore semi-empirical relationships such as Eqs. (1) and (2), on the basis that ionic resistance is given by
R¼q
Z
dz ; Across ðzÞ
ð4Þ
where resistivity q is a constant, Across(z) is the cross sectional area of the pore (constant if the pore is cylindrical) and the integral is over the length of the pore in the zdirection, which is normal to the membrane surface. For example, when the pore resistance is most sensitive to actuation in Fig. 5a, the ionic resistance is approximately 0.5 MX. This value corresponds to a pore radius of 5.0 lm, assuming a cylindrical pore in a 50 lm thick membrane and 0.1 M KCl electrolyte (q = 0.776 Xm at 25 °C [33]). Eqs. (1) and (2) owe their physical origin to simple elastic models for material deformation [10,12]. As an intuitive starting point, one can consider ‘affine’ material stretching, in which the pore area in plane of the membrane increases proportionally to (1 + er)2. Unfortunately, this relation is not useful for describing measured TP resistances [12]. The power law expression (Eq. (1)) arises from an assumption that pore dimensions within the membrane plane (perpendicular to the the z-direction) scale linearly with er. This expression has proved most useful for other TP experiments [11,12], but has the feature that resistance is infinite at zero stretch. To address this shortcoming, the exponential expression (Eq. (2)) is also used. The data in Fig. 6 provide further evidence for the utility of Eq. (1), although the data point at zero stretch is excluded from the fit. The applied strain is 1D, with clamps applied in the unstretched direction. Actuation is likely to generate a nearelliptical pore (even if it was initially circular) [10], forming a progressively longer slit of approximately constant width with increasing applied strain. For comparison with 2D actuation, we can approximate that predicted changes in Across(z) scale as if one linear dimension of the pore moves, with the other stationary. This approximation is consistent
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with the observed difference in power laws (n = 1.2 for strains between 0.05 and 0.25 in [11], n = 0.656 in Fig. 6). A key advantage of the present experiments is that, because the far-field strain is applied more directly to the pore, one can assume with some confidence that near-pore actuation is proportional to applied stretch er. One important lesson arising from the comparison of fits is that it is difficult to predict the measured resistance at the onset of stretching. This observation reflects that wrinkling can occur adjacent to mechanically formed holes at low strains, resulting in some ‘slack’ to be taken up before the pore geometry is altered. Some experiments were more consistent with the power law than Fig. 6, because the through-pore resistance was observed to suddenly increase many orders of magnitude when the pore was closed in a small (2 lm) step. It is likely that such a step pushed the pore walls together, causing the pore to dewet, possibly under the influence of surface forces in the TPU polymer.
3.3. Changes in electrical conductance in response to sinusoidal actuation
These results refine the step-change measurements (Fig. 6) which indicated that the majority of the response occurred in less than 100 ms. A physical interpretation is that, in addition to the viscoelasticity in the TPU membrane and attached TPU tubes already discussed in relation to Fig. 6, above 50 Hz another factor comes into play. This could be inertia due to the mass of the arm attached to the moving jaw. The analogy can be made between this damped mechanical system and an electrical low-pass filter. The response of such a circuit is characterised by frequency fc giving a 3 dB drop in response (0.707 of the low frequency amplitude) - in this case, at 100 Hz. On this basis the time constant, given by s = 1/(2pfc), is estimated to be s = 1.6 ms. It is of interest to estimate whether the response time of the elastomer is sufficiently fast for applications. The obvious model system is that of a particle passing through a cylindrical pore in pressure-driven flow, where the pore is required to close within the time that the particle is within the pore. Assuming Hagen–Poiseuille flow due to a pressure DP applied across the ends of a pore of radius r and length d, the dwell time within the pore is 2
In order to better resolve the activation response, the piezo driving voltage and the resulting pore conductance were displayed on an oscilloscope. A sine-wave drive of constant amplitude was applied over a frequency range between 5 Hz and 200 Hz. Results in Fig. 7a show that up to about 50 Hz, the amplitude of pore actuation is not greatly affected compared to low-frequency values. However at higher frequencies the pore appears unable to respond, as evidenced by the drop in measured amplitude. Moreover, over the entire frequency range there is an increasing phase shift between the response and the driving signal. An example of this phase shift is seen in Fig. 7b.
(a)
t¼
8ld ; r 2 DP
ð5Þ
where l is the fluid viscosity (1 mPa s for water at room temperature). Using indicative values for the specific pores in our experiments (d = 50 lm, r = 5 lm) and DP = 50 Pa, equivalent to a 5 mm gravitational pressure head, we find a dwell time of 16 ms. This value is greater than s and comparable to the oscillation period at fc (10 ms), indicating both that particle trapping with our device should be possible, and that the limitations of material response could be an important consideration. Particle detection and triggering of the actuation can be carried out electronically, so it
(b)
Fig. 7. Sinusoidal piezo-actuation of a micropore. (a) Results of an experiment in which the piezo-actuator is driven over a range of frequencies. At the same time a constant voltage is applied across the pore and the resultant through-pore current (and therefore conductance) is measured. (b) Example of data at 100 Hz: through-pore conductance (lower, blue trace) lags a 100 Hz voltage (upper, yellow trace) applied to drive the piezo-actuator, which controls pore opening and closing. In this record the current trace is displayed inverted: the phase shift between actuator voltage and through-pore conductance is about 76°. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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likely that the material or the inertia of the transmission link would provide the response time bottleneck if still faster actuation were required. As Eq. (5) shows, t is strongly dependent on pore geometry, and pressure-driven flows through thinner, longer cylinders will provide much greater dwell times, with the trade-off that fewer particles will pass through the pore in any given time (with particle concentration held constant). The applied pressure can be controlled to increase the dwell time or otherwise manipulate the particle, and indeed control and understanding of transport mechanisms (pressure-driven, electrokinetic, magnetic, etc.) has been an important consideration in recent TP research [17,18]. When using conical pores (such as TPs [9,13], which are also mechanically formed) rather than cylindrical pores, particle trapping is likely to be more difficult. When a particle is far from the constriction of a conical pore, resistive pulses are less prominent and mechanical interactions between the pore and the particle may be hindered. At smaller length scales, surface chemistry also becomes more important. Finally, we note that particles which are significantly longer than the pore (such as rods, fibres and chains) will have an extended dwell time.
4. Conclusions Results of the step-change work (Figs. 5 and 6) indicated that the majority of the mechanical response of an elastomeric micropore to piezo-actuation occurred faster than the sampling rate (100 ms). After each step change, there was a subsequent (smaller) response of up to several seconds as the pore settled into a new equilibrium conformation. For faster, oscillatory actuation, the response could be explained by a single time-constant model with a 3 dB drop at about 100 Hz, indicating a time constant of 1.6 ms. On this basis, 95% (3 time constants) of the actuation seen at low frequencies will be attained within 5 ms. This represents a significantly more rapid response than previously achieved using tunable pores in elastomeric membranes. Conventionally [3,8–12], actuation steps have been applied over 1 s or more, and attempts at faster actuation have been frustrated by slow pore response due to the amount of elastomer between the pore and the point of actuation. Rapid actuation has been achieved by using piezo-actuation and by greatly reducing the amount of viscoelastic material between the pore area and the point of rigid actuation. The site of rigid actuation was located 250 lm from the pore by embedding bundles of glass fibres in the TPU elastomer, and attaching these bundles to the actuator jaws. Furthermore, by virtue of the rigidity of the glass fibres, this actuation was effective in both the opening and closing directions. In this work actuation was carried out in 1D, with the membrane held stationary in the orthogonal direction. Notwithstanding the interesting elliptical geometry, this configuration probably represents an initial step towards practical applications in which 2D actuation is achieved by replacing the clamps with a second, identical actuating unit. This capability, while more technically complicated,
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