Thermoactuated Diffusion Control in Soft Matter Nanofluidic Devices

Nov 18, 2007 - The diffusive transport rate in a soft matter nanofluidic device is controlled with a thermoactuated hydrogel valve. The device consist...
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Langmuir 2008, 24, 5166-5171

Thermoactuated Diffusion Control in Soft Matter Nanofluidic Devices Martin Markstro¨m, Ludvig Lizana, Owe Orwar, and Aldo Jesorka* Department of Chemical and Biological Engineering, Chalmers UniVersity of Technology, SE-41296 Go¨teborg, Sweden ReceiVed NoVember 18, 2007. In Final Form: February 13, 2008 The diffusive transport rate in a soft matter nanofluidic device is controlled with a thermoactuated hydrogel valve. The device consists of three giant unilamellar vesicles linearly conjugated by lipid nanotubes, with a solution of the stimuli-responsive polymer poly(N-isopropyl acrylamide) (PNIPAAm) in the central vesicle. The valve states “high (transport) rate” and “low (transport) rate” are obtained by heat-activated switching between PNIPAAm’s dissolved and compact aggregated states. We show that three parameters influence the diffusion rate within the device: the increase of the transport rate caused by a decrease in PNIPAAm concentration upon compaction, the temperature dependence of the buffer viscosity, and the volume excluded by the PNIPAAm hydrogel compartment.

Introduction Since the development of the first microfluidic device more than 20 years ago, several technological advancements have been made to yield reliable, flexible, and robust devices. However, seemingly trivial functions such as flow control, mixing and fluid switching in micro-sized environments have presented considerable challenges. For example, sophisticated valve implementations to achieve flow control have been reported, based on a variety of actuation mechanisms, e.g., micro mechanical,1,2 heat,3-5 or magnetic field,6 but inexpensive technological solutions7 are rare and suffer from limitations. Today, nanofluidics is clearly state of the art. Several approaches for creating nanofluidic devices are in existence and were recently reviewed by Mijatovic et al.8 Our group has developed soft matter nanofluidic devices constructed of phospholipid membranes.9 The nanotube-vesicle network devices (NVNs), consisting of giant unilamellar vesicles (GUVs) conjugated by flexible lipid nanotubes, have been subjected to a range of studies over the past years.10,11 They display several intriguing features, e.g., they allow initiation and control of chemical reactions in confined biomimetic compartments, they make it possible to incorporate membrane proteins, and they are small enough to allow diffusion to be the main, but not only, means of transport.12-18 * Corresponding author. Address: Chalmers University of Technology, Department of Chemical and Biological Engineering, Physical Chemistry, Kemiva¨gen 10, 412 58 Go¨teborg, Sweden. E-mail: aldo@ chembio.chalmers.se. Fax: +46-31-7722785. Telephone: +46-31-7723069. (1) Cardenas-Valencia, A. M.; Dlutowski, J.; Bumgarner, J.; Munoz, C.; Wang, W.; Popuri, R.; Langebrake, L. Sens. Actuators, A: Phys. 2007, 136, 374. (2) Gu, W.; Zhu, X. Y.; Futai, N.; Cho, B. S.; Takayama, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 15861. (3) Kim, D.; Beebe, D. J. Sens. Actuators, A: Phys. 2007, 136, 426. (4) Wang, J.; Chen, Z. Y.; Mauk, M.; Hong, K. S.; Li, M. Y.; Yang, S.; Bau, H. H. Biomed. MicrodeVices 2005, 7, 313. (5) Park, J. M.; Cho, Y. K.; Lee, B. S.; Lee, J. G.; Ko, C. Lab Chip 2007, 7, 557. (6) Jackson, W. C.; Tran, H. D.; O’Brien, M. J.; Rabinovich, E.; Lopez, G. P. J. Vac. Sci. Technol., B 2001, 19, 596. (7) Samel, B.; Griss, P.; Stemme, G. J. Microelectromech. Syst. 2007, 16, 50. (8) Mijatovic, D.; Eijkel, J. C. T.; van den Berg, A. Lab Chip 2005, 5, 492. (9) Karlsson, A.; Karlsson, R.; Karlsson, M.; Cans, A. S.; Stromberg, A.; Ryttsen, F.; Orwar, O. Nature 2001, 409, 150. (10) Karlsson, A.; Karlsson, M.; Karlsson, R.; Sott, K.; Lundqvist, A.; Tokarz, M.; Orwar, O. Anal. Chem. 2003, 75, 2529. (11) Karlsson, R.; Karlsson, A.; Ewing, A.; Dommersnes, P.; Joanny, J. F.; Jesorka, A.; Orwar, O. Anal. Chem. 2006, 78, 5960. (12) Davidson, M.; Karlsson, M.; Sinclair, J.; Sott, K.; Orwar, O. J. Am. Chem. Soc. 2003, 125, 374.

Directed transport within NVNs, e.g., electrophoresis and Marangoni-flows, is difficult to control, and as long as the compound or particle is significantly smaller than the diameter of the nanotube, diffusion will disturb the process. In this work we address this problem by demonstrating how internalized poly(N-isopropyl acrylamide) (PNIPAAm) allows a single GUV in a network to function as a valve. PNIPAAm has previously been used to provide valve function in different micro- and nanometersized systems, e.g., in microfluidic chips19 and nanocapillary array membranes (NCAMs).20 In aqueous solution, PNIPAAm displays a lower critical solution temperature (LCST), meaning that, only below this temperature, PNIPAAm is fully soluble. At the LCST, which is at 32 °C in pure water, hydrophobicity increases, and the polymer molecules undergo a coil-to-globule transition.21 We have previously shown that PNIPAAm chains that are confined in a GUV at high enough concentration and with certain polymer or ionic additives will form a single hydrogel structure instead of a collective of microaggregates when heated to the LCST.22 If temperature is further increased, the PNIPAAm hydrogel will shrink and form a compact compartment with a temperaturedependent equilibrium size. Compaction, intrachain aggregation and coil-to-globule transition are reversible, i.e., at temperatures below the LCST, PNIPAAm chains will deaggregate and return to the initial dissolved state.22 Below we will show that the formation of a compact hydrogel within a GUV can be utilized to control the rate of diffusion inside an NVN. As a result of several factors, the transport rates of internalized molecules through a single GUV within a network (13) Karlsson, R.; Karlsson, M.; Karlsson, A.; Cans, A. S.; Bergenholtz, J.; Akerman, B.; Ewing, A. G.; Voinova, M.; Orwar, O. Langmuir 2002, 18, 4186. (14) Sott, K.; Lobovkina, T.; Lizana, L.; Tokarz, M.; Bauer, B.; Konkoli, Z.; Orwar, O. Nano Lett. 2006, 6, 209. (15) Tokarz, M.; Akerman, B.; Olofsson, J.; Joanny, J. F.; Dommersnes, P.; Orwar, O. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 9127. (16) Nomura, S.; Tsumoto, K.; Hamada, T.; Akiyoshi, K.; Nakatani, Y.; Yoshikawa, K. ChemBioChem 2003, 4, 1172. (17) Chiu, D. T.; Wilson, C. F.; Ryttsen, F.; Stromberg, A.; Farre, C.; Karlsson, A.; Nordholm, S.; Gaggar, A.; Modi, B. P.; Moscho, A.; Garza-Lopez, R. A.; Orwar, O.; Zare, R. N. Science 1999, 283, 1892. (18) Noireaux, V.; Libchaber, A. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 17669. (19) Luo, Q. Z.; Mutlu, S.; Gianchandani, Y. B.; Svec, F.; Frechet, J. M. J. Electrophoresis 2003, 24, 3694. (20) Lokuge, I.; Wang, X.; Bohn, P. W. Langmuir 2007, 23, 305. (21) Schild, H. G. Prog. Polym. Sci. 1992, 17, 163. (22) Markstrom, M.; Gunnarsson, A.; Orwar, O.; Jesorka, A. Soft Matter 2007, 3, 587.

10.1021/la7035967 CCC: $40.75 © 2008 American Chemical Society Published on Web 04/08/2008

Diffusion Control in Soft Matter Nanofluidic DeVices

Figure 1. Experimental setup for controlling phase transitions of PNIPAAm enclosed in NVNs under a confocal microscope. The components are not drawn to scale.

are different for the dissolved state and the compact aggregated state of PNIPAAm. By switching between the two states, this GUV functions as a diffusion control valve. Materials and Methods

Langmuir, Vol. 24, No. 9, 2008 5167 Markstro¨m et al.22 To simplify the process, the more common S1813 photoresist was utilized instead of UV-5. Temperature Measurement. The microthermocouple temperature measurement setup as outlined in the work of Markstro¨m et al.22 was further improved and extended by an in-house built heat control circuit, consisting of a Linear Technologies LTK001 thermocouple amplifier and a matched LT1025 junction potential compensator. The conditioned and amplified thermocouple voltage was A/D converted with a Contec ADA 16-32 AIO PC-card and processed to remotely control an external power supply by means of a PI control algorithm. Viscosity Measurement. The kinematic viscosity measurements were carried out with a Cannon-Ubbeholde dilution type viscometer obtained from Cannon Instrument Co. (Pennsylvania) in a thermostated water bath (Heto Birkerod, Denmark). The density measurements used to obtain the dynamic viscosity were carried out at 21 °C with a DMA 5000 density meter (Anton Paar GmbH, Austria). Fluorescence Correlation Spectroscopy (FCS). FCS measurements were performed on a Leica SP2 confocal microscope (see above) fitted with a two-channel FCS module (dichroic mirror and band-pass emission filters 505-580, 605-660 nm) with PMT detectors (ISS, Inc., USA). The samples were excited with the 488nm line of an Ar+ laser selected by the AOBS with a pinhole setting to Airy 1. All samples were measured for 20 s at 294 K. The data was analyzed with the ISS Vista FCS LE 3.6_22 (ISS, Inc., USA) software (Supporting Information).

Results and Discussion

Chemicals. Soybean lecithin (polar lipid extract) was obtained from Avanti Polar Lipids, Inc. (Alabaster, AL). Chloroform, Trizma, glycerol, EDTA, MgSO4, KH2PO4, K3PO4, CaCl2, KCl, and PNIPAAm (Mn∼ 300 000) were obtained from Sigma-Aldrich Europe. Deionized water was prepared using a MilliQ system (Millipore Corp., Bedford, MA). Blue dextran (Mn∼ 2 000 000 g/mol) was obtained from Sigma-Aldrich, Europe. Alexa Fluor 488 hydrazide (sodium salt) was obtained from Invitrogen (USA). Preparation of Surface Immobilized Giant Vesicles. Vesicles were prepared from soybean lecithin, using a modification of a dehydration/rehydration technique described by Criado and Keller.22,23 Injection of Cosolutes. PNIPAAm and blue dextran (PBD) were dissolved in buffer to reach a final concentration of 20 mg/mL PNIPAAm and 0.5 mg/mL blue dextran. The mixture was microinjected according to a procedure described elsewhere.24 Microscopy, Fluorescence, and Bright-Field Imaging. A confocal laser scanning microscopy system (Leica TCS SP2 RS, Wetzlar, Germany), with a PL APO CS 63x/1.2 W CORR objective, was used for acquisition of confocal fluorescence images. The 488nm line of an Ar+ laser was used for excitation, and emission was collected by a photomultiplier tube (500-600 nm). Simultaneously, DIC images from the reflected light of the scanning lasers were collected. The collected data was evaluated using the Leica Lite program. Experimental Setup. The principal experimental setup22 has been adapted to a confocal microscope (Figure 1). Briefly, rectangular cover slip glasses (no. 1) with surface printed thin film heating structures are used. The coil shaped structures are located on the top side of the cover slip, coated with an approximately 10 µm thick hardbaked epoxy film (SU-8 resist) as a protective and insulating layer. The layer also ensures that heat is dissipated homogeneously onto the whole surface above the coil structure. Modified IC test clamps are used to attach the coverslip to the microscope stage and electrically connect the heating structures to a regulated current source. Microfabrication of Surface Printed Resistive Heating Structures. Four individual rectangular thin film structures (10 nm Cr/ Au) in sets of two with different loop size and width were microfabricated on a borosilicate glass cover slip. Photolithography, film deposition, and epoxy-coating were performed according to

Fabrication of a Nanotube-Vesicle Network with a Hydrogel Valve. Creation of linear NVNs with typical vesicle diameters between 10 and 50 µm, nanotube diameters of ∼100 nm, and nanotube lengths of up to hundreds of micrometers by micro-electroinjection has been thoroughly described in the past.9 An NVN with a PNIPAAm valve was created by following the adapted procedure outlined in Figure 2. First, a daughter vesicle is created using a pipet filled with 20 mg/mL PNIPAAm and 0.5 mg/mL blue dextran solution (hereafter referred to as PBD solution) (Figure 2 A, B). The vesicle is immobilized on the surface, and the pipet is exchanged for a buffer-filled pipet. Subsequently, a buffer-filled vesicle is created and the nanotube connection point is translated across the network to the PBDfilled vesicle (Figure 2C-E), exploiting the fluidity of the membrane. The buffer-filled vesicle is then immobilized on the surface. A second buffer-filled vesicle is created and translated so that it is connected to both mother vesicle and PBD-filled vesicle before immobilization on the surface (Figure 2F-H). The pipet is exchanged for a pipet filled with Alexa Fluor 488 dissolved in buffer, and the vesicle between the mother vesicle and the PBD-filled vesicle is injected with Alexa (Figure 2 I). Note that NVNs with more complex geometry and/or connectivity can be constructed25 with one or several PBD-filled vesicles at arbitrarily chosen positions. Valve Actuation. We define the PNIPAAm valve to having two clearly distinguishable individual states: At temperatures below the LCST, PNIPAAm is fully soluble and present in the whole volume of the container. The valve is in its “low rate” state. At temperatures above the LCST, PNIPAAm aggregates and forms a hydrogel that shrinks to a temperature-dependent equilibrium size.22 PNIPAAm is largely removed from the container and concentrated in a compartment of reduced diameter. Thereby the valve is in its “high rate” state. The transition between the two states only takes 1-2 s. A more detailed description of the conditions and specifics of the generation of PNIPAAm

(23) Criado, M.; Keller, B. U. FEBS Lett. 1987, 224, 172. (24) Karlsson, M.; Nolkrantz, K.; Davidson, M. J.; Stromberg, A.; Ryttsen, F.; Akerman, B.; Orwar, O. Anal. Chem. 2000, 72, 5857.

(25) Karlsson, M.; Davidson, M.; Karlsson, R.; Karlsson, A.; Bergenholtz, J.; Konkoli, Z.; Jesorka, A.; Lobovkina, T.; Hurtig, J.; Voinova, M.; Orwar, O. Annu. ReV. Phys. Chem. 2004, 55, 613.

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An example of experimental results with a PNIPAAm valve can be seen in Figure 4. Since the fluorescence intensity increase in vesicle 3 (Figure 3B,D) depends on both the diffusive transport rate and the dissipation of the dye, e.g., photobleaching and leakage, it is not immediately obvious how changes in dI/dt should be interpreted. A first rough approach can nevertheless be used to evaluate the valve’s function: dI/dt changes in a high-low-high-low pattern (Figure 4) that cannot be explained with diffusion and dissipation alone. This indicates in a qualitative manner that the diffusion between vesicles 1 and 3 (Figure 3) is influenced by the PNIPAAm valve. Modeling the Diffusion. A more thorough analysis is performed using the approach by Lizana et al.26 A theory for diffusive transport in containers interconnected by thin tubes was developed earlier,26 and is used to model diffusion in complex NVNs.14 Briefly, the equation describing diffusion of a compound in a NVN is given by

dc(j)(t) dt Figure 2. Schematic creation of a four-vesicle NVN with a PNIPAAm valve. (A) A pipet filled with PBD solution (gray) is inserted into the mother vesicle with a multi-lamellar protrusion (black). (B) By injecting while retracting the pipet, a daughter vesicle filled with PBD solution is created. The vesicle is immobilized on the surface. (C) A buffer-filled pipet is used to create an ordinary buffer-filled vesicle. (D) The nanotube connection is translated over the network (arrows) (E) The vesicle is immobilized on the surface in the chain after the PBD vesicle. (F) A second buffer-filled vesicle is created, (G) translated across the network, and (H) immobilized in the chain before the PBD vesicle. (I) The vesicle before the PBD vesicle is injected with Alexa Fluor 488. The pipet is subsequently removed. The numbering inside the vesicles is used to identify the vesicles in the micrographs (Figure 3). 1: injection vesicle (source); 2: PNIPAAm vesicle (valve); 3: drain.

hydrogel compartments in GUVs is available in an earlier report.22 Heating was performed with resistive heating structures, printed as thin film coils on the surface of the coverslips, which allows fast and accurate temperature control.22 The temperature was monitored with a micrometer thermocouple in direct vicinity of the network. A PI regulator controlled the output of the power supply connected to the heating coils, keeping the temperature constant at the selected temperature. The temperatures used were 294 K (21 °C) for the “low rate” and 306 K (33 °C) for the “high rate” state. Control of Diffusional Transport Rate. To investigate valve function, we monitored diffusion of a fluorescent dye (Alexa Fluor 488) in the NVNs by scanning confocal microscopy (Figure 3). After construction of the NVN with PBD in vesicle 2 and injection of dye into vesicle 1 (Figures 2 and 3), the change in fluorescence intensity in the vesicles due to diffusion of the dye was followed by acquiring images of the network every 30-60 s. During the acquisition, the state of the valve was changed in different time intervals. The interval lengths were chosen during the experiment as a compromise between maximizing the use of the microscope’s dynamic range, and a clear visualization of the change in dI/dt between the states (where I is the average fluorescence intensity). In reference experiments without PBD in vesicle 2, similar switching-intervals were applied. The average fluorescence intensity in vesicle 3 (Figure 3) was then plotted vs time. In Figure 3, confocal bright-field and fluorescence micrographs are presented for the “low rate” (A,B) and the “high rate” (C,D) valve states. Panel D shows a schematic representation of the system with the factors influencing the transport rate.

N

)

ΛijkD ∑ i)1

(ij)

(j) [c(i)(t) - c(j)(t)] - k(j) ∆c

(1)

where N is the number of containers making up the network, Λij ) Λji is a binary matrix describing how the containers are linked together (Λij ) 1(0) if containers i and j are (not) connected), and c(i)(t) is the concentration in container i at time t. The quantity

k(ij) D

πa2Dij ) Vjlij

(2)

is the diffusive transport rate where Dij is the diffusion coefficient in the tube connecting containers i and j, a is the tube radius (considered equal for all tubes throughout the entire network), lij ) lji is the length of the tube connecting containers i and j, and Vj is the volume of container j. The rate of dissipation (leakage and bleaching) is given by k (j) ∆ and is a free parameter in the model. Equation 1 was integrated numerically using the Euler backward method. For more details, see the work of Lizana et al.26 The geometry entered into the model was obtained from the microscope images, and the dissipation factor was used to fit the curve to experimental data. Factors Affecting Diffusion in NVNs. Viscosity. The diffusive transport rate k(ij) D is linearly dependent on the diffusion coefficient (eq 1), and, according to the Stokes-Einstein relation, the diffusion coefficient is inversely proportional to the viscosity:

D)

kBT 6πηR

(3)

with D being the diffusion constant, kB the Boltzmann’s constant, T the absolute temperature, η the solvent viscosity, and R the radius of the diffusing molecule. In this experiment, there are two factors that affect the viscosity: temperature and polymer concentration. The dynamic viscosity of PBD solutions was determined at different concentrations and temperatures with an Ubbeholde-type viscometer combined with density measurements (Table 1). Since the polymer collapses in the NVN into a single hydrogel compartment, the dye diffuses at high temperature in pure buffer (except in the hydrogel compartment, see below). Therefore, the viscosities at elevated temperature were determined in buffer only. The experimentally determined viscosities are in good agreement with PNIPAAm literature data.27 (26) Lizana, L.; Konkoli, Z. Phys. ReV. E 2005, 72. (27) Tam, K. C.; Wu, X. Y.; Pelton, R. H. J. Polym. Sci., Part A: Polym. Chem. 1993, 31, 963.

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Figure 3. A three-vesicle lipid bilayer NVN with a hydrogel valve in “high rate” and “low rate” state. Dashed lines indicate nanotube connections. The green color results from Alexa Fluor 488 emission upon excitation at 488 nm. (A) DIC image of the NVN at 294 K (21 °C). The difference in background intensity is due to lower optical transmission of the heating structures. (B) Fluorescence image of the NVN at 21 °C. (C) DIC image of the NVN at 306 K (33 °C). A hydrogel compartment has formed in vesicle 2. (D) Fluorescence image of the NVN at 33 °C. The average fluorescence intensity has increased in vesicle 3 compared to that in panel B because of diffusion of the dye. (E) Schematic representation of the system. The development of transport rate, buffer viscosity, polymer concentration, and excluded volume for each valve state is shown. Images A and B have been taken at an earlier time than C and D, therefore the total fluorescence in vesicle 3 has increased regardless of the polymer state. Table 1. Viscosity of Buffer Solution with Different PBD Concentrations and at Different Temperatures cPNIPAAm [mg/mL]

cBlueDextran [mg/mL]

temperature [°C]

viscosity [10-3 kg/(m‚s)]

relative changea

0 5 10 15 20 0 0 0

0 0.125 0.25 0.375 0.5 0 0 0

21 21 21 21 21 25 29 33

1.0 1.7 2.7 4.1 5.9 0.92 0.84 0.77

1.00 1.70 2.69 4.04 5.84 0.91 0.83 0.77

a

Figure 4. Average fluorescence intensity in vesicle 3 (see Figure 3) vs time. The valve was opened (high rate) by temperature change after 30 s, closed (low rate) at 270 s, opened (high rate) at 510 s, and closed (low rate) at 720 s. Diamonds denote experimental data, the line connects the first and last data point of each “high rate” or “low rate” period. The inset shows the slope of the lines connecting the first and last data point of each period.

The viscosity decreases with increasing temperature and decreasing PBD concentration (Table 1). The decrease in buffer viscosity from 21 °C to 33 °C (Table 1), combined with the temperature increase, results in a diffusion coefficient increase by a factor of ∼1.35 (eq 3). The local viscosity experienced by molecules diffusing in polymer solution is, however, not necessarily the same as the macroscopic viscosity. For example, the diffusion coefficient of a small ion diffusing in aqueous polyethylene glycol (PEG) solutions is independent of the macroscopic viscosity and approximately the same as that for the pure solvent, if the PEG molecular weight is g100 kDa. Small PEGs and ethylene glycol gives an inverse relation between diffusion coefficient and viscosity, as shown in eq 3.28 (28) Shimizu, T.; Kenndler, E. Electrophoresis 1999, 20, 3364.

°C.

The viscosity divided by the viscosity of the buffer solution at 21

Since 300 kDa PNIPAAm molecules have length and persistence length similar to those of 100 kDa PEG,28,29 the diffusion of Alexa in PBD and PEG solution can be expected to be very similar. Therefore, FCS was used to determine the relative change in diffusion coefficient between buffer and a 20 mg/mL PNIPAAm/0.5 mg/mL blue dextran (PBD) solution. The diffusion coefficient in PBD solution at 21 °C was determined as ∼0.77 times the diffusion coefficient in buffer at 21 °C. FCS data also excludes that the fluorescent dye has affinity for PNIPAAm in the dissolved state, since there is clearly only one correlation time. Fluorescence correlation data are available as Supporting Information. The original theoretical model26 had to be modified slightly to include different diffusion coefficients in different parts of the NVNs: Using the theory outlined by Dagdug et al.,30 it can be shown that the transport rate k(ij) D (eq 2) in such a situation is given by (29) Ito, K.; Chuang, J.; Alvarez-Lorenzo, C.; Watanabe, T.; Ando, N.; Grosberg, A. Y. Prog. Polym. Sci. 2003, 28, 1489. (30) Dagdug, L.; Berezhkovskii, A. M.; Shvartsman, S. Y.; Weiss, G. H. J. Chem. Phys. 2003, 119, 12473.

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1 D πa ij Dij + +1 4lij Di Dj

(

)

(4)

where kij(0)) πaDij/Vjlij, and Di and Dj denote diffusion constants in vesicles i and j, respectively. Dij/Di < 1.35 at any time in these experiments, and, since a/lij is small (∼10-2), the expansion 1/(1 (0) + x) ≈ 1 - x can be applied to eq 4 leading to k(ij) D ) kij [1 Ο(a/lij)] ≈ kij(0). Thus, we conclude that the rate constant given by eq 2 is valid also when the difference in diffusion constants in different parts of the NVNs is taken into account, i.e., the relative difference in diffusion constant between vesicle and tube must be much larger to have significant effect on the diffusion rate in the NVN. Vesicle Volume Change. Another factor that could affect the diffusion in an NVN is the volume available to the dye in vesicles containing PBD solution, which could be different in the “low rate” and “high rate” states. As the hydrogel shrinks, PNIPAAm density could become high enough to make the hydrogel compartment function as a hard sphere that excludes the diffusing molecule(s). Decreasing the effective vesicle volume increases the diffusion rate constant (eq 2). It could be questioned whether the density becomes sufficiently high for the hydrogel to exclude the diffusing molecule. Lokuge et al. have recently used surface-grafted PNIPAAm chains to control the flow through nanometer-sized pores in NCAMs.20 In their work, the area per grafted PNIPAAm chain was approximately 200 Å2, which can be used to estimate the concentration of PNIPAAm close to the surface. Assuming a bond angle of 109.5° between the carbon atoms in the backbone and a bond length of 150 pm, the PNIPAAm concentration would be about 400 mg/mL (for fully extended chains). Even at this density, the PNIPAAm chains could not fully close the pores to a 4 kDa molecule. However, the diffusion rate was shown to be modulated to some degree. This indicates that the PNIPAAm hydrogel in the vesicles would have to reach concentrations higher than 400 mg/mL to fully exclude molecules of Alexa’s size. Starting from 20 mg/mL, r/r0 (where r and r0 are the hydrogel and vesicle radii, respectively) must be smaller than 0.37 to increase the concentration to 400 mg/mL or more. The compartment volume expected from the microscope images is about 5-10% (r/r0 ∼ 0.4) of the vesicle volume, possibly enough to let an excluded volume effect contribute to the valve’s function by decreasing the effective volume of the valve vesicles by ∼5% in the “high rate” state. Summary of Contributing Factors. At least three factors contribute to the change in diffusion rate. (i) The temperature increase from 21 °C to 33 °C increases the diffusion coefficient by a factor of ∼1.35 in the entire NVN. (ii) At 21 °C, the PBD solution decreases the diffusion coefficient to ∼0.77 times the diffusion coefficient in buffer. This will only affect the diffusion through the NVN if the diffusion coefficient changes in the tubes (see above). (iii) At 33 °C, the volume available to the diffusing dye in the valve vesicles may be decreased by ∼5%. All three effects can be included in the model and fitted to experimental data. Theoretical Fits to Experimental Data. In Figure 5A, data from a measurement with a PNIPAAm valve is plotted together with a theoretical fit. It can clearly be seen that the valve state affects the diffusion of dye in the network. The model was fitted to experimental data using a combination of all three factors, i.e., at 21 °C the diffusion coefficient was multiplied by 0.77 (polymer effect) and at 33 °C it was multiplied by 1.35 (temperature effect). The volume of the valve vesicle was decreased by 5% (volume

Figure 5. Average fluorescence intensity in vesicle 3 in an NVN. Vertical dashed lines denote state changes of the valve, starting in the “high rate” state. (A) With a PNIPAAm valve. The diffusion coefficient in the model (eq 1) was multiplied by 0.77 (polymer effect) in the “low rate” state and by 1.35 (temperature effect) in the “high rate” state. A volume decrease of 5% in the “high rate” state is also included. The dashed line shows the predicted fluorescence intensity development for a buffer-to-PDB diffusion coefficient ratio of 6 (polymer concentration of 40% (w/w)). (B) Without a PNIPAAm valve (reference experiment without PNIPAAm in the internal volume of vesicle 3). The diffusion coefficient in the model (eq 1) is multiplied by 1.35 (temperature effect) for the “high rate” state.

effect) at 33 °C. Removing the polymer effect contribution from the model clearly reduces fit quality (Supporting Information). This is a strong indication that diffusion coefficients in the nanotubes connected to the valve vesicle are also affected by the polymer’s presence. For comparison, reference experiments with temperature changes without PBD solution were performed. The theoretical model was fitted to the experimental data (Figure 5B). To account for the temperature changes, the diffusion coefficient in the model is multiplied by 1.35 at 33 °C. The slow increase in the beginning is due to the initially small concentration difference between vesicles 2 and 3. At t ∼ 90 min, dissipation becomes the dominating factor, and the intensity starts to decrease. The effect of the viscosity change between 21 °C and 33 °C is fairly small, but can be well distinguished both in the experimental data and the theoretical fit. The model allows us to separate the different contributions to the change in diffusion rate, by keeping the other factors constant.

Diffusion Control in Soft Matter Nanofluidic DeVices

No factor alone can explain most of the change in diffusion rate; however, the temperature and polymer effects combined give a rather good agreement between the model and experimental data. The effect of a 5% volume change is small, but including it yields a slightly better fit to experimental data. Since the different contributions to the transport rate constant are multiplicative, the increase in the rate constant when the volume effect is included will be ∼1.42 instead of ∼1.35 (for the rates containing the volume of the valve vesicle), which is a considerable difference. A selection of fitting results for single and combined contributions of solvent viscosity, polymer concentration, and excluded volume is available as Supporting Information. Since the theoretical model agrees well with experimental data, it can be used to predict how the valve will affect the diffusion rates in the NVN for hypothetical cases. Figure 5A (lower graph, dashed line) contains a prediction of how the average fluorescence intensity would develop over time for a diffusion coefficient in buffer (D) to PBD solution (Dp) ratio D/Dp of 6, while all other parameters remain the same. Larger D/Dp ratios are expected if the concentration of PNIPAAm is considerably increased. At the moment, the PNIPAAm concentration is limited to e20 mg/mL, since higher concentration results in solutions with viscosities too high to inject. Work to increase the polymer concentration in the vesicles by means other than injection is underway.

Summary and Conclusions We have constructed a PNIPAAm polymer/hydrogel valve with two distinguishable states enclosed in a nanofluidic nanotube-vesicle network. The valve gives a degree of control over the passive diffusion rate of compounds between different nodes in an NVN. Valve function is based on changing between PNIPAAm’s dissolved and compact aggregated states, which is achieved by increasing and decreasing local temperature. Accurate and fast temperature adjustment is obtained with surface-printed resistive heating elements and a micrometer-sized thermocouple. A theoretical model for diffusion in NVNs is employed, sometimes with modifications, to investigate different contributing factors to the valve’s function. We established that the product of three factors explains the change in diffusion rate in the NVN when changing temperature. The change in buffer viscosity between 21 °C and 33 °C results in an increase in diffusion coefficient by a factor of ∼1.35 in the entire NVN. The polymer solution decreases the diffusion coefficient in the tubes connected to the valve vesicle to ∼0.77 of that in buffer at 21 °C. There are also indications that the hydrogel compartment decreases the effective volume of the valve vesicle by ∼5% in the “high rate” state.

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All three factors combined yield the most accurate fit of our model to the experimental data. However, the effect of a 5% volume change is comparatively small with respect to the other contributing factors. The good agreement between model and the experimental data allows us to predict the effect of other sets of parameters, such as the polymer concentration. In addition, the model is suitable to take the influence of more complex network geometries on the diffusion rate in valve-controlled NVNs into consideration. The ability to control the diffusion of compounds between different vesicles in NVNs is crucial in order to obtain devices where more complex reaction schemes can be accomplished. Without compromising membrane integrity, this is inherently difficult, mainly because of the length scale, membrane compatibility issues, and the NVN fabrication protocol. Our PNIPAAm polymer valve represents a straightforward way to achieve control over the diffusion of compounds within the NVNs without the need of changing established NVN production and manipulation techniques. The position of PNIPAAm valves in the NVNs can be arbitrarily chosen, and as such, temperature is a physical parameter that is comparatively easy to implement and control. The surface-printed resistive heating coils can, for example, be made small enough to allow individual heating of vesicles in the network, thereby giving independent control of the valves in a multivalve NVN. Other heating mechanisms, e.g., using IR laser or RF radiation, can be considered. The device presented here is a starting point for the future development of biomembrane-compatible flow control protocols in nanofluidic devices. The possibility to open (high rate) and close (low rate) valves independently provides a great advantage compared to an all-open/all-closed system, and a diffusion-driven nanofluidic soft-matter device with polymer-gated channels is clearly within reach. Acknowledgment. The work was supported by the Royal Swedish Academy of Sciences and the Swedish Foundation for Strategic Research (SSF) through a donation from the Wallenberg Foundation and the Nano-X project. Supporting Information Available: Fluorescence correlation data; a selection of fitting results for single and combined contributions of solvent viscosity, polymer concentration, and excluded volume. This material is available free of charge via the Internet at http://pubs.acs.org. LA7035967