Langmuir 2002, 18, 8241-8245
Anomalous Sorption in Thin Films of Fluoroalkyl-Ended Poly(ethylene glycol)s Giyoong Tae,† Julia A. Kornfield,*,† Jeffrey A. Hubbell,‡ and Diethelm Johannsmann§ Division of Chemistry and Chemical Engineering, 210-41 California Institute of Technology, Pasadena, California 91125, Institute for Biomedical Engineering and Department of Materials, ETH-Zurich and University of Zurich, CH-8044 Zurich, Switzerland, and Max Planck Institute fur Polymerforschung, Postfach 3148, D-55021 Mainz, Germany Received March 13, 2002. In Final Form: June 12, 2002
Introduction Absorption, desorption and swelling behavior of polymers play important roles in polymer processing and performance, ranging from issues of dimensional stability and permeability to controlling adhesion. Rich, nonlinear phenomena are associated with transient swelling and drying of glassy and semicrystalline polymers. Anomalous, non-Fickian behaviors are broadly associated with the nonlinear effects of the penetrant on the dynamics of the polymers. Here we describe anomalous behavior of a different type that is associated with a sorbent-triggered first-order phase transition. The system of interest is a hydrophilic, semicrystalline polymer with hydrophobic end groups, placed in contact with humid air. Due to the strong tendency to absorb water, the melting transition of the crystallites can be induced by contact with sufficiently humid air; during desorption, a sufficient supersaturation must be reached before nucleation and regrowth of crystals occur. This leads to very different hysteresis in the sorption isotherm and overshoot in transient sorption than has been reported previously in polymers. Poly(ethylene glycol)s (PEGs) modified with hydrophobes at both ends have been investigated widely as model associative polymers.1,2 Of particular interest to us are fluorocarbon-terminated (Rf) PEGs,3,4 due to their potential application in biomedical technologies.5 In contrast to the previously examined, glassy polymers in which anomalous penetrant transport has been investigated, PEG has a very low glass transition temperature (Tg ≈ 207 K),6 and thus Rf-PEGs do as well.7 Therefore, complexities associated with the glass transition are not expected to play a role. On the other hand, the sorption behavior of Rf-PEGs may be influenced by relaxation processes associated with the crystallization/melting of * To whom correspondence may be addressed. Tel: 626 395 4138. Fax: 626 568 8743. E-mail:
[email protected]. † California Institute of Technology. ‡ ETH-Zurich and University of Zurich. § Max Planck Institute fur Polymerforschung. (1) Annable, T.; Buscall, R.; Ettelaie, R. J. Rheo. 1993, 37 (4), 695. (2) Xu, B.; Li, L.; Yekta, A.; Masoumi, A.; Kanagalingam, S.; Winnik, M. A.; Zhang, K.; Macdonald, P. M.; Menchen, S. Langmuir 1997, 13, 3 (9), 2447. (3) Tae, G.; Kornfield, J. A.; Hubbell, J. A.; HogenEsch, T. E.; Johannsmann, D. Macromolecules, 2001, 34, 6409. (4) Tae, G.; Kornfield, J. A.; Hubbell, J. A.; Lal, J. A. Macromolecules 2002, 35, 4448. (5) Tae, G.; Kornfield, J. A.; Hubbell, J. A. In preparation. (6) Young, R. J.; Lovell, P. A. Introduction to polymers, 2nd ed.; Chapman & Hall: London, 1991. (7) Tg of Rf-PEGs have not been measured directly, but melting temperatures of Rf-PEGs are lower than those of unmodified PEGs, so low glass transition temperatures are expected for Rf-PEGs.
8241
the PEG midblock and the formation/disruption of the physical network during swelling/deswelling. Hysteresis during sorption/desorption has been observed for both glassy polymers and semicrystalline polymers. In glassy polymers, the lower swelling ratio during absorption than during desorption at the same fugacity (or partial pressure) of the penetrant8 results from the asymmetry of removal of the penetrant from the rubbery state vs addition of the penetrant to the glassy state.9 In the case of semicrystalline polymers, the crystalline lamellae present an additional barrier for penetrant transport.10 Sorption isotherms have been reported for low levels of penetrant absorbed (less than a few percent by mass), such that the materials maintained their crystallinity during the experiments.10-12 The effect of melting/crystallization on sorption in polymers has not been investigated. Regarding the kinetics of sorption and desorption, semicrystalline polymers and glassy polymers show similar asymmetry in their responses to step-up vs stepdown transients (following a step-up, the monotonic transient is initially slow and becomes more rapid; following a step-down, the transient is initially rapid and slows), attributed to different diffusivity and permeation during absorption and desorption.13-15 Overshoot sorption has also been reported for some glassy polymers,16-20 interpreted to be related to the different time scales of penetrant transport and polymer relaxation,16-18 as well as the soluble fractions in the polymers19 or penetrantinduced crystallization.20 None of these effects can be invoked to explain the overshoot behavior in our system; instead the distinctive transient overshoot is attributed to the transformation from a semicrystalline state to a physical gel. Here, we report the sorption isotherms and transient sorption behavior of thin films (∼0.1 µm) of Rf-PEG observed using a quartz crystal resonator (QCR) in humidity ramp and humidity step tests. The humidity range investigated is sufficiently wide to probe the melting and crystallization of the PEG midblock. Experimental Section Materials (Rf-PEGs). Poly(ethylene glycol) (PEG) (with alcohol functionality at both ends) of nominal molecular weight 6000 g/mol (6 kD) and 10 kD were modified at both ends with fluorocarbon groups (-CqF2q+1CH2CH2, q ) 8 or 10) using a diisocyanate linkage. A polymer with a PEG midblock molar mass (8) Vrentas, J. S.; Vrentas, C. M. Macromolecules 1996, 29, 4391. (9) Bouchard, C.; Guerrier, B.; Allain, C.; Laschitsch, A.; Saby, A.-C.; Johannsmann, D. J. Appl. Polym. Sci. 1998, 69, 2235. (10) Sato, Y.; Yurugi, M.; Yamabiki, T.; Takishima, S.; Masuoka, H. J. Appl. Polym. Sci. 2001, 79, 1134. (11) Pope, D. S.; Koros, W. J. J. Polym. Sci.: Polym. Phys. 1996, 34, 1861. (12) Hsu, W.-P.; Myerson, A. S.; Kwei, T. K. J. Appl. Polym. Sci. 1998, 70, 39. (13) Ngui, M. O.; Mallaparagada, S. K. Polymer 1999, 40, 5393. (14) Crank, J.; Park, G. S. Diffusion in Polymers; Academic Press: New York, 1968. (15) Hedenqvist, M.; Johnsson, G.; Trankner, T.; Gedde, U. W. Polym. Eng. Sci. 1996, 36, 271. (16) Vrentas, J. S.; Duda, J. L.; Hou, A.-C. J. Appl. Polym. Sci. 1984, 29, 399. (17) Smith, M. J.; Peppas, N. A. Polymer 1985, 26, 569. (18) Kim, D.; Caruthers, J. M.; Peppas, N. A.. Macromolecules 1993, 26, 1841. (19) Scranton, A. B.; Klier, J.; Peppas, N. A. Polymer 1990, 31, 1288. (20) Titow, W. V.; Braden, M.; Currell, B. R.; Loneragan, R. J. J. Appl. Polym. Sci. 1974, 18, 867.
10.1021/la020255l CCC: $22.00 © 2002 American Chemical Society Published on Web 09/17/2002
8242
Langmuir, Vol. 18, No. 21, 2002
Notes
Table 1. Rr-PEGs
a
sample
PEG-block (kg/mol)
Rf end groupa
10KC8 10KC10 6KC8
10
-C8F17 -C10F21 -C8F17
6
Full end group is -IPDU-(CH2)2-CnF2n+1, where IPDU is
of n kg/mol and with q-carbon fluoroalkyl end groups is denoted nKCq (Table 1). Synthesis and characterization were described previously.3 Mass Determination by QCR under Controlled Humidity. The complex resonance frequency of a QCR, f* ) f + iΓ (with bandwidth 2Γ), shifts with the mass and dynamic compliance of a viscoelastic load. For a film with mass per unit area m and shear compliance J*, δf*/f ≈ -(2iff/Zq)m[1 + J*(f)(4π2m2/3F)f 2], where Zq is the acoustic impedance and ff the fundamental frequency. From the intercept of δf/f vs f2, m can be obtained.21 A QCR placed in a humidity-controlled chamber was used to measure the change of mass with humidity.9 AT-cut, plane parallel quartz, optically polished, with 4 MHz fundamental frequency was used. The data acquisition has been described elsewhere,22 and relative humidity (Hr), measured near the sample, was regulated using feedback control of two air flows, one saturated by passing through a water reservoir and the other dried by passing through desiccant. Temperature was controlled at 24 °C. The polymer film was spin-coated onto the quartz from ∼1 wt % polymer solution in ethanol. To confirm the integrity of the deposited layer, the resonance spectrum was recorded at Hr ≈ 90% for a series of normal modes of the quartz crystal (typically eight modes, ranging from ∼28 to ∼84 MHz). Uniform films with good adhesion to the substrate give consistent results over this range (δf/f decreases linearly with f2).21 Since the sorption isotherms were obtained after annealing the film at high humidity, no effect of the history of spin casting is seen.
Results and Discussion Sorption Isotherm. With increasing Hr, the thin film absorbs water and swells, but with an unusual dependence on fugacity of the penetrant. At low Hr, the usual gradual increase of mass with increasing Hr is observed (inset of Figure 1). Then, a distinctive swelling starts at Hr ≈ 85%, followed by further increase of mass at higher humidity. With decreasing Hr, even with a slow rate of humidity decrease (2%/h), the swelling behavior shows hysteresis: while the thin film starts to show a rapid swelling from Hr ≈ 85% under increasing humidity, a rapid deswelling occurs from Hr ≈ 75% as the humidity is decreased (Figure 1). The plausible cause of this peculiar sorption curve is the crystallinity of the PEG midblock at low humidity conditions. Since the experimental temperature is well above Tg of PEG, the hysteresis cannot be attributed to a solvent-induced transition between the glassy and rubbery states. Instead, this hysteresis could result from the transition between the semicrystalline and gel states. Under increasing humidity, a critical activity of water is required to induce melting of the crystalline domains in the semicrystalline PEG; once this humidity is reached, an abrupt increase in swelling is expected. This “deliquescence transition” is well-known in inorganic salts, which abruptly absorb water when Hr increases to the deliquescence relative humidity, DRH, producing a saturated solution.23 Upon drying, a substantial supersatu(21) Wolf, O.; Seydel, E.; Johannsmann, D. Faraday Discuss. 1997, 107, 91. (22) Johannsmann, D.; Mathauer, K.; Wagner, G.; Knoll, W. Phys. Rev. B 1996, 46, 7808.
Figure 1. Change of swelling state of 6KC8 thin film (∼1.0 × 102 nm when dry) caused by for the change in humidity of 2%/h (inset: magnification of the low humidity region).
ration is required before nucleation and growth of crystals of PEG occurs, also similar to aqueous aerosols containing salts.23,24 Once crystallization begins, a substantial expulsion of water occurs, associated with a threshold humidity that is lower than the critical value upon swelling. The sorption behavior in the solid state can be described using Henry’s law for vapor-solid equilibrium.25 We did not find literature on vapor-solid equilibrium for the PEG-water system. Our results indicate a Henry’s law coefficient (defined as PH2O/wH2O, where PH2O is the vapor pressure of water and wH2O is the weight fraction of water in the solid phase) of ∼18 kPa at 24 °C for the present Rf-PEGs. Given our physical interpretation of the behavior, we envision that water absorbs into the noncrystalline regions of the semicrystalline polymer. The vapor-liquid equilibrium can be compared with existing literature on the PEG-water system: the shape of the isotherm at Hr > DRH is in good agreement with the reported isotherm of PEG (aq)-water (vapor),26,27 with the quantitative values of water sorbed being shifted to lower values due to the presence of Rf groups, as would be expected (e.g., at 24 °C and Hr ) 93%, an aqueous solution of PEG would swell to wH2O ) 0.5, while 10KC10 swells to wH2O ) 0.4). At the deliquescence relative humidity, the system absorbs water to the point that it forms a saturated solution, so the swelling ratio just above the DRH can be compared to the solubility limit of PEG at 24 °C. The phase diagram of PEG 4K and water shows that the boundary of the crystalline phase is at wH2O ≈ 0.3,28 in accord with the swelling ratio just above the DRH. To probe rate effects, successive cycling (sorptiondesorption) was done with increasing ramp rate. During absorption, with each successive run, the overall sorption curve shifts slightly to lower humidity, so the critical humidity where the thin film starts to show a rapid swelling also shifts to a somewhat lower value, and the swelling ratio (SR) at a given humidity increases (Figure 2b). During desorption, with increasing ramp rate in successive runs, the overall desorption curve changes from (23) Seinfeld, J. H.; Pandis, S. N. Atmospheric Chemistry and Physics; Wiley Interscience: New York, 1998; Chapter 9. (24) Clegg, S. L.; Brimblecombe, P.; Liang, Z.; Chan C. K. Aerosol Sci. Technol. 1997, 27, 345. (25) Pope, D. S.; Koros, W. J. J. Polym. Sci., Part B: Polym. Phys. 1996, 34, 1861. (26) Bae, Y. C.; Shim, J. J.; Soane, D. S.; Prausnitz, J. M. J. Appl. Polym. Sci. 1993, 47, 1193. (27) Ninni, L.; Camargo, M. S.; Meirelles, A. J. A. Thermochim. Acta 1999, 328, 169. (28) Hager, S. L.; Macrury, T. B. J. Appl. Polym. Sci. 1980, 25, 1559.
Notes
Figure 2. Change of swelling state of 6KC8 thin film (∼1.0 × 102 nm when dry) for humidity ramps at various rates: (a) with decreasing humidity; (b) with increasing humidity.
the sudden deswelling at Hr ≈ 75% to more gradual deswelling behavior (Figure 2a). With repetition at the same ramp rate, at low rates (e2%/h) the successive runs retrace the first one, whereas some history dependency is observed for higher rates. The effects of increasing ramp rate also accord with an explanation based on crystallization. The hypothesis that the deswelling is governed by nucleation and growth is consistent with the shift of the threshold humidity for deswelling (corresponding to a sufficiently high supersaturation that significant nucleation occurs on the time scale of the experiment). Similarly, the decrease in the abruptness of deswelling with increasing ramp rate can be attributed to a reduced degree of crystallinity by the time a given Hr is reached due to the kinetic limitations of nucleation and growth. The sorption behavior during successive cycles also suggests that the degree of crystallinity in the material at the beginning of each successive run is lower due to the memory of the ramp rate used in the preceding desorption cycle. Similar swelling is observed for film thickness from ∼1.0 × 102 to 1.5 × 102 nm. Holding PEG midblock length fixed (10KC10 vs 10KC8), no effect of end group length is found in the absorption isotherm (Figure 3a), suggesting that the behavior is controlled by PEG, consistent with the role of crystallization. The effect of molecular weight of the PEG midblock is also weak (Figure 3b), consistent with the similar crystallization and melting behavior of these polymers.29 We attempted to determine if PEG homopolymer shows similar hysteresis, but we were unable to prepare uniform films with adequate adhesion; we infer that the higher degree of crystallinity of pure PEG relative to Rf-PEG30 results in greater shrinkage
Langmuir, Vol. 18, No. 21, 2002 8243
Figure 3. Changes of swelling states with decreasing humidity at 2%/h: (a) comparison of 10KC10 thin film (∼1.5 × 102 nm) and 10KC8 thin film (∼1.8 × 102 nm); (b) comparison of 10KC10 thin film (∼1.0 × 102 nm) and 6KC8 thin film (∼1.0 × 102 nm).
during solidification as the solvent evaporates, which causes the thin film to partially detach. It is interesting that prior studies of sorption behavior in covalently cross-linked PEG did not show hysteresis or abrupt transitions in swelling and deswelling:31 the sorption isotherm shows significant absorption even in the low-humidity regime (SR increases from ≈1.05 at Hr ≈ 10% to SR ≈ 1.20 at Hr ≈ 65%) and a steeper increase in sorption in the high humidity regime (increasing from SR ≈ 1.20 at Hr ≈ 65% to SR ≈ 1.35 at Hr ≈ 75%) at 20 (29) Unpublished calorimetry measurements show weak effects of molecular weight on crystallization and melting of PEG over the range from 6k to 10k g/mol. The melting transition peaks at 66 °C for 10k PEG and at 63 °C for 6k PEG using 10 °C/min heating rate after preheating to 120 °C and subsequent cooling to -150 °C at -20 °C/min. Attaching fluoroalkyl groups to both ends reduces this somewhat: 59 °C for 10KC10, 57 °C for 10KC8, and 55 °C for 6KC8. The melting points remain similar to one another, suggesting that the lamellar thickness of the crystallites is nearly the same and that the presence of fluoroalkyl groups excluded into the noncrystalline regions is responsible for the depression in the melting point (increasing the interfacial free energy cost of each face of a lamellar crystal). The enthalpy of melting is also a weak function of Mw in this range: ∆Hm is 172 J/g for 10k PEG and 175 J/g for 6k PEG. Adding Rf end groups decreases the degree of crystallinity by 30-35%: ∆Hm is 126 J/g for 10KC10, 119 J/g for 10KC8, and 115 J/g for 6KC8. Given that both Tm and ∆Hm are fairly constant across the series of Rf-PEG materials, their solid-state sorption behavior and the activity of water required to trigger melting upon increase of Hr would be expected to be similar, as observed. In the swollen state, increasing PEG length would be expected to correlate with somewhat greater swelling, as observed, mainly due to the lower concentration of fluoroalkyl groups (the higher molecular weight between physical crosslinks is not likely to be a significant factor at the high polymer concentrations observed, >50 wt % PEG even at the highest Hr). (30) ∆Hm of Rf-PEG is ∼70% of homo-PEG (see above). (31) Ranucci, E.; Opelli, P.; Ferruti, P. Polym. Gel. Net. 1994, 2, 119.
8244
Langmuir, Vol. 18, No. 21, 2002
Notes
Figure 4. Change of swelling state of 6KC8 thin film (∼1.0 × 102 nm) for a step change of humidity from 20% to 90%.
°C. Chemical cross-linking tends to suppress crystallization of semicrystalline polymers.32 Reduced crystallinity in cross-linked PEG would permit greater swelling in the low-humidity regime. Furthermore, cross-linking tends to lock in locally heterogeneous environments, causing the distribution of crystallite sizes to be very broad. A broad distribution of crystallite sizes would spread the enhanced sorption associated with their melting over a broad range of humidity. The stronger increase in sorption at high humidity might reflect the melting of crystallites present in the cross-linked PEG resin. The absence of significant hysteresis in cross-linked PEG materials is in accord with the inference that much of the swelling is associated with amorphous material in the network. Therefore, the abrupt swelling and deswelling and pronounced hysteresis of the sorption isotherm observed in our system appear to be distinctive characteristics of a semicrystalline polymer with sufficiently high and uniform degree of crystallinity. Transient Sorption. Two intriguing features of the transient swelling behavior are observed: first, there is a significant overshoot in mass uptake following a step up in Hr that crosses the DRH; second, the subsequent relaxation to equilibrium takes a remarkably long time (Figure 4). In contrast, following a step down from high to low humidity, the film tracks the equilibrium state very rapidly (in ∼30 s) and monotonically. With increase in the high humidity value, the magnitude of the overshoot, the time to reach the maximum overshoot, and the time to reach the equilibrium state all increase (Figure 5a). With increasing film thickness from ∼1.0 × 102 to ∼1.5 × 102 nm, the degree of overshoot decreases (Figure 5b). Qualitatively similar overshoot sorption behavior was found when dried thin films of the Rf-PEGs used in this study were immersed in water.3 The overshoot cannot be attributed to transient heating on hydration because the heat of melting actually overcompensates the heat of hydration;33 furthermore, due to the small film thickness, the maximum temperature change is negligible (∼10-7 K).34 Instead, the overshoot behavior indicates that the physical structure in the hydrated state immediately after swelling is compatible with a substantially higher swelling than the equilibrium value. The approach to equilibrium takes a few hours. Having swollen from a dry state to a gel with a SR of ∼2, the crystals can be considered fully melted and the PEG chains well solvated. The Rf groups are likely to have formed clusters, but these micelle cores may not have reached (32) Vaughan, A. S.; Stevens, G. C. Polymer 2001, 42, 8891. (33) Brandrup, J., Immergut, E. H., Ed. Polymer Handbook; Wiley: New York, 1989.
Figure 5. Change of swelling states for the step changes of humidity: (a) the effect of the upper value of humidity (from 20% to various Hr for 6KC8 thin films (∼1.0 × 102 nm)); (b) the effect of film thickness (10KC10 thin films, one of ∼1.0 × 102 nm thickness and the other of ∼1.5 × 102 nm thickness, for the step change of humidity from 20% to 90%).
their equilibrium size (Rf groups per hydrophobic core, Nag ∼ 50 for C10 and ∼30 for C8).4 Irregularities in the physical network may allow this transient state to swell substantially more than the equilibrium gel. The relaxation of the network structure to equilibrium requires sufficient time for the system to probe a substantial portion of the configuration space of all the end groups among all the micelle cores. As the configuration of the network becomes tighter and more uniform, water is forced out and the SR drops gradually to its equilibrium value. The effect of the upper value of humidity in the step-up experiments is consistent with this physical picture; the higher the upper value, the higher the driving force for water absorption by the PEG midblock before the full (34) The maximum temperature change associated with the jump in swelling is very small due to the submicrometer thickness of the film and due to the compensation of the heat of fusion and heat of hydration (the heat of solubilization of PEG into water at infinite dilution is -120 J/g [exo] for molten PEG, but 10 J/g [endo] for crystalline PEG). The maximum heat upon jumping from the swollen solid to the solvated gel will be between -29 J/g (based on 70% crystallinity and the values above) and 122 J/g (upper bound based on 70% crystallinity and a heat of melting of ∼175 J/g). Thus, an upper bound on the energy change per unit area of film is readily made based on the measured mass of PEG per unit area, leading to ∼12 J/m2. This phase transition occurs over a few minutes time; based on ∼5 min, the maximum heat flux is ∼0.04 J/(m2/s). Since the film has thermal conductivity greater than 0.3 W/(m/ K) (poly(methylene oxide) 0.292 W/(m/K), water 0.609 W/(m/K)) and the film thickness is ∼10-7 m, the temperature change to drive the required heat flux is no more than 1.2 × 10-7 K.
Notes
connectivity among end groups can assemble, so the peak value is higher and the overshoot extends to longer time. Thus, the overall swelling process is as follows: At low humidity, the aggregated state of the end groups is partially disturbed compared to the fully swollen state due to the crystallization of the PEG midblocks, similar to the disruption of the ordered state in block copolymers by crystallization.35-37 Upon the sudden increase of humidity, PEG midblocks melt from the semicrystalline state and absorb water, and small, nonequilibrium clusters of the flourocarbon groups form (the time scale associated with the melting of PEG crystallites is relatively short, since humidity ramp rates from 10%/h to 160%/h show very similar sorption curves, Figure 2b). Subsequently, the connectivity among end groups increases, leading to a more uniformly cross-linked gel state and to significant chain stretching of PEG near the hydrophobic cores as the number of Rf groups aggregated together increases to the large values seen at equilibrium (Nag ) 30). This proposed mechanism for the abnormal sorption suggests structural studies for the future. To clarify the origin of the hysteresis observed in the humidity ramp test, in situ observation of crystallinity of the thin film (35) Quiram, D. J.; Register, R. A.; Marchand, G. R. and Ryan, A. J. Macromolecules 1997, 30, 8338. (36) Fairclough, J. P. A.; Mai, S. M.; Matsen. M. W.; et al. J. Chem. Phys. 2001, 114, 5425. (37) Massey, J. A.; Temple, K.; Cao, L.; et al. J. Am. Chem. Soc. 2000, 122, 11577.
Langmuir, Vol. 18, No. 21, 2002 8245
under the controlled humidity ramp in both directions would be valuable. Similarly, to prove the mechanism of the overshoot sorption following a humidity step, in situ observation of the aggregated state of Rf-PEGs will be needed. However, preliminary experiments performed in transmission through a single film did not provide adequate signal to track transient structure as it evolved in situ. Conclusion The swelling behavior of thin films of Rf-PEGs show anomalies relative to prior studies of sorption in polymers: as humidity increases, little swelling occurs until Hr ≈ 85%, then the film swells rapidly; as the humidity decreases, a rapid deswelling occurs near Hr ≈ 75%. The transition between the semicrystalline and gel states is proposed as a plausible cause. Following a step-up in humidity, an overshoot of mass increase followed by the slow reduction to the equilibrium value is observed. The change of the aggregated state of Rf-PEG molecules (increase in connectivity among end groups) is proposed as a mechanism. Acknowledgment. This research was supported in part by a grant from NSF (CTS-9729443), a graduate fellowship from the Korean Ministry of Education (Giyoong Tae), and by the MRSEC Program of NSF (DMR-0080065). LA020255L
