Letter pubs.acs.org/NanoLett
Curie Transitions for Attograms of Ferroelectric Polymers A. Serghei,*,† W. Zhao,‡ D. Miranda,‡ and T. P. Russell‡ †
Ingénierie des Matériaux Polymères, Université Lyon 1, CNRS, UMR 5223, F-69622 Villeurbanne, France Department of Polymer Science and Engineering, University of Massachusetts Amherst, Amherst, Massachusetts 01003, United States
‡
ABSTRACT: Polymer systems having one, two, or three dimensions on the nanometer length scale can exhibit physical properties different from the bulk. The degree of disorder characteristic for large amounts of matter is strongly reduced and changes in symmetry are imposed by means of geometrical confinement. This could be used to inducethrough orientation and orderenhancement in the material properties. Experiments on extremely small amounts of matter, however, are naturally characterized by large fluctuations in the measured signals, especially in the case of polymer objects having three dimensions on the nanometer length scale. This imposes the necessity of repeating the measurements until a statistical distribution is obtained. Here we show that investigations on statistical ensembles of attograms of material (1 ag = 10−18 g) are possible in a single experiment by employing highly ordered arrays of identical, independent, additive nanocontainers. Phase transitions corresponding to attograms of a ferroelectric polymer are measured by this approach. As compared to one- or two-dimensional confinement, significant changes in the Curie transitions are found. KEYWORDS: Attograms of matter, nanocontainers, ferroelectric polymers, ferroelectric Curie transitions, electrical properties
O
of nanometers (Figure 1a)were kept in contact with the underlying aluminum substrates. These substrates were subsequently used as electrodes for permittivity measurements. The counter electrodes were fabricated by sputtering a thin layer of gold on top of the nanoporous membranes.18−20 A careful optimization of the sputtering process allows one to deposit thin electrodes of gold without closing the nanopores. Measurements by SEM and AFM have been carried out to ensure that the nanopores remained open after the deposition of the gold layers (Figure 1a). The nanocontainers with integrated electrodes have volumes on the order of zeptoliters (1 zeptoliter = 10−21 liter) and can be employed as experimental cells, to hold and measure extremely small amounts of matter. The sample cell is schematically illustrated in Figure 1b. The aluminum substrate and the gold layer were connected to a dielectric spectrometer and used as electrodes to carryout measurements of the permittivity of the sample cell. The present study is focused on investigations of a ferroelectric polymer, poly(vinylidene fluoride-co-trifluoroethylene) (PVDF−TrFE, 75% PVdF and 25% TrFE, Mn = 79 000 g/mol, PDI = 1.37). The amount of material investigated by this approach is controlled by the concentration of the polymer solution and the volume of the nanopores. Using dilute solutions leads to polymer amounts on the order of attograms per nanocontainer. Since the nanocontainers are identical, independent, and additive, the
rientation and ordering are important means to induce enhancement in the performance of polymeric materials. Because of the decrease in the entropy induced in geometrical confinement as well as to changes in symmetry imposed by the presence of confining interfaces, finite size systems could represent an effective approach to exploit this potential. Because of thermodynamic reasons, experiments on very small amounts of material are commonly characterized by large fluctuations in the measured signals. Consequently, measurements must be repeatedly carried out until a statistical distribution is obtained. Here we show that measurements on statistical ensembles of attograms of material are possible in a single experiment by employing highly ordered arrays of identical, independent, additive nanocontainers. This approach is used in the current study to investigate the phase transition behavior corresponding to attograms of a ferroelectric polymer,1−15 poly(vinylidene fluoride-co-trifluoroethylene) (PVDF−TrFE). Investigations on attograms of matter may open a door for fundamental questions in soft matter physics, such as for instance: what is the minimum amount of matter necessary to “define” the material properties? Highly ordered arrays of nanocontainers (Figure 1a) were fabricated by electrochemical anodization of pure aluminum in aqueous solutions of sulfuric acid and oxalic acid. The diameter and the depth of the nanocontainers can be precisely controlled by adjusting the anodization conditions: type of electrolyte, concentration, temperature, and applied voltage. A detailed description of the anodization procedure can be found elsewhere.16,17 After the fabrication process, the nanoporous membraneswith typical thicknesses in the order of hundreds © 2013 American Chemical Society
Received: November 6, 2012 Revised: January 14, 2013 Published: January 16, 2013 577
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between permittivity ε′ and density ρ described by the Clausius−Mossotti equation:21 Nα ε′ − 1 = A mol ρ ε′ + 2 3ε0M
(1)
where NA is Avogadro’s number, αmol the molecular polarizability, ε0 the vacuum permittivity, and M the molecular mass. Differentiating eq 1 with respect to temperature leads to ⎞ ∂ρ ∂ε′ ⎛ 3ε0M − ρ⎟ = (ε′ + 2) ⎜ ∂T ⎝ NAαmol ∂ T ⎠
(2)
which yields a proportionality relation between the first derivative of permittivity and the first derivative of density, i.e., ∂ε′/∂T ∼ ∂ρ/∂T. Since phase transitions are commonly accompanied by changes in density, this approach can be used to assess phase transitions of polymeric materials. Investigations at different frequencies prove that the dielectric measurements presented in Figure 2 do not show a frequency dependence. This indicates thatin the frequency and temperature window of our experimentsthe permittivity measurements are not affected by dielectric dispersions. This is an essential condition for the validity of eq 1. An excellent agreement between the calorimetric and the dielectric results is observed (Figure 2). Upon cooling from the melt, PVDF−TrFE undergoes a crystallization process at ∼405 K, followed by a bimodal Curie transition (with two peaks at ∼330 and 350 K). These two Curie transitions were attributed to two different paraelectric phases (spatially coexisting in the volume of the measured sample) undergoing a solid−solid transition to a ferroelectric phase upon cooling. The subsequent measurements upon heating show a Curie transition at 388 K followed by a bimodal melting process. The two melting peaks observed in the experiment confirm the spatial coexistence of two different paraelectric phases. A close resemblance but as well significant differences between the calorimetric and the permittivity measurements are observed. The first derivative of permittivity does not only accurately predict the temperature position of the phase transitions of PVDF−TrFE but can also describe subtle experimental features. For instance, the shallow shoulder on the low temperature side of the crystallization process, suggesting the formation of two different paraelectric phases during crystallization, is correctly recovered. The relative strengths and the shapes of the phase transitions are also accurately reflected in ∂ε′/∂T (Figure 2). An essential difference between the calorimetric and the permittivity data is observed in the signs (positive or negative) of the detected phase transitions. The calorimetric measurements show similar signatures for the crystallization/melting and for the ferroelectric transitions, i.e., “positive peaks”. This is due to the exothermic nature of these processes. On the contrary, the signs of these transitions are opposite in the permittivity data. The negative peak observed at 405 K (Figure 2d) indicates an increase in density upon crystallization, while the positive peaks at 330 and 350 K (Figure 2d) correspond to a decrease in density which accompanies the ferroelectric transitions. This aspect emphases the great potential of the permittivity measurements in discriminating phase transitions: processes giving rise to similar signatures in the heat capacity can be discriminated by analyzing the density changes reflected in ∂ε′/∂T.
Figure 1. Nanocontainers as experimental cells to hold and measure attograms of material. The nanocontainers are identical, independent, and additive. (a) SEM image of the nanocontainers in cross section. A thin layer of gold was deposited on top of the nanoporous membrane. (b) Schematic representation of the sample cell. The lower electrode and the upper electrode (the aluminum substrate and the thin layer of gold deposited by sputtering, respectively) are connected to the dielectric spectrometer and used to measurein dependence on frequency and temperaturethe permittivity of the sample cell.
measurements reflect a statistical ensemble corresponding to attograms of material. The phase transition behavior of PVDF−TrFE in the bulk is discussed in Figure 2. A recent study20 has demonstrated that
Figure 2. Heat flow as measured by differential scanning calorimetry (a, b) and first derivative of permittivity at different frequencies as measured by broadband dielectric spectroscopy (c, d) upon cooling (a, d) and heating (c, b) for PVDF−TrFE in the bulk.
the first derivative of permittivitymeasured in spectral regions not affected by dielectric dispersionsrepresents a very effective means to investigate density fluctuations. By this method, phase transitions of polymeric materials can be readily assessed. The method is illustrated in Figure 2, showing calorimetric and permittivity measurements of PVDF−TrFE in the bulk. The first derivative of permittivity turns out to closely mirror the phase transition behavior as measured by differential scanning calorimetry. This is due to the well-known relation 578
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The typical dielectric response of the empty nanocontainers is shown in Figure 3. Except for the low-frequency region of the
Figure 4. First derivative of permittivity measured upon cooling (a, c) and heating (b, d) with 1 K/min for PVDF−TrFE in the bulk (black), for 80 ag of PVDF−TrFE per nanocontainer (red), and for the empty nanocontainers (green). Figure 3. Typical dielectric response of the empty nanocontainers: permittivity (a) and dielectric loss (b) as a function of frequency at different temperatures, as indicated. Inset: permittivity of the empty nanocontainers as a function of temperature at different frequencies, as indicated.
in Figure 2: the crystallization/melting transitions and the Curie transitions show opposite signs in the first derivative of permittivity; i.e., crystallization and melting are manifested by negative peaks while ferroelectric transitions by positive ones. Upon cooling from the melt, the polymer system comprising 80 ag of PVDF−TrFE undergoes a crystallization process at ∼362 K. As compared to the behavior of PVDF−TrFE in the bulk, a reduction by 38 K in the crystallization temperature is observed. Retardations and undercooling effects are commonly well-known for the crystallization of nanoscopically confined materials. At lower temperatures, two positive peaks are detected at 345 and 265 K. Based on the results discussed in Figure 2, these peaks are attributed to two ferroelectric transitions. While the temperature position of the first Curie transition is negligibly affected in confinement, a large shift (∼65 K) is observed for the second one. This finding may suggest an interfacial segregation of the two paraelectric phases of PVDF−TrFE formed upon crystallization. The permittivity measurements on heating show a positive peak at 265 K and a negative one at ∼400 K, attributed to a ferroelectric transition and a melting process, respectively. The melting point is reduced by ∼12 K.This finding is characteristic for finite size systems and is attributed to the limitation of the crystal size and the increase in the surface-to-volume ratio induced in geometrical nanoconfinement. As compared to the Curie transition of the PVFD−TrFE in the bulk (detected at 388 K upon heating), the Curie transition for 80 ag of material manifested as a positive peak in the first derivative of permittivityis observed at much lower temperatures. A much lower Curie transition has been also reported for twodimensional ferroelectric films of PVDF−TrFE,22 and it has been associated with the influence of the surface layers. However, the study reported no significant shifts in the bulk ferroelectric transition down to thicknesses as small as two monolayers.22 This observation has been considered to indicate the existence of two-dimensional ferroelectrics. In accordance with this study, another recent work on PVDF−TrFE nanowires20 has reported that the bulk Curie transition was preserved down to pore diameters as small as 15 nm. As opposed to one- or two-dimensional confinement,20,22 the current investigations on attograms of PVDF−TrFE
dielectric spectra whereat high temperaturesresidual contributions arising from charge transport and interfacial polarization effects are detected, the permittivity of the empty nanocontainers does not show any dielectric dispersions in the temperature window of our experiments. The dielectric losses have low values, typically around 0.02. This indicates good insulating properties of the empty nanocontainers, which is essential for their use as dielectric cells. The temperature dependence of the permittivity for different frequencies of the applied electric field is shown in the inlet of Figure3. In a broad temperature range, no dielectric dispersions are observed. The phase transition behavior of a polymer system comprising ∼80 ag of PVDF−TrFE per nanocontainer is shown in Figure 4. The amount of polymer per nanocontainer is controlled by the concentration of the polymer solution and the volume of the nanocontainers. Since the electric field is parallel to the long axis of the nanocontainers, the measured permittivity is additive: the global response is a linear combination of all local signals given by the individual nanocontainers. In a single experiment, a number of ∼3.7 × 109 nanocontainers is measured. Considering also the fact that the nanocontainers are identical and independent, the net permittivity measurements reflect a statistical ensemble which corresponds to a polymer system comprising 80 ag of PVDF− TrFE confined in the volume of a nanocontainer. Large signal fluctuations characteristic for experiments on individual nanoobjects, which impose the necessity of repeating the measurements until a statistical distribution is realized, are completely avoided by the current approach. A statistical distribution is obtained in a single “parallel” experiment. The phase transitions for 80 ag of PVDF−TrFE are compared to those measured for this polymer in the bulk (Figure 4). The response of the empty nanocontainers does not show, as expected, any significant features in the frequency and temperature window of our experiments (Figure 4). The results are interpreted based on the discrimination criterion explained 579
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(9) Furukawa, T.; Johnson, G. E.; Bair, H. E.; Tajitsu, Y.; Chiba, A.; Fukada, E. Ferroelectrics 1981, 32, 61−67. (10) Lovinger, A. J. Developments in Crystalline Polymers; Bassett, D. C., Ed.; Applied Science: London, 1982. (11) Tashiro, K.; Takano, K.; Kobayashi, M.; Chatani, Y.; Tadokoro, H. Polymer 1984, 25, 195−208. (12) Tajitsu, T.; Chiba, A.; Furukawa, T.; Date, M.; Furukoda, E. Appl. Phys. Lett. 1980, 36, 286−288. (13) Koga, K.; Nakano, N.; Hattori, T.; Ohigashi, H. J. Appl. Phys. 1990, 67, 965−974. (14) Lopez Cabarcos, E.; Gonzalez Arche, A.; Baltá Calleja, F. J.; Bösecke, P.; Röber, S.; Bark, M.; Zachmann, H. G. Polymer 1991, 32, 3097−3102. (15) Tashiro, K.; Takano, K.; Kobayashi, M.; Chatani, Y.; Tadokoro, H. Polymer 1981, 22, 1312−1314. (16) Masuda, H.; Fukuda, K. Science 1995, 268, 1466−1468. (17) Masuda, H.; Hasegwa, F.; Ono, S. J. Electrochem. Soc. 1997, 144, 127−130. (18) Serghei, A.; Chen, D.; Lee, D. H.; Russell, T. P. Soft Matter 2010, 6, 1111. (19) Serghei, A.; Zhao, W.; Chen, D.; Russell, T. P. Eur. Phys. J.: Spec. Top. 2010, 189, 95−101. (20) Serghei, A.; Lutkenhaus, J. L.; Miranda, D. F.; McEnnis, K.; Kremer, F.; Russell, T. P. Small 2010, 6, 1822−1826. (21) Broadband Dielectric Spectroscopy; Kremer, F., Schönhals, A., Eds.; Springer: Berlin, 2003. (22) Bune, A. V.; Fridkin, V. M.; Ducharme, S.; Blinov, L. M.; Palto, S. P.; Sorokin, A. V.; Yudin, S. G.; Zlatkin, A. Nature 1998, 391, 874− 877.
indicate a complete suppression of the bulk ferroelectric transition upon heating. The Curie transition measured at lower temperatures is attributed, in accordance with ref 22, to the presence of confining interfaces. It is also observed that, as opposed to the Curie transitions of PVDF−TrFE in the bulk which are naturally exhibiting a thermal hysteresis, no hysteresis is detected for the Curie transition measured at 265 K for 80 ag of PVDF−TrFE (the experimental curves measured upon cooling and heating are identical below 310 K). Unlike in the bulk, the ferroelectric transition for 80 ag of PVDF−TrFE appears to gain the character of a second-order phase transition. Ferroelectric properties are generated by the nonsymmetric character of the crystalline units specific to ferroelectric materials. This functionality arising at the atomic and molecular scale cannot be exploited at its full potential at the macroscopic scale due to the influence of entropy. Geometrical nanoconfinement represents a very effective means to reduce the entropy due to orientation and finite size effects. By developing a novel experimental concept, we have shown here that ferroelectric systems preserve their ferroelectric properties down to amounts of matter as small as attograms. At the same time, we demonstrated how attogram partitions of a material can be realized by dividing a macroscopic system into a parallel arrangement of identical, independent, additive entities (nanocontainers) carrying attograms of material. This approach relies on the combinationto our knowledge, for the first timeof two functions provided by ordered arrays of nanocontainers: the nanocontainers are used as confining media and, at the same time, as measurement cells. By this development, investigations on the statistical behavior of attograms partitions can be readily carried out in a single experiment, which may have a great impact in the field of statistical physics.
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AUTHOR INFORMATION
Corresponding Author
*E-mail
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS A.S. and T.P.R. are grateful to the support of the US Department of Energy, Office of Basic Energy Science, under Contract DEFG02-96ER45612 in the design and execution of these studies, and W.Z. and D.M., who assisted with the electron microscopy measurements, are supported by the NSF Materials Research Science and Engineering Center at the University of Massachusetts.
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