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Molecular Dynamics of a Biodegradable Biomimetic Ionomer Studied by Broadband Dielectric Spectroscopy Ken Welch,*,† Fredrik Nederberg,‡ Tim Bowden,‡ Jo¨ns Hilborn,‡ and Maria Strømme† Department of Engineering Sciences, The Ångstro¨m Laboratory, Uppsala UniVersity, Box 534, SE-751 21 Uppsala, Sweden, and Department of Materials Chemistry, The Ångstro¨m Laboratory, Uppsala UniVersity, Box 538, SE-751 21 Uppsala, Sweden ReceiVed March 28, 2007. In Final Form: June 29, 2007 Broadband dielectric spectroscopy was used to investigate the bulk molecular dynamics of a recently developed biodegradable biomimetic ionomer potentially useful for biomedical applications. Isothermal dielectric spectra were gathered for a phosphoryl choline (PC)-functionalized poly(trimethylene carbonate) (PTMC) ionomer and unfunctionalized PTMC at temperatures ranging from 2 to 60 °C over a broad frequency range of 10-3 to 106 Hz. Four relaxations were clearly identified, two of which were shown to stem from the PTMC polymer backbone. A detailed analysis showed that the formation of zwitterionic aggregates was responsible for the material’s bulk functionality and that bulk conduction processes may provide useful information for assessing the PC ionomer as a candidate for drug delivery applications. Finally, it was concluded that absorbed water concentrates around the aggregates, resulting in an increased mobility of the PC end-groups.
Introduction The past decade has witnessed the development of an increasing number of novel synthetic polymers that show great promise for applications such as hemocompatible coatings and controlled release vehicles for drug delivery.1-4 The success of these materials is largely due to their biomimetic properties and ability to biodegrade into harmless degradation products. For example, both polyesters5 and polycarbonates6 have been found to degrade in vivo. As well, the use of hydrophilic polymers such as poly(ethylene glycol) or the incorporation of biomimetic groups such as phosphoryl choline (PC) increases the acceptance of these biomaterials in the body.7,8 PC is the hydrophilic moiety in the naturally occurring phospholipid phosphatidylcholine present in the cell membrane and is a zwitterionic group, meaning that it contains both a positive and a negative charge. In this work, we focus on a recently developed biomimetic ionic polymer (ionomer), consisting of a poly(trimethylene carbonate) (PTMC) polymer backbone functionalized with PC end-groups. This biodegradable ionomer has been shown to exhibit dual activity with the zwitterionic PC group, forming physical cross-links in the bulk as well as providing a hydrophilic and hemocompatible surface.9 Earlier attempts using PC endfunctionalized poly(-caprolactone), being semicrystalline, demonstrated that the lack of molecular mobility suppressed the possibility of spontaneous surface rearrangement.10 Conversely, * Corresponding author. E-mail address:
[email protected]; telephone: +46 (0)18-471 7944. † Department of Engineering Sciences. ‡ Department of Materials Chemistry. (1) Ishihara, K.; Iwasaki, Y.; Nakabayashi, N. Mater. Sci. Eng., C: Biomimetic Supramol. Syst. 1998, 6, 253-259. (2) Iwasaki, Y.; Ishihara, K. Anal. Bioanal. Chem. 2005, 381, 534-546. (3) Pillai, O.; Panchagnula, R. Curr. Opin. Chem. Biol. 2001, 5, 447-451. (4) Uhrich, K. E.; Cannizzaro, S. M.; Langer, R. S.; Shakesheff, K. M. Chem. ReV. 1999, 99, 3181-3198. (5) Ikada, Y.; Tsuji, H. Macromol. Rapid Commun. 2000, 21, 117-132. (6) Pego, A. P.; Van Luyn, M. J. A.; Brouwer, L. A.; van Wachem, P. B.; Poot, A. A.; Grijpma, D. W.; Feijen, J. J. Biomed. Mater. Res., Part A 2003, 67, 10441054. (7) Hayward, J. A.; Chapman, D. Biomaterials 1984, 5, 135-142. (8) Zalipsky, S. Bioconjugate Chem. 1995, 6, 150-165. (9) Nederberg, F.; Bowden, T.; Nilsson, B.; Hong, J.; Hilborn, J. J. Am. Chem. Soc. 2004, 126, 15350-15351.
the use of a low glass transition temperature (Tg ) -40 °C) PTMC introduced enough mobility for spontaneous surface enrichment of the hydrophilic PC group against water. In the bulk, the PC end-groups are most likely captured in zwitterionic aggregates,9,11 where they form physical cross-links that restrict molecular mobility. Figure 1 shows a schematic representation of the postulated bulk structure of the PC ionomer. The formation of aggregates results in enhanced mechanical properties compared to those of the unfunctionalized backbone polymer, PTMC. At ambient and physiological temperatures, PTMC behaves as an amorphous melt and has no mechanical integrity, whereas the PC ionomer behaves like a rubber with a shear modulus of several megapascals.9 PTMC is hydrolytically stable under in vitro conditions, but degrades in vivo, most likely through enzymatic degradation.6 The addition of PC end-groups not only tailors the degradation properties of the material, but it also dramatically affects the hygroscopicity. It has been shown that, while PTMC does not absorb water, a PC ionomer having a molecular weight of 4000 g/mol can absorb an amount of water equivalent to 90% of its original mass.11 This suggests that the PC ionomer may serve as a material for controlled drug release vehicles since dissolved drugs can be loaded into the PC ionomer bulk through water uptake and swelling.11 Hence, molecular motions in the dry state and in the presence of water appear to govern the uptake, storage, and release of substances such as drugs from these materials. In order to be able to use and tailor the specific properties of biomaterials such as the PC ionomer, a deeper understanding of the relationship between the material structure and its function is crucial. While characterization methods such as scanning electron microscopy, size exclusion chromatography, nuclear magnetic resonance, and so forth are useful in providing information about the structure and static properties of materials, methods that provide information about molecular dynamics are invaluable in understanding how the material functions and behaves in different environments. Broadband dielectric spec(10) Nederberg, F.; Bowden, T.; Hilborn, J. Macromolecules 2004, 37, 954965. (11) Nederberg, F.; Watanabe, J.; Ishihara, K.; Hilborn, J.; Bowden, T. Biomacromolecules 2005, 6, 3088-3094.
10.1021/la7009012 CCC: $37.00 © 2007 American Chemical Society Published on Web 08/21/2007
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Figure 1. Schematic representation of the bulk structure of the PC ionomer showing the formation of zwitterionic aggregates.
Figure 3. Mechanical behavior of the PC ionomer compared with that of the PTMC starting material. Measurements were made using an oscillating torque experiment at 1 Hz. The glass transition of the two materials is indicated, as well as the prominent rubbery plateau of the ionomer.
Figure 2. Molecular structure of (a) PTMC (n ∼ 20) and (b) PC ionomer (n ∼ 20).
troscopy (BDS) is a powerful technique that measures the dielectric properties of matter through its interactions with electromagnetic waves and has proven to be a particularly useful tool for studying the molecular dynamics of polymers.12 Ionomers, because of their inherently large dipole moments or bound ions, are well suited for BDS studies and have been frequently investigated in the past.13-16 Although ionomers functionalized with PC groups have not been previously investigated with BDS, the PC group in phospholipid bilayers and lecithins has been studied using BDS.17-20 In this paper, the PC ionomer and the unfunctionalized polymer backbone, PTMC, are investigated using BDS over a frequency range of 10-3 to 106 Hz and a temperature range of 2-60 °C. By comparing the dielectric response of the ionomer to that of its polymer backbone, the unique relaxation contributions and added functionality of the PC end-groups can thus be better understood. Experimental Section Materials. The low molecular weight polycarbonate PTMC (Figure 2a) was synthesized by ring-opening polymerization of tri(methylene carbonate), initiated from 1,4-butanediol. The degree of (12) Scho¨nhals, A. In Broadband Dielectric Spectroscopy; Kremer, F., Scho¨nhals, A., Eds.; Springer-Verlag: Berlin, 2003; pp 225-293. (13) Yano, S.; Tadano, K.; Jerome, R. Macromolecules 1991, 24, 6439-6442. (14) Hadjichristidis, N.; Pispas, S.; Pitsikalis, M. Prog. Polym. Sci. 1999, 24, 875-915. (15) Floudas, G.; Pispas, S.; Hadjichristidis, N.; Pakula, T. Macromol. Chem. Phys. 2001, 202, 1488-1496. (16) Atorngitjawat, P.; Klein, R. J.; Runt, J. Macromolecules 2006, 39, 18151820. (17) Klosgen, B.; Reichle, C.; Kohlsmann, S.; Kramer, K. D. Biophys. J. 1996, 71, 3251-3260. (18) Smith, G.; Shekunov, B. Y.; Shen, J.; Duffy, A. P.; Anwar, J.; Wakerly, M. G.; Chakrabarti, R. Pharm. Res. 1996, 13, 1181-1185. (19) Haibel, A.; Nimtz, G.; Pelster, R.; Jaggi, R. Phys. ReV. E 1998, 57, 48384841. (20) Schrader, W.; Halstenberg, S.; Behrends, R.; Kaatze, U. J. Phys. Chem. B 2003, 107, 14457-14463.
polymerization was 40 (n ) 20 on each side), as obtained by 1H NMR end-group analysis, giving a molecular weight of approximately 4000 g/mol.9 The ionomer (Figure 2b) was subsequently prepared by functionalizing both ends of the PTMC polymer with the zwitterionic PC group. Rheology measurements gathered from an oscillating torque experiment at 1 Hz illustrate the enhanced mechanical performance of the PC ionomer, as shown in Figure 3, where the shear storage modulus is presented as a function of temperature for the PC ionomer and the unfunctionalized backbone polymer, PTMC. Both materials have a Tg of approximately -20 °C, while the PC ionomer exhibits a rubbery plateau region at ambient and physiological temperatures with a shear storage modulus of ∼3 MPa. Sample Preparation. Prior to the BDS measurements, the polymer sample was dissolved in chloroform and precipitated in chilled methanol in order to remove impurities. Excess chloroform was removed by placing the polymer under a flow of dry nitrogen gas until the majority of chloroform had evaporated, after which the polymer was placed in a vacuum oven at a temperature of 50 °C for 48 h. The sample was then placed on the lower electrode of the dielectric measurement cell (described below), and the cell was heated to approximately 80 °C for 10 min to ensure that the polymer sample was sufficiently soft to be molded between the electrodes. The upper electrode was lowered via a micrometer screw to obtain an electrode separation of 300 µm. Probing Molecular Motions through BDS Measurements. BDS measurements were carried out with a Novocontrol Alpha-AN dielectric measurement system (Novocontrol Technologies, Hundsangen, Germany). The samples were placed between two goldplated brass electrodes having a diameter of 10 mm and positioned with a separation of 300 µm. A guard ring was incorporated around the signal electrode to reduce stray capacitance and edge effects, and the entire electrode arrangement was enclosed in a sealed stainless steel container to provide a thermally insulated and electrically shielded environment. A temperature sensor with an accuracy of ( 0.2 °C was located inside the measurement cell to record the sample temperature. The temperature was controlled with an incubator (Incucell IC 55, BMT a.s., Brno, Czech Republic) for temperatures above ambient temperatures and a laboratory refrigerator for temperatures below ambient temperatures. Nine isothermal dielectric spectra were collected for the PC ionomer sample, and seven were collected for the PTMC sample at temperatures ranging from 2 to 60 °C in a frequency range of 10-3 to 106 Hz. Subsequent to these dielectric measurements, the ionomer sample was maintained in the measurement cell at 30 °C and 37% relative humidity (RH) and allowed to equilibrate with its surroundings for
Molecular Dynamics of PC-Functionalized PTMC
Langmuir, Vol. 23, No. 20, 2007 10211
a period of 1 month. A final dielectric spectrum was obtained to ascertain the affect of absorbed moisture in the ionomer bulk. Independently, the amount of moisture absorbed by the ionomer at 30 °C and 37% RH was determined by weighing (AX504DR, Mettler Toledo, Switzerland) an initially dry 1 g disk of ionomer at 1-day intervals until the maximum water uptake was achieved. Analysis Techniques Used in Interpreting BDS Data. The Novocontrol Alpha-AN measures the complex impedance of the sample, and, utilizing the sample geometry, the data can be converted to a number of intrinsic material functions such as complex conductivity σ*, complex permittivity *, or complex modulus M* ) 1/*, all of which are functions of the angular frequency ω. For this study, the complex permittivity representation * ) ′ - i′′ was chosen. With this representation, the dielectric loss ′′(ω) is often chosen to present the results of the dielectric spectra because it reveals features in the data better than the real part of the permittivity ′(ω). Since ′(ω) and ′′(ω) are related through the Kramer-Kronig (KK) relations, essentially all of the information in the dielectric spectra is contained in either quantity.21 However, in situations where long-range ionic conduction (hereafter referred to as dc conduction) is present, as is often the case for glass-forming liquids and polymers, low-frequency dipole relaxations can be masked by the strong contributions of dc conduction in the loss spectra. One way to remove the dc conduction from the loss spectra is to utilize the KK relations to calculate the loss spectra from the real part of the complex dielectric permittivity since ′(ω) only includes contributions due to relaxation phenomena. This technique works well in many cases, but has significant shortcomings in the presence of electrode polarization (EP).22 In the present study, an analysis technique suggested by Wu¨bbenhorst and van Turnhout23,24 was employed in which the logarithmic derivative of the real part of the dielectric permittivity, ′′der(ω) ) -
π ∂′(ω) 2 ∂ln(ω)
(1)
is used to approximate the dc conduction-free dielectric loss. For broad loss peaks, ′′der(ω) ≈ ′′(ω), while for Debye,25 single relaxation peaks ′′der(ω) ) (′′(ω))2/′′max. Here, ′′max denotes the value of ′′(ω) at the loss peak frequency. One of the major advantages of this technique is that the locations of loss peaks in the derivative representation and the dielectric loss spectra are identical, while the widths of the peaks become narrower with the derivative representation. This aids in resolving nearby or overlapping peaks. Another advantage is that the masking effect of EP can be suppressed since the strong EP contribution observed in ′′(ω) is shifted to lower frequencies in the logarithmic derivative representation.23 Coelho has shown in a theoretical work that an ideal EP takes on the form of a Debye relaxation since the space charges created by the blocked charge carriers relax as a macroscopic dipole.26,27 It can be noted that, without blocking electrodes, these mobile charges would produce a dc conduction contribution in ′′(ω) without a corresponding part in ′(ω); however, with blocking electrodes, the contribution in the loss spectra due to these mobile charges corresponds to the strong EP part in ′(ω). Because of the peaksharpening properties of the logarithmic derivative technique, this conduction contribution is shifted to lower frequencies and thus unmasks potentially “hidden” features. This shift is caused by the fact that the dc conduction contribution (theoretically having a ω-1 frequency dependence in the experimental ′′(ω) spectra) falls off (21) Scho¨nhals, A.; Kremer, F. In Broadband Dielectric Spectroscopy; Kremer, F., Scho¨nhals, A., Eds.; Springer-Verlag: Berlin, 2003; pp 1-33. (22) Axelrod, N.; Axelrod, E.; Gutina, A.; Puzenko, A.; Ben Ishai, P.; Feldman, Y. Meas. Sci. Technol. 2004, 15, 755-764. (23) Wubbenhorst, M.; van Turnhout, J. J. Non-Cryst. Solids 2002, 305, 4049. (24) Wubbenhorst, M.; van Koten, E. M.; Jansen, J. C.; Mijs, W.; van Turnhout, J. Macromol. Rapid Commun. 1997, 18, 139-147. (25) Debye, P. In Polar Molecules; Chemical Catalogue Company: New York, 1929; p 94. (26) Coelho, R. ReV. Phys. Appl. 1983, 18, 137-146. (27) Coelho, R. J. Non-Cryst. Solids 1991, 131, 1136-1139.
as ω-2 in the ′′der representation. In reality, however, the experimental data does not exactly follow the simplified theory presented by Coelho. Because of factors such as electrode topography and surface chemistry, the frequency dependence of the EP contribution in both ′(ω) and ′′(ω) is fractionally smaller,28 and, consequently, the frequency dependence of the ′′der representation of EP is also reduced. The main disadvantage of using the derivative representation lies in the fact that the derivative is sensitive to noise and the accuracy to which ′(ω) can be measured. A low loss portion of the permittivity spectra corresponds to a relatively “flat” section of ′(ω) with only small changes that are often less than the measurement resolution of ′(ω). Noise and measurement inaccuries can lead to negative values of the logarithmic derivative, and therefore this method may not be able to represent a (very) low loss portion of *(ω). In order to more accurately identify the loss peak locations in the cases where the peak sharpening did not resolve nearby peaks, nonlinear least-squares fitting of multiple Havriliak-Negami29 (HN) model functions to the ′′der data was carried out. The HN function is a model function that is commonly fitted to relaxation data where *(ω) ) ∞ +
∆ (1 + (iωτHN)ξ)γ
(2)
Here, ∞ is the permittivity at frequencies much greater than τHN, the characteristic relaxation time, ∆ is the relaxation strength, and ξ and γ are dimensionless relaxation peak shape parameters. Finally, the dc conductivity, σdc, was extracted from the ′′(ω) data using a technique introduced by Strømme et al.30 The technique extracts the dc conduction process from a spectrum for which the dc conductivity is superimposed on a power-law process. One of the benefits with the technique is that the actual dielectric process superimposed on the dc conduction does not have to be of true power-law nature. In a small frequency interval, most dielectric processes (Debye, Cole-Cole, Davidson-Cole, HN, etc.) behave as power laws and thus make the employed extraction method very general.31,32
Results and Discussion Dielectric Landscape of the PC Ionomer versus PTMC. The ′′der spectra for the PC ionomer and the unfunctionalized polymer PTMC are presented in Figure 4. Comparing the spectra, two relaxations are observed in both materials, viz., the R and β relaxations. In the PTMC sample, the R relaxation appears at the low-frequency portion of the spectrum as a shoulder emerging from the strong EP contribution, while, in the PC ionomer sample, the R relaxation peak is well resolved because of a lower level of conductivity. The level of conductivity in the samples is primarily due to the amount of impurity ions. In both samples, the β relaxation becomes visible only at lower temperatures whereby the process has been slowed down sufficiently to enter the upper part of the measured frequency window. The lack of data in the central portion of the PTMC spectra is due to the inability of the logarithmic derivative to resolve the low loss portions of the spectra, as previously detailed in the analysis techniques section. In the PC ionomer spectra, two additional relaxations are immediately obvious, labeled Rionomer and λ. The EP contribution to the spectra is seen as the steep increase in ′′der at low frequencies for both samples, and (28) Bates, J. B.; Chu, Y. T.; Stribling, W. T. Phys. ReV. Lett. 1988, 60, 627-630. (29) Havriliak, S.; Negami, S. Polymer 1967, 8, 161-210. (30) Strømme, M.; Niklasson, G. A.; Forsgren, K.; Hårsta, A. J. Appl. Phys. 1999, 85, 2185-2191. (31) Ha¨gerstro¨m, H.; Strømme, M.; Edsman, K. J. Pharm. Sci. 2005, 94, 10901100. (32) Niklasson, G. A.; Jonsson, A. K.; Strømme, M. In Impedance Spectroscopy, 2nd ed.; Barsoukov, Y., MacDonald, J. R., Eds.; Wiley: New York, 2005; pp 302-326.
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Figure 5. ′′der spectrum of the PC ionomer compared with the ′′der spectrum of PTMC. Both measurements were performed at 23 °C. While the R and β relaxations are present in both materials, the presence of the PC end-groups in the ionomer gives rise to two additional relaxations between the R and β relaxations. Lines are guides for the eyes.
used in a preliminary investigation for this study. The conductivity in this sample was less than that for the PTMC sample shown in Figure 4, and therefore the R relaxation peak is resolved. The dipole associated with the polar carbonate groups in the polymer backbone of the PC ionomer and PTMC is most likely responsible for the R and β relaxations. The dipole moment should be similar to that of diethyl carbonate, which has a dipole moment of µ ) 1.1 D.34 Because the R relaxation is dependent on the free volume of the system, it normally departs from Arrhenius behavior close to the glass transition and obeys instead the Vogel-Fulcher-Tammann (VFT) equation,35-37 Figure 4. Dielectric loss ′′der spectra as a function of frequency and temperature for (a) PC ionomer and (b) PTMC. The logarithmic derivative technique reveals additional processes (R and λ relaxations) that are otherwise not visible in the normal ′′ loss spectra because of dc conductivity. See the Supporting Information for the original ′ and ′′ spectra of the ionomer.
is due to the blocking of mobile charges (impurity ions) at the sample/electrode interface. These relaxations and conduction processes will be described in more detail below, particularly with regard to the functional properties of the PC ionomer. Relaxation Processes and their Relation to the Corresponding Molecular Moieties. A common characteristic of essentially all amorphous polymers is that they exhibit both a principal relaxation related to the dynamic glass transition, termed the R relaxation, and a secondary relaxation called the β relaxation.12,33 It is generally accepted that the R relaxation is due to segmental motion (i.e., conformational changes) along the polymer chain. On the other hand, the dielectric β relaxation stems from localized rotational fluctuations of the dipole vector.12 The molecular motion giving rise to the β relaxation can be thought of as the chain segments or side chains rattling inside their cages. Because the ionomer consists of the PTMC polymer functionalized with PC end-groups, one expects both materials to exhibit similar dielectric features relating to the polymer backbone. Such similarity is clearly seen in Figure 5 in which the room-temperature spectra of a PC ionomer and a PTMC sample are overlaid. The PTMC data were collected from a sample (33) Williams, G. In Polymer Spectroscopy; Fawcett, A. H., Ed.; John Wiley & Sons: Chichester, U.K., 1996; pp 275-296.
(
ν(T) ) ν∞ exp -
DT0 T - T0
)
(3)
where ν is the frequency of the relaxation loss peak, D and ν∞ are constants, and T0 is the Vogel temperature, which is 30-70 K below Tg.12 Figure 6 displays an Arrhenius plot of the loss peak frequency for the PC ionomer R relaxation. A VFT fit to the data produces a T0 of 212 ( 13 K, which is 56 K below Tg. It was not possible to accurately assess the behavior of the PTMC R relaxation, as the peaks were masked by the strong EP contributions. Another characteristic of the R process for glass-forming systems is that it is well modeled by the stretched exponential function, or the Kohlrausch-Williams-Watts function.38 This gives a distinctive shape to the relaxation spectrum in which the slope of the high-frequency side of the loss peak is not as steep as the low-frequency side (viewed in a log-log plot). This shape is observed with the PC ionomer and can be seen in Figure 7, where HN functions are fitted to a PC ionomer ′′der spectrum gathered at 37 °C (parameters listed in Table 1). The β relaxation, observed with the combination of low temperatures and high frequencies in both the PC ionomer and PTMC samples, is known to follow the Arrhenius law.12 Figure 6 displays the PC ionomer β relaxation behavior for which an (34) Lide, D. R. CRC Handbook of Chemistry and Physics 2004-2005, 85th ed.; CRC Press: Boca Raton, FL, 2004. (35) Vogel, H. Phys. Z. 1921, 22, 645-646. (36) Fulcher, G. S. J. Am. Ceram. Soc. 1925, 8, 339-345. (37) Tammann, G.; Hesse, W. Z. Anorg. Allg. Chem. 1926, 156, 245-257. (38) Williams, G. J. Non-Cryst. Solids 1991, 131, 1-12.
Molecular Dynamics of PC-Functionalized PTMC
Langmuir, Vol. 23, No. 20, 2007 10213 Table 1. Parameters for the Curve Fitted to the ′′der Data of the Ionomer at 37 °Ca HN parameter relaxation
∆e
β Rionomer λ R δ
0.4833 0.4672 0.1397 0.6843 0.0506
EP
1/τ HN (Hz) 6.9991e + 6 10511 225.6 0.8060 0.0639 a 0.00039
ζ
γ
0.7574 0.8668 1.1001 1.0954 1.2532
1.0000 0.6547 0.7606 0.5357 1.0000
s -1.5059
a The curve, shown in Figure 7, consists of 5 HN relaxations (see eq 2) and a power-law term a‚ωs representing EP. Note that the parameters for the β relaxation were first derived from low-temperature data, as insufficient data were available at 37 °C.
Figure 6. Arrhenius plot of loss peak frequencies for the four main relaxation processes observed in the PC ionomer. While the β and λ processes show Arrhenius behavior, the R and Rionomer relaxations follow the VFT law. The activation energies for the β and λ processes were found to be 0.6 and 0.22 ( 0.05 eV, respectively. The Vogel temperatures T0 for the R and Rionomer processes were calculated to be 212 ( 13 and 212 ( 6 K, respectively. Solid lines are fits to the Arrhenius equation, while dashed lines are fits to the VFT equation. The unit for ν is Hz.
Figure 7. HN function fits to the ′′der spectrum of the PC ionomer at 37 °C. The solid line is the combined fit of five relaxations (β, Rionomer, λ, R, and δ) and the EP. Dashed lines show the individual components to the total fit. Circles are the experimental data. Note that curve fitting identified the δ relaxation, which was otherwise not apparent.
activation energy of 0.6 eV was extracted. In comparison, the activation energy for the PTMC β relaxation was found to be 1.0 eV. However, as so few peaks were observable, there is a large uncertainty in these values. Another characteristic of the β relaxation is that the relaxation strength generally increases with temperature. This behavior was observed with both the PC ionomer and the PTMC samples for the peaks that were visible. As mentioned earlier, the PC ionomer shows two additional relaxations compared to the PTMC polymer. The Rionomer and λ relaxations are both related to the presence of the zwitterionic PC moieties. It is thought that the formation of zwitterionic aggregates, as shown in Figure 1, restricts the translational mobility of the polymer backbone and thereby gives rise to the rubbery plateau shown in Figure 3. Judging by the relaxation behavior of the Rionomer relaxation shown in Figure 6, which follows the VFT law, one expects that the PC groups will affect the glass transition. Additionally, the VFT fit to the data gave a Vogel temperature of 212 ( 6 K, which is the same as that
of the R relaxation within the standard error of the fitted parameter. It has long been known that the restricted molecular mobility caused by the physical cross-links in ionomers results in a significant increase in Tg.39 However, from Figure 3 it can be noted that the presence of the PC end-groups results in a broadening of the glass transition rather than an increase in Tg. This may be due to the fact that the ionic groups are not distributed along the entire polymer backbone, but instead are only situated at the ends. As a result, the free volume experienced by the PTMC backbone will be more affected closer to the ends where the localized formation of zwitterionic aggregates occurs. Since the glass transition is dependent on the free volume of the system, the location of the physical cross-links would thus play an important role in determining the nature of the glass transition. While conformational changes of individual PC dipoles are most likely responsible for the Rionomer relaxation, the molecular motion giving rise to the λ relaxation is more ambiguous. From Figures 4 and 6 it is clear that the λ relaxation has an entirely different temperature dependence, obeying the Arrhenius law and having a relatively low activation energy of 0.22 ( 0.05 eV. The λ relaxation does not appear to be a “β ” relaxation corresponding to the individual PC dipoles, as one would expect it to be present at higher frequencies than the Rionomer relaxation. As well, the normal behavior of R and β relaxations is that they coalesce at higher temperatures to form an Rβ relaxation.12 Instead, the Rionomer and λ relaxations diverge as the temperature increases. Thus, it is unlikely that the λ relaxation is coupled to the individual PC dipoles. A possible cause of this relaxation may be the movement of adjacent PC groups in the zwitterionic aggregates. This will be discussed further in a subsequent section. Interestingly, as seen in Figure 7, the curve-fitting procedure identified an additional relaxation, labeled the δ relaxation, at lower frequencies than those of the R peak in each of the PC ionomer spectra. In order to justify the addition of this relaxation to the spectra, the statistical significance of the δ parameters in the model was determined. Without the δ relaxation, the sum of squares of the error was 0.132, while the sum of squares with the δ relaxation was 0.0077. Taking into account the degrees of freedom in the model, an F test was applied and p < 0.001 was found, indicating that the parameters of the δ relaxation were statistically significant. Furthermore, the presence of the δ relaxation was found in the PC ionomer spectra at all measured temperatures. The origin of this relaxation is unknown, but it may be associated with the conduction process, as discussed in the following section. Conduction and EP Processes. Figure 8 shows the Arrhenius plot of the dc conductivity and the EP process. The frequency (39) Eisenberg, A. Macromolecules 1971, 4, 125-128.
10214 Langmuir, Vol. 23, No. 20, 2007
Figure 8. Arrhenius plot of the dc conduction and EP process. The frequency of the EP was taken at the point of the spectra where ′′der ) 100. Solid lines are fits to the data according to the Arrhenius equation. The activation energies for σdc and EP were 1.30 ( 0.01 and 1.32 ( 0.07 eV, respectively, for the PC ionomer, and 1.02 ( 0.02 and 1.03 ( 0.02 eV, respectively, for PTMC. The units for σdc and VEP are S/cm and Hz, respectively.
of the EP process used in this calculation was taken from the spectra at the point where ′′der ) 100. At this point, the EP process had taken on a power-law behavior (i.e., it appeared as a straight line on the log-log plot). The activation energies for the PTMC σdc and EP were 1.02 ( 0.02 and 1.03 ( 0.02 eV, respectively, while the activation energies for the PC ionomer σdc and EP were 1.30 ( 0.01 and 1.32 ( 0.07 eV, respectively. This indicates that the dc conduction and EP stem from the same process, as expected. The increase in activation energy for the PC ionomer conductivity relative to the PTMC conductivity could be attributed to the PC end-groups. Greater ion affinity for these polar groups would create a larger energy barrier to the conduction process and thus show higher activation energy. Since charge transport in disordered systems takes place because of hopping conduction,40,41 the ionic conductivity is expected to follow the Arrhenius law, as it does for the two materials under study. Arrhenius behavior of the conduction process is, however, not generally observed in glass-forming systems. In such materials, dc conductivity is usually correlated with the R relaxation and thus exhibits a VFT behavior.42-44 This is logical since polar groups such as the PC end-groups and the carbonate groups along the polymer backbone are expected to facilitate the conduction, and therefore one might expect the conduction process to follow the same behavior as the segmental processes. However, the contradictory results of the present work are supported in a previous study where Arrhenius temperature dependence of the conduction process in PTMC was observed.45 Returning to Figure 7, a possible mechanism for the δ relaxation is the ionic conduction process. According to the DebyeHu¨ckel-Falkenhagen theory,40,46,47 the motion of a charge in a disordered system is accompanied by an electrical relaxation due to the movement of the polarization cloud that follows the (40) Kremer, F.; Rozanski, S. A. In Broadband Dielectric Spectroscopy; Kremer, F., Scho¨nhals, A., Eds.; Springer-Verlag: Berlin, 2003; pp 475-494. (41) Dyre, J. C. J. Appl. Phys. 1988, 64, 2456-2468. (42) Zhang, S. H.; Runt, J. J. Phys. Chem. B 2004, 108, 6295-6302. (43) Psurek, T.; Hensel-Bielowka, S.; Ziolo, J.; Paluch, M. J. Chem. Phys. 2002, 116, 9882-9888. (44) Elmer, A. M.; Jannasch, P. J. Polym. Sci., Part A: Polym. Chem. 2006, 44, 2195-2205. (45) Smith, M. J.; Silva, M. M.; Cerqueira, S.; MacCallum, J. R. Solid State Ionics 2001, 140, 345-351. (46) Debye, P.; Falkenhagen, H. Phys. Z. 1928, 29, 121, 401-426. (47) Debye, P.; Hu¨ckel, E. Phys. Z. 1923, 24, 185-206.
Welch et al.
Figure 9. Two ′′der spectra for the same PC ionomer sample collected at 30 °C, but with different moisture contents. In the spectrum corresponding to higher moisture content, the Rionomer relaxation has shifted to higher frequencies, while the λ relaxation appears to have disappeared. Lines are guides for the eyes.
charge.40 However, it must also be noted that the conduction process would not simply just give rise to an independent relaxation process. Because the ions primarily move via the polar moieties, which give rise to relaxations themselves, one can expect the presence of mobile ions to affect these other relaxations as well. Absorbed Moisture and Possible Implications for the Ionomer Bulk Dynamics. Figure 9 shows two isothermal spectra taken at 30 °C for the PC ionomer sample in which the water content was varied. The low humidity spectrum corresponds to the measurements discussed previously in this paper. The moisture content in the sample was very low, as the measurements were performed directly after the material was removed from the vacuum oven. The high humidity spectrum corresponds to the measurement carried out after the sample was left in the measurement cell at 30 °C for a period of 1 month and allowed to equilibrate with the surroundings at 37% RH. Mass measurements of water uptake in a separate ionomer sample at 30 °C and 37% RH showed that 8.4% w/w water was absorbed in the ionomer bulk. From Figure 9 it can be observed that the Rionomer relaxation in the highhumidity sample has shifted to higher frequencies, indicating an increased mobility of the PC moieties. Water is expected to concentrate around the zwitterionic aggregates, resulting in a swelling of the aggregates and consequently giving rise to the greater mobility of the PC end-groups. The fact that the R relaxation associated with the polymer backbone has not moved significantly is also an indication that the absorbed water is not located along the main chain. Additionally, it can be noted that the λ relaxation has disappeared, or at least been significantly reduced in strength. If this relaxation is associated with adjacent PC groups in the aggregate as suggested earlier, the swelling of the aggregates could result in a decreased interaction between PC end-groups and a subsequent decrease in the relaxation strength. Finally, it can be noted that, although the water content was increased, the dc conduction remained the same. Assuming that the number of ions did not change during the time between the two measurements, then the average mobility of the ions would also be unaltered. If the absorbed water were evenly distributed throughout the PC ionomer, one would expect an increase in conductivity. The unchanged conductivity provides further
Molecular Dynamics of PC-Functionalized PTMC
evidence that the absorbed water is concentrated in isolated domains around the zwitterionic aggregates. The swelling of the ionomer as well as the apparent concentration of water around the zwitterionic aggregates suggest possible advantages with the use of the ionomer in drug delivery applications. Appropriately chosen drugs could be loaded into the bulk and the subsequent release may be governed by factors such as the biodegradability of the material and the drug’s affinity for the zwitterionic aggregates.
Conclusion We have shown that BDS is a valuable tool for probing the molecular dynamics of a biomimetic ionomer and understanding its functionality. By comparing the dielectric spectra of a PC ionomer with an unfunctionalized PTMC polymer, relaxations were identified that could be traced to the polymer backbone as well as the polar PC end-groups. The VFT behavior of the Rionomer relaxation suggested that PC moieties play a role in the glass transition and helped explain the enhanced mechanical properties
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of the ionomer due to the formation of zwitterionic aggregates. The conduction process was also studied and showed Arrhenius temperature dependence instead of the anticipated VFT behavior. Finally, it was concluded that absorbed water concentrates around the aggregates, resulting in the increased mobility of the PC end-groups. Acknowledgment. M.S. is a Royal Swedish Academy of Sciences (KVA) Research Fellow, and thanks the Academy for their support. The Swedish Foundation for Strategic Research (SSF), the Swedish Research Council (VR), The Go¨ran Gustafsson Foundation, as well as the Knut and Alice Wallenberg Foundation are also acknowledged for their support. Supporting Information Available: Original real and imaginary permittivity data for the ionomer. This material is available free of charge via the Internet at http://pubs.acs.org. LA7009012
