4436
Langmuir 1996, 12, 4436-4441
Dielectric and Mechanic Relaxation in Polyelectrolyte-Supported Bilayer Stacks: A Model for the Dynamics of Membranes? Markus Antonietti* and Martin Neese Max-Planck-Institut fu¨ r Kolloid- & Grenzfla¨ chenforschung, Kantstrasse 55, D-14513 Teltow-Seehof, Germany
Gernot Blum and Friedrich Kremer Institut fu¨ r Physik, Universita¨ t Leipzig, Linne´ strasse 5, D-04103 Leipzig, Germany Received March 11, 1996. In Final Form: June 21, 1996X The dielectric and mechanical relaxation of two different polyelectrolyte-lipid complexes with a stackof-bilayer morphology is characterized by broad band dielectric spectroscopy in the frequency range between 10-2 and 107 Hz and by dynamic shear relaxation experiments. With these experiments, we compare a synthetic model system consisting of polyacrylic acid and didodecyldimethylammonium counterions (PAAC122) with the complex of a fraction of soybean lecithine and a cationic polyelectrolyte (PDADMAC-Lec). The lamellar morphologies consisting of stacks of bilayers are characterized by quantitative small angle X-ray scattering measurements. PAA-C122 shows in the mechanical experiment two β-relaxation processes and exhibits at room temperature a storage modulus of G′ ≈ 200 MPa which issconsidering the observed good deformabilitysvery high. The whole behavior is similar to high-performance loaded rubbers and reflects the extraordinary mechanical response of the lamellar superstructure. For PDADMAC-Lec, a less structured relaxation behavior and lower moduli are found. Above the glass transition, a transition zone is observed which is followed by a rubbery plateau with G′ being still on the order of 1 MPa. Considering the very high deformability of this material, the natural polyelectrolyte lipid complex turned out to be an excellent rubbery material. In the dielectric relaxation experiment, both systems show a very similar behavior which is regarded to be typical for a stack-of-bilayer order. At low temperatures, localized β-relaxations are described which are tentatively assigned to lipid motions. In addition, both systems exhibit a transition from a nonohmic to an ohmic conductivity which occurs close to the softening point of the polyelectrolyte layers.
I. Introduction Polyelectrolyte-surfactant complexes (PE-surfs) consisting of a charged polymer and oppositely charged surfactants form highly defined structures in the bulk.1-3 In the last years, it was shown that this building principle can be extended toward the complexation of bilayerforming lipids,4-9 thus combining the stack-of-bilayer structure of the lipid mesophases with the mechanical properties of the polyelectrolyte backbone. In a previous publication, we have described the formation and phase morphology of the complex between soybean lecithin and a cationic polyelectrolyte.10 This complex with its mixture of head groups and tail lengths exhibits, opposite to all one-component synthetic counterparts, a quite unconventional phase structure where the stack of lamellar bilayers undulates with very high amplitudes. In addition, a rubbery behavior of the X
Abstract published in Advance ACS Abstracts, August 1, 1996.
(1) Antonietti, M.; Conrad, J.; Thu¨nemann, A. Macromolecules 1994, 27, 6007. (2) Antonietti, M.; Conrad, J. Angew. Chem., Int. Ed. Engl. 1994, 33, 1869. (3) Antonietti, M.; Burger, C.; Effing, J. Adv. Mater. 1995, 7, 751. (4) Shimomura, M.; Kunitake, T. Polym. J. 1984, 16, 187. (5) Okahata, Y.; Taguchi, K.; Seki, T. J. Am. Chem. Soc. 1985, 107, 5300. (6) Okahata, Y.; Enna, G. J. Phys. Chem. 1988, 92, 4546. (7) Ishikawa, Y.; Kunitake, T. J. Am. Chem. Soc. 1991, 113, 621. (8) Higashi, N.; Kunitake, T.; Ringsdorf, H. Macromolecules 1987, 20, 29. (9) Tirrell, D. A.; Turek, A. B.; Wilkinson, D. A.; McIntosh, T. J. Macromolecules 1985, 18, 1512. (10) Antonietti, M.; Kaul, A.; Thu¨nemann, A. Langmuir 1995, 11, 2633.
S0743-7463(96)00221-1 CCC: $12.00
lecithine-complex film accompanied by the depression of the glass transition of the ionic layers to Tg ) 10 °C was observed. This combination of properties allowed largeamplitude deformations and mechanical orientation as well as thermomechanical processing of the complexes; consequently, we call these systems “plastic membranes”. By variation of the lipid composition, it was also possible to adjust new phase structures, such as the “egg-cartonphase”.11 In the present paper, we want to characterize the dynamic behavior of such polymer-supported membranes by means of dynamic mechanical shear experiments as well as with broad band dielectric spectroscopy. Especially from the latter we expect to learn about local relaxation processes, since the very different dielectric behavior of both microphases, ionic lamellae, and the bilayers formed by the lipid tails gives rise to rather strong dielectric effects, as seen for ion-containing polymer glasses12,13 or for the closely related PE-surfs.14 The aim of these experiments is to learn about the dynamics and some of the material properties of these highly ordered but simple-to-make mesomorphous materials. In addition, it is expected that these stack-ofbilayer systems might act as a 3D model for the rather two-dimensional polymer-supported membranes, which are regarded to be the most effective housing material created by nature. (11) Antonietti, M.; Wenzel, A.; Thu¨nemann, A. Langmuir 1996, 12, 2111. (12) Kremer, F.; Dominguez, L.; Meyer, W. H.; Wegner, G. Polymer 1989, 30, 2023. (13) Rietz, R. R.; Meyer, W. H. Polym. Adv. Technol. 1993, 4, 164. (14) Antonietti, M.; Andre, M.; Blum, G.; Kremer, F. In preparation.
© 1996 American Chemical Society
Relaxation in Polyelectrolyte-Supported Bilayer Stacks
II. Experimental Part II.1. Synthesis and Purification of PE-Lipid Complexes and Film Casting. As a synthetic model system, we chose the complex between poly(sodium acrylate) and didodecyldimethylammonium counterions (PAA-C122), since it shows no crystalline mesophases over the temperature range applied in the following measurements and therefore allows characterization of a liquid membrane system. Opposite to that, the “synthetic lipid” used in previous work, dihexadecyl phosphate, shows in the complexed state a melting transition at 84 °C.10 To model also a natural polymer-supported membrane as closely as possible, we took the recently described complexes made of soybean lecithine, where the natural mixture of phospholipids with its distribution of tails and head groups is taken as it is. The soybean lecithin mixtures were complexed with poly(diallyldimethylammonium chloride), PDADMAC, since it was shown in the earlier work that it combines good binding properties with an appropriate charge density (the length of a monomer unit is ca. 0.54 nm). For the synthetic procedure, we essentially followed the procedure already presented in our earlier paper.10 PDADMAC was made using a standard technique of a water-in-oil dispersion cyclopolymerization, initiated with AIBN.15 With this technique, as uncross-linked, linear polymer material in which the repeat unit mainly consists of a five-membered ring species is obtained. The molecular weight is checked by viscometry in a 0.5 mol/L NaCl salt solution and was determined to be on the order of Mw ) 76 000 g/mol. Polyacrylic acid, PAA, was purchased from Aldrich Co. A molecular weight of Mw ) 250 000 was given. Neutralization with NaOH was performed in 1% solutions. Didodecyldimethylammonium bromide (DDMA, 99%, Aldrich Co.) and oil-free soybean lecithin (Lipopur, from Lucas Meyer Co., 96%) were taken as the lipids. Lipopur is a mixture of 22% phosphatidylcholine, 23% phosphatidylethanolamine, 20% phosphatidylinositol, 10% phosphatidylserine, 5% free phosphatidic acid, 10% glycolipid, 6% carbohydrate, 3% triglycerides, and 1% water (information of the manufacturer). During the experiments, it turned out that some of the components of the commercial Lipopur deteriorate the sample handling during dielectric spectroscopy. For improving the quality of the spectra, Lipopur was extracted with ethanol, which gave rise to a much better relaxation curve but also changed the lipid composition. This has to be considered in the discussion of the dielectric data, where we have to expect a possible perturbation due to a changed lipid composition. For complexation, 2.0 g of the lecithin (DDMA) was dispersed in 50 mL of water to form a vesicular phase, and a 1% solution of PDADMAC (Na-PAA) was added dropwise with stirring until no further precipitation is obtained. The spontaneously formed crude complexes were separated and redissolved in THF. The complexes were purified by repeated precipitation from THF solutions in water until the water phase was practically free of Cl- ions, as tested with AgNO3 solution. Complexation between polyelectrolytes and lipids results in a balance which is about 1:1 with respect to the charged species, only. This was certified by weight uptake. For DDMA, the 1:1 complexation was rechecked with elementary analysis where sodium and bromide contents of less than 0.1% were stated. Therefore, the presence of sodium chloride as well as a surplus of unattached repeat units (by Na+) or DDMA (by Br-) could be excluded. For film casting, the redissolution of the solid complexes in THF was cast on a planar glass plate hydrophobically coated with octadecyltrichlorosilane. The two-dimensional geometry of the film was controlled with glass frames of variable size which were mounted on top of the glass plate. After slow evaporation of the solvent at 25 °C, the transparent films were easily removed with the frames and cut. Since the presented polyelectrolytelipid complexes are highly rubbery at room temperature, freezing is recommended for optimal sample handling. II.2. Small Angle X-ray Scattering (SAXS). All the SAXS curves were obtained with an Anton Paar compact Kratky camera with a Phillips PW1830 generator as the source of the Cu KR incident radiation. Monochromatization was accomplished using a nickel filter and pulse height discrimination. The measurements were perfored in an s-range of 1.0 × 10-2 nm- < s < 9.0 (15) Bartl, H.; Falbe, J. Huben-Weyl E20/II; Thieme: Stuttgart/New York, 1987, p 1027.
Langmuir, Vol. 12, No. 18, 1996 4437 × 10-1 nm-1 (the scattering vector s is defined as s ) 2/λ sin θ where 2θ is the angle between incident and scattered light. The data were corrected for parasitic scattering (max. 2% of the signal). The beam profile was measured without the detector slit and convoluted with the detector slit profile. The resulting slit length profile and the corrected data were used for desmearing using the method of generalized Laguerre orthogonal functions by Burger and Ruland.16 No slit width correction was performed because of the small width of the primary beam (integral width of 1 × 10-2 nm-1) compared to the width of the observed scattering peaks. II.3. Dynamic Mechanical Shear Experiments. To obtain an optimal precision in the whole range of moduli, the measurements below room temperature were performed with a transducer using a rectangular geometry, whereas for measurements in the lower moduli range, a plate/plate geometry was applied. For the plate/plate rheometer, the dried polyelectrolyte-lipid complexes were pressed to disks with a diameter of 13 mm and thicknesses of up to 2 mm; the rectangular stripes showed dimensions of 20 mm × 5 mm. A Rheometrics RMS 800 apparatus was used in an oscillating low-amplitude mode at a fixed frequency of 1 Hz, sweeping the temperature. The temperature sweep was chosen since it was not possible to apply frequency-temperature superposition in these complicated ordered materials, which is presumably due to the temperature dependent coupling between lipids and the polyelectrolyte. Additionally, it was checked that the deformations applied during the measurements are within the regime of linear response. Since ordering effects in such lyotropic materials (induced for instance by large-amplitude preshearing) significantly change the mechanical behavior, the sample was deformed as low as possible to maintain the macroscopically isotropic state. The measurements were controlled by a FRT2000 frequency response analyzer which also recorded the complex torque. A stream of dry nitrogen was blown over the sample in order to avoid thermal-oxidative damage during the measurements performed at 213-423 K. After heating the sample to the maximum temperature, the room temperature measurement was repeated to check for alterations. Only measurements are presented where no changes were observed. II.4. Dielectric Spectroscopy and Sample Preparation. For the dielectric measurements, the complex films were placed between two polished, gold-plated stainless steel electrode (diameter of 20 mm) that were pressed together by a micrometer screw. A spacing of 50 µm was maintained by use of two glass fibers inserted in the sample material. The dielectric measurements were carried out with a Solartron frequency response analyzer (FRA1260) with a Novocontrol dielectric interface, covering the frequency range from 10-4 to 107 Hz. Between 10-3 and 106 Hz, a resolution in the loss tangent tan δ < 10-3 is realized.17 The sample temperature was varied from 240 to 295 K with an accuracy better than 0.05 K using the nitrogen gas heating system in combination with a Novocontrol Quatro temperature controller. The sample temperature was measured by use of a Pt100 sensor, which was inserted in one of the condenser plates (accuracy of the temperature measurement: ∆T ) (0.01 K). The dielectric properties of the polyelectrolyte surfactant complexes are characterized by the superposition of a strong conductivity contribution and one or more dielectric relaxation processes. With decreasing frequency and increasing temperature the conductivity contribution dominates over the dielectric relaxation processes, which can be described using the generalized relaxation function of Havriliak and Negami:18
′′(ω) )
{
}
aσ0 -s S - ∞ ω + Im 0 ((1 + iωτ)R)γ
(1)
with S and ∞ the values of the real part of the dielectric function of the relaxation contribution for ωτ , 1 and ωτ . 1, respectively, with τ being the relaxation time. The dielectric strength ∆ is defined as ∆ ) S - ∞. The constants R and γ determine symmetric and assymmetric broadening of the relaxation time distribution. In the conductivity contribution σ0 describes the (16) Burger, C.; Ruland, W. Presented at the IXth International Meeting on Small Angle Scattering, Saclay, 1993. (17) Novocontrol Broadband Dielectric Converter, Owners Manual (1994). (18) Havriliak, S.; Negami, S. J. Polym. Sci. 1966, C14, 99.
4438 Langmuir, Vol. 12, No. 18, 1996
Figure 1. Smeared SAXS diffractogram of a PAA-C122 film; the scattering vector s is defined as s ) 2/λ sin θ, where 2θ is the angle between incident and scattered light. Inset: logarithmic presentation of the same set of data to enlarge the scattering peaks of higher order.
Figure 2. Isochronal mechanical relaxation of PAA-C122. The storage modulus G′, the loss modulus G′′, and the mechanical loss tan δ are plotted against temperature. direct current conductivity. The exponent s describes the character of the charge transport. The scaling exponent s reflects for s < 1 nonohmic charge transport and the influence of electrode polarization. The factor a has the dimension (s)1-s.
III. Results and Discussion III.1. PAA-C122. In the first part, the behavior of the “model lipid” didodecyldimethylammonium complexes with PAA is discussed. Figure 1 shows the result of small angle X-ray analysis of the film of PAA-C122. Already in the smeared state, we observe for a liquid system extremely narrow scattering peaks which can be indexed according to a lamellar superstructure up to the third order. A quantitative description of the curves with a stack mode according to J. J. Hermans19 results in a long period of d ) 3.18 nm and a correlation length exceeding 80 nm, which is about the limit which can be measured due to instrumental broadening of the peaks. In other words, the packing of the lamellae is very good. Since the length of the stretched surfactant tail is only 1.6 nm, we can assume a stackof-bilayer-like structure, in good agreement with density calculations and the geometry of DDMA. It must be stated that PAA-C122 can also exhibit an inverse hexagonal morphology, where the phase structure is triggered by minor amounts of impurities.20 Figure 2 shows the temperature sweep of the storage modulus G′, the loss modulus G′′, and the mechanical loss tan δ for PAA-C122 at the constant frequency ω ) 1 s-1. Starting from very low temperatures, we found a storage modulus of G′ ≈ 2 GPa, a typical value for glassy polymers. (19) Hermans, J. J. Recl. Trav. Chim. Pays-Bas 1944, 63, 211. (20) Neese, M. Diploma thesis, Marburg, 1995.
Antonietti et al.
As best seen by the two peaks in G′′, two β-relaxations are detected centered around -95 and -55 °C, which are attributed to increasing mobilities of the side chains. The nature of these phase transitions is still rather unclear but is not a subject of the present paper. At room temperature where the material behaves macroscopically as a rubber and can for instance be stretched by a factor of 10, the modulus is still very high: a G′ ≈ 200 MPa exceeds standard rubbers by not less than two orders of magnitude and lies in the region of high modulus thermoplastic elastomers or rubbers highly loaded with carbon black.21 Obviously, also for the model PE-lipid complex we take advantage of the microphaseseparated structure consisting of the hard ionic phase and the soft alkyl phase. In this region where the electrolyte chains seem to behave as “glassy”, tan δ is always on the order of tan δ ≈ 0.1. At about 293 K, a stepwise change of the moduli toward smaller values is observed, thus indicating an increased mobility of the polymer chains. Although the storage modulus constantly drops with temperature, it still significantly exceeds the values of standard rubbers up to temperatures of 373 K. This shows that the polymer chains are remarkably coupled via the lipid phase, which might be translated in some effective cross-linking density which is rather high. It was already stated in the Experimental Part that temperature-frequency superposition cannot be applied, since the moduli drop with temperature. Within the framework of the present discussion, this is explained by a decreasing coupling of the polyelectrolyte chains with the charged surface of the lipid layers; i.e., the temporary splitting of polyions and counterion becomes faster and faster. In the whole range, the mechanical loss is on the order of tan δ ≈ 0.5, whichsto our understandingssimply reflects the presence of the highly mobile alkyl tail phase, making up the majority of the volume and giving the coupled system a number of possibilities to dissipate energy. It is seen from the mechanical master curve that the material becomes finally fluid at 423 K. This is tenatively explained by the fact that the dynamic coupling between polyelectrolytes and tails becomes so fast that it does not hinder viscous flow. It must be stated that Taguchi et al.22 also examined the viscoelasticity of polyelectrolyte-lipid complexes of polystyrenesulfonate and diverse cationic two-tail surfactants, however, restricted to the low-temperature and high-modulus range. Although their described moduli were much lower, a similar drop of the storage modulus between the glassy and liquid states was described. This was attributed by the authors to the melting of the alkyl tails, whereas this explanation can be strictly excluded in our case. Dielectric relaxation shows a similarity rich behavoir. Figure 3a shows the different dielctric loss ′′(ω) in dependence of the frequency ω at different temperatures. At lower temperatures and higher frequencies, a rather pronounced β-relation process is found. The perfect description of the complete loss curve according to eq 1 with a conductivity contribution and a Havriliak-Negami type of relaxation is shown in Figure 3b. Fitting the whole set of loss curves, we find for the β-process a relaxation strength increasing with an Arrhenius-activated averaged relaxation rate. The latter temperature dependence is shown in the inset of Figure 3b. We end up with an apparent activation enery of 58 ( 1 kJ/mol, a value which is also typical for other polyelectrolyte-surfactant complexes. With the data of Figure 4, it is possible to relate (21) Ferry, J. D. Viscoelastic properties of polymers; Wiley: New York, 1980. (22) Taguchi, K.; Yano, S.; Hiratani, K.; Minoura, N.; Okahata, Y. Macromolecules 1988, 21, 3336.
Relaxation in Polyelectrolyte-Supported Bilayer Stacks
Langmuir, Vol. 12, No. 18, 1996 4439 Table 1. Numerical Fit Constants of the Temperature Dependent Dielectric Loss of PAA-C122 with the Data Fitted According to Eq 1 T/K
∆/
R
β
THN/s
Tmax/s
σ0/10-14 s cm-1
s
261.14 257.12 253.14 249.15 245.14 241.12 237.12 233.12 229.14 225.14 221.12 217.12
0.264 0.191 0.167 0.138 0.136 0.134 0.118 0.112 0.101 0.082 0.064 0.056
0.300 0.384 0.409 0.463 0.451 0.481 0.470 0.493 0.471 0.509 0.536 0.530
1.00 1.00 1.00 1.00 1.00 0.74 1.00 0.78 0.96 0.76 0.77 0.72
2.9 E -6a 7.3 E -6 0.00001 0.00002 0.00003 0.00008 0.00007 0.00018 0.00020 0.00051 0.00085 0.00171
2.9 E -6 7.3 E -6 0.00001 0.00002 0.00003 0.00005 0.00007 0.00011 0.00018 0.00030 0.00054 0.00094
4.978 2.663 1.470 0.819 0.522 0.357 0.253 0.200 0.165 0.153 0.149 0.149
0.498 0.450 0.416 0.357 0.335 0.298 0.255 0.215 0.187 0.133 0.105 0.102
a
Figure 3. (a) Dielectric loss ′′ of PAA-C122 plotted versus frequency for different temperatures; temperatures are indicated within the plot. (b) Dielectric loss spectra of PAA-C122 at 225 and 245 K with the corresponding numerical fits. For each fit curve the single contributions of conductivity and a relaxation process are also shown. Fit parameters for 245 K: ∆ ) 0.136, R ) 0.451, β ) 1, τ ) 30 µs, σ0 ) 5.23 pS/m, s ) 0.335. Fit parameters for 225 K: ∆ ) 0.082, R ) 0.509, β ) 0.756, τ ) 0.51 ms, σ0 ) 1.53 pS/m, s ) 0.335. The inset shows the activation behavior of the relaxation process. The activation energy calculated from the fit is Ea ) 58 kJ/mol.
Figure 4. Temperature dependence of the conductivity σ0 (solid circles, left axis) and the conductivity exponent s (open circles, right axis) for PAA-C122.
the dielectric β-process to one of the mechanic β-processes. Extrapolating the data to 1 Hz, we obtain a temperature of Tβ(max.,1Hz) ≈ 190 K; i.e., dielectric relaxation is presumably related to the second β-relaxation at lower temperatures, where presumably the side chains start to move. A relaxation strength which increases with temperature underlines that the number of dielectric active species is raised with temperature, i.e., more molecules start to move. The resulting fit parameters describing the dielectric relaxation curves for all temperatures are numerically summarized in Table 1. As seen in Figure 3, the relaxation curves at higher temperatures and frequencies are dominated by a conductivity contribution, the exponent of which changes with
Read as 2.9 × 10-6.
temperature. The temperature dependence of the fitted dc conductivity and the conductivity exponent is shown in Figure 4. It is seen that σ0 is constantly increasing with temperature and reaches a value of σ0 ≈ 10-11 S/cm at T ) 293 K, the temperature which was attributed to the glass transition of the ionic phase by mechanical relaxation. This glass transition is invisible in the conductivity curve, since it is passed without changing the slope. Interestingly, the glass transition becomes visible in the thermal behavior of the conductivity exponent s. In Figure 4, it is shown that s goes from s ) 0.5 at 260 K to s ) 1 at 290 K. This is classically described as a transition from nonohmic to an ohmic charge transport.23,24 One might analyze that ohmic charge transport by ion hopping requires an increased mobility of the polyelectrolyte; otherwise, a transport of the small counterions produces a strong polarization of the material which stays unrelaxed and influences the charge transport in the observed frequency dependent way. The same characteristic behavior was already observed for internally plasticized polyelectrolyte surfactant complexes very close to the glass transition of the ionic phase20,25 and for ion-containing polysoaps.26 It is concluded that both mechanic and dielectric relaxation allow a localization of the softening point of the ionic phase in PAA-C122 close to 290 K, where the presence of strong β-relaxations in both experiments as well as the absolute height of the storage modulus proves the presence of a liquid-like alkyl phase which is mobile down to 173 K. III.2. PDADMAC-Lecithin. This copolymer is similar to the previous system. Since we had to “purify” the lecithin mixture for the dielectric experiments by extraction with ethanol, the structure of the complex of PDADMAC with lecithin is rechecked. The resulting SAXS diffractogram is shown in Figure 5. As judged by the width of the primary scattering peak and the absence of higher order reflections, this complex is far less ordered than its synthetic counterpart. The quantitative data valuation results in a longer period of d ) 4.84 nm, a thickness of the ionic phase of d1 ) 2.17 nm and of the alkyl phase of d2 ) 2.67 nm, and an averaged surface roughness of A/A0 ) 1.12. The interface between the ionic and alkyl phase is rather sharp, i.e. below 0.1 nm. For all details regarding the quantitative evaluation of the X-ray data, the interested reader is referred to our earlier publication.10 A comparison with the soybean lecithin (23) Boettger, H.; Bryskin, U. V. Hopping Conductivity in Solids; Akademie Verlag: Berlin, 1986. (24) Kremer, F.; Ru¨he, J.; Meyer, W. H. Makromol. Chem., Macromol. Symp. 1990, 37, 115. (25) Antonietti, M.; Maskos, M.; Blum, G.; Kremer, F. Acta Polymer, accepted. (26) Rozanski, S. A.; Kremer, F.; Ko¨berle, P.; Laschewsky, A. Macromol. Chem. Phys. 1995, 196, 877.
4440 Langmuir, Vol. 12, No. 18, 1996
Antonietti et al.
Figure 5. Smeared SAXS diffractogram of the PDADMACLec film; for the definition of s, see Figure 1. Inset: logarithmic presentation of the same set of data.
Figure 6. Isochronal mechanical relaxation of PDADMACLec. The storage modulus G′, the loss modulus G′′, and the mechanical loss tan δ are plotted against temperature.
prior to the ethanol treatment shows that the long period has increased by ca. 1 nm and that the surface roughness has significantly decreased. Obviously, we have interfered with the natural lecithin composition, and all further conclusions have to be seen in light of this restriction. The temperature sweep of the dynamic mechanical properties is shown in Figure 6. Starting from low temperatures, we observe that the relaxation curves already exhibit a storage modulus of G′ ≈ 200 MPa. In addition, there is no marked structure of the mechanical relaxation in this range, such as a β-peak. This simply reflects the facts that the mobility in the alkyl layer had already set in at the lowest temperature of our measuring range and that this mobility is significantly higher in the natural lipid system as compared to the synthetic twotail surfactant. It is assumed that this is due to a more flexible suspension of the alkyl tails by the bridging glycerol unit of the natural lipids. At about 290 K, a broad maximum of tan δ appears, related to a stepwise decrease of the moduli which is caused by the softening of the ionic layers. The softening is comparable low; that is, the drop of G′ only amounts to one order of magnitude. In other words, the polyelectrolyte chains get mobile, but the increase in mobility is rather restricted, far less than that of a linear polymer chain in a homogeneous environment. At about 313 K, the storage modulus levels off, and a value of G′ ≈ 1 MPa is obtained. In this temperaure region, PDADMAC-Lec is more elastic, shows a lower tan δ, and is less temperature sensitive than its synthetic counterpart, PAA-C122. Above 383 K, the material starts to decompose, which has to be expected for a material based upon natural lipids. The dielectric relaxtion experiments are summarized in Figure 7a, which shows the frequency and temperature dependence of the dielectric loss of PDADMAC-Lec.
Figure 7. (a) Dielectric loss ′′ of PDADMAC-Lec plotted versus frequency for different temperatures. (b) Temperature dependence of the β-relaxation processes in PDADMAC-Lec. The estimation of the mean relaxation times for the faster process (open circle) is inflicted with rather large errors, which are indicated by the error bars. The activation energy for the slower process is found to be Ea ) 53 kJ/mol.
Again, all curves are perfectly described by the sum of a conductivity contribution and a Havriliak-Negami-type relaxation; at the lowest temperaures, even a second relaxation mechanism showed up. As in the case of the synthetic model system, only the averaged relaxation rate but not its strength is Arrhenius activated. The temperature dependence of the averaged relaxation rate is shown in Figure 7b; for the slower process, the data base is good enough to obtain an activation energy of Ea ) 53 ( 1 kJ/mol. It must be underlined that both the absolute rate and the activation behavior are very similar to those of the β-process of the synthetic model system. Table 2 recapitulates the numerical parameters of the fitting procedure of this data set. The resulting temperature dependence of the dc conductivity as well as of the conductivity exponent s is shown in Figure 8. A very similar increase of the dc conductivity with temperature as compared to the case of PAA-C122 is observed. Again, the conductivity change are not related to the structural glass transition. The conductivity exponent s changes from s ) 0.17 to its limiting value s ≈ 1 at about 280 K. This temperature again compares well with the calorimetric glass transition centered at Tg ) 281 K, as determined with DSC.10 At this temperature, the conductivity is on the order of σ0 ≈ 10-11 s/cm, which goes well with the behavior of PAA-C122. A value of s ) 0.17 indicates that the charge transport in PDADMAC-Lec is even more restricted by polarization effects at the inner surfaces. With increasing mobility of the polyelectrolyte chains, the polarization effects vanish in a typical sigmoidal curve, and again ohmic conductivity is obtained. IV. Discussion and Outlook The synthetic and natural polyelectrolyte-supported bilayer morphologies, PAA-C1222 and PDADMAC-Lec,
Relaxation in Polyelectrolyte-Supported Bilayer Stacks Table 2. Numerical Fit Constants of the Temperature Dependent Dielectric Loss of PDADMAS-Lec with the Data Fitted According to Eq 1 T/K
∆/
R
β
THN/s
Tmax/s
261.11 257.11 253.14 249.14 245.11 241.14 237.14 233.13 229.14 225.14 221.14 217.14 213.15 209.14 205.14 201.14 197.14 193.14 189.14
1.729 1.587 1.419 1.243 1.249 1.204 1.103 0.9954 0.9793 0.929 0.894 0.872 0.874 0.793 0.761 0.628 0.627 0.566 0.519
0.299 0.292 0.296 0.302 0.281 0.315 0.303 0.312 0.300 0.285 0.282 0.282 0.261 0.287 0.280 0.314 0.304 0.372 0.399
Process 1 0.780 0.814 0.865 0.985 1.000 0.679 0.824 0.869 0.874 1.000 0.994 1.000 0.918 0.875 0.871 0.998 0.996 0.708 0.678
3.2 E -5a 3.7 E -5 3.99 E -5 4.09 E -5 5.38 E -5 0.00026 0.00023 0.00029 0.00057 0.00054 0.00092 0.00151 0.00372 0.00813 0.01647 0.02188 0.02931 0.18920 0.32870
1.4 E -5 1.9 E -5 2.5 E -5 3.9 E -5 5.4 E -5 7.9 E -5 1.2 E -4 1.8 E -4 3.7 E -4 5.4 E -4 9.1 E -4 15.1 E -4 2.7 E -3 5.1 E -3 1.0 E -2 2.1 E -2 2.9 E -1 7.7 E -2 1.3 E -1
205.14 201.14 197.14 193.14 189.14 185.14 181.14
0.245 0.382 0.509 0.293 0.610 0.519 0.425
0.497 0.369 0.290 0.248 0.233 0.264 0.303
Process 2 1.000 1.000 1.000 1.000 1.000 1.000 1.000
1.142 E -6 1.146 E -6 1.172 E -6 1.548 E -6 1.756 E -6 3.091 E -6 6.972 E -6
1.142 E -6 1.146 E -6 1.172 E -6 1.548 E -6 1.756 E -6 3.091 E -6 6.972 E -6
a
Read as 3.2 × 10-5.
Figure 8. Temperature dependence of the conductivity σ0 (solid circle, left axis) and the conductivity exponent s (open circle, right axis) for PDAMAC-Lec.
show remarkable similarities in the mechanical as well as in the dielectric relaxation experiments. Since the chemistry involved in the different structures is rather different, the found properties are regarded to be typical for all these mesomorphous, stack-of-bilayer-type structures. Both systems show at temperatures above softening of the side chains and below the Tg of the ionic layers a rather high modulus which is for PAA-C122 on the order of 200 MPa and for PDADMAC-Lec 20 MPa. This is worth mentioning, since these systems are in the same range highly deformable and behave as a high performance rubber or a filled thermoplastic elastomer. The “thermoplastic range” is much larger for the natural lipid system, since the mobility sets in already at very low temperatures. This was tentatively explained by the increased local mobility of the phospholipid tails as compared to the simple surfactant system which is enabled by the additional glycerol spacer. Above the softening, the materials behave mechanically rather differently: PAA-C122 shows an extraordinarily high modulus well above the one of typical rubbers which
Langmuir, Vol. 12, No. 18, 1996 4441
decreases with temperature. This is explained by a coupling of the different polyelectrolyte chains via the mesophase structure, the strength of which is decreasing with temperature. At 423 K, the complex behaves in a fluid-like manner, which means that the exchange processes occur faster than the polymer mobility. PDADMAC-Lec exhibits a lower modulus and a behavior which is more the one of a standard rubber. Obviously, the coupling between the lipids and/or polyelectrolytes is larger for the natural system. Elastic behavior is maintained until decomposition of the complex, which occurs at 383 K. It must be underlined that only part of the charged lipids of the soybean lecithine are expected to bind strongly to the polyelectrolyte backbone, as shown by the stoichiometry of the complex. With broad band dielectric spectroscopy, we found for both systems very similar looking β-relaxation processes, which exhibit very similar absolute rates, widths, and temperature dependencies. Since the underlying molecular phenomena have to be dielectric active and occur well below plastization of the ionic polymer layer, we attribute these relaxations to mobility of the grafted surfactant chains. At frequencies below the β-relaxation, a continuous buildup of an electric conductivity contribution is observed. Within the layered structure which consists of glassy polyelectrolytes and mobile surfactant molecules, each surfactant migration leaves a polarization of the internal surfaces behind; consequently, a highly nonohmic charge flow as expressed by a low conductance exponent s is observed. Within our frame of description, s becomes smaller when the mobility differences between the ionic polyelectrolyte layer and the lipid layer become larger. This goes well with the observation that the polymer complex with the more mobile natural lipid mixture exhibits at low temperatures s ) 0.17, whereas the more rigid synthetic system shows in the same temperature range s ) 0.5. Approaching the glass transition of the ionic layers, this effect levels off, and ohmic conductivity (s ) 1) is recovered. The temperature where s reaches 1 goes very well with a glass transition observed in the DSC experiment and a stepwise decrease of the moduli at this temperature seen in the mechanical relaxation. These high-performance material properties clearly stay for themselves, but one might speculate if some of the characteristics of the presented three-dimensional volume systems can really be used to model the more important case of the two-dimensional, polymer-supported cell membranes. A direct comparison is undoubtedly prevented by neglect of the influence of water, which is omnipresent in the biomembrane but practically excluded in our 3D system. We expect a shift of the glass transition of the ionic layers toward smaller temperatures, which means that the biologically relevant behavior is not the reinforced elastic one but the rubber-like one. For more definite answers related to this topic, further mechanical experiments on water swollen samples, but also involving biological polyelectrolytes as the supporting polymers, are certainly required. Acknowledgment. We thank T. Pakula for his help with the mechanical relaxation experiments and C. Burger for everything related to the X-rays. Financial support by the Max Planck Society is gratefully acknowledged. F.K. wants to thank the German Science Foundation for financial support within the framework of the SFB 294. LA960221B
