pubs.acs.org/Langmuir © 2010 American Chemical Society
Molecular Weight Dependence of Surface Dilatational Moduli of Poly(n-hexyl isocyanate) Films Spread at the Air-Water Interface Takako Morioka,*,†,‡ Osamu Shibata,† and Masami Kawaguchi‡ †
Department of Biophysical Chemistry, Faculty of Pharmaceutical Sciences, Nagasaki International University, 2825-7 Huis Ten Bosch, Sasebo, Nagasaki 859-3298, Japan, and ‡Division of Chemistry for Materials, Graduate School of Engineering, Mie University 1577 Kurimamachiya, Tsu, Mie 514-8507, Japan Received June 11, 2010. Revised Manuscript Received July 15, 2010
The surface dilatational modulus of the monolayer of a well-known semiflexible polymer, poly(n-hexyl isocyanate) (PHIC), at the air-water interface was measured as a function of the molecular weight of PHIC. In the dilute regime, the surface dilatational modulus of PHIC showed a linear response over a measured strain range of 5%-20%. The modulus could be well-separated into the elastic component E0 and the viscous component E00 , irrespective of molecular weight of PHIC. The E0 and E00 components, respectively, are mainly attributed to static compression modulus caused by a change in the area covered by the PHIC monolayer and the semiflexibility of the PHIC chain. In the semidilute regime, the surface dilatational modulus of PHIC showed a nonlinear response to even 1% of strain due to the semiflexibility of the PHIC chain. Moreover, the surface dilatational modulus of PHIC depended on its molecular weight: at the smaller strain, the surface dilatational modulus of the high molecular weight PHIC was larger than that of the low molecular weight PHIC. The surface dilatational modulus of the high molecular weight PHIC increased with the surface concentration, whereas that of the low molecular weight PHIC remained constant. The molecular weight dependence in the semidilute regime is caused by the difference in chain entanglement between the high and low molecular weight PHICs at the air-water interface.
Introduction Poly(n-hexyl isocyanate) (PHIC) is known as a helical semiflexible polymer whose solution properties and liquid crystalline properties in bulk solutions have been carefully investigated for more than 40 years.1-3 The peptide-like structure of PHIC has attracted considerable interest of the biochemical and technological industries. Recently, the electrical properties of the solid state of PHIC have also been studied, and its potential use in a new electrical device has been proposed.4 On the other hand, the interfacial properties of PHIC films spread at the air-water interface have been studied by Kawaguchi and his co-workers.5-8 They investigated the interfacial properties through a combination of surface pressure isotherm measurements, fluorescence microscopy, and atomic force microscopy (AFM). From the combination of surface pressure isotherm measurements and fluorescence microscopy, they confirmed that PHIC formed a condensed-type film at the air-water interface because of the cohesive interaction between hexyl side chains, and the PHIC film changed from a monolayer to a multilayer with a decrease in the surface area.5 An AFM study of a Langmuir-Blodgett (LB) film of PHIC provided evidence of the formation of a bilayer from a monolayer.6 The stability of the PHIC monolayer was confirmed *To whom correspondence should be addressed. E-mail: morioka@ niu.ac.jp.
(1) Norisuye, T. Prog. Polym. Sci. 1993, 18, 543–584. (2) Rubingh, D. N.; Yu, H. Macromolecules 1976, 9, 681–685. (3) Sato, T.; Teramoto, A. Adv. Polym. Sci. 1996, 126, 85–161. (4) Sugita, A.; Yamashita, Y.; Tanaka, S. J. Polym. Sci., Part B: Polym. Phys. 2005, 43, 3093–3099. (5) Kawaguchi, M.; Yamamoto, M.; Kurauchi, N.; Kato, T. Langmuir 1999, 15, 1388–1391. (6) Kawaguchi, M.; Suzuki, S.; Yamamoto, M.; Ishokawa, R.; Kato, T. Kor. Polym. J. 1999, 7, 277–282. (7) Kawaguchi, M.; Ishikawa, R.; Yamamoto, M.; Kuki, T.; Kato, T. Lngmuir 2001, 17, 384–387. (8) Kawaguchi, M.; Suzuki, M. J. Colloid Interface Sci. 2005, 288, 548–552.
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by the compression and expansion cycles of surface pressure in the monolayer region.5 Among the compression and expansion cycles between the monolayer and multilayer regions, the surface pressure showed negative hysteresis, and the simultaneous observation of fluorescence microscopy images revealed the breakdown of solidlike fractures of PHIC domains in the uniform texture. These findings indicated that PHIC formed an extremely hard film at the air-water interface.5 In addition, our exploratory surface pressure relaxation experiment during a step compression revealed a nonequilibrium in the surface pressure isotherm of PHIC. Therefore, in order to perform quantitative surface rheological measurements on PHIC as a function of its molecular weight, an adequate surface pressure relaxation time after compressing the PHIC film at the air-water interface should be allowed before the measurements are carried out. Surface rheological measurement is important for understanding the viscoelastic property of a PHIC film at the air-water interface. Surface rheological properties consist of compression and in-plane (lateral) and/or out-of-plane (vertical) shear. Measuring the surface dilatational modulus is one of the most powerful surface rheological methods. However, the measurable frequency range in oscillatory barrier compression method is smaller than other surface rheological methods such as pendant drop, capillary pressure, and surface light scattering. The surface dilatational modulus can be measured by a simple surface pressure apparatus: when a sinusoidal oscillatory dilatational strain is imposed on a spread film, the response of surface pressure is recorded and then the surface dilatational modulus is calculated. Since a sinusoidal strain is imposed, a complex surface dilatational modulus is obtained. If a linear relationship is confirmed between the strain and the detected surface pressure, a complex surface dilatational modulus can be separated into elastic and viscous components (or storage modulus and loss modulus). In recent years, surface dilatational modulus measurement has been
Published on Web 07/28/2010
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applied to a variety of simple synthetic polymers,9-12 surfactants,13,14 and proteins.15-18 In particular, surface rheological properties of various flexible polymers as a function of the solvent quality have been investigated (e.g., poly(vinyl acetate) under good solvent conditions19,20 and poly(4-hydroxystyrene), poly(octadecyl acrylate), and poly(vinyl stearate) under poor solvent conditions).9,11 Good and poor solvent conditions for polymer films spread at the air-water interface can be classified into expanded- and condensed-type films, respectively, from the shape of the surface pressure-area isotherm. According to Hilles et al.,11 the surface dilatational modulus of polymer films under poor solvent conditions showed that the maximum strain of the linear response region of surface pressure was less than 3%, beyond which the response were nonlinear. As mentioned above, although the surface dilatational modulus of flexible polymers has been investigated, that of semiflexible polymers has not been examined. In this study, we focus on the molecular weight dependence of the surface dilatational modulus of PHIC films in the monolayer region. To quantitatively treat the surface dilatational modulus, a sufficient surface pressure relaxation time after spreading the PHIC film should be allowed before the surface dilatational modulus is measured.
Experimental Section Materials. A PHIC sample was synthesized by polymerizing hexyl isocyanate in dimethylformamide with NaCN dispersed in dimethylformamide as the initiator.2,5 The resulting PHIC sample was diluted with toluene, purified by dropwise precipitation in a large amount of methanol, and dried under vacuum. The PHIC sample was separated into eleven fractions in a toluene-methanol mixture. We chose two fractionated samples designated as PHIC41 and PHIC-245; their weight average molecular weights (Mw) were determined to be Mw = 41 103 and 245 103, respectively. From a characterization of PHIC in dilute solution based on the wormlike chain model23 (persistence length Lp = 43 nm, molar mass per unit counter length ML =730 nm-1, and cylinder diameter d = 1.8 nm), the PHIC-41 chain length of 56 nm is slightly longer than the persistence length, 43 nm, and the PHIC245 chain length of 336 nm is considerably longer than the persistence length. The solvent used to prepare PHIC solutions was chloroform (Nacalai Tesque, spectrum grade). The concentration of the spreading solution was 0.5 mg mL-1. A time interval of 15-30 min was allowed to elapse for solvent evaporation before performing the surface pressure measurements. (9) Monroy, F.; Ortega, F.; Rubio, R. G.; Ritacco, H.; Langevin, D. Phys. Rev. Lett. 2005, 29, 056103. (10) Hilles, H.; Monroy, F.; Bonales, L. J.; Ortega, F.; Rubio, R. G. Adv. Colloid Interface Sci. 2006, 122, 67–77. (11) Hilles, H.; Maestro, A.; Monroy, F.; Ortega, F.; Rubio, R. G.; Velarde, M. G. J. Chem. Phys. 2007, 126, 124904. (12) Monroy, F.; Ortega, F.; Rubio, R. G.; Velarde, M. G. Adv. Colloid Interface Sci. 2007, 134 - 135, 175–189. (13) Patino, J. M. R.; Sanchez, C. C.; Ni~no, M. R. R.; Fernandez, M. C. Langmuir 2001, 17, 4003–4013. (14) Erni, P.; Fischer, P.; Windhab, E. J. Langmuir 2005, 21, 10555–10563. (15) Petkov, J. T.; Gurkov, T. D. Langmuir 2000, 16, 3703–3711. (16) Freer, E. M.; Yim, K. S.; Fuller, G. G.; Radke, C. J. J. Phys. Chem. B 2004, 108, 3835–3844. (17) Freer, E. M.; Yim, K. S.; Fuller, G. G.; Radke, C. J. Langmuir 2004, 20, 10159–10167. (18) Cicuta, P.; Terentjev, E. M. The Eur. Phys. J. E 2005, 16, 147–158. (19) Monroy, F.; Ortega, F.; Rubio, R. G. Phys. Rev. E 1998, 58, 7629–7641. (20) Monroy, F.; Hilles, H. M.; Ortega, F.; Rubio, R. G. Phys. Rev. Lett. 2003, 91, 268302. (21) Biegajski, J. E.; Burzynski, R.; Cadenhead, D. A.; Prasad, P. N. Macromolecules 1986, 19, 2457–2459. (22) Biegajski, J. E.; Burzynski, R.; Cadenhead, D. A.; Prasad, P. N. Macromolecules 1990, 23, 816–823. (23) Norisuye, T.; Tsuboi, A.; Teramoto, A. Polym. J. 1996, 28, 357–361.
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Surface Pressure Measurements. The surface pressure was recorded at 298.2 ( 0.1 K for all measurements. The surface pressure isotherm was determined by using an automated custommade Wilhelmy system. The surface pressure balance (AG245, Mettler Toledo, Switzerland) had a resolution of 0.01 mN m-1. The surface pressure balance system was equipped with a filter paper (Whatman 541, periphery length=4.0 cm). The trough was made from Teflon-coated brass (area=720 cm2), and a Teflonmade barrier was used. The areas were compressed at a barrier speed of 20 mm min-1. Reproducibility was confirmed at least 3 times, and the surface pressures coincided within 1%. In order to check the transition points more precisely, the surface potential was recorded with an electrometer (Keithley 6517, Keithley Instruments Inc.), whereas the monolayer was simultaneously compressed at the air-water interface. It was monitored with an ionizing 241Am electrode 1-2 mm above the interface while a reference electrode was dipped in the subphase. Surface pressure relaxation measurements were carried out with a KSV minitrough (KSV Instruments Ltd., Finland). The measurements were carried out 15 min after the PHIC solution was spread at the interface, in order to allow the solvent to evaporate. The PHIC film was then continuously compressed at a rate of 5 mm min-1. Surface dilatational measurements were also performed with a KSV minitrough. The surface dilatational measurements were carried out soon after the surface pressure relaxation measurements were performed. Two barriers were mounted on both ends of the trough in this system to allow the study of oscillating barriers. Oscillatory barrier experiments at a given frequency ω were carried out with sinusoidal oscillatory strain u given by eq 1. u ¼ u0 sin ωt
ð1Þ
where u0 is the sinusoidal oscillatory strain amplitude. When strain is imposed on a film spread at the air-water interface, the surface pressure response can be expressed as π ¼ π0 sinðωt þ δÞ
ð2Þ
where the π0 is surface pressure amplitude and δ is the phase delay of the surface pressure response due to the viscous component of the monolayer. Therefore, the complex surface dilatational modulus (E*) is defined as E ¼ ðπ0 =u0 Þeiδ ¼ jE jeiδ ¼ E 0 þ E 00
ð3Þ
where E0 and E00 are the elastic and viscous components of the dilatational modulus, respectively. It is possible to separate E0 and E00 within the linear response region of the function relating the surface pressure and imposed strain. When the surface pressure response is nonlinear, the apparent surface dilatational modulus |E*|app is defined by eq 4. jE japp ¼ Δπ=A0
ð4Þ
where Δπ is the difference between the maximum and the minimum surface pressures against an imposed strain and A0 is the surface area at strain 0. The linear response of the surface pressure against the imposed strain is confirmed by the shape of the Lissajous orbit of the former against the latter. The value of A0 and the frequency were fixed at 89 cm2 and 20 mHz, respectively, and the barrier speed c was conventionally changed (u0 = c/ω) in this study. Moreover, the surface dilatational modulus was estimated from the first cycle of the sinusoidal strain. To check the reproducibility, respective measurements was repeated at least twice for every strain in the dilute regime. On the other hand, the surface pressure response against strain was stable in semidilute regime and the error of surface dilatational modulus was less than 4 mN m-1. DOI: 10.1021/la1023983
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Figure 1. Surface pressure-area (π-A) and surface potentialarea (ΔV-A) isotherms for PHIC-41 and PHIC-245 films. BAM images were captured at areas of a and b for PHIC-41 and c-e for PHIC-245, respectively.
Brewster Angle Microscopy (BAM) Measurements. The PHIC films spread at the air-water interface were directly visualized by a Brewster angle microscope (KSV Optrel BAM 300, KSVInstruments Ltd., Finland) coupled to the KSV minitrough. The application of a 20 mW He-Ne laser emitting p-polarized light of 632.8 nm wavelength and a 10 objective lens allowed a lateral resolution of ∼2 μm. The angle of the incident beam to the air-water interface was fixed at the Brewster angle (53.1°) at 298.2 K. The reflected beam was recorded with a high-grade CCD camera (EHDkamPro02, EHD Imaging GmbH, Germany), and the BAM images were then digitally saved to the computer hard disk. In order to check the lateral homogeneity of the PHIC, especially in the vicinity of the barrier, the trough was moved to different location. The intensity of the reflected beam at the Brewster angle was estimated from the histogram of BAM image by using ImageJ (National Institute of Health). The net intensity of the reflected beam from PHIC film on water should be provided by subtracting the intensity of the reflected beam from only water as back ground from the intensity of the reflected beam from PHIC film on water.
Results and Discussions Surface Pressure Isotherms. Figure 1 shows surface pressure-area (π-A) and surface potential-area (ΔV-A) isotherms for PHIC-41 and PHIC-245 at the air-water interface. Both samples show typical condensed-type isotherms, as we have previously reported.5 The respective π-A isotherms show the same trend in that zero surface pressure zones are observed at larger areas, and that surface pressure increases with decreasing area to reach a plateau region beyond which it increases monotonically. Isotherms with this kind of shape have usually been observed for several polypeptides in the R-helix state and for rigid rod polymers.21,22 In the π-A isotherm, the area obtained by extrapolating the straight-line portion of the first steep rising zone to zero surface pressure can be defined as the extrapolated area Aex in this study. An overlapping surface concentration of Γ* (mg m-2) in the two-dimensional polymer film spread at the airwater interface is related to the Aex value as follows: Γ ¼ 1=Aex 14060 DOI: 10.1021/la1023983
ð5Þ
The resultant Aex values for PHIC-41 and PHIC-245 are 0.25 and 0.23 nm2 repeating unit-1, respectively. The repeating unit means the monomer unit of polymer. The molecular weight of the repeating unit of PHIC is M = 127.18. The values of Γ* for PHIC41 and PHIC-245 are then determined as 0.84 and 0.93 mg m-2, respectively. According to the solution properties of PHIC,23 the area occupied by a segmental unit Aseg is estimated to be 0.28 nm2 repeating unit-1, assuming that a wormlike cylindrical PHIC molecule lies on the water surface and this value is larger than the Aex value for both PHIC samples. That the Aex values are smaller than the Aseg value could be explained by the chain entanglement effect of PHIC at the air-water interface. As reported in our previous study,7 the Aex value, the plateau region range, and the surface pressure at the plateau region were significantly dependent on the molecular weight of PHIC. The lower the molecular weight, the larger the extrapolated area, the wider the plateau region range, and the lower the surface pressure in the plateau region. These results are attributed to the degree of chain entanglement of PHIC chains at the air-water interface. Thus, it can be expected that entanglement would be extremely difficult for PHIC-41 chains because the counter length is smaller than the Kuhn segment length of PHIC (which is twice as large as the persistence length of PHIC). A jump of ΔV was observed in the ΔV-A isotherm for both PHIC-41 and PHIC-245. The appearance of such a jump is known to be an indicator of a condensed-type film; this result is also an evidence of the fact that PHIC films spread at the air-water interface behave as a condensed-type film. The jump in the ΔV-A isotherm for PHIC-245 was detected at ∼0.5 nm2 repeating unit-1 as seen in Figure 1, and that for PHIC-41 was detected at ∼1 nm2 repeating unit-1. Moreover, an inflection point in the ΔV-A isotherm could indicate any kind of phase transition. The inflection point in the ΔV-A isotherm for PHIC41and for PHIC-245 coincides with the inflection point at the plateau region in the π-A isotherm for corresponding PHICs. Therefore, the transition area from monolayer to multilayer is clearly confirmed by a combination of the π-A and ΔV-A isotherms for PHIC. In addition, the formation of multilayer from monolayer can be confirmed by means of analyzing the intensity of the reflection beam of BAM images. (It is assumed that a linear relation between the film thickness and the square root of intensity of the reflected beam at the Brewster angle if the film is homogeneous and isotropic.) From the BAM images analysis, it was confirmed that the square root of intensity became at an overlapping surface concentration of Γ* was 1.6 times as low as that at 2Γ*; the intensities at Γ* and 2Γ* for PHIC-41 were 7 ( 3 and 11 ( 3, respectively, whereas the corresponding intensities for PHIC-245 were 7 ( 4 and 11 ( 4. That the square root of intensity at Γ* was not twice as low as that at 2G* should means that PHIC have some roughness at the air-water interface. Therefore, the higher surface pressure in the plateau region for PHIC-245 than that for PHIC-41 can be attributed to less cohesive interaction between PHIC in multilayer region for PHIC-245 than for PHIC-41. Surface Pressure Relaxation. In the dilute regime (Γ < Γ*), surface pressure relaxation of the PHIC monolayer could not be detected since it occurred too rapidly. In the semidilute regime (Γ>Γ*), the surface pressure relaxation of PHIC was observed as expected. The relaxation curves of the poly(vinyl acetate) monolayer under good solvent conditions20 were well-fitted with a single exponential curve (eq 6) with relaxation time τ, whereas those of the poly(vinyl stearate) monolayer under poor solvent Langmuir 2010, 26(17), 14058–14063
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Figure 2. Typical surface pressure relaxation curve for PHIC-245 in semidilute regime at Γ = 1.0 mg m-2. The curve can be fitted by an equation of π = 0.66e-t/3.0 þ 0.65e-t/36 þ 0.53.
Figure 4. BAM images at (a) 0.42 mg m-2 for PHIC-41, (b) 0.89 mg m-2 for PHIC-41, (c, e) 0.42 mg m-2 for PHIC-245, and (d) 1.0 mg m-2 for PHIC-245. The corresponding areas of a-e are indicated by arrows in Figure 1.
Figure 3. Plots of the short relaxation time τ1 (filled symbols) and long relaxation time τ2 (open symbols) as a function of surface concentration for PHIC-41 (circles) and PHIC-245 (squares).
conditions were well-fitted with a double exponential curve.11 πðtÞ ¼
X
e - t=τ
ð6Þ
Figure 2 shows the typical relaxation curve for PHIC-245 at Γ = 1.0 mg m-2. It can be fitted by a double exponential curve with an accuracy of R2 >0.99, which is far better than that of a single exponential fit. Figure 3 shows relaxation times for PHIC41 and PHIC-245 as a function of the surface concentration in the semidilute regime. Short and long relaxation times are denoted by τ1 and τ2, respectively. For both samples, the long relaxation time τ2 appears to decrease exponentially with an increase in surface concentration. This dependence of the long relaxation time on the surface concentration is opposite to that observed for poly(vinyl acetate) (PVAc) film under good solvent conditions. Under such conditions, the relaxation time of the PVAc film increased exponentially with an increase in surface concentration,20 suggesting that such dependence is caused by the entanglement of PVAc chains in the PVAc film. Since PHIC films can be regarded as condensed matter at the air-water interface, they can be assumed to be two-dimensional glass materials. Thus, the surface pressure relaxation of PHIC films might be explained by the concept of osmotic pressure for a percolating network of 2D-soft spheres.9 This concept has been validated experimentally with a Langmuir film of the condensed coiled polymer, poly(4-hydroxystyrene).9 A characteristic of a percolation network is that the relaxation time decreases exponentially with an increase in surface concentration at concentrations above the percolation threshold, where collective diffusion is prevented and interfacial energy Langmuir 2010, 26(17), 14058–14063
becomes the main actor in the relaxation scenario. Thus, the higher the interfacial energy stored as a consequence of compression, the faster the relaxation of the arrangement. In addition, assuming the diffusion of a hard sphere with a size of ca.10 μm, the relaxation time can be easily estimated from the Stokes-Einstein relationship ΔT = kBT/6πηRF and τ ∼ RF2/ΔT ∼ 3600 s.12 The assumed domain size is considerably larger than the isolated size of a PHIC chain, so the resulting relaxation time τ2 does not correspond to that of chain diffusion. Rather, the relaxation time should coincide with the reorientation time associated with the deformation of inhomogeneous fractured domains formed with PHIC chains. On the other hand, the short relaxation time τ1 is largely independent of the surface concentration, irrespective of the molecular mass of PHIC. The diffusion domain size can be estimated to be ca. 4 μm by the Stokes-Einstein relationship mentioned above. Since this size is still significantly larger than the size of PHIC polymer chains, the relaxation time τ1 might relate to a certain kind of inner structure consisting of the fracture of PHIC chains. The constant value of τ1 suggests that the inner structure of the fracture is not deformed by the compression pressure in the semidilute regime. Figure 4a-e shows the preliminary BAM images for PHIC41at 0.42 mg m-2, PHIC-41 at 0.89 mg m-2, PHIC-245 at 0.42 mg m-2, PHIC-245 at 1.0 mg m-2, and PHIC-245 at 0.42 mg m-2, respectively. The areas of a-e where the BAM images were captured are indicated in Figure 1. Moreover, it was confirmed that the BAM images did not change during relaxation time by means of capturing the BAM images each 15 min from zero relaxation time to 60 min in dilute regime and to 180 min in semidilute regime. The presence of inhomogeneous PHIC structures can be confirmed in the dilute regime (Figure 4a,c). As previously reported, such structures in PHIC films can be related to the relatively strong cohesive interaction between the hexyl groups in PHIC.5,7 The area occupied by the inhomogeneous structures increases with an increase in surface concentration and the domain size increases with an increase in surface concentration and finally make a almost uniform domain as shown in Figure 4b, DOI: 10.1021/la1023983
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Figure 6. Static compression modulus (Es) of PHIC-41 (filled circles) and PHIC-245 (filled squares) as a function of surface concentration.
Figure 5. (a) Plots of surface dilatational moduli of PHIC-41 (circles) and PHIC-245 (squares) in dilute regime of 0.42 mg m-2 as a function of strain: E0 (filled symbols) and E00 (open symbols). Lissajous orbits at 0.42 mg m-2 for (b) PHIC-41 at strain of 8% and (c) PHIC-245 at strain of 10%.
d. Therefore, it can be expected that the PHIC film in the semidilute regime is easily deformed by the compression pressure, after which a relatively long time is required to relax the deformation. Although the domain size in Figure 4a was the same as in Figure 4c, unexpected larger domains than the domains seen in Figure 4a,c were partially observed for PHIC-245 as shown in Figure 4e, suggesting that PHIC chains easily gather together to form a larger domain at the air-water interface for PHIC-245 than for PHIC-41, consistent with previous fluorescence microscopic observations.7 However, such a dependence of the domain size on molecular weight is hardly explored by the surface pressure relaxation measurements mentioned above. Surface Dilatational Rheology. The surface dilatational moduli of PHIC-41 and PHIC-245 were measured in the dilute regime of 0.42 mg m-2. A relaxation time of 30 min was allowed before measuring the surface dilatational modulus since no surface pressure relaxation was observed in dilute regime. Figure 5a shows the surface dilatational moduli of PHIC-41 and PHIC-245 in the dilute regime as a function of the sinusoidal oscillatory strain. Because the surface pressure responses of PIHC films become linear throughout the applied dilatational strain region of 5-20%, the surface dilatational moduli can be well separated into the E0 and E00 components. The E0 is larger than E00 , indicating a predominantly elastic dilatational response even in the dilute regime, irrespective of the molecular weight of PHIC. As shown in Figure 5b,c, the linear responses of surface pressure for the respective PHIC samples are confirmed by the symmetrical shapes of the Lissajous orbits of the surface pressure against the strain A A0-1. On the other hand, the static compression modulus Es can be estimated from eq 7 ð7Þ E s ¼ - AðDπ=DAÞT Figure 6 shows the values of Es as a function of surface concentration for the two PHIC samples. The Es values were 14062 DOI: 10.1021/la1023983
Figure 7. Plots of surface pressure of π90 after relaxation time of 90 min for PHIC-41 (filled circles) and PHIC-245 (filled squares) as a function of surface concentration in semidilute regime.
estimated from the π-A isotherms shown in Figure1. Although the Es values in the dilute regime contain some errors due to experimental uncertainties, Es and E0 are on the same order of the magnitude. This result indicates that E0 is mainly attributable to the static compression modulus caused by changes in the area covered by the PHIC monolayer. Therefore, the E00 component might originate from the rigidity of PHIC chain. From Figure 5a, E0 for PHIC-41 is slightly larger than that of PHIC-245. Since the domain size of PHIC-245 captured by BAM is partially larger than for PHIC-41, the difference of E0 between PHIC-41 and PHIC-245 can come from the difference of the domain size. In the semidilute regime, surface pressure relaxation was clearly observed as discussed above. Therefore, 90 min of surface pressure relaxation time was allowed before measuring the surface dilatational modulus. We assumed that the PHIC film attained an apparent equilibrium state during this relaxation time because the reduction rate of surface pressure at the end of 90 min was less than 0.1 mN m-1 per 30 min. Figure 7 shows the surface pressure values of π90 for PHIC-41 and PHIC-245 after a relaxation time of 90 min. The π90 value is independent of the molecular weight of PHIC and its magnitude is almost constant in the semidilute regime. Such an independence of π90 on surface concentration and molecular weight means that the static modulus caused by changes in the area covered by the PHIC film is negligible. Figure 8a shows the surface dilatational moduli at 0.89 mg m-2 for PHIC-41 and at 1.0 mg m-2 for PHIC-245 as a function of the dilatational strain. These values are considerably larger than those in the dilute regime and are roughly of the same magnitude as those for some other polymer monolayers.11,12,20 Since nonlinear responses of surface pressure were observed even at a strain of 1%, it might be more suitable to employ the apparent surface pressure modulus |E*|app. The strong nonlinear responses of Langmuir 2010, 26(17), 14058–14063
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Figure 9. Apparent surface dilatational modulus (|E*|app) of PHIC-41 (filled circles) and PHIC-245 (filled squares) as a function of surface concentration.
strain, attains a maximum value of ∼30 mN m-1 at strains of ∼3%, and then drastically decreases with strain. Figure 8b-e shows the Lissajous orbits of surface pressure against strain A A0-1 for PHIC-41 at strains of 3%, 5%, 10%, and 15%, respectively. Figure 8f-h shows the Lissajous orbits of surface pressure against strain A A0-1 for PHIC-245 at strains of 3%, 5%, and 10%, respectively. The resulting Lissajous orbits exhibit positive hysteresis loops at strains less than 5%, whereas at the strains larger than 10% they show negative hysteresis loops for two PHIC samples. The maximum value of |E*|app for PHIC-245 is larger than that for PHIC-41 indicating that the PHIC-245 film is denser and harder than the PHIC-41 film at the air-water interface. The value of |E*|app is smaller than the Es value indicating that the π-A isotherm for PHIC is in the nonequilibrium state, as mentioned in the introduction. Figure 9 shows the maximum value of |E*|app as a function of the surface concentration of PHIC. If chain entanglement is effective, the maximum value of |E*|app should increase with the surface concentration.20 The maximum value of |E*|app for PHIC-41 exhibits constancy in the semidilute regime. This surface concentration independence of the maximum value of |E*|app indicates the extremely weak chain entanglement of PHIC-41 at the air-water interface. On the other hand, the maximum value of |E*|app for PHIC-245 increases with the surface concentration despite the narrow range of concentrations and the plot can be fitted with a power law of |E*| µ Γ4.6. This dependence of the maximum value of |E*|app on the surface concentration provides evidence that sufficient entanglement of PHIC-245 chains occurs at the air-water interface.
Conclusions
Figure 8. (a) Plots of apparent surface dilatational modulus (|E*|app) at 0.89 mg m-2 for PHIC-41(filled circles) and at 1.0 mg m-2 for PHIC-245 (filled squares) as a function of strain. Lissajous orbits at 0.89 mg m-2 for PHIC-41 at strains of (b) 3%, (c) 5%, (d) 10%, and (e) 15% and those at 1.0 mg m-2 for PHIC-245 at strains of (f) 3%, (g) 5%, and (h) 10%.
surface pressure should be attributed to the semiflexibility of PHIC chains. In contrast, for condensed-type monolayers of flexible polymers, linear responses were obtained within strains of a few percentages.11 Moreover, it should be noticed that the |E*|app value in the semidilute regime is dependent on the molecular weight of PHIC: the |E*|app value for PHIC-41 gradually increases with strain, attains a maximum value of ∼10 mN m-1 at strains of 5-10%, and then gradually decreases with strain. On the other hand, the |E*|app value for PHIC-245 increases with Langmuir 2010, 26(17), 14058–14063
The surface dilatational modulus of a PHIC monolayer at the air-water interface after an adequate surface pressure relaxation time was measured as a function of the molecular weight of PHIC. The surface dilatational modulus in the dilute regime showed a linear response at the measured strain range of 5-20%, irrespective of the molecular weight of PHIC. On the other hand, the surface dilatational modulus in the semidilute regime showed a nonlinear response even at a 1% strain due to the semiflexibility of PHIC chains. Further, the modulus was dependent on the molecular weight of PHIC: the surface dilatational modulus of PHIC-245 showed a larger maximum value of |E*|app at a smaller strain, indicating that PHIC-245 formed a dense and hard monolayer at the air-water interface, as compared to the PHIC-41. Moreover, the maximum value of |E*|app for PHIC245 increased with surface concentration, whereas that for PHIC41 remained constant. Such a dependence on surface concentration was attributed to the stronger chain entanglement effect in PHIC-245 than in PHIC-41 at the air-water interface. DOI: 10.1021/la1023983
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