Langmuir 1996, 12, 6315-6319
6315
Extensional Flow in Two-Dimensional Amphiphilic Networks Peter Fischer*,† and Dietmar Go¨ritz‡ Department of Chemical Engineering, Stanford University, Stanford, California 94305-5025, and Universita¨ t Regensburg, Institut fu¨ r Experimentelle und Angewandte Physik, Universita¨ tsstraβe 31, 93053 Regensburg, Germany Received July 8, 1996. In Final Form: October 18, 1996X A systematic investigation on the extensional flow properties of two polymerized amphiphilic monolayers is discussed. To perform those experiments a new method is developed that allows a direct rheological investigation by using a modified film balance device.
Introduction A method is developed to directly investigate extensional flow in two-dimensional amphiphilic networks at the air/ water interface. This method gives the advantage that the sensible network would not be destroyed or modified during preparation before the rheological investigation or transportation. Further, a clear defined rheological geometry gives the advantage of easy interpretation of data. The preparation of networks and the rheological investigation take place in the same device and therefore allowed a direct investigation of the extensional flow properties in monolayers. In comparison to the slightly similar Wilhelmy methods, there is a clear defined direction of flow and no mixture of extensional and shear flow.1,2 This investigation was performed using amphiphilic monolayers from N-lysyl-lysineoctadecylamide trihydrobromide (Dilysin) and N-L-lysyl-N-L-lysyllysinedocosylester tetrahydrobromide (Trilysin). Both systems show a structural breakdown by slight mechanical stresses. In combination with electron microscopy and ellipsometry results, we proposed a glassy film with Hookeian flow properties.3-5
Figure 1. Schematic drawing of the Langmuir film balance including the compression barrier, floating barrier, measuring compartment, and reference compartment. The dimensions of the device are 15 cm wide (A) and 50 cm in lenght (B).
tigated amphiphiles. According to eq 1 this difference of surface tensions is equal to the surface pressure
π ) γ - γ*
(1)
* To whom correspondence should be addressed. E-mail:
[email protected]. † Stanford University. ‡ Universita ¨ t Regensburg. X Abstract published in Advance ACS Abstracts, December 15, 1996.
where γ is the surface tension of a clear surface and γ* is the surface tension of the covered surface. An extensive description of the statistical thermodynamics of liquid surfaces is given by several authors.7,8 To obtain phase diagrams π(A) of two-dimensional films, one spreads the amphiphilic molecules at the air/water interface on a Langmuir film balance between two barriers. In Figure 1 the film balance device is schematically shown. Here the surface pressure π is detected as an isothermic function of the surface area A. The compression barrier now reduces the accessible surface area A while the floating barrier measures the surface pressure. Due to the difference in the surface tension in the measurement compartment γ* and the surface tension in the reference compartment γ, one obtains the surface pressure of the film as a function of surface area A. When the accessible surface area in the measurement compartment is reduced, the amphiphilic molecules are force through several phase transitions. Analogous to three-dimensional phases, one observes a gas state phase, a liquid state phase, and two solid state phases.7-10 Rheology. Rheology is the science of flow and deformation of matter. To state the observed properties,
(1) Halperin, K.; Ketterson, J. B.; Dutta, P. Langmuir 1989, 5, 161. (2) Cardenas-Valera, A. E.; Bailey, A. I. Colloids Surf. A 1993, 79, 115. (3) Lucassen, J.; Akamatsu, S.; Rondelez, F. J. Colloid Interface Sci. 1991, 144, 434. (4) Pauchard, L.; Meunier, J. Phys. Rev. Let. 1993, 70, 3565. (5) Fereshtehkhou, S.; Neumann, R. D.; Ovalle, R. J. Colloid Interface Sci. 1986, 109, 385. (6) Langmuir, I. J. Am. Chem. Soc. 1917, 39, 1848.
(7) Birdi, K. S. Lipid and Biopolymere Monolayer at Liquid Interfaces; Plenum Press: New York, 1989. (8) Chattoraj, D. K.; Birdi, K. S. Adsorption and the Gibbs Surface Excess; Plenum Press: New York, 1984. (9) Meunier, J.; Langevin, D.; Boccara, B. Physics of Amphiphilic Layers; Springer-Verlag: Berlin, 1987; Vol. 21. (10) Roberts, G. Langmuir-Blodgett Films; Plenum Press: New York, 1990.
Theory Langmuir-Blodgett Films. Surface-active molecules at liquid interfaces possess a dual character, i.e. a hydrophilic and a hydrophobic part, and are therefore called amphiphiles. Due to this molecular design, one obtains a lower free energy when the amphiphiles are adsorbed at an interface than when it is within the aqueous bulk phase.6 As a consequence, these amphiphiles are changing the surface tension of the surface. The oldest method to determine the surface tension is to compare the surface tension of a clear aqueous surface with the surface tension of a covered surface. The difference between both values is given as surface pressure and allows us to determine the surface activity of the inves-
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Fischer and Go¨ ritz
Figure 2. Schematic drawing of the total stress tensor τ.
Figure 4. Schematic drawing of the floating barrier in different states. In the first picture the barrier is shown in the zero position without any forces. In the second picture the barrier is shown with a spreaded monlayer in the measuring compartment, and in the last picture the barrier is shown in the elongation modulus.
free flow as shown in eq 5
(
τxx 0 0 t ) 0 τyy 0 0 0 τzz
Figure 3. Schematic drawing of the elongation in planar elongation flow. The original shape of the body was a cube where all dimensions were one. The elongation flow is along the z-axis.
rheological constitutive equations are introduced which are based upon the correlation among shear stress, shear rate, and the intrinsic parameters and functions of the investigated material. The most simple constitutive equations are those proposed by Hooke and Newton. These linear equations are defined by the linear relationship between shear stress and shear rate or deformation, and they are limited to the ideally elastic solid or Newtonian liquid. The correlation coefficient is defined as viscosity and elasticity. In extensional flow experiments one may detect elastic, viscous, and rubberlike properties. The Hookeian model describes the elastic properties by
τ ) E(λ - 1)
(2)
where τ is the stress, E is the elastic modulus, and λ is the elongation. In extensional flow experiments one detects the stress τ in the sample as a function of deformation λ. The elongation is defined as
λ)
l l0
(3)
where l is the actual length and l0 is the length before elongation.11 The Newtonian model describes the viscous properties as shown in eq 4
τ ) ηλ˙
(4)
where η is the viscosity and λ˙ is the rate of elongation. The stress τ is derived from the total stress tensor τ in shear (11) Vanderlick, T. K.; Mo¨hwald, H. J. Phys. Chem. 1990, 94, 886.
)
(5)
with τij as components of stress. The total stress tensor is shown in Figure 2. Simple shear-free flows are given by the velocity field
vx ) -
1 dλ (1 + B)x 2 dt
(6)
vy ) -
1 dλ (1 - B)y 2 dt
(7)
vz )
dλ z dt
(8)
In planar elongation flow, i.e. sheet stretching, one proposes B ) 1 and therefore obtains for eq 6 a more simple form
vx ) -
dλ x dt
(9)
while eq 7 vanished and eq 8 remains unaffected.12,13 In Figure 3 a planar elongation flow experiment is schematically shown. For simplification purposes we propose that two-dimensional films do not have a third dimension. Therefore we neglect this component of the deformation and stress tensor and use the nontensorial notation in eqs 2 and 4. Because eq 8 is, apart from the sign, equal to eq 9, it is only necessary to measure the mechanical stress in one of these directions. In our case the stress is in the direction of positive elongation τzz. Method The Lauda film balance LW 1 has approximately the dimensions of 15 cm wide and 50 cm in length, as shown in Figure 1. A linear force transducer detects the difference between both surface tensions as mentioned in eq 1. The applied force is detected by a linear leaf spring that moves a magnet in a coil. (12) Bird, R. B.; Armstrong, R. C.; Hassager, O. Dynamic of Polymer Liquids: Fluid Mechanics; John Wiley & Sons: New York, 1987. (13) Macosko, C. W. RheologysPrinciples, Measurements, and Applications; VCH Publisher: New York, 1994.
Extensional Flow in 2D Amphiphilic Networks
Langmuir, Vol. 12, No. 26, 1996 6317
Figure 5. Schematic drawing of the modified barrier construction. Figure 8. Elongation experiment of Dilysin. The twodimensional elongation stress τ is plotted as a function of elongation λ (T ) 5.2 °C).
Figure 6. Phase diagram of Dilysin; the surface pressure π is plotted as function of surface area A (T ) 4.6 °C; the length of the compression barrier is 12 cm).
Figure 9. Elongation experiment of a full established Trilysin network. The two-dimensional elongation stress τ is plotted as function of elongation λ (T ) 5.3°C).
Figure 7. Phase diagram of Trilysin; the surface pressure π is plotted as function of surface area A (T ) 3.6 °C; the length of the compression barrier is 12 cm). The obtained electrical current is proportional to the applied force as long as the linear regime of the leaf spring is not exceeded. On the other hand, the transducer can also detect stresses from elongation, or in other words, negative surface pressure. The elongation is performed by stretching the chemical cross-linked film on the air/water interface in the measurement compartment. Due to the chemical reaction mentioned in the next section, the film is stabilized in shape. Therefore one measures just the rheological properties and not the reverse phase diagram during the stretching. To emphasize this method, in Figure 4 the different positions of the measurement barrier and the force transducer are shown. Without amphiphilic molecules in the measurement compartment, the barrier is in the center, with amphiphilic molecules spread, the barrier is pushed to the left, and, while elongated, the barrier is pulled to the right. In elongation measurements one could neglect the surface tension and can define the detected surface pressure as a zero point for elongation stress. To obtain suitable results, keep in mind that only complete cross-linked networks are measurable and that the film has to be attached to both barriers. Therefore small modifications are necessary to use the film balance for elongation
Figure 10. Elongation experiment of more or less established (45% up to 90%) Trilysin networks. The two-dimensional elongation stress τ is plotted as function of elongation λ (T ) 5.2 °C). purposes to ensure proper adhesion to the barrier. Due to the inefficient attachment of the network to the original barriers, we designed slightly modified devices. First, the barriers were not more covered with Teflon, and second, there are tilt sides, as shown in Figure 5. As a consequence the film is strongly attached
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Figure 11. Electron micrograph of a fully established Trilysin network. The network is indicated by the bright areas, while the dark spots and areas are failures. to the modified barrier and the stretching experiments could be performed. To ensure that the film is not attached to the side walls, the film balances are totally made out of Teflon. Further, the cross-linked reaction is stopped by a special hood device near the side walls.
Materials Two amphiphilic molecules are used to perform the following investigation. The first sample is N-L-lysylL-lysineoctadecylamide trihydrobromide (Dilysin), which contains two single lysine groups and one C18H37 carbon chain, as shown in eq 10. The second sample is N-L(10)
lysyl-N-L-lysyl-L-lysinedocosylester tetrahydrobromide (Trilysin), which is designed from three lysine groups and one C22H45 carbon chain, as shown in eq 11. As subphase for Dilysin and Trilysin we used an alkaline NaHCO3 solution with pH 8.4. (11)
To establish a monolayer, the amphiphilic molecules are spread in the gas phase on the whole measurement compartment of the film balance. The surface pressure in this state should not exceed 0.5 mN/m. By reducing the accessible surface the film is transferred into the solid state. The phase diagram π(A) for Dilysin is shown in Figure 6, and that for Trilysin, in Figure 7. The chemically initiated network formation is performed by constant surface pressure from 28.0 to 38.0 mN/m for Dilysin and from 28.0 to 35.0 mN/m for Trilysin. Both monolayers clearly show the solid state phase in the mentioned regime of surface pressure. The network formation is performed
by the attached functional groups NH3+Br-.14 These groups are first protonized by the alkaline subphase and afterward react with some phosgene (COCl2). Dilysin has three attached functional groups and therefore may build up two-dimensional chain molecules but no networks with a permanent character. Trilysin has four functional groups and therefore may build up chemical networks. As a function of reaction time, one obtains fully or partly cross-linked networks. In our investigation we used Trilysin films with approximately 45%, 60%, 85%, 90%, and 100% established networks. The percentage of the established film is controlled by the reaction time and tested by previous flow measurements.14 During the network formation the surface area per molecule is reduced by 20%. Keeping a constant surface pressure during the chemical reaction, one maintains a homogeneous network. Results and Discussion Dilysin. The stress increases and reaches a plateau value after a certain elongation. A breakdown follows, indicated by a sudden decrease of the stress, as shown in Figure 8. Due to the amount of reaction groups in the head group, one can obtain chainlike macromolecules but no network formation. Therefore one observes just a short region of viscoelastic properties denoted by the plateau. A final glide off of the chains is shown in the breakdown of stress. Trilysin. The elongation flow experiment of fully established Trilysin film is shown in Figure 9. With a strong increase of stress τ as function of elongation λ, after an elongation of 5%, one detects a structural breakdown of the system denoted by a sudden decrease of stress. Trilysin is building up a tetrafunctional network structure with a Hookeian flow characteristic. In contrast we compile in Figure 10 the results of elongation experiments with partly established Trilysin (14) Kulzer, M. Diploma Thesis, Universta¨t Regensburg, 1986.
Extensional Flow in 2D Amphiphilic Networks
films. A strong correlation between the network quality and the maximal stress is observable. Further one obtains with increasing quality a steeper slope of all curves. Here the surface pressure of single amphiphilic molecules becomes an increasingly important contribution to stress. As a consequence, the stress does not decrease to zero after the structural breakdown but to a constant value equal to the surface pressure. The amphiphilic molecules cover more and more the mechanical properties of the remaining network. Nevertheless these networks show a similar behavior as compared to that of the fully established film. A Hookeian behavior is observable, and a strong correlation between the quality of the networks and the mechanical stress is shown. An inhomogeneous monolayer assembly during the preparation and during the phase transitions is not taken into account. It turns out that for proper investigations these effects cannot be neglected and therefore the lysine monolayers are not very suitable for establishing twodimensional networks. This effect is not unique to lysine monolayers as discussed here because it is seen in several other monolayer systems. An electron micrograph of Trilysin is shown in Figure 11. It emphasizes our difficulties in establishing a homogeneous network without failures and large regions of discontinuity. The formation of several islands is also
Langmuir, Vol. 12, No. 26, 1996 6319
shown in ellipsometric measurements performed on Trilysin.15 Conclusion Two amphiphilic monolayers are established in a film balance device and transformed into a permanent chemical network. On this network we performed elongation flow experiments by using the film balance as a rheological stretching device. Both investigated two-dimensional films show clear positive resonance with this newly developed method. The films show Hookeian flow properties and not rubberlike properties, as one might expect. Due to the large inhomogenious regions in the network, it turns out that lysine monolayers are not very suitable for establishing two-dimensional networks. Acknowledgment. The authors thank Klaus Heckmann for the sample material and for using the film balance device and Edgar Duschl for the preparation of the electron micrographs. We are indebted to Carlton F. Brooks for reading the manuscript. P.F. acknowledges the “Deutsche Forschungsgemeinschaft” (Fi 665/1-1), which gave us the opportunity to finish this work. LA960668K (15) Stuhlfellner, F. Diploma Thesis, Universita¨t Regensburg, 1991.
