Langmuir 2004, 20, 2977-2978
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Initial Spreading Dynamics of Supported Lipid Monolayers T. D. Blake* and J. De Coninck Center for Research in Molecular Modelling, Materia NovasUniversity of Mons Hainaut, Parc Initialis, Av. Copernic 1, 7000 Mons, Belgium Received December 17, 2003. In Final Form: January 22, 2004
In a recent paper,1 Baumgart and Offenha¨user describe the lateral spreading of substrate-supported lipid monolayers as a function of ambient humidity. LangmuirBlodgett monolayers of phospholipids were deposited onto thin, water-swellable polysaccharide films, and the influence of substrate, humidity, and lateral deposition pressure on the spreading dynamics was investigated. In particular, it was observed that the spreading front remained sharp and that initial spreading rates were a nonlinear function of deposition pressure. Figure 1 shows the results obtained for DMPC (1,2-dimyristoyl-sn-glycero3-phosphatidylcholine) monolayers on a thin film of chitosan on glass at two different humidities, 85% and 90%, respectively. As can be seen, the slope of the graph increases monotonically. Such nonlinear behavior is in contrast to that observed for the spreading of lipids on mesoscopically thin films of water,2 where it is supposed that the force opposing spreading is simply the hydrodynamic (viscous) dissipation within the underlying water film. Baumgart and Offenha¨user modeled the spreading behavior on the polysaccharide films by balancing viscous friction at the monolayer/substrate interface by the gain in surface free energy, effectively balancing frictional dissipation by a Marangoni surface-tension force. For spreading over small distances, this gave a constant spreading velocity, as observed experimentally, rather than the square root of time (t1/2) dependence found for lipid bilayers spreading from a reservoir.2 Spreading velocities were observed over distances that were less than 90 µm, i.e., much smaller than the lateral dimensions of the monolayers. It is therefore possible that t1/2 dependence might still be found at long times. The influence of humidity was accounted for through its effect on the friction. An explanation advanced for the nonlinear dependence of spreading velocity on deposition pressure was that the friction varied with monolayer density. But, as Baumgart and Offenha¨user also pointed out, the selfdiffusion coefficient for the monolayer is expected to increase with decreasing monolayer density (i.e., with decreasing film pressure), which is not consistent with the data of Figure 1. Another suggested mechanism was that the coupling between the monolayer and the substrate was dependent on the deposition pressure through its effect on protrusion forces. Here, we propose a complementary explanation based upon the molecular-kinetic theory of dynamic wetting,3,4 * To whom correspondence should be addressed. Tel: +32 (0)65 37 38 80. Fax: +32 (0)65 37 38 81. E-mail: terrydblake@ btinternet.com,
[email protected]. (1) Baumgart, T.; Offenha¨user, A. Langmuir 2002, 18, 5899. (2) He, S.; Ketterson, J. B. Philos. Mag. B 1998, 77, 831. (3) Blake, T. D.; Haynes, J. M. J. Colloid Interface Sci. 1969, 30, 421.
Figure 1. Spreading velocities of DMPC monolayers at different deposition pressures at 85% and 90% RH. The data are from ref 1. The lines were obtained by fitting eq 3 simultaneously to both data sets.
which is itself an extension of the classical Frenkel-Eyring model of liquid flow as a stress-modified molecular rate process. This approach leads directly to the nonlinear dependence, as required. The molecular-kinetic theory of dynamic wetting was first put forward some 35 years ago. Since then it has proved useful in explaining wetting behavior in a range of experimental systems,4 but it is only recently that molecular dynamics simulations have shown that the underlying ideas have a fundamental validity.5 According to the theory, the dynamics of wetting depend on the collective statistics of the individual molecular displacements that occur within the three-phase zone, the microscopic region where the fluid/fluid interface meets the solid surface. The key parameters are κ0 and λ, the natural frequency and average distance of each displacement, respectively. In the simplest case, λ is supposed to be the distance between adsorption sites on the solid surface. Assuming a uniform distribution of such sites, the number per unit area is 1/λ2. In the partial wetting case, the driving force for the wetting line to move is taken to be the uncompensated surface tension force that arises when mechanical equilibrium is disturbed. The physical manifestation of this disturbance is the change in the contact angle from its equilibrium value θ0 > 0 to some dynamic value θD. The resulting equation for the wettingline velocity is then
v ) 2κ0λ sinh[γLV(cos θ0 - cos θD)λ2/2kBT]
(1)
where γLV is the surface tension of the liquid and kB and T are the Boltzmann constant and temperature, respectively. In a recent publication6 we pointed out that for a completely wetting liquid (θ0 ) 0), the driving force for wetting γLV(cos θ0 - cos θD) should be augmented by the surface pressure of the liquid at the solid/vapor interface, πL,SV. This is the same surface pressure that gives rise to (4) Blake, T. D. In Wettability; Berg, J. C., Ed.; Marcel Dekker: New York, 1993; p 251. (5) de Ruijter, M. J.; Blake, T. D.; De Coninck, J. Langmuir 1999, 15, 7836. (6) Blake, T. D.; De Coninck, J. Adv. Colloid Interface Sci. 2002, 96, 21.
10.1021/la036386j CCC: $27.50 © 2004 American Chemical Society Published on Web 02/20/2004
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Langmuir, Vol. 20, No. 7, 2004
Notes
Table 1. Parameters Obtained by Fitting Equation 3 to the Data of Figure 1 % RH 85 90
κ0/s 3.0 14.9
λ/cm
D ) κ0λ2/cm2 s-1
10-8
7.8 × 7.8 × 10-8
1.8 × 10-14 8.9 × 10-14
the precursor film by which such liquids spread.7 Thus, eq 1 becomes
[( )
v ) 2κ0λ sinh
λ2 (γ (1 - cos θD) + πL,SV) 2kBT LV
]
(2)
For a Langmuir-Blodgett monolayer, such as those described by Baumgart and Offenha¨user, the natural driving force for spreading would appear to be simply the lateral surface pressure at which the layer was confined during deposition, πLB. Given that the leading edge of the DMPC film remains sharp, we can assume two-dimensional liquidlike behavior. Therefore, if such a film were allowed to spread from confinement at this pressure, we might anticipate that the initial kinetics of its leading edge would be described by the same equations as for a bulk liquid, but now written as
v ) 2κ0λ sinh[πLBλ2/2kBT]
(3)
This simple expression predicts a nonlinear relationship between v and πLB that is logarithmic for sufficiently large πLB, becoming linear only when πLB is small. Evidently, the data obtained by Baumgart and Offenha¨user offer us a unique opportunity to test this relationship. In fact, as shown in Figure 1, the agreement is very good. Thus, we are able to fit the data for both 85% and 90% relative humidity (RH) using a common value for λ and a value of κ0 that is dependent on the humidity, being smaller (indicating slower kinetics) when the humidity is lower. The values obtained for κ0 and λ are shown in Table 1. The value of λ seems reasonable, being of molecular size and equivalent to a site area A ) λ2 of about 60 Å2, which is close to the mean cross-sectional area of DMPC over the range of deposition pressures investigated.1 However, we also expect λ to be strongly influenced by the molecular structure of the substrate across which the monolayer spreads; hence the rational for holding λ constant during the fitting procedure, rather than using values obtained directly from the DMPC πLB/A isotherm. The values of κ0 are more intriguing. They are low compared with those reported in the literature for dynamic wetting of simple liquids on solids4 but not necessarily unreasonable given the fact that the layers spread only very slowly (
