Dilatational and shear rheology of soluble and insoluble monolayers with a Langmuir trough

Abstract

Hypothesis: The surface dilatational and shear moduli of surfactant and protein interfacial layers can be derived from surface pressures measured with a Wilhelmy plate parallel, ΔΠ_par and perpendicular ΔΠ_perp to the barriers in a Langmuir trough.

Experimental: Applying area oscillations, A₀+ ΔAe^iωt, in a rectangular Langmuir trough induces changes in surface pressure, ΔΠ_par and ΔΠ_perp for monolayers of soluble palmitoyl-lysophosphatidylcholine (LysoPC), insoluble dipalmitoylphosphatidylcholine (DPPC), and the protein β-lactoglobulin to evaluate E^s∗+G^s∗=A₀ΔΠ_parΔA and E^s∗-G^s∗=A₀ΔΠ_perpΔA. G^s∗ was independently measured with a double-wall ring apparatus (DWR) and E^s∗ by area oscillations of hemispherical bubbles in a capillary pressure microtensiometer (CPM) and the results were compared to the trough measurements.

Findings: For LysoPC and DPPC, A₀ΔΠ_parΔA≅A₀ΔΠ_perpΔA meaning E^s∗≫G^s∗ and E^s∗≅A₀ΔΠ_parΔA≅A₀ΔΠ_perpΔA. Trough values for E^s∗ were quantitatively similar to CPM when corrected for interfacial curvature. DWR showed G^∗ was 4 orders of magnitude smaller than E^s∗ for both LysoPC and DPPC. For β-lactoglobulin films, A₀ΔΠ_parΔA>A₀ΔΠ_perpΔA and E^s∗ and G^s∗ were in qualitative agreement with independent CPM and DWR measurements. For β-lactoglobulin, both E^s∗ and G^s∗ varied with film age and history on the trough, suggesting the evolution of the protein structure.

Keywords: DPPC; Dilatational modulus; Interfacial dilatational rheology; Interfacial rheology; Interfacial shear rheology; Lysolipids; Phospholipids; Soluble surfactant; β-lactoglobulin.

Figure 1.

A 2-D shape deformation at constant area, A₀, is pure shear. An area change from A₀ to A₀ ± ΔA at constant shape is pure dilatation. A general deformation is a combination of these two. Designing experiments to probe the individual shear and dilatational moduli requires creating imposed shape deformations at constant area (shear) or constant imposed area deformations at constant shape (dilatation).

Figure 2.

Schematic diagram of a Langmuir trough with two suspended Wilhelmy plates to measure the surface pressure parallel, Δ∏_par, and perpendicular, Δ∏_perp, to the barriers. The interfacial area changes are a combination of shear and dilatation which include both E^s* and G^s*(1).

Figure 3.

The variation in surface pressure for LysoPC measured with a Wilhelmy plate parallel, $\frac{A_0\Delta {\Pi }_{par}}{\Delta A}$ and perpendicular, $\frac{A_0\Delta {\Pi }_{\mathit{\text{perp}}}}{\Delta A}$ to the trough barriers are the same within experimental error. Hence, E^s* + G^s* ≈ E^s* − G^s* ≈ E^s* from Eqn. 3. E^s* ranges from 40 – 75 mN/m, while G^s* < 0.1 mN/m. Double wall ring (DWR) shear measurements show that G^s* is below the sensitivity of the DWR suggesting that G^s* < 0.1 mN/m.

Figure 4.

E^s* of 5 μM LysoPC measured with the Langmuir trough and the CPM using an 80 μm diameter bubble. The solid lines are fit to Eqn. 5 with the same value of ω₀, which depends only on the surfactant type and concentration. The curvature of the interface is important for $\omega <2{\omega }_R=\raisebox{1ex}{$2D$}\!\left/ \!\raisebox{-1ex}{$R^2$}\right.$ (dotted red line) for the bubble. Curvature causes E^s* to decrease faster with decreasing frequency than for a flat trough surface (Eqn. 5 and Fig. 6). The trough data is below the CPM data at high frequency, which may be related to packing differences due to the interfacial curvature in the CPM.

Figure 5.

Schematic diagram of the surfactant exchange at a planar (as in the Langmuir trough) air-water interface undergoing periodic oscillations in surface area of frequency, ω. LysoPC has a characteristic exchange frequency, ${\omega }_0=D/h_p^2$ in which h_p = Γ_eq/C₀ is the depletion depth needed to fully saturate the interface to a surface concentration of Γ_eq from a bulk solution of concentration C₀. If the alveolar surface oscillation frequency, ω > ω₀, lysolipid remains at the interface and the dilatational modulus remains high. If ω > ω₀, the lysolipid has sufficient time to diffuse off the interface, the surface concentration and surface tension remain roughly constant, and the dilatation modulus goes to zero.

Figure 6.

Schematic representation of depletion depths: (A) for a planar interface, the depletion depth, ${\text{h}}_{\text{p}}=\raisebox{1ex}{$\Gamma $}\!\left/ \!\raisebox{-1ex}{$C_0$}\right.$, is the thickness of the volume of concentration C₀ required to cover the interface of area dA with a surface concentration, Γ. (B). The depletion depth for a spherical interface is h_s. R is the radius and A_s is the surface area of the sphere. As the volume of the fluid contained within the dotted line increases faster with distance than in the planar case, the spherical depletion length is less than h_p. (Adapted from Alvarez et al.(4))

Figure 7.

$\frac{A_0\Delta {\Pi }_{par}}{\Delta A}$ (black squares) and $\frac{A_0\Delta {\Pi }_{\mathit{\text{perp}}}}{\Delta A}$ (red triangles) for the insoluble surfactant DPPC spread from chloroform solution for 1% area strain at 0.6 sec⁻¹ in the Langmuir trough at 22° C. The green circles are CPM data for E^s* taken from Kotula et al. (5). $\frac{A_0\Delta {\Pi }_{par}}{\Delta A}\cong \frac{A_0\Delta {\Pi }_{\mathit{\text{perp}}}}{\Delta A}\cong E^{s*}$ within experimental error, consistent with E^s* ≫ G^s*. Independent microbutton shear rheometer measurements of G^s* (25) (pink triangles) show that the shear modulus of DPPC is roughly four orders of magnitude less than E ^s*.

Figure 8.

A) Quantitative surface pressure-area isotherm for DPPC. At large mean molecular areas, DPPC is in a low-density gas phase, G. As the molecular area decreases, the surface pressure increases and DPPC forms a disordered liquid expanded (L_E) phase (red in Figures 9 B, C). At 5– 8 mN/m, a semi-crystalline liquid condensed (L_C) nucleates at the coexistence plateau consistent with a nearly first order phase transition (black in Figures 9B, C). At the highest surface pressures, a solid phase (S) may be present (1). B) “Quasi-static” dilatational modulus determined from the slope of the surface pressure - area isotherm in (A). The red line shows the smoothed data (black points). At the L_E-L_C coexistence, E^s* shows a dramatic dip to < 1 mN/m. At a true first order phase transition, the surface pressure remains constant as the interfacial area changes, hence, E^s* → 0.

Figure 9.

A) Average trough value of E^s* at coexistence for DPPC as a function of applied frequency. For frequencies below ~ 2 rad/sec, E^s* is low and independent of frequency. For 0.3 Hz and higher, E^s* increases and approaches that of the L_C phase. B) On the Langmuir trough, the L_E (red) phase is continuous, while the L_C phase (black) forms discrete domains. Expanding the trough area causes the black domains to decrease in area fraction, while compressing the trough area causes the black domains to increase in area fraction. C) On a highly curved bubble interface in a hydrophobic capillary in the CPM, the L_C phase (black) forms an interconnected network separating the red L_E phase (3). This L_C phase network morphology may be responsible for the larger value of E^s* measured in the CPM compared to the trough.

Figure 10.

A). $\frac{A_0\Delta {\Pi }_{par}}{\Delta A}$ (black squares) and $\frac{A_0\Delta {\Pi }_{\mathit{\text{perp}}}}{\Delta A}$ (red triangles) for 10 μM β-lactoglobulin for 1% area strain in the Langmuir trough. For the 18 kDa protein, $\frac{A_0\Delta {\Pi }_{par}}{\Delta A}>\frac{A_0\Delta {\Pi }_{\mathit{\text{perp}}}}{\Delta A}$ suggesting that G^s* is of the same magnitude as E^s*. B) Comparison of trough values with E^s* measured with the microbubble in the CPM and G^s* measured with the DWR. The agreement is qualitative, and the quantitative differences may be related to the complex evolution of the protein at the interface (See Fig. 11) (2, 3).

Figure 11.

A). Compressing the protein film from the initial 13 mN/m to 23 mN/m increases both and similar to insoluble DPPC. β-lactoglobulin has a dilatational modulus similar to soluble LysoPC but has a shear modulus orders of magnitude greater than LysoPC or DPPC. B) Following an initial compression of β-lactoglobulin in the trough to a surface pressure of 23 mN/m, both and slowly decay with time. become less than due to the rearrangement of β-lactoglobulin at the air-water interface inconsistent with Eqn. 3. Proteins unfold due to the change in the hydrophobic environment at the interface.