Non-contact mechanics of soft and liquid interfaces by hydrodynamic confinement using a frequency-modulated AFM

Technical Deep Dive: Non-Contact Mechanics of Soft and Liquid Interfaces

Overview

This work presents a frequency-modulation atomic force microscopy (FM-AFM) method for probing the mechanics of soft and liquid interfaces in a non-contact manner. The technique uses hydrodynamic confinement to measure the elastic and dissipative components of the interfacial mechanical impedance, providing a quantitative window into the deformation and flow of these interfaces.

Problem & Context

Characterizing the mechanical response of liquid interfaces is a major experimental challenge, particularly for liquid-liquid systems where no solid reference exists. Existing techniques like Langmuir troughs and oscillating drop methods provide access to interfacial properties, but do not clearly separate elastic and dissipative contributions or operate under strictly contactless conditions.

The authors developed an FM-AFM approach that probes interfaces through the hydrodynamic stresses generated by an oscillating probe. This allows simultaneous measurement of the conservative and dissipative components of the interfacial impedance.

Methodology

The key aspects of the methodology are:

• Probe design: A quartz tuning fork with a tapered glass fiber and 5 μm spherical tip, providing high sensitivity and well-defined sphere-plane geometry.
• Experimental setup: A custom vertical FM-AFM system operating in liquid environments, with humidity control and fine positioning.
• Data processing: Subtracting the linear bulk hydrodynamic response to isolate the interfacial contributions, then converting the frequency shift and dissipation signals into the real (elastic) and imaginary (viscous) impedance components.

Data & Experimental Setup

Experiments were performed on two systems:

1. Liquid-solid: A water-glycerol mixture confined against a cross-linked PDMS surface.
2. Liquid-liquid: A PDMS oil phase and a water-glycerol mixture.

Approach-retract cycles were conducted at 50 nm/s, with the probe oscillating at ~6 μm/s, ensuring a low Reynolds number (Re ≈ 2×10^-7) and Stokes flow regime.

Results

Liquid-Solid Interface

• The measured impedance components agreed quantitatively with elastohydrodynamic theory, validating the method.
• The real (elastic) and imaginary (viscous) impedance followed predicted scalings of D^-2.6 and D^-0.94, respectively, as the probe approached the PDMS surface.
• The measured confinement thickness Dc varied with the PDMS Young's modulus E as Dc ∝ E^-2/3, again matching theory.

Liquid-Liquid Interface

• Both the real and imaginary impedance components were over an order of magnitude smaller than for the liquid-solid case.
• The impedance components exhibited a D^-1 dependence, characteristic of a predominantly viscous response.
• The confinement thickness increased to D_c ≈ 1.1 μm, about an order of magnitude larger than the liquid-solid interface.
• The real impedance saturated at a value (108 ± 20 mN/m) significantly higher than the interfacial tension (37 ± 1 mN/m), indicating the response is not solely due to capillary forces.

Interpretation

• The liquid-liquid interface exhibits a viscous-dominated response, in contrast to the viscoelastic behavior of the liquid-solid system.
• The large increase in confinement thickness for the liquid-liquid case reflects the absence of bulk elastic restoring forces.
• The in-phase impedance component appears to arise from viscous stresses and interfacial hydrodynamics, rather than simple capillary effects.

Limitations & Uncertainties

• The elastohydrodynamic model does not directly apply to liquid-liquid interfaces, where interfacial motion and viscous flow play a central role.
• At the highest interaction stiffnesses, probe mechanical stability became a limiting factor for the liquid-solid system.

What Comes Next

This work establishes FM-AFM as a powerful tool for quantitative, non-contact probing of soft and liquid interfaces. The authors highlight its potential for studying complex fluid interfaces like biological membranes, polymer films, and capsules, where interfacial flow and confinement are key to the mechanical response.