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Measurement and analysis of forces in bubble and droplet systems using AFM

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Abstract

The use of atomic force microscopy to measure and understand the interactions between deformable colloids – particularly bubbles and drops – has grown to prominence over the last decade. Insight into surface and structural forces, hydrodynamic drainage and coalescence events has been obtained, aiding in the understanding of emulsions, foams and other soft matter systems. This article provides information on experimental techniques and considerations unique to performing such measurements. The theoretical modelling frameworks which have proven crucial to quantitative analysis are presented briefly, along with a summary of the most significant results from drop and bubble AFM measurements. The advantages and limitations of such measurements are noted in the context of other experimental force measurement techniques.

Highlights

Atomic force microscopy measures forces between drops and bubbles. ► Modelling frameworks for quasi-equilibrium and dynamic forces are presented. ► Highlights of recent experimental advances in forces from soft matter AFM. ► Van der Waals, electrical double-layer, structural and hydrodynamic forces.

Introduction

In the quarter-century since Binnig, Quate and Gerber invented the atomic force microscope (AFM) [1], the instrument has grown to prominence as a tool for measuring nano-scale topology and interaction forces. By monitoring the bending or deflection of a micro-cantilever, information can be gained on the forces acting on the cantilever’s sharp tip [2], with pico-Newton resolution. When the tip is raster-scanned over a surface, this sensitivity is used to provide a 3-dimensional reconstruction of the surface’s form, down to Ångstrom (atomic) resolution.

In the early 1990s, it was demonstrated that, by attaching a colloidal particle of a few microns diameter to the end of an AFM cantilever, the force between the particle and a surface could be measured [3]. Using this method, precise information on electrical double-layer and Van der Waals forces was obtained, with specific relevance to colloidal systems [3]. Although the surface forces apparatus (SFA) [4] had previously been able to provide such insight for specific systems, the AFM offered several complementary advantages in terms of the material combinations and geometries which could be explored, no longer relying on crossed-cylinder approaches between transparent materials.

Some years later, the concept of extending the measurement of colloidal forces using the AFM to include deformable bodies emerged. The initial attempts were measurements of equilibrium forces between a solid particle on the cantilever and a bubble immobilised on a solid surface [5], [6], [7], [8], and later between a particle and oil droplet [9], [10], [11], [12], [13], [14]. However, it was soon noted that significantly more insight could be gained by picking up an emulsion-scale droplet onto the AFM cantilever [15]. This allowed interactions between pairs of droplets to be examined, where relatively high velocities could be used to explore hydrodynamic drainage effects.

The information gained in such measurements of inter-droplet collisions was underpinned by theoretical analysis [16], [17], [18], [19]. A model had been previously developed which accounted for the force seen when a solid particle approached a deformable oil droplet, predicting the static force at any approach distance [16], [20]. By introducing time as a variable, and accounting for fluid flow by lubrication theory, dynamic interactions between droplets could be modelled, which afforded major advances in understanding [17], [18], [19].

This article draws from the significant body of work pertaining to measuring interactions between soft bodies (bubbles and droplets) using the AFM. Experimental and theoretical considerations are detailed, and key outcomes and advances to date are summarised. This is relevant because of (a) velocity and deformation effects that are important in considering emulsion stability, gel interactions, and soft biological systems, and (b) film drainage studies, where the displacement and its time variation are well-controlled as the (time-dependent) force of interaction is measured.

Section snippets

Scope and intention of the article

This article is intended as an introduction to techniques and theories pertaining to performing AFM force measurements specifically on soft, colloidal systems – droplets, bubbles, etc. By force measurements, we mean the determination of force vs. distance or force vs. time relationships for soft surfaces, as distinct from AFM imaging studies, which will not be covered here. It is hoped that the experimental methods and approaches detailed herein will prove useful to other researchers in this

AFM

Due to its sensitivity and precision of motion, afforded by piezoelectric elements, the AFM represents an ideal tool for analysing interactions between colloidal objects at nanometre separations. At such close approach, electrical double-layer, Van der Waals and other, more exotic colloidal forces come into play.

Although all commercial AFMs contain the same basic set of components (a cantilever combined with a laser/photodiode setup to measure its deflection, a sample stage and piezo elements

Modelling framework

In the operation of the AFM as discussed in section B and Fig. 2a, the relative displacement, Z, of the cantilever is set by the piezo motion, and measured independently by some means. In the case of the Asylum MFP-3D that we often use, the displacement is measured by a linear variable differential transformer, LVDT. The deflection of the cantilever, S, is measured by the optical lever, and the interaction force, F, can then be obtained using the cantilever spring constant, K, via Hooke’s Law: F

Conclusions and outlook

The analysis of interactions between soft materials by atomic force microscopy, and in particular bubbles and drops, has become a vital tool for the modern colloid scientist. Whereas such measurements present complex challenges, in terms of understanding the interplay of surface forces, deformation and absolute separations, significant insight has been gained through careful experimental design [15], [49] and theoretical analysis and modelling [18], [19]. Measurements of both static and dynamic

Acknowledgment

The authors would like to express their gratitude to co-workers, both past and present, who have provided much of the data and insight which has supported this work: T. Chau, R. Manica, I. Vakarelski, G. Webber, H. Lockie, O. Manor, C. Wu, E. Klaseboer. X. S. Tang and S. O’Shea are thanked for preparing the cantilevers used in many of the experiments. The ARC is thanked for financial support, and the Particulate Fluids Processing Centre, a special research centre of the ARC, provided

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