The pull-off test for viscoelastic soft solids 1. Introduction The adhesive interactions between adhesive soft solids covered with viscoelastic film are crucial for a number of problems related to biological systems like cell adhesion and mucoadhesion. The mucoadhesive interactions are of particular interest to Unilever since most Unilever products interact with mucosa substrates in a certain way. Foods and beverages interact with oral mucosa including salivary films; this interaction influences taste, mouthfeel and flavour release. Further down to the GI tract, mucoadhesive interactions condition nutrient uptake and, to a certain extent, enable food digestion. In oral care products, mucoadhesion is an important aspect of the functionality of the product. Generally, mucoadhesion can be described as an interaction of solid/semisolid particles or even liquid droplets with a mucosa substrate that can be defined as a “thick” (~0.1-200 µm) proteinaceous film. Such an adhesive interaction is different from that with solid surfaces, even soft ones. The complexity stems from the fact that several contributions can be identified within the adhesive contact or during rupture of such an adhesive contact, including 1. The adhesive force; 2. The extension of the viscoelastic film that leads to the formation of either a single filament or multiple ones and subsequent necking failure; 3. Interfacial tension (usually small due to low interfacial energy between two water based phases, e.g. bound and un-bound layers) that leads to a capillary effect; 4. The deformation of the substrates and soft bodies. 2. Motivation for theoretical analysis In many instances we need to perform an in-vitro assessment of the mucoadhesive properties of materials that are subject to a screening assay. One of the screening methods is a pull-off test using an atomic force microscope (AFM), in which a particle is pushed into and then pulled away from a surface. We can vary the speed of approach and/or retraction, applied load, dwell time, geometry of interacting surfaces, solvent, etc. This leads to a force versus indentation/separation curve that measures the combined effect of all the interactions, but does not allow us to directly extract the parameters of interest, e.g the extensional viscosity of the proteinaceous mucosa layer or the thickness of this layer. Even the adhesive energy between the mucosa and the probe is not measured directly. Since pull- off measurements are dynamic, it should be possible to describe the whole process using differential equations, some of them nonlinear. The main purpose of the theoretical analysis is therefore to find a method of extracting the parameters of interest by modelling the experimental force versus distance curve. In addition, a theoretical model could provide some physical insight into what part of the system is dominating the interaction. It is anticipated that the theoretical analysis of a force curve should provide the following information: - adhesive energy (presumably for each of interfaces – substrate1/film1, film1/film2, film2/substrate2) - elastic parameters of the viscoelastic substrate - viscoelastic parameters of a thin polymer/proteinaceous film adjacent to a viscoelastic substrate - thickness of this thin polymer/proteinaceous film The overall aim is to develop an assay-type of test for mucoadhesive interaction, avoiding the need for numerous additional experiments to disentangle the various contributions. 3. Definition of the problem and experiment Consider two cases; (i) a viscoelastic solid sphere interacting with a flat mucosa substrate; and (ii) an elastic solid sphere coated with a viscoelastic polymer layer of thickness d interacting with mucosa substrate. Both cases are illustrated below. i ii Experiments suggest that the rupture of the adhesive coating happens in two stages. The first stage is hypothesised to be the rupture of a true adhesive contact, followed by a second stage due to the stretching of the polymer/proteinaceous filament. One has also to consider a number of physicochemical phenomena such as hydrodynamic drag, time- dependent adhesion, nonlinear load-dependent adhesion, as well as capillary adhesion aggravated by elasto-capillary balance and necking failure. A schematic illustration of rupture, together with the corresponding force curve, is presented below F = F elasto- F = F pull-off capillary F=0 20 F[mN] retraction approach 0 -20 Fpull-off Felasto-cappillary elasto-cappillar elasto-capillary y 0.0 0.2 0.4 0.6 0.8 Separation [mm] The time-dependent contact adhesion effects are related to the dynamics of polymer chains in the gap between the surfaces. The nonlinear load effects stem from the fact that the contact adhesive interaction can vary across the contact area following non-uniform stress distribution; thereby polymer properties that are highly susceptible to the pressure/stress lead to a radial distribution in adhesive energy as well as its dependency on applied load. The elasto-capillary force arises from the extension of the viscoelastic polymer bridge that has been formed during the contact.