The pull-off test for viscoelastic soft solids

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					    The pull-off test for viscoelastic soft
       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,
       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



          -20               Fpull-off             Felasto-cappillary
                                                   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.

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Description: The pull-off test for viscoelastic soft solids