Hemicelluloses at Interfaces: Some Aspects of the Interactions - The Nanoscience and Technology of Renewable Biomaterials - page 153

where E diss is the total dissipated energy during one oscillation cycle and E stor is the
total energy stored in the oscillation.

6.3.1.1 Interpretation of Viscoelastic Properties
Using appropriate models, the QCM-D data, f and D , can be interpreted in terms
of adsorbed mass and structural changes in the adsorbed layer. The interpretation of
the viscoelastic properties of the adsorbed layer film was based on the model presented
by Voinova et al . (1999). In this model, the adsorbed layer is represented by a single
Voigt element and it is described using a frequency dependent complex equation when
the layer is subjected to oscillated stress:
G = G + iG = µ f + 2 πifη f = µ f ( 1 + 2 πifτ f ) (6.3)

where µ f is the shear elastic (storage) modulus, η f is the shear viscosity (loss modulus),
f is the oscillation frequency, and τ f is the characteristic relaxation time of the film. The
quartz crystal is assumed to be purely elastic and the surrounding solution is assumed
to be purely viscous and Newtonian. Further, it is assumed that thickness ( h f )and
density of the adsorbed layer are uniform, that the viscoelastic properties are frequency
independent and that there is no slip between the adsorbed layer and the crystal during
shearing. For detailed equations showing correlations between frequency and dissipation
changes and shear elastic modulus ( µ f ), shear viscosity ( η f ) and film thickness ( h f ),
see Voinova et al . (1999) and Tammelin et al . (2004).

6.3.2 Measuring Interaction Forces with AFM

A unique property of AFM, initially developed for imaging sample topography (Binnig
et al . 1986), is the possibility for measuring interaction forces between surfaces and
between molecular pairs directly (Butt et al . 2005). In a force measurement the tip and
the sample are first brought into contact (approach curve) and then withdrawn (retract or
separation curve). The interaction forces between surfaces are recorded during the force
measurement cycle. The nature of the interaction, i.e. whether repulsion or attraction is
involved, can be seen in the approach curve. Theoretical analysis of the data obtained
in different environments, for example in different electrolyte concentrations, may yield
information about whether the studied system is electrostatically or sterically stabilized
(Butt et al . 2005). The retract curve can, in addition to the adhesion data, also show
stretching and unfolding of polymers (Butt et al . 2005).
The raw data obtained from the force measurements is a plot of cantilever deflec-
tion as a function of the sample position. In order to analyze the interaction forces
between surfaces, the raw data is converted to force-versus-distance curves, so-called
'force curves'. The cantilever acts like a spring so the actual force can be calculated
according to Hooke's law:

F = k · x (6.4)

where k is the spring constant (nN nm − 1 )and x the deflection of the cantilever (nm).
The nominal spring constants delivered by the manufacturers are often used directly,
but for obtaining more quantitative data, the cantilevers must be calibrated. There
are several different methods available for determining the spring constant (Burnham