force is a direct access to the volume variation (or displacement) during the oscillatory stress measurement and therefore is directly related to surface tension. Figure 9
illustrates the values of the normal force and of the shear stress measured simultaneously and displayed on the same scale. No variation of the normal force is
observed during the measurement, while the sinusoidal waves corresponding to
the shear stress or the shear strain are easily identifiable.
The (linear) low-frequency shear elasticity is accessible upon low displacement
excitation (low strain amplitude regime or low sample thickness) and is prior to the
conventional viscoelastic regime which is obtained at larger strain amplitudes (next
paragraph). A variable waiting time is required prior the terminal elastic behavior
emerges. Close equilibrium conditions are thus much more fulfilled for the
low-frequency elasticity measurement than for the conventional viscoelastic regime
obtained at larger strain amplitudes and even more than in the so-called LAOS (large
amplitude oscillatory strain) regime where interfacial surface tension parameters
might be integrated.
Relationships Between Low-Frequency Shear Elasticity
and Conventional Viscoelasticity
If the shear elasticity of the fluid is observable at submillimeter scale by improving
the wettability of the substrate, it is progressively lost by increasing the strain
amplitude (or by increasing the sample thickness) giving rise in the case of polymer
melts to the conventional flow behavior identical to partial wetting conditions
(Fig. 10). A transition from total to partial wetting conditions is thus achieved by
increasing the strain amplitude. The strain-induced transition can be interpreted as a
selection process with respect to the boundary contacts between the polymer and the
substrate. Fast relaxation time contacts are easily restored and give rise to the
conventional flow behavior, whereas long relaxation (solid-like) contacts bear only
small strains and exhibit the elastic response. The elastic response corresponds to a
primary linear regime. The viscoelastic behavior is thus the nonlinear product of the
first elastic regime.
Similar shear elasticity collapses are observed in other viscoelastic fluids or
liquids as, for example, in the case of the heptadecane (Fig. 11).
The identification of a finite shear elasticity indicates a collective
(intermolecular) response. It rules out an interpretation in terms of single molecular
response solely due to intrachain elasticity modelled by the Maxwell function
(viscoelasticity theory). Low-frequency shear elasticity is the firm demonstration
that intermolecular interactions contribute also to the dynamic response. This
scheme is in agreement with the identification of finite shear elasticity at low
frequency on low molecular liquids as illustrated here in the case of the heptadecane (Fig. 12).
9 Probing Submillimeter Dynamics to Access Static Shear Elasticity from. . .
263
illustrates the values of the normal force and of the shear stress measured simultaneously and displayed on the same scale. No variation of the normal force is
observed during the measurement, while the sinusoidal waves corresponding to
the shear stress or the shear strain are easily identifiable.
The (linear) low-frequency shear elasticity is accessible upon low displacement
excitation (low strain amplitude regime or low sample thickness) and is prior to the
conventional viscoelastic regime which is obtained at larger strain amplitudes (next
paragraph). A variable waiting time is required prior the terminal elastic behavior
emerges. Close equilibrium conditions are thus much more fulfilled for the
low-frequency elasticity measurement than for the conventional viscoelastic regime
obtained at larger strain amplitudes and even more than in the so-called LAOS (large
amplitude oscillatory strain) regime where interfacial surface tension parameters
might be integrated.
Relationships Between Low-Frequency Shear Elasticity
and Conventional Viscoelasticity
If the shear elasticity of the fluid is observable at submillimeter scale by improving
the wettability of the substrate, it is progressively lost by increasing the strain
amplitude (or by increasing the sample thickness) giving rise in the case of polymer
melts to the conventional flow behavior identical to partial wetting conditions
(Fig. 10). A transition from total to partial wetting conditions is thus achieved by
increasing the strain amplitude. The strain-induced transition can be interpreted as a
selection process with respect to the boundary contacts between the polymer and the
substrate. Fast relaxation time contacts are easily restored and give rise to the
conventional flow behavior, whereas long relaxation (solid-like) contacts bear only
small strains and exhibit the elastic response. The elastic response corresponds to a
primary linear regime. The viscoelastic behavior is thus the nonlinear product of the
first elastic regime.
Similar shear elasticity collapses are observed in other viscoelastic fluids or
liquids as, for example, in the case of the heptadecane (Fig. 11).
The identification of a finite shear elasticity indicates a collective
(intermolecular) response. It rules out an interpretation in terms of single molecular
response solely due to intrachain elasticity modelled by the Maxwell function
(viscoelasticity theory). Low-frequency shear elasticity is the firm demonstration
that intermolecular interactions contribute also to the dynamic response. This
scheme is in agreement with the identification of finite shear elasticity at low
frequency on low molecular liquids as illustrated here in the case of the heptadecane (Fig. 12).
9 Probing Submillimeter Dynamics to Access Static Shear Elasticity from. . .
263