Thermo-thickening during melting of dibenzylidene sorbitol fibre networks

Abstract

Gels of dibenzylidene sorbitol (DBS) in poly(propylene oxide) (PPO) show an increase in viscosity in a certain temperature range during melting. This so-called thermo-thickening behaviour is quite uncommon. In the few already known cases, the thermo-thickening is caused by simple thermodynamic processes that result in the formation of structures. We show for the first time that, in the case of PPO-DBS gels, experimental parameters like sample volume and heating rate play an important role and indicate non-equilibrium behaviour. It turns out that the peculiar thermo-thickening is the result of a reformation of the fibre network structure, which was destroyed earlier due to a strong temperature gradient within the sample.

Appendix

As shown by Kühne and Friedrich (2009), DBS-PPO gels can be considered as a network of semiflexible DBS fibres in a PPO matrix.

Following MacKintosh et al. (1995), the elastic modulus of such a network can be explained as`

$$ \label{eq1} G_{\rm p} \cong \frac{\kappa ^2}{k_{\rm B} T}L_{\rm M}^{-2} L_{\rm e}^{-3} , $$

(1)

where κ is the bending modulus of the fibres, L _M is the mesh size, and L _e is the entanglement length. For such networks

$$ \label{eq2} L_{\rm M} \approx L_{\rm e} , $$

(2)

and these lengths are assumed to be almost temperature independent, so Eq. 1 can be written as

$$ \label{eq3} G_{\rm p} \cong \frac{\kappa ^2}{k_{\rm B} T}L_{\rm M}^{-5} . $$

(3)

The temperature dependence of the mesh size determines the temperature dependence of the sample’s density. Due to the fact that this density is almost temperature independent, this assumptions seem to be reasonable.

The bending modulus of such fibres is itself temperature dependent, following

$$ \label{eq4} \kappa =E\left( T \right)I, $$

(4)

in which E(T) is the Young modulus of the fibre and I its moment of inertia. We assume as for many crystalline materials that the Young modulus scales with

$$ \label{eq5} E\left( T \right)\propto E_0 T^0. $$

(5)

Inserting Eqs. 4 and 5 into Eq. 3 leads to the following scaling of the elastic modulus:

$$ \label{eq6} G_{\rm p} \propto T^{-1}, $$

(6)

the observed temperature dependence.