Normal stresses in semiflexible polymer hydrogels

Biopolymer gels such as fibrin and collagen networks are known to develop tensile axial stress when subject to torsion. This negative normal stress is opposite to the classical Poynting effect observed for most elastic solids including synthetic polymer gels, where torsion provokes a positive normal stress. As recently shown, this anomalous behavior in fibrin gels depends on the open, porous network structure of biopolymer gels, which facilitates interstitial fluid flow during shear and can be described by a phenomenological two-fluid model with viscous coupling between network and solvent. Here we extend this model and develop a microscopic model for the individual diagonal components of the stress tensor that determine the axial response of semi-flexible polymer hydrogels. This microscopic model predicts that the magnitude of these stress components depends inversely on the characteristic strain for the onset of nonlinear shear stress, which we confirm experimentally by shear rheometry on fibrin gels. Moreover, our model predicts a transient behavior of the normal stress, which is in excellent agreement with the full time-dependent normal stress we measure.Comment: 12 pages, 8 figure

Porosity governs normal stresses in polymer gels

When sheared, most elastic solids such as metals, rubbers and polymer hydrogels dilate in the direction perpendicular to the shear plane. This well-known behaviour known as the Poynting effect is characterized by a positive normal stress [1]. Surprisingly, biopolymer gels made of fibrous proteins such as fibrin and collagen and many tissues exhibit the opposite effect, contracting under shear and displaying a negative normal stress [2, 3]. Here we show that this anomalous behaviour originates from the open network structure of biopolymer gels, which facilitates interstitial fluid flow during shear. Using fibrin networks with a controllable pore size as a model system, we show that the normal stress response to an applied shear is positive at short times, but decreases to negative values with a characteristic time scale set by pore size. Using a two-fluid model, we develop a quantitative theory that unifies the opposite behaviours encountered in synthetic and biopolymer gels. Synthetic polymer gels are impermeable to solvent flow and thus effectively incompressible at typical experimental time scales, whereas biopolymer gels are effectively compressible. Our findings suggest a new route to tailor elastic instabilities such as the die swell effect that often hamper processing of polymer materials and furthermore show that poroelastic effects play a much more important role in the mechanical properties of cells and tissues than previously anticipated