Liviu Iulian Palade

Physical properties of polyacrylamide gels probed by AFM and rheology

Polymer gels have been shown to behave as viscoelastic materials but only a small amount of data is usually provided in the glass transition. In this paper, the dynamic moduli and of polyacrylamide hydrogels are investigated using both an AFM in contact force modulation mode and a classical rheometer. The validity is shown by the matching of the two techniques. Measurements are carried out on gels of increasing polymer concentration in a wide frequency range. A model based on fractional derivatives is successfully used, covering the whole frequency range. , the plateau modulus, as well as several other parameters are obtained at low frequencies. The model also predicts the slope a of both moduli in the glass transition, and a transition frequency is introduced to separate the gel-like behavior with the glassy state. Its variation with polymer content c gives a dependence , in good agreement with previous theories. Therefore, the AFM data provides new information on the physics of polymer gels.

THE STEADY STATE CONFIGURATIONAL DISTRIBUTION DIFFUSION EQUATION OF THE STANDARD FENE DUMBBELL POLYMER MODEL: EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR ARBITRARY VELOCITY GRADIENTS

The configurational distribution function, solution of an evolution (diffusion) equation of the Fokker-Planck-Smoluchowski type, is (at least part of) the corner stone of polymer dynamics: it is the key to calculating the stress tensor components. This can be reckoned from \cite{bird2}, where a wealth of calculation details is presented regarding various polymer chain models and their ability to accurately predict viscoelastic flows. One of the simplest polymer chain idealization is the Bird and Warners model of finitely extensible nonlinear elastic (FENE) chains. In this work we offer a proof that the steady state configurational distribution equation has unique solutions irrespective of the (outer) flow velocity gradients (i.e. for both slow and fast flows).

The FENE Dumbbell Polymer Model: Existence and Uniqueness of Solutions for the Momentum Balance Equation

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker–Planck–Smoluchowski diffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coefficients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.

Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation

The Greer, Pujo-Menjouet and Webb model [Greer et al., J. Theoret. Biol., 242 (2006), 598--606] for prion dynamics was found to be in good agreement with experimental observations under no-flow conditions. The objective of this work is to generalize the problem to the framework of general polymerization-fragmentation under flow motion, motivated by the fact that laboratory work often involves prion dynamics under flow conditions in order to observe faster processes. Moreover, understanding and modelling the microstructure influence of macroscopically monitored non-Newtonian behaviour is crucial for sensor design, with the goal to provide practical information about ongoing molecular evolution. This papers results can then be considered as one step in the mathematical understanding of such models, namely the proof of positivity and existence of solutions in suitable functional spaces. To that purpose, we introduce a new model based on the rigid-rod polymer theory to account for the polymer dynamics under flow conditions. As expected, when applied to the prion problem, in the absence of motion it reduces to that in Greer et al. (2006). At the heart of any polymer kinetical theory there is a configurational probability diffusion partial differential equation (PDE) of Fokker-Planck-Smoluchowski type. The main mathematical result of this paper is the proof of existence of positive solutions to the aforementioned PDE for a class of flows of practical interest, taking into account the flow induced splitting/lengthening of polymers in general, and prions in particular.