Coupled multi-field formulation

To gain a more precise insight into the phenomena occurring in gels, the Theory of Porous Media (TPM), or the coupled chemo-electro-mechanical formulation is a good choice. Normally, the TPM is applied for the gel only, while the coupled multi-field formulation incorporates the gel and the surrounding solution. 

Ionic polymer gels Polyelectrolyte gels Modeling Numerical simulation Statistical theory Transport model Continuum model Coupled multi-field formulation... 

The coupled chemo-electro-mechanical multi-field formulation is a model on the micro-mesoscopic scale. It has been developed to gain a more precise insight into... 

In this chapter numerical simulations by applying the coupled chemo-electro-mechanical multi-field formulation on a deforming mesh have been performed. It has been shown that this formulation is an excellent method for describing the coupled behaviour of polymer gels in a solution. This method is capable to explain the mechanisms of the behaviour of polyelectrolyte gels under chemical and electrical stimulation, the ion distributions as well as the swelling and bending behaviour. 

In the previous sections, the Born-Oppenheimer approximation was assumed, i.e. nuclear motion on a single PES was considered. However, in many simations, the dynamics of the nuclei need to be treated on several PESs corresponding to coupled electronic state. The coupling between the electronic states can be due to the presence of an external electric field or to internal vibronic interactions. There exists two different ways of treating several coupled electronic states with the MCTDH method [60], the single-set formulation and the multi-set formulation. 

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