Microscopic network parameter

Deriving Microscopic Network Parameters from Macroscopic Hydrogel Properties... 

It is demonstrated that the quasi-static stress-strain cycles of carbon black as well as silica filled rubbers can be well described in the scope of the theoretic model of stress softening and filler-induced hysteresis up to large strain. The obtained microscopic material parameter appear reasonable, providing information on the mean size and distribution width of filler clusters, the tensile strength of filler-filler bonds, and the polymer network chain density. In particular it is shown that the model fulfils a plausibility criterion important for FE applications. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. 

Here, stands as an empirical parameter signifying the proportionality of S to the microscopic strains in the manner shown. Its rational relation to network parameters awaits further theoretical and experimental work. 

By microscopic measurements of the degree of swelling (Flory-Rehner theory) or rather by compression measurements (rubber elasticity theory (RET)) the network parameters, such as cross-linking density or the molecular weight of network chains Me can also be determined vc = p2lMc) (Flory et al. 1976 James and Guth 1943 Wall 1942, 1943, 1951 Hermans 1947). 

In this technique, the local dipolar interaction of individual protons in the liquid crystalline state can be obtained via resonances in the isotropic phase [51-53]. A phase transition from a nematic to an isotropic phase is completed rapidly within the spin-lattice relaxation times of nuclei by applying a pulsed microwave. By this method, homonuclear dipolar interactions associated with individual protons can be separately observed without applying a multiple pulse sequence, and hence a detailed information on the microscopic order parameters, geometry of different chemical groups and IH spin networks can be obtained. In particular, recent technical improvements in the microwave temperature jump probe have realized a transition in even less than 10 ms [52, 53], and enable us to obtain simpler dipolar patterns. In this Chapter, SC-2D NMR experiments between the nematic and the isotropic phase of liquid crystalline samples are described, in which well separated dipolar pattern for individual protons are observed as cross sectional spectra. Besides, this technique can also provide spin diffusion pathways among proton spin networks. These pieces of information provide insights into the microscopic order of liquid crystalline materials. 

More recently Morse produced a complete microscopic tube theory for stiff polymers that successfully interpolates between the rigid-rod and flexible chain limits. This theory explains many features of semiflexible polymer rheology, including the two mechanisms for plateau moduli described above (which depend on a comparison of timescales), with the tube diameter being the sole fitting parameter as in the Doi-Edwards theory. More recently, Morse successfully computed a tube diameter from two different approaches (self-consistent binary collision and continuum effective medium) that give similar results, e.g. modulus G p and respectively). An elastic network approximation... 

During the first operation hydrogel elements often shows a poor repeatability and a drift of the parameters. This is caused by changes in the microscopic structure of the polymer network. By swelling and shrinking the too short polymer chains have to be cracked and the chains in general have to find their optimal moving way and position. 

The mean field approach can be applied in different stages of elaboration. In the first stage, models are introduced that contain additional free parameters which are not determined by microscopic theory. Using these models, the influence of the constraints on network properties has been calculated and discussed. Box models slip-link models constraining springs constrained junction fluctuation and different tube models are predominantly used. The main charac-... 

Polymer networks (e.g., elastomers and gels) can be described on the microscopic scale by typical structural parameters like mesh size but also on the macroscopic scale by their bulk properties like swelling (uptake of liquids) or mechanical behavior. As the most important polymer networks used in bionanotechnology and biomedicine are hydrogel networks, we will focus on experimental methods and theories that are commonly used to analyze such hydrogel networks. 

The structure of hydrogel networks is usually characterized by the following microscopic parameters (Fig. 4.14) ... 

The process of intersite electron hopping has been discussed in terms of a quasi-diffusional process. We now take a more detailed view of the intersite electron transfer reaction in a fixed-site redox polymer. The approach adopted here is due to Fritsch-Faules and Faulkner. These researchers developed a microscopic model to describe the electronhopping diffusion coefficient Z>e in a rigid three-dimensional polymer network as a function of the redox site concentration c. The model takes excluded volume effects into consideration, and it is based on a consideration of probability distributions and random-walk concepts. The microscopic approach was adopted by these researchers to obtain parameters that could be readily understood in the context of the polymer s molecular architecture. A previously published related approach was given by Feldberg. ... 

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