Modeling of Chain Dynamics and Predictions for NMR Measurands

Polymers are molecules subject to complex intra- and intermolecular interactions combined with many intramolecular degrees of motional freedom. The degree of polymerization e typically ranges from 10 to 10 . Assuming only three rotamers per monomer, the number of possible conformations already takes the astronomical number value of the order 3. The time constants characterizing the molecular motions are spread over up to six orders of magnitude. In view of these facts, it is a rather demanding task to model polymers and their molecular dynamics. 

At room temperatures TwSOO K, conformational transitions typically take rs=10 -10 s. All elementary conformational changes displace atoms of the polymer on a distance length scale l 1 nm. These characteristic quantities permit the distinction of local and global properties. 

A detailed description of statically or dynamically local properties must be based on the stereochemical composition of the monomers and their potential energy landscape [1, 37-44]. On the other hand, the global, i.e., large-scale, properties of macromolecules tend to be insensitive to the stereochemical details of the monomers. Therefore, a coarse-grained description becomes adequate by considering model chains. All chemical specificity can then be represented by a few characteristic parameters to be specified in the following. 

In the Rouse model to be discussed below, each Kuhn segment is subdivided into a bead (where the segment mass is concentrated) and a massless spring . The elasticity of these springs is based on the conformational entropy of the segments which depends on how far they are stretched. This bead/spring model is characterized by the following basic parameters partially also illustrated in Fig. 6. 

The Kuhn segment length is defined by the root mean squared value 

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Apart from the introductory section, the article is subdivided into four major sections NMR Methods Modeling of Chain Dynamics and Predictions for NMR Measurands Experimental Studies of Bulk Melts, Networks, and Concentrated Solutions and Chain Dynamics in Pores. First, the NMR techniques of interest in this context will be described. Second, the three fundamental polymer dynamics theories, namely the Rouse model, the tube/reptation model, and the renormalized Rouse theories are considered. The immense experimental NMR data available in the literature will be classified and described in the next section, where reference will be made to the model theories wherever possible. Finally, recent experiments, analytical treatments, and Monte Carlo simulations of polymer chains confined in pores mimicking the basic premiss of the tube/reptation model are discussed. 

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