Flexible string properties

In order to illustrate the mathematics of classical waves, we now analyze the vibrations of a flexible string, which is a model system designed to resemble a real vibrating string. It is defined to have the following properties ... 

Such molecules have very specific properties, due to their size and flexibility. A linear molecule with n = 104, built of monomers with a molar mass of 30 Da, will be taken as an example. The molecule is thus very large, molar mass 300 kDa. Its length-to-diameter ratio is like that of a 10 m string of about 1 mm thickness. If it were tightly coiled up in a sphere, it would assume a diameter of about 10 nm. In other words, it would be of colloidal rather than molecular size, and many polymer molecules are even far larger. 

Only a few compounds screened in early lead identification phases are synthesized in-house. More flexible and cost effective is to purchase chemicals from external suppliers. Most vendors provide lists of some ten to himdred thousand chemicals on compact discs and guarantee delivery within days to weeks. To explore this huge amount of data with the aid of computers, chemical information is transformed to computer-readable strings, e.g., smiles code, and different descriptors are determined. 1-dimensional (1-D) descriptors encode chemical composition and physicochemical properties, e.g., molecular weight, stoichiometry (C O Hj,), hydrophobicity, etc. 2-D descriptors reflect chemical topology, e.g., connectivity indices, degree of branching, number of aromatic bonds, etc. 3-D descriptors consider 3-D shape, volume or surface area. 

This is the basis of all the analyses used in peeling and has an attractive simplicity. Note that the thickness of the strip, h, does not appear in the result, nor do any material properties. This is because we have assumed that the strip is perfectly flexible in bending and also is inextensible in tension (i.e. the peel arm behaves as a piece of string which is infinitely rigid in axial tension hence the superscript ooE ), so that it simply transfers the external work to the surface in an non-prescribed way. 

As the polymer concentration increases, the polymer size and thermodynamic properties of the solution are significantly modified in ways unique to the string-like nature of the polymers. Let us consider a solution of volume V, containing n flexible chains with N Kuhn segments per chain. The monomer concentration... 

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