Valence angle model

The simplest modification to the freely jointed chain model is the introduction of bond angle restrictions while still allowing free rotation about the bonds. This is known as the valence angle model and for a polymer chain with backbone bond angles all equal to 6, it leads to Eq. (2.5) for the mean square end-to-end distance... 

Problem 2.7 For a linear molecule of polyethylene of molecular weight 1.4x10 what would be the RMS end-to-end distance according to the valence angle model as compared to that according to the freely-jointed chain model and the end-to-end distance of a fully extended molecule. Comment on the values obtained, indicating which one is a more realistic estimate of chain dimensions. 

The RMS end-to-end distance according to valence angle model is obtained from Eq. (2.5) ... 

The valence angle model, though more realistic than the freely jointed model, still underestimates the true dimensions of polymer molecules, because it ignores restrictions upon bond rotation arising from short-range steric interactions. Such restrictions are, however, more difficult to quantify theoretically. The usual procedure is to assume that the conformations of each sequence of three backbone bonds are restricted to the rotational... 

Comment The most realistic of the above three estimates of chain dimensions is that afforded by the valence angle model. This is because it takes into account coiling of the molecule and also restriction due to fixed valence bond angle. 

The simplest modification to the freely jointed chain model allows for a fixed valence angle, 6, between successive bonds (Fig. 2.3), although it is assumed that free rotation about these bonds is still possible (i.e. 0 can take any value). This is called the valence angle model. Here... 

The structural features of methane ethane and propane are summarrzed rn Ergure 2 7 All of the carbon atoms have four bonds all of the bonds are srngle bonds and the bond angles are close to tetrahedral In the next sectron we 11 see how to adapt the valence bond model to accommodate the observed structures... 

Figure 4 Time step dependence of the average total energy for two models of a partially hydrated dodecamer DNA duplex. Thinner traces show results for virtually harmonic conditions when temperature was lowered to 1 K. The DNA molecule has fixed bond lengths, rigid bases, and fixed valence angles except for the mtra- and extracyclic bond angles m sugars, (a) No modifications of inertia (b) inertia modified as explained m the text. (From Ref. 54.)...

In constructing the initial model of PANI, standard values of C-H, C-C, and C-N valence bond lengths were originally adopted. The valence angles were taken to be 120 degrees. The results of calculations of PANI and AC s PANI-oxygen are listed in Tables 1 and 2. 

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