Rotational isomeric-state approximation

The energy is at a minimum when )2 = 0 and all three bond vectors lie in the same plane. This value of )2 is called the trans state. The energy is at an absolute maximmn when )2 = Jt. This conformation is called the cis state. Local minima are observed when the dihedral angle is near (2jt/3). These conformations are called states. An empirical function that represents 

The probability of observing a butane molecule with a particular conformation is given by Equation 2.5 for the case of a molecule with a single internal rotation angle. 

Many of the properties of the rnolecule depend on its conformation. Consider some typical property A11M j. The average value of this property for an equilibrium ensemble of molecules is 

Centered about the trans state and including the value of the first local maximum, designated as t 

These ranges are called rotational isomeric states (RIS). Any conformation of the molecule can be assigned a particular set of RIS values, s. The average can then be expressed as  

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W AXS-pattern of a polymer melt if these Boltzmann-weighted distance fluctuations are not accounted for. They characterize a relevant feature of polymer melt structures. We treat this in terms of the Rotational Isomeric State Approximation (RISA) discussed in the next section. 

M. L. Mansfield, Macromolecules, 16, 1863 (1983). Effect of Fluctuating Internal Coordinates on the Rotational Isomeric States Approximation. 

The modulation technique mentioned above has been used to identify triplet excimers in 1,2-benzanthracene and 1,2 3,4-dibenzanthracene at high solute concentrations167 and the differences between luminescence from naphthalene in fluid solution in the temperature range 353—173 and naphthalene in a rigid solution at 77 have been ascribed to phosphorescence from a triplet excimer.168 Excimer formation in solid poly-(2-vinylnaphthalene) and polystyrene is found to be dependent on the temperature at which the film is cast, and a statistical model based on the rotational isomeric state approximation has been used to formulate an expression for the fraction of excimer sites in the solid systems.168 Kinetic equations for dimer formation and decay, based on the statistical mechanics of ideal gases, have been obtained. These equations, derived from the N-atom von Neumann equation, take into account both bimolecular and termolecular equations.157 158 160... 

What matters, however, for ensuring that the states are essentially discrete, is that the energy barrier between the two states is about five times thermal energies at room temperature, so that most of the time the molecule will simply perform small oscillations around a discrete tram or gauche state. The various conformations of a molecule are often called rotational isomers and the model of a polymer chain introduced by Flory in which the chain is imagined to take up only discrete conformational states is called the rotational isomeric-state approximation. 

Photinos, D. J., Janik, B., Samulski, E. T., Terzis, A. F., and Toriumi, H., n-Hexane proton dipolar couplings and the rotational isomeric state approximation. Mol. Phys., 72, 333-344... 

Table 1 Thermal pressure coefficients y, transition volumes A 7, and volume-dependent transition entropies ASy of n-alkanes and polyoxyethylene (POE) for the crystal-isotropic (Cl) phase transitions conformational entropy changes estimated by the rotational isomeric state approximation are included for comparison...

Chains with Interdependent Rotational Potentials. The Rotational Isomeric State Approximation 71... 

CHAINS WITH INTERDEPENDENT ROTATIONAL POTENTIALS. THE ROTATIONAL ISOMERIC STATE APPROXIMATION... 

The coarse grained models we have considered thus far are valuable for examining qualitative trends. However, in order to make comparisons directly with experimental data, more local structural details presumably need to be taken into account in the calculation of d>(k). A realistic way of incorporating monomer structure is through the rotational isomeric state approximation, successfully employed [16] by Flory and others to describe isolated polymer chains in a theta solvent. In this description the continuous rotational potentials are replaced by discrete rotational states corresponding to the lowest vibrational... 

The motions of a flexible aliphatic chain attached to a rigid molecular core are analyzed theoretically by means of a master equation for random walk between the sites identified with the stable conformers of the chain, as an extension in the time domain of the Rotational Isomeric State approximation. 

NORDIO - According to the Rotational Isomeric State approximation, the geometry dependent interactions are simply expressed by additional terms in the total energy. On the other hand, the hydrodynamic interactions give rise to configuration dependent friction coefficients. Under these assumptions, the stationary distribution function is uniquely defined, but the construction of the site functions requires identification of a reactive path. This is done by quadratic expansion of the multivariate diffusion equation about the saddle point connecting two stable conformers, followed by a normal mode analysis. 

The rotational isomeric state approximation, which is a convenient procedure for dealing with the conformational states of polymers, was introduced by Flory. Each molecule is treated as existing only in... 

This angular dependence of the interaction parameter can be extended by using the rotational isomeric state approximation to calculate the conformer populations. This approach was used to interpret the solid-state spectrum of poly(3-methyl-l-pentene), which in the amorphous state can have either a four-fold right-handed helix or a nearly equi-energetic four-fold left-handed helix. Three of the six ehemical shifts of a right-handed unit differ from the corresponding resonances of a left-handed unit, and these stereochemical differences are observed [35]. 

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