Partial rigidity

It can be shown that log log PC+ 0.94, assuming that both solutions are dilute such that the solvent molarity is approximately 55 in the aqueous phase and 6.3 in the octanol phase. As a result, the mole fraction solubility for partially rigid molecules can be written as... 

Modern-day interest in LCPs had its origin with the molecular theories of Onsager (5) and Flory (6). They predicted that rod-like molecules would spontaneously order above a critical concentration that depended on the aspect ratio of the molecule. These theories were later expanded to include other effects such as polydispersity (2) and partial rigidity (g). 

Many properties of polymer solutions are well explained in terms of the freely-jointed-chain model. The present work constitutes a part of a program of study of polymer chains in solution which are partially rigid (or partially flexible). 

Finally, there is no reason why partial rigidity in solution should be limited to very long chains. Oligomeric molecules of alkynes have interesting properties pointed out by Kehiaian (21), related to differences in rigidity 3-hexyne is more rigid than... 

A partially rigid foldamer system was recently reported by Parquette et al. [79]. The oligomers were derived from alternating sequences of pyridine-2,6-dicarboxamides and raeta-(phenylazo)azobenzenes. The helical conformations were revealed by crystal structures. In solution, the folded conformations and their corresponding dynamics were probed by NMR. 

Each of these two approaches is in principle applicable to molecular models of both the types encountered in MD simulations the totally rigid molecular models used in simulations of, for example, nitrogen and water, and the partially rigid molecular models (i.e., where only some of the internal degrees of freedom are constrained) used in early simulations of butane, for example. In practice, the first approach above is truly effective only when applied to totally rigid molecular models, whereas the second approach is equally effective for molecular models of both types, as described next. 

Partially rigid models In the general case of a molecular model that is only partially rigid (i.e., has more than six degrees of freedom, if nonlinear) ... 

M. Ferrario and J. P. Ryckaert, Mol. Phys., 54, 587 (1985). Constant Pressure-Constant Temperature Molecular Dynamics Simulations for Rigid and Partially Rigid Molecular Systems. 

The experimental and hypothetical crystal structures are superimposed in Figure 6.9 using the COMPACK algorithm. The RMS deviation between these structures is fairly small. The W99 potential with the multipole description of the electrostatics, after a minimization of the structures using a partial rigid body model and the DREIDING potential, is a potential good model for this systan. 

Normal mode relaxation is usually studied by the frequency dependence of the shear viscosity. An extensive literature exists on this topic (l6) and a number of features have been successfully identified which can be used to characterize such motion. For a flexible polymer the shape of the relaxation curve and its position will primarily be determined by the strength of the interaction of the polymer with the solvent, the length of the chain and its flexibility as defined by the intramolecular interaction constants. Theoretical analysis has been developed for the flexible coil with virtually no interaction with the solvent, with interaction of the solvent and the chain and also for the partially rigid polymer. Numerous examples of polymer-solvent combinations which possess the desired characteristics can be found in the literature (17 - ll). In general the theory predicts the initial shape of the low frequency viscoelastic behaviour of the polymer quite well but fails to describe the limiting high frequency properties. This apparent... 

Complex 114 has a f/oto-trigonal-bipyramidal structure with the phosphinidene ligand capping one face of the OS4 tetrahedron. No X-ray crystallography data are available for 114, but its structure is based on the similarity of the synthetic route and of its IR spectrum to that of the ruthenium analog, 27. Unlike the Ru analog, there is partial rigidity of the carbonyls in 114 as shown by C NMR spectroscopy. 

A series of 4-alkyl- 225 and 4,4 -dialkyl-substituted cyclopentadithiophenes 226 synthesized and polymerized by Berlin and Zotti et al. resulted in soluble and highly conductive polymers. The partial rigidity of the polythiophene backbone causes anomalously red-shifted absorption spectra in the neutral state which... 

Although an ordinary beam-column element is used to represent a PR connection element for numerical analyses, its stiffness needs to be updated at each iteration since the stiffness representing the partial rigidity depends on 6. This can be accomplished by updating the Young s modulus as ... 

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