Rigid solutions, partially, model

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, we saw that universities took initiatives fiivoring applied chemistry, but these emerged much more to solve internal career problems of faculty members than in response to the nation s fundamental worries. Each university reacted as if it were alone and, consequently, each evolved its own particular solution, often dictated by local needs and opportunities. Since no professional group existed, no one could help to harmonize university programs with industry s needs. In short, the French situation was so disorderly as to preclude the production of a specific and coherent solution by industrial chemists themselves. In practice, decisions remained very much in the hands of the managers and the ingenieurs from the Crandes Ecoles. The model would have to come from the outside and somehow be fitted within rather rigid and partially incompatible institutions. 

In other cases, however, and in particular when sublattices are occupied by rather immobile components, the point defect concentrations may not be in local equilibrium during transport and reaction. For example, in ternary oxide solutions, component transport (at high temperatures) occurs almost exclusively in the cation sublattices. It is mediated by the predominant point defects, which are cation vacancies. The nearly perfect oxygen sublattice, by contrast, serves as a rigid matrix. These oxides can thus be regarded as models for closed or partially closed systems. These characteristic features make an AO-BO (or rather A, O-B, a 0) interdiffusion experiment a critical test for possible deviations from local point defect equilibrium. We therefore develop the concept and quantitative analysis using this inhomogeneous model solid solution. 

A partitioning function for a system of rigid rod-like particles with partial orientation around an axis is derived from the use of a modified lattice model. The free energy of mixing is shown as a function of the mole numbers, the axis ratio of the solute particles and a disorientation parameter this function passes through a minimum with increase in the disorientation parameter. The chemical potentials display discontinuities at the concentration at which the minimum appears and then separation into an isotropic phase and a somewhat more concentrated anisotropic phase arises. The critical concentration, v, is given in the form 13) ... 

We consider a generic donor-acceptor complex solute at infinite dilution in a polyatomic solvent. Both the solute and solvent molecules are represented by rigid and non-polarizable ISM models. In the ISM models the potential energy of interaction between two molecules is a sum of pairwise-additive site-site terms, including Coulombic interactions between partial charges located at the molecular sites. Throughout the paper the subscript A refers to interaction sites of the solute, while the subscript aj refers to interaction site j of solvent molecule a. 

We first consider the A contribution. Equation 1, and an explanation in terms of a two-site model i.e., a model in which a water molecule exchanges between solution and sites (or class of sites) on or near a protein molecule such that at least one direction fixed in the water molecule is constrained to move rigidly with the protein molecule. In the simplest case, a water molecule attaches rigidly to the protein, moves with it for a while, and then leaves. In a somewhat more complex case, the attachment may be less rigid so that the water molecule is free to rotate about an axis fixed with respect to the protein. Additionally, a situation in which water molecules partially orient in the electric fields near the protein surface because of their electric dipole moments would also be a two-site model. Characteristic of a two site-model is that a time Tj, or a distribution of such times, can be defined that measures the mean lifetime of a water molecule in the protein-associated state. Moreover, such a time is in principle a measurable quantity, and its value must satisfy two criteria it must be at least comparable to if not longer than Tj, otherwise the nuclei of the bound water molecules could not sense the rotational motion of the protein molecules and it must be comparable to or shorter than the nuclear relaxation time of a bound water molecule, else it could not communi-... 

Upon cryo-cooling, the unit cell dimensions of the l-Ppol crystals shrunk 0.6-1 A on each edge (e.g. from a=59.19A to a=58.58 A, from b=62.13 A to b=61.10 A, and from c=l 12.69 A to c=l 11.70 A for the metal soaked crystal). Simple rigid body minimization followed by Powell minimization of the partially refined room temperature structure or the AMoRe solution did not did not drop the R ge below 40 % for either cryo-cooled data set. The structures were then subjected to torsion angle dynamics protocols (48) at several temperatures. Both starting models, with either data set, failed to produce a structure with an Rfree below 39 % for data between 8 and 2 A. In addition, the resulting maps did not look very good. 

For some highly crosslinked thermosetting polymers with rigid backbones, topological restrictions limit the maximum attainable conversion. For the reaction between epoxidized novolacs and cresol-based novolacs, a maximum conversion, Xmax= 0.80 was reported (Hale et al., 1991). A similar value of x ,ax was reported for the cure of an epoxidized novolac with 4,4 -diaminodiphenylsulfone (DDS) (Oyanguren and WilKams, 1993a). In these cases, partially reacted networks may be modeled as a random solution of reacted functionalities with a concentration equal to x/x ax... 

The tube concept was successfully used for studying the diffusion and rheological characteristics of an isotropic solution of rigid rods [96,97,102,107-110] and macrcMnolecules with low partial flexibility of a persistent character [103-106]. The dynamic properties of nematic polymer solutions were studied using the tube model in [98, 111-114]. 

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