Chain flexible model

In this section we compare actual polymer chains with the perfectly flexible model discussed in the last section. There are four respects in which an actual molecule differs from the idealized model ... 

G. Guillot, L. Leger, F. Rondelez. Diffusion of large flexible polymer chains through model porous membranes. Macromolecules 5 2531-2537, 1985. 

Applying the TABS model to the stress distribution function f(x), the probability of bond scission was calculated as a function of position along the chain, giving a Gaussian-like distribution function with a standard deviation a 6% for a perfectly extended chain. From the parabolic distribution of stress (Eq. 83), it was inferred that fH < fB near the chain extremities, and therefore, the polymer should remain coiled at its ends. When this fact is included into the calculations of f( [/) (Eq. 70), it was found that a is an increasing function of temperature whereas e( increases with chain flexibility [100],... 

A lattice model of uniaxial smectics, formed by molecules with flexible tails, was recently suggested by Dowell [29]. It was shown that differences in the steric (hard-repulsive) packing of rigid cores and flexible tails - as a function of tail chain flexibility - can stabilize different types of smectic A phases. These results explain the fact that virtually all molecules that form smectic phases (with only a few exceptions [la, 4]) have one or more flexible tail chains. Furthermore, as the chain tails are shortened, the smectic phase disappears, replaced by the nematic phase (Fig. 1). 

The main parameters used to describe a polymer chain are the polymerization index N, which counts the number of repeat units or monomers along the chain, and the size of one monomer or the distance between two neighboring monomers. The monomer size ranges from a few Angstroms for synthetic polymers to a few nanometers for biopolymers. The simplest theoretical description of flexible chain conformations is achieved with the so-called freely-jointed chain (FJC) model, where a polymer consisting of N + I monomers is represented by N bonds defined by bond vectors r/ with j= Each bond vector has a fixed length r,j = a corresponding to the... 

Values of B calculated from the ordinate intercepts are shown in Fig. 23 as a plot of B/(2q)3 against the number of the Kuhn segments N. For N<4, the data points for the indicated systems almost fall on the solid curve which is calculated by Eq. (78) along with Eqs. (43), (51), (52), and Cr = 0. A few points around N 1 slightly deviate downward from the curve. Marked deviations of data points from the dotted lines for the thin rod limit, obtained from Eq. (78) with Le = L and de = 0, are due to chain flexibility the effect is appreciable even at N as small as 0.5. The good lit of the solid curve to the data points (at N 4) proves that the effect of chain flexibility on r 0 has been properly taken into account by the fuzzy cylinder model. 

The Sharpless epoxidation is sensitive to preexisting chirality in selected substrate positions, so epoxidation in the absence or presence of molecular sieves allows easy kinetic resolution of open-chain, flexible allylic alcohols (Scheme 26) (52, 61). The relative rates, kf/ks, range from 16 to 700. The lower side-chain units of prostaglandins can be prepared in high ee and in reasonable yields (62). A doubly allylic alcohol with a meso structure can be converted to highly enantiomerically pure monoepoxy alcohol by using double asymmetric induction in the kinetic resolution (Scheme 26) (63). A mathematical model has been proposed to estimate the degree of the selectivity enhancement. 

Interest in thermotropic liquid crystals has focussed mainly on macroscopic properties studies relating these properties to the microscopic molecular order are new. Lyotropic liquid crystals, e.g. lipid-water systems, however, are better known from a microscopic point of view. We detail the descriptions of chain flexibility that were obtained from recent DMR experiments on deuterated soap molecules. Models were developed, and most chain deformations appear to result from intramolecular isomeric rotations that are compatible with intermodular steric hindrance. The characteristic times of chain motions can be estimated from earlier proton resonance experiments. There is a possibility of collective motions in the bilayer. The biological relevance of these findings is considered briefly. Recent similar DMR studies of thermotropic liquid crystals also suggest some molecular flexibility. 

The second independent motion requires a suitable dynamic model that reflects the geometric constraints of chain flexibility characteristic of polysaccharides. However, no model is yet available that takes polysaccharide structural details into account or describes possible modes of reorientation in the carbohydrate chain. 

The degree of ionization/ and the scaled expansion parameter l as a function of the various parameters that enter the model are obtained by minimizing the total free energy. Analysis revels that the degree of ionization decreases if the chain flexibility or the salt concentration increases [48]. This decease is also observed if the chain length or the dielectric constant is decreased [48],... 

More work needs to be done to develop increasingly accurate representations of the electronic states of peptides and various side chain chromophores. Once this is completed, the models are in place to examine interactions between these states for a given protein conformation. An accurate and flexible model which can calculate CD spectra of a variety of protein structures would be invaluable in the study of protein folding, stability, and structure. 

A racemic mixture of three-layered [3.3]paracyclophane (45) was resolved into two enantiomers by chiral HPLC (on a Daicel OD column), and their absolute configuration was determined by a comparison of the experimental CD spectrum with the theoretical one at the TD-DFT-B3-LYP/TZVP level [55]. A simple model, composed of two p-xylenes and durene (the side chains were modeled again by methyl groups), was used to explain the origin of the chiroptical properties of the three-layered cyclophane system. Due to the flexibility of the [3.3]paracyclophanes, the solvent effects on the conformer distribution and thus on the chiroptical properties were significant (Fig. 10). 

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