Normalized coil dimension

The radius of the spherical reflecting wall around each segment of the coil in solution should be connected to the concentration of the solution. At least it is reasonable to assume a relation c in the semidilute region. The function ft2e(c)/h as a function is shown in Fig. 7, which should simulate the concentration dependence of the flexible polymer coil dimension in a 0-solution. It is interesting to note that the normalized coil dimension, A20(c)/h o decreases with increasing concentration to a minimum value of 0.69 at = 1 and then it will increase with further increase in concentration in a concentrated solution. The function h Q c)/ o given by (Eq. 4) approaches unity when t 0, i.e., c - < , in accord with the experimental fact that in an amorphous solid film the coil dimension is the same as that in a dilute 0-solution. 

In Eq. (III-9) the deformation ratios are defined with respect to a reference state in which the chain dimensions are such that they do not exert any elastic forces on the crosslinks (state of normal coiling). In general, the chains in a network may not actually be in this state at the beginning of a deformation experiment, because the ciosslinking process may quite well exert a, largely unknown, influence on the chain dimensions. 

The interactions between fixed charges on the polymer chain in dilute solution normally expand (repulsive) or contract (attractive) coil dimensions. Counterion binding also influences hydrodynamic volume and involves specific ion binding as well as atmospheric ion binding. Theoretical discussions of these effects can be foimd in References 123 and 124. 

Portions of the polypeptide chains that are not accounted for by a helix or /3 conformation consist of bends and irregularly coiled or extended stretches. Segments of a helix and j3 conformation sometimes deviate slightly from their normal dimensions and geometry. 

Fig. 18. The calculated strength of the magnetic field on the axis of the optimized six-turn 8-mm-long and 5.4-mm-diameter coil (curve v). For comparison, curve c gives the field in a six-turn, constant-pitch coil with the same overall dimensions. Both curves are normalized to the strength B (Q) of the field in the center of the coil. The lower part is a sketch of the optimized coil with the spacings of the turns, the diameter, and the length drawn to scale.

In another characterization of the main direction in a chain molecule according to Kuhn, vector h, joining two ends of the chain is chosen for this purpose In this evaluation of the degree of asymn try of a Gaussian coil, length h can be compared with transverse dimensions of the coil determined by distances hj and hj from vector h relative to the chain points situated at the greatest distance from h in two mutually perpendicular directions normal to It has... 

Animal fibers are made from proteins and the long molecules are built from some 20 or so different types of amino acid molecule. The proportion and arrangement of these different units determine the structure of the protein molecule and the nature of the protein itself. Wool cells come in two different types the para cortex and the ortho cortex, which lie on opposite sides of the fiber and grow at slightly different rates. This causes a three-dimensional corkscrew pattern of coiled springs, giving wool high elasticity and a memory that allows the fibers to recover and resume normal dimensions. 

First of all we shall consider general aspects of the three indicated parameters influence on MWD curves shape. For this purpose we shall constmct the theoretical dependences P CN) with a serial variation when only one from the indicated parameters varies, whereas the other two are constant. In Fig. 29 the curves P OSl) are shown for the case when the coil fractal dimension is variable (or d is variable) and = const = 0.25, b = const = 1.0. In Figs. 29-31 the normalization constant A was chosen so that the maximum magnitude P was equal to about 0.4 for all curves P CN). As follows from the data of Fig. 29, increasing results to displacement of maximum of distribution to the higher N side. This effect is most strongly expressed for Dj,= 2.0, corresponding to 0-conditions [16]. 

At theta-conditions, the intramolecular interactions of the polymer chain are compensated by the solvation force of the solvent molecules and the polymer coil resumes its unperturbed dimensions ( Dimensions of a real polymer coil in Chap. 8). These theta-solvents correspond to thermodynamically poor solvents. The temperature at which the theta-conditions occur (theta-temperature) is normally close to the precipitation point of the polymer-solvent system. 

The ability to predict a band intensity profile opens up an important additional dimension in vibrational analysis. It means that we will be able to relate subtle spectral differences to small structural changes with a greater degree of confidence. Thus, it has been possible to confirm that an observed three-component contour of the amide I band of tropomyosin is indeed expected for a coiled-coil a-helix [142]. Extensions to understanding the normal modes of proteins become possible [143]. The systematic incorporation in an SDFF of dipoles and dipole fluxes to calculate IR intensities [144] will finally bring to the vibrational analysis of polymeric molecules the completeness and flexibility needed to make it a much more powerful structural tool. 

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