Chain fluctuations

Polymer liquid crystals, 75 107-111 Polymer matrices, 26 761-765 Polymer-matrix composites, 73 502 26 751, 755-756 fabrication of, 26 765 Polymer melts, 75 108-109 27 730-731 chain fluctuations in, 27 714 viscosity of, 20 99 21 712-714 Polymer metal composites, smart, 22 718 Polymer microspheres, 9 73-75 Polymer microstructure, polychloroprene, 79 836-838... 

The reaction described above can also be carried out at higher concentration whereby the probability of intramolecular reaction (cyclization) vanishes. So called chain extension processes result from the stoichiometric reaction of a "living" bifunctional precursors with an efficient bifunctional electrophilic deactivator. This polycondensation reaction induces a very large increase of the molecular weight, but is also results in an enhanced polydispersity. - Fractionation is necessary if well defined substances are required. However the average distance between successive hinges along the chain fluctuates only very little. 

The quantum average A1/2 G characterises spin-spin interactions established in the absence of any chain fluctuations. The ratio defined by ... 

This does not mean that at equilibrium there is zero displacement between the ends of the chain at some instant of time, hut rather the average distance between the ends, = 0. Remember that the shape of die chain fluctuates all the time and therefore so does the distance between its ends. Also, although 0, ° 5 0. 

These results, as compared to a previous study [29], illustrate a better agreement between theory and experiments. This can be attributed to a better approximation of the mode distribution involved in the chain fluctuation process and to which the end of the chains are quite sensitive. These data also prove that under our experimental conditions, the relaxation of the chain is dominated by the chain retraction and chain-length fluctuation process. The... 

Alexov, E. Role of the protein side-chain fluctuations on the strength of pairwise electrostatic interactions Comparing experimental with computed pK(a)s. Proteins 2003, 50,94-103. 

Fig. 7 Dynamics of DMPC (a) Berry parameter Ab evolution with temperature (b) Short period chain fluctuations at 250 K, showing variation of the four involved dihedral angles. Reproduced...

There are, of course, two transverse degrees of freedom, and so this last answer incorporates a factor of two appropriate for a chain fluctuating in 3D. 

Statistical distribution of the contour length In the previous sections we regarded the primitive chain as an inexten-sible string of contour length L. In reality, the contour length of the primitive chain fluctuates with time, and the fluctuation sometimes plays an important role in various dynamical processes. 

In summary, the common feature of all constrained chain models is that they impose only limited constraints on chain fluctuations. [101] The constrained-junction fluctuation model restricts fluctuations of junctions and of the center of mass of network chains. The diffused constraint model restricts fluctuations of a single randomly chosen monomer for each network strand. Consequently, all these models can only represent the crossover between the phantom and afflne limits. [101] The phantom limit corresponds to a weak constraining case, while the affine limit corresponds to a very strong constraining potential. 

The only forces driving U towards the saddle point are now those related to the single chain fluctuations (cf. Sect. 4.2), and U will be widely distributed on the imaginary axis. Thus it is not clear whether the Monte Carlo method will work for incompressible systems. 

A hydrocarbon chain is in a constant thermal motion, and without external force field, the chains fluctuate around the most stable position given by the distribution of possible conformations at the temperature. The action of external forces at the ends of a molecule causes displacements of chains from their equilibrium conformations and evokes retractive forces. For a hydrocarbon chain of M = 14,000, extended length 125.5 nm, and the end-to-end distance r = 1 mn, the maximum exerted force is 10 MPa. The level of forces exerted by the random coil macromolecules are much lower than the theoretical strength of the primary bonds. The presence of strong intermolecular interactions, such as hydrogen bonds in polyamides, affects the retractive force substantially, causing a restriction of the number of possible chain conformations. In addition, the transitions... 

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