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>Nuclear spinhyphen;lattice relaxation dispersion and segment diffusion in entangled polymers. Renormalized Rouse formalism
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Nuclear spinhyphen;lattice relaxation dispersion and segment diffusion in entangled polymers. Renormalized Rouse formalism
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机译：Nuclear spinhyphen;lattice relaxation dispersion and segment diffusion in entangled polymers. Renormalized Rouse formalism
A formalism for polymer melts was derived linking the spinhyphen;lattice relaxation timeT1, the correlation function of chain tangent vectors and the meanhyphen;square segment displacement with memory functions. Potential normalhyphen;mode number dependences are included. In the limit of infinitely fast decaying memory functions the theory reproduces known expressions characteristic for Rouse dynamics. Interchain excludedhyphen;volume forces were taken into account in the frame of the renormalized Rouse approach lsqb;K. S. Schweizer, J. Chem. Phys.91,5802 (1989)rsqb;. The power law limits predicted on this basis areT1prop;ohgr;1/2,T1prop;ohgr;1/4, andT1prop;ohgr;1/5for theT1dispersion in a sequence of regimes from high to low frequencies. The meanhyphen;square segment displacement obeys lang;r2rang;prop;t1/4, lang;r2rang;prop;t3/8, and lang;r2rang;prop;t2/5in a sequence of limits for increasing times. The spinhyphen;lattice relaxation dispersion of different polymers was studied mainly by the aid of the fieldhyphen;cycling NMR technique. The covered proton frequency range is less than 103Hz to more than 108Hz. The frequency dependence can be described by a series of power laws arising from chain dynamics. Two of these, namelyT1prop;ohgr;0.5andT1prop;ohgr;0.25tending to appear at high and low frequencies, respectively, can be perfectly explained on the basis of the derived renormalized Rouse limits. The third power law,T1prop;ohgr;0.44, which was observed only at rather low frequencies, has no theoretical counterpart in the frame of the renormalized Rouse theory. Some hints that farther reaching polymer theories such as the modendash;mode coupling approach lsqb;K. S. Schweizer, J. Chem. Phys.91,5822 (1989)rsqb; can help to understand this finding are discussed. thinsp;
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