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The interpenetration of two chain polymers in a good solvent
dc.contributor.authorWitten, T. A. (Thomas A.) Jr.en_US
dc.contributor.authorPrentis, J. J.en_US
dc.date.accessioned2010-05-06T21:50:26Z
dc.date.available2010-05-06T21:50:26Z
dc.date.issued1982-10-15en_US
dc.identifier.citationWitten, T. A.; Prentis, J. J. (1982). "The interpenetration of two chain polymers in a good solvent." The Journal of Chemical Physics 77(8): 4247-4253. <http://hdl.handle.net/2027.42/70233>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70233
dc.description.abstractThe interpenetration of two excluded‐volume chain molecules of different size in dilute solution is studied via scaling and renormalization methods. The chains are found to interpenetrate much more strongly than smoothed‐density models suggest, in accordance with recent work by Khokhlov. The pair correlation funtion g(r) goes to zero at the origin only as a weak power of r. This power is related to Des Cloizeaux’s exponents ϑi describing intrachain correlations. The power is also related to the scaling exponents of star polymers. The mutual excluded volume MSL of two chains with greatly different length is proportional to the volume of the smaller chain and to the mass of the larger. Thus MSL is much smaller than a smoothed density model would predict. We discuss which chain correlations give rise to this small MSL. The universal coefficient relating MSL to the radius of gyration of the smaller chain is strongly dependent on the dimension d of space, according to our second‐order expansion in 4‐d. The interpenetration behavior predicted here affects measurable thermodynamic, scattering, and physical–chemical properties of the solution.en_US
dc.format.extent3102 bytes
dc.format.extent555167 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleThe interpenetration of two chain polymers in a good solventen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumPhysics Department, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.contributor.affiliationumPhysics Department, University of Michigan, Ann Arbor, Michigan 48109en_US
dc.contributor.affiliationotherPhysique de la Matière Condensée College de France, Paris, Franceen_US
dc.contributor.affiliationotherCorporate Research Science Laboratories, Exxon Research and Engineering, Linden, New Jersey 07036en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70233/2/JCPSA6-77-8-4247-1.pdf
dc.identifier.doi10.1063/1.444336en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
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dc.identifier.citedreferenceThe exponent analogous to A4A4 for a grand ensemble of branch lengths N1⋯N4N1⋯N4 is known, and is related to the correctionsto‐scaling exponent ω described by E. Brézin, J. C. Le Guillou, and J. Zinn‐Justin, in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976), Vol. 6and E. Brézin, C. De Dominicis and J. Zinn‐Justin, Lett. al Nuovo Cimento 9, 483 (1974).In this ensemble chains of all lengths are present, with a statistical weight τ−N1−N2−N3−N4.τ−N1−N2−N3−N4. If the Dranches do not interact, their lengths are comparable as τ→Tcτ→Tc and ⟨N1⟩→∞.⟨N1⟩→∞. But when the branches repel each other this is no longer true. The monomer density ρ increases near the junction point as r1/ν‐d,r1∕ν‐d, and is larger by some factor than the density at the same distance from an arbitrary monomer. Thus a monomer saves repulsive energy by moving from the end of a short branch to the end of a long one. The saving is greater if the short branch is shorter. This indicates that a long branch is unstable against growing at the expense of a shorter one. Thus, the stars in the grand ensemble should have almost all their monomers in one branch. The scaling of their partition function thus has no reason to be the same as that for equal‐branched stars.en_US
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dc.owningcollnamePhysics, Department of


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