Universal_aspects of macrom_in_polymer_blends_SC_Phys_RE_E_65_Wignall (2002)

Universal_aspects of macrom_in_polymer_blends_SC_Phys_RE_E_65_Wignall (2002)

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Universal aspects of macromolecules in polymer blends, solutions, and supercritical mixtures Y. B. Melnichenko, 1 G. D. Wignall, 1 and D. Schwahn 2 1 Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 2 Forschungszentrum Ju ¨lich GmbH, D-52425 Ju ¨lich, Germany ~ Received 17 December 2001; published 19 June 2002 ! We demonstrate that macromolecules in miscible polymer blends may behave as good, Q , and poor poly- meric solvents for each other. We construct a conceptual phase diagram, delineating the range of validity of the random-phase approximation, outside of which polymers contract or expand beyond their unperturbed dimen- sions, contrary to common assumptions. Remarkably, the correlation length for polymer blends, solutions, and supercritical mixtures collapses onto a master curve, reflecting universal behavior for macromolecules in polymeric and small-molecule Q solvents. DOI: 10.1103/PhysRevE.65.061802 PACS number ~ s ! : 61.41. 1 e, 61.12.Ex Polymer blends are of increasing scientific and commer- cial importance, and over the past two decades there has been a significant increase in the use of small-angle neutron scattering ~ SANS ! to determine the miscibility of various macromolecules, based on the de Gennes random-phase ap- proximation ~ RPA ! @ 1–4 # : S t 2 1 ~ Q ! 5 S s , A 2 1 ~ Q ! 1 S s , B 2 1 ~ Q ! 2 2 x . ~ 1 ! S t ( Q ) is the total scattering structure factor, which contains information on both intramolecular and intermolecular corre- lations between polymer segments and is related to the cor- relation length of the concentration fluctuations, j . S s , i ( Q ) is the single-chain structure factor which contains informa- tion on the intramolecular correlations, and thus on the di- mensions ~ e.g., the radius of gyration R g , i ! of the polymer components ( i 5 A , B ); the scattering vector is given by Q 5 4 p l 2 1 sin u , where 2 u is the scattering angle and l is the neutron wavelength, and x is the Flory interaction parameter which accounts for all nonideal contributions to the free en- ergy of mixing. The RPA @ Eq. ~ 1 !# is based on the assump- tion that the dimensions of polymer chains remain un- changed on mixing and retain the unperturbed radius of gyration R g ( Q ) ~ as in a melt or in a polymer solution at the Q temperature ! . However, several theoretical @ 5–7 # , com- puter simulation @ 8,9 # , and experimental results @ 10–12 # have suggested that this assumption may not hold universally and that R g may shrink or expand with temperature ~ T ! or concentration ~ f ! . The deviation of R g from R g ( Q ) is well documented in polymer solutions, i.e., mixtures of macromolecules with small molecule solvents ~ liquids or supercritical fluids @ 13 #! . In the ‘‘good’’ solvent domain ( T . Q ), polymer coils swell due to excluded volume interactions, and for T , Q ~ in the ‘‘poor’’ solvent domain ! they collapse due to dominating at- tractive forces between monomers. The effect of temperature on the degree of swelling a 5 R g / R g ( Q ) is maximal in dilute solutions ~ weakly interacting chains ! and diminishes when f ; f * , where f * is the polymer overlap concentration. The
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