Concentration and chain-length dependence of thermodynamic interactions in polyethylene isotope blends

Crist, Buckley

doi:10.1002/(sici)1099-0488(199712)35:17<2889::aid-polb12>3.0.co;2-3

Cited by 8 publications

(26 citation statements)

References 12 publications

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“…Figure gives a plot χ s as a function of 1/ N . This predicted N dependence agrees with the reanalysis of the isotopic polyethylene blend data of Londono et al performed by Crist . We also found that in the long chain limit ( N → ∞), where compositional fluctuations are expected to be negligible based on the Ginzburg criterion, , χ s does not approach the mean field value, χ o , for either temperature considered.…”

Section: Resultssupporting

confidence: 90%

Molecular Weight and Compositional Dependence of Isotopic Blends

Melenkevitz

1998

Macromolecules

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The chain length and compositional dependence of the effective chi parameter, χs, in model isotopic polyethylene blends were determined at two different temperatures using our recently developed optimized cluster theory for polymer mixtures. χs was found to have a concave-up compositional dependence that decreased with increasing temperature and molecular weight, in agreement with neutron scattering measurements. A best fit to the chain length dependence of χs at constant temperature and composition had the form, χs = χs(∞) + D/N, where N is the number of segments comprising the polymers. In addition, the calculated compositional dependence of χs could be accurately described by a simple functional form that was previously proposed to fit experimental data on isotopic blends. However, the theory underestimates the breadth of the compositional dependence reported in the literature.

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Section: Resultssupporting

confidence: 90%

Molecular Weight and Compositional Dependence of Isotopic Blends

Melenkevitz

1998

Macromolecules

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“…Experiments with offcritical blends can yield volume fractions and/or phase concentrations 18,19 that can in principle test the concentration dependence of the thermodynamic χ and hence the significance of χ NS (φ). However, the shape of the binodal is scarcely altered, even when χ has a (small) φ dependence consistent with the (large) concentration dependence of χ NS in Figure 1, 9,10 meaning that phase-separated structures cannot practically distinguish between real and error-generated concentration dependence of χ NS . While this situation is frustrating from the perspective of assessing the reality of χ NS (φ), it also means that phase behavior can be interpreted confidently by the Flory-Huggins model with interaction parameters (constant χ ) χ NS (0.5)) measured for symmetric blends.…”

Section: Discussionsupporting

confidence: 63%

“…Nevertheless, the dominance of experimental reports of upward curvature of χ NS (φ) implies that such responses are genuine reflections of the thermodynamics of the mixed state. This sort of “non-Flory−Huggins” behavior does not affect the relation between χ NS measured for critical blends and macroscopic phase separation. , …”

Section: Discussionmentioning

confidence: 91%

“…Any concentration dependence of the thermodynamic χ will lead to a larger change in the SANS quantity χ NS . It was shown 9 that the ca. 4-fold increase in χ NS seen in Figure 1 corresponds to a much smaller, ca.…”

Section: Introductionmentioning

confidence: 99%

“…Another observation is that the concentration dependence of χ NS is a function of N (or molecular weight) and appears to vanish in the limit of infinite N (Figure 2). Following Krishnamoorti et al, 10 these effects can be summarized by the following empirical expression: 9 Here N e ) N 1 N 2 /(φ 1 N 1 + φ 2 N 2 ) is the appropriate average degree of polymerization for blends in which N 1 * N 2 . The dashed line in Figure 1 is a fit of the PE/ d-PE data to eq 5.…”

Section: Introductionmentioning

confidence: 99%

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Thermodynamic Interactions in Isotope Blends: Experiment and Theory

Crist

1998

Macromolecules

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Small-angle neutron scattering (SANS) studies of binary mixtures provide χNS, a measure of thermodynamic interactions between dissimilar polymer chains, one of which is usually labeled with deuterium. For polymers differing only in isotopic substitution (isotope blends), χNS is seen to diverge strongly upward (or sometimes downward) at low concentrations of either blend component. This concentration dependence seems to vanish in the limit of large degree of polymerization N. Experimental results can be described by χNS(φ,N) = β + γ/Nφ(1 − φ), where φ is the volume fraction of deuterated polymer. For SANS from a series of blends with different φ it is shown that systematic errors in N and/or the static structure factor S(0) lead to precisely the same χNS(φ,N) when the Flory−Huggins interaction parameter χ is constant. While results for some isotope blend systems can be accounted for with reasonable error estimates, others appear to have a real dependence of χNS on φ and N. It is suggested that these “non-Flory−Huggins” effects stem from a modified entropy of mixing that is most evident in dilute blends. The concentration dependence of χNS(φ) has no practical effect on macroscopic phase behavior.

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Neutron Scattering in Analysis of Polymers and Rubbers

Bucknall

2000

Encyclopedia of Analytical Chemistry

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The neutron is in many ways an ideal probe for the investigation of the structure and dynamics of materials. Elastically scattered neutrons can be used to determine the structure of the sample from the atomic to macromolecular length scales, whilst dynamic information describing the vibration, rotation and translation of these molecules is obtained from inelastically scattered neutrons. The use of isotopic substitution provides an easy route to highlighting whole or parts of a molecule in the neutron scattering experiment. Isotopic labeling has been extensively used in polymer studies owing to the large difference between hydrogen and deuterium. The combined use of neutrons often with isotopic labeling schemes has provided a wealth of detailed information about polymer materials, which could not be derived so easily by other methods.

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Concentration and chain-length dependence of thermodynamic interactions in polyethylene isotope blends

Cited by 8 publications

References 12 publications

Molecular Weight and Compositional Dependence of Isotopic Blends

Molecular Weight and Compositional Dependence of Isotopic Blends

Thermodynamic Interactions in Isotope Blends: Experiment and Theory

Neutron Scattering in Analysis of Polymers and Rubbers

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