Small-Angle Neutron Scattering Investigation of Topological Constraints and Tube Deformation in Networks

Straube, E.; Urban, Volker S.; Pyckhout‐Hintzen, Wim; Richter, D.; Glinka, C. J.

doi:10.1103/physrevlett.74.4464

Cited by 67 publications

(94 citation statements)

References 12 publications

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“…A common observation in these experiments is that contour plots of the two dimensional scattering intensity take on a diamond or "lozenge" shape. The experiments fall mainly into two categories; for pure networks with dilute labeled chains [1] the lozenge pattern is permanent and does not relax, but if the labeled species is mobile the lozenge pattern relaxes and is a precursor to "butterfly" contour patterns [2,3]. In this Letter we demonstrate that the lozenge shape can largely be explained by taking into account those chain sections in the system which are not directly deformed by the stretch.…”

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confidence: 84%

“…Straube et al [1] presented modifications, empirically introduced at the level of the final result of Warner and Edwards, which fitted the data well and were intended to describe a deformation of the localizing tube-potential [8]. However, we have found [9] that if the assumptions of Straube et al are implemented at the fundamental level of the model, it is impossible to derive their suggested formula.…”

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confidence: 98%

“…It is found that for a specific angle between the scattering vector q and the stretch direction, the scattering is to a good approximation the same as that of the undeformed system. Experimentally [1], this angle is found to be given by the condition…”

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confidence: 99%

“…A modified form of the Warner-Edwards result has been used recently by Straube et al [1,6,7] to interpret a series of experiments on stretched, labeled networks. One experiment [1] involved scattering from networks formed by randomly crosslinking melts which contained a small fraction of deuterated chains, providing a crucial test for the Warner-Edwards result.…”

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confidence: 99%

“…One experiment [1] involved scattering from networks formed by randomly crosslinking melts which contained a small fraction of deuterated chains, providing a crucial test for the Warner-Edwards result. It was found that the original Warner-Edwards expression did not consistently fit the neutron scattering patterns obtained.…”

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confidence: 99%

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``Lozenge'' Contour Plots in Scattering from Polymer Networks

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McLeish

1997

Phys. Rev. Lett.

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We present a consistent explanation for the appearance of "lozenge" shapes in contour plots of the two dimensional scattering intensity from stretched polymer networks. By explicitly averaging over quenched variables in a tube model, we show that lozenge patterns arise as a result of chain material that is not directly deformed by the stretch. We obtain excellent agreement with experimental data.[ S0031-9007(97)

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confidence: 98%

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``Lozenge'' Contour Plots in Scattering from Polymer Networks

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McLeish

1997

Phys. Rev. Lett.

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Small‐Angle Neutron Scattering

Urban

2012

Characterization of Materials

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Small‐angle neutron scattering (SANS) probes structural details at the nanometer scale in a nondestructive way. This chapter gives an introduction to scientists who have no prior small‐angle scattering knowledge but seek a technique that allows elucidating structural information in challenging situations that thwart approaches by other methods. SANS is applicable to a wide variety of materials including metals and alloys, ceramics, concrete, glasses, polymers, composites, and biological materials. Isotope and magnetic interactions provide unique methods for labeling and contrast variation to highlight specific structural features of interest. In situ studies of a material's responses to temperature, pressure, shear, magnetic and electric fields, etc., are feasible as a result of the high penetrating power of neutrons. SANS provides statistical information on significant structural features averaged over the probed sample volume, and one can use SANS to quantify with high precision the structural details that are observed, for example, in electron microscopy. Neutron scattering is nondestructive; there is no need to cut specimens into thin sections, and neutrons penetrate deeply, providing information on the bulk material, free from surface effects. The basic principles of a SANS experiment are fairly simple, but the measurement, analysis, and interpretation of small‐angle scattering data involve theoretical concepts that are unique to the technique and that are not widely known. This chapter includes a concise description of the basics, as well as practical know‐how that is essential for a successful SANS experiment.

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