Thermal expansion and Grüneisen parameter of polyethylene between 5 and 320 K

Engeln, I.; Meissner, M.; Pape, H.

doi:10.1016/0032-3861(85)90195-8

Cited by 20 publications

(9 citation statements)

References 24 publications

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“…Much more precise dilatometric measurements can be made on bulk samples, with results extrapolated to 100% crystallinity. 10,11 Isotropic material 10,12 then gives a single coefficient ␣ poly . Drawn material 12 gives two, ␣ ʈ along the draw direction and ␣ Ќ perpendicular to it; these are approximately equal to ␣ c and (␣ a ϩ␣ b )/2, leaving undetermined the anisotropy in the ab plane at low temperatures.…”

Section: Crystal Structure and Thermal Expansionmentioning

confidence: 99%

Thermal expansion of polymers: Mechanisms in orthorhombic polyethylene

et al. 1998

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Quasiharmonic lattice dynamics is used to examine the mechanisms underlying the anisotropic thermal expansion of orthorhombic polyethylene, with particular attention to low temperature behavior. Several sets of interatomic potentials all give good qualitative agreement with experiment. Tensions caused by vibrations with components away from the bond directions are responsible for the negative expansion along the polymer chains, and contribute significantly to the expansion perpendicular to the chains; associated torques on the bonds have only a small effect, except at very low temperatures. The anisotropy of the expansion perpendicular to the chains results from a subtle interplay of thermal stress and elasticity. The results suggest that this anisotropy will be greatly reduced or even reversed at low temperatures. ͓S0163-1829͑98͒06437-6͔

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Section: Crystal Structure and Thermal Expansionmentioning

confidence: 99%

Thermal expansion of polymers: Mechanisms in orthorhombic polyethylene

et al. 1998

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“…Tension effects can become larger and even dominant in crystals of open structure, where there are many vibrations polarized well away from any bond directions, and in crystals (such as polymers) where there are interactions of greatly differing magnitudes (1). These points are conveniently illustrated by the work of Choy et al (3) and Engeln et al (2). To represent the thermal expansion of polymers, Choy et al employed a model of parallel linear chains, in which central forces were supplemented by a bending force constant to keep the chains stiff; the intrachain bonds were stronger than the interchain bonds by about three orders of magnitude.…”

Section: The R61e Of Central Forcesmentioning

confidence: 99%

“…In the necessity of providing theories to discuss experimental results, many different ad hoc simplifications, assumptions, and approximations have been employed (see, for example, the brief review of Gibbons (I); also Engeln et al (2), Choy et al (3), and references therein). In an attempt to clear u p one area of uncertainty, we have begun at Bristol to make a systematic study of the behaviour of ideal polymer crystals and its dependence both upon structure and upon the nature of the interatomic forces, starting from the simplest models and aiming towards models representing real polymers.…”

Section: Introductionmentioning

confidence: 99%

Thermal expansion and Grüneisen functions of polymer crystal models: 1. Central forces

Barron¹,

Barron²,

Mummery³

et al. 1988

Can. J. Chem.

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. Can. J. Chem. 66,718 (1988).With typical pair potentials, a bond is stretched by vibrations along the bond directions, while contraction is caused by the tension set up by vibrations normal to the bond direction. The r6le of these two effects is studied in calculations for parallel linear-chain and zigzag-chain models. For linear chains and rigid zigzag chains, expansion is positive in the plane normal to the chain direction, although it may be strongly anisotropic in this plane. Expansion along the chain direction is negative, and typically an order of magnitude less than that normal to the chain. For a flexible zigzag chain with bond angle 90°, expansion is positive in all directions; the Griineisen tensor is approximately isotropic, but elastic anisotropy leads to smaller expansion coefficients in the molecular planes. The Reuss-averaged Griineisen function derived from (6-12) pair potentials is about 3.5 for most of the models; this is higher than observed experimentally in polycrystalline polyethylene, indicating the need for more realistic models of organic polymers.RUTH MARGARET BARRON, THOMAS HUGH KENNETH BARRON, PAUL MALCOLM MUMMERY et MICHAEL SHARKEY. Can. J. Chem. 66,718 (1988).Avec des paires typiques de potentiel, une liaison est allongte par des vibrations le long des directions de la liaison, alors qu'une contraction rCsulte d'une tension causte par des vibrations normales a la direction de la liaison. On Ctudie le r61e de ces deux effets dans des calculs sur des modtles de chaines paralltles, 1inCaires ou en zigzag. Pour les chaines linkaires ou en zigzag rigides, l'expansion est positive dans 1e plan normal i la direction de la chaine, mime si cette expansion peut Ctre fortement anisotrope dans ce plan. L'expansion le long de la direction de la chaine est negative et, d'une f a~o n gCnCrale, elle est d'un ordre de grandeur plus faible que celle qui est normale ? i la chaine. Pour une chaine en zigzag flexible avec un angle de liaison de 90°, l'expansion est positive dans toutes les directions; le tenseur de Griineisen est approximativement isotrope, mais l'anisotropie Clastique conduit i des coefficients d'expansion qui sont plus faibles dans les plans molCculaires. La fonction de Griineisen moyenne selon Reuss, obtenue B partir de paires (6-12) de potentiels, est peu pres Cgale i 3,5 pour la plupart des modtles; cette valeur est plus ClevCe que celle observCe exptrimentalement dans le polyCthylene polycristallin et elle indique qu'il est nCcessaire d'avoir des modtles plus rCalistes pour les polymeres organiques.[Traduit par la revue]

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“…For protoacoustic pressure simulations, additional parameters are required: mass density, specific heat, thermal expansion coefficient, and the Grüneisen parameter. Acoustic impedance and Grüneisen parameter were calculated from these table values (Azhari 2010; Engeln, et al 1985; Harris and Avrami 1972; Huang, et al 2007; Petrova, et al 2013; Prakash and Joshi 1970; Villanueva, et al 2014; Yao, et al 2014). Table IV lists parameters collected from experimental data, literature, National Institute of Standard and Technology (NIST) database and the Eclipse treatment planning system.…”

Section: Resultsmentioning

confidence: 99%

“…Other references: (Azhari 2010) g Grüneisen parameter was calculated by Γ=βcs2Cp. Other references: (Engeln, et al 1985; Harris and Avrami 1972; Huang, et al 2007; Petrova, et al 2013; Prakash and Joshi 1970; Villanueva, et al 2014; Yao, et al 2014) …”

Section: Figurementioning

confidence: 99%

Proton range verification in homogeneous materials through acoustic measurements

et al. 2018

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Clinical proton beam quality assurance (QA) requires a simple and accurate method to measure the proton beam Bragg peak (BP) depth. Protoacoustics, the measurement of the pressure waves emitted by thermal expansion resulting from proton dose deposition, may be used to obtain the depth of the BP in a phantom by measuring the time-of-flight of the pressure wave. Rectangular and cylindrical phantoms of different materials (aluminum, lead, and polyethylene) were used for protoacoustic studies. Four different methods for analyzing the protoacoustic signals are compared. Data analysis shows that, for Methods 1 and 2, plastic phantoms have better accuracy than metallic ones because of the lower speed of sound. Method 3 does not require characterizing the speed of sound in the material, but it results in the largest error. Method 4 exhibits minimal error, less than 3 mm (with an uncertainty ⩽1.5 mm) for all the materials and geometries. Psuedospectral wave-equation simulations (k-Wave MATLAB toolbox) are used to understand the origin of acoustic reflections within the phantom. The presented simulations and experiments show that protoacoustic measurements may provide a low cost and simple QA procedure for proton beam range verification as long as the proper phantoms and calculation methods are used.

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Thermal expansion and Grüneisen parameter of polyethylene between 5 and 320 K

Cited by 20 publications

References 24 publications

Thermal expansion of polymers: Mechanisms in orthorhombic polyethylene

Thermal expansion of polymers: Mechanisms in orthorhombic polyethylene

Thermal expansion and Grüneisen functions of polymer crystal models: 1. Central forces

Proton range verification in homogeneous materials through acoustic measurements

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