Redefinition of the mode Grüneisen parameter for polyatomic substances and thermodynamic implications

Abstract. While the biomechanical properties of bone are reasonably well understood at many levels of structural hierarchy, surprisingly little is known about the response of bone to loading at the ultrastructural and crystal lattice levels. In this study, our aim was to examine the response (i.e., rate of change of the vibrational frequency of mineral and matrix bands as a function of applied pressure) of murine cortical bone subjected to hydrostatic compression. We determined the relative response during loading and unloading of mineral vs. matrix, and within the mineral, phosphate vs. carbonate, as well as proteinated vs. deproteinated bone. For all mineral species, shifts to higher wave numbers were observed as pressure increased. However, the change in vibrational frequency with pressure for the more rigid carbonate was less than for phosphate, and caused primarily by movement of ions within the unit cell. Deformation of phosphate on the other hand, results from both ionic movement as well as distortion. Changes in vibrational frequencies of organic species with pressure are greater than for mineral species, and are consistent with changes in protein secondary structures such as alterations in interfibril cross-links and helix pitch. Changes in vibrational frequency with pressure are similar between loading and unloading, implying reversibility, as a result of the inability to permanently move water out of the lattice. The use of high pressure Raman microspectroscopy enables a deeper understanding of the response of tissue to mechanical stress and demonstrates that individual mineral and matrix constituents respond differently to pressure.Key words: Raman spectroscopy -Bone -Biomechanics -Diamond anvil cell -High pressureThe chemical composition and crystal structure of bone play an essential role in its biological and structural functions [1,2]. Bone tissue can be described as a composite of an organic matrix reinforced with an inorganic mineral phase. The organic matrix is about 90% type I collagen fibrils locally oriented predominantly parallel to each other (in long bone) that provide a supporting matrix upon which the mineral crystals grow. The mineral fraction of bone is a highly impure carbonated apatite situated between collagen fibril cross-links and fibril ends. Both the organic and mineral components and the interactions between the two contribute to boneÕs mechanical properties, including strength, toughness and elasticity. It is not clear though how mineral crystallites deform in response to mechanical loading nor how the matrix deforms. This is particularly true at the atomic level. To better understand deformation it is useful to extract atomic-level compositional information about the changes in inorganic and organic phases that occur when bone undergoes mechanical loading.Raman spectroscopy is a powerful technique for relating bone mechanical properties with bone ultrastructural and crystal lattice changes [3]. Raman spectroscopy provides bone vibrational spectra and, like infrared spectros...

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“…The mode Gru¨neisen parameter equation can be extended to include crystals containing polyatomic ions [23],…”

Section: Discussionmentioning

confidence: 99%

Bone Chemical Structure Response to Mechanical Stress Studied by High Pressure Raman Spectroscopy

et al. 2005

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“…19 A way to obtain an estimation of its value near the room temperature range can be done if the gr€ uneisen parameters of all the Raman active vibrational modes are known. The average gr€ uneisen parameter c av is related to the total molar heat capacity at constant volume, C v ¼ P C i and the linear thermal expansion coefficient a according to c av ¼ 3aV m B 0 /C v , 20,21 where V m is the molar volume and C i is the contribution to the total molar heat capacity of the mode i. The quantity c av can be also obtained as c av ¼ P C i c i /C v .…”

Section: Methodsmentioning

confidence: 99%

Room-temperature vibrational properties of multiferroic MnWO4 under quasi-hydrostatic compression up to 39 GPa

Ruiz‐Fuertes

Errandonea

Gomis

et al. 2014

Journal of Applied Physics

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The multiferroic manganese tungstate (MnWO 4 ) has been studied by high-pressure Raman spectroscopy at room temperature under quasi-hydrostatic conditions up to 39.3 GPa. The low-pressure wolframite phase undergoes a phase transition at 25.7 GPa, a pressure around 8 GPa higher than that found in previous works, which used less hydrostatic pressure-transmitting media. The pressure dependence of the Raman active modes of both the low-and high-pressure phases is reported and discussed comparing with the results available in the literature for MnWO 4 and related wolframites. A gradual pressure-induced phase transition from the low-to the high-pressure phase is suggested on the basis of the linear intensity decrease of the Raman mode with the lowest frequency up to the end of the phase transition. V C 2014 AIP Publishing LLC.

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“…20 On the other hand, for a series of polyamides at room temperature, eq 5b gave: c G ¼ 0.45 to 0.64. 14 Its magnitude was found increasing with T and decreases with P. [21][22][23] The diversity of Grüneisen parameter values originates from the applied methods of measurements, calculation procedures, and extension of the original concept to polyatomic substances having a variety of morphologies.…”

mentioning

confidence: 99%

Equations of state for polyamide‐6 and its nanocomposites. 1. Fundamentals and the matrix

Utracki

2008

J Polym Sci B Polym Phys

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The pressure‐volume‐temperature (PVT) surface of polyamide‐6 (PA‐6) was determined in the range of temperature T = 300–600 K and pressure P = 0.1–190 MPa. The data were analyzed separately for the molten and the noncrystalline phase using the Simha‐Somcynsky (S‐S) equation of state (eos) based on the cell‐hole theory. At Tg(P) ≤ T ≤ Tm(P), the “solid” state comprises liquid phase with crystals dispersed in it. The PVT behavior of the latter phase was described using Midha‐Nanda‐Simha‐Jain (MNSJ) eos based on the cell theory. The data fitting to these two theories yielded two sets of the Lennard‐Jones interaction parameters: ε*(S‐S) = 34.0 ± 0.3 and ε*(MNSJ) = 22.8 ± 0.3 kJ/mol, whereas v*(S‐S) = 32.00 ± 0.1 and v*(MNSJ) = 27.9 ± 0.2 mL/mol. The raw PVT data were numerically differentiated to obtain the thermal expansion and compressibility coefficients, α and κ, respectively. At constant P, κ followed the same dependence on both sides of the melting zone near Tm. By contrast, α = α(T) dependencies were dramatically different for the solid and molten phase; at T < Tm, α linearly increased with increasing T, then within the melting zone, its value step‐wise decreased, to slowly increase at higher temperatures. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 299–313, 2009

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Redefinition of the mode Grüneisen parameter for polyatomic substances and thermodynamic implications

Cited by 75 publications

References 39 publications

Bone Chemical Structure Response to Mechanical Stress Studied by High Pressure Raman Spectroscopy

Bone Chemical Structure Response to Mechanical Stress Studied by High Pressure Raman Spectroscopy

Room-temperature vibrational properties of multiferroic MnWO4 under quasi-hydrostatic compression up to 39 GPa

Equations of state for polyamide‐6 and its nanocomposites. 1. Fundamentals and the matrix

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