Higher‐Order Elastic Constants and Thermoelastic Properties of Ionic Solids

Shanker, J.; Bhende, W. K.

doi:10.1002/pssb.2221360102

Cited by 32 publications

(9 citation statements)

References 134 publications

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“…ref. [23][24][25], knowledge about TOECs can be of immense value for the better understanding of molecular cohesion and organisation in so matter. In particular, the testing of theoretical concepts, for instance related to the Landau theory of phase transitions, 22 may demand for quantitative values of TOECs.…”

Section: 22mentioning

confidence: 99%

Immense elastic nonlinearities at the demixing transition of aqueous PNIPAM solutions

et al. 2013

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Elastic nonlinearities are particularly relevant for soft materials because of their inherently small linear elasticity. Nonlinear elastic properties may even take over the leading role for the transformation at mechanical instabilities accompanying many phase transitions in soft matter. Because of inherent experimental difficulties, only little is known about third order (nonlinear) elastic constants within liquids, gels and polymers. Here we show that a key concept to access third order elasticity in soft materials is the determination of mode Grüneisen parameters. We report the first direct observation of third order elastic constants across mechanical instabilities accompanying the liquid-liquid demixing transition of semi-dilute aqueous poly(N-isopropylacrylamide) (PNIPAM) solutions. Immense elastic nonlinearities, leading to a strong strain-softening in the phase-separating PNIPAM solutions, are observed. Molecular mechanisms, which may be responsible for these immense elastic nonlinearities, are discussed. The importance of third order elastic constants in comparison to second order (linear) elastic constants in the demixing PNIPAM solutions evidences the need to focus more on the general role played by nonlinear elasticity at phase transitions within synthetic and biological liquids and gels. A IntroductionFor so condensed matter, knowledge about its continuum mechanics plays a decisive role in understanding the molecular cohesion and organization.1-21 When so matter is subjected to a sufficiently small static strain, the mechanical response is controlled by linear elastic, but not viscoelastic, properties.21 If liquids, gels or polymers are excited by a dynamical mechanical probe, their viscoelastic properties become relevant. This relevance increases with the complexity of the molecular structure in terms of inter-and intramolecular degrees of freedom. At sufficiently high probe frequencies, oen lying in the upper MHz or GHz regime, the mechanical relaxation processes are dynamically clamped and the mechanical response of the system is purely elastic again. Hence, for so materials the mechanical response may be of linear elastic nature when probed either statically or at sufficiently high probe frequencies. In such case, it can be described by Hooke's law, using the second order elastic constants (SOECs) provided by the linear elastic stiffness tensor of 4 th order.Of course linear elasticity only describes one aspect of the complex mechanical behaviour of so matter. The regime of linear elastic response is oen soon abandoned for so materials as the stress or strain amplitude is increased in stress-strain or dynamic mechanical experiments (e.g. ref. 4-6, 8 and 11-14). In order to quantify this nonlinear elastic response of the material within the frame of continuum mechanics, Hooke's law must be extended. Usually the consideration of third order elastic constants (TOECs), but no higher order elastic constants, is sufficient to describe the nonlinear elastic response. 21,22Because of the usually...

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Section: 22mentioning

confidence: 99%

Immense elastic nonlinearities at the demixing transition of aqueous PNIPAM solutions

et al. 2013

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“…It was also assumed that the parameter b does not change with the lattice spacing. However, b must depend on the Gruneisen parameter y (Ida used the relationship b x 3y) and y normally depends strongly on the volume or the lattice parameter of the crystal [29].…”

Section: (4)mentioning

confidence: 99%

Studies on Melting of Alkali Halides

Shanker

Kumar

1990

Physica Status Solidi (b)

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“…On the basis of overall achievements, we may conclude that the present model I1 is much better than our model I and earlier models [l to 31 in reproducing the cohesive and anharmonic properties, which exhibit important aspects and are directly related to the thermal, elastic, dielectric, and dynamical behaviour of solids [15]. The present results may be further improved with the inclusion of zero-point energy effects.…”

Section: Resultsmentioning

confidence: 47%

Study of elastic properties and their pressure dependence of zincblende structure semiconductors

Singh

1987

Physica Status Solidi (b)

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A three-body force potential is used to derive the correct expressions for third-order elastic constants and pressure derivatives of second-order elastic constants for the zincblende structure semiconductors following the lines of Sharma and Verma. These corrected expressions are used for the first time to study the elastic properties and their pressure dependence of ZnS, ZnSe, and ZnTe. It is found that the inclusion of the corrections and the van der Waals interactions yield more reasonable values of the third-order elastic constants and the pressure derivatives of secondorder elastic constants than those obtained by earlier workers from their somewhat erroneous expressions.Ein Dreikorperkraftpotential wird benutzt, um die korrekten Ausdriicke fur die elastischen Konstanten dritter Ordnung und die Druckableitungen der elastischen Konstanten zweiter Ordnung fur Halbleiter mit Zinkblendestruktur entsprechend dem Herangehen von Sharma und Verma abzuleiten. Diese korrigierten Ausdriicke werden benutzt, um erstmals die elastischen Eigenschaften und ihre Druckabhgngigkeit fur ZnS, ZnSe und ZnTe zu untersuchen. Es wird gefunden, daB die Einbeziehung der Korrekturen und die van der Waals-Wechselwirkungen vernunftigere Werte der elastischen Konstanten dritter Ordnung und der Druckableitungen der elastischen Konstanten zweiter Ordnung liefern als die von anderen Autoren friiher aus ihren etwas fehlerhaften Ausdriicken erhaltenen.

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Higher‐Order Elastic Constants and Thermoelastic Properties of Ionic Solids

Cited by 32 publications

References 134 publications

Immense elastic nonlinearities at the demixing transition of aqueous PNIPAM solutions

Immense elastic nonlinearities at the demixing transition of aqueous PNIPAM solutions

Studies on Melting of Alkali Halides

Study of elastic properties and their pressure dependence of zincblende structure semiconductors

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