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Landau theory
About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.
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TL;DR: In this paper, the authors show that cross-linking in the isotropic state lowers the nematic-isotropic phase transition temperature compared with the unlinked case and the application of suitable stress raises it again.
Abstract: Using classical elasticity theory, the rise in free energy upon crosslinking nematogenic polymers into a network is calculated for the isotropic and nematic phases. Spontaneous strains are allowed for in the network. The consequence of network formation upon nematic–isotropic equilibria is calculated by adding these elastic contributions to a conventional Landau theory. Memory of the crosslinking conditions yields quartic and quadratic additions to the standard Landau theory. We find that crosslinking in the isotropic state lowers the nematic–isotropic phase transition temperature compared with the unlinked case and the application of suitable stress raises it again. Crosslinking in the nematic state raises the transition temperature. We recover the mechanical critical point proposed long ago by de Gennes. Our Gaussian theory encompasses both main‐ and side‐chain polymers. The hairpin limit for main chain networks yields a modulus varying exponentially with temperature. The Landau–de Gennes free energy for comb polymers is presented for the first time.
152 citations
151 citations
Book•
15 Jan 2009
TL;DR: In this paper, the authors present the Landau Theory of Phase Transitions (LTP) and the second quantization of Gaussian Integrals (SINR) for low-dimensional systems.
Abstract: I.- Gaussian Integrals.- Quantum Mechanics.- Statistical physics.- Path Integrals.- Second Quantization.- II.- Functional Integrals.- Interactions and Feynman Diagrams.- Landau Theory of Phase Transitions.- Atomic Physics.- Bose-Einstein Condensation.- Condensation of Fermionic Pairs.- Symmetries and Symmetry Breaking.- Renormalization Group Theory.- III.- Low-Dimensional Systems.- Optical Lattices.- Feshbach Resonances.
148 citations
TL;DR: Renormalization-group recursion relations are used to construct equations of state to first order in this paper in a continuous spin model of critical behavior. But this technique is used to discuss critical behavior along a line of critical points, together with the effect of imposing an ordering field.
Abstract: Renormalization-group recursion relations are used to construct equations of state to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ for continuous spin models of critical behavior. The recursion relations map Hamiltonians out of the critical regime into regions of small correlation length, where Landau theory with fluctuation corrections is employed. This technique is used to discuss critical behavior along a $\ensuremath{\lambda}$ line of critical points, together with the effect of imposing an ordering field. An application of the method to tricritical phenomena is described briefly.
148 citations
TL;DR: In this article, the authors address various aspects on estimating the magnetocaloric effect from magnetization measurements, and the use of a Maxwell relation in first-and second-order phase transitions, including (a) magnetization as a thermodynamic variable in an inhomogeneous situation (structural or chemical distributions, magnetic domains) and (b) non-equilibrium conditions (irreversibility) on first order phase transition, including mixed-phase conditions.
148 citations