How To Get Unlimited Energy In Phase 10
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How To Get Unlimited Energy In Phase 10
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Direct Free Energy Evaluation Of Classical And Quantum Many Body Systems Via Field Theoretic Simulation
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Shubnikov Institute of Crystallography, Federal Scientific Research Center “Crystallography and Photonics”, Russian Academy of Sciences, 119333 Moscow, Russia.
Received: 20 August 2021 / Revised: 23 September 2021 / Approved: 24 September 2021 / Published: 1 October 2021
Experimental And Calculation Approach For Phase Equilibria Among γ/tcp/gcp Op6 Phases At Elevated Temperatures
A molecular-statistical theory of coil-rod-coil triblock copolymers with orientally ordered rod-like fragments was developed using the density functional approach. A clear expression for the free energy was obtained in terms of the direct correlation function of the disordered reference phase, the Florey–Huggins parameter, and the anisotropic interaction potential between the rigid rods. The principle was used to obtain multiple phase diagrams and to calculate numerical orientation and translation order parameter profiles for different polymer architectures as a function of Florey–Huggins parameters, with short-range repulsion and temperature. was specified as a function. In triblock copolymers, the nematic–lamellar transition is accompanied by a breakdown of translational symmetry, which can be caused by two different subtle mechanisms. The first mechanism resembles a low-dimensional crystallization and is typical for conventional smectic liquid crystals. The second mechanism is related to the repulsion between the rod and coil segments and is specific to block copolymers. Both mechanisms are analyzed in detail, along with the effects of temperature, coil fraction and triblock asymmetry on the lamellar phase transition.
Rod–coil block copolymers attract significant attention because they combine the anisotropic properties of smectic liquid crystals with the microphase-separation properties of coiled–coil block copolymers. Molecules contain both flexible chains and rod-like segments of various chemical structures [1, 2, 3, 4, 5, 6] and exhibit several anisotropic phases that are involved in translation and orientational order [7, 8, 9]. Characterized by. Rod-coil block copolymers are promising polymeric materials and can be applied, for example, in polymeric photovoltaics [1, 10, 11] and chickens [12, 13, 14]. From a materials science point of view, triblock copolymers are of particular interest because they have the most flexible molecular architecture. For example, it may be possible to tune the properties of these materials by changing the parameters of the third block. The overall structure of the coil-rod-coil triblock copolymer is reminiscent of conventional liquid crystals, typically consisting of a rigid rod-like core and two flexible tails. At the same time, triblock macromolecules are much larger than typical low molecular weight mesogenic molecules, and their flexible chains are much longer.
Coil-rod-coil triblock copolymers can exhibit several different phases, but the most common one is the orthogonal lamellar phase, similar to the smectic liquid crystal phase A. Although it has the same symmetry as smectic phase A, the translational symmetry transition mechanism is clearly very different. Indeed, the classical statistical theory of conventional smectic liquid crystals assumes that the transition to the smectic phase is analogous to effective one-dimensional crystallization, which is determined by anisotropic interactions between molecules of ordered orientation [15, 16, 17]. On the other hand, one can consider a second mechanism of translational symmetry breaking, which is determined by microphase separation. This is a major mechanism of translational order in lyotropic liquid crystals and block copolymers. In block copolymers, the local separation related to the repulsion between different types of monomers, and the regular layer structure appears mainly due to entropic reasons. At the same time, an element of microphase separation (more precisely separation at the nanoscale) between different molecular fragments (that is, between the rigid core and the flexible tail) in thermotropic liquid crystals may also be important. The related molecular theory, which takes into account both mechanisms, was developed in reference . It is reasonable to assume that the properties of rod-coil block copolymers are mainly determined by the dissociation effect. On the other hand, the orientational interactions between rod-like fragments of macromolecules can be relatively large, and therefore the “crystallization” mechanism of translational symmetry breaking may also be important in these systems. Thus, it is important to evaluate the relative role of these two mechanisms in the coil-rod-coil triblock copolymer, which is the main objective of this paper.
One notices that triblock macromolecules can occur in the lamellar phase in a loop and bridge configuration. In the loop configuration, the coil end chain resides in a single layer, whereas in bridge one, the end chain resides in two separate layers, separated by a layer occupied by the rods. The presence of these bridges greatly affects the mechanical stiffness of coil-rod-coil block copolymer materials, for example, thermoplastic elastomers.
Unveiling The Role Of 2d Monolayer Mn Doped Mos 2 Material: Toward An Efficient Electrocatalyst For H 2 Evolution Reaction
The theory of triblock copolymers is mainly based on the Landau–de Gaines approach to phase transition theory [19, 20, 21] and is mainly limited to coiled–coil triblock copolymers. In this approach, the density–density correlation function of the ideal Gaussian series is used to calculate the parameters of the theory. The advantage of this approach lies in its generality, and has been used to describe many unconventional morphologies. However, one notices that in this theory, the equilibrium inhomogeneous density has only one Fourier harmonic, and the amplitude of this harmonic is assumed to be small. Thus, the approach is mainly justified in the region of the phase diagram, which is close to the isotropic phase, that is, for weak separation.
A statistical theory of rod–coil diblock copolymers was also developed within the framework of SCFT theory [22, 23, 24, 25, 26, 27]. In this approach, the free energy of a copolymer macromolecule in a self-contiguous region is evaluated by solving generalized diffusion equations for quasi-flexible chains with the respective path integral or numerically. Over the past decades, the SCFT principle based on the generalized diffusion equation has been repeatedly applied to rod-coil diblock copolymers [28, 29, 30, 31, 32, 33, 34, 35, 36, 37]. One notices that in systems of fragments of long chains and rigid rods, which are characterized by both orientational and translational degrees of freedom, SCFT theory remains computationally challenging in view of newly developed numerical algorithms  , 38]. This may explain why the current theory of rod–coil triblock copolymers [39, 40] does not account for the orientational interactions between rigid rod segments and their orientational order.
Recently, the authors have developed a new molecular-statistical theory of rod–coil diblock copolymers [41, 42, 43] that employs the same general density functional principle, previously used for nematic and smectic liquid crystals . , 44, 45,] was used to describe it. 46, 47, 48]. This principle is based on the free energy functional, which depends on the single-particle distribution function of the rod and coil segments and does not extend to the power of the order parameter. The equilibrium distribution functions, obtained by free energy minimization, depend on the order parameters and are characterized by an infinite series of Fourier harmonics. Consequently, the molecular theory is expected to be approximately valid even in the region away from the isotropic phase, when the separation is relatively strong. In the region close to the disordered phase, the theory can be reduced to the related Landau–de Gaines theory , as it uses the same correlation function calculated for Gaussian series. Such a molecular-statistical theory is computationally simpler (although they are not as accurate) than the full SCFT theory and can be efficiently used to numerically evaluate all-order parameter profiles.
The paper is arranged as follows. In section 2, we derive the molecular principle of the coil-rod-coil triblock copolymer and treat the associated free energy as functional. In Section 3, the density–density correlation functions between different segments of the triblock copolymer are considered in detail along with the corresponding direct correlation functions. Order parameters and the result of numerical calculation of the corresponding stage
Boron Based Intramolecular Heterocyclic Frustrated Lewis Pairs As Organocatalysts For Co2 Adsorption And Activation
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