scholarly journals Liquid-Crystal Ordering and Microphase Separation in the Lamellar Phase of Rod-Coil-Rod Triblock Copolymers. Molecular Theory and Computer Simulations

Polymers ◽  
2021 ◽  
Vol 13 (19) ◽  
pp. 3392
Author(s):  
Mikhail A. Osipov ◽  
Maxim V. Gorkunov ◽  
Alexander A. Antonov ◽  
Anatoly V. Berezkin ◽  
Yaroslav V. Kudryavtsev
Keyword(s):  
Free Energy ◽  
Correlation Functions ◽  
Density Functional ◽  
Diblock Copolymers ◽  
Microphase Separation ◽  
Triblock Copolymers ◽  
Molecular Model ◽  
Lamellar Phase ◽  
Density Correlation ◽  
Huggins Parameter

A molecular model of the orientationally ordered lamellar phase exhibited by asymmetric rod-coil-rod triblock copolymers has been developed using the density-functional approach and generalizing the molecular-statistical theory of rod-coil diblock copolymers. An approximate expression for the free energy of the lamellar phase has been obtained in terms of the direct correlation functions of the system, the Flory-Huggins parameter and the Maier-Saupe orientational interaction potential between rods. A detailed derivation of several rod-rod and rod-coil density-density correlation functions required to evaluate the free energy is presented. The orientational and translational order parameters of rod and coil segments depending on the temperature and triblock asymmetry have been calculated numerically by direct minimization of the free energy. Different structure and ordering of the lamellar phase at high and low values of the triblock asymmetry is revealed and analyzed in detail. Asymmetric rod-coil-rod triblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter and for several values of the triblock asymmetry. It has been found that the lamellar phase appears to be the most stable one at strong segregation. The density distribution of the coil segments and the segments of the two different rods have been determined for different values of the segregation strength. The simulations confirm the existence of a weakly ordered lamellar phase predicted by the density-functional theory, in which the short rods separate from the long ones and are characterized by weak positional ordering.

scholarly journals Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers

Polymers ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1262
Author(s):  
Mikhail A. Osipov ◽  
Maxim V. Gorkunov ◽  
Alexander A. Antonov
Keyword(s):  
Liquid Crystal ◽  
Order Parameter ◽  
Density Functional ◽  
Diblock Copolymers ◽  
Microphase Separation ◽  
Hexagonal Phase ◽  
Orientational Order ◽  
Order Parameters ◽  
Copolymer Composition ◽  
Rigid Rod

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.

TOWARD A RIGOROUS THEORY OF THE SCREENED ELECTRON-ELECTRON INTERACTIONS IN METALS

1991 ◽  
Vol 05 (18) ◽  
pp. 2951-2972 ◽  
Author(s):  
HUA CHEN ◽  
DANIEL C. MATTIS
Keyword(s):  
Free Energy ◽  
Spin Density ◽  
Correlation Functions ◽  
Linear Response ◽  
Effective Interaction ◽  
Linear Response Theory ◽  
Density Correlation ◽  
Hubbard Interaction ◽  
Zero Range ◽  
New Formula

A microscopic formula for the effective two-body interaction between electrons or holes in an ideal metal is derived within the linear response theory. Both the zero-range Hubbard interaction U0 and the long-range Coulomb interaction, denoted by ΔV(q), are included. The effective interaction, which is necessarily spin-dependent, is expressed in terms of the exact charge and spin density-density correlation functions and of their higher order mixtures. These correlation functions are analyzed diagrammatically. Attention is paid to clarifying the different roles played by U0 and ΔV(q). We also display the corresponding new formula for the free energy. Comparison is made with previous theories.

scholarly journals Different Mechanisms of Translational Symmetry Breaking in Liquid-Crystal Coil–Rod–Coil Triblock Copolymers

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1834
Author(s):  
Mikhail A Osipov ◽  
Maxim V. Gorkunov ◽  
Alexander A. Antonov
Keyword(s):  
Symmetry Breaking ◽  
Density Functional ◽  
Triblock Copolymers ◽  
Translational Symmetry ◽  
Smectic Liquid Crystals ◽  
Huggins Parameter ◽  
Rigid Rods ◽  
Short Range Repulsion ◽  
Effects Of Temperature ◽  
Low Dimensional

A molecular-statistical theory of coil–rod–coil triblock copolymers with orientationally ordered rod-like fragments has been developed using the density functional approach. An explicit expression for the free energy has been obtained in terms of the direct correlation functions of the reference disordered phase, the Flory–Huggins parameter and the potential of anisotropic interaction between rigid rods. The theory has been used to derive several phase diagrams and to calculate numerically orientational and translational order parameter profiles for different polymer architecture as a function of the Flory–Huggins parameter, which specifies the short-range repulsion and as functions of temperature. In triblock copolymers, the nematic–lamellar transition is accompanied by the translational symmetry breaking, which can be caused by two different microscopic 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 rod and coil segments and is typical for block copolymers. Both mechanisms are analyzed in detail as well as the effects of temperature, coil fraction and the triblock asymmetry on the transition into the lamellar phase.

DFT study on the hydrolysis of metsulfuron-methyl: A sulfonylurea herbicide

2018 ◽  
Vol 17 (08) ◽  
pp. 1850050 ◽  
Author(s):  
Qiuhan Luo ◽  
Gang Li ◽  
Junping Xiao ◽  
Chunhui Yin ◽  
Yahui He ◽  
...  
Keyword(s):  
Free Energy ◽  
Water Molecule ◽  
Carbonyl Group ◽  
Energy Barrier ◽  
Density Functional ◽  
Free Energy Barrier ◽  
Functional Theory ◽  
Metsulfuron Methyl ◽  
Catalytic Role ◽  
Hydrolysis Of

Sulfonylureas are an important group of herbicides widely used for a range of weeds and grasses control particularly in cereals. However, some of them tend to persist for years in environments. Hydrolysis is the primary pathway for their degradation. To understand the hydrolysis behavior of sulfonylurea herbicides, the hydrolysis mechanism of metsulfuron-methyl, a typical sulfonylurea, was investigated using density functional theory (DFT) at the B3LYP/6-31[Formula: see text]G(d,p) level. The hydrolysis of metsulfuron-methyl resembles nucleophilic substitution by a water molecule attacking the carbonyl group from aryl side (pathway a) or from heterocycle side (pathway b). In the direct hydrolysis, the carbonyl group is directly attacked by one water molecule to form benzene sulfonamide or heterocyclic amine; the free energy barrier is about 52–58[Formula: see text]kcal[Formula: see text]mol[Formula: see text]. In the autocatalytic hydrolysis, with the second water molecule acting as a catalyst, the free energy barrier, which is about 43–45[Formula: see text]kcal[Formula: see text]mol[Formula: see text], is remarkably reduced by about 11[Formula: see text]kcal[Formula: see text]mol[Formula: see text]. It is obvious that water molecules play a significant catalytic role during the hydrolysis of sulfonylureas.

scholarly journals Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 195
Author(s):  
Pavel A. Korzhavyi ◽  
Jing Zhang
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Complex Materials ◽  
Predictive Capability ◽  
Temperature Dependent ◽  
Disordered Alloys ◽  
Thermal Disorder ◽  
Structure Calculations

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials.

scholarly journals Quadruple Hydrogen Bond-Containing A-AB-A Triblock Copolymers: Probing the Influence of Hydrogen Bonding in the Central Block

Molecules ◽  
2021 ◽  
Vol 26 (15) ◽  
pp. 4705
Author(s):  
Boer Liu ◽  
Xi Chen ◽  
Glenn A. Spiering ◽  
Robert B. Moore ◽  
Timothy E. Long
Keyword(s):  
Hydrogen Bonding ◽  
Self Assembly ◽  
Microphase Separation ◽  
Triblock Copolymers ◽  
Random Copolymer ◽  
Thermomechanical Properties ◽  
Structure Property ◽  
Scanning Calorimetry ◽  
Central Block ◽  
Quadruple Hydrogen Bonding

This work reveals the influence of pendant hydrogen bonding strength and distribution on self-assembly and the resulting thermomechanical properties of A-AB-A triblock copolymers. Reversible addition-fragmentation chain transfer polymerization afforded a library of A-AB-A acrylic triblock copolymers, wherein the A unit contained cytosine acrylate (CyA) or post-functionalized ureido cytosine acrylate (UCyA) and the B unit consisted of n-butyl acrylate (nBA). Differential scanning calorimetry revealed two glass transition temperatures, suggesting microphase-separation in the A-AB-A triblock copolymers. Thermomechanical and morphological analysis revealed the effects of hydrogen bonding distribution and strength on the self-assembly and microphase-separated morphology. Dynamic mechanical analysis showed multiple tan delta (δ) transitions that correlated to chain relaxation and hydrogen bonding dissociation, further confirming the microphase-separated structure. In addition, UCyA triblock copolymers possessed an extended modulus plateau versus temperature compared to the CyA analogs due to the stronger association of quadruple hydrogen bonding. CyA triblock copolymers exhibited a cylindrical microphase-separated morphology according to small-angle X-ray scattering. In contrast, UCyA triblock copolymers lacked long-range ordering due to hydrogen bonding induced phase mixing. The incorporation of UCyA into the soft central block resulted in improved tensile strength, extensibility, and toughness compared to the AB random copolymer and A-B-A triblock copolymer comparisons. This study provides insight into the structure-property relationships of A-AB-A supramolecular triblock copolymers that result from tunable association strengths.

scholarly journals The planar limit of $$ \mathcal{N} $$ = 2 chiral correlators

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Bartomeu Fiol ◽  
Alan Rios Fukelman
Keyword(s):  
Free Energy ◽  
Infinite Number ◽  
Correlation Functions ◽  
Hermitian Matrix ◽  
Hooft Coupling ◽  
Planar Limit ◽  
Single Trace ◽  
Hermitian Matrix Model ◽  
Combinatorial Expression ◽  
Do So

Abstract We derive the planar limit of 2- and 3-point functions of single-trace chiral primary operators of $$ \mathcal{N} $$ N = 2 SQCD on S4, to all orders in the ’t Hooft coupling. In order to do so, we first obtain a combinatorial expression for the planar free energy of a hermitian matrix model with an infinite number of arbitrary single and double trace terms in the potential; this solution might have applications in many other contexts. We then use these results to evaluate the analogous planar correlation functions on ℝ4. Specifically, we compute all the terms with a single value of the ζ function for a few planar 2- and 3-point functions, and conjecture general formulas for these terms for all 2- and 3-point functions on ℝ4.

scholarly journals Dissipative Particle Dynamics Study on Interfacial Properties of Symmetric Ternary Polymeric Blends

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1516
Author(s):  
Dongmei Liu ◽  
Kai Gong ◽  
Ye Lin ◽  
Tao Liu ◽  
Yu Liu ◽  
...  
Keyword(s):  
Interfacial Tension ◽  
Chain Length ◽  
Triblock Copolymer ◽  
Diblock Copolymers ◽  
Triblock Copolymers ◽  
Dissipative Particle Dynamics ◽  
Interfacial Properties ◽  
Particle Dynamics ◽  
Polymeric Blends ◽  
Polymer Component

We investigated the interfacial properties of symmetric ternary An/AmBm/Bn and An/Am/2BmAm/2/Bn polymeric blends by means of dissipative particle dynamics (DPD) simulations. We systematically analyzed the effects of composition, chain length, and concentration of the copolymers on the interfacial tensions, interfacial widths, and the structures of each polymer component in the blends. Our simulations show that: (i) the efficiency of the copolymers in reducing the interfacial tension is highly dependent on their compositions. The triblock copolymers are more effective in reducing the interfacial tension compared to that of the diblock copolymers at the same chain length and concentration; (ii) the interfacial tension of the blends increases with increases in the triblock copolymer chain length, which indicates that the triblock copolymers with a shorter chain length exhibit a better performance as the compatibilizers compared to that of their counterparts with longer chain lengths; and (iii) elevating the triblock copolymer concentration can promote copolymer enrichment at the center of the interface, which enlarges the width of the phase interfaces and reduces the interfacial tension. These findings illustrate the correlations between the efficiency of copolymer compatibilizers and their detailed molecular parameters.

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