Isotropic Mixing Research Articles

Effects of carbon nanotubes on the isotropic to nematic phase transition in nematic liquid crystal elastomer

The isotropic to nematic phase transition on nematic liquid crystal elastomer - carbon nanotubes composites has been studied theoretically. The model free energy density has been constructed using Flory Huggins theory of isotropic mixing and Landau-de Gennes theory. The effects of carbon nanotubes and external mechanical stress on the isotropic to nematic phase transition of the nematic liquid crystal elastomer-carbon nanotubes composites have been discussed. The volume fraction of carbon nanotubes dependence of the isotropic to nematic transition temperature, mechanical strain and strain birefringence has been calculated. The weak first-order character of the isotropic to nematic phase transition on nematic liquid crystal elastomer-carbon nanotubes composites has been predicted.

Effects of quantum dots on the nematic to smectic-A phase transition

ABSTRACT Experiments on the composites of liquid crystals and quantum dots showed the significant role of quantum dots on the properties of the nematic–smectic-A phase transition. The effects of quantum dots on the nematic-smectic-A phase transition have been discussed using Flory- Huggins theory of isotropic mixing and Landau-de Gennes theory. The impact of quantum dots on the smectic-A order parameters, nematic–smectic-A transition temperature, splay and bend elastic constants has been discussed. The smectic-A order parameters, transition temperature and elastic constants decrease with the increase of volume fraction of quantum dots.

Magnetic field induced isotropic ferrofluid to ferronematic phase transition in thermotropic liquid crystal

Experiments on liquid crystals doped with ferromagnetic nanoparticles predicted the isotropic ferrofluid to ferronematic phase transition. The magnetic field induced isotropic ferrofluid to ferronematic phase transition in thermotropic liquid crystal has been studied theoretically. Theoretical model is based on Flory–Huggins theory of isotropic mixing and Landau-de Gennes theory. The impact of ferromagnetic nanoparticles and magnetic field on the isotropic ferrofluid to ferronematic phase transition and transition temperature has been discussed. Theoretical results predict the magnetic field induced critical point of the isotropic ferrofluid to ferronematic phase transition. The temperature and volume fraction of ferromagnetic nanoparticles dependence of the magnetic birefringence and Cotton-Mouton constant are calculated.

Theoretical study of the nematic to isotropic phase transition in the mixtures of nematic liquid crystal and quantum dots nanoparticles

ABSTRACTThe nematic to isotropic phase transition in the mixtures of nematic liquid crystal and quantum dots nanoparticles has been studied. Flory Huggins theory of isotropic mixing and Landau-de Gennes theory have been used to study the nematic to isotropic phase transition. The effects of quantum dots nanoparticles on the nematic order parameter, transition temperature, and splay elastic constant have been discussed. The decrease of nematic order parameter, transition temperature, and splay elastic constant with the increase in volume fraction of quantum dots nanoparticles has been observed.

Theoretical study of the effects of carbon nanotubes on the rotator phase transitions of pentacosane

ABSTRACT The effects of carbon nanotubes (CNT) on the rotator phase transitions of pentacosane have been studied theoretically. A model has been developed using Flory–Huggins theory of isotropic mixing and Landau theory. The effects of CNT on the lattice distortion and tilt angle on the rotator phases have been discussed. The decrease of lattice distortion and increase of tilt angle in the CNT+pentacosane mixtures have been observed. The first order character of the R I − R I I and R V − R I phase transitions both in pure pentacosane and CNT+pentacosane mixtures have been observed.

Effect of graphene nanoparticles on the isotropic to nematic phase transition

ABSTRACT A model combining with Flory-Huggins theory of isotropic mixing and Landau theory is developed to describe the effect of graphene nanoparticles on the isotropic to nematic phase transition. The temperature and concentration of graphene nanoparticles dependence on the orientational order parameter, transition temperature and thermodynamic quantities near the isotropic to nematic phase transition are discussed. The orientational order parameter, transition temperature and enthalpy near the isotropic to nematic phase transition increase with the increase of graphene nanoparticles.

Stochastic homogenization on perforated domains Ⅰ – Extension Operators

<abstract><p>In this first part of a series of 3 papers, we set up a framework to study the existence of uniformly bounded extension and trace operators for $ W^{1, p} $-functions on randomly perforated domains, where the geometry is assumed to be stationary ergodic. We drop the classical assumption of minimally smoothness and study stationary geometries which have no global John regularity. For such geometries, uniform extension operators can be defined only from $ W^{1, p} $ to $ W^{1, r} $ with the strict inequality $ r < p $. In particular, we estimate the $ L^{r} $-norm of the extended gradient in terms of the $ L^{p} $-norm of the original gradient. Similar relations hold for the symmetric gradients (for $ {\mathbb{R}^{d}} $-valued functions) and for traces on the boundary. As a byproduct we obtain some Poincaré and Korn inequalities of the same spirit.</p> <p>Such extension and trace operators are important for compactness in stochastic homogenization. In contrast to former approaches and results, we use very weak assumptions: local $ (\delta, M) $-regularity to quantify statistically the local Lipschitz regularity and isotropic cone mixing to quantify the density of the geometry and the mesoscopic properties. These two properties are sufficient to reduce the problem of extension operators to the connectivity of the geometry. In contrast to former approaches we do not require a minimal distance between the inclusions and we allow for globally unbounded Lipschitz constants and percolating holes. We will illustrate our method by applying it to the Boolean model based on a Poisson point process and to a Delaunay pipe process, for which we can explicitly estimate the connectivity terms.</p></abstract>

Accurate analysis and perspectives for systematic design of magnetic resonance experiments using single-spin vector and exact effective Hamiltonian theory

Aimed at fundamental understanding and design of advanced magnetic resonance experiments on basis of Hamiltonians, we describe highly convergent and exact effective Hamiltonian methods which alleviate important deficits of current less accurate methods. This involves single-spin vector effective Hamiltonian theory (SSV-EHT) to first order in the interaction frame of rf and chemical shift offsets as well as exact effective Hamiltonian theory (EEHT) being an exact approach to average Hamiltonian theory not relying on interaction frame transformations. Bringing these methods together, we present tools to analyze challenging experiments in need of considering large static components in Hamiltonian (e.g., offsets) while economizing with radiofrequency irradiation power. It is demonstrated how the two complementary tools may provide important new insight into the detailed effective Hamiltonians of advanced NMR experiments, noting that the methods are by no means restricted to NMR. This is demonstrated for isotropic mixing in liquid-state NMR and dipolar recoupling in solid-state NMR where insight into the delicate interplay between bilinear two-spin and linear single-spin terms in the effective Hamiltonian may increase understanding of determinants for broadband excitation and the formation of recoupling resonances. Furthermore, we demonstrate how simple products single-spin effective Hamiltonians may be used as generators of multiple-spin effective Hamiltonians and though this a new approach to density operator calculations for large multiple-spin systems.

Effects of graphene on the smectic-A to chiral smectic-C* phase transition

ABSTRACT The smectic-A to chiral smectic-C* (SmA–SmC*) phase transition in the mixture of graphene nanoparticles and ferroelectric liquid crystal is studied. Combination of Flory–Huggins free energy of isotropic mixing and Landau theory is applied to explain the effects of graphene nanoparticles on the SmA–SmC* phase transition. The temperature and concentration of graphene nanoparticles dependence of tilt angle, spontaneous polarization and dielectric susceptibility in the smectic-C* phase of the SmA–SmC* phase transition are discussed. A qualitative agreement between theoretical results and experimental results is found.

Enhanced Nuclear Magnetic Resonance Spectroscopy with Isotropic Mixing as a Pseudodimension.

Chemical analysis based on liquid-state nuclear magnetic resonance spectroscopy exploits numerous observables, mainly chemical shifts, relaxation rates, and internuclear coupling constants. Regarding the latter, the efficiencies of internuclear coherence transfers may be encoded in spectral peak intensities. The dependencies of these intensities on the experimental parameter that influences the transfer, for example, mixing time, are an important source of structural information. Yet, they are costly to measure and difficult to analyze. Here, we show that peak intensity build-up curves in two-dimensional total correlation spectroscopy (2D TOCSY) experiments may be quickly measured by employing nonuniform sampling and that their analysis can be effective if supported by quantum mechanical calculations. Thus, such curves can be used to form a new, third pseudodimension of the TOCSY spectrum. Similarly to the other two frequency dimensions, this one also resolves ambiguities and provides characteristic information. We show how the approach supports the analysis of a fragment of protein Tau Repeat-4 domain. Yet, its potential applications are far broader, including the analysis of complex mixtures or other polymers.

Effect of silica nanoparticles on the heat capacity of the rotator phase transitions of alkanes

ABSTRACT Experimental studies have shown that quenched disorder induced by silica nanoparticles changes the hysteresis behavior and the heat capacity of the rotator phase transitions of n-alkanes. We theoretically study the effect of silica nanoparticles on the heat capacity near the Liquid–R, R–R and R–R phase transitions of normal alkanes by combining Flory–Huggins free energy of isotropic mixing and Landau free energy. This is followed by theoretical calculations and plotting figures. A qualitative agreement between theoretical and experimental results is observed.

HORRENDOUS NMR: Establishing correlations in solution-state NMR by reinstating non-secular J-coupling terms

Homonuclear isotropic mixing modules allow J-coupled spins to exchange magnetization even when separated by chemical shift offsets that exceed their couplings. This is exploited in TOtal Correlation SpectroscopY (TOCSY) experiments and its variants, which facilitate these homonuclear polarization exchanges by applying broadband RF pulses. These then establish an effective Hamiltonian in which chemical shift offsets are erased, while J-coupling terms –including flip-flop components– remain active. The polarization that these non-secular terms will transfer among systems of chemically inequivalent sites over the course of a mixing period, are widely used modules in 1D and in multidimensional liquid-state NMR. Homonuclear correlation experiments are also common in solids NMR, particularly among X = 13C or 15N nuclei. Solids NMR experiments are often challenged by high-power RF demands which have led to a family of homonuclear solid-state correlation experiments that avoid pulsing on the nuclei of interest, and focus instead on the 1Hs that are bonded to them. These solid experiments usually reintroduce/strengthen 1H-X dipolar couplings; these, in conjunction with assistance from rotational resonance effects, bring back the truncated X-X dipolar interactions and facilitate the generation of cross peaks. The present study explores whether a similar goal can be achieved for solution-state counterparts, based on the reintroduction of truncated flip-flop terms in the J-coupling Hamiltonian via the pulsing on other, heteronuclear species. A proposal to achieve this is derived, and the resulting HOmonucleaR Recoupling by hEteroNuclear DecOUplingS (HORRENDOUS) approach to provide correlations between like nuclei without pulsing on them, is demonstrated.

Smectic-A to chiral smectic-C∗ phase transition in the mixture of ferroelectric liquid crystal and ferromagnetic nanoparticles

Experimental results showed the significant impact of ferromagnetic nanoparticles on the smectic-A to chiral smectic-C∗ (SmA-SmC∗) phase transition. This article presents the thermodynamical description in the mixture of ferroelectric liquid crystal and ferromagnetic nanoparticles. The model is based on Flory-Huggins free energy of isotropic mixing and Landau free energy. The impact of ferromagnetic nanoparticles on the spontaneous polarization, tilt angle, transition temperature and dielectric susceptibility near the SmA-SmC∗ phase transition is discussed. Various topologies in the phase diagrams are discussed clearly. Both the qualitative quantitative agreement between experiments and theory are observed.

Subchannel analysis of thermal-hydraulic performance in rod bundle with spacer grid considering anisotropic turbulent mixing

Combined with the relationship between the time averaged parameters of flow field and the inter-subchannel transverse turbulent mixing velocity, a method for solving the mixing velocity between adjacent subchannels is presented in this paper. Then an anisotropic mixing model, which is based on subchannel-wise inhomogeneous turbulent mixing, is presented to reflect the three-dimensional mixing effect in rod bundle with spacer grid. By comparing the anisotropic mixing model with isotropic mixing model, it is found that the anisotropic mixing model agrees well with the experimental data from literature. In addition, based on the anisotropic mixing model, analysis on the subchannels with different spacer grids is also performed, including configurations with or without the mixing vanes and different arrangements of mixing vanes. It is found that the forced mixing effect between subchannels is mainly caused by the mixing vanes of the spacer grid. Besides, the continuous change of the flow and temperature fields is also caused by mixing vanes, which improves the Departure from Nucleate Boiling Ratio (DNBR) of the rod bundle channel. Also, the effect of different mixing vane arrangements on flow and heat transfer in the rod bundle is analyzed in detail.

Total Correlation Spectroscopy across All NMR-Active Nuclei by Mixing at Zero Field

Multidimensional nuclear magnetic resonance (NMR) is based on a combination of well-established building blocks for polarization transfer. These blocks are used to design correlation experiments through one or a few chemical bonds or through space. Here, we introduce a building block that enables polarization transfer across all NMR-active nuclei in a coupled network of spins: isotropic mixing at zero and ultralow field (ZULF). Exploiting mixing under ZULF-NMR conditions, heteronuclear TOtal Correlation SpectroscopY (TOCSY) experiments were developed to highlight coupled spin networks. We demonstrate 1H-13C and 1H-15N correlations in ZULF-TOCSY spectra of labeled amino acids, which allow one to obtain cross-peaks among all heteronuclei belonging to the same coupled network, even when the direct interaction between them is negligible. We also demonstrate the potential of ZULF-TOCSY to analyze complex mixtures on a growth medium of isotope-labeled biomolecules. ZULF-TOCSY enables the quick identification of individual compounds in the mixture by their coupled spin networks. The ZULF-TOCSY method will lead to the development of a new toolbox of experiments to analyze complex mixtures by NMR.

Crystal - Rotator-I - Rotator-II Phase Transitions in the Mixtures of Alkanes

Using the combination of Flory–Huggins theory of isotropic mixing and Landau theory, we discuss the crystal – rotator-I – rotator-II phase transitions in the binary mixture of alkanes. The influence of concentration on the order parameters and the transition temperatures is discussed. Theoretical results show the first order character of both the rotator-I to crystal and rotator-II to rotator-I phase transitions in the mixture of alkanes. A good agreement between theoretical and experimental results are presented in this paper.

Nematic to smectic-A phase transition in mixture of liquid crystal and nonmesogenic impurities: existence of tricritical point

ABSTRACTExperiments on the mixture of liquid crystals and nonmesogenic impurities showed the significant role of nonmesogenic impurities on the nematic–smectic-A phase transition. Using both Flory–Huggins theory of isotropic mixing and Landau–de Gennes theory, we present a phenomenological theory that discusses the role of such impurities on the nematic–smectic-A phase transition in a mixture of smectic liquid crystal and nonmesogenic impurities. We discuss the impact of nonmesogenic impurities on the order parameters, Frank elastic constants (splay and bend) and transition temperature of the nematic–smectic-A phase transition. Our theoretical results show that there exists a tricritical point for which the second-order nematic–smectic-A phase transition becomes first order at a tricritical point by increasing the concentration of nonmesogenic solute. We find a remarkable agreement between theoretical and experimental results.

Numerical investigation on mixing performance in rod bundle with spacer grid based on anisotropic turbulent mixing model

The interchannel mixing effect is very important for the thermal-hydraulic performance of fuel assembly subchannels in Pressurized Water Reactor (PWR), especially for that of the fuel assembly with spacer grid. In this study, an anisotropic turbulent mixing model with a turbulent mixing coefficient matrix is developed and embedded in an in-house code to analyze the thermal-hydraulic performance of the fuel assembly. The validation of the present turbulent mixing model has been performed by comparing the numerical results with the experimental results for the outlet temperature distribution of the fuel assembly. Then, the thermal-hydraulic performance of 5 × 5 rod bundle with spacer grid is analyzed by comparing the present turbulent mixing model and the conventional isotropic turbulent mixing model which uses a constant value to consider the average mixing effect. It is found that stronger diversion crossflow, more uniform outlet temperature distribution, higher Critical Heat Flux (CHF) and higher Departure from Nuclear Boiling Ratio (DNBR) of the fuel assembly are achieved when using anisotropic turbulent mixing model. In summary, the anisotropic turbulent mixing model depicts the interchannel mixing characteristics of spacer grid more reasonably.

Looped-PROjected SpectroscopY (L-PROSY): A simple approach to enhance backbone/sidechain cross-peaks in 1H NMR

Cross-relaxation and isotropic mixing phenomena leading to the Nuclear Overhauser Effect (NOE) and to the TOCSY experiment, lie at the center of structural determinations by NMR. 2D TOCSY and NOESY exploit these polarization transfer effects to determine inter-site connectivities and molecular geometries under physiologically-relevant conditions. Among these sequences’ drawback, particularly for the case of NOEs, are a lack of sensitivity arising from small structurally-relevant cross peaks. The present study explores the application of multiple Zeno-like projective measurements, to enhance the cross-peaks between spectrally distinct groups in proteins –in particular between amide and aliphatic protons. The enhancement is based on repeating the projection done by Ramsey or TOCSY blocks multiple times, in what we refer to as Looped, PROjected Spectroscopy (L-PROSY). This leads to a reset of the amide/aliphatic transfer processes; the initial slopes of the NOE- or J-transfer effects thus define the cross-peak growth, and a faster cross-peak buildup is achieved upon looping these transfers over the allotted time T1. These projections also help to better preserve the magnetization originating in the amides, resulting in an overall improvement in sensitivity. L-PROSY’s usefulness is demonstrated by incorporating it into two widely used protein NMR experiments: 2D 15N-1H HMQC-NOESY and 15N-filtered 2D NOESY. Different parameters dictating the overall SNR improvement, particularly the protein correlation times and the amide-water chemical exchange rates, were examined, and L-PROSY’s enhancements resulted for all tested proteins. The largest cross-peak enhancements were observed for unstructured proteins, where chemical exchanges with the solvent of the kind that tend to average out NOE cross-peaks in conventional NMR, boost L-PROSY’s cross-peaks by replenishing the amide’s magnetizations within each loop. Enhanced cross-peaks were also found in extensions involving TOCSY-based experiments when applied to proteins with unfolded segments.

Effect of magnetic nanoparticles on the nematic-smectic-A phase transition

Recent experiments on mixed liquid crystals have highlighted the hugely significant role of ferromagnetic nanoparticle impurities in defining the nematic-smectic-A phase transition point. Structured around a Flory-Huggins free energy of isotropic mixing and Landau-de Gennes free energy, this article presents a phenomenological mean-field model that quantifies the role of such impurities in analyzing thermodynamic phases, in a mixture of thermotropic smectic liquid crystal and ferromagnetic nanoparticles. First we discuss the impact of ferromagnetic nanoparticles on the isotropic-ferronematic and ferronematic-ferrosmectic phase transitions and their transition temperatures. This is followed by plotting and discussing various topologies in the phase diagrams. Our model results indicate that there exists a critical concentration of nanoparticle impurities for which the second order N-SmA transition becomes first order at a tricritical point. Calculations based on this model show remarkable agreement with experiment.