Spin relaxation in cubic liquid crystals. The role of symmetry

Cubic liquid-crystalline phases are usually regarded as isotropic systems. This view is justified for physical properties that transform as second rank tensors. However, the time correlation functions describing spin relaxation in cubic phases include components that transform as fourth rank tensors, which distinguish between cubic and spherical symmetry. In this work we explore the consequences of this fact for spin relaxation behaviour in cubic phases using group theoretical methods. We identify the two irreducible crystal frame time correlation functions of a cubic phase, derive the orientation dependence of the laboratory frame time correlation functions for single crystal samples, and discuss the relation of the cubic (fourth rank) order parameter to the microstructure of the phase. Finally, as an illustration of the general results, we derive the time correlation functions for a specific model of a micellar cubic phase.     

Dielectric relaxation of water molecules in different lyotropic structures of nonylphenoxypoly(ethylenoxy)ethanol (Ark. 9)

Abstract

Dielectric relaxation of water molecules in the lamellar, L_α, cubic and hexagonal, H_α, lyotropic structures of nonylphenoxy-poly(ethylenoxy)ethanol (Ark. 9) has been studied by dielectric time domain spectroscopy in the frequency range between 10 MHz and 10 GHz. The values of the relaxation times, obtained at room temperature, are the following: 41 ps for the L_α phase, 29 ps for the cubic phase and 22 ps for the H_α phase. As is seen, the relaxation time of bound water is distinctly higher than that of pure water, and it depends strongly on the phase structure. The relaxation times measured for the liquid-crystalline phases as well as for pure Ark. 9 obey the Arrhenius law, and the energy barriers obtained have the following values: (20 ± 2) kJ/mol for all the liquid-crystalline phases, and (30 ± 3) kJ/mol for pure Ark. 9. The former is in good agreement with the value found for bound water in lipid systems whereas the latter is characteristic of the isotropic phase of thermotropic liquid crystals.     

Microstructure and dynamics in lyotropic liquid crystals. Principles and applications of nuclear spin relaxation

Abstract

Nuclear spin relaxation of quadrupolar nuclei provides access to a wide range of properties of lyotropic liquid crystals, ranging from the molecular ordering and dynamics at the interface to the macroscopic viscoelastic behaviour. We emphasize here the unique capability of the spin relaxation method to provide detailed geometric and dynamic information relating to the microstructure of lyotropic liquid crystals, i.e. the metric, curvature, and fluctuations of the dividing interface that separates polar and non-polar regions. This information is conveyed to the spin system via the translational diffusion of surfactants or counterions over the interface. The general principles of the spin relaxation method, as applied to lyotropic liquid crystals, are described, with emphasis on the model-independent information content of the relaxation observables and on the relation to microstructure. Specific results for lamellar, hexagonal, cubic, and nematic phases are also described.     

Spin‐State Ordering on One Sub‐lattice of a Mononuclear Iron(III) Spin Crossover Complex Exhibiting LIESST and TIESST

The two‐step spin crossover in mononuclear iron(III) complex [Fe(salpm)₂]ClO₄ ? 0.5 EtOH ( 1 ) is shown to be accompanied by a structural phase transition as concluded from ⁵⁷Fe Mössbauer spectroscopy and single crystal X‐ray diffraction, with spin‐state ordering on just one of two sub‐lattices in the intermediate magnetic and structural phase. The complex also exhibits thermal‐ and light‐induced spin‐state trapping (TIESST and LIESST), and relaxation from the LIESST and TIESST excited states occurs via the broken symmetry intermediate phase. Two relaxation events are evident in both experiments, that is, two T(LIESST) and two T(TIESST) values are recorded. The change in symmetry which accompanies the TIESST effect was followed in real time using single crystal diffraction. After flash freezing at 15 K the crystal was warmed to 40 K at which temperature superstructure reflections were observed to appear and disappear within a 10 000 s time range. In the frame of the international year of crystallography, these results illustrate how X‐ray diffraction makes it possible to understand complex ordering phenomena.     

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.     

Asymmetric electron spin relaxation in ClO2 solution. Deviation of the motional correlation time from modified Debye theory

In highly viscous solutions the ESR spectra of chlorine dioxide are asymmetrically broadened. Modulation of the anisotropic hyperfine and g tensors accounts for the observed broadening but the correlation time for the motion is much smaller than expected from Debye theory. The calculated hydrodynamic radius is compared with that derived from spin rotational relaxation.     

Irreducible half-integer rank unit spherical tensors

A new class of half-integer rank spherical tensors is introduced. The motivation for investigating this new class of tensors originated from a desire to be able to partition matrices using mixtures of fictitious integer and half-integer spin labels. However, it is shown that they can also be used as annihilation/creation operators for spin-1/2, 3/2, etc., particles. In particular, half-integer rank tensors can be used to add/subtract a spin-1/2 particle from a given ensemble. Thus they can be viewed as the natural generalization of the raising and lowering operatorsI _±, in that they change bothI andM, simultaneously.The concept of a universal rotator is introduced and it is demonstrated that half-integer rank tensors obey the same contractional and rotational properties as their integer counterparts, but with half-integer rank. In addition, it is shown that half-integer rank tensors can be used to factorize the Pauli spin matrices. Finally, an example of the use of half-integer rank tensors in the block-diagonalization of a simple 3 x 3 matrix is presented and discussed.     

A study of molecular dynamics and phase transitions in solid MBBA

Abstract

The solid state polymorphism of liquid crystalline MBBA was investigated by temperature dependent NMR spin-lattice relaxation time measurements. The sensitivity of the method could be utilized because the correlation time of the measurement is in the correlation time region of molecular motion. Motional correlation time and activation energy values were determined and the results show some interesting changes between the different solid phases. Non-trivial variation in the end-chain rotational motion in two crystalline phases has been observed. Conclusions were drawn on the relationship between rotational molecular dynamics, intermolecular order and phase transitions.     

Reorientational eigenmode dynamics: a combined MD/NMR relaxation analysis method for flexible parts in globular proteins

An approach is presented for the interpretation of heteronuclear NMR spin relaxation data in mobile protein parts in terms of reorientational eigenmode dynamics. The method is based on the covariance matrix of the spatial functions of the nuclear spin interactions that cause relaxation expressed as spherical harmonics of rank 2. The approach was applied to characterize the dynamics of a loop region of ubiquitin. The covariance matrix was determined from a conformational ensemble generated by a 5 ns molecular dynamics simulation. It was found that the time correlation functions of the dominant eigenmodes decay in good approximation with a single correlation time. From the reorientational eigenmodes, their eigenvalues, and correlation times, NMR relaxation data were calculated in accordance with Bloch-Wangsness-Redfield relaxation theory and directly compared with experimental (15)N relaxation parameters. Using a fitting procedure, agreement between calculated and experimental data was improved significantly by adjusting eigenvalues and correlation times of the dominant modes. The presented procedure provides detailed information on correlated reorientational dynamics of flexible parts in globular proteins. The covariance matrix was linked to the covariance matrix of backbone dihedral angle fluctuations, allowing one to study the motional behavior of these degrees of freedom on nano- and subnanosecond time scales.     

Low and high frequency dielectric spectroscopy on a liquid crystal with the phase sequence N*-SA-S*c

Abstract

Broadband dielectric measurements on a multicomponent ferroelectric liquid crystal mixture have been performed. The alignment was homeotropic and the cell and sample holder were the same in the whole frequency range. Two relaxation processes have been observed in all liquid crystal phases with shapes given by the Havriliak-Negami and inverted Havriliak-Negami functions. Strengths and frequencies of both modes have been obtained for the different phases. The values of the latter and their activation energies allowed us to assign the low and high frequency mechanism to the molecular reorientation around the transversal axis and around the longitudinal axis, respectively. The behaviour of this high frequency mode does not show any jump in the S_A-S*_c phase transition, neither in the amplitude nor in the frequency, indicating that the appearance of the spontaneous polarization in the S*_c phase is not the consequence of the freezing of this mode.     

Microscopic Motion of Atoms in Simple Liquids at Equilibrium and with Shear Flow

Abstract

We investigate the microscopic mechanism of atomic motion and local stress relaxation in Lennard-Jones, LJ liquids using a new class of correlation functions that emphasise the interplay between an abitrary atom in the fluid and its surrounding shells of atoms. We use the linear momenta and stress tensor to characterise the time dependence of this interaction. We consider a series of correlation functions that give complementary information and build a picture of the single particle and small cluster motion. The central particle and first shell undergo a reversal in momentum at different times after the ‘collision’ of the central particle and its first shell of neighbours. This ‘phase difference’ becomes manifest in the subsequent dynamics probed by the new correlation functions. We also consider the effect of a non-newtonian shear flow on this local dynamical relaxation, using profile biased laminar flow equations of motion. In non-newtonian shear flow we find the momentum transfer between particle and cage to be less pronounced and occur over a wider time range.     

New application of proton nuclear spin relaxation unraveling the intermolecular structural features of low-molecular-weight organogel fibers

Proton nuclear spin relaxation has been for the first time extensively used for a structural and dynamical study of low-molecular-weight organogels. The gelator in the present study is a modified phenylalanine amino acid bearing a naphthalimide moiety. From T(1) (spin-lattice relaxation time in the laboratory frame) and T(1ρ) (spin-lattice relaxation time in the rotating frame) measurements, it is shown that the visible gelator NMR spectrum below the liquid-gel transition temperature corresponds to a so-called isotropic compartment, where gelator molecules behave as in a liquid phase but exchange rapidly with the molecules constituting the gel structure. This feature allows one to derive, from accessible parameters, information about the gel itself. Nuclear Overhauser effect spectroscopy (NOESY) experiments have been exploited in view of determining not only cross-relaxation rates but also specific longitudinal rates. The whole set of relaxation parameters (at 25 °C) leads to a correlation time of 5 ns for gelator molecules within the gel structure and 150 ps for gelator molecules in the isotropic phase. This confirms, on one hand, the flexibility of the organogel fibers and, on the other hand, the likely presence of clusters in the isotropic phase. Concerning cross-relaxation rates, a thorough theoretical investigation in multispin systems of direct and relayed correlations in a NOESY spectrum allows one to make conclusions about contacts (around 2-3 ?) not only between naphtalimide moieties of different gelator molecules but also between the phenyl ring and the naphtalimide moiety again of different gelator molecules. As a result, not only is the head-to-tail structure of amino acid columns confirmed but also the entangling of nearby columns by the naphthalimide moieties is demonstrated.     

How to measure absolute P3HT crystallinity via 13C CPMAS NMR

We outline the details of acquiring quantitative ¹³C cross‐polarization magic angle spinning (CPMAS) nuclear magnetic resonance on the most ubiquitous polymer for organic electronic applications, poly(3‐hexylthiophene) (P3HT), despite other groups' claims that CPMAS of P3HT is strictly nonquantitative. We lay out the optimal experimental conditions for measuring crystallinity in P3HT, which is a parameter that has proven to be critical in the electrical performance of P3HT‐containing organic photovoltaics but remains difficult to measure by scattering/diffraction and optical methods despite considerable efforts. Herein, we overview the spectral acquisition conditions of the two P3HT films with different crystallinities (0.47 and 0.55) and point out that because of the chemical similarity of P3HT to other alkyl side chain, highly conjugated main chain polymers, our protocol could straightforwardly be extended to other organic electronic materials. Variable temperature ¹H NMR results are shown as well, which (i) yield insight into the molecular dynamics of P3HT, (ii) add context for spectral editing techniques as applied to quantifying crystallinity, and (iii) show why T_1ρ^H, the ¹H spin–lattice relaxation time in the rotating frame, is a more optimal relaxation filter for distinguishing between crystalline and noncrystalline phases of highly conjugated alkyl side‐chain polymers than other relaxation times such as the ¹H spin–spin relaxation time, T₂^H, and the spin–lattice relaxation time in the toggling frame, T_1xz^H. A 7 ms T_1ρ^H spin lock filter, prior to CPMAS, allows for spectroscopic separation of crystalline and noncrystalline ¹³C nuclear magnetic resonance signals. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.     

Torque and atomic forces for Cartesian tensor atomic multipoles with an application to crystal unit cell optimization

New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3ⁿ redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θ_pqr are given by introducing Cartesian tensor rotation matrix elements X( R ). A polynomial expression and a recursion relation for X( R ) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D( R ). The expressions for X( R ) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.     

Time‐Resolved Phase Transitions of the Nanocrystalline Cubic to Submicron Monoclinic Phase in Zirconia

The nanocrystalline cubic, tetragonal, and submicron monoclinic phases of pure zirconia were prepared by thermal decomposition of carbonate and hydroxide precursors. The crystallization and isothermal phase transformations of the oxide were studied using high temperature X‐ray diffraction, X‐ray diffraction and Raman spectra of quenched samples. Cubic zirconia formed first, and then progressively transformed to tetragonal and monoclinic phases at temperatures as low as 320°C. The cubic, tetragonal, and monoclinic phases for ZrO₂ were found to be distinct functions of crystallite size, indicating the nanocrystalline nature of these phases. They were found to exist within critical size ranges of 50 to 140 Å, 100 to 220 Å and 190 to 420 Å (±5 Å), respectively. Thus, as the crystallites grow during annealing, they first transform from cubic to tetragonal and then from tetragonal to monoclinic at critical sizes. The classical Avrami equation for nucleation and growth was applied to the tetragonal to monoclinic phase transition.     

CP/MAS Carbon-13 NMR Study of Spin Relaxation Phenomena of Cellulose Containing Crystalline and Noncrystalline Components

Abstract

Cross-polarization, ¹³C rotating frame spin-lattice relaxation and C laboratory frame spin-lattice relaxation processes have been studied for different cellulose samples by CP/MAS ¹³C NMR spectroscopy. It was found that the CP process can be described by a simple thermodynamic model and relative intensities of the respective resonance lines are consistent with the atomic ratios for the spectra obtained at a contact time of about 1 ms. The observed rotating frame spin-lattice relaxation times T^C ₁₀ were dominantly dependent on the time constant T^D _CH by which ¹³C nuclei were coupled to the ¹H dipolar spin system. It was, therefore, impossible to obtain information about molecular     

Twist-bend nematics,liquid crystal dimers,structure–property relations

ABSTRACT

One of the current challenges in liquid crystal science is to understand the molecular factors leading to the formation of the intriguing twist-bend nematic phase (N_TB) and determine its properties. During our earlier hunt for the N_TB phase created on cooling directly from the isotropic phase and not the nematic phase, we had prepared 30 symmetric liquid crystal dimers. These had odd spacers and methylene links to the two mesogenic groups; desirable but clearly not essential features for the formation of the N_TB. Here, we report the phases that the dimers exhibit and their transition temperatures as functions of both the lengths of the spacer and the terminal chains. In addition we describe the transitional entropies, their optical textures, the X-ray scattering patterns and the ²H NMR spectra employed in characterising the phases. All of which may lead to important properties of the twist-bend nematic phase.     

Moments and distribution functions for polypeptide chains. Poly-L-alanine.

Statistical mechanical averages of vectors and tensors characterizing the configurations of polypeptides have been calculated for poly-L-alanines (PLA) of xu = 2-400 peptide units. These quantities are expressed in the reference frame of the first peptide unit, the X axis being situated along the virtual bond, the Y axis in the plane of the peptide unit. The persistence vector a identical to (r) converges rapidly with chain length to its limit a infinity which lies virtually in the XZ plane. Configurational averages of Cartesian tensors up to the sixth rank formed from the displacement vector p = r-a have been computed. For xu greater than 50 the even moments of fourth and sixth rank formed from the reduced vector p for the real chain are well repreented by the freely jointed chain with 21.7 virtual bonds equivalent to one of the model. The moments of p display assymmetry for xu less than 50. Density distribution functions Wa(p), evaluated from the three-dimensional Hermite series truncated at the term in the polynomial involving the tensors of p of sixth rank, display no obvious symmetry for xu less than 50. Approximate spherical symmetry of the distribution of p about a is observed only for xu greater than or equal to 100.