Bimodal Floquet description of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance

A theoretical treatment of heteronuclear dipolar decoupling in solid-state nuclear magnetic resonance is presented here based on bimodal Floquet theory. The conditions necessary for good heteronuclear decoupling are derived. An analysis of a few of the decoupling schemes implemented until date is presented with regard to satisfying such decoupling conditions and efficiency of decoupling. Resonance conditions for efficient heteronuclear dipolar decoupling are derived with and without the homonuclear (1)H-(1)H dipolar couplings and their influence on heteronuclear dipolar decoupling is pointed out. The analysis points to the superior efficiency of the newly introduced swept two-pulse phase-modulation (SW(f)-TPPM) sequence. It is shown that the experimental robustness of SW(f)-TPPM as compared to the original TPPM sequence results from an adiabatic sweeping of the modulation frequencies. Based on this finding alternative strategies are compared here. The theoretical findings are corroborated by both numerical simulations and representative experiments.     

An adaptable NMR broadband decoupling scheme

A broadband heteronuclear decoupling scheme for high resolution liquid phase NMR spectroscopy is described, based on adiabatic fast passage with a linear frequency sweep. It is shown that the flexible choice of shaping function for the radiofrequency amplitude profile allows the method to be adapted to fit a wide range of sample parameters and experimental conditions. The practical limitations on phase cycling are emphasized. Expressions are derived to guide the choice of operating parameters so as to achieve a large effective bandwidth, low radiofrequency power dissipation, or weak cycling sidebands in the decoupled spectrum.     

Effect of Decoupling of Molecular Segments,Microscopic Stress‐Transfer and Confinement of the Nanophases in Semicrystalline Polymers

Summary: Semi‐crystalline macromolecules are globally metastable, multi‐phase systems with phase dimensions ranging from micrometers to nanometers. The polymer molecules, being usually longer than one micrometer, cross the boundaries and decouple at the interfaces. This decoupling is often not complete and different degrees of influence are extended across the interfaces. Thermodynamically, crystals can be characterized by their melting behavior and non‐crystalline phases by their glass transition. On weak coupling, the non‐crystalline segments only show a broadening of the glass transition to higher temperature. With stronger coupling, non‐crystalline material may remain solid at the transition of the bulk‐amorphous phase and form a separate, rigid‐amorphous nanophase, or rigid amorphous fraction, RAF. The RAF undergoes its glass transition either below, at, or even above, the melting temperature. In the presence of a RAF, the semi‐crystalline polymers may be a system of three or more types of phases with different relaxation effects due to the coupling between the phases. This and other examples of decoupling are discussed here and a general concept is developed. This applies to positional decoupling at positions of chemical changes within the molecule, such as in copolymers, and to physical changes, such as in entanglements, and is not limited to decoupling at interfaces. Finally, it is pointed out that there is also the possibility of a temporal decoupling of thermodynamically simultaneous changes, which on sufficiently slow kinetics in one may change to consecutive changes. Many of these aspects of decoupling on a molecular scale influence the macroscopic properties and must be considered for the analysis and application of modern materials.

Illustration of reversible melting of folded chain crystals.     

Infrared linear dichroism as a tool to evaluate volatile guest partition between amorphous and nanoporous‐crystalline polymer phases

Desorption kinetics of ethene, propene, and butadiene from films exhibiting axially oriented nanoporous‐crystalline δ phases of syndiotactic polystyrene (s‐PS) have been followed by gravimetric and infrared linear dichroism measurements. The reported data can be rationalized by assuming that, after the initial desorption mainly involving molecules absorbed in the amorphous phase, most gaseous molecules are included as guest in the nanoporous‐crystalline phase. This allows establishing a simple method to evaluate guest partition between nanoporous‐crystalline and amorphous polymeric phases, which possibly can be applied for most volatile guest molecules. The described method also allows establishing the presence of one guest molecule (ethene, propene, or butadiene) per cavity of the nanoporous δ form. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006     

Phase Behavior and Mesophase Structures of 1,3,5‐Benzene‐ and 1,3,5‐Cyclohexanetricarboxamides: Towards an Understanding of the Losing Order at the Transition into the Isotropic Phase

One of the simplest and most‐versatile motifs in supramolecular chemistry is based on 1,3,5‐benzenetricarboxamides. Variation of the core structure and subtle changes in the structures of the lateral substituents govern the self‐assembly and determine the phase behavior. Herein, we provide a comprehensive comparison between the phase behavior and mesophase structure of a series of 1,3,5‐benzene‐ and 1,3,5‐cyclohexanetricarboxamides that contain linear and branched alkyl substituents. Depending on the substituent, different crystalline, plastic crystalline, and liquid crystalline phases were formed. The relatively rare columnar nematic (N_C) phase was only observed in cyclohexane‐based trisamides that contained linear alkyl substituents. Of fundamental interest in liquid crystalline supramolecular systems is the transition from the mesomorphic state into the isotropic state and, in particular, the question of how the order decreases. Temperature‐dependent IR spectroscopy and XRD measurements revealed that columnar H‐bonded aggregates were still present in the isotropic phase. At the clearing transition, mainly the lateral order was lost, whilst shorter columnar aggregates still remained. A thorough understanding of the phase behavior and the mesophase structure is relevant for selecting processing conditions that use supramolecular structures in devices or as fibrillar nanomaterials.     

A common theory for phase-modulated homonuclear decoupling in solid-state NMR

We propose a new framework for homonuclear dipolar decoupling in solid-state NMR that provides a theoretical link between the FSLG, PMLG and DUMBO families. We show that through the use of a Legendre polynomial basis, the phase modulation of these decoupling schemes can be described by the same set of parameters, permitting for the first time a direct theoretical comparison between these methods. Use of this common basis reveals that the central decoupling mechanism is the same for DUMBO and FSLG/PMLG and that a similar vector picture can be used to describe both methods. In addition to the common root of decoupling efficiency, this new analysis highlights two major points of difference between the methods. First, the DUMBO phase modulation consists not only of a linear change in phase with time à la PMLG but also smaller high-order oscillations, which act to improve line-narrowing performance. Second, we show how the DUMBO phase waveforms are generated from a four-step permutation of a single asymmetric unit, in contrast to the two-step permutation of PMLG. Numerical simulations and experimental results suggest that this latter point of difference is responsible for the superior performance of DUMBO in the presence of significant RF inhomogeneity.     

Equilibrium short‐range order in the isotropic phase of a poly(ester‐imide) with a C22H44 alkane spacer

Small‐angle X‐ray scattering (SAXS) was performed on a sample of poly(4,4′‐ phthaloimidobenzoyldoeicosamethyleneoxycarbonyl) (PEIM‐22) as a function of temperature. Wide‐angle X‐ray diffraction and differential scanning calorimetry were used to follow the isotropization of the crystalline PEIM‐22. The crystals of PEIM‐22 consist of biphasic layers up to the isotropization temperature. A series of SAXS peaks are observed for the crystals between θ = 0.3 and 3.5°. The width of these peaks indicates the formation of a smectic‐like, crystalline layer structure of a coherently scattering domain size of only 3–4 repeating units. In the isotropic phase, a single, broader peak remained at a spacing of ≈2.6 nm, suggesting even at high temperature the existence of equilibrium, short‐range, local order. The SAXS profiles were calculated based on a model of alternating layers of a linear, paracrystalline lattice. The results were discussed together with similar data on model compounds in the literature, and it is suggested that the short‐range order in the isotropic phase is due to a nanometer‐scale separation of the polar, aromatic phthaloimidobenzoyl from the flexible doeicosamethyleneoxycarbonyl. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 611–621, 2000     

An experimental study of decoupling sequences for multiple-quantum and high-resolution MAS experiments in solid-state NMR

Recently, a sequence for heteronuclear dipolar decoupling in solid-state NMR, namely SWf-TPPM, was introduced by us. Under magic-angle spinning (MAS), the decoupling efficiency of the sequence was unaffected over a range of values for various experimental parameters such as the pulse length, pulse phase, and 1H resonance offset. We here demonstrate its use in multiple-quantum (MQ) and high-resolution (HR) MAS experiments. This sequence further improves the MQMAS spectra compared to the earlier reported decoupling sequences with improved immunity to any missets of the pulse length, pulse phase and decoupler offset. In contrast, for HRMAS, the simple CW scheme is as efficient as any of the decoupling schemes that were studied.     

Pulsed‐laser–deposited and plasma‐polymerized polytetrafluoroethylene (PTFE)‐like thin films: A comparative study on PTFE‐specific properties

Glass‐like and structural first‐order phase transitions are investigated in polytetrafluoroethylene (PTFE) foils and PTFE‐like films prepared by pulsed‐laser deposition (PLD) and plasma polymerization (PP). A structural comparison of the investigated polymers is performed by infrared spectroscopy and dielectric dilatometry. It is shown that dielectric dilatometry (the measurement of the susceptance vs. temperature) provides a simple and elegant means for detecting volumetric transitions in thin nonpolar polymer films. In conventional PTFE foils, the known glass‐like and structural first‐order phase transitions are identified. The structure of pulsed‐laser deposited PTFE strongly depends on the target material, ranging from highly crystalline films showing only structural phase transitions to films strongly deviating from PTFE foils, with structural characteristics comparable to plasma‐polymerized fluorocarbons. The dielectric loss of the highly crystalline PLD films compares favorably with conventional PTFE foils, making the films attractive for new applications in miniature electret devices. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2115–2125, 1999     

Improved Proton Decoupling in NMR Spectroscopy of Crystalline Solids Using the SPINAL-64 Sequence

Summary.  The performance of three different spin decoupling schemes, CW, TPPM, and SPINAL-64 is compared, by recording proton decoupled ¹³C NMR spectra of a crystalline glycine sample, with 20% isotopic labelling. At a magnetic field of B ₀ = 14.1 T, the two phase modulated pulse schemes, TPPM and SPINAL-64, are shown to give decisively better results than CW decoupling, and the SPINAL-64 sequence is found to perform better than TPPM. It is suggested that in NMR of crystalline solids, SPINAL-64 offers a viable and competitive alternative to the well established TPPM decoupling technique, especially at higher magnetic fields. Corresponding author. E-mail: thomas.braeuniger@durham.ac.uk Received May 6, 2002; accepted May 22, 2002     

Influence of measurement frequency on the pretransitional behaviour of the no-linear dielectric effect in the isotropic phase of liquid crystalline materials

Results are presented of the non-linear dielectric effect (NDE) as a function of temperature (T) in the isotropic phase on approaching the nematic phase for the liquid crystalline materials 4-cyano-4-hexylbiphenyl (6CB), 5-heptyl-2-(4-cyanophenyl)pyrimidine smectic A phase of 4-cyano-4-decylbiphenyl (10CB). For low measurement frequencies (f) the NDE 1(T) exhibits linear behaviour from the clearing temperature (T) up to about C TC50 K. Increase of f causes an increased deviation from this dependence near T C. The influence of the measurement frequency can be associated with the link between the system time-scale, and the measurement time-scale defined by the relaxation time of pretransitional processes (tau ),(f1). A quantitative agreement with de Gennes model NDE 1(T) analysis and with the results of time- and frequency-resolved the relation derived from the Landauof Kerr effect studies is shown. A possible influence of the intensity of the weak measurement field on the pretransitional effect in the immediate vicinity of TC is discussed. Similiarities between pretransitional behaviour in the isotropic phase of the nematogens and in the homogeneous phase of a critical binary solution are considered. (HCPP) and the     

Theoretical studies of the influence of backflow on the dynamical behaviour of a Fredericks transition of a ferroelectric smectic C* liquid crystal in the bookshelf geometry

The elastic-hydrodynamic theory for the ferroelectric smectic C* phase is reviewed and the governing equations for the dynamical behaviour of a surface stabilized ferroelectric liquid crystalline cell are written down, taking the possibility of macroscopic mass flow in the system into account. The influence of backflow effects on the dynamical cell behaviour and a control parameter, determining whether backflow effects will be of importance or not, is derived. It is shown that when backflow effects are pronounced, the response time of the switching can be considerably decreased. Also, the shape of the c-director and velocity profiles across the cell are shown to be strongly dependent on the presence of backflow.     

Crystalline/Crystalline Phase Transitions in Polymer Systems Consisting of Finite‐Size Crystals in Each Crystalline Phase: Generalized Gibbs‐Thomson Equation

For polymer systems of two crystalline phases of one polymer component, each phase being consisted of polymer crystals of a finite size, we derive the crystalline‐crystalline phase transition relationship, i.e., generalized Gibbs‐Thomson equation. Its application combined with the crystalline‐liquid transition relationship (usual Gibbs‐Thomson equation) to the phase behavior of PT phase diagram of polyethylene (PE) is investigated, where the orthorhombic‐hexagonal phase transition of PE crystal under high pressure being involved. Comparison with experimental data leads to the estimates of the structural characteristics such as the ratios of (the end surface free energy of polymer crystal/crystal length) for the respective crystalline phases.

     

Solid‐state NMR characterizations on phase structures and molecular dynamics of poly(ethylene‐co‐vinyl acetate)

Solid‐state nuclear magnetic resonance spectroscopy and relaxation measurements, together with DSC, have been used to elucidate the structures and molecular dynamics in poly(ethylene‐co‐vinyl acetate) (EVA). It has been found that besides immobile orthorhombic and monoclinic crystalline phases, the third mobile crystalline phase (possibly the phase) of a considerable amount (36% of total crystalline phases) appears in the EVA samples, which forms during room‐temperature aging as a result of the secondary crystallization and melts at temperature somewhat higher than room temperature. Such a mobile crystalline phase has not only the well‐defined chemical shift of its own, but also has different molecular mobility from the orthorhombic phase. The mobile crystalline phase is characterized by the rapid relaxation of the longitudinal magnetization, which is caused by conventional spin‐lattice relaxation, while the slow relaxation of the longitudinal magnetization occurring in the orthorhombic phase is originated from the chain diffusion. In addition, the amorphous phase also contains two components: an interfacial amorphous phase and a melt‐like amorphous phase. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2864–2879, 2006     

Heteronuclear isotropic mixing separated local field NMR spectroscopy

This paper presents a theoretical, numerical, and experimental study of a new class of separated local field (SLF) techniques. These techniques are based on the heteronuclear isotropic mixing leading to spin exchange via the local field (HIMSELF). It is shown that highly efficient and robust SLF experiments can be designed based on double channel windowless homonuclear decoupling sequences. Compared to rotating frame techniques based on Hartmann-Hahn cross polarization, the new approach is less susceptible to the frequency offset and chemical shift interaction and can be applied in the structural studies of macromolecules that are uniformly labeled with isotopes such as (13)C and (15)N. Furthermore, isotropic mixing sequences allow for transfer of any magnetization component of one nucleus to the corresponding component of its dipolar coupled partner. The performance of HIMSELF is studied by analysis of the average Hamiltonian and numerical simulation and is experimentally demonstrated on a single crystalline sample of a dipeptide and a liquid crystalline sample exhibiting motionally averaged dipolar couplings.     

Phase behavior and structure of liquid crystalline solutions of cellulose derivatives

Summary Structural and thermodynamic characteristics of liquid-crystalline solutions of four cellulose derivatives in a range of solvents were studied. Basic observations were made on these systems using polarized light microscopy, small angle light scattering, dilute solution and concentrated solution viscosities. The polymers studied include hydroxypropyl cellulose (HPC), cellulose acetate butyrate (CAB), ethyl cellulose (EC), and cellulose triacetate (CT). The formation of the liquid crystalline phase was shown to strongly depend on polymer concentration, solvent type and temperature. The critical volume fraction of polymer required to form the liquid crystal phase varied significantly as the solvent changed. The critical volume fraction decreased with increasing solvent acidity and polymer intrinsic viscosity in a given solvent. The breadth of the two phase region seems to decrease with increasing acidity. The liquid crystalline phase was in most cases determined to be cholesteric. In all cases positively birefringent cellulose derivatives form negative spherulitic domains. In one case, the negativity birefringent system (cellulose triacetate) formed positively birefringent spherulitic liquid crystalline domains. This is interpreted to mean the structure organizes itself by a tangential alignment of polymer chains within the domain. SALS measurements appear to detect domains and in some cases cholesteristic pitch.With 5 figures and 4 tables     

Capillary Thermodynamics of Nematic Polymer Interfaces

The Cahn‐Hoffman capillarity vector thermodynamics formalism for curved anisotropic interfaces is adapted to soft liquid crystalline polymer‐isotropic fluid interfaces. The Cahn‐Hoffman formalism in conjunction with the interfacial Landau‐de Gennes model is used to derive compact expressions for the capillary pressure, tangential Marangoni force, and interfacial torque. It is shown that the interfacial thermodynamics of nematic polymers can be analyzed in terms of three distinct modes: (i) area size change, (ii) area rotation, and (iii) tensor order parameter curvature. The formalism allows to clearly identify the nature and magnitude of these three contributions. Characteristic cases biaxial and uniaxial nematic ordering states are analyzed. Anisotropic liquid crystal surfaces display a number of novel interfacial effects: (a) capillary pressure even for flat surfaces, (b) tensor order parameter‐dependent renormalization of the tension coefficients due to anchoring energy, (c) tensor order parameter‐driven transitions between classical Laplace pressure and non‐classical behavior, (d) Laplace‐like capillary pressure due solely to orientation curvature, (e) generation of Marangoni forces through interfacial order and/or orientation gradients, and (f) surface torques generation.

Schematic of the geometry considered in this article.     

Methodological problems in pressure profile calculations for lipid bilayers

From molecular dynamics simulations of a dipalmitoyl-phosphatidyl-choline (DPPC) lipid bilayer in the liquid crystalline phase, pressure profiles through the bilayer are calculated by different methods. These profiles allow us to address two central and unresolved problems in pressure profile calculations: The first problem is that the pressure profile is not uniquely defined since the expression for the local pressure involves an arbitrary choice of an integration contour. We have investigated two different choices leading to the Irving-Kirkwood (IK) and Harasima (H) expressions for the local pressure tensor. For these choices we find that the pressure profile is almost independent of the contour used, which indicates that the local pressure is well defined for a DPPC bilayer in the liquid crystalline phase. This may not be the case for other systems and we therefore suggest that both the IK and H profiles are calculated in order to test the uniqueness of the profile. The second problem is how to include electrostatic interactions in pressure profile calculations when the simulations are conducted without truncating the electrostatic potential, i.e., using the Ewald summation technique. Based on the H expression for the local pressure, we present a method for calculating the contribution to the lateral components of the local pressure tensor from electrostatic interactions evaluated by the Ewald summation technique. Pressure profiles calculated with an electrostatic potential truncation (cutoff) from simulations conducted with Ewald summation are shown to depend on the cutoff in a subtle manner which is attributed to the existence of long-ranged charge ordering in the system. However, the pressure profiles calculated with relatively long cutoffs are qualitatively similar to the Ewald profile for the DPPC bilayer studied here.