Dynamic NMR investigation of plastic crystals in bulk and confined in porous materials

In this work, the molecular dynamics of four organic compounds confined in silica pores of nominal diameter 6 and 20 nm are studied by high-field (9.4 T) nuclear magnetic resonance (NMR), and the results are discussed with reference to the bulk substances. By using organic compounds forming soft plastic crystals on freezing as adsorbates, damage to the pore structures can be avoided. NMR lineshapes, spin-lattice relaxation times (T ₁), spin-spin relaxation timesT ₂ and diffusivities are reported as a function of temperature. Since the porous grains are much greater than the distance travelled by the molecules during the experiment, intracrystalline NMR parameters were obtained. However, the shortT ₂ (∼1 ms) encountered in both the bulk and confined samples prohibited measurements ofT ₂ and the diffusivity in the low-temperature ordered phases. The confinement in the pores gives rise to substantial changes in the phase behavior and molecular dynamics. Thus, the¹H lineshape observations of the confined samples clearly reveal a narrow-line component superimposed on a broad resonance at temperatures well below the transition point of the bulk material. In the freezing region, the narrow-line component is attributed to the surface layer and the undercooled liquid in the smaller pores that remains unfrozen. In the two-component, low-temperature region, the narrow component corresponds to the surface layer, while the broad component originates from the crystalline phase at the center of the pores.     

<Superscript>1</Superscript>H NMR studies of cyclohexane confined in mesoporous solids: Melting point depression and pore size distribution

The pore size distributions of four controlled pore glasses and two silica gels with nominal diameters ranging from 6–24 nm were determined by measuring the¹H nuclear magnetic resonance (NMR) signal from the nonfrozen fraction of confined cyclohexane as a function of temperature, in steps of ca. 0.1–1 K. The intensity curves of the liquid component are well represented by a sum of two error functions. The mean melting point depression of cyclohexane confined in pores with radiusR follows the simplified Gibbs-Thompson equation δT=k _p/R with ak _p value of 72.4 Knm. To our knowledge, this is the first time that thek _p value of cyclohexane has been directly and accurately calibrated by NMR. As expected, thek _p value mainly determines the position of the pore size distribution curve, i.e., the mean pore radius. The overall pore size distributions determined by NMR are in reasonable agreement with the results specified by the manufacturer, or measured by us by the N₂ sorption technique. Although the melting point depression of confined cyclohexane is found to be less than previously assumed, this compound is still one of the most suitable candidates for NMR-based pore size determinations. However, pore sizes larger than approximately 50 nm in diameter will be difficult to determine accurately by NMR unless adsorbates undergoing larger melting point depressions than cyclohexane can be found.     

An NMR investigation of naphthalene nanostructures

The molecular mobility of naphthalene molecules in porous silica has been studied over the temperature range 223?K to 363?K using NMR relaxation times T ₂, T ₁ and T _1ρ. The investigations were conducted in silicas with nominal pore diameters of 4?nm, 6?nm, 10?nm, 20?nm and 50?nm. The confined solid behaved in a way that indicated it formed a dual phase system consisting of a solid core in the centre of the pores surrounded by a mobile surface layer. The core naphthalene had the same line width as the bulk. The surface layer exhibited a narrower line of a width that suggested the onset of motional narrowing. This behaviour was characteristic of a plastic crystal phase for naphthalene that does not exist in the bulk. The T ₁ and T _1ρ results were dominated by surface interactions between the confined naphthalene and the pore wall. Magnetization transfer experiments showed that enhanced relaxation occurred throughout the confined material in a time long compared to T ₂ but short compared to T ₁ and T _1ρ. Since the line shape ruled out diffusional motion through the rigid lattice naphthalene core, the magnetization transfer must have occurred via spin diffusion.     

Geometrical forms of Abelès'' equations involving film thickness

Abelès' equations (in terms of ₁; ₂ and optical film thickness x) for all the eight optical functions (R_s; R_p; T_s; T_p; F_s; F_p; X_s and X_p) have been expressed in the form of equations representing standard geometrical three-dimensional figures. X_s and X_p are represented by plane surfaces whilst the remainder are skew cones. Translated into the n; k notation; X_s and X_p generate hyperboloids whilst the remainder produce paraboloids whose cross-sections are parts of figures of eight.     

Connection between elastic scattering and inclusivek T 2 distribution

A connection between the elastic scattering and the inclusive one-particlek _T ² distribution is pointed out in the context of thes channel unitarity. One of the implications of this connection is that the slope of thek _T ² distribution atk _T ² =0 is about a factor two larger than the slope of the elastic scattering att=0.     

Polarization stokes polarimetry of the amplitude and phase characteristics of surface plasmon polariton resonance

The amplitude and phase characteristics of internal reflection of gold nanofilms have been investigated using polarization modulation of electromagnetic radiation in the Kretschmann geometry. The component Q (the difference between the reflection coefficients R _s ² and R _p ² for the s and p polarizations, respectively) and the component V of the Stokes vector (the difference between the phases of the orthogonal components of linearly polarized radiation) of light reflected from a half-cylinder of the total internal reflection with gold films of different thicknesses on its flat surface have been measured as a function of the angle of incidence of light in the wavelength range 500–1000 nm. It has been demonstrated that, in the range of parameters corresponding to the manifestation of the plasmon polariton resonance (the angle of incidence of light, the wavelength, the metal film thickness), the dispersions of the amplitude and phase characteristics are in quantitative and qualitative agreement with the model concepts of a classical oscillator.     

Relaxation Times and Population Inversion of Excited States of Arsenic Donors in Germanium

The relaxation times of excited states of arsenic dopant in germanium at cryogenic temperatures T < 15 K have been experimentally studied by the optical pump-probe method using radiation of a free-electron laser. Two variants of the excitation of impurity centers have been used in the experiment: (i) from the 1s(A₁) ground state of the dopant and (ii) from the 1s(T₂) first excited state having a finite thermal population. In the former variant, it has been shown that the decay times of the 2p₀ and 3p_± states are about 0.8 and 0.6 ns, respectively. In the latter variant, a single measurement can simultaneously provide the relaxation times of two 2p_± and 1s(T₂) states about 0.6 and no more than 0.16 ns, respectively. The data obtained have indicated the possibility of forming population inversion and the gain of terahertz radiation at the 2p_± → 1s(T₂) and 2p₀ → 1s(T₂) transitions at the optical excitation of the mentioned impurity centers.

     

Further studies of the sensitivities attainable in using three optical functions to calculate n, k and thickness for thin films

All 56 combinations of three optical functions chosen from R_s, R_p, T_s, T_p, Φ_rs, Φ_rp, Φ_ts and Φ_tp have been investigated to discover their regions of sensitivity in n, k and d/λ coordinate space. When the arrays of error parallelepipeds were plotted, single quadrant patterns of high sensitivity were generated by 21 of these combinations, these being the ones containing one photometric and two polarimetric functions; the best combination was R_pΦ_rpΦ_tp which was viable at all angles of incidence and all thicknesses up to d/λ = 0.08. The remaining 35 combinations produced two-lobe patterns which were insensitive at small angles of incidence but improved as the angle of incidence increased and were best at 60°.     

A Light and X‐Ray Scattering Study of Aqueous Micellar Solutions of a Diblock Copolymer of Propylene Oxide and Ethylene Oxide with Solubilized Alkylcyanobiphenyl Liquid Crystals

Abstract

The temperature and concentration dependences of the physicochemical properties of aqueous solutions of the diblock copolymer P₄₃E₃₁₂ (P = oxypropylene, E = oxyethylene) with solubilized liquid crystal (LC) have been studied using static and dynamic light scattering (SLS and DLS), small‐angle x‐ray scattering (SAXS), and ultraviolet (UV) spectroscopy. Relaxation time distributions from DLS obtained from inverse Laplace transformation of intensity correlation functions are multimodal, where the two fastest modes are attributed to diblock copolymer unimers and micelles, respectively. The remaining modes at longer decay times reflect the presence of free LC with hydrodynamic radii (R _h) of hundreds of nm. The R _h of both unimers and micelles were independent of temperature (T), while the hydrodynamic virial coefficient k _D and the second virial coefficient, A ₂, decreased with increasing T. The UV spectroscopy measurements showed that there is a reduction in the amount of solubilized LC per gram of copolymer (c _s) as the copolymer concentration (c _p) is increased. The SAXS results agree well with a model of a homogeneous system of polydisperse interacting hard spheres. In solution, both the effective micellar radius of interaction (R _eff) and the hard‐sphere micellar radius (R¯_s) increase in the presence of LC due to solubilization of the latter in the hydrophobic micellar core. Both SAXS and SLS results show that intermicellar interactions become important at c _p > 1% (w/w) at high temperatures [T > the critical micelle temperature (cmt)].     

Model-Free Approach beyond the Borders of Its Applicability

Model calculations presented in this article show that commonly used methodology of¹⁵N relaxation data analysis completely fails in detecting nanosecond time scale motions if the major part of the molecule is involved in these motions. New criteria are introduced for the detection of such cases, based on the dependence of the apparent overall correlation time, derived from theT₁/T₂ratio, on the spectrometer frequency. Correctly estimating the overall rotation correlation time τ_Rwas shown to play the key role in model-free data analysis. It is found, however, that in cases of slow internal motions with characteristic times of more than 3–4 ns, the effective τ_Rprovided by theT₁/T₂ratio for individual amide nitrogens can be used for the characterization of the fast picosecond internal dynamics.     

Influence of surface interactions on the dynamics of the glass former ortho-terphenyl confined in nanoporous silica

We present results on investigations of the dynamics of the glass forming ortho-terphenyl (oTP) confined in nanoporous silica. Calorimetry experiments showed that the glass transition temperature of the confined liquid, T_gconf, has a non-trivial pore size dependence and is strongly affected by surface interactions. Fluid-wall interactions introduce gradients of structural relaxation times in the pores. The molecules at the surface of the pores are slowed down compared to those at the center of the pores. We focus here on a pore diameter range (7 σ< d < 12 σ, where σ is the molecular diameter), where a large variety of dynamical behavior were observed. Depending on surface properties of the confined media, T _gconf may be smaller or larger than the bulk one. In a quite attractive matrix with a pore size of around 7 nm, the structural relaxation times gradient is important enough to allow the observation of two glass transitions for the same liquid. Effects of fluid wall interactions on the short time dynamics at high temperature were also investigated by quasielastic neutron scattering. The self and collective motions exhibit well above the bulk melting point the same dependence on fluid-wall interactions as at T_g.     

Dispersion of cerebral on-resonanceT 1 in the rotating frame (T 1ρ) in global ischaemia

T ₁ in the rotating frame (T _1ρ) has been recently shown to be an early magnetic resonance imaging index of ongoing pathology in vivo. Dispersion ofT _1ρ at aB ₁ range from 620 to 160500 rad/s was quantified in the rat brain to study the effects of ischaemia onT _1ρ relaxation and to elude the role of physico-chemical mechanisms underlying the relaxation changes. The results show a biphasic effect of the dispersion ofR _1ρ (1/T _1ρ) in ischaemic brain. In the lowB ₁ region (less than 5000 rad/s), an increase was detected, while at the highB ₁ end of the experiments,R _1ρ was reduced. This was accompanied by a change in the fitted values describing the dispersion characteristics. Injection of a superparamagnetic contrast agent, AMI-227, before ischaemia shifted theR _1ρ curve upwards by 4% but showed no effect on the shape of theR _1ρ dispersion curve. The present results argue for a specific effect of endogenous susceptibility on cerebralR _1ρ in the early moments of ischaemia due to a relaxation enhancement in the blood pool. Our results confirm that quantitativeR _1ρ dispersion nuclear magnetic resonance (NMR) improves the sensitivity ofR _1ρ NMR to detect ischaemia in vivo. Simple empirical linear or exponential fits proved to be efficient ways to describe dispersion data in the limitedB ₁ range, as more detailed models may not offer additional information in a physically relevant manner for complex systems, such as the brain.     

Analysis of transverse momentum distributions forpp interactions at 360 GeV/c in the framework of a quark-diquark fragmentation model

Using a quark-diquark fragmentation model, in which either the Field-Feynman or the Lund model is coupled with a quark-diquark distribution function, we study transverse momentum distributions,p _T, for the inclusive reactionspp→hadron +anything at 360 GeV/c. We find that a primordial mean transverse momentum 〈k _T〉?0.4 GeV/c can well reproduce thep _T ² distributions of charged hadrons, π⁰,K _s ⁰ , Λ⁰,K ^* and Σ^* and the Feynmanx?p _T correlations. We confirm that a diquark in a proton plays an important rôle in reproducing thex?p _T correlation of Λ⁰.     

Temperature dependence of surface impedance of Tl2Ba2CaCu2O8−δ and YBa2Cu3O6.95 single crystals measured in the microwave band

The real part R _s and the imaginary part X _s of the surface impedance Z _s=R _s+ iX _s of Tl₂Ba₂CaCu₂O_8−δ and YBa₂Cu₃O_6.95 single crystals have been measured with high precision at frequency ω/2π=9.4 GHz in the temperature range 0<T<140 K. In the Tl₂Ba₂CaCu₂O_8−δ crystal a linear temperature dependence R _s(T) has been found for T⩽50 K, and the magnetic field penetration depth λ(4.2 K)=X _s(4.2 K)/ω μ ₀≈3760 Å has been measured. Along with well known features of the function Z _s(T) in high-quality YBa₂Cu₃O_6.95 single crystals, such as the linearity of λ(T) and R _s(T) for T<T _c/3 and a maximum of R _s(T) at T∼T _c/2, the linearity range of λ(T) extends to T≃50 K, and this curve has a plateau in the range 60<T<85 K. The curve of R _s(T) in both the superconducting and normal states of YBa₂Cu₃O_6.95 is well described by a two-fluid model with the electron-phonon mechanism of quasiparticle relaxation. A formula describing the curve of λ ²(0)/λ ²(T) throughout the studied temperature range is also given. Zh. éksp. Teor. Fiz. 112, 2210–2222 (December 1997)     

Size-dependent freezing of n-alcohols in silicon nanochannels

We present a study on the phase behavior of several linear n-alcohols (heptanol, nonanol and undecanol) in their bulk state as well as confined in mesoporous silicon. We were able to vary the mean pore radii of the nanochannels from r = 3.5  nm to 7 nm and to determine the respective temperatures of the freezing and melting transitions using infrared and dielectric spectroscopy. The smaller the chain length the lower the freezing point, both in the bulk and in the confined state. Under confinement the freezing temperature decreases by up to 28 K compared to the bulk value. In accordance with the Gibbs-Thompson model the lowering is proportional to the inverse pore radius, ΔT _fr ∝ 1/r. Moreover, the ratio of freezing temperature depression to melting temperature depression is close to the theoretical value of ΔT _fr /ΔT _melt = 3/2. The spectra also indicate a structural change: while the solid bulk alcohols are a polycrystalline mixture of the orthorhombic β- and monoclinic γ-form, geometrical confinement forces the alcohol-chains into the more simple orthorhombic structure. In addition, a part of the material does not crystallize. Such an additional amorphous phase seems to be a logical consequence of the size mismatch between molecular crystals and irregular shaped pores.     

Proton magnetic relaxation studies of molecular diffusion in the liquid crystal 40.5

Nuclear magnetic relaxation spectroscopy is used to study the molecular dynamics in a liquid crystal butoxy benzylidene pentylaniline (40.5) in the frequency range 4 to 30 MHz and the results are compared with two other members of the same homologous series (viz 40.8 and 40.6). Spin lattice relaxation time studies indicate that molecular self diffusion (SD) and reorientation processes (R) dominate the relaxation process and their relative contributions are quantified. This contrasts with the case where order director fluctuations (ODF) effectively mediate relaxation process and all the three processes are found to be important in 40.6 in a similar frequency range.T _1D in 40.5 in the nematic phase shows temperature dependence indicating that ODF that is present at low frequencies might be diffusion assisted. These relaxation data are analysed in theS _B phase of this compound also to obtain contributions to the relaxation process. These results are also analysed to obtain different parameters associated with the above dynamical processes.     

Molecular dynamics investigation of the size effect upon the β → α transformation in Zr nanocrystals

The stability of the β phase in cubic zirconium nanoparticles has been calculated as a function of the size r (r varies in the range from 2.5 to 11.5 nm) by the molecular dynamics method with the many-body interatomic interaction potential obtained within the embedded-atom model. It has been demonstrated that the temperature T _k at which the cubic cluster of body-centered cubic zirconium becomes structurally unstable depends nonlinearly on the particle size. The curve T _k (r) exhibits a pronounced maximum in the range r ≈ 4.3−4.7 nm. It has been established that the mechanism of the structural transition from the body-centered cubic phase to the hexagonal close-packed phase depends substantially on the particle size. For particles with sizes in the range from 2.5 to 5.0 nm, there exists a temperature range in which the transition from the body-centered cubic phase to the hexagonal close-packed phase remains incomplete for a long time. In this case, two phases coexist and the initial particle undergoes a strong deformation along the habit plane.     

Hebel-Slichter peak and superconducting energy gap in Rb3C60 observed by muon spin relaxation

Muon spin relaxation has been observed in both the normal and superconducting states of Rb₃C₆₀ (T _c=29.3K). The field dependence of theT ₁ spin relaxation rate is due to muonium undergoing spin-exchange scattering with conduction electrons, making this the first observation of muonium in a metal. The temperature dependence ofT ₁ ^–1 shows a Hebel-Slichter coherence peak just belowT _c which is not seen in¹³C spin relaxation. The peak can be fit assuming spin relaxation due to interaction with the quasiparticle excitations of a BCS superconductor provided the density of states is broadened relative to that of BCS. Such fits yield a value for the zero temperature energy gap, ₀/k _B , of 53(4)K, consistent with weak-coupling BCS.     

A field-cycling NMR study of nematic 4-pentyl-4′-cyanobiphenyl confined in porous glasses

The proton spin-lattice relaxation time T₁, in the nematic liquid crystal 4-pentyl-4′-cyanobiphenyl confined in a glassy porous matrix has been measured in a wide Larmor frequency range of 1 · 10²?2 · 10⁷ Hz employing the fast field-cycling NMR technique. A strong influence of the restricted geometry on the character of the T₁ dispersion was found. Our investigation clearly demonstrates the importance of the translationally induced molecular reorientations in inhomogeneous director field for the relaxation in the samples with 200 and 80 nm mean pore size. The experimental results are in a good agreement with the theoretical predictions. In the sample with 7 nm pore size the main contribution to the relaxation is ascribed to the slowing down of the molecular motion in the near-surface layer. Zero-field 1H NMR spectra of a microconfined liquid crystal are reported for the first time.     

Linear low-temperature dependence of the surface impedance of a Ba0.6K0.4BiO3 single crystal

The temperature dependences of the real part R _s and the imaginary part X _s of the surface impedance Z _s =R _s +iX _s of the superconductor Ba_0.6K_0.4BiO₃ (T _c ≃30 K) are measured at a frequency of 9.4 GHz. Its temperature dependence _{Z s} (T) and that of the complex conductivity σ _s (T) can be described on the basis of a two-fluid model under two assumptions: The density of superconducting carriers increases linearly, and the relaxation time increases as a power law (∝1/T ⁵), with decreasing temperature T<T _c . This model also describes well the curves Z _s (T) and σs (T) recently measured for YBa₂Cu₃O_6.95 and Bi₂Sr₂CaCu₂O₈ single crystals. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 11, 783–788 (10 December 1996)