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Electron spin resonance pulsed dipolar spectroscopy (PDS) has become popular in protein 3D structure analysis. PDS studies yield distance distributions between a pair or multiple pairs of spin probes attached to protein molecules, which can be used directly in structural studies or as constraints in theoretical predictions. Double-quantum coherence (DQC) is a highly sensitive and accurate PDS technique to study protein structures in the solid state and under physiologically relevant conditions. In this work, we have derived analytical expressions for the DQC signal for a system with N-dipolar coupled spin-1/2 particles in the solid state. The expressions are integrated over the relevant spatial parameters to obtain closed form DQC signal expressions. These expressions contain the concentration-dependent "instantaneous diffusion" and the background signal. For micromolar and lower concentrations, these effects are negligible. An approximate analysis is provided for cases of finite pulses. The expressions obtained in this work should improve the analysis of DQC experimental data significantly, and the analytical approach could be extended easily to a wide range of magnetic resonance phenomena. [ABSTRACT FROM AUTHOR]

Two-dimensional electron–electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In previous work, we provided simulations for the case of domain motions within proteins that are themselves slowly tumbling in a solution. In order to perform these simulations, it was found that the standard approach of solving the relevant stochastic Liouville equation using the efficient Lanczos algorithm for this case breaks down, so algorithms were employed that rely on the Arnoldi iteration. While they lead to accurate simulations, they are very time-consuming. In this work, we focus on a variant known as the rational Arnoldi algorithm. We show that this can achieve a significant reduction in computation time. The stochastic Liouville matrix, which is of very large dimension, N, is first reduced to a much smaller dimension, m, e.g., from N ∼ O(104) to m ∼ 60, that spans the relevant Krylov subspace from which the spectrum is predicted. This requires the selection of the m frequency shifts to be utilized. A method of adaptive shift choice is introduced to optimize this selection. We also find that these procedures help in optimizing the pruning procedure that greatly reduces the dimension of the initial N dimensional stochastic Liouville matrix in such subsequent computations. [ABSTRACT FROM AUTHOR]

Two-dimensional electron–electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In this work, simulations are provided for the example of domain motions within proteins that are themselves slowly tumbling in solution. These show the nature of the exchange cross-peaks that are predicted to develop in real time from such domain motions. However, we find that the existing theoretical methods for computing 2D-ELDOR experiments over a wide motional range begin to fail seriously when applied to very slow motions characteristic of proteins in solution. One reason is the failure to obtain accurate eigenvectors and eigenvalues of the complex symmetric stochastic Liouville matrices describing the experiment when computed by the efficient Lanczos algorithm in the range of very slow motion. Another, perhaps more serious, issue is that these matrices are "non-normal," such that for the very slow motional range even rigorous diagonalization algorithms do not yield the correct eigenvalues and eigenvectors. We have employed algorithms that overcome both these issues and lead to valid 2D-ELDOR predictions even for motions approaching the rigid limit. They are utilized to describe the development of cross-peaks in 2D-ELDOR at 95 GHz for a particular case of domain motion. [ABSTRACT FROM AUTHOR]

The development, applications, and current challenges of the pulsed ESR technique of twodimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane, vesicles can be observed. These 2D ELDOR experiments are performed as a function of mixing time, Tm, i.e., the time between the second and third π/2 pulses, which provides a third dimension. In fact, a fourth dimension may be added by varying the ESR frequency/magnetic field combination. Therefore, (3) it is shown how continuous-wave multifrequency ESR studies enable the decomposition of complex dynamics of, e.g., proteins by virtue of their respective time scales. These studies motivate our current efforts that are directed to extend 2D ELDOR to higher frequencies, 95 GHz in particular (from 9 and 17 GHz), in order to enable multi-frequency 2D ELDOR. This required the development of quasi-optical methods for performing the mm-wave experiments, which are summarized. We demonstrate state-of-the-art 95 GHz 2D ELDOR spectroscopy through its ability to resolve the two signals from a spin probe dissolved in both the lipid phase and the coexisting aqueous phase. As current 95 GHz experiments are restricted by limited spectral coverage of the π/2 pulse, as well as the very short T2 relaxation times of the electron spins, we discuss how these limitations are being addressed [ABSTRACT FROM AUTHOR]

The Lanczos algorithm (LA) is a useful iterative method for the reduction of a large matrix to tridiagonal form. It is a storage efficient procedure requiring only the preceding two Lanczos vectors to compute the next. The quasi-minimal residual (QMR) method is a powerful method for the solution of linear equation systems, Ax = b. In this report we provide another application of the QMR method: we incorporate QMR into the LA to monitor the convergence of the Lanczos projections in the reduction of large sparse matrices. We demonstrate that the combined approach of the LA and QMR can be utilized efficiently for the orthogonal transformation of large, but sparse, complex, symmetric matrices, such as are encountered in the simulation of slow-motional 1D- and 2D-electron spin resonance (ESR) spectra. Especially in the 2D-ESR simulations, it is essential that we store all of the Lanczos vectors obtained in the course of the LA recursions and maintain their orthogonality. In the LA-QMR application, the QMR weight matrix mitigates the problem that the Lanczos vectors lose orthogonality after many LA projections. This enables substantially more Lanczos projections, as required to achieve convergence for the more challenging ESR simulations. It, therefore, provides better accuracy for the eigenvectors and the eigenvalues of the large sparse matrices originating in 2D-ESR simulations than does the previously employed method, which is a combined approach of the LA and the conjugate-gradient (CG) methods, as evidenced by the quality and convergence of the 2D-ESR simulations. Our results show that very slow-motional 2D-ESR spectra at W-band (95 GHz) can be reliably simulated using the LA-QMR method, whereas the LA-CG consistently fails. The improvements due to the LA-QMR are of critical importance in enabling the simulation of high-frequency 2D-ESR spectra, which are characterized by their very high resolution to molecular orientation. [ABSTRACT FROM AUTHOR]

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics. [ABSTRACT FROM AUTHOR]

The echo amplitude decay of a diffusing electron-spin-bearing molecule interacting with a diffusing many-spin bath of proton-containing molecules has been studied theoretically in the slow motional limit. Closed-form asymptotic expressions for the short- and long-time behavior of the echo envelope have been obtained. In contrast to the well-studied fast-motional limit, the echo envelope cannot be described by a simple exponential decay, and its rate exhibits a D[sup ⅓, sub T] dependence on the relative translational diffusion coefficient, D[sub T]. For low proton concentrations and long pulse delay times, τ, an exponential τ[sup &frac9/8;-decay of the echo amplitude is found, whereas for high proton concentrations and short τ's the decay exhibits an exponential τ³-behavior. These limiting analytical results are compared with the exact numerical solutions to establish their range of validity. [ABSTRACT FROM AUTHOR]

Time resolved electron paramagnetic resonance (EPR) measurements on a photoexcited chromium doped forsterite (Cr:Fo) single crystal are reported. The spectral changes with time, magnetic field, crystal orientation, microwave power and, in particular, photoexciting wavelength, provide a selective picture of the various chromium dopants and the absorption–relaxation cycle associated with each optical excitation. Both Cr+4 ions lodged at tetrahedral (Td) and octahedral (Oh) sites as well as Cr+3 ions are detected. In particular, the laser-EPR technique enabled us to monitor the spin dynamics associated with the lasing center (Cr+4/Td) in the time regime of 200 ns–100 ms following a selective photoexcitation of the crystal between 532 and 1064 nm. The transient EPR signals associated with the lasing Cr+4/Td ions, exhibit a noticeable dependence on even small changes (∼0.5 nm) in the exciting wavelengths that correspond to the visible 3A2→3T1 and the near infrared 3A2→3T2 transitions. The transient magnetization associated with each absorption–relaxation cycle is quantitatively analyzed in terms of site selectivity due to the narrow band (i.e., low intensity) microwave detection following a narrow band optical excitation. Given this observed selectivity, it is suggested that laser-EPR may be employed to study intersite interactions and site structure versus optical function relationships in forsterite as well as other solids doped with transition metal ions. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A theoretical model is developed for treating molecular dynamics at the nematic–smectic-A (N–SA) phase transition, which is frequently second order. This model is motivated by electron-spin-resonance (ESR) spin-relaxation studies of molecular probes. The critical dynamics of the hydrodynamic modes is described in accordance with dynamic scaling arguments of Brochard. Following Zager and Freed, the molecular dynamics of a probe molecule (governed by the molecular orientation and/or rotational diffusion) is assumed to couple to fluctuations in the smectic order parameter, because these molecular properties are a function of the precise location of the probe within the transient smecticlike layer. Two limiting cases of (1) (nearly) free translational diffusion of the probe across the smecticlike layer; and (2) expulsion of the probe to the aliphatic chains with highly hindered diffusion (i.e., jump diffusion) across the smecticlike layer are considered. The relevant spectral density shows critical types of divergence, where the exponent depends strongly on the details of the model. It is found that only the (near) zero-frequency spectral densities can show such divergences. It is pointed out that spectral densities available for spin relaxation do not truly diverge as the N–SA transition is approached arbitrarily closely, because ultimately motional-narrowing theory will no longer be valid, and fluctuations begin to be frozen on the ESR time scale. This matter is briefly analyzed. Also considered briefly are the effects of anisotropies in the smectic phase and of fluctuations in nematic director near the N–SA transition. [ABSTRACT FROM AUTHOR]

We describe our pulsed two-dimensional Fourier transform ESR experiment and demonstrate its applicabilty for the double resonance of motionally narrowed nitroxides. Multiple pulse irradiation of the entire nitroxide spectrum enables the correlation of two precessional periods, allowing observation of cross correlations between hyperfine lines introduced by magnetization transfer in the case of a three-pulse experiment (2D ELDOR), or coherence transfer in the case of a two-pulse experiment (COSY). Cross correlations are revealed by the presence of cross peaks which connect the autocorrelation lines appearing along the diagonal ω1=ω2. The amplitudes of these cross peaks are determined by the rates of magnetization transfer in the 2D ELDOR experiment. The density operator theory for the experiment is outlined and applied to the determination of Heisenberg exchange (HE) rates in 2,2,6,6-tetramethyl-4-piperidone-N-oxyl-d15 (PD-tempone) dissolved in toluene-d8. The quantitative accuracy of this experiment is established by comparison with the HE rate measured from the dependence of the spin echo T2 on nitroxide concentration. [ABSTRACT FROM AUTHOR]

Presents a formulation for calculating double quantum two-dimensional electron spin resonance spectra in the rigid limit corresponding to recent experimental spectra obtained from a nitroxide biradical. Inclusion of dipolar interaction between the nitroide moieties; Effects of arbitrary pulses.

Reports on an electron spin resonance (ESR) study of the probe rotational dynamics in the fragile glass former ortho-terphenyl using nitroxide spin probes. Theories for the liquid to glass transition; ESR experiments at high temperatures; Spectral simulations; Dynamic parameters; Molecular dynamics above T[sub c]; Correlation functions for the dynamic cage model.

Two-dimensional Fourier transform (2D-FT)-electron spin resonance (ESR) studies on the small globular spin probe perdeuterated tempone (PDT) in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments, over the temperature range of 95 °C to 24 °C, cover the isotropic (I), nematic (N), smectic A (SA), smectic B (SB), and crystal (C) phases. The 2D-ELDOR (two-dimensional electron–electron double resonance) spectra confirm the anomalously rapid reorientation of PDT, especially in the lower temperature phases. The model of a slowly relaxing local structure (SRLS) leads to generally very good non-linear least squares (NLLS) global fits to the sets of 2D-ELDOR spectra obtained at each temperature. These fits are significantly better than those achieved by the standard model of Brownian reorientation in a macroscopic orienting potential. The SRLS model is able to account for anomalies first observed in an earlier 2D-ELDOR study on PDT in a different liquid crystal in its smectic phases. Although it is instructional to extract the various spectral densities from the COSY (correlation spectroscopy) and 2D-ELDOR spectra, the use of NLLS global fitting to a full set of 2D-ELDOR spectra is shown to be more reliable and convenient for obtaining optimum model parameters, especially in view of possible (incipient) slow motional effects from the SRLS or dynamic cage. The cage potential is found to remain fairly constant at about kBT over the various phases (with only a small drop in the SB phase), but its asymmetry increases with decreasing temperature T. This value is significantly larger than the weak macroscopic orienting potential which increases from 0.1 to 0.3kBT with decreasing T. The cage relaxation rate, given by Rc is about 3×107 s-1 in the I phase, but increases to about 108 s-1 in the SA, SB, and C phases. The rotational diffusion tensor for PDT shows only a small T-independent asymmetry, and its mean... [ABSTRACT FROM AUTHOR]

Two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) studies on the rigid rodlike cholestane (CSL) spin-label in the liquid crystal solvent 4O,8 (butoxy benzylidene octylaniline) are reported. These experiments were performed over a wide temperature range: 96 °C to 25 °C covering the isotropic (I), nematic (N), smectic A (SA), smectic B (SB), and crystal (C) phases. It is shown that 2D-FT-ESR, especially in the form of 2D-ELDOR (two-dimensional electron–electron double resonance) provides greatly enhanced sensitivity to rotational dynamics than previous cw-ESR studies on this and related systems. This sensitivity is enhanced by obtaining a series of 2D-ELDOR spectra as a function of mixing time, Tm, yielding essentially a three-dimensional experiment. Advantage is taken of this sensitivity to study the applicability of the model of a slowly relaxing local structure (SRLS). In this model, a dynamic cage of solvent molecules, which relaxes on a slower time scale than the CSL solute, provides a local orienting potential in addition to that of the macroscopic aligning potential in the liquid crystalline phase. The theory of Polimeno and Freed for SRLS in the ESR slow motional regime is extended by utilizing the theory of Lee et al. to include 2D-FT-ESR experiments, and it serves as the basis for the analysis of the 2D-ELDOR experiments. It is shown that the SRLS model leads to significantly improved non-linear least squares fits to experiment over those obtained with the standard model of Brownian reorientation in a macroscopic aligning potential. This is most evident for the SA phase, and the use of the SRLS model also removes the necessity of fitting with the unreasonably large CSL rotational asymmetries in the smectic phases that are required in both the cw-ESR and 2D-ELDOR fits with the standard model. The cage potential is found to vary from about kBT in the isotropic phase to greater than 2kBT in the N and SA phases, with... [ABSTRACT FROM AUTHOR]

In paper I of this series, a molecular dynamics (MD) study of liquid chlorine was performed, and it includes the definition and observation of operational cage variables. These cage variables were used to describe the local environment of a rotating axially symmetric molecule, or probe. Probe and cage properties of interest, such as rotational correlation functions and momentum correlation functions, were computed, together with an effective distribution of librational cage frequencies. In the second part of this work, we develop a stochastic model which includes the relevant elementary relaxation processes previously identified by the MD study. This stochastic model is based upon a multi-dimensional Fokker–Planck equation for the coupled dynamics of the probe and cage orientations, the angular momentum of the probe, and the librational frequencies for the probe in the cage. Semi-analytical approximations, based upon a ‘‘Born–Oppenheimer’’-type separability of fast and slow variables, are used in order to calculate probe and cage correlation functions, and they are found to be in reasonable agreement with the MD results. In an appendix the Born–Oppenheimer approximation for stochastic operators is developed. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This work represents the synthesis of the 2+1 pulse sequence for the study of electron spin-echo envelope modulation (ESEEM) with the technique of spin-echo correlated spectroscopy (SECSY), which has previously been used to study nuclear modulation by two-dimensional Fourier transform ESR methods. This example of ‘‘pulse adjustable’’ spectroscopy, wherein the pulse width and pulse amplitude of the second pulse in a three pulse sequence are introduced as adjustable parameters, leads to enhanced resolution to the key features of the nuclear modulation that are important for structural studies. This is demonstrated in studies on (i) a single crystal of irradiated malonic acid and (ii) a frozen solution of diphenylpicrylhydrazyl in toluene. In particular, it is shown for (i) how the nuclear modulation cross peaks can be preferentially enhanced relative to the autopeaks and to the matrix proton peaks, and also how the autopeaks can be significantly suppressed to enhance resolution for low-frequency cross peaks. For (ii) the low-frequency 14N nuclear modulation could be suppressed leaving just the high-frequency matrix 1H modulation. Additionally, the T2 homogeneous linewidth broadening in the f1 frequency direction is removed in 2+1 SECSY. These features significantly improve resolution to the modulation decay, which is the main observable utilized for distance measurements by ESEEM, compared to SECSY. A simple example of a distance measurement to matrix protons is presented for (ii). It is shown that a major advantage of the 2D format is that the full spin-echo shape is collected, which permits one to study how the effect of the nuclear modulation upon the echo varies with evolution time t1 after the first pulse, and thereby to detect the important modulation features. Additionally it allows for correlating the modulation cross peaks in making spectral assignments. A detailed quantitative theory for 2+1 SECSY is also presented. In... [ABSTRACT FROM AUTHOR]

An operational definition of collective cage variables previously introduced for liquid argon is extended, via a molecular dynamics study, to the rotational properties of axially symmetric molecules. Quantitative measures of the static and dynamic cage properties are extracted for liquid Cl2 near the triple point. The collective cage variables are well described by the potential acting on an arbitrary molecule (i.e. solute) for a fixed configuration of the other molecules (i.e. solvent). A dynamic separability of the solute orientation relative to the cage potential and of the relative solute displacement is justified in part by the faster relaxation found for the latter. Large and persistent orientational cage potentials (∼15–20 kBT) lead to substantial alignment of the solute in the cage with an average local order parameter of 0.87. The reorientational correlation times for the cage are consistent with axially symmetric Brownian motion. The reorientational correlation times for the solute are nearly equal to the equivalent ones of the cage, consistent with the strong coupling of solute within its cage which leads to a collective reorientation of solute and cage (e.g. τcage(2)=1.4 ps, and τsolute(2)=1.2 ps). Solute librations within the cage are much faster (τ libr(2)=0.12 ps) and are comparable to the relaxation of the relative solute displacements (τr=0.15 ps). The solute angular momentum exhibits the fastest correlation time (τ J=0.06 ps). While the orientational cage potential shows rapidly and slowly relaxing components (τωf=0.14 ps and τωs=2.87 ps, respectively), its dominant portion shows a very long persistence. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A comprehensive theory for interpreting two-dimensional Fourier transform (2D-FT) electron spin resonance (ESR) experiments that is based on the stochastic Liouville equation is presented. It encompasses the full range of motional rates from fast through very slow motions, and it also provides for microscopic as well as macroscopic molecular ordering. In these respects it is as sophisticated in its treatment of molecular dynamics as the theory currently employed for analyzing cw ESR spectra. The general properties of the pulse propagator superoperator, which describes the microwave pulses in Liouville space, are analyzed in terms of the coherence transfer pathways appropriate for COSY (correlation spectroscopy), SECSY (spin–echo correlation spectroscopy), and 2D-ELDOR (electron–electron double resonance) sequences wherein either the free-induction decay (FID) or echo decay is sampled. Important distinctions are made among the sources of inhomogeneous broadening, which include (a) incomplete spectral averaging in the slow-motional regime, (b) unresolved superhyperfine structure and related sources, and (c) microscopic molecular ordering but macroscopic disorder (MOMD). The differing effects these sources of inhomogeneous broadening have on the two mirror image coherence pathways observed in the dual quadrature 2D experiments, as well as on the auto vs crosspeaks of 2D-ELDOR, is described. The theory is applied to simulate experiments of nitroxide spin labels in complex fluids such as membrane vesicles, where the MOMD model applies and these distinctions are particularly relevant, in order to extract dynamic and ordering parameters.The recovery of homogeneous linewidths from FID-based COSY experiments on complex fluids with significant inhomogeneous broadening is also described. The theory is applied to the ultraslow motional regime, and a simple method is developed to determine rotational rates from the broadening of the autopeaks of the 2D-ELDOR... [ABSTRACT FROM AUTHOR]

Chromium-doped forsterite single crystals grown under conditions that produce a high Cr4+/Cr3+ ratio were examined by electron paramagnetic resonance (EPR) at 9.6 and 34 GHz. The crystals were grown in 2–3 atm of oxygen by the floating-zone method starting from polycrystalline chromium-doped forsterite powder synthesized via a sol–gel method. Three crystals with chromium concentrations of 110, 300, and 390 ppm were studied. At 34 GHz, transitions are observed for the laser-active tetrahedral Cr4+ species that are not observable at 9.6 GHz, which improve the resolution and accuracy with which the magnetic parameters can be measured by EPR. In addition, peaks for a non-Kramers species appear at 34 GHz that were not observed at 9.6 GHz. These peaks are not analyzed in detail, but are tentatively ascribed to Cr4+ in the octahedral substitution sites of the crystal. At the highest chromium concentration, the Cr3+ spectra show evidence of direct interaction with Cr4+. A global least-squares fit of the combined 9.6 and 34 GHz data for the 300 ppm crystal gives D=64.26±0.18 GHz, E=-4.619±0.009 GHz, gx=1.955±0.009, gy=2.005±0.040, gz=1.965±0.006, and places the magnetic z axis in the ab plane at an angle of 43.8±0.3° from the b crystallographic axis (in Pbnm).A method for accurately measuring the Cr4+/Cr4+ ratio using EPR line intensities is given. The EPR linewidth of the Cr4+ center exhibits a strong orientation dependence that is well-modeled by including site variations in the D and E zero-field splittings and in the orientation of the z magnetic axis. The linewidth analysis reveals a high degree of correlation between the distributions in D and E, and a somewhat weaker correlation between E and the z axis orientation. These results are interpreted to suggest that the tetrahedral Cr4+ sites vary mainly in the degree of compression of the tetrahedral cage along the a crystallographic axis. The Cr4+ EPR linewidths... [ABSTRACT FROM AUTHOR]

The method of dynamic imaging of diffusion (DID)-ESR (electron spin resonance) has been utilized to study the anisotropy of translational diffusion of spin probes in the smectic A phase of a eutectic liquid crystal, S2. In particular, the nearly spherical perdeuterated-TEMPONE (PDT) and the rigid and elongated cholestane spin label (CSL) molecules were studied. Whereas D⊥ (the coefficient of diffusion perpendicular to the nematic director) showed simple Arrhenius dependence for both probes, diffusion parallel to the director displayed two different temperature regimes with a changeover of D|| at t*≊26–27 °C. The regime above (below) t* is characterized by weak (strong) translational ordering. For CSL the ratio D⊥/D||<1 above t* which indicates nematiclike behavior, but below t* the behavior is more smecticlike, i.e., D⊥/D||>=1; for PDT D⊥/D||>=1 over the whole temperature range. A free volume model is developed to interpret the activation energies associated with D⊥ and D|| (i.e., E⊥ and E||) in terms of the orientational and translational order parameters for the smectic phase and those for the spin probes. Also included are the variation of the compressibility across the smectic layer and the length of the probe relative to that of the thickness of the smectic layer. The fact that above t* E||/E⊥ is unity for CSL but a little greater that unity for PDT is interpreted as due to the weaker coupling of the larger CSL molecule to the weak translational ordering and compressibility variation. Below t*, E||/E⊥ becomes 1.52 and 1.80 for CSL and PDT, respectively, which may be interpreted in terms of enhancement of these smectic features. The free volume model may be used to analyze E|| and E⊥ for self-diffusion and for a wide range of spin probes, including such very small probes like methane, as a function of the key parameters. [ABSTRACT FROM AUTHOR]

Nuclear modulation in electron-spin-echo spectroscopy is conventionally studied by one-dimensional electron-spin-echo envelope modulation (1D-ESEEM). Two-dimensional Fourier transform electron-spin resonance (2D-FTESR) studies of nuclear modulation have the promise of enhancing the spectral resolution and clarifying the key details of the relaxation processes. We present a 2D-FTESR study on single proton nuclear modulation from γ-irradiated malonic acid single crystals to test the validity of the Gamliel–Freed theory and to assess the value of the new methods. The two pulse spin-echo correlation spectroscopy (SECSY) spectra as a function of orientation of the single crystal show very good agreement with the Gamliel–Freed theory extended to the general case of nonaxially symmetric hyperfine interaction. It is very simply affected by spin relaxation, such that relative intensities are essentially unaffected. Thus SECSY-ESR can most reliably be utilized for studying nuclear modulation. Stimulated SECSY provides the simplest nuclear modulation patterns, which, however, do exhibit the suppression effect well known in three-pulse ESEEM studies. Two-dimensional electron–electron double resonance (2D-ELDOR) provides nuclear modulation patterns similar to that of SECSY-ESR, so the suppression effect is absent. Both three-pulse methods exhibit complex relaxation behavior which can affect relative intensities. This is a feature characteristic of three-pulse ESEEM, but is not well understood.It is shown how the 2D-FTESR methods enable one to obtain the details of the complex spin relaxation, and in the process, obtain very good agreement between experiment and theory. 2D-ELDOR exhibits exchange cross peaks as well as coherence peaks from the nuclear modulation. It is shown how experiments, as a function of mixing time, enable one to separate the effects of the two. It is pointed out that such experiments are in the spirit of 3D spectroscopy. A... [ABSTRACT FROM AUTHOR]

Electron spin resonance (ESR) relaxation studies at nematic–isotropic (N–I), and nematic–smectic-A (N–SA ) phase transitions in two liquid crystals, 4O,6 and 6OCB–8OCB, using the three spin probes, PD-tempone, MOTA, and P are described. In general, one finds that (i) at the N–I transition, as TNI is approached, the linewidths diverge with a critical exponent of 1/2; (ii) at the N–SA transition, the linewidths diverge with a 1/3 power law as the transition is approached from the nematic side. The nature of the critical divergences in the relaxation parameters is interpreted and analyzed in terms of fluctuations in the nematic and smectic order parameters at the respective transitions and the coupling of the orientational dynamics of the probe to these modes. Good quantitative agreement with theory for the N–I transition required the inclusion of the effects of asymmetric probe ordering. The theory developed in detail in paper I is applied to interpret the results at the N–SA transition. This theory is extended to include the effects of the measured anisotropies in (a) translational diffusion of the probe, (b) smectic correlation lengths, and (c) dynamic scaling exponents. In general, the magnitudes of the observed effects as well as their critical exponents are of the order expected, provided the averaging of the effects of density fluctuations within a smectic layer by probe diffusion is incomplete as a result of hindered diffusion. [ABSTRACT FROM AUTHOR]

Heisenberg spin exchange (HE) studies of translational diffusion of the nitroxide radicals PD-tempone and P probe in two liquid crystalline solvents 6OCB–8OCB and 4O,6 are described. It is shown that while PD-tempone undergoes strong exchange in the two solvents, the more anisotropic P-probe exhibits a tendency toward weak exchange which becomes more prominent in the low temperature mesophases. The molecular diffusion rates measured from our HE studies are compared with rates measured over larger distances using electron-spin resonance (ESR) imaging methods; we find that, in similar thermotropic liquid crystals, the former are somewhat faster. Also, while diffusion rates for PD-tempone (using HE) in the ordered phases of 6OCB–8OCB are consistent with a single activation energy, those in 4O,6 show variations; suggesting that probe expulsion from core to chain regions in the former most likely occurs prior to SA formation, whereas in the latter it occurs in the SA phase. The absence of discontinuities in our diffusion data at the N–SA–RN transitions supports the belief that these transitions are subtle, with nothing dramatic occurring as the reentrant nematic (RN) phase is formed. The effect of including a potential of mean force U(r) between colliding radicals due to the liquid-crystal structure, is also considered. Our analyses indicate that the potential is of a repulsive nature [i.e., U(d)>0] suggesting the possibility of solvent molecules inhibiting collisions of radicals at distances shorter than the sum of their solvated radii. The influence of orientational ordering on HE involving nonspherical radicals is considered, but changes from strong to weak exchange in the ordered phases appear to depend on how τ1 the lifetime of the interacting radical pair is influenced by U(r). A careful effort is made to separate the HE effects from the intermolecular electron–electron dipolar (EED) interactions. It is suggested that... [ABSTRACT FROM AUTHOR]

Static and dynamic properties related to the internal configurational motions have been calculated for the alkyl chains of phospholipid molecules in a membrane environment in the liquid crystal phase. The calculations have been performed for the chain 1 of 1,2-dipalmitoyl 3-sn-phosphatidylcholine (DPPC), a typical constituent of phospholipid membranes. Under the assumption of fixed bond lengths and bond angles, the internal dynamics of the chain is described in terms of 15 dihedral angles. The time evolution of the angular variables is assumed to be diffusional in character, and a master equation for transitions among the stable conformers is constructed from the energetics and hydrodynamics of the chain. This method is an extension to the time domain of the rotational isomeric state (RIS) approximation, which has been widely used to compute static properties of the chains. After calculation of the suitable correlation functions, effective rate constants relevant for spectroscopic and kinetic observables have been computed, and the results have been compared with those obtained by recent Brownian dynamics (BD) calculations. The position dependence of the rate constants along the chain has been examined with special reference to understanding the effects resulting from cooperativity in the conformational transitions. The overall spinning and tumbling of the chain has also been described by a diffusive model. The calculated spectral densities for the composite motional process have been used to rationalize the behavior of the relaxation times T1, T2, and T1ρ measured in deuterium nuclear magnetic resonance (NMR) experiments. [ABSTRACT FROM AUTHOR]

Electron spin–echo (ESE) and two-dimensional electron–electron double resonance (2D ELDOR) experiments have been performed as a function of director orientation and temperature in the smectic A phase of the liquid crystal S2 for the spin–probe PD-tempone(2×10-3 M). Over the entire temperature range studied (288–323 K) we observe significant 2D ELDOR cross peaks only for ΔMI =±1 indicative of 14N spin–relaxation and negligible Heisenberg exchange. From the angular dependent 14N spin–relaxation rates we obtain the dipolar spectral densities at the hyperfine (hf) frequency, whereas from a combination of ESE and 2D ELDOR we obtain the dipolar and Zeeman-dipolar spectral densities at zero frequency. The angular dependent spectral densities were successfully decomposed into their basic components in accordance with theory. The angular dependent spectral densities at the hf frequency are not predicted by a model of anisotropic rotational diffusion in a nematic orienting potential, but are consistent with predictions of a model due to Moro and Nordio of solute rototranslational diffusion in a McMillan-type potential. The angular dependence also indicates that order director fluctuations in the smectic phase are suppressed at frequencies on the order of 10 MHz. An additional contribution to solute reorientation due to cooperative hydrocarbon chain fluctuations is suggested to account for the behavior of the observed spectral densities at zero frequency. An evaluation of the relevance of several other dynamical models to this experimental work is also presented. [ABSTRACT FROM AUTHOR]