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See All Customer Reviews. Shop Textbooks. Add to Wishlist. USD Sign in to Purchase Instantly. Temporarily Out of Stock Online Please check back later for updated availability. Overview A definitive work on ESR and polymer science by today's leading authorities The past twenty years have seen extraordinary advances in electron spin resonance ESR techniques, particularly as they apply to polymeric materials.

Show More. Parker Philip M. Moebius Klaus, Savitsky Anton N. In German. Hagen Wilfred R. Year Hemminga Marcus A. Rieger Philip H. Zavoiskaja Natalija E. In Russian. Weil John A. Wiley Year Bender Christopher J. Dolinsek J. Maier K. ISBN: Vij D. Webb Graham A. Year Bakhmutov Vladimir I. Eaton Sandra S. Yadav Lal Dhar S. Year Berliner Lawrence J. Genguyn Li, What is the Electron Spin? This is a bit out of the mainstream. Krishna N. Nagakura S. ISBN , Davies J. Eaton Gareth R. Rudowicz C. Year Poole Charles P.

Year Atherton N. Bertini I. ISBN X. Clark R. Ghim B. Year Kochelaev B. Ohya-Nishiguchi H. Williams R. Poole Charles P. Berliner Lawrence J. With CD. Evans M. Hennel J. Novikov V. Zavoiskij , Nauka, Moskow In Russion.

Book Advanced Esr Methods In Polymer Research

Year Bagguley D. Hahn , Oxford University Press, Oxford Dikanov Sergei A. Mabbs F. Year Banci L. Parish Richard V. Pilbrow J. Pregosin P. Robinson James W. Whole Section 8 is about ESR. Wendisch D. Cameron, Comprehensive Polymer Science , Vol. Hoff A. Yordanov N. World Scientific Pub. Year Symons M. Year McConnel J. Sigel H. Year Abragam A. Lenk R. Morrill T. Year Ayscough P. Year Lever A. Salikhov K. Willett R.

The subsequently detected signal can be considered as an FID of the polarization pattern. While the FID of a broad unstructured hole decays within the dead time after the pulse and cannot be observed, the FID of the polarization grating has the form of the Fourier transform of this grating. Additional pulsed ESR experiments have been used, which are beyond the scope of this introductory chapter. An overview of these experiments, as well as on the theoretical background of pulsed ESR, can be found in Ref.

Jeschke gratefully acknowledges financial support by a Dozentenstipendium of Fonds der Chemischen Industrie. Research in the laboratory of S. Carrington, A. Alger, R. Abragam, A. Poole, C. Pilbrow, J. Weil, J. Schweiger, A. Wasserman, A.

Goldfarb, D. Smirnov, A. Reichmanis, E. Hill, D. Carswell, T. In Polymer Spectroscopy; Fawcett, A. Macromolecule-Metal Complexes; Ciradelli, F. Biological Magnetic Resonance. Spin Labeling; Berliner, L. Motyakin, M. Molecular Motions in Polymers by E. Symposium Series Vol. Cameron, G. Gerson, F. Molin, Yu. Spin Exchange, Springer: Berlin, Spiess, H. A , 42, Owenius, R. A , , Altenbach, C. USA , 91, Nordio, P. Bednarek, J. Leporini, D. Spin—Spin Couplings 2.

Dipole—Dipole Coupling 2. Exchange Coupling 2. Fermi Contact Interaction 2. Spin Density in p and d Orbitals 3. Electron—Electron Double Resonance 3. General Considerations 3. Experimental Techniques 3. Direct Computation of Distance Distributions 4. Electron—Nuclear Double Resonance 4. General Considerations 4. Experimental Techniques 4. Electron Spin Echo Envelope Modulation 5. Principles 5.

Experimental Techniques 5. Data Analysis 6. If g-values and hyperfine splittings liquid state or g and hyperfine tensors solid state can be extracted, additional information is obtained on the molecular structure in the immediate vicinity of the atom s on which the spin is centered. Finally, for spin probes with well-known ESR parameters, such as nitroxides, line shape analysis of continuous wave CW ESR spectra yields information on the rotational dynamics of the probe.

Information on that length scale may, however, not be complete. Hyperfine couplings to nuclei in neighboring molecules are usually unresolved even if these molecules are in direct contact with the spin-bearing molecule. For many applications in polymer science, intermolecular interactions and structural information on a somewhat longer range, up to a few nanometers, is of considerable interest.

Length scales between 0. However, they are not resolved in ESR spectra, as there are too many of these interactions and, in solids, the lines are broadened due to anisotropy of the g-value and of the larger hyperfine couplings of nearby nuclei. The long-range information is contained in weak couplings between distant spins. Such couplings are discussed in Section 2. They can be extracted by separation of interactions, that is, by techniques that detect a certain type of small interaction in the presence of larger interactions.

The most important class of such techniques are double-resonance experiments. By electron—electron double resonance ELDOR it is possible to separate weak couplings between two electron spins from all other interactions. The accessible frequency range from 15 MHz down to kHz corresponds to a distance range between 1. By electron—nuclear double resonance ENDOR weak couplings between an electron spin and a nuclear spin can be measured Section 4. The accessible frequency range is approximately the same.

As such hyperfine couplings often have a Fermi contact contribution that is not easily related to spin—spin distances, it may be more difficult to extract precise structural information than it is for electron—electron couplings. However, in many cases even semiquantitative information is helpful. The Fermi contact contribution can usually be neglected for intermolecular hyperfine couplings. The hyperfine couplings are then purely dipolar, so that ENDOR directly provides distance information for supramolecular structures. In this situation, electron and nuclear spin states are mixed and formally forbidden transitions, in which both the electron and nuclear spin flip, become partially allowed.

Oscillations with the frequency of nuclear transitions then show up in simple electron spin echo experiments. Although such electron spin echo envelope modulation ESEEM experiments are not strictly double-resonance techniques, they are treated in this chapter Section 5 because of their close relation and complementarity to ENDOR. The ESEEM experiments allow for extensive manipulations of the nuclear spins and thus for a more detailed separation of interactions. Double-resonance methods, such as ELDOR, can also be used to obtain information on the dynamics of paramagnetic species.

Technical aspects and theory of CW ELDOR4 and ENDOR5 experiments will not be discussed, as pulsed techniques are nowadays more common, in particular for work on the highly viscous or solid systems that are typical for polymer research. Finally, this chapter is devoted exclusively to the description of the theoretical background and the concepts of double-resonance experiments. Applications are described in Chapter 7. Dipole—Dipole Coupling The magnetic moments that are associated with electron and nuclear spins interact through space by the dipole—dipole coupling.

This coupling is a pair interaction. Furthermore, in all these experiments we can distinguish between an observer spin S and pumped spins Ii that are coupled to the observer spin. We may neglect the couplings of the pumped spins Ii among themselves. All described experiments require that the electron Zeeman interaction of the electron spin S be much larger than all spin—spin couplings.

Coupling terms containing Sx and Sy spin operators are thus negligible nonsecular , as they act perpendicular to the quantization axis z. The Hamiltonian of the dipole—dipole dd interaction can then be written as in Eq. In Eq. Dipole—dipole coupling between two spins I and S.

The local field imposed by the pumped spin I has a different sign for I being parallel left or antiparallel to the external field B0. Hence, a flip of spin I shifts the resonance frequency of spin S. A mw pulse then excites not only the formally allowed transitions in which only the magnetic quantum number of the electron spin changes, but also formally forbidden transitions, in which both the electron and nuclear spin are flipped. At the usually applied magnetic fields of 0. This is the case only if both spins are well localized on the length scale of r.

If an unpaired electron is significantly delocalized, the dipole—dipole coupling tensor has to be averaged over the spatial distribution of the electron spin. In general, the orientation dependence of the dipolar coupling terms is then no longer described by Eqs. A detailed discussion of this situation is beyond the scope of this chapter. Calculated dipolar powder spectra for two electron spins with resonance frequencies of 9. Unpaired electrons that are localized in weakly overlapping orbitals are best treated as individual spins. As electrons are indistinguishable from each other, they can be exchanged even between weakly overlapping orbitals.

This exchange leads to a small coupling of the two electrons. Unfortunately, J is sometimes defined with opposite sign or may even be defined as one-half of the negative value of J in Eq. Hence, comparison of J couplings from literature always requires some caution. In the definition used here, a positive sign of J corresponds to the case where the triplet state of the two electrons is higher in energy at zero field than the singlet state.

This is antiferromagnetic coupling and corresponds to weak bonding overlap of the orbitals. The opposite case of J 0 is ferromagnetic coupling, which corresponds to weak antibonding overlap. Within the same class of compounds, weak exchange couplings decay exponentially with the distance between the two spins centers of the spatial distribution. However, the decay constant and prefactor strongly depend on the type of bonding network and the conductivity of the medium between the two spins.

Fully conjugated systems may have sizeable exchange couplings at distances as large as 3.

ESR Spectroscopy in Polymer Research

The modification of dipolar coupling patterns by J coupling has been discussed earlier in some detail. This effect leads to changes in the ESR line shape,8 but is not important in the context of double-resonance experiments on soft matter or solids. Fermi Contact Interaction Unpaired electrons located in s orbitals have a finite probability to reside inside the atomic nucleus.

Such contact between the electron and nuclear spin results in an isotropic coupling Fermi contact interaction , which can be as large as MHz for the electron of a hydrogen atom or a few hundred megahertz MHz for electrons localized at a transition metal ion. Isotropic hyperfine couplings in organic radicals or in ligands of transition metal ions do not usually exceed MHz. In other cases, intermolecular hyperfine couplings are not expected to exceed kHz. Spin Density in p and d Orbitals If some spin density is transferred to a p or d orbital on a certain nucleus, this spin density contributes to the dipole—dipole interaction between the two spins.

Such a contribution to the dipole—dipole interaction may exceed the contribution from through-space interaction between the nuclear spin and the center of electron spin density. The distance between the nucleus and the center of spin density cannot be computed directly from the anisotropic hyperfine coupling in this situation.

Distance determination by ENDOR or ESEEM thus requires that either nuclei without significant spin density in p or d orbitals are used protons, deuterons, alkali, and alkali earth metal ions or that spin density transfer to the atom under consideration is negligible intermolecular couplings. This is achieved by refocusing all interactions, including the coupling between the two electron spins, in an echo experiment on the observer spin S. The spin—spin coupling is then reintroduced by a pump pulse that ideally exclusively excites spin I.

The minimum excitation bandwidth of the pump pulse is the width of the dipolar Pake pattern, since both transitions of the pumped spin must be excited to fully reintroduce the coupling. If the total width of the ESR spectrum is narrower than that, single frequency techniques11—13 have to be used for distance measurements. Distances down to 1. Both orientation and nuclear magnetic quantum number are constant during an experiment.

The lower end of the distance range for reliable measurements by pulse ELDOR techniques is set by three complications. First, if the dipolar splitting exceeds the excitation bandwidth of the pump pulse, the pump pulse typically excites only one of the transitions of the dipolar doublet. In this situation, the coherence is not exchanged between the two transitions of the observer spin, but is rather converted to zero-quantum or double-quantum coherence involving both spins. The magnetization is thus lost and does not contribute to the signal. Second, a larger dipolar splitting increases the probability that observer spins are excited by the pump pulse.

Third, if the dipolar splitting is of the order of the difference of the resonance frequencies in the absence of coupling, the pseudo-secular term of the coupling Eq. The three complications are not independent of each other. For these reasons, measurements of distances and, in particular, distance distributions of nitroxides 1. The higher end of the distance range is determined by the maximum time tmax for which dipolar evolution of the observer spin can be measured.

Generally, this depends on the transverse relaxation time T2 of the observer spin, so that measurements are best performed at low temperatures, where T2 reaches its maximum. Due to contributions from instantaneous diffusion, the apparent T2 also depends on concentration. If S and I spins correspond to chemically different species with different T2, observer spin S should be the more slowly relaxing spin. This advice may, however, conflict with the requirement to maximize the fraction of pumped spins, which is fulfilled by pumping at the global maximum of the total ESR spectrum of both species.

If such a conflict exists, it is advisable to test both settings of pump and observer frequency. Here, d is the spin—spin coupling including dipole—dipole and exchange contributions. For the variable-time version, see the text. The spin—spin coupling d can thus be measured by recording the echo intensity as a function of interpulse delay t and Fourier transformation of the data. Due to the orientation dependence of d and a possible distribution of distances r, d is usually distributed. Oscillations for different d values interfere destructively at long times t. In particular, there is always a large number of I spins of remote paramagnetic centers with small intermolecular couplings that lead to a decay of the signal toward zero at infinite times.

For a homogeneous spatial distribution of the remote radicals, this decay is exponential. This leads to signal distortions unless the two frequencies are applied to two well-isolated modes of a bimodal resonator. The requirement for such specialized hardware and the restriction to a fixed frequency difference imposed by the bimodal resonator is overcome by using the four-pulse double electron-electron resonance DEER experiment Fig.

Research Methods - Introduction

The pulse sequences shown in Fig. Such constant-time experiments have the advantage that the variation of the echo amplitude is not influenced by relaxation. Loss of magnetization of the observer spins by transverse relaxation is the same at all times t. On the other hand, constant-time experiments have the disadvantage that the entire data set is measured with a relaxational loss of magnetization that corresponds to tmax. In principle, data points at t tmax can be measured with smaller loss.

As relaxation is exponential, this can lead to a significant sensitivity gain. Part of this gain is lost again by the necessity to measure a reference data set that contains only the relaxational decay and dividing two data sets. In all cases, the primary data set is a variation V t of echo intensity with time. The dipolar evolution function contains the information on the distribution P r of spin—to—spin distances. For distances up to at least 5 nm, ESR spectroscopy can complement results from scattering, since spin labeling opens up a different and very versatile approach to contrast variation.

Less sample is needed than for SANS and more precise distance measurements are possible. Combined scattering and ESR studies require a common framework for the description of structures. Scattering experiments are based on different scattering cross-sections of atoms in the particles of interest and in the surrounding medium. The variation of scattering intensity with the wave vector q [scattering curve I q ] is the product of an instrumental constant and of two q-dependent contributions related to the structure of the investigated material, the form and the structure factors.

The form factor depends on the shape of the particle, while the structure factor contains information on any regularity of the spatial distribution of the particles. Symmetry of the particles may be nicely seen in the scattering curves that correspond to reciprocal space, but in many cases data are more easily interpreted in real space.

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Indirect Fourier transformation is an ill—posed problem just as the computation of distance distributions from pulsed ELDOR data that is described below. Complementary information can be obtained by spin-labeling only specific sites, such as the surface of the particle or the ends of a polymer chain.

Scattered waves totally cancel by destructive interference if there are no regularities in the structure. Such a signal contribution from a homogeneous distribution may be advantageous, as it allows for precise determination of particle concentrations and for the detection of subtle deviations from a homogeneous distribution by a deviation of B t from an exponential decay.

In scattering, such deviations contribute only a very broad background to I q that is easily missed. By using the analytical solution of the Poisson—Boltzmann equation for a charged planar plate in an electrolyte solution,19 we have calculated the concentration profiles of monovalent ions in solution with the opposite Fig.

Assuming that the observer spins S are attached to the surface of the platelet and the pumped spins are located at the ions in solution, we obtain the dipolar evolution functions B t shown as solid lines in Fig. For enrichment of unlike charges near the surface, B t has a positive deviation from an exponential fit dashed line in Fig. This positive deviation generally occurs if short distances are overrepresented compared to a homogeneous distribution.

For depletion of like charges near the surface, B t has a negative deviation from an exponential fit dashed line in Fig.

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The negative deviation generally occurs if short distances are underrepresented. A concentration of 1. This information is contained either in the primary time-domain data variation of echo intensity as a function of dipolar evolution time t or in the dipolar spectrum obtained from these data by Fourier transformation. Time- and frequencydomain data contain exactly the same information, since Fourier transformation is a linear operation.

However, some features are easier to recognize in time domain e. The wanted information is usually the distribution of distances P r. Some deviations can be seen in frequency domain, but with proper data processing, as explained below, they do not cause artifacts in the distance distribution P r. The mathematical problem of data analysis is thus to convert P d to P r.

This problem is ill-posed, that is, a mild distortion of P d by noise can cause a strong distortion of P r. In contrast to the true solution, this superposition may also fit part of the noise and may thus be preferred in a least-squares solution of the problem. As a result, one obtains an illusory set of narrow peaks in the distance range where the true distribution exhibits just one broad peak for illustrative examples, see Ref.

Two strategies can stabilize the solution. First, the algorithm should allow only for nonnegative values of P r. This is reasonable, as a distance distribution cannot have negative contributions. Second, if the primary data are fitted equally well by a broad distribution and a complicated pattern of narrow peaks, we know that the broad distribution is more likely the correct solution. This can be considered in data analysis by requiring that the solution P r be both reasonably smooth and a good fit of the original data.

The optimum regularization parameter corresponds to the corner of the L. Instead, one should use existing information about the investigated material to estimate a minimum realistic width of peaks in the distance distribution. General Considerations The interaction between electron and nuclear spins causes line splittings in both ESR and nuclear magnetic resonance NMR spectra. However, since usually many nuclear spins Ik are coupled to a single electron spin S, the NMR spectra are easier to interpret and are better resolved. A further resolution advantage arises in the ENDOR spectra since the line width is limited by the longitudinal relaxation time T1e of the electron spins or the transverse relaxation time T2n of nuclear spins, rather than by the transverse relaxation time T2e of the electron spins.

The ESR frequencies are given in Eq. They thus do not contain any information on the nature of the coupled nucleus. The information is best obtained at high fields, where the nuclear Zeeman interaction dominates. By analyzing the dependence of ENDOR spectra as a function of the ESR observer field, it is possible to determine the full hyperfine and nuclear quadrupole tensors and their orientations with respect to the g-tensor. Information on the structure can then be obtained by quantifying proximity of nuclei of a certain element to the electron spin.

For protons, distance information can be derived from the dipolar part of the hyperfine coupling. For 19F, small s spin densities already lead to a sizeable Fermi contact interaction. This simplifies semiquantitative detection of proximity of 19F to a spin probe,33 but makes it nearly impossible to determine a distance of closest proximity. Resonant radio frequency rf irradiation can then change this magnetization and the change can be detected again on an electron spin transition. A resonant rf pulse partially shifts this hole into side holes, as it changes the nuclear spin state and thus the resonance frequency of the electron spin transition.

The frequency shift is equal to the hyperfine coupling A. A third part is unchanged, as the rf pulse excites only one of the two lines of the hyperfine doublet. The two final mw pulses detect the depth of the center hole as a spin echo signal. An off—resonance rf pulse corresponds to maximum hole depth at point II rf pulse induces no change , while an on-resonant pulse corresponds to reduced hole depth point III. It is thus best suited for large hyperfine couplings. For small couplings, the experiment needs to be performed with very long mw pulses to create a very narrow hole.

The rf pulse again leads to a shift of parts of the hole pattern by A. The shifted gratings and the center grating interfere destructively, leading to a reduction in the amplitude of the stimulated echo. The frequency of the rf pulse is varied and integrated echo intensity is recorded. At point I before the first pulse, the whole line comprises equilibrium polarization. A resonant rf pulse shifts one-half of the hole to two side holes at frequency difference A point III. The frequency of the rf pulse is varied and integrated intensity of the stimulated echo is recorded.

These shifted gratings may interfere destructively with the remaining grating in the center, so that just a broad hole remains point II. In this case, no echo is formed. At 95 GHz, there may still be overlap of signals in groups of nuclei with similar gyromagnetic ratio. ENDOR at even higher frequencies may sometimes be required to separate signals from these elements and is currently developed in several groups around the world.

High-field ENDOR also improves orientation selection, which allows for determination of the relative orientation of the hyperfine tensor with respect to the g tensor and also leads to resolution enhancement. At high fields, one often observes a pronounced difference between ENDOR intensities at frequencies above and below the nuclear Zeeman frequency.

ESR Imaging

This is in turn due to the fact that the Zeeman energy is comparable to or exceeds the thermal energy kBT. Such build-up occurs when longitudinal nuclear relaxation rates and electron-nuclear cross-relaxation rates are smaller than the repetition rate of the experiment. This condition is more often encountered at high fields, where the relaxation rates tend to be lower.

Nuclear Zeeman frequencies vertical markers and ENDOR frequency ranges horizontal bars for selected isotopes at magnetic fields of 0. When the hyperfine coupling and the nuclear Zeeman frequency are of the same order of magnitude, transition probabilities for certain ENDOR frequencies become very small.

Counting the number of nuclei of a given type that are coupled to an electron spin also appears to be difficult with ENDOR techniques. Another incentive for pursuing an alternative to ENDOR comes from the wealth of information that can be obtained by time-domain experiments, in particular, two-dimensional spectroscopy. Principles For an anisotropic hyperfine interaction, the local field imposed by the electron spin at the site of the nuclear spin is not in general parallel to the z axis defined by the external magnetic field.

The pseudo-secular B term differs from zero except along the principal axes of the hyperfine tensor and leads to a deviation of the local field from the z direction. In other words, there is state mixing. Such forbidden transitions, in which both the electron and nuclear spin are excited, allow for measurements of nuclear frequencies by applying exclusively mw pulses. After this pulse sequence, a spin echo is observed. For part of the coherence only the phase is inverted, it remains on the same transition. Allowed ESR transitions are shown as solid lines, forbidden ESR transitions as dotted lines, and nuclear transitions as dashed lines.

Hence, the echo envelope is modulated. The depth of this modulation depends on the probability of forbidden transitions. A detailed examination of all coherence transfer pathways3 reveals that the four frequencies seen in Eqs. The square in the modulation depth is due to the fact that any coherence transfer pathway that leads to echo envelope modulation contains either two forbidden transfers or one forbidden transfer and the observation of forbidden coherence.

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times T2n and thus smaller line widths.

The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. The second-order shift with respect to twice the nuclear Zeeman frequency is small. In the latter case, the simplification comes about since hyperfine couplings mainly lead to a frequency dispersion perpendicular to the diagonal while quadrupolar couplings mainly lead to a dispersion parallel to the diagonal.

The higher order hyperfine shift parallel to the diagonal Fig. Data Analysis The most basic use of ESEEM is the detection of proximity of nuclei of certain elements to an electron spin local elemental analysis. The reason can be seen in Eq. Furthermore, ESEEM spectra usually cannot be properly phased and have to be displayed as magnitude spectra rather than absorption spectra.

One-dimensional ESEEM spectra are useful for well-defined coordination environments in transition metal complexes, in particular, if single crystals are available. This situation is, however, unusual in polymer applications. If 1D ESEEM data are dominated by contributions from a single element, timedomain analysis can provide estimates for the distance of closest approach of nuclei of this element and of the average number of such nuclei. This technique relies on the distance dependence of the modulation depth Eq. The decay of the modulation is due to the frequency dispersion, which to first order depends only on the distance.

By analyzing depth and decay of the modulation, the two parameters can thus be separated. A popular way of doing this is ratio analysis. Intensity tends to zero at the edges and varies throughout the correlation ridges. The decay of the modulation, characterized by the time dependence of the ratio of the upper and lower envelopes dotted lines , depends only on the distance of the closest shell of nuclei, but not their number. Although such a model of one sphere of nuclei with the same distance of shortest approach is certainly idealized, ratio analysis can give useful hints for the structure of a material.

Furthermore, trends of the modulation depth in a series of similar materials can be interpreted in terms of changing distances or coordination numbers. To use this approach in the presence of significant modulations from nuclei of two elements, one may record the data at a blind spot for one of the elements and suppress the unwanted contribution by digital filtering in spectral domain.

If the frequency shift according to Eq. In favorable cases, several of these ridges may be resolved. For deuterium, analysis of the HYSCORE patterns provides an estimate of the nuclear quadrupole coupling,3,45 which can then be introduced as a fixed correction parameter in ratio analysis. Taken together, the whole toolbox of CW and pulsed ESR techniques can thus characterize the structure of materials with a low degree of order in the range between the shortest intermolecular contacts and typical extensions of polymer molecules or proteins.

Success in this kind of structure characterization depends critically on selecting the right experiment or combination of experiments and on using proper techniques for data analysis. Schneider, D. In Biological Magnetic Resonance, Vol. Kevan, L. Kurreck, H. Wautelet, P. Jeschke, G. Spin Exchange.

Springer: Berlin, Kolodziejski, W. Borbat, P. Raitsimring, A. Milov, A. Lindner, P. North-Holland: Amsterdam, The Netherlands, Glatter, O. In Encyclopedia of Computational Chemistry, Vol. Wiley: New York, , pp. Milov A. Hinderberger, D. B , , Tikhonov, A. Weese, J. Miller, K. SIAM J. Chiang, Y. Rist, G. Hoffman, B. Cramer, S. Davies, E. A , 47, 1. Mims, W. London A , , Berliner, L. Epel, B.

Ernst, R.

Fler böcker av Schlick Shulamith Schlick

A , 33, Reijerse, E. Ichikawa, T. Physical Parameters of Nitroxide Labels 2. Magnetic Tensors of the Nitroxide 2. Diffusion Models 2. Orientational Ordering in Spin-Labeled Polymers 2. Slowly Relaxing Local Structure Model 3. Other Stochastic Liouville Calculation Parameters 3. Basis Set for the Stochastic Liouville Calculation 3.