Characteristics of stability boundary and frequency in nonlinear ion trap mass spectrometer

In this article, the Poincare-Lighthill-Kuo (PLK) method is used to derive an analytical expression on the stability boundary and the ion trajectory. A multipole superposition model mainly including octopole component is adopted to represent the inhomogeneities of the field. In this method, both the motional displacement and secular frequency of ions have been expanded to asymptotic series by the scale of nonlinear term ε, which represents a weak octopole field. By solving the zero and first-order approximate equations, it is found that a frequency shift exists between the ideal and nonlinear conditions. The motional frequency of ions in nonlinear ion trap depends on not only Mathieu parameters, a and q, but also the percentage of the nonlinear field and the initial amplitude of ions. In the same trap, ions have the same mass-to-charge ratio (m/z) but they have different initial amplitudes or velocities. Consequently, they will be ejected at different time through after a mass-selective instability scan. The influences on the mass resolution in quadrupole ion trap, which is coupled with positive or negative octopole fields, have been discussed respectively.     

Study of Nonlinear Resonance Effect in Paul Trap

In this article, we investigated the nonlinear resonance effect in the Paul trap with a superimposed hexapole field, which was assumed as a perturbation to the quadrupole field. On the basis of the Poincare-Lighthill-Kuo (PLK) perturbation method, ion motional equation, known as nonlinear Mathieu equation (NME) was expressed as the addition of approximation equations in terms of perturbation order. We discussed the frequency characteristics of ion axial-radial (z-r) coupled motion in the nonlinear field, derived the expressions of ion trajectories and nonlinear resonance conditions, and found that the mechanism of nonlinear resonance is similar to the normal resonance. The frequency spectrum of ion motion in nonlinear field includes not only the natural frequency series but also nonlinear introduced frequency series, which provide the driving force for the nonlinear resonance. The nonlinear field and the nonlinear effects are inevitable in practical ion trap experiments. Our method provides better understanding of these nonlinear effects and would be helpful for the instrumentation for ion trap mass spectrometers.      

Simulation protocols for coherent femtosecond vibrational spectra of peptides

Two algorithms for simulating the response of peptides to sequences of IR pulses are developed and applied to N-methyl acetamide (NMA) and a 17 residue alpha-helical peptide (YKKKH17) in D(2)O. A fluctuating vibrational-exciton Hamiltonian for the amide I mode is constructed from molecular dynamics trajectories. Coupling with the environment is described using a density functional theory electrostatic map. The cumulant expansion of Gaussian fluctuation incorporates motional narrowing due to fast frequency fluctuations and is adequate for NMA and for isotopically labeled bands in large peptides. Real-space truncation of the scattering matrix of the nonlinear exciton equations significantly reduces the computational cost, making it particularly attractive for slow fluctuations in large globular proteins.     

An effective method for the discrimination of motional anisotropy and chemical exchange

Analysis of the ratio of transverse and longitudinal relaxation rates (R2/R1) is an approach commonly used for estimation of overall correlation time and identification of chemical exchange in biological macromolecules. However, this analysis fails to distinguish between chemical exchange and motional anisotropy. We describe a simple method for identifying chemical exchange and motional anisotropy using the product, R1R2. In the slow tumbling regime, the R1R2 product results in a constant value that is independent of overall correlation time and motional anisotropy. This analysis provides a simple method for rapidly estimating and dissociating the effects of motional anisotropy and chemical exchange in NMR heteronuclear spin relaxation data. We demonstrate the utility of the method with 15N relaxation data collected on the proteins E. coli ribonuclease H and the trimeric E. coli membrane associated lipoprotein lpp.     

A Ca2+‐, Mg2+‐, and Zn2+‐Based Dendritic Contractile Nanodevice with Two pH‐Dependent Motional Functions

A contractile dendritic motional device is reported where metal ions with biological importance—Ca²⁺ (the main regulatory and signaling species of the natural muscles), Mg²⁺, and Zn²⁺—initiate two kinds of motional functions. The first motional function is the metal‐ion‐induced contraction of a linear strand into a Z‐shaped dinuclear complex, and the second one is the change of the height of Z‐shaped complexes via transmetalation. By means of the pH‐dependent counterligand tren, the two motional features of the machine can depend on alternate additions of acid and base. An optical response is associated with the conversion of the linear form (which is yellow) into the metalated Z‐shaped one (which is red).     

Langevin-Bloch equations for a spin bath

We derive the Bloch equations for a two-level system coupled to a spin bath of infinitely many two-level atoms to examine phase and energy relaxation of an optically excited system. We show that increasing temperature assists coherence. This is reflected in a number of anomalous features of relaxation of the system, e.g., decrease of integrated absorption coefficient with temperature, nonlinear variation of linewidth with incident power. We also predict that thermally induced coherence may result in anomalous narrowing of linewidth, reminiscent (but distinct) of "motional narrowing" of spectral line. The theoretical results are discussed in the light of absorption-emission experiments on single quantum dots.     

Four-level optical line shape of a single molecule coupled to a single tunneling two-level system

We propose a density-matrix theory for the four-level system consisting of a single optical two-level system (OTLS) coupled to a single two-level system tunneling along a vibrational coordinate (VTLS). Phonons induce jumping rates of the VTLS, but coherent tunneling has to be considered explicitly as well, because the Born-Oppenheimer potential of the tunnel variable may change upon optical excitation. The OTLS is subject to spontaneous emission and driven by a laser wave with arbitrary strength. Numerical simulations for various coupling cases reproduce limiting behaviors previously discussed separately in the literature, such as motional narrowing, cross transitions, optical saturation and pumping, and nonlinear effects. Our model also perfectly fits recent measurements of the spectra of a single molecule coupled to a single tunneling system in a disordered crystal.     

Solid state N.M.R. relaxation study of liquid crystal polymers employing a two dimensional technique

Molecular motions of liquid crystal polymers in the solid state cover a broad dynamic range, extending from the fast rotational to the ultra slow motional regime. Two dimensional N.M.R. relaxation spectroscopy is designed to follow these motions and to differentiate the various motional modes. In addition, different types of molecular order, modulated by these regions, are also discriminated. The solid state dynamics of the polyesters studied depends sensitively upon their thermal history. Annealed samples show a typical semicrystalline behaviour, manifested by two different motional components. The molecular order is characterized by a high degree of conformational and orientational order of the polymer chains, which is strongly correlated with the exceptional mechanical properties of these systems.     

ESR-spin labelling study of semi-interpenetrating networks and polymer mixtures based on functionalized polyurethanes and polymethacrylates

Semi-interpenetrating polymer networks, SIPNs, and polymer mixtures (1:1 mass ratio) based on segmented polyester polyurethane, PU, with carboxylic groups and methacrylic copolymer, PM, with tertiary amine groups were prepared. Electron spin resonance, ESR, spin label method was used to study the effect of functional groups concentration on the segmental motion, motional transitions and phase separation. The concentration of functional groups varied from 0 to 0.45 mmol g⁻¹. From the temperature dependent composite ESR spectra of PU labelled component motional heterogeneity was deduced. Restriction of segmental motion of PU segments in the PU/PM mixtures increases with the augmentation of functional groups content due to the additional noncovalent interactions. The critical concentration (0.35 mmol g⁻¹) above which the motional restriction decreases is observed. The effect of functional groups is discussed in terms of the change of local packing density. According to the fractions of the slow component and temperatures of motional transitions SIPNs reveal better interpenetration and interactions of both polymer components. Additional functional groups contribute to a very strong influence of restricted PM chains on the PU hard segments.     

Decoding the components of dynamics in three‐domain proteins

In this study, we examine the feasibility and limitations of describing the motional behavior of three‐domain proteins in which the domains are linearly connected. In addition to attempting the determination of the internal and overall reorientational correlation times, we investigate the existence of correlations in the motions between the three domains. Since in linearly arranged three‐domain proteins, there are typically no experimental data that can directly report on motional correlation between the first and the third domain, we address this question by dynamics simulations. Two limiting cases occur: (1) for weak repulsive potentials and (2) when strong repulsive potentials are applied between sequential domains. The motions of the terminal domains become correlated in the case of strong interdomain repulsive potentials when these potentials do not allow the angle between the sequential domains to be smaller than about 60°. Using the model‐free (MF) and extended MF formalisms of Lipari and Szabo, we find that the motional behavior can be separated into two components; the first component represents the concerted overall motion of the three domains, and the second describes the independent component of the motion of each individual domain. We find that this division of the motional behavior of the protein is maintained only when their timescales are distinct and can be made when the angles between sequential domains remain between 60° and 160°. In this work, we identify and quantify interdomain motional correlations. © 2013 Wiley Periodicals, Inc.     

Three-dimensional-IR spectroscopy: beyond the two-point frequency fluctuation correlation function

Three-dimensional-IR spectroscopy is proposed as a new spectroscopic technique that is sensitive to three-point frequency fluctuation correlation functions. This will be important when the statistics of the underlying stochastic process is non-Gaussian, and hence when the system does not follow the linear response hypothesis. Furthermore, a very general classification of nonlinear spectroscopy in terms of higher order frequency fluctuation correlation functions is introduced, according to which certain moments of a multidimensional spectrum are related to certain frequency fluctuation correlation functions. The classification is rigorous in the so-called inhomogeneous limit, but remains valid approximately also when motional narrowing becomes important. The work also puts a recent paper [J. Bredenbeck et al., Phys. Rev. Lett. 95, 083201 (2005)] onto solid theoretical grounds, where we have shown for the first time that fifth-order spectroscopy--in this case transient two-dimensional spectroscopy--is indeed sensitive to the three-point frequency fluctuation correlation function.     

Interdependence of motional processes in polymers: correlation functions for nmr relaxation

The roles of both anisotropic motion and the interdependence of multiple motions in leading to nonexponential correlation functions for NMR relaxation data are explored. A motional model is developed in which rotational motions of segments of various lengths are controlled by the formation and disappearance of a suitable conformation. Such a model gives correlation functions which can be made, through adjustment of parameters, to be almost identical to correlation functions from other, quite different, models. The ability of NMR relaxation data to identify unique motional models is thus questioned.     

Wideline NMR studies of polyacrylonitrile

NMR linewidth studies of molecular motion in several polyacrylonitrile samples have been carried out. The motional transition temperature is found in the 105–124°C. range and depends upon polymerization conditions. In addition, the thermal activation energy for the motional process underlying this transition was evaluated at 16.4 kcal./mole. Finally, measurement of the transition temperature for one of the specimens in three different physical states (bulk, spun only, and spun and drawn with a ratio of 3:1), revealed that no change in the transition temperature was effected by either spinning or drawing.     

Determination of protein structures consistent with NMR order parameters

Order parameters obtained from NMR experiments characterize distributions of bond vector orientations. Their interpretation, however, usually requires the assumption of a particular motional model. We propose a multiple-copy simulation method in which the experimental order parameters are used as restraints in conjunction with a standard molecular force field. The latter effectively acts as a sophisticated motional model, allowing ensembles of structures consistent with the experimental order parameters to be determined.     

The slow molecular mobility in amorphous trehalose.

The molecular mobility in amorphous trehalose is studied by thermally stimulated depolarisation currents (TSDC). The effect of aging on the sub-T(g) motional processes was analysed during annealing at a given aging temperature, some degrees below the calorimetric glass transition temperature T(g)=115 degrees C. The features of different motional components of the secondary relaxation are monitored as a function of time as the glass structurally relaxes on aging. The faster components of the secondary relaxation are negligibly dependent on aging and may be ascribed to intramolecular modes of motion, while the slower motional modes show a significant dependence on aging consisting of some kind of local motions with some intermolecular nature. The dielectric strength of this relaxation decreases with increasing aging time, and there is no evidence for any modification with aging of the relaxation time of this local mobility. The TSDC study of the molecular mobility of amorphous trehalose in the temperature region of the glass transformation provides the unexpected result that no glass transition signal is observable in this temperature region.     

Wideline NMR studies of oriented nylon 66 under tensile stress

NMR linewidth studies of nylon 66 as a function of temperature and applied tensile stress have been conducted. The principal motional transition temperature was found to be shifted to higher temperatures with stress application by 9°C./g./den. At any given temperature, increased stress resulted in an increased linewidth. An attempt was made to correlate the shift in the motional transition temperature with the concept that a segment experiencing motion must do work against the applied tensile stress.     

QCM/HCC as a platform for detecting the binding of warfarin to an immobilized film of human serum albumin

Quartz crystal microbalance/heat conduction calorimetry (QCM/HCC) is a new measurement technology that has been used to monitor simultaneously the mass and motional resistance of a thin film in conjunction with the heat flow produced by a chemical change in the film initiated by reaction with a gas. In this work we examine the applicability of the QCM/HCC in detecting chemical changes at the solution/thin film interface. Human serum albumin (HSA) was bound to the gold electrode of a 5 MHz AT-cut quartz resonator using three types of linkers and then exposed to buffered solutions of the anticoagulant drug warfarin. Changes in resonator frequency and motional resistance as well as changes in heat flow produced by warfarin binding to HSA were monitored as a function of the warfarin concentration. Differences in frequency and motional resistance changes depend upon the linker and vary both in magnitude and sign, whereas the integrated heat signal is proportional to the concentration of warfarin and independent of the linker chemistry. Quartz crystal microbalance/heat conduction calorimetry can thus be a useful tool for studying protein-ligand interactions at the solution-surface interface, even though the quartz resonator does not behave as a microbalance.     

Nonlinear Effects in Paul Traps Operated in the Second Stability Region: Analytical Analysis and Numerical Verification

Paul trap working in the second stability region has long been recognized as a possible approach for achieving high-resolution mass spectrometry (MS), which however is still far away from the experimental implementations because of the narrow working area and inefficient ion trapping. Full understanding of the ion motional behavior is helpful for solving the problem. In this article, the ion motion in a superimposed octopole field, which was characterized by the nonlinear Mathieu equation, was solved analytically using Poincare-Lighthill-Kuo (PLK) method. This method equivalently described the nonlinear disturbance by an effective quadrupole field with perturbed Mathieu parameters, a _u ^′ and q _u ^′ , which would bring huge convenience in the studies of nonlinear ion dynamics and was, therefore, used for rapid evaluation of the nonlinear effects of ion motion. Fourth-order Runge-Kutta method (4th R-K) indicated the error of PLK for characterizing the frequency shift of ion motion was within 15%. Figure

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Secondary molecular mobility in amorphous ethyl cellulose: Aging effects and degree of co‐operativity

The secondary relaxations in amorphous ethyl cellulose are studied using thermally stimulated depolarization currents (TSDCs) in the temperature region from 165 °C (108 K) up to 145 °C (418 K). The influence of aging on the current peaks of the secondary relaxation is discussed, and it is concluded that some modes of motion of this mobility are aging independent, while others are affected by aging. A particular attention is focused on the discussion of the degree of co‐operativity of the motional modes of the secondary relaxation. The conclusion to be driven from the obtained TSDC results is that the aging‐independent motional modes, as well as those that are aging dependent, do not show any appreciable co‐operative character. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 820–829, 2009     

2H NMR study of dynamics of benzene-d6 interacting with humic and fulvic acids

Samples of three humic acids and one fulvic acid with 1% loading of benzene-d(6) in sealed glass tubes have been studied with solid-state deuterium quadrupole-echo nuclear magnetic resonance spectroscopy. Calculated spectra combining three motional models, two isotropic models and a third more restricted small-angle wobble (SAW) motional model, are fit to the experimental spectra. One isotropic motion (ISO(v)) is assigned to vaporous benzene-d(6) due to the small line width, short T(1), and the loss of this component by about -25 °C when the temperature is lowered. The remaining two motional components, ISO(s) and SAW, are sorbed by the humic or fulvic acid. Benzene-d(6) slowly interacts with the humic substances, progressively filling SAW sites as ISO(s) motion diminishes. Both the sorption and increase in percentage of SAW motion are for the most part complete within 200 days but continue to a lesser extent over a period of a few years. For the SAW motion there are at least two and most likely a series of T(1) values, indicating more than one adsorption environment. Enthalpies of sorption, obtained from application of the van't Hoff equation to the percentages of the different motional models derived from a series of variable temperature spectra, are comparable in magnitude to the enthalpy of vaporization of benzene. In Leonardite humic acid, ΔH and ΔS for the ISO(s) to SAW transition change from positive to negative values with age, implying a transition in the driving force from an entropic effect associated with expansion and deformation in the molecular structure of the humic substance to accommodate benzene-d(6) to an enthalpic effect of strong benzene-d(6)-humic substance interactions. In contrast, at advanced ages, Suwannee River humic and fulvic acids have small positive or near zero ΔH and positive ΔS for the ISO(s) to SAW transition.