Slow global motions in biosolids studied by the deuteron stimulated echo NMR experiment.

Recent 15N R1ρ-relaxation studies have shown that proteins in the solid state undergo slow, low amplitude global motion in the sub-millisecond time range. This range is at the edge of the time window for R1ρ experiments and, therefore, the motional parameters obtained by this method are not precise or reliable. In this paper, we present a 2H stimulated echo study of this type of molecular dynamics.

On the theory of the spin I = 1/2 double quantum NMR: Effects of spins spatial displacements between RF pulses.

Spatial displacements of spins between radio frequency pulses in a Double-Quantum (DQ) nuclear magnetic resonance pulse sequence generate additional terms in the effective DQ Hamiltonian. We derive a simple expression that allows the estimation and control of these contributions to the initial rise of the DQ build up function by variation of experimental parameters in systems performing anomalous diffusion. The application of polymers is discussed.

On the theory of deuteron NMR free induction decay of reptating polymer chains: Effect of end segment dynamics.

A self-consistent approximation beyond the Redfield limit and without using the Anderson-Weiss approximation for the Free Induction Decay (FID) of deuteron spins belonging to polymer chains undergoing reptation is formulated. The dynamical heterogeneity of the polymer segments created by the end segments is taken into account. Within an accuracy of slow-changing logarithmic factors, FID can be qualitatively described by a transition from an initial pseudo-Gaussian to a stretched-exponential decay at long times.

NMR Relaxometry: The Canonical Case Glycerol.

We present a quantitative description of the proton spin-lattice relaxation rate (,ω) of glycerol including temperatures from 191 to 360 K and a frequency range 10 kHz < ω/2π < 20 MHz covered by the field-cycling technique. The analysis encompasses the data compiled by Noack and co-workers in 1971, so far, the most complete data set (10 kHz > ω/2π < 117 MHz). Applying frequency-temperature superposition, master curves are constructed extending over 15 decades in frequency/time.

The dynamics of the plastically crystalline phase of cyanoadamantane revisited by NMR line shape analysis and field-cycling relaxometry.

The dynamics of cyanoadamantane (CN-ADA) in its plastically crystalline phase encompasses three processes: overall tumbling of the rigid molecule, rotation around the molecular symmetry axis, and vacancy diffusion. This makes CN-ADA a prototypical case to be studied by field-cycling as well as by conventional NMR relaxometry. Data are collected from 430 K down to about 4 K and frequencies in the range of 10 kHz-56 MHz are covered.

Scaling analysis of the viscoelastic response of linear polymers.

Viscoelastic response in terms of the complex shear modulus G(ω) of the linear polymers poly(ethylene-alt-propylene), poly(isoprene), and poly(butadiene) is studied for molar masses (M) from 3k up to 1000k and over a wide temperature range starting from the glass transition temperature T (174 K-373 K). Master curves G'(ωτ) and G″(ωτ) are constructed for the polymer-specific relaxation. Segmental relaxation occurring close to T is independently addressed by single spectra.

Segmental dynamics of polyethylene-alt-propylene studied by NMR spin echo techniques.

Segmental dynamics of a highly entangled melt of linear polyethylene-alt-propylene with a molecular weight of 200 kDa was studied with a novel proton nuclear magnetic resonance (NMR) approach based upon H → H isotope dilution as applied to a solid-echo build-up function I(t), which is constructed from the NMR spin echo signals arising from the Hahn echo (HE) and two variations of the solid-echo pulse sequence. The isotope dilution enables the separation of inter- and intramolecular contributions to this function and allows one to extract the segmental mean-squared displacements in the millisecond time range, which is hardly accessible by other experimental methods. The proposed technique in combination with time-temperature superposition yields information about segmental translation in polyethylene-alt-propylene over 6 decades in time from 10 s up to 1 s.

Self-diffusion studies by intra- and inter-molecular spin-lattice relaxometry using field-cycling: Liquids, plastic crystals, porous media, and polymer segments.

Field-cycling NMR relaxometry is a well-established technique for probing molecular dynamics in a frequency range from typically a few kHz up to several tens of MHz. For the interpretation of relaxometry data, it is quite often assumed that the spin-lattice relaxation process is of an intra-molecular nature so that rotational fluctuations dominate. However, dipolar interactions as the main type of couplings between protons and other dipolar species without quadrupole moments can imply appreciable inter-molecular contributions.

On the theory of the proton dipolar-correlation effect as a method for investigation of segmental displacement in polymer melts.

A thorough theoretical description of the recently suggested method [A. Lozovoi et al. J.

Communication: Proton NMR dipolar-correlation effect as a method for investigating segmental diffusion in polymer melts.

A simple and fast method for the investigation of segmental diffusion in high molar mass polymer melts is presented. The method is based on a special function, called proton dipolar-correlation build-up function, which is constructed from Hahn Echo signals measured at times t and t/2. The initial rise of this function contains additive contributions from both inter- and intramolecular magnetic dipole-dipole interactions.

On the theory of double quantum NMR in polymer systems: the second cumulant approximation for many spin I = 1/2 systems.

General analytical expressions for Double Quantum Nuclear Magnetic Resonance (DQ NMR) kinetic curves of many-spin I = 1∕2 systems are derived with an accuracy of the second cumulant approximation. The expressions obtained exactly describe the initial part of the kinetic curves and provide a reasonable approximation up to times of about the effective spin-relaxation time. For the case when the system contains two isolated spins, this result exactly reproduces known expressions.

On the theory of the proton free induction decay and Hahn echo in polymer systems: the role of intermolecular magnetic dipole-dipole interactions and the modified Anderson-Weiss approximation.

The influence of the intermolecular magnetic dipole-dipole interaction on the free induction decay (FID) as well as on the Hahn-echo of proton spins in polymer melts is investigated. It is shown that for isotropic models of polymer dynamics, when polymer segment displacements do not correlate with an initial chain conformation, the influence of the intermolecular magnetic dipole-dipole interactions to the FID and Hahn echo is increasing more rapidly with evolution time than the corresponding influence of the intramolecular magnetic dipole-dipole interactions. On the other hand, the situation is inverted for the tube-reptation model: here the influence of the intramolecular magnetic dipole-dipole interactions to the FID and Hahn echo is increasing faster with time than the contribution from intermolecular interactions.

Features of polymer chain dynamics as revealed by intermolecular nuclear magnetic dipole-dipole interaction: model calculations and field-cycling NMR relaxometry.

Proton NMR phenomena such as spin-lattice relaxation, free-induction decays, and solid echoes are analyzed with respect to contributions by intermolecular dipole-dipole interactions in polymer melts. The intermolecular dipole-dipole correlation function is calculated by taking into account the correlation hole effect characteristic for polymer melts. It is shown that the ratio between the intra- and intermolecular contributions to NMR measurands depends on the degree of isotropy of chain dynamics anticipated in different models.

Spin-lattice relaxation dispersion in polymers: dipolar-interaction components and short- and long-time limits.

The Mori-Zwanzig projection operator technique was employed to derive the effective Hamiltonian for spin-segment coupling. The fluctuations of this operator are responsible for spin-lattice relaxation in polymer chains. In detail, dipolar interaction of spins is rigorously analyzed by components representing fluctuations of the Kuhn segment end-to-end vectors and local fluctuations on a length scale shorter than the root mean square Kuhn segment length.

Deuteron and proton spin-lattice relaxation dispersion of polymer melts: intrasegment, intrachain, and interchain contributions.

Proton and deuteron field-cycling NMR relaxometry was applied to deuterated and undeuterated bulk polyethyleneoxide and polybutadiene melts and mixtures thereof with molecular weights above the critical value. Spin-lattice relaxation data due to intrasegment (quadrupolar) couplings and intra- and interchain (dipolar) interactions were evaluated. Diverse dynamic limits are identified both with the proton and deuteron frequency dispersion data.

Investigations of polymer dynamics in nanoporous media by field cycling NMR relaxometry and the dipolar correlation effect.

The chain dynamics of short-chain perfluoropolyether melts confined in Vycor nanoporous media has been characterized by field cycling nuclear magnetic resonance relaxometry and the dipolar correlation effect. The slowdown of motions under confinement, leading to larger residual dipolar couplings, has been probed by looking at the quotient of stimulated and primary echoes. Using field cycling relaxometry, it has been shown that there is strong evidence of reptation-like motion, even for such short-chain polymers as shown by the frequency and molecular weight dependences of the spin-lattice relaxation time.

Cooperative polymer dynamics under nanoscopic pore confinements probed by field-cycling NMR relaxometry.

Reptational dynamics of bulk polymer chains on a time scale between the Rouse mode relaxation time and the so-called disengagement time is not compatible with the basic thermodynamic law of fluctuations of the number of segments in a given volume. On the other hand, experimental field-cycling NMR relaxometry data of perfluoropolyether melts confined in Vycor, a porous silica glass of nominal pore dimension of 4 nm, closely display the predicted signatures for the molecular weight and frequency dependences of the spin-lattice relaxation time in this particular limit, namely T1 proportional M-1/2nu1/2. It is shown that this contradiction is an apparent one.

Molecular diffusion on a time scale between nano- and milliseconds probed by field-cycling NMR relaxometry of intermolecular dipolar interactions: application to polymer melts.

A formalism is presented permitting the evaluation of the relative mean-squared displacement of molecules from the intermolecular contribution to spin-lattice relaxation dispersion of dipolar coupled spins. The only condition for the applicability is the subdiffusive power law character of the time dependence of the mean-squared displacement as it is typical for the chain mode regime in polymer liquids. Using field-cycling NMR relaxometry, an effective diffusion time range from nano- to almost milliseconds can be probed.

Confinement effect of chain dynamics in micrometer thick layers of a polymer melt below the critical molecular weight.

Polymer melts confined in micrometer thick layers were examined with the aid of field-cycling NMR relaxometry. It is shown that chain dynamics under such moderate confinement conditions are perceptibly different from those observed in the bulk material. This is considered to be a consequence of the corset effect, which predicts a crossover between Rouse and reptationlike dynamics for molecular weights below the critical value at confinement length scales much larger than 10RF, where RF is the Flory radius of the bulk polymer coil [Fatkullin et al.

Field-gradient NMR diffusometry in poly(ethylene oxide) melts confined to nanoscopic pores of solid methacrylate matrices.

Depending on the choice of matrix constituents, the diameters of strands of linear, monodisperse poly(ethylene oxide) confined to nanoscopic pores of cross-linked methacrylate matrices can be varied considerably. The samples were characterized by DSC, TEM, SEM and fringe field-gradient NMR diffusometry with respect to the strand diameter. A formalism evaluating diffusive spin echo attenuation curves based on the tube/reptation model allows the determination of the strand diameter.

Polymer chain dynamics under nanoscopic confinements.

It is shown that the confinement of polymer melts in nanopores leads to chain dynamics dramatically different from bulk behavior. This so-called corset effect occurs both above and below the critical molecular mass and induces the dynamic features predicted for reptation. A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined to nanoscopic strands that are in turn embedded in a quasi-solid and impenetrable methacrylate matrix.

Polymer dynamics under nanoscopic constraints: the "corset effect" as revealed by NMR relaxometry and diffusometry.

A spinodal demixing technique was employed for the preparation of linear poly(ethylene oxide) (PEO) confined in nanoscopic strands, which in turn are embedded in a quasi-solid methacrylate matrix impenetrable to PEO. Both the molecular weight of the PEO and the mean diameter of the strands are variable to a certain degree. Chain dynamics of the PEO in the molten state were examined with the aid of field-gradient NMR diffusometry and field-cycling NMR relaxometry.

Segment diffusion and flip-flop spin diffusion in entangled polyethyleneoxide melts: A field-gradient NMR diffusometry study.

Chain dynamics in melts of entangled polyethyleneoxide melts has been investigated using fringe field nuclear magnetic resonance diffusometry. As already demonstrated in our previous work, intermolecular flip-flop spin diffusion strongly influences spin echo attenuation for long diffusion times and high molecular weights. The experimental data have been evaluated taking this phenomenon quantitatively into account.