Ion and polymer dynamics in polymer electrolytes PPO–LiClO4.II. H2 and Li7 NMR stimulated-echo experiments

Vanishing amplitude of backbone dynamics causes a true protein dynamical transition: 2H NMR studies on perdeuterated C-phycocyanin

Using a combination of H2 nuclear magnetic resonance (NMR) methods, we study internal rotational dynamics of the perdeuterated protein C-phycocyanin (CPC) in dry and hydrated states over broad temperature and dynamic ranges with high angular resolution. Separating H2 NMR signals from methyl deuterons, we show that basically all backbone deuterons exhibit highly restricted motion occurring on time scales faster than microseconds. The amplitude of this motion increases when a hydration shell exists, while it decreases upon cooling and vanishes near 175 K. We conclude that the vanishing of the highly restricted motion marks a dynamical transition, which is independent of the time window and of a fundamental importance. This conclusion is supported by results from experimental and computational studies of the proteins myoglobin and elastin. In particular, we argue based on findings in molecular dynamics simulations that the behavior of the highly restricted motion of proteins at the dynamical transition resembles that of a characteristic secondary relaxation of liquids at the glass transition, namely the nearly constant loss. Furthermore, H2 NMR studies on perdeuterated CPC reveal that, in addition to highly restricted motion, small fractions of backbone segments exhibit weakly restricted dynamics when temperature and hydration are sufficiently high.

Interpretation of 1H and 2H spin-lattice relaxation dispersions: insights from molecular dynamics simulations of polymer melts

We demonstrate that molecular dynamics simulations are a versatile tool to ascertain the interpretation of spin-lattice relaxation data. For (1)H, our simulation approach allows us to separate and to compare intra- and inter-molecular contributions to spin-lattice relaxation dispersions. Dealing with the important example of polymer melts, we show that the intramolecular parts of (1)H spectral densities and correlation functions are governed by rotational motion, while their inter-molecular counterparts provide access to translational motion, in particular, to mean-squared displacements and self-diffusion coefficients. Exploiting that the full microscopic information is available from molecular dynamics simulations, we determine the range of validity of experimental approaches, which often assume Gaussian dynamics, and we provide guidelines for the determination of free parameters required in experimental analyses. For (2)H, we examine the traditional methodology to extract correlation times of complex dynamics from relaxation data. Furthermore, based on knowledge from our computational study, it is shown that measurement of (2)H spin-lattice relaxation dispersions allows one to disentangle the intra- and inter-molecular contributions to the corresponding (1)H data in experimental work. Altogether, our simulation results yield a solid basis for future (1)H and (2)H spin-lattice relaxation analysis.

Signal intensities in ¹H-¹³C CP and INEPT MAS NMR of liquid crystals

Spectral editing with CP and INEPT in (13)C MAS NMR enables identification of rigid and mobile molecular segments in concentrated assemblies of surfactants, lipids, and/or proteins. In order to get stricter definitions of the terms "rigid" and "mobile", as well as resolving some ambiguities in the interpretation of CP and INEPT data, we have developed a theoretical model for calculating the CP and INEPT intensities as a function of rotational correlation time τc and C-H bond order parameter SCH, taking the effects of MAS into account. According to the model, the range of τc can at typical experimental settings (5kHz MAS, 1ms ramped CP at 80-100kHz B1 fields) be divided into four regimes: fast (τc<1ns), fast-intermediate (τc≈0.1μs), intermediate (τc≈1μs), and slow (τc>0.1ms). In the fast regime, the CP and INEPT intensities are independent of τc, but strongly dependent on |SCH|, with a cross-over from dominating INEPT to dominating CP at |SCH|>0.1. In the intermediate regime, neither CP nor INEPT yield signal on account of fast T1ρ and T2 relaxation. In both the fast-intermediate and slow regimes, there is exclusively CP signal. The theoretical predictions are tested by experiments on the glass-forming surfactant n-octyl-β-d-maltoside, for which τc can be varied continuously in the nano- to millisecond range by changing the temperature and the hydration level. The atomistic details of the surfactant dynamics are investigated with MD simulations. Based on the theoretical model, we propose a procedure for calculating CP and INEPT intensities directly from MD simulation trajectories. While MD shows that there is a continuous gradient of τc from the surfactant polar headgroup towards the methyl group at the end of the hydrocarbon chain, analysis of the experimental CP and INEPT data indicates that this gradient gets steeper with decreasing temperature and hydration level, eventually spanning four orders of magnitude at completely dry conditions.

2H NMR studies of glycerol dynamics in protein matrices

We use (2)H NMR spectroscopy to investigate the rotational motion of glycerol molecules in matrices provided by the connective tissue proteins elastin and collagen. Analyzing spin-lattice relaxation, line-shape properties, and stimulated-echo decays, we determine the rates and geometries of the motion as a function of temperature and composition. It is found that embedding glycerol in an elastin matrix leads to a mild slowdown of glycerol reorientation at low temperatures and glycerol concentrations, while the effect vanishes at ambient temperatures or high solvent content. Furthermore, it is observed that the nonexponential character of the rotational correlation functions is much more prominent in the elastin matrix than in the bulk liquid. Results from spin-lattice relaxation and line shape measurements indicate that, in the mixed systems, the strong nonexponentiality is in large part due to the existence of distributions of correlation times, which are broader on the long-time flank and, hence, more symmetric than in the neat system. Stimulated-echo analysis of slow glycerol dynamics reveals that, when elastin is added, the mechanism for the reorientation crosses over from small-angle jump dynamics to large-angle jump dynamics and the geometry of the motion changes from isotropic to anisotropic. The results are discussed against the background of present and previous findings for glycerol and water dynamics in various protein matrices and compared with observations for other dynamically highly asymmetric mixtures so as to ascertain in which way the viscous freezing of a fast component in the matrix of a slow component differs from the glassy slowdown in neat supercooled liquids.

Secondary water relaxation in a water/dimethyl sulfoxide mixture revealed by deuteron nuclear magnetic resonance and dielectric spectroscopy

We exploit the potential of a combined dielectric spectroscopy (DS) and deuteron nuclear magnetic resonance ((2)H NMR) approach to investigate the molecular dynamics in a supercooled 2:1 molar mixture of deuterated water (D(2)O) and dimethyl sulfoxide (DMSO). While DS probes the rotational motion of both components, application of (2)H NMR allows us to single out the dynamical behavior of the water molecules. Combining the results of both methods, we can follow the slowdown of the α-process of the mixture over more than 10 orders of magnitude in time, revealing that the Vogel-Fulcher-Tammann (VFT) equation describes well its temperature dependence down to the glass transition temperature, T(g) = 146 K. While the (2)H NMR data do not provide evidence for a secondary relaxation process in the weakly supercooled regime, they indicate that, in the deeply supercooled regime, T(g) ≤ T ≤ 160 K, the water molecules do show a secondary dynamical process, which is faster and exhibits a weaker temperature dependence than the α-process of the mixture. Consistently, the shape of the dielectric spectra changes in this temperature range. (2)H NMR rotational correlation functions reveal that this faster secondary water process destroys essentially all orientational correlation. In addition, these data show that the water reorientation process is characterized by a mean elementary jump angle smaller than 13°. Possible origins of the faster secondary water process in the deeply supercooled mixture are discussed.

Origins of apparent fragile-to-strong transitions of protein hydration waters

2H NMR is used to study the mechanisms for the reorientation of protein hydration water. In the past, crossovers in temperature-dependent correlation times were reported at Tx1 approximately 225 K (X1) and Tx2 approximately 200 K (X2). We show that neither X1 nor X2 are related to a fragile-to-strong transition. Our results rule out an existence of X1. Also, they indicate that water performs thermally activated and distorted tetrahedral jumps at T < Tx2, implying that X2 originates in an onset of this motion, which may be related to a universal defect diffusion in materials with defined hydrogen-bond networks.

Nonexponential polymer segmental motion in the presence and absence of ions: H2 NMR multitime correlation functions for polymer electrolytes poly(propylene glycol)-LiClO4

The authors measure 2H NMR multitime correlation functions to investigate the segmental motion of poly(propylene glycol) containing various amounts of the salt LiClO4. 2H NMR two-time correlation functions indicate that addition of salt affects not only the time scale of the segmental motion, but also the degree of the nonexponential relaxation behavior. To quantify the origin of the nonexponential segmental motion, the authors analyze 2H NMR three-time correlation functions. In general, nonexponential relaxation can result from homogeneous dynamics, i.e., intrinsic nonexponentiality, and from heterogeneous dynamics, i.e., existence of a distribution of correlation times G(ln tau). For the studied high and low salt concentrations, including neat poly(propylene glycol), the analysis shows that both homogeneous and heterogeneous contributions are important. 2H NMR four-time correlation functions allow the authors to measure the lifetime of the dynamical heterogeneities. For the studied salt concentrations, the rate exchange occurs on the same time scale as the segmental motion, indicating short-lived dynamical heterogeneities. To arrive at these results, the authors reconsider the interpretation of (2)H NMR three-time correlation functions. Results of analytical calculations and computer simulations show that it is necessary to extend the previous way of analysis so as to include effects due to correlated back-and-forth jumps.