Measurement of NMR cross-polarization (CP) rate constants in the slow CP regime: relevance to structure determinations of zeolite-sorbate and other complexes by cp magic-angle spinning NMR

When analyzing I --> S variable contact time cross-polarization (CP) curves, the spin dynamics are usually assumed to be describable in the "fast CP regime" in which the growth of the S spin magnetization is governed by the rate of cross polarization while its decay is governed by the rate of I spin T1rho relaxation. However, in the investigation of the structures of zeolite-sorbate and other complexes by polarization transfer this will not necessarily be the case. We discuss the measurement of I --> S CP rate constants under the "slow CP regime" in which the rate of T1rho relaxation is fast compared to the rate of cross polarization, leading to a reversal of the usual assumptions such that the rate or growth is governed by the rate of I spin T1rho relaxation while the decay is governed by the rate of cross polarization (and the S spin T1rho relaxation). It is very important to recognize when a system is in the slow CP regime, as an analysis assuming the normal fast CP will lead to erroneous data. However, even when the slow CP regime is recognized, it is difficult to obtain absolute values for the CP rate constants from fits to standard CP curves, since the CP rate constant is correlated to the scaling factor, the contribution from 29Si T1rho relaxation is ignored, and it is difficult to obtain reliable data at very long contact times. The use of a 29Si{1H} CP "drain" or "depolarization" experiment, which measures absolute values of the CP rate constants, is therefore proposed as being most appropriate for theses situations. To illustrate the importance of these observations, measurements of the 1H-29Si CP rate constants in the p-dichlorobenzene/ZSM-5 sorbate-zeolite complex by 29Si{1H} CP and CP drain magic-angle spinning (MAS) NMR experiments are presented and compared and used to determine the location of the guest sorbate molecules in the cavities of the host zeolite framework.     

Pulsed field gradient NMR study of phenol binding and exchange in dispersions of hollow polyelectrolyte capsules

The distribution and exchange dynamics of phenol molecules in colloidal dispersions of submicron hollow polymeric capsules is investigated by pulsed field gradient NMR (PFG-NMR). The capsules are prepared by layer-by-layer assembly of polyelectrolyte multilayers on silica particles, followed by dissolution of the silica core. In capsule dispersion, (1)H PFG echo decays of phenol are single exponentials, implying fast exchange of phenol between a free site and a capsule-bound site. However, apparent diffusion coefficients extracted from the echo decays depend on the diffusion time, which is typically not the case for the fast exchange limit. We attribute this to a particular regime, where apparent diffusion coefficients are observed, which arise from the signal of free phenol only but are influenced by exchange with molecules bound to the capsule, which exhibit a very fast spin relaxation. Indeed, relaxation rates of phenol are strongly enhanced in the presence of capsules, indicating binding to the capsule wall rather than encapsulation in the interior. We present a quantitative analysis in terms of a combined diffusion-relaxation model, where exchange times can be determined from diffusion and spin relaxation experiments even in this particular regime, where the bound site acts as a relaxation sink. The result of the analysis yields exchange times between free phenol and phenol bound to the capsule wall, which are on the order of 30 ms and thus slower than the diffusion controlled limit. From bound and free fractions an adsorption isotherm of phenol to the capsule wall is extracted. The binding mechanism and the exchange mechanism are discussed. The introduction of the global analysis of diffusion as well as relaxation echo decays presented here is of large relevance for adsorption dynamics in colloidal systems or other systems, where the standard diffusion echo decay analysis is complicated by rapidly relaxing boundary conditions.     

Practical route to relative diffusion coefficients and electronic relaxation rates of paramagnetic metal complexes in solution by model-independent outer-sphere NMRD. Potentiality for MRI contrast agents

The relaxation of electronic spins S of paramagnetic species is studied by the field-dependence of the longitudinal, transverse, and longitudinal in the rotating frame relaxation rates R1, R2, and R1rho of nuclear spins I carried by dissolved probe solutes. The method rests on the model-independent low-frequency dispersions of the outer-sphere (OS) paramagnetic relaxation enhancement (PRE) of these rates due to the three-dimensional relative diffusion of the complex with respect to the probe solute. We propose simple analytical formulas to calculate these enhancements in terms of the relative diffusion coefficient D, the longitudinal electronic relaxation time T1e, and the time integral of the time correlation function of the I-S dipolar magnetic interaction. In the domain of vanishing magnetic field, these parameters can be derived from the low-frequency dispersion of R1 thanks to sensitivity improvements of fast field-cycling nuclear relaxometers. At medium field, we present various approaches to obtain these parameters by combining the rates R1, R2, and R1rho. The method is illustrated by a careful study of the proton PREs of deuterated water HOD, methanol CH3OD, and tert-butyl alcohol (CH3)3COD in heavy water in the presence of a recently reported nonacoordinate Gd(III) complex. The exceptionally slow electronic relaxation of the Gd(III) spin in this complex is confirmed and used to test the accuracy of the method through the self-consistency of the low- and medium-field results. The study of molecular diffusion at a few nanometer scale and of the electronic spin relaxation of other complexed metal ions is discussed.     

Thermodynamic scaling of diffusion in supercooled Lennard-Jones liquids

The manner in which the intermolecular potential u(r) governs structural relaxation in liquids is a long standing problem in condensed matter physics. Herein, we show, in agreement with recent experimental results, that diffusion coefficients for simulated Lennard-Jones m-6 liquids (8 < or = m < or = 36) in normal and moderately supercooled states are a unique function of the variable rhogamma/T, where rho is density and T is temperature. The scaling exponent gamma is a material specific constant whose magnitude is related to the steepness of the repulsive part of u(r), evaluated around the distance of closest approach between particles probed in the supercooled regime. Approximations of u(r) in terms of inverse power laws are also discussed.     

Direct calculation of (1)H(2)O T(1) NMRD profiles and EPR lineshapes for the electron spin quantum numbers S = 1, 3/2, 2, 5/2, 3, 7/2, based on the stochastic Liouville equation combined with Brownian dynamics simulation

Direct calculation of electron spin relaxation and EPR lineshapes, based on Brownian dynamics simulation techniques and the stochastic Liouville equation approach (SLE-L) [Mol. Phys., 2004, 102, 1085-1093], is here generalized to high spin systems with spin quantum number S = 3/2, 2, 5/2, 3 and 7/2. A direct calculation method is demonstrated for electron spin-spin and spin-lattice relaxation, S-, X- and Q-band EPR-lineshapes and paramagnetic enhanced water proton T(1)- NMRD profiles. The main relaxation mechanism for the electron spin system is a stochastic second rank zero field splitting (ZFS). Brownian dynamics simulation techniques are used in describing a fluctuating ZFS interaction which comprises two parts namely the "permanent" part which is modulated by isotropic reorientation diffusion, and the transient part which is modulated by fast local distortion, which is also modelled by the isotropic rotation diffusion model. The SLE-L approach present is applicable both in the perturbation (Redfield) regime as well as outside the perturbation regime, in the so called slow motion regime.     

Two-stage model for molecular orientational relaxation in liquid crystals

The molecular reorientation in anisotropic fluids is considered as twostage process—fast single molecule rotation in the volume restricted by close neighbours and slow collective relaxation of the local surrounding. The theoretical results are applied to explain the discrepancy between the rotational diffusion coefficients D_⊥^r obtained by infrared bandshape analysis and polarized fluorescence techniques.     

Determination of Proton Diffusion Coefficient in Spherical Nickel Hydroxide Using Potential Step Measurement on Single Beads

The Potential step measurements are carried out on single beads of nickel hydroxide and the results are interpreted with a dual structure model featuring fast and slow diffusing components The intrinsic diffusion coefficients for the two components are found to be in the order of magnitude 10^-7 and 10^-13-10^-14 cm^2s^-1, respectively, with an apparent value for the slow component in the order of 10^-10 cm^2s^-1.     

Particulate hematite diffusion in sodium polyacrylate solutions. The effect of ionic strength

The diffusion coefficients of hematite particles in polyelectrolyte solution have been investigated using dynamic light scattering. Two apparent diffusion coefficients, a fast and a slow diffusional mode, are observed for the hematite particles in high-molecular-weight sodium polyacrylate solution at pH 10.5. The slow diffusion coefficient (Dslow) shows a decrease with increase in polyelectrolyte concentration. The fast diffusion coefficient (Dfast) shows an increase to a maximum with increasing polyelectrolyte concentration and then a rapid decrease as the polyelectrolyte concentration increases further. With an increase in ionic strength from 10(-4) to 0.1 M NaNO3, the maximum value of Dfast increased in magnitude, while the polyacrylate concentration at which the maximum occurs is seen to increase. The dependence of Dfast on the measurement angle indicates that it is coupled to the fluctuations of the chains. The observed behavior is attributed to the hematite probe particle sensing both macroscopic (viscous) and elastic fluctuations associated with the polyelectrolyte motion.     

Relaxation phenomena in dense,glassy membranes prepared from a polymer solution,monitored by changes in dielectric properties

The drying of a solvent-cast polymer film is monitored in a non-invasive way, by measuring the changes in time of dielectric properties, using interdigitated or comb electrodes. Experimentally, the vitrification of the polymer solution is observed at a distinct time, followed by the slow evaporation of solvent from the glassy state. As the solvent diffusion coefficient is a strong function of the concentration in the polymer film, removal of residual solvent proceeds at a self-decreasing rate. With a simple model, solvent mass transfer coefficients in the glassy state are determined from the experiments. It is shown that volume relaxation may be slow compared to the drying process, when preparing thin solvent-cast membranes and using solvents that diffuse relatively fast through the glassy polymer film.     

Hydrogen NMR of H2-TDF-D2O clathrate

The three-component clathrate H2-TDF-D2O offers hydrogen storage at lower pressure, but with reduced weight fraction of H2, compared to H2-H2O clathrate. In H2-TDF-D2O, H2 resides exclusively and singly in the small cages of structure II, allowing the rotational behavior of H2 in this nominally uniform environment to be probed. Here we report NMR measurements of the H2 line shape and relaxation times T1, T2, and T1rho. The principal differences in the results, compared to the H2-D2O binary system, are the dips in T2 and T1rho near 28 K due to thermally activated reorientation of TDF molecules, line-narrowing and decreases in T2 and T1rho near 175 K due to D2O reorientations and diffusion, and the apparent absence of H2 diffusion between small cages.     

Diffusivity of gases and main-chain cooperative motions in plasticized poly(vinyl chloride)

Permeability and time-lag measurements for H₂ and CO in poly(vinyl chloride) (PVC) plasticized with tricresyl phosphate show that the apparent diffusion coefficients at first decrease as the plas-ticizer concentration is increased. The diffusion coefficients then increase as the additive concentration is raised above 15 wt %. These changes in the apparent diffusion coefficients can be related to the behavior of a variety of mechanical properties and are attributed to antiplasticization and plasticization effects of low and high concentrations of tricresyl phosphate, respectively. The antiplasticization-plasticization effects reflect altered molecular motions of the polymer. Carbon-13 NMR rotating-frame relaxation rate measurements show directly that the cooperative main-chain molecular motions of PVC are reduced when the additive acts as an antiplasticizer and are increased when the polymer is plasticized. Both the apparent diffusion coefficient and the rotating-frame relaxation rate have a similar dependence on additive concentration. An application of the molecular theory of diffusion of Pace and Datyner accounts qualitatively for the way in which additives alter the average chain interaction energy, cooperative polymer main-chain motions, and the diffusion coefficients of gaseous penetrants.     

Two-stage model for molecular orientational relaxation in liquid crystals

Abstract

The molecular reorientation in anisotropic fluids is considered as twostage process—fast single molecule rotation in the volume restricted by close neighbours and slow collective relaxation of the local surrounding. The theoretical results are applied to explain the discrepancy between the rotational diffusion coefficients D_⊥ ^r obtained by infrared bandshape analysis and polarized fluorescence techniques.     

The “fast” and “slow” mode theories of interdiffusion in polymer mixtures: Resolution of a controversy

The theory of interdiffusion of a pair of components in multicomponent polymer mixtures is reviewed from a statistical point of view, and the foundation of the “fast” and “slow” mode theories, as well as the more recent “ANK” theory of interdiffusion is critically examined. The ANK theory reproduces the results of the slow and fast mode theories as the two limits when the vacancy concentration is varied from zero to a large value, and shows that the interdiffusion coefficient in a binary compressible mixture at finite vacancy concentrations can not in general be expressed only in terms of the tracer diffusion coefficients of the components, but it involves in addition the cooperative diffusion coefficient which characterizes the relaxation of total density fluctuations. The predictions of the ANK expression for the molecular dependence of the kinetic factor is compared with recent scattering experiments.     

Salt effect on microstructures in cationic gemini surfactant solutions as studied by dynamic light scattering

A cationic gemini surfactant, dodecanediyl-1,12-bis(dodecyldiethylammonium bromide) (C12C12C12(Et)), in aqueous solutions with varying NaBr concentration was studied by dynamic light scattering (DLS). As a comparison, its single-chained counterpart, dodecyl triethylammonium bromide (DTEAB), was also investigated under the same conditions. Similar to the case of a polyelectrolyte, C12C12C12(Et) underwent a typical "ordinary-to-extraordinary (o-e) transition" with decreasing salt concentration to zero. At higher salt concentration, a single relaxation mode, corresponding to the diffusion of regular micelles, was observed. While in the "extraordinary regime", DLS detected two characteristic relaxation modes with the values of the diffusion coefficient being different by at least 2 orders. The fast mode was consistent with the polyion-small ion coupled-mode theories, as well as the direct polyion-polyion repulsion interactions. Because the slow mode disappeared at elevated salt concentrations and generated negligible scattered intensity, we attributed it to multimacroion domains.     

Low‐bandwidth space/frequency component separation for quantitative imaging

Quantitative MRI is often used to analyse multicomponent systems. The analysis requires the contributions from different species to be isolated. Species with distinct chemical shifts can be separated by using a low acquisition bandwidth, which is easy to achieve in common quantitative imaging protocols. The bandwidth reduction leads to separation of NMR contributions from different species in the image space. This new method was implemented and tested on two multicomponent systems containing several spectrally and spatially unresolved components with both distinctly different and similar diffusion coefficients and relaxation times. Separation was achieved with routine MRI diffusion and relaxation measurement pulse sequences in a microimaging environment for water/polyethylene glycol solution and for chloroform/TMS/polyethylene glycol solution. Conventional monoexponential fitting was used to determine diffusion coefficients and relaxation times from the spectrally separated data, whereas biexponential or triexponential fitting was required in the unseparated reference experiments. In the two‐component sample, the variation in the determined fast diffusing components was on the same order of magnitude for all experiments, while the variation in the slow diffusing polyethylene glycol was larger when no separation was present. The separation technique provided lower variability for all the determined diffusion coefficients and relaxation times in the three‐component sample. The low‐bandwidth separation method can provide separation of multicomponent systems based on the chemical shift difference between the species. The accuracy of the technique is comparable with the commonly used methods for bicomponent system analysis and surpasses those when there are more than two components in the sample. Copyright © 2016 John Wiley & Sons, Ltd.     

Review of polystyrene diffusion studies in latex particles by small‐angle neutron scattering

This paper reviews small‐angle neutron scattering (SANS) and some results from direct nonradiative energy transfer (DET), for the observation of the diffusion coefficients of polystyrene chains at latex interfaces. To compare SANS with DET, doubly labeled polystyrene with deuterium and fluorescence groups were synthesized, showing that while SANS and DET produce comparable data in terms of diffusion coefficients, both results differ in detail, each having their own advantages. Chain confinement, ionic end groups, and short branch effects on interdiffusion were studied. Large polymer chains confined in small particles have non‐Gaussian shapes that store rubber elastic energy. Rapid, non‐diffusion relaxation is inhibited because the density would be required to become less than normal. Hence confinement effects on the diffusion rate are not significant. Using the DET method, ionic end‐groups were found to increase the early‐time apparent interdiffusion coefficients during film formation. The early‐time apparent diffusion coefficients of polystyrene with varying end‐groups were found to increase as follows: The higher apparent diffusion coefficients of the chains with ionic groups are presumably due to a surface segregation of the end‐groups caused by the polar, aqueous environment during latex synthesis. The interdiffusion behavior of sulfite‐ended polystyrene (M_n ? 300 000 g/mol) with H‐ends, one sulfite end, and two sulfite ends were compared via SANS and DET. The diffusion coefficients of polystyrene with one or two sulfite end groups were five times and ten times lower than that of polystyrene, respectively. The ionic end group effects on the reduced diffusion coefficients are interpreted as the competition between enhancement by the surface segregation of end groups and reduction by end group aggregation. Noting that sulfate end groups diffused faster, while sulfite end groups diffused slower, the effect is complex, and not yet fully resolved. Diffusion coefficients of polystyrene with branches were studied by DET. Short branches work to decrease the T_g and hence increase the diffusion coefficients. However, after the experimental temperature, T, is converted to a normalized temperature, T‐T_g, the diffusion coefficients are found to be almost independent upon the number of branches and the length of branches. The branch length ranged from one‐carbon to 40 carbons. Side chains of entanglement molecular weight or longer may be required to significantly reduce the diffusion coefficient. Copyright © 2002 John Wiley & Sons, Ltd.     

Dynamics of end-grafted polystyrene brushes in theta solvents

The dynamics of the concentration fluctuations in end-grafted polystyrene brushes in a theta solvent (cyclohexane) are probed by evanescent wave dynamic light scattering at different wavevectors q and temperatures. When the solvent quality changes from marginal to poor, the relaxation function C(q, t) exhibits strong effects as compared with the smooth variation of the brush density profile. From a single exponential above 50 °C, C(q, t) becomes a two-step decay function. The fast decay is still assigned to the cooperative diffusion albeit slower than in the good solvent regime whereas the slow nonexponential and nondiffusive process might relate to microsegragated and/or chain dynamics in the present polydisperse brush. The relaxation function of the present three brushes with different grafting density reveals similarities and disparities between wet brushes and semidilute polymer solutions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3590–3597, 2006     

RECOVERY OF AMORPHOUS POLY(ETHYLENE TEREPHTHALATE)FILM UNIAXIALLY DRAWN JUST BELOW THE GLASS TRANSITION TEMPERATURE*

Isothermal recovery in the macroscopic length of homogeneously deformed specimens of amorphous poly(ethyleneterephthalate) (PET) film sample uniaxially drawn at 69℃ to the draw ratios λ_0=1.26～2.20 were studied at temperaturesaround the glass transition temperature (T_g = 73℃). Experimental results indicate that the length recovery took place in twodistinct steps: a fast first step (fast relaxation) followed by a slow second step (slow relaxation). The relaxation processeswere accompanied by the reversion of trans-conformers (1340 cm~(-1)) to gauche, and the dichroic function of the 1340 cm~(-1)band characterizing the segmental orientation along the chain direction decreased to a very low value at the end of the fastrelaxation. This fact led us to assign the fast relaxation as the segmental orientation while the slow relaxation as relaxation ofthe global chain orientation. It was found that the slow relaxation follows a single exponential function, with relaxation timesstrongly dependent on the temperature resembling the glass transition process. The fast relaxation does not follow a singleexponential decay, presumably a distribution of relaxation times is involved.     

Dynamics and thermodynamics of water in PAMAM dendrimers at subnanosecond time scales

Atomistic molecular dynamics simulations are used to study generation 5 polyamidoamine (PAMAM) dendrimers immersed in a bath of water. We interpret the results in terms of three classes of water: buried water well inside of the dendrimer surface, surface water associated with the dendrimer-water interface, and bulk water well outside of the dendrimer. We studied the dynamic and thermodynamic properties of the water at three pH values: high pH with none of the primary or tertiary amines protonated, intermediate pH with only the primary amines protonated, and low pH with all amines protonated. For all pH values we find that both buried and surface water exhibit two relaxation times: a fast relaxation ( approximately 1 ps) corresponding to the libration motion of the water and a slow ( approximately 20 ps) diffusional component related to the escaping of water from one domain to another. In contrast for bulk water the fast relaxation is approximately 0.4 ps while the slow relaxation is approximately 14 ps. These results are similar to those found in biological systems, where the fast relaxation is found to be approximately 1 ps while the slow relaxation ranges from 20 to 1000 ps. We used the 2PT MD method to extract the vibrational (power) spectrum and found substantial differences for the three classes of water. The translational diffusion coefficient for buried water is 11-33% (depending on pH) of the bulk value while the surface water is about 80%. The change in rotational diffusion is quite similar: 21-45% of the bulk value for buried water and 80% for surface water. This shows that translational and rotational dynamics of water are affected by the PAMAM-water interactions as well as due to the confinement in the interior of the dendrimer. We find that the reduction of translational or rotational diffusion is accompanied by a blue shift of the corresponding libration motions ( approximately 10 cm(-1) for translation, approximately 35 cm(-1) for rotation), indicating higher local force constants for these motions. These effects are most pronounced for the lowest pH, probably because of the increased rigidity caused by the internal charges. From the vibrational density of states we also calculate the enthalpies and entropies of the various waters. We find that water molecules are enthalpically favored near the PAMAM dendrimer: energy for surface water is approximately 0.1 kcal/mol lower to that in the bulk, and approximately 0.5-0.9 kcal/mol lower for buried water. In contrast, we find that both the buried and surface water are entropically unfavored: buried water is 0.9-2.2 kcal/mol lower than the bulk while the surface water is 0.1-0.2 kcal/mol lower. The net result is a thermodynamically unfavored state of the water surrounding the PAMAM dendrimer: 0.4-1.3 kcal/mol higher for buried water and 0.1-0.2 kcal/mol for surface water. This excess free energy of the surface and buried waters is released when the PAMAM dendrimer binds to DNA or metal ions, providing an extra driving force.     

Diffusivities of tris(2,2'-bipyridyl)ruthenium inside silica-nanochannels modified with alkylsilanes.

The apparent diffusion coefficients of tris(2,2'-bipyridyl)ruthenium ([Ru(bpy(3))](2+)) are estimated in silica-nanochannels which are assembled inside columnar alumina pores in an anodic alumina membrane, and are modified with alkylsilanes such as trimethylchlorosilane (C1), butyldimethylchlorosilane (C4), and dodecyldimethylchlorosilane (C12). The estimation is performed by observing the lag-time, which is defined as the time required for [Ru(bpy)(3)](2+) to diffuse through alkylsilane-modified silica-nanochannels in the alumina membrane. When ethanol is used as a solvent, the apparent diffusion coefficients of [Ru(bpy)(3)](2+) are estimated as 2.1 x 10(-10) and 3.2 x 10(-10) cm(2) s(-1) in the C1- and C4-modified silica-nanochannels, respectively. These values are about 10(4) times smaller than that obtained in bulk ethanol. Based on the experimental results on the solvent dependency of the lag-time, the hydrogen-bonding interaction between ethanol molecules is considered to be stronger in the C1- and C4-modified silica-nanochannels than in bulk ethanol, and the hydrogen-bonding interaction plays a critical role for the slow diffusivity in those nanochannels. In contrast, the apparent diffusion coefficient in the C12-modified silica-nanochannel is at least two orders of magnitude larger than those in the C1- and C4-modified silica-nanochannels. This relatively fast diffusion is most likely explained by the presence of a long alkyl chain of C12, which reduces a hindrance effect that is originates in the hydrogen-bonding interaction.