Pseudo-Restricted Self-Diffusion of Molecules in Biporous Structures: Study by Pulsed Field Gradient NMR

The mobility of liquid (n-decane) that fills the system of primary and secondary pores of a biporous sample (granular Vycor porous glass) is studied by the pulsed field gradient NMR technique. The anomalous time dependence of the slow component of diffusion decay is revealed: the self-diffusion coefficient decreases with an increase in diffusion time t_d and, at large t_d values, this dependence satisfies the feature of completely restricted self-diffusion. It is established that this component is related to the mobility of liquid molecules filling the system of primary pores. By use of computer simulation, it is shown that the effect of “pseudo-restricted” diffusion is explained by the exchange processes between the phases, where the molecules of the liquid that are present in the systems of primary and secondary pores and differ in self-diffusion coefficients are understood as the phases. The effect of interfacial exchange is confirmed by the time dependence of the fraction of molecules with the lowest self-diffusion coefficients. The revealed phenomenon of “pseudo-restricted” diffusion is not related to real spatial constraints and can be observed in any systems with two (or more) phases with different self-diffusion coefficients, provided that these “phases” are bulky and can be subjected to molecular exchange.     

Fluid self-diffusion in Scots pine sapwood tracheid cells

The self-diffusion coefficients of water and toluene in Scots pine sapwood was measured using low field pulsed field gradient nuclear magnetic resonance (PFG-NMR). Wood chips of 8 mm diameter were saturated with the respective liquids, and liquid self-diffusion was then traced in one dimension orthogonal to the tracheid cell walls in the wood's radial direction. The experimental echo attenuation curves were exponential, and characteristic self-diffusion coefficients were produced for diffusion times spanning from very short times to times on the order of magnitude of seconds. Observed self-diffusion coefficients were decaying asymptotically as a function of diffusion time, an effect which was ascribed to the cell walls' restriction on confined liquid diffusion. The observed self-diffusion behavior in Scots pine sapwood was compared to self-diffusion coefficients obtained from simulations of diffusion in a square. Principles of molecular displacements in confined geometries were used for elucidating the wood's cellular structure from the observed diffusion coefficients. The results were compared with a mathematical model for diffusion between parallel planes.     

Mobility of molecules of liquid diols in the temperature range of 303–318 K

The self-diffusion coefficients of diols (ethylene glycol (EG), 1,2- and 1,3-propanediols (PD), and 1,4-butanediol (BD)) are measured using the spin echo approach on protons in the temperature range of 303–318 K. The activation energies of self-diffusion are calculated and compared to the activation energies for viscous flow and dipole relaxation in these systems. A conclusion is reached as to the correlation of rotational and translational movements in liquid diols, due to the presence of a spatial network of hydrogen bonds in these solvents.     

Diffusions of β-cyclodextrins in mucus studied by <Superscript>19</Superscript>F diffusion NMR

β-Cyclodextrin (β-CD) based materials have been widely used as drug carriers for pharmaceutical applications. To understand the diffusion of β-CDs in mucus is important for selecting β-CD based drug carriers for applications targeting mucosal absorption because the surfaces of many biological membranes are covered with a highly viscous aqueous mucus layer which forms relatively effective diffusion barriers for drugs. In this study, ¹⁹F self-diffusion NMR technique has been applied to study the self-diffusions of β-CDs in mucus. The ¹⁹F NMR signals arose from 1-fluoroadamantane molecules entrapped in the cavities of β-CDs. The diffusive abilities of different β-CDs in mucus were assessed through analyzing the diffusion coefficients using the presented kinetic model, and Ogston’s and Renkin’s diffusion models for hydrogel systems. The kinetic results show that 2-hydroxypropyl-β-CD and 2-Carboxyethyl-β-CD have the smallest binding affinities to bovine submaxillary mucin and human nasal mucin among five tested β-CDs. The mesh sizes of the bovine submaxillary mucus at different concentrations and that of the human nasal mucus were evaluated using the diffusion models. We hope that this ¹⁹F diffusion method will be useful to study the diffusion of β-CD based materials in other biological systems.     

Further comments on the relation between hydraulic permeation and diffusion

We feel that the lengthy comments given here come down to a few simple points. For uniform, homogeneous swollen membranes the internal driving force for transport in hydraulic permeation experiments is a concentration gradient not a pressure gradient. Equation (1) is in error because it neglects the frame of reference term 1/(1 ? ν₁). Equation (19) shows properly the connection between K₀ and the various diffusion coefficients. In the particular case discussed here and previously we see no evidence to say that a viscous flow mechanism is operative since we can explain all of the K₀ data in terms of reasonable diffusion coefficients if proper consideration is given to the frame of reference correction. This is not to say that in many other cases a viscous flow mechanism will not be present or even predominate.     

Diffusion of methane and carbon dioxide in carbon molecular sieve membranes by multinuclear pulsed field gradient NMR

Carbon molecular sieve (CMS) membranes are promising materials for energy efficient separations of light gases. In this work, we report a detailed microscopic study of carbon dioxide and methane self-diffusion in three CMS membrane derived from 6FDA/BPDA(1:1)-DAM and Matrimid polymers. In addition to diffusion of one-component sorbates, diffusion of a carbon dioxide/methane mixture was investigated. Self-diffusion studies were performed by the multinuclear (i.e., (1)H and (13)C) pulsed field gradient (PFG) NMR technique which combines the advantages of high field (17.6 T) NMR and high magnetic field gradients (up to 30 T/m). Diffusion measurements were carried out at different temperatures and for a broad range of the root-mean-square displacements of gas molecules inside the membranes. The diffusion data obtained from PFG NMR are compared with the corresponding results of membrane permeation measurements reported previously for the same membrane types. The observed differences between the transport diffusivities and self-diffusion coefficients of carbon dioxide and methane are discussed.     

Computer modelling of adsorbate transport in nanospaces

The passage of adsorbed molecules, through pores of nanometre dimensions, under a concentration gradient, is important in several processes. The basic equations for single-component flow in pores identify a diffusive and cooperative (viscous) component to the flux. Three simulation techniques, including non-equilibrium molecular dynamics (NEMD), have been used to investigate (spherical) methane and ethane adsorbates in model graphite pores at ambient temperatures. The NEMD method measures flux directly and shows an interesting behaviour in the total diffusion coefficients, including transitions and values substantially in excess of the Darken diffusion coefficient, calculated from self-diffusion. A simple Stokes–Einstein type of model can account for some results. The instances where this model fails can be rationalised in terms of confinement effects, and the relative contribution of kinetic energy to the Hamiltonian.     

分子动力学模拟苯和萘在超临界二氧化碳中的无限稀释扩散系数

采用球型模型和点位-点位模型对超临界二氧化碳的自扩散系数及苯或萘在超临界二氧化碳中的无限稀释扩散系数进行了分子动力学模拟。结果表明,球型模型及点位-点位模型均可较准确地预测二氧化碳的自扩散系数,球型模型因形式简单,准确度相对较差;点位-点位模型准确度虽高,但需较长的模拟机时。两种位能模型所获得的准确度相当,但点位-点位模型可以更精细地反映体系的微观结构。     

Structure,thermodynamics and diffusion in asymmetric binary mixtures: a molecular dynamics simulation study

Structural and thermodynamic properties as well as diffusion coefficients of binary fluid mixtures with asymmetry in mass, size, charge and their combinations have been studied using classical molecular dynamics simulations. The fluid mixture is modelled as spherical particles interacting via the Weeks–Chandler–Andersen and Coulomb potential. The diameter, charge and mass of the fluid particles are in the range 6–60 Å, 1–10e and 1—500 amu, respectively. Systematic variations in pair-correlation functions, thermodynamic properties as well as the self-diffusion coefficient are found with the size, charge and mass ratio of the particles. The self-diffusion coefficient for systems having more than one type of asymmetry is calculated and expressed in terms of diffusion coefficients of systems with only one type of asymmetry.     

Room temperature ionic liquids containing low water concentrations-a molecular dynamics study

We have performed classical molecular dynamics to study the properties of a water-miscible and a water-immiscible room-temperature ionic liquid when mixed with small quantities of water. The two ionic liquids consist of the same 1-ethyl-3-methylimidazolium ([EMIM]) cation combined with either the boron tetrafluoride ([BF(4)]) or bis(trifluoromethylsulfonyl)imide ([NTf(2)]) anion. It is found that, in both ionic liquids, water clusters of varying sizes are typically hydrogen bonded to two anions with the cation playing a minor role. We also highlight the difficulties of obtaining dynamic quantities such as self-diffusion coefficients from simulations of such viscous systems.     

Tracer and self-diffusion of rosebengal sodium131I in 1% agar gel medium

Tracer and self-diffusion coefficients for Rosebengal labelled with¹³¹I are determined in agar gel medium at different temperatures and the activation energies for the two processes are determined by zone diffusion technique. The slight difference in tracer and self-diffusion values observed is small enough to be consistent with Hertz's recent theory of linear response of tracer diffusion coefficients in electrolyte and non-electrolyte systems.     

Diffusion des additifs du polyethylene—I: Influence de la nature du diffusant

Chemical efficiency and stabilizer migration are the most important factors to be considered in connection with the ageing of polyethylene. This paper gives diffusion coefficients and solubilities for various industrial additives in low density polyethylene. The results, together with activation energies for diffusion, allow study of the diffusion process. It seems that it is necessary to consider deformations of the diffusing molecules and the polymer molecules. Additives of low molecular weight diffuse as gases, those of high molecular weight behave like polymer chains in self-diffusion.     

Molecular dynamics simulation of self- and mutual diffusion coefficients for confined mixtures

The self- and mutual diffusion coefficients for binary mixtures of Ar-Kr both in the bulk and in the nanopores were studied by molecular dynamics simulations. The composition dependences and the relationships between the self- and the mutual diffusion coefficients both in the bulk and in the nanopores were further discussed. It was found that the simulation results (D(c.m.)) are close to the calculated ones (D(s)) for the Ar-Kr system. Both self- and mutual diffusion coefficients in nanopores are much lower than that of the bulk, and they ever decrease as the pore width decreases. Nevertheless, the self- and mutual diffusion coefficients increase as the mole fraction of Ar increases, and as expected, increase as the temperature increases. The self-diffusion coefficients of mixtures both in the bulk and in the nanopores are predicted by the Carman model and by the molecular cluster model.     

用脉冲梯度场核磁共振技术研究乙醇-水混合液在壳聚糖渗透汽化膜中的自扩散过程

用脉冲梯度场核磁共振技术(PFG—NMR)研究了水、乙醇和乙醇一水混合液在硫酸交联的壳聚糖渗透汽化膜和未交联的壳聚糖渗透汽化膜中的自扩散过程,得到了乙醇和水的溶解度和自扩散系数,阐述了水和乙醇透过壳聚糖膜的机理;实验结果表明：水和乙醇是分别由两种不同类型的扩散通道透过膜的;水是由亲水性的离子化通道扩散透过膜,而乙醇是由亲油性的高分子无定形区扩散透过膜;PFG—NMR方法所得到的结果与渗透汽化实验所得到的结果完全一致。     

Pore Modification in Porous Ceramic Membranes With Sol-Gel Process and Determination of Gas Permeability and Selectivity

Summary: The aim of the study was to investigate the variation in total surface area, porosity, pore size, Knudsen and surface diffusion coefficients, gas permeability and selectivity before and after the application of sol-gel process to porous ceramic membrane in order to determine the effect of pore modification. In this study, three different sol-gel process were applied to the ceramic support separately; one was the silica sol-gel process which was applied to increase porosity, others were silica-sol dip coating and silica-sol processing methods which were applied to decrease pore size. As a result of this, total surface area, pore size and porosity of ceramic support and membranes were determined by using BET instrument. In addition to this, Knudsen and surface diffusion coefficients were also calculated. After then, ceramic support and membranes were exposed to gas permeation experiments by using the CO₂ gas with different flow rates. Gas permeability and selectivity of those membranes were measured according to the data obtained. Thus, pore surface area, porosity, pore size and Knudsen diffusion coefficient of membrane treated with silica sol-gel process increased while total surface area was decreasing. Therefore, permeability of ceramic support and membrane treated with silica sol-gel process increased, and selectivity decreased with increasing the gas flow rate. Also, surface area, porosity, pore size, permeability, selectivity, Knudsen and surface diffusion coefficients of membranes treated with silica-sol dip coating and silica-sol processing methods were determined. As a result of this, porosity, pore size, Knudsen and surface diffusion coefficients decreased, total surface area increased in both methods. However, viscous flow and Knudsen flow permeability were detected as a consequence of gas permeability test and Knudsen flow was found to be a dominant transport mechanism in addition to surface diffusive flow owing to the small pore diameter in both methods. It was observed that silica-sol processing method had lower pore diameter and higher surface diffusion coefficient than silica-sol dip coating method.     

Temperature control algorithms in dual control volume grand canonical molecular dynamics simulations of hydrogen diffusion in palladium

The effectiveness of five temperature control algorithms for dual control volume grand canonical molecular dynamics is investigated in the study of hydrogen atom diffusion in a palladium bulk. The five algorithms, namely, Gaussian, generalized Gaussian moment thermostat (GGMT), velocity scaling, Nosé-Hoover (NH), and its enhanced version Nosé-Hoover chain (NHC) are examined in both equilibrium and nonequilibrium simulation studies. Our numerical results show that Gaussian yields the most inaccurate solutions for the hydrogen-palladium system due to the high friction coefficient generated from the large velocity fluctuation of hydrogen, while NHC, NH, and GGMT produce the most accurate temperature and density profiles in both equilibrium and nonequilibrium cases with their feedback control mechanisms. However, this feedback control also overestimates the self-diffusion coefficients in equilibrium systems and the diffusion coefficient in nonequilibrium systems. Velocity scaling thermostat produces slight inhomogeneities in the temperature and density profiles, but due to the dissipated heat accumulated in the control volumes it still yields accurate self-diffusion coefficients that are in good agreement with the experimental data at a wide range of temperatures while others tend to deviate.     

Investigations on the effect of flow rate,loading and other factors upon the effectiveness of radiochemical separations by ion exchange chromatography

It is shown that, depending on the ion exchange system and experimental conditions, the plate height can either increase or decrease with flow rate. The results are interpreted using the modified Glueckauf equation containing an additional term which allows for longitudinal diffusion in the resin phase. A new method for estimating the diffusion coefficients in the resin phase is suggested. Different susceptibility of various chromatographic systems to loading effects is demonstrated and discussed. Other factors influencing the degree of separation like particle size, magnitude of distribution coefficients, temperature and resin cross-linking are briefly mentioned.     

Modified free volume theory of self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.     

Precise Control of Molecular Self-Diffusion in Isoreticular and Multivariate Metal-Organic Frameworks

Understanding the factors that affect self-diffusion in isoreticular and multivariate (MTV) MOFs is key to their application in drug delivery, separations, and heterogeneous catalysis. Here, we measure the apparent self-diffusion of solvents saturated within the pores of large single crystals of MOF-5, IRMOF-3 (amino-functionalized MOF-5), and 17 MTV-MOF-5/IRMOF-3 materials at various mole fractions. We find that the apparent self-diffusion coefficient of N,N-dimethylformamide (DMF) may be tuned linearly between the diffusion coefficients of MOF-5 and IRMOF-3 as a function of the linker mole fraction. We compare a series of solvents at saturation in MOF-5 and IRMOF-3 to elucidate the mechanism by which the linker amino groups tune molecular diffusion. The ratio of the self-diffusion coefficients for solvents in MOF-5 to those in IRMOF-3 is similar across all solvents tested, regardless of solvent polarity. We conclude that average pore aperture, not solvent-linker chemical interactions, is the primary factor responsible for the different diffusion dynamics upon introduction of an amino group to the linker.     

Correlation between thermal diffusion and solvent self-diffusion in semidilute and concentrated polymer solutions

We have performed measurements of thermal diffusion coefficients DT and solvent self-diffusion coefficients Dss in semidilute to concentrated polymer solutions. Solutes of different glass transition temperatures and solvents of different solvent qualities have been used. The investigated systems are in detail: poly(dimethyl-siloxane) in toluene, tristyrene in toluene, polystyrene in toluene, polystyrene in tetrahydrofuran, polystyrene in benzene, and polystyrene in cyclohexane. The thermal diffusion data are compared to our data and literature data for solvent self-diffusion coefficients. In all systems the concentration dependence of DT closely parallels the one of Dss which may be viewed as a local probe for friction on a length scale of the size of one polymer segment. This identifies local friction as the dominating parameter determining the concentration dependence of DT. Solvent quality, in contrast, has no influence on DT.