Self-diffusion Coefficient Ds Research Articles

Macromolecular insight into the adsorption and migration properties of CH4/CO2/N2 in bituminous coal matrix under uniaxial strain loading

Gas adsorption–migration in coal is of crucial importance for coalbed methane (CBM) recovery; however, the effect of coal deformation on it is not yet very clear, especially at the molecular level. In this study, the effects of uniaxial tension–compression strains on the CH4/CO2/N2 adsorption–migration characteristics in bituminous coal matrix were investigated by integrating the grand canonical Monte Carlo and molecular dynamics methods. The results show that the dual-mode equation fits the isothermal adsorption results, and the adsorption concentration and Langmuir volume are positively correlated with strain. Tension strain has a small effect on a thermodynamic factor but a large effect on Henry constant. In addition, the swelling resistance of coal matrix is positively correlated with tension strain which has a greater impact on the shear resistance of coal matrix containing CO2. The average mass density of the gas is linearly positively correlated with strain that has a large impact on N2 stability. More significantly, the self-diffusion coefficient (Ds) of CH4 is larger than that of CO2/N2, and the relationship between Fick diffusion coefficient and strain is roughly similar to that between Ds and strain. Also, the mass transfer of CO2 permeation is more significant compared to N2, especially for tension strain. These research results provide a basis for the optimization design of CBM recovery in deformed coal reservoirs.

Viscosity and Stokes-Einstein relation in deeply supercooled water under pressure.

We report measurements of the shear viscosity η in water up to 150MPa and down to 229.5K. This corresponds to more than 30K supercooling below the melting line. The temperature dependence is non-Arrhenius at all pressures, but its functional form at 0.1MPa is qualitatively different from that at all pressures above 20MPa. The pressure dependence is non-monotonic, with a pressure-induced decrease of viscosity by more than 50% at low temperature. Combining our data with literature data on the self-diffusion coefficient Ds of water, we check the Stokes-Einstein relation which, based on hydrodynamics, predicts constancy of Dsη/T, where T is the temperature. The observed temperature and pressure dependence of Dsη/T is analogous to that obtained in simulations of a realistic water model. This analogy suggests that our data are compatible with the existence of a liquid-liquid critical point at positive pressure in water.

Review: Kirkwood-Riseman Model in Non-Dilute Polymeric Fluids.

In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood-Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood-Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient Ds and the low-shear viscosity η. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger-Dahler positive-function renormalization group are presented. The rationales correctly predict how Ds and η depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted.

Molecular self-diffusivity and separation of CH4/H2S in metal organic framework MIL-47(V)

The loading dependence of self-diffusion coefficient (Ds), diffusion selectivity (sdiff), and structural properties of pure CH4, H2S, and their mixtures in MIL-47(V) material were investigated using Molecular Dynamics (MD) simulations. The preferential adsorption sites of gas molecules in the lattice, as well as the molecular structure of gases were determined using Radial Distribution Functions (RDFs). The diffusion behavior of gas molecules diffusing in the lattice was further investigated utilizing the 2D probability density plots and free energy profiles derived by the Histogram Sampling method. Furthermore, the findings of our computational study are examined and compared to previous research.

The Water Polymorphism and the Liquid–Liquid Transition from Transport Data

NMR spectroscopic literature data are used, in a wide temperature-pressure range (180–350 K and 0.1–400 MPa), to study the water polymorphism and the validity of the liquid–liquid transition (LLT) hypothesis. We have considered the self-diffusion coefficient DS and the reorientational correlation time τθ (obtained from spin-lattice T1 relaxation times), measured, respectively, in bulk and emulsion liquid water from the stable to well inside the metastable supercooled region. As an effect of the hydrogen bond (HB) networking, the isobars of both these transport functions evolve with T by changing by several orders of magnitude, whereas their pressure dependence become more and more pronounced at lower temperatures. Both these transport functions were then studied according to the Adam–Gibbs model, typical of glass forming liquids, obtaining the water configurational entropy and the corresponding specific heat contribution. The comparison of the evaluated CP,conf isobars with the experimentally measured water specific heat reveals the full consistency of this analysis. In particular, the observed CP,conf maxima and its diverging behaviors clearly reveals the presence of the LLT and with a reasonable approximation the liquid–liquid critical point (LLCP) locus in the phase diagram.

Methanol dynamics in H-ZSM-5 with Si/Al ratio of 25: a quasi-elastic neutron scattering (QENS) study

Methanol dynamics in zeolite H-ZSM-5 (Si/Al of 25) with a methanol loading of ~ 30 molecules per unit cell has been studied at 298, 323, 348 and 373 K by incoherent quasi-elastic neutron scattering (QENS). The elastic incoherent structure factor (EISF) reveals that the majority of methanol is immobile, in the range between 70 and 80%, depending on the measurement temperature. At 298 K, ≈ 20% methanol is mobile on the instrumental timescale, exhibiting isotropic rotational dynamics with a rotational diffusion coefficient (DR) of 4.75 × 1010 s−1. Upon increasing the measurement temperature from 298 to 323 K, the nature of the methanol dynamics changes from rotational to translational diffusion dynamics. Similar translational diffusion rates are measured at 348 and 373 K, though with a larger mobile fraction as temperature increases. The translational diffusion is characterised as jump diffusion confined to a sphere with a radius close to that of a ZSM-5 channel. The diffusion coefficients may be calculated using either the Volino–Dianoux (VD) model of diffusion confined to a sphere, or the Chudley–Elliot (CE) jump diffusion model. The VD model gives rise to a self-diffusion co-efficient (Ds) of methanol in the range of 7.8–8.4 × 10–10 m2 s−1. The CE model gives a Ds of around 1.2 (± 0.1) × 10–9 m2 s−1 with a jump distance of 2.8 (either + 0.15 or − 0.1) Å and a residence time (τ) of ~ 10.8 (either + 0.1 or − 0.2) ps. A correlation between the present and earlier studies that report methanol dynamics in H-ZSM-5 with Si/Al of 36 is made, suggesting that with increasing Si/Al ratio, the mobile fraction of methanol increases while DR decreases.

An empirical relation between the limiting ionic molar conductivities and self-diffusion coefficients of pure solvents

The limiting ionic molar conductivity (λ∞) of an electrolyte solution depends on the self-diffusion coefficient (Ds) of the pure solvent when the temperature (T) changes. To study the Ds-dependence of λ∞, we proposed a new empirical relation λ∞∝(Ds/T)t, with a parameter t. The relation is applied to the λ∞ and Ds of alkali, tetra-alkyl ammonium, and halogen ions in water or methanol. All ions except for tetra-alkyl ammonium ions in water exhibit excellent linear relationships in their λ∞∝(Ds/T)tplots, with t in the range from 0.88 to 1.26. This is the first report showing an affirmative linear correlation between λ∞ and Ds.

String-like collective motion and diffusion in the interfacial region of ice.

We investigate collective molecular motion and the self-diffusion coefficient Ds of water molecules in the mobile interfacial layer of the secondary prismatic plane (112¯0) of hexagonal ice by molecular dynamics simulation based on the TIP4P/2005 water potential and a metrology of collective motion drawn from the field of glass-forming liquids. The width ξ of the mobile interfacial layer varies from a monolayer to a few nm as the temperature is increased towards the melting temperature Tm, in accordance with recent simulations and many experimental studies, although different experimental methods have differed in their precise estimates of the thickness of this layer. We also find that the dynamics within this mobile interfacial ice layer is "dynamically heterogeneous" in a fashion that has many features in common with glass-forming liquids and the interfacial dynamics of crystalline Ni over the same reduced temperature range, 2/3 < T/Tm < 1. In addition to exhibiting non-Gaussian diffusive transport, decoupling between mass diffusion and the structural relaxation time, and stretched exponential relaxation, we find string-like collective molecular exchange motion in the interfacial zone within the ice interfacial layer and colored noise fluctuations in the mean square molecular atomic displacement 〈u2〉 after a "caging time" of 1 ps, i.e., the Debye-Waller factor. However, while the heterogeneous dynamics of ice is clearly similar in many ways to molecular and colloidal glass-forming materials, we find distinct trends between the diffusion coefficient activation energy Ea for diffusion Ds and the interfacial width ξ from the scale of collective string-like motion L than those found in glass-forming liquids.

Diffusion of Binary CO2/CH4 Mixtures in the MIL-47(V) and MIL-53(Cr) Metal–Organic Framework Type Solids: A Combination of Neutron Scattering Measurements and Molecular Dynamics Simulations

The dynamics of CO2 and CH4 in a mixture of different compositions has been explored in two metal–organic frameworks, namely, MIL-47(V) and MIL-53(Cr), by combining molecular dynamics (MD) simulations and quasi-elastic neutron scattering (QENS) measurements. The experimental and simulated self-diffusion coefficient (Ds) values for CH4 are in very good agreement in the whole range of the CO2 explored loadings. It is clearly stated that CH4 which shows a fast diffusivity at low loading becomes significantly slower in both metal–organic frameworks (MOFs) when CO2 molecules are introduced within the porosities of these materials. Further, compared to its behavior in a single component, CH4 tends to diffuse slightly faster in the presence of CO2. The MD simulations revealed that this speeding up is concomitant with a mutual speeding up or a slowing down of the slower CO2 molecules in MIL-47(V) and MIL-53(Cr), respectively. Analysis of the MD trajectories emphasizes that both gases in the mixture follow individually a 1D-type diffusion mechanism in both MOFs, where the CO2 molecules diffuse close to the pore wall while the motions of CH4 are restricted in the central region of the tunnel.

Dynamic equivalence between atomic and colloidal liquids

We show that the kinetic-theoretical self-diffusion coefficient of an atomic fluid plays the same role as the short-time self-diffusion coefficient DS in a colloidal liquid, in the sense that the dynamic properties of the former, at times much longer than the mean free time, and properly scaled with DS, will be indistinguishable from those of a colloidal liquid with the same interaction potential. One important consequence of such dynamic equivalence is that the ratio DL/DS of the long-time to the short-time self-diffusion coefficients must then be the same for both an atomic and a colloidal system characterized by the same inter-particle interactions. This naturally extends to atomic fluids a well-known dynamic criterion for freezing of colloidal liquids (Löwen H. et al., Phys. Rev. Lett., 70 (1993) 1557). We corroborate these predictions by comparing molecular and Brownian dynamics simulations on the hard-sphere system and on other soft-sphere model systems, representative of the “hard-sphere”dynamic universality class.

Synthesis and characterization of a colloidal novel folic acid–β-cyclodextrin conjugate for targeted drug delivery

A novel folic acid–β-cyclodextrin (β-CD) conjugate was synthesized and preliminarily characterized by 1H NMR, ESI-MS, and MALDI-MS. 1H NMR shows the presence of α- and γ-conjugates which are generated by β-CD linkage in turn with both carboxylic functions of folic acid. Moreover ROESY evidences supramolecular interactions between the benzene ring of the folic acid and the β-CD cavity. DOSY suggests that ethylenediamine derived β-CD–folic acid forms a colloidal dispersion difficult to purify from free folic acid. An analysis of self-diffusion coefficient (Ds) of the three species (α-, γ-conjugates, and free folic acid) and relaxation times (T1 and T2) is reported to tentatively explain the colloidal behaviour of the new species in an aqueous solution.

A Fluorescence Correlation Spectroscopy Study on the Self-Diffusion of Polystyrene Chains in Dilute and Semidilute Solution

The self-diffusion coefficient Ds of dye-labeled polystyrene chains having Mw = 3.90 × 105 g/mol and Mw/Mn < 1.10 was measured over almost 4 decades of polymer concentration in toluene solution, from 10-4 to 0.4 g/mL, by fluorescence correlation spectroscopy. In the dilute regime up to 5 × 10-3 g/mL, Ds remains practically constant. The transition to the semidilute regime is observed around 0.01 g/mL, and from 0.02 to 0.4 g/mL Ds decreases strongly with rising concentration. This decrease is well represented by a power law, Ds ∼ c-1.75, as predicted by scaling and reptation theory. As an alternative, a good fit over the whole concentration range can be obtained with a stretched exponential function, Ds = D0 exp(−15c0.65), with D0 = 2 × 10-7 cm2/s and c given in g/mL.

Rodlike polymer gelatination as studied by PFG NMR: Fibrin polymerization in human plasma

The structure formation in rodlike polymers was investigated by the example of polymerization of fibrin rodlike, molecules in native plasma. Translational mobility of fibrin, molecules in anticoagulated plasma and native plasma during fibrin polymerization was studied by pulse field gradient nuclear magnetic resonance. It was shown that the diffusion decay of anticoagulated plasma can be fitted by the sum of exponents and fibrin molecules have the self-diffusion coefficientD f of 1.53·10−11 m2/s. The diffusion decay of native plasma during fibrin polymerization becomes nonexponential and is described by the lognormal distribution of fibrin self-diffusion coefficients. Qualitative and quantitative changes of the spectrum of fibrin self-diffusion coefficients (SDCs) during polymerization were investigated and analyzed. A symmetrical broadening of the spectrum at the beginning of polymerization and symmetrical narrowing at its final stages with conservation of the most probable SDC was explained on the basis of the hypothesis about the simultaneous action of fibrin polymerization and lyses.

Ultramicroelectrode Voltammetric Investigation of Intermicellar Interaction and Micellar Growth of Sodium Dodecyl Sulfate in Aqueous NaCl Solutions

Ultramicroelectrode voltammetric measurements have been carried out to calculate the micellar self-diffusion coefficient (Ds) and intermicellar interaction parameter (Kd) of sodium dodecyl sulfate (SDS) in aqueous NaCl solutions at 298.15 K. The hydrodynamic radius ( ), the aggregation number, and the molecular weight of SDS micelles at various NaCl concentrations are also estimated. It is found that the Ds value is a function of SDS concentrations and the electrolyte concentration dependence on Ds exhibits two regions of behavior. With increasing NaCl concentration, Ds initially increases because of increasing Coulombic screening and, then, decreases linearly because of a linear spherical expansion of the micelles resulting from the increasing aggregation number. Kd is found to be a function of electrolyte concentrations. The stepwise decrease of Kd reflects that, due to Coulombic repulsion, the electrostatic interaction is gradually screened with increasing NaCl concentration. As the linear interaction theory applies rigorously over the electrolyte concentration range from 0.20 to 1.00 mol dm-3, it suggests that the micellar structure remains effectively spherical in the region, the linear spherical expansion of the micelle is occurring, and no dramatic structural changes have taken place in the micellar solutions. In addition, the micellar interaction energy is calculated, which implies that it is the Coulombic nature of the interaction between micellar particles that controls the micellar self-diffusion behavior in aqueous solutions.

Diffusion and Rheology of Binary Polymer Mixtures

This work studies the diffusion and rheological behavior of binary mixtures (of long and short chains) based on 1,4-polybutadiene over the full composition range as a function of both long and short chain lengths using pulse-gradient NMR spin echo and oscillatory shear measurements. The first set of rheological and diffusion measurements reveals that the terminal relaxation rate 1/τd and self-diffusion coefficient Ds of the long chains both decrease systematically with increasing short chain length NS and with the weight fraction φ of the long chain in the mixtures. The second set of data indicates that the short chain's diffusion coefficient Ds decreases with increasing φ, leading to insightful comparison between the self-diffusion coefficient Ds at φ = 0 and trace diffusion coefficient Dtr in the limit of φ = 1.0: Dtr recovers the asymptotic molecular weight scaling of M-2.0, whereas Ds scales nonideally as M-2.4 due to the considerable constraint release effect in the explored range of molecular weight. Third, short chains of molecular weight below Me are found to diffuse in entangled matrices of different chain length NL with a self-diffusion coefficient Ds that is independent of NL at all compositions.

Dynamic Structure Factor of Diblock Copolymers Solutions in the Disordered State. 3. The Non-Mean-Field Regime

The dynamic structure factor S(q,t) of seven diblock copolymers in a common solvent was measured by photon correlation spectroscopy as a function of concentration (φ) in the disordered state near the disordered-to-order transition (ODT). Both symmetric and asymmetric diblock copolymers of styrene-b-isoprene (SI) with molecular masses ranging from 0.95 to 3.6 million g/mol and their hydrogenated styrene-b-(ethylene-alt-propylene) (SEP) counterparts have been considered. The maximum of the static structure factor S(q*) and the characteristic spacing 1/q* do not conform to theoretical predictions over the whole φ range up to φODT. The S(q,t) is determined mainly by the relative contribution of two relaxation processes one of which is diffusive (q2-dependent rate). When composition fluctuation corrections become important for S(q*) at φx < φODT, S(q,t) exhibits a dynamic crossover from a dominant pure relaxational (q-independent rate) to a dominant diffusive character. This new dynamic behavior in the shape of S(q,t) of narrowly distributed diblock copolymer solutions is captured theoretically. Above about φx, the self-diffusion coefficient Ds(φ) obtained from the S(q,t) at low q/q* values becomes thermodynamically retarded. The real phase morphology of diblock copolymers is well complemented by their dynamic structure.

Self-Consistency of Hydrodynamic Models for the Zero-Shear Viscosity and the Self-Diffusion Coefficient

The hydrodynamic model treatments of the zero-shear viscosity η and the self-diffusion coefficient Ds of polymers in nondilute solution are shown to be self-consistent. Hydrodynamic models for poly...

Self-diffusion of Native Proteins and Dextran in Heat-set Globular Protein Gels

Heat denatured β-lactoglobulin (β-lg) in aqueous solution aggregates and eventually gels. The fraction of residual nonaggregated proteins decreases with heating time but is still detectable at long heating times after the gels are formed. Aggregated β-lg does not have a significant NMR signal. Polysaccharide (dextran) with three different sizes was added to the system in small amounts so as not to perturb the gelation of the globular proteins. Pulsed field gradient NMR was used to determine the self-diffusion coefficient (Ds) of residual nonaggregated protein and dextran as a function of heating time. Ds of the protein increased with heating time, whereas that of the dextran decreased. The decrease stopped when the gel was formed, and Ds remains constant at longer heating times. The results indicate that the pore size of the protein gel is fixed close to the gel point, possibly involving a process of microphase separation. The pore size decreases with increasing protein concentration, and Ds is much large...

Self-Diffusion and Cooperative Diffusion of Globular Proteins in Solution

The globular protein β-lactoglobulin (β-lg) was studied in aqueous solution at pH = 7.0 using pulsed field gradient nuclear magnetic resonance (PFG-NMR) and static (SLS) and dynamic light scattering (DLS). The concentration dependence of the self-diffusion coefficient (Ds) and the cooperative (or mutual) diffusion coefficient (Dc) were determined as a function of the concentration up to volume fraction φ = 0.15. The effect of electrostatic interactions was investigated by comparing systems with 0.003 and 0.1 M added salt. The concentration dependence of Ds with 0.1 M added salt is found to be the same as for other globular proteins reported in the literature. Directly measured values of Dc using DLS are consistent with values derived from a combination of PFG-NMR and SLS assuming that the protein−protein friction coefficient is small compared to the protein−solvent friction coefficient.

Electrical Transport in a Disordered Medium: NMR Measurement of Diffusivity and Electrical Mobility of Ionic Charge Carriers

Electrical transport in porous media plays an important role in many fields of pure and applied science. The basic microscopic processes of the charge transport have attracted considerable theoretical interest for a long time. However, on a microscopic level there was up to now no experimental access to this problem. In the present paper we demonstrate, by using a suited porous system, that two combined NMR methods can offer such a first experimental access. We apply common PFG NMR methods and the special electrophoretic NMR (ENMR) technique for the measurement of self-diffusion coefficientD+and electric mobilityu+of a cation ((C4H9)+4) in a disordered gel-like medium (Sephadex LH-20) filled with electrolyte solution. We find a, qualitatively expected, observation time-dependence ofD+,but for the first time such a time-dependence is also observed foru+,which means the detection of the phenomenon of “anomalous field assisted diffusion” or “anomalous mobility.” For the measurement of the short-time behavior of the mobility a new pulse sequence is presented. The time-dependent mobilities were measured at three different external electrical fieldsE.From the long-time behavior ofD+, u+,andDH2Othree independent values for the tortuosityTof the porous system could be derived. We find equality of the tortuositiesT(D+)andT(u+),which represents a first experimental proof of the validity of the Einstein relation(D+∼ u+)in a disordered medium. Finally, we discuss advantages of the possible use of “anomalous field assisted diffusion” over the commonly used “anomalous diffusion” in morphology studies by dynamic imaging in porous media.