Toluene diffusion in butyl rubber

The sorption isotherm and the polymer mass-fixed diffusion coefficients, D, for toluene in butyl rubber have been measured by the incremental sorption method to concentrations of 130%, corresponding to a solvent volume fraction of 0.578. The increase in D with concentration is strongly exponential to a concentration of 30% and then begins to level out. Since the nature of the dimensional change occurring in vapor sorption was not known, the values of D were converted to solvent self-diffusion coefficients, D₁, assuming both swelling in the thickness direction (1D) and isotropically (3D). The free volume (FV) theory of Fujita was fitted to the resulting D₁ with the zero concentration diffusion coefficient and the self-diffusion coefficient of toluene as limiting values leaving only a single arbitrary parameter. In this form the FV theory was able to describe the trend of the experimental D₁ for the 1D and 3D cases equally well. Values of D were back-calculated from the FV relations for the 1D and 3D cases for comparison with the experimental results and with the diffusion coefficient determined by immersion in toluene. These comparisons favor the assumption that swelling is isotropic. It appears that the simple free volume relation is capable of providing a satisfactory representation of the experimental data with only a single fitting parameter, although there are moderate quantitative discrepancies. © 1994 John Wiley & Sons, Inc.     

A model for predicting solvent self-diffusion coefficients in nonglassy polymer/solvent solutions

Cohen-Turnbull diffusion theory is used to develop a model for predicting solvent self-diffusion coefficients D₁ in nonglassy polymer/solvent solutions. Polymer molecules are envisioned as hindering solvent mobility by reducing the average free volume per unit mass in the system and through the lower mobility of polymer segments relative to solvent molecules. The concentration dependence of D₁ predicted by the model is in reasonable agreement with data for the solvents heptane, hexadecane, benzene, cyclohexane, and decalin in polyisobutylene (PIB), and for toluene in polystyrene, poly(methyl mothacrylate), and PIB. Although none of the data is for high concentrations of polymer (volume fractions ?≥0.9) it is anticipated the model will be less representative in this regime where the assumptions in its development are unsure. The model also demonstrates the correct temperature and concentration dependence of the apparent activation energy for diffusion. The only experimental data needed to use the model are the viscosity and critical volume of the pure solvent, and the specific volume of both the solvent and mixture. No binary transport data are required.     

Kinetics of Heterogeneous Isotopic Exchange Reaction in Finite Bath

A general method to find the rate constant and particle self-diffusion coefficient is suggested for a heterogeneous isotopic exchange reaction which is controlled by surface mass reaction or controlled by a combination of surface mass reaction and intraparticle diffusion. The values of the kinetic parameter, ξ₁ (ratio of the forward surface mass reaction rate to the intraparticle diffusion rate), particle self-diffusion coefficient D and rate constant k are obtained by the proposed method for the isotopic exchange reaction systems CaCO₃(s)/Ca²⁺(aq) and CaC₂O₄(s)/Ca²⁺(aq).     

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.     

The chain length dependence of self-diffusion in melts of polyethylene and polystyrene

The self-diffusion coefficients in melts of polyethylene fractions and polystyrene standards were measured by the NMR pulsed field gradient technique and compared with those measured by other techniques. The data agree very well if one takes into account the molar mass distribution of the samples and the free volume of the matrix. For molar masses much higher than the critical molar massM _c, reptation is confirmed,D M ^–2 holds. BelowM _e=M_c/2 the self-diffusion coefficients corrected for constant free volume show approximately the dependenceD M ^–1 confirming Rouse-like diffusion. This result was also obtained by investigating the self-diffusion of the molecules with different molar masses of a polyethylene fraction with a rather broad molar mass distribution aroundM _e andM _c, i. e. diffusion in a constant matrix. In the molar mass region betweenM _c and about 3 ·M _c the observed molar mass dependence of self-diffusion can be explained by tube formation. The constraint release model of Graessley seems to slightly overestimate the self-diffusion coefficients.     

Diffusion of water in solutions of alkali metal bromides,tetraalkylammonium bromides and ammonium bromide

The diffusion coefficient of water D _w in aqueous solutions of the alkali metal bromides, tetraalkylammonium bromides (methyl, ethyl, n-propyl, and n-butyl) and ammonium bromide at 25°C is reported for concentrations up to 2 mol-dm^–3. In addition, values for D _w in 2 mol-dm^–3 solutions of CsBr, KBr, NaBr, LiBr, and fully deuterated methanol, acetonitrile, and acetone have been measured for temperatures in the range 5 to 50°C. The concentration dependence of the relative water diffusion coefficient D _w /D _o , where D _o is the self-diffusion coefficient of water, has been analyzed in terms of an equation analogous to the Jones-Dole equation for relative viscosity. The B-coefficient for diffusion is well correlated with the viscosity B-coefficient. For the structure-breaking electrolytes CsBr and KBr, D _w /D _o decreases rapidly with increasing temperature, whereas for the structure-makers NaBr and LiBr, the temperature dependence of D _w /D _o has the same sign but is much smaller in magnitude. For the nonelectrolyte solutions, the structure-making effect decreases with increasing temperature and the temperature coefficient of D _w /D _o is positive. It is apparent that, when diffusion of the solvent is being considered, the temperature must be taken into account in the classification of an electrolyte as a structure-breaker or structure-maker.     

Molecular Dynamics Simulation of Diffusion of Vitamin C in Water Solution

Under different temperatures and concentrations, the diffusion of Vitamin C (VC) in water solution was examined by molecular dynamics simulation. The diffusion coefficients were calculated based on the Einstein equation. The influences of temperature, concentration, and simulation time on the diffusion coefficient were discussed. The results showed that at higher temperature and lower concentration the normal diffusions appear relatively late, but the linear range of mean square displacement curves continues longer than that at lower temperature and higher concentration. At the same temperature, the normal diffusion time increases and the diffusion coefficient decreases as the simulation concentration increases. These simulation results are in good agreement with experiments. Analyses of the pair correlation functions of the simulation systems showed that hydrogen bonds are mainly formed between the hydrogen atoms of VC molecules and oxygen atoms of H₂O molecules, rather than between the O atoms of VC molecules and H atoms of H₂O molecules. The diffusion coefficient is higher as the interaction between water molecules and VC molecules is stronger when VC concentration is lower. The water in the model systems affects the diffusion of VC molecules by the short‐range repulsion of O(H₂O)‐O(H₂O) pairs and the non‐bond interaction of H(H₂O)‐H(H₂O) pairs. The short‐range repulsion of O(H₂O)‐O(H₂O) pairs is greater when VC concentration is higher, the diffusion of VC is weaker. The greater the non‐bond interaction of H(H₂O)‐H(H₂O) pairs is, the higher the VC diffusion is. It is expected that this study can provide a theoretical direction for the experiments on the mass transfer of VC in water solution.     

Influence of concentration on the activation energy for diffusion in polymer-solvent systems

The self-diffusion of benzene, toluene, and ethylbenzene in polystyrene have been analyzed using the Vrentas/Duda free-volume diffusion model. Diffusion coefficient predictions suggest an exponential concentration dependence of the activation energy required to overcome attractive forces, E. Without the use of any diffusion data approximating E as zero over the entire concentration range yields self-diffusion coefficient predictions which are in good agreement with experimental data. © 1992 John Wiley & Sons, Inc.     

H 2 O-D2O Solvent Isotope Effect on Excess Molar Volumes of 3-Methylpyridine Solutions

Densities of 3-methylpyridine (3-MP) + water and 3-methylpyridine + heavy water were measured in the 3-MP mole fraction range 0.002–0.04 from 298 to 318 K. The excess molar volumes of 3-MP + D₂O mixtures were found to be more negative than those of 3-MP + H₂O mixtures. The partial molar volume of 3-MP at infinite dilution is smaller in D₂O than in H₂O which suggests that 3-MP causes a structure-breaking effect in water which is more pronounced in D₂O. It was found that the volume change with concentration in dilute solutions of 3-MP in water and heavy water can be adequately described by the pair-wise interaction of the solute molecules. The molal volume second-virial coefficient, V _xx , is positive indicating that the water molecules are less structured in the cospheres of the solute pairs than in the bulk solvent. The temperature dependence of V _xx displays a maximum at around 308 K in the case of D₂O solutions, whereas V _xx increases almost linearly with temperature in H₂O solutions.     

The effect of polymers on the phase behavior of balanced microemulsions: diblock-copolymer and comb-polymers

The effect of some amphipilic diblock-copolymers and comb-polymers on a balanced Winsor III microemulsion system is investigated with the quaternary system n-octyl-β-d-glucoside/1-octanol/n-octane/D₂O as basis system. The diblock-copolymers are polyethyleneoxide-co-polydodecenoxide (PEO _x PEDODO _y ) and polyethyleneoxide-co-polybutyleneoxide (PEO _x PEBU _y ), constituted of a straight chain hydrophilic part and a bulky hydrophobic part. Addition of the diblock-copolymer leads to an enhancement of the swelling of the middle phase by uptake of water and oil; a maximum boosting factor of 6 was obtained for PEO₁₁₁PEDODO₂₅. Nuclear magnetic resonance diffusometry yields the self-diffusion coefficients of all the components in the system. The diffusion experiments provide information on how the microstructure of the bicontinuous microemulsion changes upon addition of the polymers. The reduced self-diffusion coefficients of water and oil are sensitive to the type of polymer that is incorporated in the film. For the diblock-copolymers, as mainly used here, the reduced self-diffusion coefficient of oil and water will respond to how the polymer bends the film. When the film bends away from water, the reduced self-diffusion of the water will increase, whereas the oil diffusion will decrease due to the film acting as a barrier, hindering free diffusion. The self-diffusion coefficient of the polymer and surfactant are similar in magnitude and both decrease slightly with increasing polymer concentration.     

The effect of pressure and temperature of self-diffusion coefficients in several concentrated deuterium oxide diamagnetic electrolyte solutions

The pressure dependences of the self-diffusion coefficients of deuterium oxide in 4.5m solutions of LiCl–D₂O and CsCl–D₂O (also 7m) and 3.06m CaCl₂–D₂O have been measured by the NMR spin-echo method at 30°C, 60°C, and 90°C. Shear viscosities and densities of these solutions have also been determined over the same range of experimental conditions. The experimental data show that the diffusion constantD decreases with the increasing structure-making ability of the electrolyte cation Ca⁺²>Li⁺. In contrast, the diffusion coefficient for D₂O in the 4.5 and 7m CsCl solutions is equal to that for pure D₂O at 30°C but lower at 60°C and 90°C. It has been found that the Stokes-Einstein equation relates well the diffusion coefficients to shear viscosity in these concentrated electrolyte solutions.     

Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH₂)₃CH₃, –(CH₂)₇CH₃, and –(CH₂)₁₁CH₃ nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.     

Emission of occluded volatiles during deformation of polycarbonate due to strain-enhanced diffusion

Measurements of the emission of purposely entrained volatiles (Ar and D₂O) during the loading and unloading of a bisphenol-A polycarbonate in vacuum are made by quadrupole mass spectrometry. Transient loading events are accompanied by dramatic increases in emission, reflecting a similar rise in the diffusion constant of the measured species. We attribute this change to an increase in size of molecular voids in the polymer network, which accompany the increase in sample volume under load. The results are interpreted in terms of the Dolittle relation in which the diffusion constant depends exponentially upon v^*/v_f0, the ratio between an activation volume for diffusion and the average size of the relevant voids in the polymer network. Our data suggests that v^*/v_f0 is unusually low in the D₂O-polycarbonate system, which we attribute to a relatively large value of v_f0; this would be consistent with the relatively long distance between flexible links in the polycarbonate structure. © 1994 John Wiley & Sons, Inc.     

A pulsed field gradient NMR study of diffusion in semicrystalline polymers: self-diffusion of alkanes in polyethylenes

By means of the pulsed field gradient NMR technique the self-diffusion of six alkanes (from n-butane to n-pentadecane) in three low density polyethylenes and one high density polyethylene differently thermally treated was examined. The concentration dependence could be described very satisfactorily with the free volume theory in the form of Fujita (Adv. Polymer Sci. 3(1961) 1). The parameter B of the diffusants and the fractional free volumef ₂ of the polyethylenes were determined from the experimental data. The fractional free volumesf ₂ show a strong dependence on the type of polyethylene, the main influence results from the different content of CH₃ groups or short chain branches. The diffusion coefficient extrapolated to zero diffusant concentration is proportional to the eighth power of the amorphous content. This strong dependence shows that the free volumes of the amorphous parts of the polyethylenes are intimately connected with crystallinity, both determined by the different degrees of short chain branching. The pre-exponential factor in the free volume expression decreases with increasing amorphous content of the polyethylenes and increases with increasing length of the diffusants. It was found that the spherulite boundaries in the polyethylenes do not act as diffusion barriers.     

Thermal diffusion of alkaline chlorides in D2O

Heats of transport of 0.01m (molality) LiCl, NaCl, KCl, RbCl, and CsCl as well as the concentration dependence of the heat of transport of NaCl (up to 1.5m) and KCl (up to 2m) were studied potentiometrically from the measurement of thermoelectric powers of the silver-silver chloride thermocell at a mean temperature of 25°C. Heats of transport of alkaline chlorides were found to be smaller in D₂O than in H₂O. Effective diffusion coefficients were also found to be smaller. The solvent isotope effect observed is discussed, and possible rationalization is given in terms of solvent properties, structural effects, and motions of ions and solvent molecules.     

Diffusion of camphorquinone in uniaxially drawn polycarbonate films

Employing the laser-induced holographic grating relaxation technique, we have measured tracer diffusion coefficients of a phtochromous dye, camphorquinone, in uniaxially drawn polycarbonate films as a function of stretch ratio. Anisotropy in the tracer diffusion coefficient has been observed with D_∥ greater than D_⟂ by at least a factor of 4 for the film stretched to the stretch ratio δ = 2.3. The diffusion coefficient along the direction of stretch D_∥ increases significantly with increasing δ, whereas D_⟂ decreases slightly with increasing δ. The stretch ratio dependence of D_∥ and D_⟂ is interpreted according to a modified free volume theory. The strain rate and stretch temperature dependence of the anisotropic tracer diffusion coefficient has also been investigated. © 1992 John Wiley & Sons, Inc.     

Diffusion behavior of pharmaceutical O/W microemulsions studied by dynamic light scattering

Dynamic light scattering experiments have been performed at various concentrations, of pharmaceutical oil-in-water microemulsions consisting of Eutanol G as oil, a blend of a high (Tagat O2) and a low (Poloxamer 331) hydrophilic–lipophilic balance surfactant, and a hydrophilic phase (propylene glycol/water). We probe the dynamics of these microemulsions by dynamic light scattering. In the measured concentration range, two modes of relaxation were observed. The faster decaying mode is ascribed classically to the collective diffusion D _c (total droplet number density fluctuation). We show that the slow mode is also diffusive and suggest that its possible origin is the relaxation of polydispersity fluctuations. The diffusion coefficient associated with this mode is then the self-diffusion D _s of the droplets. It was found that D _c and D _s had opposite volume fractions of oil plus surfactants (ϕ) dependence and a common limiting value D ₀ for ϕ=0. Average hydrodynamic radius (R _h=10.5 nm) of droplets was calculated from D ₀. R _h is supposed to compose the inner core, a surfactant film including possible solvent molecules, which migrate with the droplet. The concentration dependence of diffusion coefficients reflects the effect of hard sphere and the supplementary repulsive interactions which arises due to loss of entropy, when absorbed chains of surfactant intermingle on the close approach of the two droplets. This mechanism could also explain the observed stability of our systems. The estimated extent of polydispersity is 0.22 from the amplitude of slower decaying mode. The polydispersity in microemulsion systems is dynamic in origin. Results indicate that the time scale for local polydispersity fluctuations is at least three orders of magnitude longer than the estimated time between droplet collisions.     

Crystallization-induced composition inhomogeneities in PVDF/PMMA blends

Composition profiles develop around growing PVDF spherulites in a blend with PMMA. These profiles assume stationary courses after a certain crystallization time provided that the overall degree of crystallinity is not too high. The composition-dependent growth rate and the diffusion-controlled remove of the surplus PMMA from the spherulite surface are then in a stationary equilibrium. The internal structure of the spherulites will then be homogeneous, too. Upon isothermal crystallization of a PVDF/PMMA = 60/40 (wt %) blend at 160°C for at least 4 h, the spherulites internal degree of crystallinity x_c as related to the PVDF fraction obeys the inequality 55 wt % ≤ x_c ≤ 84 wt %. The overall PMMA content within the spherulites as averaged over its whole inside has been determined by IR microscopy. It amounts to about 15 wt %. In contrast, the PMMA content of the amorphous phase within the spherulites (averaged again over its whole inside) ranges between 28 and 52 wt %. This composition jumps at the spherulite surface to 52 wt %. From the slope of the composition profiles outside the spherulites that have a width of more than 50 μm, the effective chain diffusion coefficient in blends as averaged over both components can be calculated to amount to (250 ± 100) μm²h⁻¹. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2923–2930, 1998     

The use of the cohen–turnbull model for calculation of the self-diffusion coefficients of liquid dichloroalkanes

The paper presents the self-diffusion coefficients calculated for liquid dichloroalkanes C₆H₁₂Cl₂, C₈H₁₆Cl₂, C₁₀H₂₂Cl₂ and C₁₂H₂₄Cl₂, with the use of the Cohen and Turnbull model. Determination of self-diffusion coefficients permits a separate analysis of intra- and intermolecular motions and provides information on geometrical and dynamical properties of molecules. The self-diffusion coefficients of selected dichloroalkanes have been determined by X-ray diffraction and compared with the corresponding NMR results. The suitability of the Cohen–Turnbull model of the translating motion for prediction of self-diffusion coefficients for molecules whose shape significantly differs from the spherical symmetry is analysed. Angular distributions of X-ray scattered intensity were measured, and differential radial distribution functions of electron density (DRDFs) were calculated. The mean coordination numbers were obtained from the area delimited by the minima of the DRDFs, and their dependence on the length of the methylene chain is also presented subsequently. On the basis of the DRDFs the average free volume of the molecules and total free volume of the liquids were calculated. The activation volume of the diffusion was found to make about 0.6 of the van der Waals volume of the molecule. As expected the diffusion coefficients decrease with increasing molecular weight. The equation relating the self-diffusion coefficient with the volume of the coordination spheres in the liquid has been derived.