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.     

Transient permeation of organic vapors through elastomeric membranes

The permeation of benzene and acetone vapors through sulfur-cured natural rubber was studied by the time-lag method. The experimental results were analyzed by a method suggested by Meares. The zero concentration diffusion coefficient D₀ was obtained by the early-time method. The Frisch time-lag equation was utilized to estimate both the solubility coefficient s and the additional parameter b required to define the concentration dependence of the diffusion coefficient: D(c) = D₀ exp {bc}. This form of concentration dependence was manifested by the corresponding permeability coefficient values. At low entering penetrant pressure, where the transport coefficients are constant, indirect evidence was obtained that D₀ is the mechanistically correct diffusion coefficient. The solubility coefficient values calculated for benzene vapor in natural rubber are in reasonable agreement with published equilibrium sorption data for a similar rubber compound. At higher entering penetrant pressures, average diffusion coefficients obtained at steady state tended to be larger than the corresponding average diffusion coefficients derived from the time lags. This same effect has been detected by other experimental approaches. Permeation experiments designed for this rapid method of analysis appear capable of yielding information consistent with that obtained by more time-consuming traditional methods.     

Interaction of simple acids with nylon. Part 2: Diffusion of simple acids

The paper deals with the diffusion of two mineral acids, hydrobromic and sulfuric acids, and two simple dye acids, NOG (C. I. Acid Orange 7) and SY (C.I. Food Yellow 3), in water-swollen nylon 66. Anion self-diffusion coefficients were obtained by radiotracer techniques. The bromide ion and the SY anion self-diffusion coefficients show very little variation with concentration in the amino-dyeing region, whereas the H₂SO₄ and NOG anion diffusion coefficients are concentration-dependent. The variation of the H₂SO₄ anion diffusion coefficient with concentration is consistent with the formation of small quantities of the highly mobile bisulfate ion. The low SO₄ diffusion coefficient may be explained by the interaction of this ion with single, fixed sites in the polymer. The variation of the NOG anion diffusion coefficient with concentration does not follow a simple D = D₀[1/(1 ? θ)] relationship at intermediate concentrations but the rapid increase observed as the available sites became saturated, i.e., as θ → 1, is consistent with a site saturation model.     

PGSE-NMR studies of solvent diffusion in poly(N-isopropylacrylamide) colloidal microgels

The solvent self-diffusion coefficient has been studied in thermoshrinking poly(N-isopropyl acrylamide) microgel dispersions by the pulsed-gradient spin-echo PGSE-NMR technique, as a function of temperature and mass fraction. After suitable corrections for the temperature, the H₂O/D₂O ratio and the relative volume fractions, all the self-diffusion data obtained over a temperature range of approximately 40 °C and mass fraction (2–12 % wt/wt) could be superimposed with the volume fraction as the universal factor. The observed reduction in the solvent self-diffusion coefficient with volume fraction was greater than that predicted by simple obstruction theory. After correction for-, and the subsequent removal of the obstruction effect, the diffusion of the solvent through the core of the particle is elucidated. As found for other polymer-solvent systems, there were no specific binding effects. The diffusion of the solvent in these dispersions over such temperature and mass fraction ranges could be rationalised assuming a constant solvent self-diffusion coefficient in the core of the particles.     

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.     

Incremental vapor sorption in a phase-segregated polyurethane elastomer

Incremental vapor sorption and desorption runs have been carried out with o-dichlorobenzene (ODCB) a strongly swelling solvent, in 2, 6, and 10 mil polyether polyurethane films. Two-stage sorption behavior occurs at intermediate and higher concentrations but is generally absent in the desorption runs. Analysis of the two-stage curves, using the Berens-Hopfenberg model of independent Fickian diffusion and first-order relaxation processes, leads to apparent diffusion coefficients which increase with thickness and show a pronounced maximum with concentration, whereas the relaxation rate constant decreases with concentration. Correction for the pressure drift during the runs, due to the low vapor pressure of ODCB, reduces the thickness dependence. The negative concentration dependence of the relaxation rate constant is related to the distribution of microdomain stabilities. Calculated values of the self-diffusion coefficient show that the maximum in the apparent diffusion constant with concentration can be accounted for largely, but not entirely, by the thermodynamic contributions. It is proposed that the additional factor is relaxation-controlled swelling which arises from the strong coupling between the matrix and hard-segment responses.     

Investigation on extremely dilute solution of PEO by PFG-NMR

The technique of pulsed-field gradient nuclear magnetic resonance (PFG-NMR) was applied to study the solution properties of a series of low molecular weight poly(ethylene oxide). The self-diffusion coefficients of solutions from semi-concentrated to extremely diluted were measured, leading to a critical concentration. When the concentration of solution is higher than the value of critical concentration, the diffusion coefficient of the solute decreases as the concentration increases and remains the same when the concentration is lower than it. This critical concentration agrees well with the definition of dynamic contact concentration (C _s) and confirms indirectly the Flory's scaling law between the molecular weight and D ₀. In addition, the influences of molecular weight and terminal groups on C _s were discussed. All the diffusion coefficients determined at extremely dilute condition were equivalent to the diffusion coefficients at infinite concentration (D ₀), from which the polymer coil size was estimated.     

Characterization of thermal diffusion in polymer solutions by thermal field-flow fractionation: Dependence on polymer and solvent parameters

The thermal diffusion coefficient D_T has been obtained for 17 polymer-solvent combinations, each of them spanning a range of polymer molecular weights, using thermal field-flow fractionation. The polymers examined include polystyrene, poly(alpha-methyl)styrene, polymethylmethacrylate, and polysioprene. The solvents include benzene, toluene, ethylbenzene, tetrahydrofuran, methylethylketone, ethylacetate, and cyclohexane. Although D_T was confirmed as essentially independent of polymer molecular weight, it was found to vary substantially with the chemical composition of polymer and solvent. The results were used to evaluate several thermal diffusion theories; the agreement with theory was generally found to be unsatisfactory. Attempts were then made to correlate the measured thermal diffusion coefficients with various physicochemical parameters of the polymers and solvent. A good correlation was found in which D_T increases with the thermal conductivity difference of the polymer and solvent and varies inversely with the activation energy of viscous flow of the solvent.     

Diffusion in polyacrylate aqueous systems at 25°C. Role of reference frame choice in interpreting diffusion coefficient data

Diffusion coefficients have been measured for the binary systems sodium polyacrylate-water and polyacrylic acid-water at 25°C as a function of concentration. Diffusion coefficients have been also measured for the ternary system sodium chloride-sodium polyacrylate-water at constant NaCl concentration and varying polyacrylate concentration. The experimental results have been compared with some limit expressions, available in literature, for the four D _ik diffusion coefficients of systems containing two electrolytes with a common ion. The ternary system shows strong interaction between flows: as the polyelectrolyte concentration, C₂, approaches zero, the main diffusion coefficient D₂₂ and the cross coefficient D₂₁ approach zero, while the cross coefficient D₁₂ reach quite high values. The water motion during the diffusion process is also discussed.     

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.     

Kinetics of Antibiotic Sorption by Monocarboxyl Cellulose

Kinetics of the sorption of lincomycin and gentamicin from aqueous solutions of their salts and bases, as well as a cephalosporin group antibiotic cephalexin having the zwitterionic nature, by monocarboxyl cellulose is studied. It is disclosed that the sorption of the studied antibiotics is characterized by a combined diffusion type of kinetics. Effective diffusion coefficients (D _eff) are determined, and it is shown that they correspond to the times (t _1/2) of half-equilibrium establishment and increase with passing from lincomycin to gentamicin and, further, to cephalexin. The D _eff and t _1/2 values are found to depend on solution pH and the degree of cellulose sorbent swelling.     

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.     

Water-absorption properties of an acetal copolymer

The kinetics of sorption from the liquid phase to equilibrium and desorption were studied over the temperature range 0–80°C. Equilibrium uptake was found to increase linearly with concentration in this range. Sorption-desorption kinetics showed the diffusion coefficients to decrease with increasing concentration, although the extent of this dependence did not appear in itself to be temperature-dependent. The apparent diffusion coefficient obeyed the law D = D₀ exp {? E/RT} over the temperature range studied, giving E = 9.9 kcal./mole and D₀ = 0.45 cm.² sec.^?1. These values are compared with corresponding values for other polymers.     

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.     

Sorption and diffusion of organic vapors in amorphous Teflon AF2400

Vapor sorption in amorphous Teflon AF2400 of various organic solutes was studied in a wide range of activity at 25 °C by means of the gravimetric technique. The sorption isotherms of hexane, toluene, and chloroform were shown to be concave to the pressure axis and are consistent with the dual mode sorption model (DMS). The parameters of the DMS model k_D and b reveal a linear correlation with squared critical temperature of solutes T. The third model parameter, the Langmuir sorption capacity C′_H decreases when the size of solutes (critical volume) increases. Sorption isotherms of methanol and ethanol were shown to be convex to the pressure axis and are consistent with cluster formation in this strongly hydrophobic polymer. Concentration‐dependent diffusion coefficients D were determined using a linear implicit difference scheme in analysis of sorption kinetics. It was shown that D values increase exponentially with concentration for all the solutes, except alcohols for which exponential reduction of D(C) was observed. The partitioning of the thermodynamic and mobility contributions in D indicated that the reduction of D values of alcohols is consistent with clustering phenomena in AF2400. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 832–844, 2006     

Temperature and concentration dependence of diffusion coefficients in ethylene–propylene-diene copolymers

Self-diffusion and partition coefficients were measured for two commercial ethylene–propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713–1719, 1998     

Sorption/diffusion behaviour of anionic surfactants in polyacrylamide hydrogels: from experiment to modelling

The sorption and diffusion processes of anionic surfactants with different chain length through polyacrylamide hydrogels with low swelling degree have been studied by electrical conductivity measurements. The multicomponent equilibrium equation has been used to model the sorption isotherms of different anionic surfactant in the hydrogels. Such isotherms show that initial rapid sorption of unimer surfactant into the membranes occurs, suggesting that non-freezing water can be involved in these interactions. In aqueous solution, at concentrations near and above the critical micelle concentration an anti-co-operative region is found. The diffusion coefficients of the anionic surfactants inside the hydrogel matrix show that the mobility of diffusing surfactant entities is dependent on cross-linker concentration and chain length. The Cukier hydrodynamic model and the free volume theory as modified by Peppas and Reinhart were applied to explain the dependence of the diffusion coefficients of surfactant on surfactant concentration inside the hydrogel. The hydrodynamic model was applied with success to the more hydrophilic surfactant, sodium 1-octanesulfonate, showing that the diffusion coefficients, D, increase when the resistance to hydrodynamic medium decreases; when the surfactant chain length increases (sodium dodecyl sulfate and sodium 1-hexadecane sulphonate) the variation of D with the free volume can only be understood considering the sieving effect produced by the surfactant inside gel.     

Nonstationary diffusion of polystyrenes through a cellophane membrane

Diffusion of five polystyrene fractions at various concentrations in toluene through cellophane membranes has been observed. The results have been used to calculate friction coefficients between solvent and solute, and between solute and membrane. The calculation requires measurement of the diffusion coefficient and the reflection coefficient of the solute, of the permeability for the solvent, of the pore volume of the membrane, and of the partition coefficient of the solute between membrane and solvent. By comparing the friction coefficient between solvent and solute in the membrane with this coefficient in free solution, the tortuosity factor and the pore diameter of the membrane can be estimated. The dependence of the friction coefficients on molecular weight M₂ of the solute is determined. For large values of M₂, the friction between solute and solvent is the determining factor. The friction coefficient between solute and solvent increases more strongly with M₂ in the membrane than in free solution owing to an entrance effect for the permeating solute at the interface.     

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.     

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.