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.     

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.     

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.     

Diffusing probe measurements in Newtonian and elastic solutions

The diffusion coefficients of polystyrene latex spheres and hematite particles in both Newtonian and elastic liquids have been measured using dynamic light scattering. The diffusion coefficients of the latex particles measured in glycerol/water (Newtonian) solutions obey Stokes–Einstein behaviour over a range of solvent viscosities and temperatures. Two apparent diffusion coefficients for the particles are measured in visco-elastic polyacrylamide and polyacrylate solutions and are designated D_fast and D_slow. The apparent fast diffusion coefficients measured in the elastic solutions show an increase to a maximum, above that measured in the solvent water, with increasing polyelectrolyte concentration. At higher polyelectrolyte concentrations the observed D_fast values decrease below the value obtained in the solvent water. D_fast increases with the scattering vector squared (q²) while D_slow, is independent of q².     

PGSE‐WATERGATE,a new tool for NMR diffusion‐based studies of ligand–macromolecule binding

A new pulsed gradient spin‐echo NMR diffusion sequence, PGSE‐WATERGATE, which is based on the extremely efficient WATERGATE solvent suppression sequence, is presented. The sequence is simple to set up and particularly suited to measuring the diffusion coefficients of small ligands in aqueous solution such as is commonly required in pharmaceutical and combinatorial applications. It also affords the possibility of measuring the diffusion of exchangeable resonances, which is often impossible in conjunction with other suppression schemes. Further, a trivial modification of the sequence affords the possibility of multiple solvent suppression, thereby increasing its suitability to LC–NMR applications. The utility of the sequence is demonstrated on the salicylate–bovine serum albumin system. The dissociation constant, K_d, and the number of binding sites were found to be 0.030 M and 33, respectively. Importantly, the extremely high degree of suppression provided by the new sequence allowed the salicylate diffusion coefficients to be measured over a very wide concentration range sufficient to show that the salicylate–bovine serum albumin system is not well described by a simple two‐site model. Previous studies in the literature have been based on data from a smaller concentration range, for which this model gives an apparently good fit. Copyright © 2002 John Wiley & Sons, Ltd.     

Sorption and diffusion of methanol and water in PVDF‐g‐PSSA and Nafion® 117 polymer electrolyte membranes

Sorption and diffusion properties of poly(vinylidene fluoride)‐graft‐poly(styrene sulfonic acid) (PVDF‐g‐PSSA) and Nafion® 117 polymer electrolyte membranes were studied in water/methanol mixtures. The two types of membranes were found to have different sorption properties. The Nafion 117 membrane was found to have a maximum in‐solvent uptake around 0.4 to 0.6 mole fraction of methanol, while the PVDF‐g‐PSSA membranes took up less solvent with increasing methanol concentration. The proton NMR spectra were recorded for membranes immersed in deuterated water/methanol mixtures. The spectra showed that the hydroxyl protons inside the membrane exhibit resonance lines different from the resonance lines of hydroxyl protons in the external solvent. The spectral features of the lines of these internal hydroxyl groups in the membranes were different in the Nafion membrane compared with the PVDF‐g‐PSSA membranes. Diffusion measurements with the pulsed field gradient NMR (PFG‐NMR) method showed that the diffusion coefficient of the internal hydroxyl groups in the solvent immersed Nafion membrane mirrors the changes in the diffusion coefficients of hydroxyl and methyl protons in the external solvent. For the PVDF‐g‐PSSA membranes, a decrease in the diffusion coefficient of the internal hydroxyl protons was seen with increasing methanol concentration. These results indicate that the morphology and chemical structure of the membranes have an effect on their solvent sorption and diffusion characteristics. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3277–3284, 2000     

Solvent effects in molecular complexes of porphyrins and metalloporphyrins

The apparent stability constants for porphyrin and metalloporphyrin complexes with an electron acceptor have been determined in mixed solvents. The variation of the apparent stability with solvent composition is evaluated in terms of solvation of the complex and reactant species and in terms of the exclusion of the solvent from the solvation sheath of the reactants, according to the equilibrium AS _a +DS _b =CS _x +yS.     

Matched ring diblock and linear triblock copolymers in dilute solution

A unique diblock copolymer ring and its linear triblock copolymer precursor composed of polystyrene and polydimethylsiloxane have been characterized by static and dynamic light scattering in dilute solution. The measurements were carried out with cyclohexane as the solvent over a temperature range of 12–35°C. Cyclohexane has the useful property that it is nearly isorefractive with the PDMS so that the PDMS block segments are invisible to the light-scattering technique and it is a theta solvent for polystyrene at 34.5°C. The block polymers in this work contain 35.1 wt % of styrene as determined by proton NMR. In the linear triblock polymer, the polystyrene is the center block with PDMS blocks on each side. Static light scattering measurements give 4.31 × 10⁴ for the average molecular weight of the whole polymer. Light scattering also shows that the apparent theta temperature for the linear triblock is shifted by 15°C to a value of 20°C at which point the second virial coefficient drops sharply and phase separation begins to induce aggregation. The diblock ring, however, shows a strongly positive second virial coefficient and no aggregation even at 12°C which is the limit of these experiments. The diffusion coefficients of cyclic diblock (D_c) and linear triblock copolymer (D₁) are measured by dynamic light scattering. The ratio of diffusion coefficients of cyclic and linear copolymers at 14.9°C and 30°C are D_c/D_l = 1.13 and 1.107 respectively. These compare well with prediction of 1.18 for this ratio from consideration of the hydrodynamics of matched linear and cyclic polymer chains. Dynamic light scattering quantitatively confirms that the linear copolymer experiences a solvent quality change near 20°C but the cyclic polymer remains in good solvent over the entire experimental temperature range. © 1993 John Wiley & Sons, Inc.     

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.     

Effect of molecular weight on the diffusion coefficient of carbon dioxide in polystyrene

The permeability and time lag at pressures below 1 atm were measured for carbon dioxide in five polystyrene samples with different molecular weights at 25 to 40°C. The apparent permeability coefficient decreases with increasing carbon dioxide pressure and also decreases with increasing molecular weight of polystyrene, whereas the apparent diffusion coefficient calculated from time lag increases with pressure and is independent of molecular weight. Parameters for the partial-immobilization model were determined from the apparent diffusion and permeation coefficients by using a nonlinear least-squares optimization program without using sorption data. The results suggest that the void-saturation constant C′_H decreases as the molecular weight of the polymer increases or as the chain-end free volume decreases. The significance of these observation and their interpretation is discussed in terms of free-volume theory for glassy polymers.     

Effects of diffusion on the self-termination kinetics of isopropylol radicals in solution

Rate constants for the bimolecular self-reaction of isopropylol radicals [(CH₃)₂?OH] in various solvents are determined as functions of temperature by kinetic electron spin resonance. For hydrocarbon solvents they are well described by theoretical equations for reactions controlled by translational diffusion if diffusion coefficients of 2-propanol, a constant reaction distance, and a spin statistical factor of 1/4 are applied. Deviations from 2k_t ～ D at high diffusion constants agree with trends expected from recent theoretical models. For hydrogen-bonding solvents large negative deviations are observed. They are attributed to steric constraints and slower rotational diffusion of radical–solvent aggregates. The disproportionation-to-combination ratio of isopropylol increases with solvent viscosity. As previously for tert-butyl, this is explained by anisotropic reorientation during encounters. Further, rate data are given for the decarbonylation of the 2-hydroxy-2-methylpropanoyl radical and for several hydrogen abstraction reactions of isopropylol.     

Importance of the diamine reactant in the production of polyphosphonamides by the interfacial technique

The stirred interfacial polycondensation of phenylphosphonic dichloride and 1,6-hexanediamine has been studied as a function of several reaction variables. The reaction is rapid, being completed in less than 1 min. When organic solvent is varied and reactant molar ratio is varied with an excess of the acid chloride, yield is constant. When reactant molar ratio is varied polymer yield increases with increase in amine concentration. When reactant concentration is increased yield increases. With the addition of a soluble salt in the aqueous phase yield is increased. The above indicates that the diffusion of the amine to the reaction zone is of primary importance in determining polymerization rate and that the diffusion of the acid chloride is relatively unimportant. Polymer yield was found to be dependent on the pH of the amine in the aqueous phase. The observed trend is related to the apparent solubility of the amine in the aqueous phase such that the greater the apparent solubility of the amine, the less the polymer yield. Polymer molecular weight is found to be independent of reaction variables tested. Polymer was also formed from the condensation of phenylphosphonic dichloride with p-phenylenediamine, H₂N-D-NH₂ (where D is a 36-carbon hydrocarbon chain), 1,3-di-4-piperidylpropane, and 4-aminomethylpiperidine; phenyl phosphorodichloridate with 1,6-hexanediamine; chloromethyl phosphonic dichloride with 1,6-hexanediamine.     

Influence of associations on self-diffusion of styrene–methylmethacrylate random copolymers in semidilute acetone solution

The self-diffusion of four styrene–methylmethacrylate random copolymers dissolved in acetone, a thermodynamically bad solvent for the styrene sequences in the copolymer, were investigated by pulsed-field gradient NMR. The echo attenuations S_inc(q,t) are dominated by diffusion of clusters. At higher concentrations, physical gelation sets in (formation of a transient network), which is manifested in an anomalous, restricted diffusion at short observation times. The measured fluctuations of the positions of the chain segments in the transient network have an amplitude of about 100 nm. The free long-range diffusion attained at long observation times shows a much stronger concentration dependence than in the nonassociating solvent benzene. The results are in accord with light-scattering investigations. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2931–2939, 1998     

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.     

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.     

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.     

Properties of polystyrene-poly(methylmethacrylate) random and diblock copolymers in dilute and semidilute solutions

Solution properties for random and diblock copolymers of polystyrene (PS) and poly(methyl methacrylate) (PMMA) have been measured by dynamic and total intensity light scattering in solvents of differing quality. The results are compared with the corresponding properties for PS and PMMA homopolymers of similar molecular weight, in order to determine if interactions between unlike monomers are significant. The hydrodynamic radius (R_h) and diffusion second virial coefficient (k_d) for the random copolymer are found to be larger than the corresponding values for the homopolymers in a solvent which is near-theta for the two homopolymers, whereas no such effect is observed for the block copolymer. This suggests that most intrachain interactions occur a relatively short distance along the chain backbone. In a mutual good solvent R_h and k_d of the random copolymer are comparable to the average of the values for the homopolymers, indicating that in a good solvent monomer/solvent interactions dominate over monomer/monomer interactions. For an isolated diblock copolymer in a mutual good solvent, there is no evidence that interactions between unlike monomers lead to additional expansion of the entire molecule, as measured by R_h, nor expansion of the individual blocks as probed by light scattering with one block optically masked. However, at low but finite concentration there is evidence (the coefficients of the binary interaction terms in the viscosity and the mutual diffusion coefficient, and the second and third virial coefficients) that a weak ordering effect may exist in block copolymer solutions, far from the conditions where microphase separation occurs. Finally, measurements of ternary polymer-polymer-solvent solutions show no dependence on monomer composition or monomer distribution for the tracer diffusion of probe PS-PMMA copolymers in a PMMA/toluene matrix. This indicate that the frictional interaction is largely unaffected by interactions between unlike monomers. However, there is evidence that the thermodynamic interaction is more unfavorable between a random copolymer and the homopolymer matrix than between a diblock and the matrix. © 1994 John Wiley & Sons, Inc.     

Swelling equilibrium and sorption kinetics of urethane-modified bismaleimides elastomer

The swelling equilibrium and diffusion kinetics in various solvents of the maleimide-terminated polyurethanes (UBMIs) and of the triol and tetraol-crosslinked polyurethanes (PU) were studied. The polymer volume fraction of the UBMIs at swelling equilibrium is much higher than that of the tetraol-crosslinked PU networks for the same type of polyol used in the PU. It was explained by the high functionality of the UBMIs produced in the network structure. Furthermore, the molecular weight between crosslinks (M_c) has been calculated from the swelling model and the results exhibit good agreement with the proposed network structure. The early time sorption kinetic data were obtained to investigate the diffusion mechanism of the solvent in the networks. The solubility, diffusion coefficients, and permeability of the solvent in UBMI networks were found to be lower than in the multiol-crosslinked PU networks. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1747–1755, 1997     

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

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

Polarography of some anions in aqueous organic solvent mixtures

The present investigation deals with the polarographic behaviour of iodate ions in various aqueous mixtures of methanol, ethanol, n-propanol, iso-propanol, 1,2-propanediol, 1,3-propanediol, and glycerol at 30°C. 0.1M-NaOH was used as a base electrolyte. The half-wave potential ranges from 1.24 to 1.46 and the diffusion current decreases with increasing percentage of the solvent. The plots ofi _d vs. andi _d vs.c were linear and pass through origin for all the solvent mixtures, showing that the limiting current is diffusion controlled. The plots of logi/(i_d–i) vs.E _d.e. were linear for all the aqueous organic solvent mixtures, but the value of slope suggested that the reductions are irreversible. The electrode kinetics was studied byKoutecky's method for irreversible electrode process.