Self-diffusion In Solutions Research Articles

Diffusion Coefficients of Variable-Size Amphiphilic Additives in a Glass-Forming Polyethylene Matrix.

Diffusion of additives in polymers is an important issue in the plastics industry since migratory-type molecules are widely used to tune the properties of polymeric composites. Predicting the diffusional behavior of new additives can minimize the need for repetitive experiments. This work presents molecular dynamics simulations at the microsecond time scale and uses the MARTINI force field to estimate self-diffusion coefficients, D, of six monounsaturated amides and their analogs carboxylic acids in polyethylene matrices (PE, MW = 5600 Da). The results are strongly influenced by the glass-forming properties of the PE matrix, which we characterize by three distinct temperatures. The metastability region (T < 325 K), the glass transition temperature (Tg = 256-260 K), and the end of the transition (T ≅ 200 K). Self-diffusion mechanisms are inferred from the results of the dependence of D on the molecular mass of the additive, observing a Rouse-like behavior at high temperatures and deviations from it within the metastability region of the matrix. Interestingly, D values are nonsensitive to the nature of the considered polar head for additives of similar size. The temperature-dependent behavior of D follows, at fixed additive size, a linear Arrhenius pattern at high temperatures and a super Arrhenius trend at lower temperatures, which is well represented with a power law equation as predicted by the Mode Coupling Theory (MCT). We offer a conceptual explanation for the observed super-Arrhenius behavior. This explanation draws on Truhlar and Kohen's interpretation of the available energies at both the initial and the transition states along the diffusion pathway. The matrix's mobility significantly affects solute self-diffusion, yielding equal activation enthalpies for the Arrhenius region or the same power law parameters for the super-Arrhenius regime. Finally, we establish a one-to-one time-equivalence of the self-diffusion processes between CG and all-atom systems for the largest additives and the PE matrix in the high-temperature regime.

Self-diffusion of aromatic compounds in the carbon tetrachloride – acetone binary system. NMR experiment and MD simulation

In this work, we studied the influence of the structure of molecules of aromatic compounds (methylparaben (MP), propylparaben (PP), syringic acid (SA), gallic acid (GA), protocatechualdehide (PAL), p-coumaric acid (p-CA), and caffeic acid (CA)) on their molecular association and self-diffusion in the binary carbon tetrachloride – acetone solvent. The self-diffusion coefficients of PAL, SA, and GA in the binary carbon tetrachloride – acetone‑d6 solvent were measured by the pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) method at temperatures of 288, 298, and 308 K. The data obtained at 298 K were also compared with the data on the self-diffusion coefficients of MP, PP, CFA, and p-CA in the binary solvent available in the literature. According to the presented data, the self-diffusion coefficients of all the substances under consideration become greater with an increase in the acetone‑d6 concentration and decrease in the MP > PAL > PP > p-CA > SA > CA > GA series of compounds. Quantitative assessment of the degree of influence of molecular association on solute self-diffusion was carried out within the framework of a method based on the ratio of the self-diffusion coefficient of a solute to the self-diffusion coefficient of its monomers. The study shows that the degree of influence of molecular association of the solute on its self-diffusion is determined by the number and type of active functional groups in the structure of the solute molecules (MP < PP < PAL < SA < p-CA < CA < GA), but does not depend on the composition of the binary solvent. According to the results of molecular dynamics (MD) simulation, this effect correlates with the increase in the degree of self-association of solutes and decrease in the degree of solute – acetone heteroassociation observed when the carbon tetrachloride concentration becomes higher. This effect is also responsible for the similar concentration dependencies of the self-diffusion coefficients of active and inert compounds.

Self-diffusion of nonspherical particles fundamentally conflicts with effective sphere models

Modeling diffusion of nonspherical particles presents an unsolved and considerable challenge, despite its importance for the understanding of crowding effects in biology, food technology and formulation science. A common approach in experiment and simulation is to map nonspherical objects on effective spheres to subsequently use the established predictions for spheres to approximate phenomena for nonspherical particles. Using numerical evaluation of the hydrodynamic mobility tensor, we show that this so-called effective sphere model fundamentally fails to represent the self-diffusion in solutions of ellipsoids as well as rod-like assemblies of spherical beads. The effective sphere model drastically overestimates the slowing down of self-diffusion down to volume fractions below 0.01. Furthermore, even the linear term relevant at lower volume fraction is inaccurate, linked to a fundamental misconception of effective sphere models. To overcome the severe problems related with the use of effective sphere models, we suggest a protocol to predict the short-time self-diffusion of rod-like systems, based on simulations with hydrodynamic interactions that become feasible even for more complex molecules as the essential observable shows a negligible system-size effect.

Influence of the number and type of functional groups on self-diffusion of some aromatic compounds in acetone: Nuclear magnetic resonance and molecular dynamics simulations

Self-diffusion of parabens (methylparaben and propylparaben), phenolic acids (syringic and gallic acids) and their derivative (protocatechualdehyde), hydroxycinnamic acids (caffeic, ferulic, sinapic, and p-coumaric acids), and tetramethylsilane in acetone has been investigated by the pulsed gradient spin-echo nuclear magnetic resonance (PGSE NMR) method and molecular dynamics simulation in ambient conditions. The self-diffusion coefficients obtained by the experimental and theoretical methods are in good agreement with each other. A detailed analysis of the average number of solute – acetone hydrogen bonds has made it possible to trace the influence of the molecular heteroassociation on the self-diffusion of the aromatic compounds. The degree of influence of solute – acetone molecular association on the solute self-diffusion defined as the ratio of the solute self-diffusion coefficient to the self-diffusion coefficient of its monomer has been calculated using the Stokes-Einstein equation. It has been found that for a number of aromatic compounds with the same type and number of functional groups, the parameter expressing the degree of influence of molecular association has similar values. This fact has allowed us to calculate the self-diffusion coefficients of the compounds in the given series at a known self-diffusion coefficient value of one of the series members.

Dispersion of a passive tracer in the pressure-driven flow of a non-colloidal suspension.

This paper numerically quantifies the dispersion of a solute, and in particular, the Taylor dispersion, in the pressure-driven flow of a non-colloidal suspension at moderately high volume fractions (0.2 to 0.5) through conduits of different cross-sectional shapes. An obvious intuition is that the Taylor dispersivity should increase owing to a decrease in the molecular diffusivity of the solute in the presence of particles impermeable to the solute; however, this is true only at low volume fractions. At higher volume fractions, three other physical effects become important, all of which lead to a reduction in Taylor dispersivity relative to a Newtonian fluid. The first is the blunting of the velocity profile resulting from particle migration into the low shear-stress regions, an effect that has been alluded to in the past by Roht et al. [J. Contam. Hydrol., 2013, 14, 10] and is important only at low Péclet numbers (Pe). At higher Pe, the two stronger effects are shear-induced solute self-diffusion, which arises due to shear-induced particle-particle interactions, and secondary convection, which is observed in non-axisymmetric cross-sections as a result of the second normal stress differences exhibited by concentrated suspensions. For a given volume fraction and cross-sectional geometry, a regime map, developed using a scaling analysis, delineates five regimes of dispersion involving one or a combination of the mass transfer mechanisms mentioned above. Our analysis also suggests that the cross-sectional shape can be exploited to enhance or suppress solute dispersion by modifying the secondary current strength and profile.

Towards elucidation of the drug release mechanism from compressed hydrophilic matrices made of cellulose ethers. I. Pulse-field-gradient spin-echo NMR study of sodium salicylate diffusivity in swollen hydrogels with respect to polymer matrix physical structure

Cellulose ethers have been increasingly used in the formulation of controlled release dosage forms; among them, compressed hydrophilic matrices for the oral route of administration are of special importance. Much interest has also been expressed in the study of the drug release mechanism from such swellable systems, in particular, in trying to explain deviations from Fickian diffusion. Thus, swelling-controlled transport is often invoked without any rationale. It is the purpose of the present work to provide independently determined diffusivity data for elucidating the drug release mechanism from the water-soluble cellulose derivatives. In the first part of this work, pulsed-field-gradient spin-echo nuclear magnetic resonance (PFG-SE NMR) was used to investigate the self-diffusion of the model solute sodium salicylate and, incidentally, that of water, in hydrogels made of hydroxypropyl methylcellulose (HPMC), hydroxyethylcellulose (HEC) and hydroxypropylcellulose (HPC) of varying polymer weight fraction and molecular weight in D 2O. In parallel, the extent of bound water in the gels was determined using differential scanning calorimetry (DSC), and the presence of liquid crystals in the gels was examined by polarized light microscopy, as these are the structural factors capable of affecting drug diffusion. Solute diffusivity was not significantly affected by the substitution type of the cellulose ether, and an exponential polymer weight fraction dependence of the solute's self-diffusion coefficient was observed, ascertaining the validity of the free-volume theory, with extrapolated self-diffusion coefficient values similar to those in pure solvent. This also indicates that diffusion also takes place in the so-called bound water (which represents about 40% of the hydrogel weight). This questions the existence of thermodynamically different classes of water. Slightly reduced solute diffusion was measured in the HPC hydrogel of the highest polymer concentration (45 wt.%) where a liquid crystalline mesophase was observed. This structural factor could be of importance, especially in consideration of hydrogels of higher polymer fractions. The polymer molar mass (viscosity grade) of the cellulose ethers also did not affect solute self-diffusivity. The polymer matrix displayed the same retarding effect at equal weight fraction. This confirms that solute molecules can only diffuse in the void space occupied by the solvent. Solute self-diffusivity is dictated by the microviscosity of the system, i.e., the solvent viscosity, with the polymeric matrix increasing only the diffusion pathlength. Overall, because of the similar retarding effects of the hydrated cellulose ether network, at least at the polymer concentrations tested, it would be unwise to ascribe observed differences in drug release kinetics from this type of swellable system to differences in solute diffusivity in the hydrated gel layer (see Part II of the work [J. Control. Release, to be submitted]).

Self-diffusion in solutions of carboxylated acrylic polymers as studied by Pulsed Field Gradient NMR. 2. Diffusion of macromolecules

The diffusion constants of carboxylated acrylic copolymers in isopropanol (IPA) have been investigated using the PFG NMR technique. A range of compositions of butyl methacrylate and methacrylic acid random copolymers (BMA–MAA 100/0 through to 60/40 in 10 mol% steps) have been studied. The polymer diffusivity is two orders of magnitude slower than that for the solvent. A maximum value of G max = 10 T/m for the gradient pulse was used to suppress solvent signal and to measure the low value of the self-diffusion coefficient for the polymers. Polymer diffusion studies at different diffusion times showed that the diffusion constant decreased with increasing diffusion time. The influence of the concentration on the polymer aggregation in solution and the influence of the BMA/MAA molar ratio on the diffusion constants of the polymer have been studied. The diffusion constant for the polymer at long diffusion times increased with mol% BMA which is similar to the short diffusion time studies. The data obtained have been discussed using published results and models for “anomalous diffusion” of macromolecules in polymer solutions.

Self-diffusion in Solutions of Carboxylated Acrylic Polymers as Studied by Pulsed Field Gradient NMR. 1. Solvent Diffusion Studies

The diffusion constants of solvent in solutions of carboxylated acrylic random copolymers in isopropanol (IPA) have been investigated using the PFG NMR technique. The copolymers are composed of butyl methacrylate and methacrylic acid with a range of molar ratios (BMA/MAA 100/0 through to 60/40 in 10 mol% steps). It was found that the echo attenuation function depended on the diffusion time, and experiments with short and long diffusion times have been analysed separately. Two questions are addressed: the first concerns the influence of concentration on the polymer aggregation in solution, and the second concerns the influence of the BMA/MAA molar ratio on the diffusion constants of the solvent. The data obtained have been discussed using established physical models for diffusion. Using the model of Wang gave the relative mass of bound solvent per mass of polymer which increased with the mol% of MAA in the copolymer.

Viscosity of a binary mixture: Approach to the hydrodynamic limit

We have used equilibrium and nonequilibrium molecular dynamics simulations to study the solute self-diffusion coefficient and the shear rate dependence of the solution viscosity in solutions of model nanocolloidal particles that range in mass ratio from mu=1 up to mu=50 and size ratio from s=1 up to s=4.03 at various concentrations. The zero shear rate viscosities and the initial rates of shear thinning were determined from data in the shear rate region in which the suspension is strongly shear thinning while the solvent remains Newtonian or is weakly shear thinning. The rate of shear thinning increased dramatically with solute volume fraction, regardless of whether the increase was due to increasing solute size or increasing the solute concentration. In a series of simulations in which the mass ratio was varied while keeping the size ratio fixed at s=1, we found that the approach of the viscosities and self-diffusion coefficients to their limiting mass ratio independent values was well described by a rather simple exponential dependence on mass ratio. The concentration dependence of the limiting infinite mass ratio values of the self-diffusion coefficients and zero shear rate viscosities were determined, and used to compute the hydrodynamic radius RH of the solute particles by various methods. The values of RH that were obtained by the different methods were reasonably consistent with each other, and indicated that the radius at which the slip boundary condition holds is slightly smaller than the cross-interaction radius between the solute and solvent particles.

Enhancement of solute self-diffusion in fcc alloys

Using a new simulation approach to the calculation of correlation factors in very dilute solutions, the present paper reports on results of the first calculations of the first and second solute enhancement factors for solute self-diffusion in the fourteen-frequency model postulated by Bocquet for describing the diffusion kinetics of paired and unpaired solute atoms in dilute fcc alloys. Bocquet's assumption that correlation effects do not contribute to solute self-diffusion enhancement is shown to have a fairly limited range of validity. Specifically, it is shown that this assumption is reasonable when the solvent–vacancy exchange frequency far from the solute is high compared with the others or when all of the solute–vacancy exchange frequencies are small compared with the others. The assumption is also reasonable when the vacancy is not attracted to the solute atoms and when the vacancy does not often alternate between two solute atoms. The present study would strongly suggest that many of the ratios of exchange frequencies that have been determined from experimental data on the basis of this assumption are likely to be in error.

Self-diffusion in solutions of a 20 base pair oligonucleotide: Effects of concentration and ionic strength

The long-time self-diffusion coefficients of a 20 base pair duplex oligonucleotide are measured as functions of 20-mer and added NaCl salt concentrations. The self-diffusion coefficients decrease monotonically with increasing 20-mer concentrations for the high-added salt sample and display non-monotonically decreasing 20-mer concentration dependences at lower added salt concentrations. The non-monotonic behavior is attributed to the opposing effects of the tendency to increase the interactions between 20-mers as the concentration is increased and to a decrease in the extent of the Coulomb forces as counterions from the 20-mer increasingly screen them. Attempts to account for the effect of the Coulomb forces on the self-diffusion coefficients by using effective dimensions in the hard rod theory give good agreement with experiment at the highest salt concentration studied. For the lower salt concentrations there appear to be two scaling regimes--one at low polyion concentration in which the high salt scaling of the rod dimensions by adding the Debye screening to the length and diameter of the rod is appropriate and one at high polyion concentrations where the scaling of the dimensions is the addition of 1/2 the Debye screening length. Estimates of the "overlap" concentration C*=1/L(eff) indicate that the non-monotonic decrease occurs at concentrations lower than C*. Finally, the fluorescence correlation spectroscopy self-diffusion coefficients measured here are compared with the mutual diffusion coefficients measured by dynamic light scattering.

A self-diffusion study in aqueous solution and lyotropic mesophases of amphiphilic block copolymers

Water-soluble poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) (PEO–PPO–PPO) triblock copolymers are high-molecular-weight nonionic copolymers and form micellar solutions and liquid-crystalline mesophases in water. We studied the temperature dependence of polymer and water self-diffusion in solutions and lyotropic mesophases of the PEO13 PPO30 PEO13/water and PEO21 PPO47 PEO21/water binary systems. The self-diffusion measurements were performed by means of the pulsed field gradient spin-echo NMR method. The analysis of the water mobility was realised using “the obstruction factor” and “the two-site model”, which consider the reduction of the water self-diffusion due to the microstructure of the lyotropic aggregates and to the presence of one part of the solvent bound to the polymer aggregate surfaces. We calculated the water obstruction factors and the hydration numbers as a function both of the polymer composition and of the temperature. The results are compared with the data obtained in mesophases formed by classical surfactants.

A self-diffusion study of poly(ethylene-oxide) alkyl alcohols

The self-diffusion coefficients of HDO and some surfactants in aqueous mixtures at different concentrations, below the critical micelle concentration, have been determined by means of the NMR, spin-echo pulsed field gradient method. The surfactant solutes chosen were ethylene glycol-pentyl alcohol (diethylene glycolpentylalcohol, ethylene glycol-hexyalcohol, diethylene glycol-hexyl alcohol, triethylene glycol-hexyl alcohol, tetraethylene glycol-hexyl alcohol, pentaethylene glycol-hexyl alcohol). The interactions in solution are studied by analyzing the solute self-diffusion coefficients extrapolated to infinite dilution. These values are compared with those of 1-alkanols. The slope of the self diffusion coefficientsvs. the solute concentration are correlated with the microscopic friction coefficients. A model for interpreting the experimental data is suggested.

Toluene self-diffusion in solutions of linear and crosslinked polystyrene

Toluene self-diffusion coefficients in solutions of linear and crosslinked polystyrene (PS) at concentrations up to 30 wt% polymer have been determined over the temperature range 143–230 K using the 1H n.m.r. static gradient stimulated echo method. At similar polymer concentrations, the diffusion coefficient values of toluene were higher for mixtures with crosslinked PS than for solutions containing linear PS. On cooling and approaching the solution glass transition, the amplitude decays in diffusion and spin-relaxation measurements become non-exponential and are interpreted in terms of a two-component decomposition. The estimated fraction of the toluene motionally bound to polymer increases on temperature reduction and is less for mixtures containing crosslinked PS beads.

Brownian dynamics simulations of probe and self-diffusion in concentrated protein and DNA solutions

We have developed a Brownian dynamics algorithm for simulating probe and self-diffusion in concentrated solutions of DNA and protein. In these simulations, proteins are represented as spheres with radii given by their hydrodynamic radii, while DNA is modeled as a wormlike chain of hydrodynamically equivalent spherical frictional elements. The molecular interaction potentials employed by the program allow for intramolecular stretching and bending motions of the DNA chains, short-range Lennard-Jones interactions, and long-range electrostatic interactions. To test the program, we have carried out simulations of bovine serum albumin (BSA) probe diffusion and DNA self-diffusion in solutions of short-chain DNA as a function of both DNA concentration and solution ionic strength. In addition, we report on simulations of BSA self-diffusion as a function of BSA concentration and ionic strength. Based on a comparison to available experimental data, we find that our simulations accurately predict these transport properties under conditions of physiological salt concentration and predict the stronger concentration dependence observed at lower salt concentrations. These results are discussed in light of the nature of the intermolecular interactions in such systems and the approximations and limitations of the simulation algorithm.

Self-diffusion in solutions of the polyblock polysulphone-polybutadiene copolymer

Self-diffusion of macromolecules of the polyblock copolymer polysulphone-polybuttadiene in a mixture of common and selective solvents has been studied by NMR with a pulse magnetic field gradient. In the solutions an essentially non-exponential form of the diffusional attenuations of the magnetization was found indicating a wide distribution of the self-diffusion coefficients. Its form is well approximated by a logarithmically normal distribution function. The width of the distribution σ grows with increase in the fraction of selective solvent. The large σ values are explained by the existence of longlived clusters characteristics of gel-forming systems. The concentration dependences of the mean self-diffusion coefficient are discussed. These dependences for a high content of selective solvent have an anomalous form and are explained from the phase of the solutions.

Self-diffusion in solutions of polystyrene in tetrahydrofuran: comparison of concentration dependences of the diffusion coefficients of polymer, solvent, and a ternary probe component

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSelf-diffusion in solutions of polystyrene in tetrahydrofuran: comparison of concentration dependences of the diffusion coefficients of polymer, solvent, and a ternary probe componentErnst D. Von Meerwall, Eric J. Amis, and John D. FerryCite this: Macromolecules 1985, 18, 2, 260–266Publication Date (Print):February 1, 1985Publication History Published online1 May 2002Published inissue 1 February 1985https://doi.org/10.1021/ma00144a024RIGHTS & PERMISSIONSArticle Views809Altmetric-Citations87LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (885 KB) Get e-Alerts Get e-Alerts

Self diffusion in solutions of polyvinyl chloride and polystyrene with phthalates

The self diffusion of phthalate molecules and macromolecules has been investigated in PVC and PS solutions with low polymer contents, using a pulse NMR method. The coincidence appearing in regard to activation energies of self diffusion of the macromolecules and phthalate molecules is explained on the basis of the Frenkel theory. It is proposed that the dissolved macromolecules play the role of traps for rapidly diffusing solvent molecules. It is shown that the translational mobility of phthalate molecules in the temperature region examined is mainly determined by activated jumps. The space network in PVC gels does not influence the mobility of phthalates.

Comparative investigation of the diffusion and viscosity behaviour of polybutadiene solutions

A study was made of the concentration dependence of the viscosity and the coefficients of inter- and self-diffusion of solutions of monodisperse polybutadienes in “poor” and “good” solvents over the enitre range of compositions at different temperatures. A relationship between the coefficients of inter- and self-diffusion was found by taking account of the concentration dependence of solvent activity. The micro-viscosity and monomeric coefficients of friction were determined for polybutadienes in solution. The relationship between micro-viscosity and the molecular weight of the polymers was investigated. A correlation was found between the monomeric coefficient of friction and the size of the diffusing molecule.