Effect of the solvent upon the diffusion coefficient of polydisperse polystyrene and styrene-acrylonitrile copolymer in dilute solution

A laser homodyne spectrometer was used to obtain translational diffusion coefficients for dilute polystyrene and styrene-acrylonitrile copolymer solutions at room temperature. Data were obtained in the concentration range from 0.01 to 2.0 g polymer per 100 cm³ solution for polystyrene in benzene and in decalin; and for copolymer in dimethyl formamide, in methyl ethyl ketone, and in benzene. The samples were polydisperse polystyrenes of weight average molecular weights between 80,000 and 350,000 and polydisperse copolymers of weight average molecular weights between 200,000 and 800,000. The SAN copolymers were random copolymer samples containing 24% by weight acrylonitrile. For each of the systems investigated the concentration dependence of the diffusion coefficient was linear over the concentration range studied, and was expressed as D(c) = D₀(1+k_Dc). Values of D₀ could be explained with a modified Kirkwood-Riseman expression. Values of the parameter k_D obtained from the slopes could be interpreted using the two-parameter theory approach as suggested by Vrentas and Duda. The value of k_D is positive for high-molecular-weight polymers and negative for low-molecular-weight polymers. For a particular polymer, the molecular weight at which k_D changes sign is greater for poor solvents than for good solvents. Observed values of D₀ were 1 × 10^?7 to 7 × 10^?7 cm²/sec.     

Chain dimensions and transport coefficients of sodium poly(isoprenesulfonate) in aqueous sodium chloride

Sodium poly(isoprenesulfonate) (NaPIS) fractions consisting of 1,4‐ and 3,4‐isomeric units (0.44:0.56) and ranging in molecular weight from 4.9 × 10³ to 2.0 × 10⁵ were studied by static and dynamic light scattering, sedimentation equilibrium, and viscometry in aqueous NaCl of a salt concentration (C_s) of 0.5‐M at 25 °C. Viscosity data were also obtained at C_s = 0.05, 0.1, and 1 M. The measured z‐average radii of gyration 〈S²〉_z^1/2, intrinsic viscosities [η], and translational diffusion coefficients D at C_s = 0.5‐M showed that high molecular weight NaPIS in the aqueous salt behaves like a flexible chain in the good solvent limit. On the assumption that the distribution of 1,4‐ and 3,4‐isomeric units in the NaPIS chain is completely random, the [η] data for high molecular weights at C_s = 0.5 and 1 M were analyzed first in the conventional two‐parameter scheme to estimate the unperturbed dimension at infinite molecular weight and the mean binary cluster integral. By further invoking a coarse‐graining of the NaPIS molecule, all the [η] and D data in the entire molecular weight range were then analyzed on the basis of the current theories for the unperturbed wormlike chain combined with the quasi‐two‐parameter theory. It is shown that the experimental 〈S²〉_z, [η], and D are explained by the theories with a degree of accuracy similar to that known for uncharged linear flexible homopolymers. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2071–2080, 2001     

Chain dynamics in entangled polymers: Diffusion versus rheology and their comparison

This review article scrutinizes and reanalyzes the extensively available literature data on the tracer and self chain diffusion coefficients D_tr and D_s along with the corresponding zero‐shear viscosity η₀ to show that D_s ∝ M^?ν starts with ν > 2.0 and converges to the asymptotic scaling exhibited by D_tr ∝ M^?2.0 as the molecular weight M increases beyond M/M_e = 10–20, in contrast to the onset of the asymptotic scaling M³ for η₀ taking place typically for M/M_e ? 10–20. A coherent analysis of these observations leads to the suggestion that the observed crossover in D_s is due to the constraint release effect, which diminishes around M/M_e = 10–20 and is negligible in measurements of D_tr when the matrix molecular weight P is much greater than M. The contour length fluctuation (CLF) effect, which is believed to cause the molecular weight scaling of η₀ to deviate significantly from its limiting behavior of M³, has little direct influence on the chain diffusion. The absence of the CLF effect on D_s leads to a much stronger than linear dependence of the product η₀D_s on M, which has been observed previously. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1589–1604, 2003     

Dynamic and electrophoretic light scattering of poly(dimethyldiallylammonium chloride) in salt-free solutions

Dynamic and electrophoretic light scattering were used to study the diffusion and electrophoretic mobility of poly(dimethyldiallylammonium chloride) as a function of polymer molecular weight in salt-free solutions. Two relaxation modes characterized as fast diffusion (D_f) and slow diffusion (D_s) were obtained from dynamic light scattering. Although the slow diffusion coefficient D_s strongly depends on molecular weight (M_w), the fast diffusion coefficient D_f was found to be independent of M_w over the range in the study. The fast diffusion was considered as the diffusion of a part of the polymer chain; the slow diffusion was interpreted by multichain diffusion. Electrophoretic light scattering results in the salt-free solution show that the electrophoretic mobility of the polymer is independent of M_w. © 1996 John Wiley & Sons, Inc.     

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.     

Scaling trend in diffusion coefficients of low generation G0–G3 PAMAM dendrimers in aqueous solution at high and neutral pH

Aqueous solution diffusion coefficients for G0–G3 PAMAM dendrimers were determined from DOSY-NMR spectroscopy at high and neutral pH. The study was performed in a dilute regime and diffusion coefficients at infinite dilution (D ₀) were estimated from the variation of diffusion coefficients with dendrimer concentration. Hydrodynamic radii (R _h) for each dendrimer were estimated from D ₀ using the Stoke–Einstein relationship at both pH. According to D ₀ and R _h values, the structure of G0–G1 PAMAM dendrimers is almost insensitive to pH variations, whereas G2–G3 PAMAM dendrimers undergo swelling at neutral pH, due to surface amino groups protonation. Experimental diffusion coefficients show a scaling trend with the number of dendrimer atoms (N), with scaling laws of the type D₀ μ N^a D_{0} \propto N^{\alpha } , where α takes values of −0.39 and −0.50 at pH 12 and 7, respectively. For the first time, experimental data accounts for the scaling behavior of aqueous diffusion coefficients for low generation PAMAM dendrimers, as previously reported from molecular dynamics simulations.     

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part IV. D(C)/D0=1+(αC)−β(αC)

Using the specific functional form D(C)/D₀=1+(αC)−β(αC)² an investigation has been made of (isothermal) transport through a slab membrane under ‘simple’ boundary conditions and governed by a diffusion coefficient, D(C), which, with increasing concentration, at first increases, passes through a maximum value and finally decreases. The flux, integral diffusion coefficient and concentration profile characteristic of steady-state permeation have been evaluated; special attention has been paid to the positions of such profiles in relation to the corresponding linear distribution associated with a constant diffusion coefficient.The corresponding transient-state transport has been studied within a framework of the time-lag ‘early-time’ and ‘ ’ procedures. Expressions for the ‘adsorption’ and ‘desorption’ time-lags are given. The concentration-dependence of these time-lags, of the (four) integral diffusion coefficients derived from them and of the arithmetic-mean time-lag ratios have been considered in some detail. The ‘early-time’ and ‘ ’ finite-difference procedures have likewise been employed to derive four further integral diffusion coefficients, so enabling a comparison to be made of the nine integral coefficients pertaining to established experimental techniques.Particular interest attaches to the situation for which n≡β(αC₀)=1 (where C₀ is the ingoing or upstream concentration of diffusant) resulting in D(C₀) being symmetrical about C₀/2. Some consideration has been given, in general, to features of transient-state transport when governed by a symmetrical D(C).     

Soret Coefficients for Aqueous Polyethylene Glycol Solutions and Some Tests of the Segmental Model of Polymer Thermal Diffusion

A thermogravitational cell is used to measure Soret coefficients (s) for dilute binary aqueous solutions of ethylene glycol, diethylene glycol, triethylene glycol, tetraethylene glycol, and polyethylene glycol (PEG) fractions with average molecular weights from 200 to 20,000 g-mol^–1. The cell design allows the top and bottom halves of the solution column to be withdrawn and injected into a high-precision HPLC differential refractometer detector for analysis. Previously reported mutual diffusion coefficients D and the measured Soret coefficients are used to calculate thermal diffusion coefficients D _T. s and D vary with the PEG molecular weight M as M ^+0.53 and M ^–0.52, respectively; hence, D _T = sD is essentially independent of M. The segmental model of polymer thermal diffusion predicts D _T = D_seg U _S/RT ², where D _seg is the segment diffusion coefficient, U _S the solvent activation energy for viscous flow, R the gas constant, and T the temperature. The predicted D _T values, although independent of M, are too large by a factor of five. Additional tests of the segmental model are provided using literature data for polystyrene + toluene, n-alkane + CCl₄, and n-alkane + CHCl₃ solutions. Agreement with experiment is not obtained. In particular, the measured D _T values for the alkane solutions are negative.     

A laser light-scattering study of the structure of agarose gels

Diffusion coefficients of dextran fractions within agarose gels surrounded by dextran solution have been measured by laser light scattering using the autocorrelation method. Plots were made of the diffusion coefficient relative to that in dilute solution, D/D₀, against the logarithm of hydrodynamic diameter logd for each concentration of agarose, and superimposed by displacing horizontally to produce a unified plot. In this way it was shown that D/D₀ is a function of C^bd, where C is agarose concentration, with b = 1/3 and 1/2 for the cases in which the dextrans were mixed in before gelation and allowed to diffuse in afterwards, respectively, the plots being the same for a reference concentration of 0.7%. A value of b = 1/2 is that which would be expected if the molecular weight per unit length of the gel fibers were independent of concentration, and a value of 25 kg mol^?1 nm^?1 is calculated. Mobile concentrations of dextran within the gels relative to those in the surrounding solutions were found by determining the scattered intensity associated with the diffusing dextran molecules from the zero-time value of the autocorrelation function. All results and calculations are discussed in terms of current theories, and compared with earlier work on calcium alginate gels for which a molecular weight per unit length of gel fiber of 0.59 kg mol^?1 nm^?1 was calculated. The nature of the spectral broadening of the light scattered from agarose gels in the absence of dextran is described.     

New External Calibration Curves (ECCs) for the Estimation of Molecular Weights in Various Common NMR Solvents

New external calibration curves (ECCs) for the estimation of aggregation states of small molecules in solution by DOSY NMR spectroscopy for a range of different common NMR solvents ([D₆]DMSO, C₆D₁₂, C₆D₆, CDCl₃, and CD₂Cl₂) are introduced and applied. ECCs are of avail to estimate molecular weights (MWs) from diffusion coefficients of previously unknown aggregates. This enables a straightforward and elaborate examination of (de)aggregation phenomena in solution.     

Surfactant Diffusion Near Critical Micelle Concentrations

Taylor dispersion and differential refractometry are used to measure mutual diffusion coefficients (D) for binary aqueous solutions of octylglucopyranoside, dodecylsulfobetaine, and sodium dodecyl sulfate (nonionic, zwitterionic and ionic surfactants, respectively). Aggregation causes a sharp drop in D as the concentration of each surfactant is raised through the critical micelle concentration (cmc). Differential mutual diffusion coefficients are determined in this composition region by using small initial concentration differences (3 mmol-dm^–3) and by extrapolating the measured D values to zero initial concentration difference relative to the carrier stream. The drop in D for each surfactant is more gradual than the concentration dependence predicted by the chemical equilibrium model of surfactant diffusion. Micelle polydispersity and nonideal solution behavior are discussed as possible explanations for this discrepancy. Intradiffusion coefficients (D*) for aqueous octylglucopyranoside and dodecylsulfobetaine are evaluated by integrating the relation d(cD*) = Ddc previously derived for dilute solutions of self-associating nonelectrolyte solutes.     

Ternary Solution Mutual Diffusion Coefficients and Densities of Aqueous Mixtures of Sucrose with NaCl and Sucrose with KCl at 25°C

Ternary solution isothermal mutual diffusion coefficients (interdiffusion coefficients) have been measured for aqueous mixtures of 0.250 mol-dm^–3 sucrose (component 1) with 0.5 and 1.0 mol-dm^–3 NaCl or with 0.5 and 1.0 mol-dm^–3 KCl (salt = component 2) at 25.00°C using Rayleigh interferometry with computerized data acquisition. Densities were also measured. The volume-fixed diffusion coefficients (D _ij)_V show the following characteristics. At all compositions (D ₂₁)_V is much larger than (D ₁₂)_V and (D ₂₁)_V is a fairly significant fraction (33 to 68%) of (D ₁₁)_V. In addition, (D ₁₂)_V is slightly larger for mixtures containing NaCl than for those containing KCl at the same concentration, whereas (D ₂₁)_V is significantly larger for mixtures containing KCl. Values of (D ₁₁)_V are slightly larger for solutions containing KCl than for solutions containing NaCl. The observed trends imply that (D ₂₁)_V will probably exceed (D ₁₁)_V in both mixtures if concentrations of NaCl or of KCl are increased much further while maintaining the sucrose concentration at 0.250 mol-dm^–3. Finally, the solvent-fixed cross-term diffusion coefficients (D ₁₂)₀ and (D ₂₁)₀ are significantly larger than their corresponding (D ₁₂)_V and D ₂₁)_V.     

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.     

The effect of the electrolyte concentration in the solution on the voltammetric response of insertion electrodes

A solid-state redox reaction involving an insertion of ions is analyzed with respect to the influence of the concentration of inserting ions in the solution phase. The voltammetric response is independent of the mass transfer in the solution provided that z = (D _ss/D _aq)^1/2 ρ/[C⁺]* is smaller than 0.1 (D _ss: diffusion coefficient of the cation C⁺ in the crystal; D _aq: diffusion coefficient of the cation C⁺ in the solution; ρ: density of the solid compound; [C⁺]*: concentration of cations in the bulk of the solution). In real cases this condition will be satisfied at solution concentrations above 1 mol/l. Received: 15 December 1997 / Accepted: 5 March 1998     

Self diffusion and viscoelasticity of elongated micelles from cetyltrimethyl-ammonium bromide in aqueous sodium salicylate solution. II. Temperature effect

Forced Rayleigh scattering and dynamic viscoelastic experiments are performed to study slow global motions of networks formed by elongated micelles from cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at six temperatureT from 25° to 60°C. The CTAB concentrationC _D of the solutions is fixed atC _D=0.01 M and a ratio of salt concentrationC _s toC _D is varied from 1 to 41. The self-diffusion coefficientD of the dye-labeled cetyldimethylamine incorporated in the micelles shows a complicatedC _s/C _D dependence with a maximum that is followed by a minimum at lower temperatures, but these two extremes gradually disappear with increasingT. TheC _s/C _D dependencies of both the steady-state viscosity and the terminal relaxation time are found consistent with the diffusion behaviour. TheD of all solutions tested monotonically increases withT, but shows different functional dependence onT asC _s/C _D varies. The applicability of the theory of Brownian motion of a rigid rod in the semidilute regime is examined usingD and values.     

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.     

Transport properties of alkyltrimethylammonium bromide surfactants in aqueous solutions

Differential mutual diffusion coefficients of n-alkyltrimethylammonium bromides [CH₃(CH₂)_n–1N(CH₃)₃Br, C_nTAB] (n=10, 12, 14, 16) have been measured in aqueous solutions at 298.15 K using a conductimetric cell and an automatic apparatus to follow diffusion. The cell is based on an open-ended capillary, and the technique follows the diffusion process by measuring the resistance of a solution inside the capillaries at various times. The electrical conductances of those solutions have also been measured to calculate the critical micellar concentration (cmc). Thermodynamic analysis of the data suggests that the free ion concentration decreases at concentrations above the cmc, in agreement with theoretical predictions. The obtained values of the micellization parameters were used to model the mutual diffusion coefficients of C_nTAB aqueous solutions.     

Diffusion in polyacrylic acid aqueous solutions

The four diffusion coefficients for the ternary system polyacrylic acid (mol. weight 5000)-polyacrylic acid (mol. weight 115000)-water have been measured at 25°C and at one average polyelectrolytes concentration. The experimental values of main and cross terms have been briefly discussed. The large cross term D ₁₂ in the system with water as solvent shows that, contrary to intuition, different molecular weight species do interact with each other.     

Liquid-liquid distribution of B group vitamins in polyethylene glycol-based systems

General regularities of the liquid-liquid distribution of B₁, B₂, B₆, and B₁₂ vitamins in aqueous polyethylene glycol (PEG-2000, PEG-5000) solution-aqueous salt solution systems are studied. The influence of the salting-out agent, the concentration of the polymer, and its molecular weight on the distribution coefficients and recovery factors of the vitamins are considered. Equations relating the distribution coefficients (log D) to the polymer concentration are derived.     

Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

Binary mutual diffusion coefficients D can be estimated from the width at half height W _1/2 of Taylor dispersion profiles using D=(ln 2)r ² t _R/(3W ² h) and values of the retention time t _R and dispersion tube radius r. The generalized expression D _h=−(ln h)r ² t _R/(3W ² _h ) is derived to evaluate diffusion coefficients from peak widths W _h measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D _h values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed pseudo-binary profiles. Consequently, D _h values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D _h values can however be constructed by taking appropriate linear combinations of profiles generated using different initial concentration differences. The invariant D _h values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D _h with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features are illustrated by measuring the dispersion of mixed polyethylene glycols.