Concentration dependence of the diffusion coefficient of polydisperse polystyrene in dilute solution

The concentration dependence of the diffusion coefficients (D) of two different polystyrenes in toluene was measured. The concentration dependence of D of a standard monodisperse sample (M = 498,000) for concentrations up to 1 · 25 g/dl is not linear. The dependence is adequately described by the theory of dilute polymer solutions up to about 0·7 g/dl and the second virial coefficients of the osmotic pressure can be evaluated. For a polystyrene sample having a broad molecular weight distribution, the concentration dependence of four different average diffusion coefficients was determined so indirectly characterizing the molecular weight distribution. These dependences are not linear and differ from each other owing to the different sensitivity of the individual averages to high-molecular and low-molecular weight fractions. The apparent distribution of the diffusion coefficients becomes narrower with increasing concentration. When evaluating polydispersity from the free diffusion data obtained in good solvents, it is necessary to determine directly the differential diffusion coefficients; an extrapolation of the integral diffusion coefficients can be misleading.     

Rotary friction,dipole moments,conformation and rigidity of polybutylisocyanate molecules in solution

Experimental data on the dependence of the rotatory diffusion coefficients and dipole moments on molecular weight and the theory of hydrodynamic properties and of the size of wormlike chains were used for determining the main conformational characteristics of the polyisocyanate chain S is the number of molecular units in a segment, λ is the length of the projection of the monomer unit on the axis of the molecule, and μ_o is the dipole moment of the monomer unit. The values of S and λ agree with those found previously by hydrodynamic methods. It was shown that the flat cis-structure of the polyisocyanate chain corresponds to values of λ = 2 × 10^?8cm andμ_o = 1·8D. Analysis of experimental data indicates that dimensions of “geometrical” and “electrical” segments in the PBIC chain are identical.     

Molecular quadrupole moments and magnetic anisotropies of non-dipolar 1,3,5-trisubstituted benzenes

The molecular quadrupole moments and magnetic anisotropies of a series of non-dipolar 1,3,5-trisubstituted benzenes (C₆H₃X₃; X=H, Me, t-Bu, F, Cl, Br) are analysed to obtain information concerning the charge distributions. Whereas alkyl groups have relatively little effect on benzene. halogen substituents are strongly interactive and the moments become progressively less negative from 1.3.5-tribromo-to 1.3.5-trifluoro-benzene.     

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.     

On the use of moments for describing the molecular orientation distribution

The posibilities of drawing conclusions about angular distribution functions F(ω) from measured moments [cos^lω] = ∫ cos^lω F(ω)d(ω) are discussed. F(ω) is expanded as a sum of Legendre polynomials with the moments in the coefficients. In practice only the first few moments are experimentally available. The limited use of a truncated series is demonstrated for distributions in polymers, electric fields and liquid crystals.     

Molecular weight and antioxidant effects on the structure of irradiated linear low density polyethylene

Linear copolymers of ethylene and butene-1 with uniform chemical microstructure and very narrow molecular weight distribution are used to study the effects of ionizing radiation. The well characterized copolymers are irradiated at room temperature with γ-rays from a ⁶⁰Co source. To follow the evolution of the molecular structure with the radiation doses, changes in molecular weight averages M_n and M_w are measured by membrane osmometry, light scattering and GPC.The influence of the original linear polymer molecular weight is examined in the range of 50,000–100,000. The effects of antioxidant are explored irradiating samples with and without additive.     

Dipole moments of compounds containing a cobalttin bond

The molecular electric dipole moments are reported for the series of tin-substituted tetracarbonyl cobalt compounds R_nY_m?nSn{Co(CO)₄}_4?m (m = 1–3; n ? m; R = alkyl, phenyl; Y = halogen). The effect of the substituents at the tin atom on the nature of the CoSn bond is established on calculating the (CO)₄CoSn group dipole moments. It is shown that the charge transfer in the CoSn bond is mainly determined by the inductive properties of the ligands attached to tin.     

Diffusion of Quinine with Ethanol as a Co-Solvent in Supercritical CO2

This study aims at contributing to quinine extraction using supercritical CO₂ and ethanol as a co-solvent. The diffusion coefficients of quinine in supercritical CO₂ are measured using the Taylor dispersion technique when quinine is pre-dissolved in ethanol. First, the diffusion coefficients of pure ethanol in the supercritical state of CO₂ were investigated in order to get a basis for seeing a relative change in the diffusion coefficient with the addition of quinine. We report measurements of the diffusion coefficients of ethanol in scCO₂ in the temperature range from 304.3 to 343 K and pressures of 9.5, 10 and 12 MPa. Next, the diffusion coefficients of different amounts of quinine dissolved in ethanol and injected into supercritical CO₂ were measured in the same range of temperatures at p = 12 Mpa. At the pressure p = 9.5 MPa, which is close to the critical pressure, the diffusion coefficients were measured at the temperature, T = 343 K, far from the critical value. It was found that the diffusion coefficients are significantly dependent on the amount of quinine in a small range of its content, less than 0.1%. It is quite likely that this behavior is associated with a change in the spatial structure, that is, the formation of clusters or compounds, and a subsequent increase in the molecular weight of the diffusive substance.     

Separation of linear hydrocarbons and carboxylic acids from ethanol and hexane solutions by reverse osmosis

In this study, asymmetric cellulose acetate membranes with moderate NaCl rejection (85.5%) were prepared and used to study the influence of the chemical nature of organic solutes in different organic solvents. The solute rejection and the solvent flux of linear hydrocarbons (M_w=226–563 g/mol) and linear carboxylic acids (M_w=228–340 g/mol) in ethanol and hexane were studied as a function of the molecular weight, the feed concentration and the transmembrane pressure.The ethanol flux was three times higher than the hexane flux. The rejection coefficients for both types of solute were quire acceptable (R=60–90%), when ethanol was the solvent. In hexane the linear hydrocarbons showed a rejection of 40–60%, while all carboxylic acids reached a negative rejection of −40 to −20%. This negative “observed” rejection can be attributed to accumulation of carboxylic acid at the membrane; the solute concentration at the membrane becomes much higher than in the bulk solution, due to a higher affinity of the solute with the membrane in hexane than in ethanol. Sorption experiments support this hypothesis.Furthermore, it was found that the rejection increases with increasing molecular weight and the rejection and flux are hardly affected by the feed concentration.     

Modelling free-radical copolymerization kinetics—evaluation of the pseudo-kinetic rate constant method, 1. Molecular weight calculations for linear copolymers

The moment equations for binary copolymerization in the context of the terminal model have been solved numerically for a batch reactor operating over a wide range of conditions. Calculated number- and weight-average molecular weights were compared with those found using pseudo-kinetic rate constants with the method of moments and with the instantaneous property method for homopolymerization. With the pseudo-kinetic rate constant method under polymerization conditions where number-average molecular weights (M̄_n) are below about 10³ the error in calculating M̄_n exceeds 5%. The error increases rapidly with decrease in molecular weight for M̄_n < 10³. M̄_n measured experimentally for polymer chains (homo- and copolymers) have error limits of greater than ±5% at the 95% confidence level. Therefore, for all practical purposes, the pseudo-kinetic rate constant method is valid for M̄_n greater than 10³. Errors in calculating weight-average molecular weights (M̄_w) or higher averages are always smaller than those for M̄_n when applying the pseudo-kinetic rate constant method. The assumptions involved in molecular weight modelling using the pseudo-kinetic rate constant approach are thus proven to be valid, and therefore it is recommended that the pseudo-kinetic rate constant method be employed with the instantaneous property method to calculate the full molecular weight distribution and averages for linear chains synthesized by multicomponent chain growth polymerization.     

Diffusivity of gases and main-chain cooperative motions in plasticized poly(vinyl chloride)

Permeability and time-lag measurements for H₂ and CO in poly(vinyl chloride) (PVC) plasticized with tricresyl phosphate show that the apparent diffusion coefficients at first decrease as the plas-ticizer concentration is increased. The diffusion coefficients then increase as the additive concentration is raised above 15 wt %. These changes in the apparent diffusion coefficients can be related to the behavior of a variety of mechanical properties and are attributed to antiplasticization and plasticization effects of low and high concentrations of tricresyl phosphate, respectively. The antiplasticization-plasticization effects reflect altered molecular motions of the polymer. Carbon-13 NMR rotating-frame relaxation rate measurements show directly that the cooperative main-chain molecular motions of PVC are reduced when the additive acts as an antiplasticizer and are increased when the polymer is plasticized. Both the apparent diffusion coefficient and the rotating-frame relaxation rate have a similar dependence on additive concentration. An application of the molecular theory of diffusion of Pace and Datyner accounts qualitatively for the way in which additives alter the average chain interaction energy, cooperative polymer main-chain motions, and the diffusion coefficients of gaseous penetrants.     

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.     

Molecular weight distributions and moments for condensation polymerizations characterized by two rate constants

Molecular weight distributions (MWD) and moments have been computed for condensation polymerizations of ARB-type monomers wherein the reactions involving the monomer are characterized by a rate constant k₁₁ and those involving other species, by k_p. For k₁₁/k_p < unity, the MWD curves are found to split into two, one for even n and one for odd values of n. Substantial amounts of unreacted monomer are found in the reaction mass for this case and so moments and the polydispersity index computed without the monomer are better representations of the distributions. For k₁₁/k_p > unit, conventional MWDs are observed with dispersions different from those representing polymerizations satisfying the equal reactivity hypothesis.     

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.     

Evaluation of sorption and diffusion behavior of selenium in crushed granite by through-diffusion column tests

Distribution coefficients (K _d), apparent diffusion coefficients (D _a) and retardation factor (Rf) in this work obtained by batch and through-diffusion experiments have been performed, respectively. The accumulative concentration method developed by Crank (The mathematics of diffusion, 12) was applied to realize apparent and effective diffusion coefficient (D _a and D _e) of Se. Besides, a non-reactive radionuclide, HTO, was initially conducted in through-diffusion experiment for assessing the ability of radionuclide retardation. The distribution coefficients (K _d) obtained by batch tests in 14 days under aerobic and anaerobic systems were 6.98 ± 0.35 and 5.21 ± 0.25 mL/g. Moreover, Rf^cal and K _d ^cal of Se obtained from accumulative concentration’s method in through-diffusion test showed an obvious discrepancy with the increase of length/diameter (L/D) ratio. However, it presented an agreement of Rf^H/Se and K _d ^H/Se in a various L/D ratio by comparison of apparent diffusion coefficient’s (D _a) between HTO and Se. It appears that the Rf^H/Se and K _d ^H/Se obtained from the through-diffusion experiments are lower than those derived from the batch experiments. Therefore, it demonstrates that reliable Rf and K _d of Se by through-diffusion experiments could be achieved at a non-reactive radiotracer (HTO) prior to tests and will be more confident in long-term performance assessment of disposal repository.     

Molecular geometries and moments from the maximum overlap criterion

The maximized overlap population, defined as Σ_μ≠νP_μνS_μν, and a related quantity, Σ_μ,νP_μνS²_μν are computed for a series of configurations. The extremum of both approximate molecular geometries, the latter with an accuracy suitable for predictive value. The maximum overlap orbitals predict dipole and quadrupole moments that give reasonable agreement with experimental values.     

Molecular Modeling to Estimate the Diffusion Coefficients of Drugs and Other Small Molecules

Diffusion is a spontaneous process and one of the physicochemical phenomena responsible for molecular transport, the rate of which is governed mainly by the diffusion coefficient; however, few coefficients are available because the measurement of diffusion rates is not straightforward. The translational diffusion coefficient is related by the Stokes–Einstein equation to the approximate radius of the diffusing molecule. Therefore, the stable conformations of small molecules were first calculated by molecular modeling. A simple radius r_s and an effective radius r_e were then proposed and estimated using the stable conformers with the van der Waals radii of atoms. The diffusion coefficients were finally calculated with the Stokes–Einstein equation. The results showed that, for the molecules with strong hydration ability, the diffusion coefficients are best given by r_e and for other compounds, r_s provided the best coefficients, with a reasonably small deviation of ~0.3 × 10⁻⁶ cm²/s from the experimental data. This demonstrates the effectiveness of the theoretical estimation approach, suggesting that diffusion coefficients have potential use as an additional molecular property in drug screening.     

The atomistic simulation of the gas permeability of poly(organophosphazenes). Part 1. Poly(dibutoxyphosphazenes)

Self-diffusion and solubility coefficients of six gas molecules (He, Ne, O₂, N₂, CH₄, and CO₂) in two poly(dibutoxyphosphazenes)—poly[bis(n-butoxy)phosphazene] (PnBuP) and poly[bis(sec-butoxy)phosphazene] (PsBuP)—have been investigated by means of molecular simulation using the COMPASS molecular mechanics force field. Diffusion coefficients were obtained from molecular dynamics (NVT ensemble) using up to 3 ns simulation time. Solubility coefficients were obtained by means of a Grand Canonical Monte Carlo (GCMC) method. Results of both simulations were in generally good agreement with experimental data with the exception of the simulation results for gas solubility in PsBuP where differences from the data may be attributed to microcrystallinity of the experimental sample. In the case of diffusivity, diffusion coefficients correlated well with the square of the effective diameter of the diffusing gas. Similarly a good correlation was found between the solubility coefficients obtained by GCMC simulation of sorption isotherms and the Lennard-Jones potential well depth parameter, ϵ/k.The transition-state model of Gusev and Suter was used to determine free volume and free volume distribution for PnBuP, PsBuP, and poly[bis(iso-butoxy)phosphazene] (PiBuP). The diffusion coefficient for a given gas in each polyphosphazene was found to correlate exponentially with its accessible free volume fraction. A model for the distribution of accessible free volume, derived from the Cohen–Turnbull theory for the self diffusion of a liquid of hard spheres, was found to provide excellent fit with the simulation results.     

Experimental determination of rheological properties of polydimethylsiloxane

A series of linear polydimethylsiloxane of different molecular weight and with reduced polydispersity were prepared by partial fractionation of commercial products. The rheological functions, i.e. zero shear viscosity (η₀), first and second normal stress coefficients (Ψ₁₀ and Ψ₂₀), of the materials were experimentally measured by conventional rotational rheometers and by a rotation rod apparatus. The relationships between molecular structure (molecular weight and polydispersity index) and rheological functions are presented and discussed on the basis of equations proposed in the literature. Zero shear viscosity data conform to the well-known dependence on a power 3.5 of molecular weight. However, a consistently stronger influence of molecular weight over Ψ₁₀ and Ψ₂₀ is found. The influence of polydispersity over Ψ₁₀ is also analyzed.     

A calculation of the isotropic and anisotropic spectral moments of the dipole oscillator strength distribution of N2

We calculate a range of isotropic and anisotropic spectral moments of the dipole oscillator strength distribution for N₂ in the random phase approximation. The internuclear dependence of, in particular, S∥(k) is nonnegligible and vibrationally averaged moments are reported. The results are compared to other calculations and to experiment when available, and we conclude that the scheme gives reliable results. Based on our results, we predict a 10% anisotropy in the stopping power of oriented N₂ molecules.