Semidilute solutions of poly(methacrylic acid) in the absence of salt: Dynamic light-scattering study

Water solutions of poly(methacrylic acid) of molecular weight M_w = 3.0 × 10⁴ and M_w = 4.0 × 10⁵, neutralized with NaOH, were investigated by photon correlation spectroscopy. At a low degree of neutralization α, the short-time decay only is observed. When α > 0, a second, much slower, process becomes noticeable. It gains quickly in influence when α increases. The reciprocal values of characteristic relaxation times for both dynamic processes were found to decrease linearly with the square of the scattering vector, showing that both processes are diffusive. The following interpretation of these processes founded on the concentration and angle dependences of the corresponding diffusion coefficients and scattering amplitudes is given: (1) for the low-molecular-weight sample (M_w = 3.0 × 10⁴), D_∫ (fast process) and be attributed to the Nernst-Hartley diffusion coefficient of polyions, and D_s (slow process) to a diffusion of interchain domains (clusters) with a radius of gyration R_G ≈ 50 nm; (2) for the high-molecular-weight sample (M_w = 4.0 × 10⁵), where an overlap of polymer chains occurs, D_f can be attributed to a cooperative diffusion coefficient reflecting the concentration fluctuations due to the polyions and counterions, and D_s to slow concentration fluctuations having a large correlation length (≈ 100 nm). The existence of two diffusive modes in salt-free solutions of polyelectrolytes cannot be explained within the framework of the scaling approach as proposed by de Gennes and Odijk.     

Dynamic light scattering measurements of polystyrene in semidilute theta solutions

Measurements of the co-operative diffusion coefficient, D_c, and a centre of mass translational diffusion coefficient, D_s, have been made by dynamic light scattering for the polystyrene-cyclohexane theta system as a function of molecular weight and concentration. For semidilute solutions it is established that D_s∝N^?2c^?3 which is in agreement with the predictions from scaling arguments for the self-diffusion coefficient. However, if the co-operative mode is interpreted by D_c∝N^xc^y, the results of 0 < x < 0.7 and 0 < y < 0.5 are in disagreement with scaling predictions of D_c∝N⁰c¹. A discussion of the assumptions and potential shortcomings of the blob model which is used in the derivation of the power law predictions and the dynamic scattering equations is included. In addition, monomeric friction coefficients have been obtained from the D_s results within the framework of Doi-Edwards model. A comparison is made of the concentration dependence of the monomeric friction coefficient from the present data to that from similar experiments on a good solvent (tetrahydrofuran) system and from shear relaxation modulus measurements on the polystyrene in Aroclor 1248.     

Ring-opening polymerization of various oxirane derivatives using organotin phosphate condensate; Selective synthesis of the polyether containing oxirane ring in the side chain

Ring-opening polymerization (ROP) of various oxirane derivatives of the type, 2,2-R¹,R²-CCH₂O [R¹ = H (1), CH₃ (2); R² = CH₃ (a), CH₂Cl (b), CH₂OCH₃ (c)], using organotin phosphate (Bu₂SnO-Bu₃PO₄) condensate has been explored. The ROP of monosubstituted oxiranes (1a-c) afforded ring-opened polymers in high yields (1a, 1c = 99% and 1b = 69%); the resultant polymers from monomers 1a and 1b possessed high molecular weights (M_n = 9.49 × 10⁴, 10.60 × 10⁴, respectively). In contrast, both polymer yields and molecular weights for resultant polymers in the polymerization of disubstituted oxiranes (2a-c) were considerably lower than those in the polymerization of monosubstituted monomers (1a-c). ROP of glycidyl 2-methylglycidyl ether (3) possessing two oxirane groups with different reactivity was thus conducted by organotin catalyst; the high molecular weight polyether (M_n = 9.17 × 10⁴) containing oxirane ring in the side chain has successfully been obtained in moderate yield.     

Crosslinking poly(ethylene oxide) in dilute solutions by gamma rays

A high molecular weight poly(ethylene oxide) is gelled by radiation from a ⁶⁰Co source. At concentrations of 0.25 to 1 wt-%, doses of 4.5 to 7.5 × 10⁴ rad cause gelation. The storage modulus of the gel formed increases linearly with additional dose to a plateau value and then remains constant during further irradiation. The does needed to reach the plateau, D_p in rads, and the plateau modulus G_p in dynes per square centimeter, are related to the concentration c, in weight per cent: D_p = 1.05 × 10⁶c and G_p = 1.75 × 10⁴c^2.5. The energy absorbed by the polymer per crosslink formed is about 80 ± 10 kcal/mol. The crosslink density produced by radiation is calculated from the measured modulus by using the theory of rubber elasticity. Both modulus and loss are measured in a special air-bearing, recording torsion pendulum with a coneplate geometry.     

Branched-pore model applied to the adsorption of basic dyes on carbon

The branched-pore adsorption model, expressed by an external mass transfer coefficient k_f, a solid diffusivity D_s, a lumped micropore diffusion rate parameter k_b, and the fraction of macropores f, describes kinetic data from initial contact of adsorbent-adsorbate to the long-term ( > 24 hours) adsorption stages with reasonable accuracy.In this work the model is applied for three basic dye systems, namely Basic Red 22, Basic Yellow 21 and Basic Blue 69, all on carbon. A single value of each parameter describes each dye system. The k_f values are 0.18 × 10⁻²±28%, 0.3 × 10⁻²±17% and 0.2 × 10⁻² ± 20% cm s⁻¹, the D_s values are 0.33 × 10⁻⁹ 21%, 0.72 × 10⁻⁹ ± 9% and 0.72 × 10⁻⁹ ± 9% cm² s⁻¹, the k_b values are 0.65 × 10⁻⁶ ± 7.7%, 1.8 × 10⁻⁶ 0.2 × 10⁻⁶ 1% s⁻¹, while the f values are 0.55 ± 9%, 0.60 ± 10 % and 0.18 ± 11%, each for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively.The model is based on the internal structure of the carbon particle being divided into a macropore and a micropore region. The latter has an upper-bound capacity of 241, 245 and 656 mg g⁻¹ for Basic Red 22, Basic Yellow 21 and Basic Blue 69 respectively. A sensitivity analysis for each parameter has been carried out.     

Cooperative and self-diffusion of polymers in semidilute solutions by dynamic light scattering

The quasielastic light scattering from semidilute solutions of polystyrene in tetrahydrofuran has been measured and we observe two distinct exponential decays separated by several orders of magnitude. The angular dependence of the decay constants is indicative of diffusive processes which we identify with the cooperative diffusion coefficient, D_c and the self diffusion coefficient D_s. It is found that D_c, identified with the fast decay, increases with polystyrene concentration and is independent of molecular weight. However, D_s decreases sharply with concentration and molecular weight. An explanation is given for the light scattering detection of these two diffusion coefficients which is based only on the assumptions inherent in the reptation model. In a limited region of molecular weight and concentration the experimental results appear to be consistent with the predictions of scaling theory.     

Studies on bulk diffusion and local diffusion of polystyrene in melt

Results of bulk viscosity (η) and local viscosity (ξ) of various molecular weights of polystyrene (PS) have been reported. In this paper the relationship between η and bulk diffusion coefficient (D_B), and that between ξ and local diffusion coeffizient (D_L) are presented. Data obtained lead to several conclusions. From the results of unperturbed dimensions and a universal constant (Φ), it was found that F. Bueche's equation D_B · η = const. is valid for polystyrenes with molecular weights over 600. Temperature and component concentration dependence of bulk diffusion coefficient for the two-component blend system may be interpreted in terms of the free volume theory. At an iso-free volume state, molecular weight dependences of bulk diffusion coefficients for both PS of narrow distribution of molecular weight and blend PS can be composed to a single curve, which is composed of two straight lines in a double logarithmic presentation with intersection at M_w = 1.78 × 10⁴ g/mol. The slopes of these two lines were ? 1.0 and ? 3.3, respectively. The product D_L · ξ was determined to be 1.10 × 10^?7 (c.g.s) for n-paraffines from the data of self-diffusion coefficient and ξ. This made it possible to determine D_L from ξ. For higher molecular weights of PS, log D_B is a linear function of log M_w while log D_L stays almost constant.     

Adsorption and diffusion of nitrogen and oxygen in a carbon molecular sieve

The adsorption and diffusion of N₂ and O₂ in two samples of carbon molecular sieve (Bergbau-Forschung) have been studied by gravimetric and chromatographic methods. The uptake curves (for N₂) show a rapid initial uptake followed by a much slower approach to equilibrium in the long time region. This behaviour can be accounted for by a dual stage (micropore/macropore) diffusion model. Diffusion of oxygen was too fast to be measured accurately by the gravimetric method although an approximate estimate may be obtained from the initial uptake rate. Over the range of the measurements (0–1 atm), the equilibrium isotherms for both O₂ and N₂ are almost linear and there is very little difference between them. Micropore diffusivities derived from the second moments of the chromotographic response peaks are in reasonable agreement with the values derived from the uptake curves [(D_c/r_c²)_O2 ≈ 3.7 × 10⁻³ s⁻¹; (D_c/r_c²)_N2 ≈ 1.2 × 10⁻⁴ s⁻¹ at 303 K], indicating a kinetic selectivity (D_O2/D_N2) of about 30. This is close to the kinetic ratio reported by Knoblauch (for a Bergbau-Forschung sieve) although our values of D_c/r_c² are considerably larger.     

Edible oil hydrogenation rates in the presence of a homogeneous Ziegler—Natta catalyst in a film reactor

The rates of edible oil hydrogenation in the presence of a homogeneous Ziegler—Natta catalyst has been measured in a falling-film reactor with a view to the ultimate determination of the hydrogen/edible oil interfacial area in an agitated tank under a fast reaction regime. The catalyst is a combination of nickel diisopropyl salicylate (Ni(dips)₂) and aluminium triisobutyl (Al(iBu)₃).The reaction rates have been determined by measuring hydrogen absorption rates into soyabean and safflower oils under a fast reaction regime (Ha > 3). The gas absorption has been measured as a function of pressure, temperature, catalyst concentration, molar ratio (α) of Al(iBu)₃ to Ni(dips)₂ and concentration of unsaturated triglycerides in the oils (iodine value, I.V.).The hydrogenation rates can be described by R₂ = K_nc^1.7 for 50 < I.V. < 130 and R₁ = Kc^1.7b^0.55 for 5 < I.V. < 50 (c = concentration of hydrogen in oil, b = concentration of unsaturated triglycerides in oil), under the conditions 5×10⁴<P/(Pa)<1.4×10⁵, 55 <T/(°C)<95, 1.5×10^?3<Ni(dips)₂/(kmol·m^?3)<2.75x10^?2 and 4<α<10.     

Sorption of benzene by poly(ethylene oxide)

The activity of benzene in poly(ethylene oxide), PEO, has been determined over the concentration range 0.3 to ～35 wt% benzene using the piezoelectric sorption method. The temperature range was 64° to 97°C and the molecular weights of polymer samples were 1.0 × 10⁵, 6.0 × 10⁵, and 5.0 × 10₆ g/g mol. The Flory-Huggins interaction parameters, χ, determined in this work agree within experimental error with χ values determined by gas chromatography and by vapour pressure measurement. The values of χ extrapolated to zero solvent concentration, χ^∞, have a minimum and negative value in the vicinity of 85°C for the sample of molecular weight 1.0 × 10⁵, 84°C for the sample of molecular weight 6.0 × 10⁵, and 77°C for the sample of molecular weight 5.0 × 10⁶. In the vicinity of 65°C, χ^∞ is negative for each molecular weight of polymer and increases to positive values with an increase in temperature. For all samples studied, the χ^∞ parameters reach constant values (0.22 to 0.30) at temperatures higher than 90°C.     

The diffusion coefficient of copper sulphate in aqueous solution

The diffusion coefficient, D, of CuSO₄ in aqueous solution was determined at 298.1 K by chronopotentiometry and also with a rotating disc electrode using the mixed control Levich equation. For 0 < [CuSO₄] < 0.05 mol dm^?3, D = {7.35 ± 0.18 ? (5.3 ± 1.4) [CuSO₄]^{$\text{1}\text{2}$}} × 10^?10 m² s^?1, at a constant ionic strength of 1.58 mol dm^?3 maintained with either H₂SO₄ or Na₂SO₄ (pH = 2). It was shown that substantial variations in the concentration of the supporting electrolyte had negligible effect on the above values of D. It was found that literature values of D vary over a three-fold range, even when corrected to the same temperature and CuSO₄ concentration. Much of this variation probably arises from rotating disc determinations carried out at disc potentials where activation control is significant. This problem is overcome if the mixed control Levich equation is used to treat the data instead of the commonly used simple (diffusion only) Levich equation.     

Light scattering Rayleigh linewidth measurements on some dextran solutions

Light scattering Rayleigh linewidth measurements have been made upon eight fractions of dextran from Leuconostoc mesenteroides B512 with molecular weights ranging from 10 to 500 kg/mol and the relationship D₂₀ = 2.25 × 10^?4M^?0.45 (D in mm²/s, M in kg/mol) was established. No concentration dependence of diffusion constant was detected within experimental error (±3%). The measurements were corrected for the polydispersity of the fractions. The results are compared with diffusion constants obtained by conventional techniques and with viscosity data.     

Crystal structure and thermal expansion of ammonium pentaborate NH<Subscript>4</Subscript>B<Subscript>5</Subscript>O<Subscript>8</Subscript>

Anhydrous ammonium pentaborate NH₄B₅O₈ has been synthesized by thermal dehydration of larderellite NH₄[B₅O₇(OH)₂] · H₂O at a temperature of 290°C for 7 h. The crystal structure has been determined from the X-ray powder diffraction data: a = 7.58667(5) Å, b = 12.00354(8) Å, c = 14.71199(8) Å, R _p = 6.23, R _wp = 7.98, R _B = 12.7, R _F = 8.95, and β-KB₅O₈ structure type. The double interpenetrating framework is formed by pentaborate groups, each consisting of a boron-oxygen tetrahedron and four triangles, in which all oxygen atoms are bridging. The thermal behavior of the NH₄B₅O₈ compound has been investigated using thermal X-ray diffraction. As for other pentaborates of this type, the thermal expansion of the NH₄B₅O₈ compound is anisotropic and reaches a maximum along the a axis. The thermal expansion coefficients are as follows: α _a = 39 × 10^?6, α _b = 6 × 10^?6, α _c = 20 × 10^?6, and α _V = 65 × 10^?6 °C^?1.     

Sorption of dissolved organics from aqueous solution by polystyrene resins—II. External and internal mass transfer

External and internal mass transfer were characterized for the sorption of 2,4-dichlorophenol and p-nitrophenol on polystyrene resins. An evaluation method is presented which estimated the external mass-transfer coefficient, κ_L, from the concentration uptake in an integral fixed-bed reactor. The experimental κ_L values are compared with values predicted using four different empirical correlations. The effect of axial dispersion on the values of κ_L was shown to be small under the given conditions.To quantify the intraparticle mass transfer, an effective diffusion coefficient, D_eff, was estimated using the pore diffusion model interpretation of data from a differential column reactor within a recirculated batch system. The D_eff values depend on both resin structure and solute properties. Values of D_eff between 0.3 × 10⁻⁹ and 1.8 × 10⁻⁹ m²/s were observed for macroporous resins, which exceed values that are characteristic of pore diffusion, and a value of 0.6 × 10⁻¹¹ m²/s was estimated for a microporous resin.     

Melting and crystallization behavior of poly(tetrafluoroethylene). New method for molecular weight measurement of poly(tetrafluoroethylene) using a differential scanning calorimeter

Melting and crystallization behavior of virgin polytetrafluoroethylene have been studied using a differential scanning calorimeter. Following quantitative relationship was found between number average molecular weight of polytetrafluoroethylene and the heat of crystallization in the molecular weight range of 5.2 × 10⁵ to 4.5 × 10⁷: M?_n = 2.1 × 10¹⁰ ΔH_c^?5.16, where M?_n is number average molecular weight and ΔH_c is the heat of crystallization in cal/g. The heat of crystallization is independent of cooling rate ranging from 4 to 32°C/min. This relationship provides a simple rapid and reliable method for measuring the molecular weight of polytetrafluoroethylene.     

Copper separation from nitrate/nitric acid media using Acorga M5640 extractant: Part II. Supported liquid membrane study

The facilitated transport of copper(II) from nitrate/nitric acid media through a flat-sheet supported liquid membrane (FSSLM) is investigated, using the commercially available oxime Acorga M5640 as ionophore, as a function of hydrodynamic conditions, concentration of copper (7.9×10⁻⁵ to 1.3×10⁻³ M) and H⁺ (pH 1.0–2.0) and ionic strength in the feed solution, carrier concentration (5–40% v/v) in the membrane and support characteristics. The performance of the system is also compared using various diluents for the organic phase and against other available oxime extractants (MOC-55TD, LIX 860 and LIX 622). A model is presented that describes the transport mechanism, consisting of diffusion through a feed side aqueous diffusion layer, a fast interfacial chemical reaction, and diffusion of carrier and its metal complex through the organic membrane. The organic membrane diffusional resistance (Δ_o) and aqueous diffusional resistance (Δ_a) were calculated from the proposed model, and their values were 7.6×10⁶ and 273 s/cm, respectively. It was observed that the copper flux across the membrane tends to reach a plateau at high concentration of copper or a low concentration of H⁺ owing to carrier saturation within the membrane, and leads to a diffusion-controlled process. The values of the apparent diffusion coefficient (D_o^a) and limiting metal flux (J_lim) were calculated from the limiting conditions and found to be 2.0×10⁻⁸ cm²/s and 2.3×10⁻¹¹ mol/cm² s, respectively. The values of the bulk diffusion coefficient (D_o,b) and diffusion coefficient (D_o) calculated from the model were 5.9×10⁻⁹ and 1.6×10⁻⁹ cm²/s, respectively. The polymeric microporous solid support, Durapore GVHP 04700, was selected throughout the study as it gave the best performance.     

The diffusion of 14C in nuclear graphites

The high temperature exchange of ¹⁴C between ¹⁴CO and ¹²C-graphite has been used to label a large number of samples of various nuclear graphites. The technique has made it possible to obtain data on the self-diffusion of carbon in graphite. Three nuclear graphites are used, Pile Grade A and two isotropic varieties. Diffusion constants at 2473 K lie in the range 0·64 × 10^?19to 2·97 × 10^?19m²/sec. D₀ values vary from 1 ·20 × 10^?12to 1·06 × 10^?6m²/sec and activation energies, E_a, from 337 to 621 kj/mol. The D values found in this work are lower than those found by other workers. Possible reason for this are examined. Activation energies are also compared with values found by other workers and discussed in relation to theoretical calculations on the activation energy for direct interchange, vacancy and interstitial mechanisms for diffusion. It is concluded that direct interchange is the predominant mechanism for the diffusion of ¹⁴C in the highly graphitised samples used in this work.     

AN EXPERIMENTAL STUDY OF POLYMER DIFFUSION IN CONCENTRATED SOLUTION: IMPLICATIONS FOR DIFFUSION IN POLYMERIZATION

The Trommsdorf or gel effect in free radical polymerization is due to the fact that the termination reaction becomes strongly diffusion controlled above a critical concentration associated with the onset of molecular entanglements. Therefore, an understanding of polymer self-diffusion in entangled systems becomes essential to understanding the Trommsdorf effect. Our group has previously proposed a molecular model for the gel effect which uses a specific theory for polymer diffusion (reptution). The present work represents an experimental attack on the same problem Experimental studies of polymer self-diffusion in entangled systems are scarce. Quasielastic light scattering from ternary systems composed of solvent(l)-polymer(2)-polymer(3), in which species (3) is isorefractive to the solvent (i.e. 0n/0c ₃ = 0), offers an attractive way to study the tracer diffusion coefficient of species (2) in a binary mixture of composition c ₃. In regimes of low momentum transfer (qR _G < 1,) where q is the scattered wave vector and R _G is the polymer radius of gyration, we have shown that the correlation function of the scattered electric field should decay with a single exponential decay time, given by (D₂₂ q ²)^?1 where D ₂₂(c ₂, c ₃) is the main ternary diffusion coefficient of component (2). Extrapolation to zero concentration of 2) at fixed concentration of (3) yields the tracer diffusion coefficient of (2) in the binary mixture of (1) and (3). The systems toluene(l)-polystyrene(2)-polymethylmethacrylate(3) (0n/0c ₃ ≈ 0.007 at 25°C) and toluene(l)-polystyrene(2)-polyvinylmethylether (3) (0n/0c ₃ ≈ 0.012 at 60°C) very nearly satisfy the above criteria. In both systems, we have found that the tracer diffusion coefficient of the polystyrene decreases with increasing concentration of the isorefractive polymer. Further studies have focused upon the dependence of the tracer diffusion coefficient upon polystyrene molecular weight, and upon the effect of incomplete index matching.     

Determination of diffusion coefficient of oxygen into polymers by using electron spin resonance spectroscopy. I. Poly(methyl methacrylate)

A simple technique has been proposed for the measurement of the diffusion coefficient of oxygen into polymeric spheres. The technique is based on the scavenging of radicals produced by high energy radiation by oxygen. The diffusion coefficient of oxygen determined for poly(methyl methacrylate) has shown an inverse dependency on the dose received. Diffusion coefficient determined for low doses (D = 3.4 × 10^?8 cm²/s) as well as that determined after extrapolation to zero dose (D₀ = 3.7 × 10^?8 cm²/s) are in excellent agreement with the values reported in the literature.