Pseudo diffusion of nonvolatile metals in electro graphite

The apparent diffusion coefficients for Ti, V, Cr, Nb, Mo and Hf as carbides and for elementary Fe, Ni and Cu in electro graphite have been determined by means of an electron-microprobe analyzer. These pseudo diffusion coefficients were found to vary with the heat treatment time. However, after one hour these remain constant and follow the Arrhenius type of relation D = D₀exp(?Q/RT). The activation energy Q was nearly constant for the metals investigated. An attempt was made to correlate the frequency factor D₀ with the heat of formation $\text{ΔH}{}_{\mathrm{?}}{}^{298}$ of the corresponding carbides. A plot of log D₀vsΔH_f yielded two straight lines, one for the negative $\text{ΔH}{}_{\mathrm{?}}$, the other for positive $\text{ΔH}{}_{\mathrm{?}}$. This method was satisfactorily applied to predict the diffusion coefficients of Zr, Sb and Bi.     

The θ-behaviour of heterogeneous macromolecules

A polymer chain consisting of N_r segments with a repulsive interaction (binary cluster integral β_r) and N_a ? N_r segments with a stronger, attractive and pairwise saturable interaction (β_a), which is at the averaged θ-point N²_rβ_r + N²_aβ_a = 0 deviations from the predictions of the two parameter theory: $\text{α}{}^2{}_{\mathrm{<mtext>R</mtext>}}\text{? 1 ～ δz}{}_{\mathrm{<mtext>r</mtext>}}\text{< 0}$ and A₂ ～ δz_r > 0 with $\text{δz}{}_{\mathrm{<mtext>r</mtext>}}\text{～ β}{}_{\mathrm{<mtext>r</mtext>}}\text{(}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. It is shown that the deviations from the universal behaviour are due to the existence of an intermediate length scale $\text{～}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}$.     

Quasi-elastic light scattering: separability of effects of polydispersity and internal modes of motion

The influence of a size distribution on the angular dependence of the quasielastically scattered light is studied for (i) large hard spherical particles and (ii) large flexible chain molecules. For the spherical particles the angular dependence is shown to depend solely on the size distribution and the particle scattering factor. Combination of conventional elastic light scattering with quasielastic light scattering allows the determination of the z-average radii moments $\text{r}{}^{\mathrm{<mtext>n</mtext><mtext>?</mtext>}}{}_{\mathrm{z}}\text{(n = ?1, 1, 2, …)}$ which define the size distribution. Flexible chains — linear and branched ones — show in any case a linear dependence of the apparent diffusion constant $\text{D}{}_{\mathrm{app}}\text{=}\text{Г}\text{q}{}^2$ on $\text{q = (}\text{4π}\text{λ}\text{)}$ sin $\text{θ}\text{2}$, when q becomes large. This behaviour represents the flexibility of the spring-bead model with strong hydrodynamic interaction. The initial part on the other hand form a straight line when D_app is plotted against q². The intercept of this straight line is the z-average diffusion constant while the slope is proportional to the z-average mean square radius of gyration. Thus, the polydispersity can be estimated from D_z and 〈S²〉_z while the asymptote at large q-values is determined by the internal flexibility of the molecule.     

Verification of the Maxwell–Stefan theory for tracer diffusion in zeolites

Using the Maxwell–Stefan theory for diffusion we derive a simple formula to relate the tracer (i.e. self) diffusivity D¹ and Maxwell–Stefan (MS), or jump, diffusivity $\text{D}\text{–}$. The presence of the interchange coefficient $\text{D}\text{–}{}_{\mathrm{ij}}$ in the MS formulation causes the self diffusivity to be lower than the jump diffusivity. Assuming the interchange coefficient to be given by $\text{D}\text{–}$/F we derive:$\text{D}{}^1\text{=}\text{D}\text{–}\text{1+Fθ}$where F is a factor to take account of topology effects within the zeolite matrix.The validity of the MS formulation is established by performing kinetic Monte Carlo simulations for diffusion of methane, perfluoromethane, 2-methylhexane and iso-butane in silicalite. Furthermore, it is shown that the exchange coefficient $\text{D}\text{–}{}_{\mathrm{ij}}$ is a quantification of correlation effects during the hopping of molecules. For iso-butane, the isotherm inflection leads to a sharp inflection in the diffusion behaviour. The influence of molecular repulsive forces on the loading dependence of the jump and self-diffusivities is also discussed with the aid of published Molecular Dynamics simulations for methane.     

Viscoelastic properties of poly(propylene glycols)

The relaxational and retardational properties of poly(propylene glycol) liquids, of nominal molecular weights 400 and 4000, are described. The viscoelastic behaviour of each liquid has been determined over a wide temperature range, using high frequency shear wave techniques operating at 30 and 454 MHz. It is found that the complex compliance $\text{J1(jω)}$ is described in terms of the viscosity ν, the limiting high frequency compliance J_∞, the retardational compliance J_r and a characteristic retardation time $\text{т}{}_{\mathrm{r}}$ by:

$\text{J}{}^1\text{(jω)=J}{}_{\mathrm{\infty }}\text{+}\text{1}\text{jωη}\text{+}\text{j}{}_{\mathrm{r}}\text{(1+jωτ}{}_{\mathrm{r}}\text{)}{}^{\mathrm{\beta }}$

where β is a parameter of the retardation time distribution.For the lower molecular weight liquid, $\text{J}{}_{\mathrm{r}}\text{J}{}_{\mathrm{\infty }}\text{= 17.4}$, β = 0.45 and $\text{т}{}_{\mathrm{r}}\text{т}{}_{\mathrm{m}}$ increases with decreasing temperature, reaching a limit of 170 near 0°C. This liquid shows no evidence of polymeric behaviour.For the other, $\text{J}{}_{\mathrm{r}}\text{J}{}_{\mathrm{\infty }}$, β = 0.76, $\text{т}{}_{\mathrm{r}}\text{т}{}_{\mathrm{m}}\text{= 15.4}$ and is constant over the temperature range investigated. The main difference between the two liquids appears as an additional retardational or relaxational process for the higher molecular weight material which occurs in the initial or low frequency part of the relaxation region. This process is characterized by a single time, but with relaxation time $\text{1}\text{7}$ and a stiffness 7 times the values calculated for the first Rouse mode of polymer chain motion.     

Quasi-elastic light scattering from branched polymers: 1. Polyvinylacetate and polyvinylacetate—microgels prepared by emulsion polymerization

Emulsion polymerization of vinylacetate leads to branched polymers which at high monomer conversions form microgels of the shape and size of the latex particles. Quasielastic light scattering measurements from samples in the pre-gel state give at small q² a linear angular dependence of $\text{D}{}_{\mathrm{app}}\text{=}\text{Г}\text{q}{}^2$ which resembles that of randomly branched chain molecules, where Г is the decay constant of the time correlation function. Extrapolation of D_app towards zero scattering angle yields the translational diffusion constant D_z. The diffusion constant follows the molecular weight dependence D_z = 9.78 10^?5M_w^?0.478. The diffusion constant of the microgels, i.e. at molecular weights M_w > 14 10⁶, remains constant because of the finite and constant size of the latex particles. The coefficients k_f and k_D in the concentration dependence of the frictional and diffusion coefficients are related according to the equation $\text{k}{}_{\mathrm{D}}\text{= k}{}_{\mathrm{f}}\text{? 2A}{}_2\text{M}{}_{\mathrm{w}}\text{?}\text{v}\text{?}$ where A₂ is the second virial coefficient and v? the partial specific volume of the particle. The coefficient k_f is calculated from the experimentally determined quantities k_D, A₂ and M_w, and the result is compared with the theory by Pyun and Fixman. Accordingly the branched coils in the pre-gel state resemble soft spheres, but the microgels behave more like spheres of some rigidity.     

Self-diffusion of poly(ethylene oxide) in aqueous dextran solutions measured using FT-pulsed field gradient n.m.r.

Transport in ternary polymer₁, polymer₂, solvent systems has been investigated using an n.m.r. spin-echo technique. The dependence of the self-diffusion coefficient of poly(ethylene oxide) polymers on the concentration and molecular size of dextran in aqueous solution has been measured. Monodisperse poly(ethylene oxide) fractions ($\text{M}\text{?}{}_{\mathrm{w}}\text{=7.3×10}{}^4$, 2.8·10⁵ and 1.2·10⁶) and dextrans ($\text{M}\text{?}{}_{\mathrm{w}}\text{=2·10}{}^4$, 1·10⁵ and 5·10⁵) have been employed over a range of concentration up to the miscibility limit in each system. It is found that when the molecular size of the diffusant is commensurate with or exceeds that of the matrix polymer, a relationship of the form: $\text{(}\text{D}\text{D}{}_0\text{)}{}_{\mathrm{<mtext>PEO</mtext>}}\text{=}\text{exp}\text{?k(C[η])}$ is applicable, where C[η] refers to the dextran component and is considered to describe the extent of coil overlap in concentrated solution. ($\text{D}\text{D}{}_0$) is independent of the molecular size of the poly(ethylene oxide), at least in the range studied (M_w<300 000).     

Differences in the molecular weight and the temperature dependences of self-diffusion and zero shear viscosity in linear polyethylene and hydrogenated polybutadiene

Within the context of a generalized coupling model we can support the hypothesis that, while the mode of relaxation for self diffusion (D) and shear flow (η) are the same, the entanglement interactions are different. We assume that there are two distinct coupling parameters n_D and n_η for self diffusion and shear flow respectively. The model predicts the molecular weight and temperature dependences to be scaled by the relevant coupling parameters as:

for melts with Arrhenius temperature dependences. We have found that n_n=0.43 and 0.42 for polyethylene (PE) and hydrogenated polybutadiene (HPB) which scale η as M^3.5 and M^3.4. Also the apparent flow activation energies $\text{E1}{}_{\mathrm{a}}$ of 6.35 kcal mole^?1 for PE and 7.2 kcal mol^?1 for HPB scale to primitive activation energies E_a of 3.6 and 4.2 kcal mole^?1 for PE and HPB respectively. On the other hand the M^?2 dependence of D results in n_D=1/3. Then the reported activation energies for self-diffusion in PE and HPB of 5.49 and 6.2 kcal mole^?1 scale to primitive activation energies of 3.7 and 4.1 kcal mole^?1, respectively.     

Diffusion in polyacrylamide gels

Using a novel sorption technique, the diffusion of some series of solutes in polyacrylamide gels has been investigated with regard to: (a) molecular size of solute; (b) concentration of solute and gel polymer; and (c) temperature. The approach used also yields the partition coefficient pertaining to sorption equilibrium. The ratio, $\text{D}\text{D}{}_{\mathrm{o}}$, where D_o refers to diffusion in the pure solvent, is found to reflect in part the characteristic interactions between solute and gel polymer. The temperature results indicate that the apparent activation energy for solute diffusion is approximately independent of the polymeric component for dilute gels.     

Dielectric constants of coal-water slurries at 750 MHz

Measurements of the real portion of the dielectric constant of coal-water slurries at 750MHz are reported. Slurries of 40–65wt% of either Illinois No. 6, Utah bituminous or Texas lignite coals over the temperature range 11–71 °C were studied. The dielectric constant was independent of coal type and particle size within experimental error. The measured values of dielectric constants agreed with those predicted by the Looyenga equation: $\text{?′}\text{= [?′}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_2\text{+ φ(?′}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_1\text{??′}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}{}_2\text{)]}{}^3$ where: $\text{?′}$, the mean value of the dielectric constant; ?′₁, the dielectric constant (3.8) of the dry coal; ?′₂, the dielectric constant of water; φ, the volume fraction of coal.     

Quantitative evaluation of the Gibbs—DiMarzio theory of the glass transition

The applicability of the Gibbs—DiMarzio (G—DM) theory of the glass transition (T_g) is quantitatively evaluated for PS, PVC, PαMS and PMMA. The analysis was conducted under the assumption that both the inter-/intramolecular energy ratio (r) and the effective chain segment density (n) remain constant while the fractional free volume at T_g(V₀) varies as a function of the reciprocal degree of polymerization ($\text{10}{}^3\text{P}\text{?}$). Based upon reduced parametric plots of $\text{T}{}_{\mathrm{<mtext>g</mtext>}}\text{T}{}_{\mathrm{<mtext>g\infty </mtext>}}$versus$\text{10}{}^3\text{P}\text{?}$, the results showed that the G-DM equations were satisfactory for PS and PVC but unsuccessful in the cases of PαMS and PMMA. For the former cases the analysis indicated that when 0.015 ? V₀ ? 0.045 optimum agreement occurred at n=1.80, r=10.5 and n=1.36, r=0.95, respectively. Although potential n, r values were obtained for PαMS when the allowable V₀ range was expanded to 0.010–0.050, none of these combinations satisfied all of the analytical requirements. No agreement for the PMMA data sets could be obtained even when this less stringent V₀ criterion was adopted. Attempts to improve this situation by incorporating ‘beads’ and ‘flexes’ into the statistical mechanical equations are also considered.     

Determination of type and width of a size distribution from the z-averages of the radii moments rnz

Relationships are given between the z-average radii moments $\text{r}\text{?}{}^{\mathrm{n}}{}_{\mathrm{z}}$ and the common moments $\text{r}\text{?}{}^{\mathrm{n}}$ of a size distribution. Instructions are given for finding the type and width of a size distribution from measurements of the $\text{r}\text{?}{}^{\mathrm{n}}{}_{\mathrm{z}}$ moments.     

Studies of cyclic and linear poly(dimethyl siloxanes): 12. Observation of diffusion behaviour by quasielastic neutron scattering

High resolution neutron scattering experiments have been used to observe the diffusive motion of low molecular weight linear and cyclic poly(dimethyl siloxane) molecules in dilute solution in deuterated benzene. Diffusion coefficients (D) and hydrodynamic radii (R_H) have been compared with values obtained by light scattering for higher molecular weight samples and with radii of gyration (R_g) obtained by small-angle neutron scattering. While the ratio $\text{D}{}_{\mathrm{<mtext>ring</mtext>}}\text{D}{}_{\mathrm{<mtext>chain</mtext>}}$ is close to the predicted value of 0.85, the ratio $\text{R}{}_{\mathrm{g}}\text{R}{}_{\mathrm{<mtext>H</mtext>}}$ falls below the theoretical value for both ring and chain molecules. The scattering curves show effects arising from both centre of mass diffusion and internal molecular motion, and the observed inverse correlation times are compared with calculated behaviour as a function of scattering vector, Q.     

Thermoplastic properties of coal at elevated pressures: 1. Evaluation of a high-pressure microdilatometer

Thermoplastic behaviour of a Pittsburgh seam hvA coal (PSOC1099) was characterized by the use of a high-pressure microdilatometer. Phenomena such as softening, swelling, final resolidification, and the temperatures at which they occur were measured as functions of heating rate (25 ° and 65 °C min^?1), particle size (= 75 μm and 250 × 425 μm), gaseous atmosphere (N₂, H₂, $\text{CO}\text{H}{}_2$) and applied gas pressure (atmospheric to 2.8 M Pa). The results obtained illustrate several important aspects of thermoplastic properties of this coal under the conditions utilized. It is observed that pressure alone can play a major role in determining its overall thermoplastic behaviour. Compared to that at atmospheric pressure, swelling is significantly reduced at 2.8 MPa of pressure for any given heating rate or particle size. In these experiments, the chemical composition of the gaseous atmospheres ($\text{CO}\text{H}{}_2$, H₂ and N₂) does not appear to alter significantly the plastic phenomena at any given pressure. Increasing the heating rate or decreasing the particle size results in increased swelling at all applied pressures and atmospheres.     

Macromolecular properties of heparin in dilute solution: 2. Dimensional parameters as a function of pH,ionic strength and desulphation

A bovine heparin fraction was examined by sedimentation analysis and intrinsic viscosity measurements as a function of ionic strength in the range of 0·1 to 1·0 M, and at pH 2·5 and 6·0. The following experimental parameters were obtained: M, S⁰_20,W, D⁰_20,W, $\text{V}\text{?}$, and [η]. Other physical parameters were calculated based on a random coil model (supported by the theory of Mandelkern and Flory) e.g., $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{(}\text{s}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Similar studies were made on a heparin sample as a function of desulphation as resulting from graded mild hydrolysis. Since desulphation is accompanied by decreasing anticoagulant activity of heparin, the latter was correlated with various calculated and measured physical parameters. Significantly $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ decreases with decreased desulphation and therefore decreased biological activity.     

Bulk and grain boundary diffusion of C in tungsten hemicarbide

Dense tungsten hemicarbide specimens were used to study the bulk and grain boundary diffusion of ¹⁴C into W₂C at temperatures of 1200 to 2000°C. The bulk diffusion coefficient is given by:

$\text{D}{}_{\mathrm{v}}\text{=18.3}\text{exp}\text{?}\text{91,500}\text{RT}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$

The grain boundary diffusion coefficient is represented by the expression:

$\text{P}{}_{\mathrm{GB}}\text{=1.8 10}{}^{\mathrm{?4}}\text{exp}\text{?}\text{68,880}\text{RT}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$

A comparison is give with preceding results on other carbides.     

Phase structure and adhesion in polymer blends: A criterion for rubber toughening

The effects of rubber particle size and rubber-matrix adhesion on notched impact toughness of nylon-rubber blends are analysed. A sharp tough-brittle transition is found to occur at a critical particle size, when the rubber volume fraction and rubber-matrix adhesion are held constant. The critical particle size increases with increasing rubber volume fraction, given by $\text{d}{}_{\mathrm{<mtext>c</mtext>}}\text{= T}{}_{\mathrm{<mtext>c</mtext>}}\text{{(}\text{π}\text{6Φ}{}_{\mathrm{<mtext>r</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{? 1}}{}^{\mathrm{?1}}$, d_c is the critical particle diameter, T_c the critical interparticle distance, and ø_r the rubber volume fraction. The critical interparticle distance is a material property of the matrix, independent of rubber volume fraction and particle size. Thus, the general condition for toughening is that the interparticle distance must be smaller than the critical value. Van der Waals attraction gives sufficient adhesion for toughening. Interfacial chemical bonding is not necessary. Even if there is interfacial chemical bonding, a polymer-rubber blend will still be brittle, if the interparticle distance is greater than the critical value. The minimum adhesion required is about 1000 J m^?2, typical for van der Waals adhesion. In contrast, chemical adhesion is typically 8000 J m^?2. The present criterion for toughening is proposed to be valid for all polymer—rubber blends which dissipate the impact energy mainly by increased matrix yielding.     

E.s.r. studies on oxidation processes in irradiated polyethylene: 2. Diffusion of oxygen into crystalline regions

The oxidation process in irradiated polyethylene was investigated by means of the e.s.r. method, and diffusion of oxygen molecules into the crystalline region of polyethylene was studied in detail. Computer simulation was carried out in order to determine various parameters of the process including diffusion constant. In the course of the simulation, the crystallite was assumed to have a plate-shaped form and the diffusion constant was considered to be larger at the region near the surface of the crystallite, D_f, and to be smaller at the inner region of the crystallite, D_s. Making these assumptions in the simulation gave a much better result than the assumption based on a sphere-shaped crystallite. $\text{D}{}_{\mathrm{f}}\text{D}{}_{\mathrm{s}}$ was found to be about 2 for thicker crystallite and it was 4 ～ 5 for thinner crystallite. Diffusion constants at various temperatures were determined, and the order of magnitude of diffusion constants in the crystalline region was found to be 10^?16 cm²/sec at about 320K both for thicker and thinner crystallites. The activation energy of diffusion of oxygen in the crystallites was found to be 32 kcal/mol.