A calculation of the elastic constant c33 of a graphite crystal as a function of temperature

A calculation is presented of the elastic constant C₃₃ of a graphite crystal as a function of temperature up to 2500 K, taking into account the anharmonic contribution and the changes in interlayer interactions due to the large lattice thermal expansion. Parametric variations in the theory show that the anharmonic contribution to C₃₃ depends principally on the parameter ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) Comparison of theoretical results with the experimental data, which is mainly from neutron scattering experiments, shows that the data can be accounted for if ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) lies in the range 7–10 × 10¹³ dynes/cm². A theoretical estimate of ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) based on Lennard-Jones potentials between atoms in adjacent basal planes gives a value of 9·07 × 10¹³ dynes/cm².     

Properties of extremely high molecular weight polystyrene in solution

Extremely high molecular weight polystyrenes with a $\text{M}\text{?}{}_{\mathrm{w}}$ in the range 10.8 × 10⁶ to 2.2 × 10⁷ were prepared by emulsion polymerization initiated with a heterogeneous initiator at 30°C, which has a ‘living character’. Samples of polystyrene were characterized by light scattering and viscometry in toluene and benzene at 25°C, and in θ-solvent cyclohexane at 34.8°C. Also determined were the relationships of mean-square radius of gyration 〈s²〉 (m²) and the second virial coefficient A₂ (m³ mol kg^?2) on the molecular weight, which for toluene and benzene are described in equations: Toluene (25°C) $\text{〈s}{}^2\text{〉=1.59 × 10}{}^{\mathrm{?23}}\text{M}\text{?}{}_{\mathrm{w}}{}^{1.23}$; $\text{A}{}_2\text{=4.79 × 10}{}^{\mathrm{?3}}\text{M}\text{?}{}_{\mathrm{w}}{}^{\mathrm{?0.63}}$; Benzene (25°C) $\text{〈s}{}^2\text{〉=1.23 × 10}{}^{\mathrm{?22}}\text{M}\text{?}{}_{\mathrm{w}}{}^{1.20}$; $\text{A}{}_2\text{=2.59 × 10}{}^{\mathrm{?3}}\text{M}\text{?}{}_{\mathrm{w}}{}^{\mathrm{?0.59}}$. The parameters in the Mark-Houwink-Sakurada equation were established, for extremely high molecular weight polystyrene in toluene and in benzene, at 25°C into the form giving for $\text{[η] (}\text{m}{}^3\text{kg}{}^{\mathrm{?1}}\text{): [η] = 8.52 × 10}{}^{\mathrm{?5}}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.61}$; $\text{[η] = 1.47 × 10}{}^{\mathrm{?4}}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.56}$. The mentioned relations, as well as the obtained values of Flory parameter ?₀ and of ratio $\text{[η]}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.5}$ were compared with solution properties of high molecular weight polystyrene with narrow molecular weight distribution prepared by anionic polymerization by Fukuda et al.     

Poly(ortho-vinylbenzophenone)

This article reports the synthesis and free radical polymerization of ortho-vinylbenzophenone. The glass transition temperature T_g of the homopolymer is 136°C. The products synthesized appeared to be atactic and amorphous. The Mark-Houwink constants for poly (o-vinylbenzophenone) in tetrahydrofuran are K = 4.2 × 10^?2 cm³ g^?1 and a = 0.765. The pre-exponential constant under theta conditions, K_θ, is estimated to be 5.93 × 10^?2 cm³ g^?1. The ratio of unperturbed dimensions of the actual polymer and free rotating analogue chain is 3.93, which is almost double that of polystyrene. The Flory-Huggins interaction parameter for poly $\text{(o-}\text{vinylbenzophenone}\text{)}\text{tetrahydrofuran}$ is 0.48 at room temperature. The $\text{k}{}_{\mathrm{<mtext>p</mtext>}}\text{k}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>t</mtext>}}$ ratio at 60°C is $\text{1.1 × 10}{}^{\mathrm{?2}}\text{l}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{s}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$. In free radical copolymerizations with styrene at 70°C, r₁ (o-vinylbenzophenone) = 1.216, r₂ = 0.751. This copolymerizations is virtually random.     

Poly(ethyl acrylate) in dilute solution

Poly(ethyl acrylate) (PEA), solution polymerized in methyl ethyl ketone by free radical initiation, was fractionated and the fractions were characterized by light scattering, viscometry and osmometry. Fractions obtained were in the molecular weight range of 0·3 × 10⁶ to 1·6 × 10⁶ with a polydispersity of 1.40. The following Mark-Houwink relations were established:

$\text{[η]}{}^{\mathrm{<mtext>35°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>acetone</mtext>}}\text{=4·15×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?61}}{}_{\mathrm{W}}$

$\text{[η]}{}^{\mathrm{<mtext>35°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>MEK</mtext>}}\text{=2·03×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?66}}{}_{\mathrm{W}}$

$\text{[η]}{}^{\mathrm{<mtext>39.5°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>n-propanal</mtext>}}\text{=7·89×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?50}}{}_{\mathrm{W}}$

It was found that n-propanol at 39.5°C was a theta solvent for poly(ethyl acrylate) and that acetone was a poor solvent compared to methyl ethyl ketone. A relation between the molecular dimension and the molecular weight was established. It was observed that the chain dimensions of poly(ethyl acrylate) and poly(butyl acrylate) were considerably larger than poly(ethyl methacrylate) and poly(butyl methacrylate) respectively. The validity of various extrapolation procedures that have been proposed for calculating the unperturbed dimensions have been examined. The steric factor for PEA was 2·16 compared to 2·10 for poly(ethyl methacrylate). Root mean square end-to-end distances were calculated from the Debye-Bueche and Kirkwood-Riseman methods and compared with the experimental values.     

Unperturbed dimensions of poly(phenyl acrylate)

Thirteen fractions of poly(phenyl acrylate) have been prepared with weight-average molecular weight ranging from 0.158 × 10⁶ to 2.57 × 10⁶ g mol^?1. The temperature coefficient of the unperturbed dimensions and the glass transition temperature were found to be ?1.8 × 10^?3 deg^?1 and 55.6°C respectively. Good accord was obtained among different methods for establishing θ-conditions of 11.5°C in ethyl lactate. From viscometry, osmometry and light scattering under θ-conditions, as well as in a good solvent, the unperturbed dimensions were determined via several procedures yielding a value of $\text{[〈r}{}^2\text{〉}{}_{\mathrm{0w}}\text{M}\text{?}{}_{\mathrm{w}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 6.0 (±0.2) × 10}{}^{\mathrm{?9}}\text{cm g}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. This corresponds to a steric factor υ = 2.37 (±0.08) and a characteristic ratio C_∞ = 11.3 (±0.8). The polymer chain is thus more rigid than poly(methyl acrylate), but less rigid than poly(phenyl methacrylate). With respect to its T_g and flexibility, poly(phenyl acrylate) bears a strong similarity to poly(benzyl methacrylate).     

Polymer translational diffusion: 2. Non-theta solutions,polystyrene in butan-2-one

The diffusion of linear polystyrene under non-theta conditions in butan-2-one has been studied by Rayleigh light scattered linewidth measurements for the molecular weight range of 2.08 × 10⁶ to 8.7 × 10⁶ and as a function of concentration. By extrapolation of diffusion coefficient values to zero concentration we find that $\text{D}{}_0\text{= 5.5 × 10}{}^{\mathrm{?4}}\text{M}\text{?}{}^{\mathrm{?0.561}}{}_{\mathrm{w}}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$. The first order concentration dependence $\text{k}{}_{\mathrm{<mtext>d</mtext>}}\text{c}$ changes sign as the molecular weight increases, $\text{k}{}_{\mathrm{<mtext>d</mtext>}}$ being fairly small and negative at low molecular weights and increasingly positive above $\text{M}\text{?}{}_{\mathrm{w}}\text{?230 000}$.     

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).     

Viscometric behaviour of polystyrene in tetralin/cyclohexane mixtures

For solutions of polystyrene (M=10⁵–10⁶ g mol^?1), intrinsic viscosities [η] have been measured at 34.5°C, which is the θ temperature for the polymer in cyclohexane. The solvents comprised cyclohexane in admixture with a thermodynamically good solvent, 1,2,3,4-tetrahydronaphthalene (tetralin, TET) over the whole range of solvent composition. From an assessment of several extrapolation procedures, a value of 85 × 10^?3$\text{(±1 × 10}{}^{\mathrm{?3}}\text{)}\text{cm}{}^3\text{g}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ was obtained for K_θ (in the relationship $\text{[η] = K}{}_{\mathrm{\theta }}\text{M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{α}{}^3$, where α is the expansion factor), thus yielding $\text{0.681}\text{A}\text{?}\text{g}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{mol}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, 2.25 and 10.2 for the unperturbed dimensions, steric factor σ and characteristic ratio C_∞ respectively. The value of K_θ was independent of solvent composition despite the finite excess free energy of mixing for the solvent components alone, which has been asserted elsewhere to affect K_θ. The present results, in conjunction with previous ones relating to 98.4°C, indicate a value of ?0.89 × 10^?3 deg^?1 for the temperature coefficient of the unperturbed dimensions.     

The unperturbed molecular dimensions of poly(ethylene oxide) in aqueous solutions from intrinsic viscosity measurements and the evaluation of the theta temperature

Intrinsic viscosity measurements were carried out on five well characterized fractions of poly(ethylene oxide) in aqueous solutions at 24.9°, 34.9°, and 45.5°C. The Stockmayer-Fixman extrapolation was applied to the data: it yields the unperturbed dimensions K₀ of the chain. The unperturbed root-mean-square end-to-end distance $\text{〈}\text{R}\text{?}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_0$ calculated for the polymer fractions in water indicate that the polymer molecules are expanded in this solvent as the temperature is raised. The temperature coefficient of unperturbed dimension, $\text{d In}\text{〈}\text{R}\text{?}{}^2\text{〉}{}_0\text{d}\text{t}\text{= 0.024}\text{K}{}^{\mathrm{?1}}$, calculated for poly(ethylene oxide) in water using the present data is about 100 times higher than the literature values of 0.23 (±0.02) × 10^?3 K^?1 and 0.2 (±0.2) × 10^?3 K^?1, respectively, obtained from force-temperature (‘thermoelastic’) measurements on elongated networks of the polymer in the amorphouse state and form viscosity measurements on this polymer in benzene. A value of θ=108.3°C was obtained from the temperature dependence of the interaction parameter B in the Stockmayer-Fixman equation.     

Thermomechanical heat of deformation studies on cis-polybutadiene

Thermomechanical heat of torsional deformation measurements have been made on crosslinked cis-polybutadiene by means of a Calvet microcalorimeter operated at 30°C. When corrected for volume changes utilizing the Gaussian statistical theory of elasticity, the data gave a value for the relative energy contribution to the torsional couple, $\text{M}{}_{\mathrm{e}}\text{M}$, of 0.14 ± 0.02. Measurements were also made on a sample subjected to simple tensile deformations. The relative energy contribution to the tensile force ($\text{f}{}_{\mathrm{e}}\text{f}$) was found to agree within experimental error with the value obtained for $\text{M}{}_{\mathrm{e}}\text{M}$, and the two results gave an average value for din $\text{〈r}{}^2{}_0\text{〉}\text{d}\text{T}$ of 4.1 × 10^?4 K^?1.     

Poly(sulphopropylbetaines): 2. Dilute solution properties

Solution properties of a series of aromatic ($\text{5 × 10}{}^3\text{<}\text{M}\text{?}{}_{\mathrm{w}}\text{< 2.5 × 10}{}^5$) and aliphatic ($\text{10}{}^6\text{<}\text{M}\text{?}{}_{\mathrm{w}}\text{< 1.2 × 10}{}^7$) poly(sulphopropylbetaines) have been investigated by examining three complementary phenomena: (a) solubility in organic protic solvents; (b) water solubility promoted by various (cloud point titrations), with special emphasis on the influence of the anion polarizability and a comparison between Na⁺ and Ca⁺⁺; (c) hydrodynamic and morphological properties in aqueous NaCl solutions at 25°C, as derived from the Mark-Houwink-Sakurada relations. Chain expansion is a slightly increasing function of the NaCl concentration (≤1 M) but it remains, however, relatively low, even for high molecular weights (α_η < 1.15). With respect to the polymeric amino precursors, the zwitterionic group

enhances chain rigidity (steric factor σ), as a result of its steric hindrance and specific dipolar interactions between neighbouring units.     

Phosphonitrilic chloride: 21. Synthesis of chelating polymers with cyclophosphazene thiocarbamate and the properties of chelating polymers

Chelating polymers containing copper, nickel and cobalt have been formed from cyclophosphazene thiocarbamate trimer and copper, nickel or cobalt ions. These polymers obtained from the reaction are amorphous and the values of electron conductivity are $\text{2·7 × 10}{}^{11}\text{Ω-}\text{cm}$, $\text{3·6 × 10}{}^{13}\text{Ω-}\text{cm}$ and $\text{1·5 × 10}{}^{13}\text{Ω-}\text{cm}$ for the Cu, Ni and Co polymers respectively. The Cu polymer is the most thermally stable on heating to 500°C in air.     

The effects of the bond-bending coefficient on the thermal expansion coefficient of graphite parallel to the hexagonal axis

A calculation is presented of the hexagonal axis thermal expansion coefficient of a graphite crystal up to 1000°K using the measured values of two of the three anharmonic coefficients which affect the out-of-plane acoustic vibrational mode. The third anharmonic coefficient ($\text{?δ}\text{?e}{}_{\mathrm{zz}}\text{)}$, which is determined by changes in the bond-bending constant of a layer plane with interlayer spacing, is shown to lie in the range 0 to ?0.50 × 10^?3cm²/sec.     

The concentration dependence of the angular dissymmetry of light scattered by micellar solutions

A light scattering investigation was made of micelles formed from a polystyrene-poly(ethylene/propylene) two-block copolymer in n-nexane. n-Hexane is a selectively bad solvent for polystyrene and so polystyrene blocks formed the cores of the micelles. The light scattering measurements were made at 25°C for concentrations up to 0.015 g cm^?3. The dissymetry ratio ($\text{I}{}_{\mathrm{45°}}\text{I}{}_{\mathrm{135°}}$) was found to decrease with increase in concentration and it was below unity for measurements at c > 4.8 × 10^?3 g cm^?3. The effect of concentration on the dissymmetry ratio was predicted quite well by assuming the micelle packing could be described by radial distribution functions for hard spheres.     

Influence of the molecular weight of poly(methyl methacrylate) on fracture surface energy in notched tension

Specimens of poly(methyl methacrylate) (PMMA) were prepared by the radiolysis of a polymer from an initial viscosity average molecular weight of $\text{M}\text{?}{}_{\mathrm{v}}\text{= 1.1 × 10}{}^6$ down to 1.5 × 10⁴. Corresponding values of fracture surface energy, ranging from 3.5 × 10⁵ erg/cm² to 4.5 × 10² erg/cm², were calculated from tensile data using Griffith's equation. A theoretical dependence of fracture energy on molecular weight was derived on the assumption that only molecules exceeding a critical molecular weight can contribute to the work of plastic deformation. Comparison with experimental data indicates this molecular weight to be about 1 × 10⁵. Limitations of the theoretical treatment are discussed.     

Characterization of poly(1,4-phenyleneterephthalamide) in concentrated sulphuric acid: 1. Static and dynamic properties

Laser light scattering including angular dependence of total integrated scattered intensity and of the spectral distribution has been used to characterize five samples of poly(1,4-phenylene terephthalamide), PPTA (commercially known as Kevlar), of different molecular weights in 96% sulphuric acid and 0.1 NK₂SO₄. The data are supplemented by intrinsic viscosity measurements used to detect the possible effects of association, by differential refractometry providing a measure of the refractive index increments in mixed solvents (H₂O, H₂SO₄ and K₂SO₄) and by spectrophotometry for the extinction coefficient needed in the correction of attenuation in light scattering studies. The results show 〈D〉Z = 2.11 × 10^?5$\text{M}\text{?}{}_{\mathrm{<mtext>W</mtext>}}{}^{\mathrm{?0.75}}\text{cm}{}^{\mathrm{?2}}\text{s}{}^{\mathrm{?1}}$ in reasonable agreement with an average of many of the published intrinsic viscosity data obeying [η] = 1.09 × 10?3 M_w^1.25 ml g^?1 and _w expressed in g mol^?1.     

Hydrogen mass transfer in liquid hydrocarbons at elevated temperatures and pressures

The mass transfer rate of hydrogen in tetralin and hydrogenated SRC II liquid was studied in a stirred vessel at 606–684 K and 7.0–13.5 MPa. Experiments were carried out using a newly developed in-situ hydrogen probe made of semi-permeable nickel membrane. The effects of stirrer speed, liquid height to vessel diameter ratio, temperature and pressure on mass transfer rate coefficients were investigated. The experimentally determined $\text{K}{}_{\mathrm{<mtext>l</mtext>}}\text{a}$ values were correlated in terms of power input per unit volume of liquid and liquid height to vessel diameter ratio as follows: $\text{k}{}_{\mathrm{<mtext>L</mtext>}}\text{a = 3.43 × 10}{}^{\mathrm{?4}}\text{(}\text{P}\text{V}\text{)}{}^{0.8}\text{(}\text{H}\text{D}{}_{\mathrm{<mtext>T</mtext>}}\text{)}{}^{\mathrm{?1.9}}$ Furthermore, the liquid-phase mass transfer coefficient, $\text{k}{}_{\mathrm{<mtext>l</mtext>}}$, was found to be of the order of 10^?5 m s^?1 for low agitator speeds.     

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.