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).     

Conversion of work of deformation to heat in polymers

The time dependence of the conversion of mechanical work of deformation to heat in polymers is investigated using viscoelastic models. The deformation chosen is a constant strain rate, $\text{?}\text{?}{}_0$, in tension for t?t₀ and a constant strain $\text{?}{}_0\text{=}\text{?}\text{?}{}_0\text{t}{}_0$ for t?t₀. For a simple Maxwell model with only one relaxation time, τ, the ratio of heat produced to work done (‘conversion fraction’) is calculated as a function of time for different values of $\text{t}{}_0\text{τ}$. At t=t₀ the conversion fraction is high only when τ?₀. For a continuous Maxwell model with a distribution of relaxation times H(τ) we obtain the result that the conversion fraction is near 100% at t=t₀ if H(τ) is not peaked strongly in the region τ>0·1t₀ but extends with reasonable values into the region τ < 0·1t₀. A formula is given which allows the calculation of the conversion fraction at t=t₀ from the distribution of relaxation times H(τ).     

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.     

Experiments on the small-strain behaviour of crosslinked natural rubber: 1. Torsion

The torsional behaviour of 1, 3 and 5 phr peroxide crosslinked natural rubber has been characterized over a range of strains from near the undistorted state (γ ≈ 0.017) to γ ≈ 1.0. Isochronal measurements of both torque and normal force were used to calculate values of the derivatives of the strain energy function W with respect to the first and second stretch invariants I₁ and I₂. In the course of our work we found that, contrary to many reports in the literature, $\text{?W}\text{?I}{}_1$ was affected significantly by the amount of crosslinking. Finally for the 1 phr peroxide crosslinked rubber it was found that, while ageing for 14 months at ambient conditions did not significantly affect the small-strain torsional modulus, $\text{G = 2(}\text{?W}\text{?I}{}_1\text{+}\text{?W}\text{?I}{}_2\text{)}$, it did significantly affect the individual derivatives $\text{?W}\text{?I}{}_1$ and $\text{?W}\text{?I}{}_2$.     

Studies of cyclic and linear poly(dimethyl siloxanes): 3. Neutron scattering measurements of the dimensions of ring and chain polymers

The dimensions of both cyclic and linear poly(dimethyl siloxanes) in dilute solution in benzene-d₆ have been measured by small-angle neutron scattering. The mean-square radii of gyration of the linear polymers are consistent with values predicted from published data, including experimental molar cyclization equilibrium constants. The average dimensions of the cyclic poly(dimethyl siloxanes) in fractions containing z-average numbers of bonds $\text{n}\text{?}{}_{\mathrm{z}}$ in the range $\text{130 <}\text{n}\text{?}{}_{\mathrm{z}}\text{< 550}$, were found to be considerably smaller than those of the corresponding linear polymers. The neutron scattering results give a value for the ratio of the z-average radii of gyration for linear and ring poly(dimethyl siloxanes) (containing the same number of monomer units) $\text{〈s}{}^2\text{〉}{}_{\mathrm{z,l}}\text{<s}{}^2\text{〉}{}_{\mathrm{z,r}}\text{= 1.9 ± 0.2}$. This ratio may be compared with the value of 2.0 predicted theoretically for ‘flexible’ high molecular weight linear and cyclic polymers, unperturbed by excluded volume effects.     

Anistropic thermal expansion of oriented crystalline polymers

The linear thermal expansitivity of oriented high-density polyethylene (HDPE) and polypropylene (PP) with draw ratio between 1 and 18 has been measured between 120 and 300 K. The expansivity perpendicular to the draw direction $\text{z}\text{?}\text{(α}{}_{\mathrm{\perp }}\text{)}$ increases with λ, because of the alignment of the crystallite chain axes along ?; the expansivity parallel to $\text{z}\text{?}\text{(α}{}_{\mathrm{}}\text{)}$ decreases very sharply with λ, becoming negative at about λ = 3 for HDPE and λ = 7 for PP — a consequence of the negative expansivity of the crystalline phase along its chain axis and the constraining effect of the stiff intercrystalline bridges. A model treating the drawn crystalline polymer as a composite consisting of partly aligned crystallites embedded in an isotropic amorphous matrix is adequate for explaining the behaviour of α_⊥, whereas a parallel-series model can give reasonable estimates of $\text{α}{}_{\mathrm{}}$ for ultra-oriented samples, which is largely independent of λ and decreases with increasing temperature. However, neither model can account for the behaviour of $\text{α}{}_{\mathrm{}}$ at low draw ratio.     

Temperature dependence of polymer chain dimensions in the polystyrene-cyclopentane system

The limiting viscosity number in polystyrene-cyclopentane system has been determined over the temperature range of θ_u to θ_l in which θ_u and θ_l are the θ or Flory temperature for the upper and lower critical solution temperatures. The temperature coefficient of unperturbed mean square end-to-end distance observed for the polystyrene (M_w=20×10⁴, $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}\text{<1·06}$ and M_w=67×10⁴, $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}\text{<1·10}$) in cyclopentane is negligibly small. The observed temperature dependence of the polymer chain dimension over the temperature range of θ_u=19·6° to θ_l=154·2°C shows a parabolic curve with a maximum in the neighbourhood of 90°C and is qualitatively interpreted by the free volume theory of polymer solution, which gives a new χ₁-temperature function.     

Dielectric constants of coal-derived liquids and slurries with coal at 750 MHz

The real part of the complex dielectric constants of SRC-I recycle solvent, SRC-II naphtha, middle distillate and heavy distillate, and tetralin were measured over the temperature range of 23° to 140°C. Values were strongly temperature dependent, generally increasing with temperature and increasing in the sequence naphtha < heavy distillate < recycle solvent < middle distillate, and were related to the phenolic contents of the liquids. The temperature dependence was attributed to the viscosity which in turn affects the relaxation behaviour of the dipolar molecules in the liquid. Association-dissociation equilibria of the polar components also affect the dielectric constant. Measurements of slurries of the SRC-I recycle solvent with coal show that the real part of the dielectric constant, $\text{}\text{?}$g3′, is given by the Looyenga equation, $\text{}\text{?}\text{g3′ = [ε′}\text{1}\text{3}{}_2\text{+φ}{}_1\text{(ε′}\text{1}\text{3}{}_1\text{?ε′}\text{1}\text{3}{}_2\text{)]}{}^3$, where ε′₁ and ε′₂ are respectively the real parts of the dielectric constant of the coal and the solvent and φ₁ is the volume fraction of the coal.     

Carbon formation from methane in combustion products

The rates of deposition of carbon on alumina surfaces and on soot particles, have been measured in a pilot scale tubular reactor in which cold methane was mixed with combustion products at 1920°K. A hard grey metallic film of carbon, quite free of soot, was deposited on alumina surfaces for initial methane concentrations between 12 and 24 per cent. An induction period of slow growth rate, before a film covered the surface completely, was followed by a constant growth rate. Measured growth rates were from 0·06 × 10^?6 to 1·43 × 10^?6 g/cm² sec of carbon on alumina at 1270°K to 1450°K, and from 0·1 × 10^?4 to 1·14 × 10^?4 g/cm² sec on soot particles at 1370°K to 1700°K. Methane decomposition rates were much higher than predicted by the unimolecular mechanism indicating a predominance of radical reactions. Carbon deposition rates were related to the mole fraction, χ, of hydrocarbons in the gas which bear more than three carbon atoms per molecule, by, $\text{m}\text{?}{}_{\mathrm{f}}\text{= 1·0 × 10}{}^2\text{n.χ}$. exp (?42,300/RT_f), g/cm²sec for carbon film, $\text{m}\text{?}{}_{\mathrm{s}}\text{= 4·6 × 10}{}^3\text{nχ}$ exp (? 46,100/RT_g), g/cm² sec for soot. A precoat of soot increased the growth rate of film carbon by 1·8 to 7·8 times yielding a hard adherent dull brown film     

Studies of cyclic and linear poly(dimethyl siloxanes). 4. Bulk viscosities

The bulk viscosities η of over fifty sharp fractions of cyclic and linear poly(dimethyl siloxanes) in the weight-average molecular weight range $\text{500 <}\text{M}\text{?}{}_2\text{< 25 000}$ have been measured at 298 K using a cone- and-plate microviscometer. In the Iow molecular weight region $\text{M}\text{?}{}_{\mathrm{W}}\text{< 1000}$) the η values for the cyclics were found to be at least three times as large as the values for the corresponding chain molecules. By contrast, in the highest molecular weight region ($\text{M}\text{?}{}_{\mathrm{W}}\text{> 16 000}$), the η values for the cyclics were approximately one-half those for the corresponding linears. Cyclics and linears containing about one hundred skeletal bonds were found to have similar bulk viscosities. The temperature dependence of the bulk viscosities of eighteen of the cyclic and linear fractions were investigated, and the relationship $\text{η = A}\text{exp}\text{(}\text{E}{}_{\mathrm{<mtext>visc</mtext>}}\text{RT}\text{)}$ was used to deduce values for the energies of activation for viscous flow E_visc and the constants A.     

Interaction parameters in the n-undecane/butanone/poly(dimethyl siloxane) system

Intrinsic viscosities, [η], second virial coefficients, A₂, preferential solvation coefficients, λ, and binary interaction potential as measured by light scattering, g₁₂, for the system n-undecane(1)/butanone(2)/poly(dimethylsiloxane) (3) have been determined at 20.0°C. The system shows cosolvent character, as the inversion in λ and the maxima in A₂ and in [η], at $\text{ø}{}_{10}\text{?0.65}$, seem to indicate. (g₁₃ – sg₂₃) and the ternary interaction potential, g_T, and its derivatives on system composition, and , have been evaluated. Global interaction parameters, χ_m3, have also been evaluated and a critical analysis on the approximations usually followed for χ_m3 calculations is undertaken.     

Annealing of polyethylene crystals in the hexagonal phase

The kinetics of thickening of polyethylene crystals in the hexagonal phase is studied. Distributions of thickness, L, of bands and/or lamellae are obtained by electron microscopy for a specimen annealed at p=6.1 kbar, T=242°C for 30, 300, 3600 and 86400 seconds. The dependence of the average band thickness $\text{L}\text{?}\text{(t)}$ on the annealing time t can be expressed as $\text{L}\text{?}\text{(t)=46·}\text{log}\text{(}\text{t}\text{t}{}_0\text{)+}\text{L}\text{?}\text{(t}{}_0\text{) [}\text{nm}\text{]}$. Moreover, these distributions can be superposed on each other if we scale L by $\text{L}\text{?}\text{(t)}$. A model for the thickening process of a lamellae is proposed; coalescence of two bands occurs by disappearance of the boundary with the rate proportional to exp(?αL). The value of α depends on the mobility of defects in the boundary and is discussed in detail.     

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.     

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.     

Cloud-point curves of the polystyrene-cyclohexane system near the critical point

Cloud-point curves for solutions of five polystyrene samples, including three well-fractionated polystyrenes, in cyclohexane have been examined near their critical points. Even for a solution of polystyrene characterized by $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}\text{<1.03}$, the critical point determined by the phase-volume method is generally situated on the right hand branch of the cloud-point curve. The precipitation threshold concentration is appreciably lower than the critical concentration, while the threshold temperature slightly deviates from the critical temperature. The agreement of the precipitation threshold point with the critical point has been found for a solution of polystyrene characterized by M_w=20×10⁴ and $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}\text{<1.02}$ in cyclohexane. The η(φ) function derived from critical miscibility data is expressed by $\text{χ(φ) = 0.2798+}\text{67.50}\text{T}\text{+0.3070φ+0.2589φ}{}^2$, which yields θ of 33.2°C and ψ₁ of 0.22.     

Synthesis of electroreactive polymers from poly (m,p-chloromethylstyrene) and copoly (m,p-chloromethylstyrene-styrene)

Polymerization, and copolymerization with styrene, of m,p-chloromethylstyrene have been carried out at 75°C, in chlorobenzene and in the presence of AIBN ($\text{[}\text{AIBN}\text{] ? 6 × 10}{}^{\mathrm{?2}}$, and $\text{12 × 10}{}^{\mathrm{?2}}\text{m}$, respectively). The polymer molecular weights, determined by g.p.c., are: $\text{M}\text{?}{}_{\mathrm{w}}\text{= 8670}$, $\text{M}\text{?}{}_{\mathrm{n}}\text{= 5860}$, and $\text{M}\text{?}{}_{\mathrm{w}}\text{/-M}{}_{\mathrm{n}}\text{= 1.48}$ for the homopolymer, poly(m,p-chloromethylstyrene), (1a); and $\text{M}\text{?}{}_{\mathrm{w}}\text{= 8805}$, $\text{M}\text{?}{}_{\mathrm{n}}\text{= 5144}$, and $\text{M}\text{?}{}_{\mathrm{w}}\text{/-M}{}_{\mathrm{n}}\text{= 1.71}$ for the copolymer, copoly(m,p-chloromethylstyrene-styrene), (2a). A series of phosphine derivatives of both 1a and 2a are prepared by the reaction of the polymers with either chlorodiphenylphosphine/lithium, or diphenylphosphine/potassium tert. butoxide. A number of other potentially electroreactive derivatives of 2a are obtained by reacting the polymer with 2-aminoanthraquinone, 3-N-methylamino-propionitrile, or 2-(2-aminoethyl) pyridine. The phosphinated polymers are reacted with bis-benzonitrilepalladium-(II) chloride to obtain a series of polymer-palladium(II) complexes containing 8.5–12.9% palladium. Similarly, reaction of the last-named bidentate polymeric ligand with cupric acetylacetonate, or cupric sulphate pentahydrate, produces polymer-copper(II) complexes having 5.8, or 3.3% copper, respectively. The inter/intra-chain nature of some of the side reactions during the derivatization of the chloromethylated polymers, and that of the complex formation between transition metal centres and macromolecular ligands, are briefly discussed in view of the experimental results.     

Molecular weight distribution and stereoregularity of polypropylenes obtained with Ti(OC4H9)4Al2(C2H5)3Cl3 catalyst system

The effects of temperature and catalyst homogeneity on the molecular weight distribution (MWD) and stereochemical regulation of polypropylenes produced by $\text{Ti(OC}{}_4\text{H}{}_9\text{)}{}_4\text{Al}{}_2\text{(}\text{C}{}_2\text{H}{}_5\text{)}{}_3\text{Cl}{}_3$ system have been investigated. The MWD of polymers obtained at temperatures below 21°C were unimodal and narrow ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{?2.0}$), whereas those obtained at temperatures higher than 31°C were bimodal with one narrow distribution and the other broad one ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{=18}$) at higher molecular weights. The existence of two different types of catalyst, one soluble with homogeneous catalytic centres and the other insoluble with heterogeneous catalytic centres was found in the polymerization at 41°C. At temperatures below 21°C only soluble catalyst was present and produced isotactic polypropylenes with [m]=0.65. The isospecific nature of soluble titanium-based catalyst is greatly contrasted to the syndiospecific nature of soluble vanadium-based catalyst.     

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.