The time dependent strain potential function for a polymeric glass

Torsion and normal force measurements were made during single step stress relaxation experiments on a polymeric glass (PMMA). Isochronal data were analysed using an approach adapted from that developed by Penn and Kearsley¹ (for incompressible elastic materials) to determine the derivatives $\text{?W}\text{?I}{}_1$, and $\text{?W}\text{?I}{}_2$ of the time dependent strain potential function. $\text{?W}\text{?I}{}_1$ and $\text{?W}\text{?I}{}_2$ are determined from existing solution to the torsion of an incompressible cylinder. A special solution to the torsion of a compressible cylinder is presented and it is shown that the values of $\text{?W}\text{?I}{}_1$ and $\text{?W}\text{?I}{}_2$ obtained using this solution to analyse the data do not differ greatly from those obtained using the incompressible solution. It is found from both solutions that $\text{?W}\text{?I}{}_1$ is negative and increases towards zero with increasing time and deformation while $\text{?W}\text{?I}{}_2$ is positive, greater in magnitude than $\text{?W}\text{?I}{}_1$ and decreases towards zero with increasing time and deformation. These results were unexpected and a full understanding of their meaning has yet to be reached.     

Concentration dependence of the primitive path step length

Recent experiments by Donald and Kramer have measured the extension ratio, λ_craze, for polymers in crazes under tensile strain. In this paper it is shown that $\text{λ}{}_{\mathrm{<mtext>craze</mtext>}}\text{∝I}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>e</mtext>}}\text{i}$ where I_e is the average contour length between entanglements in glassy, and not permanently crosslinked polymers and is obtained from melt elasticity experiments. It is also shown that I, the Rouse chain step length for a molten polymer, is independent of monomer density and that the average distance between entanglements, d ∝ ?^?α, where ? is the number of monomers per unit volume with $\text{1}\text{4}\text{? α ?}\text{1}\text{2}$. Finally these results are shown to provide confirmation for the configurational assumptions of the primitive path for reptation in which α appears as the determining factor for the concentration dependence of the relaxation modulus, the steady state viscosity and terminal relaxation time.     

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.     

Raman scattering from mixtures of poly(ethylene oxide) 2000 with poly(ethylene oxide) 200

The longitudinal acoustic mode fundamental (v₁) and third harmonic (v₃) in 2000 MW PEO with both hydroxy- and methody-end-groups have been observed in the Raman spectrum as a function of 200 MW PEO oligomer content. Measurements of small-angle X-ray spacing I_x permit interpretation using a composite rod model. A good fit to the measured quantities v₁I_x and $\text{v}{}_3\text{v}{}_1$ is obtained with crystal length I_c≈9 nm, crystal modulus $\text{E}{}_{\mathrm{<mtext>c</mtext>}}\text{= 9 ×}\text{10}{}^{10}\text{N}\text{m}{}^2$ and amorphous modulus $\text{E}{}_{\mathrm{a}}\text{= 1 ×}\text{10}{}^{10}\text{N}\text{m}{}^2$. The value of Ic implies a crystalline content of ～70% for the pure polymer; the value of Ec is larger than static determinations and similar discrepancies in other materials are discussed.     

A study of dilation coefficients of cis-polybutadiene in simple extension

Force-pressure measurements at constant length and temperature have been made on a sample of crosslinked cis-polybutadiene in the range1·11<α<1·77 in order to determine values of the dilation coefficient $\text{(}\text{?}\text{ln}\text{V}\text{?}{}_{\mathrm{\alpha }}\text{)}{}_{\mathrm{P,T}}$. The results obtained, together with data reported earlier for natural rubber and butyl rubber, are compared with the predictions of (a) the Gaussian theory of rubber elasticity, and (b) a relationship based on the assumption that the linear compressibility is isotropic in extension.     

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.     

Thermal expansion and Grüneisen parameter of polyethylene between 5 and 320 K

The linear thermal expansion coefficient, α, of polyethylene with crystallinity X=0.44, 0.62, 0.77 and 0.98 has been measured between 5 and 320 K with an experimental accuracy of about 5% above 15 K and 10% below 15 K using an interferometric dilatometer system. In the temperature range 40 to 100 K the thermal expansion is found to be independent of crystallinity, whereas at lower as well as higher temperatures, α increases with increasing noncrystallinity. By linear extrapolation the thermal expansion coefficient of the noncrystalline phase can be estimated. The influence of the phonon spectrum on the thermal expansion is discussed in terms of the Grüneisen parameter. For completely crystalline polyethylene, a bulk-Grüneisen parameter of $\text{γ}{}_{\mathrm{<mtext>b</mtext>}}\text{?2}$ is found below 20 K. This value is smaller than expected from theories for polymer crystals. For noncrystalline polyethylene, γ_b is constant ($\text{γ}{}_{\mathrm{<mtext>b</mtext>}}\text{?1.6}$) between 30 and 100 K, showing a rapid increase at lower temperatures with $\text{γ}{}_{\mathrm{<mtext>b</mtext>}}\text{?12.5}$ at 5 K. This high value for γ_b can be related to excess modes in the vibration spectrum of the noncrystalline phase, which have previously been found to contribute also to the heat capacity at these temperatures.     

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.     

Physical characterization of suspension-crosslinked polystyrene particles and their sulphonated products: 2. Ionic networks

Strong cationic resins have been prepared from isoporous polystyrene networks in bead form with H₂SO₄ and HSO₃Cl as sulphonating agents. The effect of the reaction time of H₂SO₄ sulphonation on ion exchange capacity has been examined. The polymer-solvent interaction parameter, X, with aqueous electrolyte solutions has been calculated after minimization of electrostatic repulsions. The average molecular weight per crosslinked unit, $\text{M}\text{?}{}_{\mathrm{<mtext>c</mtext>}}$ has been measured after sulphonation and an estimation of formation of sulphone-type crosslinks has been attempted. The average size of the network structure, r_c, has been calculated as a function of the ionic strength of aqueous electrolyte solutions for networks of different molecular weight per crosslinked unit, $\text{M}\text{?}{}_{\mathrm{<mtext>c</mtext>}}$. The ion exchange capacity of the prepared resins has been measured.     

Pulsed n.m.r. of cis-polyisoprene: 1

Proton spin-spin (T₂), and spin-lattice (T₁) relaxation time measurements are reported for six monodisperse cis-polyisoprenes ($\text{M}\text{?}{}_{\mathrm{n}}$ from 2000 to 200 000) over the temperature range from ?50° to 170°C. At low temperatures (?30° to 10°C) T₁ and T₂ are determined by the short range segmental motions but above 10°C T₂ is sensitive to the long range motions. When $\text{M}\text{?}{}_{\mathrm{n}}\text{? 30 000 T}{}_2$ becomes influenced by the presence of entanglements which produce a transient network structure and this confers on the spin-spin relaxation a pseudo-solid-like response. Similar behaviour is observed in crosslinked networks produced by irradiation. The results are discussed in terms of the types of motion occurring in amorphous polymers above T_g and the analogy with dynamic mechanical measurements is discussed.     

The pressure-dependence of the conductivity of graphite

An analysis has been made of experimental results of the pressure-dependence of the conductivity taking into account recent work on the evaluation of pressure derivatives of the band parameters (d ln $\text{γ}{}_1\text{d}{}_{\mathrm{p}}$) which are sensitive to the band model chosen and assumptions used to interrelate the derivatives. The pressure-dependence of the conductivity of pyrolytic graphite at low temperature is analyzed in detail, including the influence of the band overlap parameter γ₃ and effects related to carrier non-degeneracy, which are shown to be very important in analyzing experimental results.     

Thermoelastic and thermomechanical studies on natural rubber vulcanized in the swollen state

Three samples of natural rubber were crosslinked in n-decane solution. After the solvent had been removed, a thermodynamic investigation was made of the elastic behaviour of the samples in simple extension. Thermoelastic measurements at constant pressure and length were carried out on the first two samples. The third sample was subjected to a thermomechanical heat of extension study using a Calvet microcalorimeter. The experiments enabled the temperature coefficient of the mean-square unperturbed dimensions, 〈r²₀〉, to be derived. From the thermoelastic measurements average values for dln $\text{〈r}{}^2{}_0\text{d}\text{T}$ of (0.44 ± 0.08) × 10^?3deg^?1 and (0.38 ± 0.07) × 10^?3deg^?1 were obtained, whilst the thermomechanical measurements gave a value of (0.54 ± 0.04) × 10^?3deg^?1.     

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.     

Thermal stability and structure of graphite-antimony pentachloride compounds

It is shown that antimony chloride reacting with graphite forms lamellar compounds C_12n SbCl₅ (n = 1,2,3,4,…). The identity period along the $\text{c}\text{?}$ axis is $\text{I}{}_{\mathrm{c}}\text{= 9.42}\text{A}\text{?}$ for the first stage and $\text{I}{}_{\mathrm{c}}\text{= 9.36 + (n ?1)3.36}\text{A}\text{?}$ for the other stages. Electron diffraction and X-ray studies of the hk0 reflexions with a goniometric apparatus permit to specify the structure of the compounds of n > 2. The single graphite crystals are fragmented into many ordered fields which are themselves rotated by 60°. The structure of the carbon layers remains unchanged after intercalation. The intercalated antimony pentachloride forms a hexagonal system: $\text{a = 17.23}\text{A}\text{?}\text{(2.46}\text{A}\text{?}\text{× 7)}$ the $\text{a}\text{?}$ axis being the same as the one for graphite.     

Polymerization of poly(dimethylsiloxane) macromers: 1. Copolymerization with styrene

The synthesis and characterization of methacrylate-ended macromers ($\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ 500 to 10 000) and their copolymerization with styrene (M₂) is described. The experimental errors in the values of the reactivity ratios r₁ render them meaningless. Values of r₂ can be determined with more precision and increase from 1.06 to 1.55 as the molecular weight of the macromer increases. This behaviour is due to steric effects, not diffusion-controlled propagation. It is shown that the assumptions that $\text{1 > r}{}_1\text{[}\text{M}{}_1\text{]}\text{[}\text{M}{}_2\text{]}$ and $\text{r}{}_2\text{>}\text{[}\text{M}{}_1\text{]}\text{[}\text{M}{}_2\text{]}$ are only valid for macromers of $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}\text{> ca. 10 000}$.     

Branched poly(ethylene terephthalate) correlations between viscosimetric properties and polymerization parameters

Samples of poly(ethylene terephthalate) (PET) modified with small amounts of trimesic acid groups and hence containing long chain branching have been prepared. From the content of trifunctional modifier and from the experimental value of the extent of reaction, the weight-average molecular weight $\text{M}\text{?}{}_{\mathrm{w}}$ and branching density $\text{B}\text{?}{}_{\mathrm{w}}$ have been calculated, assuming that all the end-groups are equally reactive and intramolecular reactions are absent. The values of $\text{M}\text{?}{}_{\mathrm{w}}$ and $\text{B}\text{?}{}_{\mathrm{w}}$ have been correlated with the experimental values of intrinsic viscosity [η] and the Newtonian melt viscosity η₀. General relations of the following type have been obtained:

$\text{f}{}_1\text{([η],}\text{M}{}_{\mathrm{w}}\text{,}\text{B}{}_{\mathrm{w}}\text{) = 0; f}{}_2\text{(η}{}_0\text{,}\text{M}{}_{\mathrm{w}}\text{,}\text{B}{}_{\mathrm{w}}\text{) =0; f}{}_3\text{(η}{}_0\text{, [η],}\text{B}{}_{\mathrm{w}}\text{) = 0; f}{}_4\text{(η}{}_0\text{, [η],}\text{M}{}_{\mathrm{w}}\text{) = 0;}$

In particular, [η] and η₀ increase on increasing $\text{M}\text{?}{}_{\mathrm{w}}$ and decrease on increasing $\text{B}\text{?}{}_{\mathrm{w}}$, but, at equal [η] values, η₀ increases with $\text{B}\text{?}{}_{\mathrm{w}}$. Through the last relation, the reliability limits of which should be experimentally checked, and from measurements of [η] and η₀, it is possible to calculate $\text{M}\text{?}{}_{\mathrm{w}}$ of a branched PET.     

Copoly(m,p-chloromethylstyrene-50% styrene): Copolymer molecular weights,fractionation and derivatization

Copolymerization of an equimolar mixture of m,p-chloromethylstyrene ($\text{M}$₁) and styrene ($\text{M}$₂) was carried out in chlorobenzene in the presence of AIBN at 80°C. Molecular weight analysis (by g.p.c.) of the resulting polymer samples was performed at various conversions. $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}$, $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$, and ($\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$) value of 21 300, 13 800 and 1.54 were obtained at 8.9% conversion. At higher conversions, the value of $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}$ remained effectively constant while $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ decreased to 9200 at ca. 80% conversion, and then increased to 12 000 at about 100% conversion (16 h), and to 13 700 if the polymer solutions were maintained at 80°C for an additional 44 h. These results suggest that, although the termination step initially involves the combination of polymer radicals, at high conversions a large number of very low molecular weight, and unsaturated, polymer molecules are formed possibly by disproportionation involving polymer radicals and primary radicals. The unsaturated polymer molecules are subsequently polymerized by growing polymer radicals towards the end of the polymerization. It was noticed that further reaction occurred after complete depletion of monomer, involving radical attack on the unsaturated polymer molecules. Other reactions including chain transfer to polymer will also be important at high polymer concentrations. A copolymer of $\text{M}$₁ and $\text{M}$₂ was separated into four fractions on a preparative scale, and molecular weight analysis of the resulting polymer samples provided more evidence of the above interpretation. G.p.c. analysis of several derivatives of a copolymer of $\text{M}$₁ and $\text{M}$₂ showed that most molecular weights were much lower than that of the starting polymer. These results in some cases may reflect the chemical or dimensional changes introduced into the polymer molecules during derivatization.     

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.     

Effects of metal-support interactions on the synthesis of methanol over palladium

The synthesis of methanol and other products from CO and H₂ was studied over Pd catalysts prepared by adsorption of Pd(π-C₃H₃)₂ on MgO, ZnO, La₂O₃, γ-Al₂O₃, SiO₂, TiO₂, and ZrO₂ as well as over a SiO₂-supported Pd catalyst prepared from PdCl₂ and Pd black. Both the activity and selectivity of Pd were affected strongly by the nature of the support and the composition of the Pd precursor. The specific activity for methanol synthesis decreased in the order $\text{Pd}\text{La}{}_2\text{O}{}_3$ ? $\text{Pd}\text{SiO}{}_2$ [derived from PdCl₂] > $\text{Pd}\text{ZrO}{}_2$ > $\text{Pd}\text{ZnO}\text{≈}\text{Pd}\text{MgO}$ > PdTiO₂ > $\text{Pd}\text{Al}{}_2\text{O}{}_3\text{≈}\text{Pd}\text{SiO}{}_2$ [derived from Pd(π-C₃H₅)₂] ? Pd black, while the specific activity for hydrocarbon synthesis decreased in the order $\text{Pd}\text{TiO}{}_2\text{?}\text{Pd}\text{ZrO}{}_2$ > $\text{Pd}\text{La}{}_2\text{O}{}_3$ > $\text{Pd}\text{Al}{}_2\text{O}{}_3\text{≈}\text{Pd}\text{SiO}{}_2$ [derived from PdCl₂] ? $\text{Pd}\text{SiO}{}_2$ [derived from Pd(π-C₃3H₅)₂] ≈ Pd black ? $\text{Pd}\text{MgO}\text{?}\text{Pd}\text{ZnO}$. Dimethyl ether production was observed over four of the catalysts and the activity for formation of this product decreased in the order $\text{Pd}\text{Al}{}_2\text{O}{}_3\text{?}\text{Pd}\text{TiO}{}_2\text{?}\text{Pd}\text{MgO}\text{≈}\text{Pd}\text{ZrO}{}_2$. The effects of support composition on the catalytic properties of Pd are discussed in the light of current ideas concerning metal-support interactions and the acid-base properties of the support.     

Assessment of the activities of catalysts for the hydrocracking of coal by means of hydrogen evolution

A close relation has been found between hydrogen evolution from coal-catalyst and pitch-catalyst systems and catalytic activities of liquefaction reactions. A MoO₃?TiO₂ catalyst has the highest activity and the order of activity of the catalysts for hydrogen evolution is: MoO₃?TiO₃> MoO₃?SiO₂>10% $\text{Fe}{}_2\text{O}{}_3\text{TiO}{}_2\text{?AI}{}_2\text{O}{}_3\text{>}\text{coal alone}$. The same trend was observed for benzene-soluble materials for the hydrocracking of Akabira Coal.