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 $\text{?W}\text{?I}{}_2$.     

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.     

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 $\text{M}\text{?}{}_{\mathrm{w}}\text{?230 000}$.     

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.     

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.     

Poly(ethyleneoxide-b-styrene) copolymers as solid—liquid phase transfer catalysts

Di- and tri-block copolymers of ethylene oxide and styrene function as effective phase transfer catalysts in the reaction of solid potassium phenoxide with n-butylbromide in refluxing toluene to give virtually quantitative yields of n-butyl phenyl ether. A wide range of copolymer structures have been examined and the catalytic activity is found to increase with $\text{M}\text{?}{}_{\mathrm{n}}$ of both the styrene and the ethylene oxide segments levelling off at $\text{M}\text{?}{}_{\mathrm{n}}$ styrene block ～30 000 and $\text{M}\text{?}{}_{\mathrm{n}}$ ethylene oxide block ～60 000. Beyond $\text{M}\text{?}{}_{\mathrm{n}}$ ethylene oxide block ～100 000 rates of reaction drop again towards the value for a high molecular weight homopolymer of ethylene oxide. Kinetic analysis suggests the rate controlling process to be the bimolecular reaction between complexed potassium phenoxide and n-butyl bromide, and the activation energy for the reaction is the same as that for reactions catalysed by low molecular weight oligoethers. From the kinetic dependence of the concentration of copolymer catalysts, the dependence on the structure of individual copolymers and from the known physical behaviour of these copolymers in toluene solution, catalysis appears to involve micellar aggregates of copolymer chains.     

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.     

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).     

Configurational sequence lengths in polyacrylonitrile and poly(acrylonitrile-CO-haloalkyl acrylate/methacrylate)s determined by 13C n.m.r.

The tacticity and number average sequence length of like ($\text{n}\text{?}{}_{\mathrm{<mtext>o</mtext>}}$), meso ($\text{n}\text{?}{}_{\mathrm{<mtext>m</mtext>}}$) and racemic ($\text{n}\text{?}{}_{\mathrm{<mtext>r</mtext>}}$) acrylonitrile (AN) triad units in polyacrylonitrile (PAN) prepared in both water and water—acetone (2:1 v/v) media and AN-3-chloro, 2-hydroxypropyl acrylate/methacrylate, AN-2-bromoethyl methacrylate and AN-2-chloroethyl acrylate copolymers have been calculated using ¹³C n.m.r. spectra of the polymer solutions concerned at a field strength of 24.99 MHz. The spectra reveal that PAN prepared in water medium has a greater percentage (33.4%) of isotactic units than PAN prepared in water-acetone (2:1 v/v) medium (28.3%). The tacticity distribution of AN sequences in PAN and the copolymers is found to be random ($\text{n}\text{?}{}_{\mathrm{<mtext>m</mtext>}}\text{?}\text{n}\text{?}{}_{\mathrm{<mtext>r</mtext>}}\text{?2.0}$) and the number average sequence length of AN sequences in a copolymer containing 14.8 mole% of 3-chloro, 2-hydroxypropyl methacrylate was 15.2.     

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.     

Elution and molecular weight parameters in exclusion chromatography

The mode of the chromatogram is inadequate for characterizing experimental elution curves, which are generally dissymmetrical. It is also dependent on axial diffusion. When the molecular weight distribution is defined either by the generalized exponential function or by the log-normal function, simulation of elution at finite resolution shows that the calibration curve at infinite resolution, independent of the flow rate of the carrier fluid, is approximated validly by correlating the first moment of the chromatogram (MEV) with the geometrical compound average $\text{(}\text{M}\text{?}{}_{\mathrm{n}}\text{M}\text{?}{}_{\mathrm{w}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= M}{}_0$. The concentration effect seems to be controlled by a double extrapolation procedure defined by (1) treatment of the chromatograms using the calibration curve at zero concentration ($\text{In}\text{M}{}_0\text{versus}\text{lim}\text{c→o}\text{MEV}$), and (2) linear extrapolation to infinite dilution of the calculated molecular weight averages.     

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.     

Small-angle neutron scattering studies of molten and crystalline polyethylene

Small-angle neutron scattering studies have been made of molten and crystalline polyethylene using samples containing small amounts of deuterated polyethylene (PED) in a protonated polyethylene (PEH) matrix. Careful studies were made of PED aggregation effects, and by a combination of solution blending techniques and rapid quenching from the melt, it was possible to prepare samples with a statistical distribution of PED molecules in the PEH matrix. Measurements of radius of gyration $\text{(S}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{w}}$ at low κ [$\text{κ = (}\text{4π}\text{λ}$) sin $\text{? ≤ 2 × 10}{}^{\mathrm{?2}}\text{A}\text{?}{}^{\mathrm{?1}}$] in the melt and in the solid state gave very similar values which may be summarized as $\text{〈S}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{w}}\text{= (0.46 ± 0.05)M}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{w}}$ for both phases. This correspondence of values indicates that on a rapid quench, diffusion is sufficiently slow that the molecule crystallizes with a similar spatial distribution of mass elements to that possessed in the melt. Measurements of scattering data over a wide κ range ($\text{6 × 10}{}^{\mathrm{?3}}\text{≤ κ ≤ 0.12}\text{A}\text{?}{}^{\mathrm{?1}}$) have also been made from samples showing no aggregation effects. Calculations indicate that it is difficult to fit this data in terms of models which postulate adjacent chain re-entry in one crystallographic plane for this type of sample.     

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 $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}\text{> ca. 10 000}$.     

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.     

Synthesis of aminotelechelic polymers with the redox system TiCl3NH2OH in hydrochloric aqueous phase: 2. Polymerization of methylmethacrylate. Relation functionality/molecular weight/yield

Aminotelechelic poly(methylmethacrylates) of which number average molecular weight $\text{M}\text{?}{}_{\mathrm{n}}$ is less than 7 × 10³ are synthesized with the redox system $\text{TiCl}{}_3\text{NH}{}_2\text{OH}$ in hydrochloric aqueous phase. Functionality, molecular weight and yield are discussed on the basis of initiation, propagation and termination reactions. These considerations justify the influence of various factors such as the addition time of the TiCl₃ solution, the molar ration $\text{MMA}\text{TiCl}{}_3$ and the nature of the reducing ions. The evolution of molecular weights determined by g.p.c. confirms the interpretation of the results.     

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.     

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.     

Effects of dextran molecular weight on graft copolymerization of dextran-methyl methacrylate

Effects of the molecular weight of dextran on its graft copolymerization with methyl methacrylate (MMA), initiated by ceric ammonium nitrate (CAN), have been investigated. The results indicate that grafting (%), graft polymerization (%) (ψ), the overall rate constant (k′) for consumption of Ce⁴⁺, and branch PMMA were influenced significantly by the molecular weight of the backbone polymer dextran. The number of branch PMMA chains per dextran molecule was 0.05 ～ 0.30 for $\text{M}\text{?}{}_{\mathrm{w}}$ 9000 dextran (D1), 0.35 ～ 0.55 for $\text{M}\text{?}{}_{\mathrm{w}}$ 61 000 (D2), and 0.8 ～ 1.6 for $\text{M}\text{?}{}_{\mathrm{w}}$ 196 000 (D3), respectively. The relationship between the rate of graft polymerization and $\text{M}\text{?}{}_{\mathrm{w}}$ (the weight-average molecular weight of dextran) was expressed by the equation: $\text{R}{}_{\mathrm{p}}\text{g = ?A}\text{log}\text{M}\text{?}{}_{\mathrm{w}}\text{+ B}$. Another linear relationship was obtained between In (100 ? ψ) and reaction time (t) for both D1 and D2 samples or In t for D3. Detailed kinetic analysis has been made on the basis of the latter relationship. Mechanical properties were also studied on the moulded sample plates of these copolymers.