Structure and properties of poly(ethylene terephthalate) crystallized by annealing in the highly oriented state: 2. Melting behaviour and the mosaic block structure of the crystalline layers

The melting behaviour of drawn poly(ethylene terephthalate) bristles has been studied by means of differential scanning calorimetry. In addition the wide-angle X-ray diffraction pattern were analysed. For comparison some of the experiments were also carried out with undrawn samples. The differences in the melting curves of drawn and undrawn PET originate from the different crystallization kinetics. The density defect ($\text{?}{}^{\mathrm{id}}{}_{\mathrm{c}}\text{? ?1}{}_{\mathrm{c}}$) between the ideal crystal density ?^id_c and the effective density $\text{?1}{}_{\mathrm{c}}$ of the crystalline layers is a result of lattice vacancies introduced by the grain boundaries of the mosaic blocks. The relatively low ultimate crystallinity of PET is supposed to be caused by the hindrance of crystal growth of fibre direction during isothermal crystallization.     

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.     

Isothermal crystallization of poly(ethylene-terephthalate) of low molecular weight by differential scanning calorimetry: 1. Crystallization kinetics

The isothermal crystallization of poly(ethylene-terephthalate) (PETP) fractions, from the melt, was investigated using differential scanning calorimetry (d.s.c.). The molecular weight range of the fractions was from 5300–11750. Crystallization temperatures were from 498–513 K. The dependence of molecular weight and undercooling on several crystallization parameters has been observed. Either maxima or minima appear at a molecular weight of about 9000, depending on the crystallization temperature. The activation energy values point to the possibility of different mechanisms of crystallization according to the chain length. A folded chain process for the higher $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ chains and an extended chain mechanism for the lower $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ chains. The values of the Avrami equation exponent n vary from 2–4 depending on the crystallization temperature; non-integer values are indicative of heterogeneous nucleation. The rate constant K depends on T_c and $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$, showing maxima related to the T_c used. The plot of log K either vs. (ΔT)^?1 and (ΔT)^?2 or $\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{T(ΔT)}$ and $\text{T}{}^2{}_{\mathrm{<mtext>m</mtext>}}\text{T(ΔT)}{}^2$ is linear in every case.     

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).     

Cyclization dynamics of polymers: 9. The effect of polymer concentration on the slowest internal relaxation mode of a labelled polystyrene chain

A combination of steady-state and fluorescence decay techniques permits one to measure the dynamics of end-to-end cyclization of a polymer chain substituted at both ends with pyrene groups. In the limit of low concentration, the rate constant for cyclization, k_cy, can be identified with the slowest relaxation rate $\text{τ}{}_1{}^{\mathrm{?1}}$ of a Rouse—Zimm chain. Experiments are reported which allow k_cy to be examined for two chain lengths of polystyrene substituted on both ends with pyrene groups. These chains have $\text{M}\text{?}{}_{\mathrm{n}}\text{= 9200}$ and 25 000 ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{? 1.15}$). Added unlabelled polystyrene polymer [PS] causes $\text{k}\text{?}{}_{\mathrm{<mtext>cy</mtext>}}$ to decrease in cyclohexane just above the θ-temperature, whereas in toluene, a good solvent, k_cy is largely unaffected, even at [PS] concentrations of 50 wt%. These results are explained in terms of frictional effects—hydrodynamic screening—dominating in the poor solvent, whereas other factors tend to have offsetting effects in the good solvent.     

The kinetics of the catalytic hydrogenolysis of ethane over Ni/SiO2

The rate of hydrogenolysis of ethane over a Ni/SiO₂ catalyst, studied over a large range of pressure and of temperature, is shown to be related to the degree of hydrogen coverage θ_H, by the equation: with K₀ nearly equal to the number of ethane molecules colliding with the Ni surface, E₀ = 14 ? 1 kcal/mole, Y = ?1 ? 2 and X = 15 ? 2. The rate-limiting step is believed to be the irreversible, dissociative adsorption of ethane on an ensemble of at least 12 adjacent Ni atoms, free from adsorbed hydrogen, resulting in the complete cracking of C₂H₆: C₂H₆ + 12Ni → 2

Irreversible adsorption of ethane is assumed to compete with the reversible adsorption of hydrogen. This mechanism, which is compared with those proposed earlier, is in good agreement with data on ethane adsorption studied by magnetic methods, and with a study of ethane hydrogenolysis over NiCu/SiO₂ catalysts.     

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.     

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.     

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.     

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.     

The structure of vitreous carbon from wide angle and low angle x-ray diffraction

Both wide angle and low angle X-ray diffraction patterns have been measured for a sample of vitreous carbon which has been subjected to a maximum heat-treatment of 1800°C. The wide angle scattering was used to calculate a radial distribution function, which showed that the basic atomic arrangement was that of hexagonal graphite like sheets with no graphitic registration between the sheets. The low angle scattering pattern was interpreted in terms of a theory due to Debye, and an exponential correlation function was found to be a reasonable approximation for representing the electron density fluctuations giving rise to this scattering. The electron density fluctuations originate from pores in the matrix with a mean chord intercept length of ? 8 Å. The mean chord intercept for the matrix is ? 16 Å in reasonable agreement with “crystallite sizes” $\text{L}{}_{\mathrm{c}}\text{? 15}\text{A}\text{?}$ and $\text{L}{}_{\mathrm{a}}\text{? 22}\text{A}\text{?}$, calculated from the Scherrer equation. L_c should be interpreted as a distance between pores, and L_a as a defect distance in the matrix rather than indicating sharp crystallite boundaries.     

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

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 $\text{～}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}$.     

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.     

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.     

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.     

The determination of diffusion coefficients in activated carbons made from bituminous coal

The gas chromatographic method has been used to measure the effective diffusion coefficients D_e or the diffusion parameters $\text{D}{}_{\mathrm{e}}\text{d}{}^2$. Nitrogen was used as a carrier gas, krypton-85 as test gas. The tests were carried out on different activated carbons made from air-preoxidized bituminous coals whose pore structure as a function of the burn-off was known. The diffusion parameters for krypton were found to increase exponentially with the mean micropore diameter of the activated carbons which was varied in our tests between 5.8 and 7.0 Å. For activated carbon with the narrowest pores the activation energy of krypton diffusion was found to be 2.8 kcal/mol. In case of such a product the diffusion time is not rigidly dependent on the particle diameter as would have to be expected theoretically. With increasing micropore diameter this dependency is attenuated very rapidly, and in carbons with a mean micropore diameter above ca. 6.8 Å it exists no longer at all. To check the results, gravimetric studies on the adsorption kinetics of krypton in vacua and on the desorption kinetics using the gas flushing method were made. It was found that the results obtained by the gas chromatographic method and the gas flushing method were in good agreement, whereas the diffusion parameters obtained by measurements in vacuo were by one order of magnitude lower. The findings are discussed in relation to the pore structure of the adsorbent and the properties of the sorbate. The limits of the different measuring methods are shown.