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.     

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.     

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.     

Macromolecular properties of heparin in dilute solution: 2. Dimensional parameters as a function of pH,ionic strength and desulphation

A bovine heparin fraction was examined by sedimentation analysis and intrinsic viscosity measurements as a function of ionic strength in the range of 0·1 to 1·0 M, and at pH 2·5 and 6·0. The following experimental parameters were obtained: M, S⁰_20,W, D⁰_20,W, $\text{V}\text{?}$, and [η]. Other physical parameters were calculated based on a random coil model (supported by the theory of Mandelkern and Flory) e.g., $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{(}\text{s}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Similar studies were made on a heparin sample as a function of desulphation as resulting from graded mild hydrolysis. Since desulphation is accompanied by decreasing anticoagulant activity of heparin, the latter was correlated with various calculated and measured physical parameters. Significantly $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ decreases with decreased desulphation and therefore decreased biological activity.     

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.     

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).     

Kinetics of hydrogasification of coke catalysed by Fe,Co and Ni

The catalysis of hydrogasification of carbon by Fe, Co and Ni was studied using a special petroleum coke with extremely low reactivity. The kinetics were studied with impregnated coke in a fixed-bed flow reactor between 1133 and 1235 K and up to 2 MPa, yielding the following rate equation: Apparent activation energies and heats of adsorption are: Fe, 152 and ?92 kJ mol^?1; Co, 201 and ?82 kJ mol^?1 Ni, 165 and ?50 kJ mol^?1. These studies with impregnated coke as well as further gasification experiments with cokes heat-treated after impregnation with metal salts up to 2273 K confirmed a spillover mechanism and excluded any influence of electronic interactions between carbon and the catalyst metals.     

Study of relationship between network structure of g.p.c. gels and molecular size of permeable substance

Attempts were made to correlate the average size of the network of crosslinked vinyl acetate-glycidyl methacrylate (GMA) copolymer to the maximum size of permeable molecules when the copolymers were used as g.p.c. packing materials. The root-mean-square of the end-to-end distance $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of the hydrodynamic radius $\text{(}\text{s}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, which characterizes the maximum extent of the molecules, were calculated. Meanwhile, the average size of the copolymer network, r_c, was estimated from the average molar weight between crosslinkages, this being calculated from the equilibrium rubber elastic modulus, E_r, obtained by dynamic discoelastic measurements. It was found that the maximum size which can permeate the copolymer decreases as the content of GMA in the copolymer increases. From viscoelastic measurements, E_r was found to increase as the content of GMA in the copolymer increases. Further, linear relationships were obtained among r_c, $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and $\text{(}\text{s}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ covering the wide range of the copolymer composition.     

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.     

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.     

Non-classical free-radical polymerization: 3. Diffusion-control in degradative addition

The different kinetic features associated with polymerizations in which retardation arises through degradative transfer and degradative addition processes are considered. Reasons are given for believing that in reactions retarded by degradative transfer neglect of the interaction between ‘inactive’ radicals is justifiable, while with degradative addition this is not so. A kinetic treatment of the latter is developed in which all three termination reactions between propagating and inactive radicals are assumed to be diffusion-controlled with a single rate coefficient and equations are derived which permit from experimental data on rates of polymerization estimation of the definitive kinetic parameters $\text{k}{}_{\mathrm{p}}\text{k′}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{t}}$, $\text{k}{}_{\mathrm{pm}}\text{k′}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{t}}$ and $\text{k}{}_{\mathrm{fm}}\text{k′}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}{}_{\mathrm{t}}$ (k_p, k′_t, k_pm, k_fm are the rate coefficients of propagation, termination, reinitiation and degradative additions, respectively). The kinetic equations are satisfactorily consistent with ew experimental data on the polymerization of 1-vinylimidazole in ethanol solution at 70°C, for which there is strong evidence for the occurrence of degradative addition. A modified procedure for processing data for polymerizations with degradative transfer is put forward which is convenient for estimating the kinetic parameters and reveals in a simple manner the importance of re-initiation. It is suggested that this treatment could be generally useful in the early stages of the study of a retarded polymerization.     

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.     

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).     

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.     

Effect of temperature and frequency in fatigue of polymers

The effects of frequency and temperature on fatigue crack propagation rate in poly(methyl methacrylate) and polycarbonate have been studied using centrally notched plate specimens cycled in tension between constant stress intensity limits. Crack growth was monitored at frequencies between 0.1 Hz and 100 Hz and at temperatures between ?60°C and 40°C. A linear relationship between the cyclic crack growth rate $\text{d}\text{(2a)}\text{d}\text{N}$ and appropriate levels of toughness, K, has been proposed: $\text{d}\text{(2a)}\text{d}\text{N}\text{= A?}{}^{\mathrm{\alpha }}$, where $\text{? =}\text{(λ ? λ}{}_{\mathrm{<mtext>th</mtext>}}\text{)}\text{(K}{}^2{}_{\mathrm{<mtext>1</mtext><mtext>C</mtext>}}\text{? K}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{)}$, λ = K²_max ? K²_min, λ_th is the threshold limit and A and α are constants. Also, the influence of mean stress intensity was briefly discussed.     

Macromolecular properties of heparin in dilute solution: 1. Application of various hydrodynamic models in 0·5 M NaCl,pH 2·5

Bovine heparin was fractionated according to molecular weight by fractional precipitation utilizing a method described previously. The solution data from sedimentation analysis, intrinsic viscosities and partial specific volumes at pH 2·5 and in 0·5 M NaCl were treated according to the Mandelkern and Flory theory for random coil in calculating the constant β. It was found that the calculated β values for all the fractions were in close agreement with the theoretical value. Based on this observation, the solution data were then treated in light of various hydrodynamic theories for linear polymers to calculate various dimensional and other physical parameters, e.g., $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, α (expansion factor), A₂. In comparing $\text{(}\text{r}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of a fraction to that calculated from the experimental value of $\text{(}\text{s}\text{?}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ obtained from low angle X-ray scattering for a comparable molecular weight sample, it was found that heparin in solution with suppressed charges may best be described as approximating the closely related models of Debye and Bueche, Flory and Fox, or Kuhn and Kuhn.     

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.     

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.     

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.