On the molecular weight determination of a poly(aryl-ether-ether-ketone) (PEEK)

Attempts have been made to determine the weight average molecular weight ($\text{M}\text{?}{}_{\mathrm{<mtext>W</mtext>}}$), the radius of gyration ($\text{R}\text{?}{}_{\mathrm{<mtext>G</mtext>}}$) and the second virial coefficient (A₂) of five samples of poly(ether-ether-ketone) (PEEK) by light scattering (LS) in concentrated sulphuric acid. Account has been taken of the sulphonation of the polymer. Correlations between LS-molecular weights, melt viscosities and intrinsic viscosities in sulphuric acid or in a $\text{50}\text{50}$ phenol-trichlorobenzene mixture have been established. Gel permeation chromatography (g.p.c.) analyses at 115°C have been performed in this latter solvent and two calibration methods were compared.     

Solid and liquid state relaxations in spin-labelled poly)ethylene glycol) at high temperatures (T>Tg)

Free and covalently bonded (esterified) nitroxyl radicals experienced in poly(ethylene glycols) (PEG; $\text{M}\text{?}{}_{\mathrm{n}}$ 200–22 000) at temperatures T >T_g several different isotropic rotational relaxation regions. As a first approximation it was assumed, that in the polyglycols $\text{M}\text{?}{}_{\mathrm{n}}\text{? 1000}$ there are at least three rotational relaxation regions: the liquid state (I), the melting state (II) and the solid state (III). The existence of the fourth region, the frozen solid state (IV), was also concluded. The existence of the relaxation region (II) indicated the close interaction between radicals and the crystalline phase. The order of rotational activation energies (E_a) was E^II_a >E^III_a >E^I_a >E^IV_a ($\text{M}\text{?}{}_{\mathrm{n}}\text{? 1000}$). In the polymer melts (I) E_a values of free and bonded radicals first diminished as a consequence of the decrease of the end group effect and they achieved constant high molecular weight values (～15 and 25 kJ respectively). E_a changed in the solid state as a function of $\text{M}\text{?}{}_{\mathrm{n}}$ principally in the same manner except of the higher numerical values (～40 kJ).E_a of free and covalently bonded radicals in the transition region (II) gained a maximum at $\text{M}\text{?}{}_{\mathrm{n}}$ 1550 (125 and 170 kJ) and another at $\text{M}\text{?}{}_{\mathrm{n}}\text{> 9500}$ (130 and 165 kJ) expressing the high degree of order in these polymers in the solid state.The results obtained correlated well with the proton magnetic resonance measurements but they did not correlate with the amorphous dielectric relaxation measurements.It was concluded that the following factors may affect the rotational relaxations of nitroxyl radicals in PEG: the free volume of the polymer, the crystallinity, the chain packing and the end-group effect. The segmental character of the relaxation process was clearly indicated.     

Cyclization dynamics of polymers: 10 Synthesis,fractionation, and fluorescent spectroscopy of pyrene end-capped polystyrenes

The rate constant for end-to-end cyclization (k₁) for polymer chains is predicted to decrease sensitively with increasing chain length. In this paper the techniques are examined critically for extracting values of k₁ from experiments involving intramolecular pyrene excimer formation in polymers of the form pyrene-polystyrene-pyrene. For significance, results require samples of appropriately narrow molecular weight distribution ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{</ 1.13}$), as well as corrections for polydispersity differences among the samples. Particular attention is focussed both on experimental techniques and on the models used to interpret the kinetics of intramolecular pyrene excimer formation.     

Effect of molecular weight on spherulite growth rates of high molecular weight poly(ethylene oxide) fractions

Spherulite growth rates have been determined for a set of poly(ethylene oxide) fractions ranging in molecular weight from 10⁴ to 10⁶. At a given crystallization temperature the spherulite growth rate as a function of molecular weight passes through a maximum. At a given undercooling (as assessed by the method of Mandelkern) the spherulite growth rate is a monotonically decreasing function of molecular weight, and in the range $\text{6000 <}\text{M}\text{?}{}_{\mathrm{v}}\text{< 50 000}$ varies roughly as $\text{(}\text{M}\text{?}{}_{\mathrm{v}}\text{)}{}^{\mathrm{?3}}$. The free energy of formation of the end interface (as assessed by nucleation theory) also decreases as molecular weight increases.     

Effect of molecular weight on the partial specific volume of polystyrenes in solution

The partial specific volume $\text{v}\text{?}{}_2$ of linear and branched polystyrenes has been measured as a function of molecular weight (1300<M_w<9×10⁶). In the low molecular weight range, the effect of end-groups is predominant. In the high molecular weight range (M_w > about 20 000), we have detected small but significant variations due to the intramolecular segment-segment contacts within the coil. We have proposed an empirical relation between $\text{v}\text{?}{}_2$ and the segment density of the macromolecule; this relation has been confirmed using highly branched polystyrenes. These results relative to dissolved polystyrenes are compared to experimental data obtained by different authors on pure liquid polystyrenes at different temperatures. Starting from simple additivity rules and from the known chemical composition of liquid polymers, we have shown that the variation of specific volume with high molecular weights is due to some phenomenon different from an effect of chain-ends.     

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.     

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

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.     

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.     

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 $\text{?W}\text{?I}{}_2$.     

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.     

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.     

The dilute solution properties of maleic anhydride and maleic acid copolymers: 1. Light scattering, osmotic pressure and viscosity measurements

Dilute solution behaviour of poly(maleic anhydride-co-ethyl vinyl ether) and poly(maleic acid-co-ethyl vinyl ether) has been investigated by light scattering, osmotic pressure, and viscosity measurements. The molecular weights ($\text{M}\text{?}{}_{\mathrm{w}}$ and $\text{M}\text{?}{}_{\mathrm{n}}$), the second virial coefficients A₂, and the intrinsic viscosities [η] have been determined for three states of this copolymer: anhydride-form, H-form, and Na-salt independently. The constants in the Mark-Houwink relations were obtained for the above three states under different solvent conditions. The molecular weight of the anhydride-form is found to be higher than that of the acid-form or the Na-salt, suggesting the degradation in a process of hydrolysis. The second virial coefficient A₂ as well as the Mark-Houwink relation indicates that the anhydride-form and H-form behave as flexible polymer chains in good solvents. However, the polymer coil of Na-salt is highly expanded even at saturated NaCl concentration.     

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.     

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.     

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.     

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

Crystallization of block poly(ethylene oxide)

Urethane linked block polymers of poly(ethylene oxide) have been prepared and fractionated. Samples having 1 to 20 blocks per molecule, with molecular weights ranging from 1500 to 67 000 g/mol, have been examined by a number of techniques (small-angle X-ray scattering, differential scanning calorimetry, dilatometry, optical microscopy) in order to determine their crystallinities, melting points and spherulite growth rates. For a series of fractions having an average block length of 34 oxyethylene units with a range of 3 to 20 blocks per molecule, we find that equilibrium melting points are practically independent of molecular weight ($\text{6000 <}\text{M}\text{?}{}_{\mathrm{W}}\text{< 40 000}$). Analysis of the temperature dependence of the spherulite growth rates of these fractions leads to the conclusion that the pre-exponential factor (G₀) is practically independent of molecular weight and that the end interfacial free energy (σ_e) increases with molecular weight. Analysis of the experimental results for series of fractions having average block lengths of 45 or of 90 oxyethylene units is complicated by chain folding in the crystalline lamellae.