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.     

Small-angle neutron scattering studies of polyethylene crystallized at high pressure

The technique of small-angle neutron scattering (SANS) has been used to study the chain configuration in pressure crystallized polyethylene. Two narrow molecular weight fractions of deuterated molecules (PED) of M_w 23 000 and 54 000 were solution blended with a protonated matrix polymer of M_w 81 500. Although pressure crystallization was shown to have produced a clustering of the PED molecules, the radii of gyration $\text{〈}\text{S}{}^2\text{〉}{}_{\mathrm{z}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ were, nevertheless, shown to be consistent with a model in which the PED molecules possessed rod-like configurations. The predicted rod lengths were in close agreement with the molecular stem lengths of the PEH matrix polymer, which were independently determined by nitric acid etching. Furthermore, a doubling of the PED molecular weight produced no change in the value of $\text{〈S}{}^2\text{〉}{}_{\mathrm{z}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. This was interpreted in terms of a chain folding mechanism in which a molecule is bounded by the surfaces of a lamellar block and is therefore unable to increase its' rod length.     

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.     

Studies of cyclic and linear poly(dimethyl siloxanes): 1. Limiting viscosity number-molecular weight relationships

The limiting viscosity numbers of ten cyclic and ten linear poly(dimethyl siloxane) fractions have been measured in a π-solvent (butanone at 293K) and in two ‘good’ solvents (toluene and cyclohexane at 298K). The dimethyl siloxane fractions studied were in the molecular weight range $\text{800 <}\text{M}\text{?}{}_{\mathrm{w}}\text{< 17 000}$. The data obtained are compared with related studies published in the literature. The ratio of the limiting viscosity numbers [η]_r and [η]_l of the cyclic and linear poly(dimethyl siloxanes) with $\text{M}\text{?}{}_{\mathrm{w}}\text{> 2500}$ was found to be 0.67 in butanone at 293K. This value is identical (within experimental error) to the theoretical ratio $\text{[η]}{}_{\mathrm{r}}\text{[η]}{}_{\mathrm{l}}\text{= 0.66}$ predicted by Bloomfield and Zimm and others for ring and chain polymers in π-solvents. The ratio $\text{[η]}{}_{\mathrm{r}}\text{[η]}{}_{\mathrm{l}}$ was found to be somewhat smaller for the higher molecular weight polymers in the ‘good’ solvents.     

Studies of cyclic and linear poly(dimethyl siloxanes): 2. Preparative gel permeation chromatography

A preparative gel permeation chromatographic (g.p.c.) instrument has been constructed and used to separate broad fractions of cyclic poly(dimethyl siloxanes) into sharp fractions with heterogeneity indices $\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{= 1.05 ± 0.02}$. The number-average molecular weights $\text{M}\text{?}{}_{\mathrm{n}}$ of the cyclic polymer fractions obtained were as high as 50 000, corresponding to number-average numbers of skeletal bonds $\text{n}\text{?}{}_{\mathrm{n}}$ up to 1300. The concentrations of linear poly(dimethyl siloxanes) in all but the highest molecular weight cyclic polymer fractions prepared are believed to be negligible. The preparative g.p.c. instrument was also used to obtain some sharp fractions of linear poly(dimethyl siloxanes).     

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.     

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.     

I.r. study of solution-grown crystals of polyethylene: correlation with the model from neutron scattering

The crystal stem arrangement in solution-grown polyethylene crystals has been investigated by the mixed-crystal infra-red technique. Parallel neutron scattering measurements are reported separately. The behaviour of the CD₂ bending vibration is shown to be consistent with a model having 75% adjacent re-entry, 50% dilution of a molecule along the fold plane (110 direction) and a degree of superfolding equivalent to an average molecular weight ($\text{M}\text{?}{}_{\mathrm{w}}$) of 21 000 for each sheet. This is in agreement with results from neutron scattering, which have previously been interpreted using this model. Computer calculations of stem positions based on these parameters are used to calculate the distributions of doublet splittings for several molecular weights. The main features of low-temperature FTi.r. spectra as a function of molecular weight are reproduced in this way.     

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.     

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

Molecular weight distributions in novolactype phenol-formaldehyde polymerization

To model the reversible novolac polymerization, five reactive species A to E have been defined. Molecules having bound CH₂OH (Q_n) are distinguished from those without it (P_n) and it is assumed that molecules of Q_n do not have more than one bound CH₂OH group. A kinetic model has been written and, based upon it, balance equations for molecules of novolac polymer in batch reactors have been derived. Based upon our earlier studies, the phenomenon of molecular shielding has been neglected. As a result, the reactivities of the ortho and para positions of phenol which are available in the literature could be used. The kinetic model for the molecular weight distribution (MWD) of reversible novolac polymer formation thus involves only one parameter. The study of the MWD of novolac polymer reveals two very important design variables: the phenol-formaldehyde ratio, $\text{[P]}{}_0\text{[F]}{}_0$, in the feed and the vacuum applied on the reactor. As the $\text{[P]}{}_0\text{[F]}{}_0$ ratio is increased, the breadth of the distribution is found to increase and it undergoes a maximum at $\text{[P]}{}_0\text{[F]}{}_0\text{? 1.4}$ for the set of rate constants chosen. At this ratio, the chain length average molecular weight is also found to be the largest. Industrially, the $\text{[P]}{}_0\text{[F]}{}_0$ ratio used in producing novolac polymer is 1.67 and it is usually desired that the polymer be linear with minimal branching. On application of vacuum, for a given time of polymerization, the chain length molecular weight is found to increase when the results are compared with those of batch reactors. The breadth of the distribution is also found to reduce thus giving a lower polydispersity index of the polymer formed.     

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.     

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.     

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).     

Synthesis of aminotelechelic polymers with the redox system TiCl3NH2OH in hydrochloric aqueous phase: 3. Polymerization of methylacrylate. relation functionality/molecular weight/yield

Aminotelechelic poly(methylacrylates) of low molecular weight (M_n < 1.2 × 10⁴) are prepared 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 several factors (addition time of the TiCl₃ solution, molar ratio $\text{MA}\text{TiCl}{}_3$, solvent, nature of the reducing ion…). Gel permeation chromatography confirms the results.     

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.     

Studies of cyclic and linear poly(dimethyl siloxanes): 12. Observation of diffusion behaviour by quasielastic neutron scattering

High resolution neutron scattering experiments have been used to observe the diffusive motion of low molecular weight linear and cyclic poly(dimethyl siloxane) molecules in dilute solution in deuterated benzene. Diffusion coefficients (D) and hydrodynamic radii (R_H) have been compared with values obtained by light scattering for higher molecular weight samples and with radii of gyration (R_g) obtained by small-angle neutron scattering. While the ratio $\text{D}{}_{\mathrm{<mtext>ring</mtext>}}\text{D}{}_{\mathrm{<mtext>chain</mtext>}}$ is close to the predicted value of 0.85, the ratio $\text{R}{}_{\mathrm{g}}\text{R}{}_{\mathrm{<mtext>H</mtext>}}$ falls below the theoretical value for both ring and chain molecules. The scattering curves show effects arising from both centre of mass diffusion and internal molecular motion, and the observed inverse correlation times are compared with calculated behaviour as a function of scattering vector, Q.     

Small-angle neutron scattering studies of isotropic polypropylene

Small-angle neutron scattering studies have been made of molten and crystalline polypropylene using samples containing small amounts of deuterated polypropylene in a protonated polypropylene matrix. The specimens were characterized by small- and wide-angle X-ray scattering to determine the d-spacing and the degree of crystallinity χ and by gel permeation chromatography to determine molecular weight, M_w, and molecular weight distribution. The degree of crystallinity was varied from 0.5 to 0.7, the d-spacing from 120 to 250 Å and the molecular weight from 34 000 to 1 540 000. Clustering was not observed. The radius of gyration $\text{〈s}{}^2\text{〉}{}_{\mathrm{w}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ of the tagged molecules was approximately proportional to $\text{M}{}_{\mathrm{w}}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and almost independent of d and χ. In the melt similar values were obtained which are, within experimental uncertainties, the same as in a θ-solution. For 〈s²〉_wk²? 1 the scattering law approaches a k^?2 dependence. The results are discussed with reference to the chain-folded model but a fit cannot be obtained over all molecular weights. A simple random coil model fits the neutron scattering data partly but this does not explain the origin of the d-spacing.     

Viscoelastic properties of poly(propylene glycols)

The relaxational and retardational properties of poly(propylene glycol) liquids, of nominal molecular weights 400 and 4000, are described. The viscoelastic behaviour of each liquid has been determined over a wide temperature range, using high frequency shear wave techniques operating at 30 and 454 MHz. It is found that the complex compliance $\text{J1(jω)}$ is described in terms of the viscosity ν, the limiting high frequency compliance J_∞, the retardational compliance J_r and a characteristic retardation time $\text{т}{}_{\mathrm{r}}$ by:

$\text{J}{}^1\text{(jω)=J}{}_{\mathrm{\infty }}\text{+}\text{1}\text{jωη}\text{+}\text{j}{}_{\mathrm{r}}\text{(1+jωτ}{}_{\mathrm{r}}\text{)}{}^{\mathrm{\beta }}$

where β is a parameter of the retardation time distribution.For the lower molecular weight liquid, $\text{J}{}_{\mathrm{r}}\text{J}{}_{\mathrm{\infty }}\text{= 17.4}$, β = 0.45 and $\text{т}{}_{\mathrm{r}}\text{т}{}_{\mathrm{m}}$ increases with decreasing temperature, reaching a limit of 170 near 0°C. This liquid shows no evidence of polymeric behaviour.For the other, $\text{J}{}_{\mathrm{r}}\text{J}{}_{\mathrm{\infty }}$, β = 0.76, $\text{т}{}_{\mathrm{r}}\text{т}{}_{\mathrm{m}}\text{= 15.4}$ and is constant over the temperature range investigated. The main difference between the two liquids appears as an additional retardational or relaxational process for the higher molecular weight material which occurs in the initial or low frequency part of the relaxation region. This process is characterized by a single time, but with relaxation time $\text{1}\text{7}$ and a stiffness 7 times the values calculated for the first Rouse mode of polymer chain motion.     

Sedimentation velocity measurements close to the upper critical solution temperature and at θ-conditions: polystyrene in cyclopentane over a large concentration interval

Sedimentation velocity measurements on polystyrene (M = 110 000) in cyclopentane over an extended concentration region and from 5°C (close to the upper critical solution temperature) to 40°C are reported. The concentration dependence parameter (k_s)_w increases from 2 to 5°C to 27 at 40°C. For all temperatures except 5°C, $\text{s}{}_0\text{s}$ vs. w[η]_w shows an upward curvature at w[η]_w ≈ 1; at 5°C, on the other hand, $\text{s}{}_0\text{s}$ is independent of concentration over the region considered. Furthermore, measurements have also been performed at 20°C (θ-conditions) over a large concentration interval for the molecular weights M = 20 400, 390 000 and 950 000. The parameters s₀ and (k_s)_w were both found to be proportional to $\text{M}\text{?}{}^{\mathrm{1/2}}{}_{\mathrm{w}}$. In the ‘hydrodynamically normalized’ plot $\text{s}{}_0\text{s}$ vs. w[η]_w the sedimentation behaviour can approximately be represented by a single curve for all the molecular weights.