A study of the orientations of fluorescent molecules incorporated in uniaxially oriented poly(ethylene terephthalate) tapes

The theory of the polarized fluorescence from fluorescent molecules incorporated in an oriented solid polymer is developed for a very general model of the optical behaviour of the molecules and it is concluded that any observed intensity can be expressed in terms of the components of a fourth rank tensor. Only twelve of these components are independent for samples of orthotropic symmetry and only six for samples of uniaxial symmetry. The effects of the birefringence of the polymer and the significant polarization-dependent absorption of the exciting light on the observed intensities are considered. The results of the analysis are presented for the uniaxial case in a form which allows values of $\text{cos}{}^2\text{θ}$ and $\text{cos}{}^4\text{θ}$ to be calculated from the experimental measurements of intensity. θ is the angle between the unique axis in the polymer and a unique axis in a fluorescent molecule and the bars denote the averages over the sample. The theory has been applied to molecules of a stilbene derivative (VPBO) incorporated at concentrations of 50–200 ppm in poly(ethylene terephthalate) (PET) of low crystallinity. It is concluded that the unique axes of the VPBO molecules are more highly oriented than the PET chains, but the two distributions of orientations appear to be uniquely related over the range of drawing temperatures (65–90°C) and draw ratios (1–5·85) used.     

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.     

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.     

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

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.     

A calculation of the elastic constant c33 of a graphite crystal as a function of temperature

A calculation is presented of the elastic constant C₃₃ of a graphite crystal as a function of temperature up to 2500 K, taking into account the anharmonic contribution and the changes in interlayer interactions due to the large lattice thermal expansion. Parametric variations in the theory show that the anharmonic contribution to C₃₃ depends principally on the parameter ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) Comparison of theoretical results with the experimental data, which is mainly from neutron scattering experiments, shows that the data can be accounted for if ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) lies in the range 7–10 × 10¹³ dynes/cm². A theoretical estimate of ($\text{?}{}^2\text{C}{}_{33}\text{?e}{}^2{}_{\mathrm{zz}}$) based on Lennard-Jones potentials between atoms in adjacent basal planes gives a value of 9·07 × 10¹³ dynes/cm².     

Static and dynamic structure factors calculated for flexible ring macromolecules

The influence of hydrodynamic pre-averaging on the first cumulant Γ of the dynamic structure factor of Gaussian ring molecules has been calculated. Similar to star-branched macromolecules, the relative error $\text{ΔΓ}\text{Γ}$ introduced by the pre-average approximation exhibits a maximum at intermediate $\text{q = (}\text{4π}\text{λ}\text{)}$ sin $\text{θ}\text{2}$ which does not ocour for the corresponding linear chain. This maximum is related to the increase of segment density by ring formation. The static structure factor also shows a maximum in the Kratky plot (q²〈S²〉P(q) against q²) and has an asymptote at large q which is half that of linear chains. Furthermore, the S:R ratio ($\text{〈S}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{〈R}{}^{\mathrm{?1}}{}_{\mathrm{h}}\text{〉}$), which can be determined from combined integrated and quasi-elastic scattering, proves to be significantly lower than for the linear chain. Thus, ring molecules and open chains can easily be distinguished from combined integrated and quasi-elastic light scattering, without comparison with linear chains as has been necessary hitherto. The accuracy will be particularly high with instruments which allow the recording of both types of scattering measurements simultaneously.     

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.     

The unperturbed molecular dimensions of poly(ethylene oxide) in aqueous solutions from intrinsic viscosity measurements and the evaluation of the theta temperature

Intrinsic viscosity measurements were carried out on five well characterized fractions of poly(ethylene oxide) in aqueous solutions at 24.9°, 34.9°, and 45.5°C. The Stockmayer-Fixman extrapolation was applied to the data: it yields the unperturbed dimensions K₀ of the chain. The unperturbed root-mean-square end-to-end distance $\text{〈}\text{R}\text{?}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_0$ calculated for the polymer fractions in water indicate that the polymer molecules are expanded in this solvent as the temperature is raised. The temperature coefficient of unperturbed dimension, $\text{d In}\text{〈}\text{R}\text{?}{}^2\text{〉}{}_0\text{d}\text{t}\text{= 0.024}\text{K}{}^{\mathrm{?1}}$, calculated for poly(ethylene oxide) in water using the present data is about 100 times higher than the literature values of 0.23 (±0.02) × 10^?3 K^?1 and 0.2 (±0.2) × 10^?3 K^?1, respectively, obtained from force-temperature (‘thermoelastic’) measurements on elongated networks of the polymer in the amorphouse state and form viscosity measurements on this polymer in benzene. A value of θ=108.3°C was obtained from the temperature dependence of the interaction parameter B in the Stockmayer-Fixman equation.     

Investigation of the methyl torsion in isotactic polypropylene — comparison between neutron inelastic scattering spectra and normal coordinate calculations

Incoherent neutron scattering spectra for polypropylene and its partially deuterated analogue allow identification of the methyl torsion at 230 cm^?1. Comparison of the experimental spectra with the calculated densities of states shows discrepancies with the expected intensity of the methyl torsional band. Results from a stretch-oriented sample arranged so that the wave vector $\text{Q}$ is first parallel ($\text{Q}{}^{\mathrm{\parallel }}$) and then perpendicular ($\text{Q}{}^{\mathrm{\perp }}$) to the helical chain axis indicate that the torsion is more intense and probably has a small frequency dispersion around 240 cm^?1 for $\text{Q}{}^{\mathrm{\parallel }}$ and is weaker with a broad dispersion centred at 220 cm^?1 for $\text{Q}{}^{\mathrm{\perp }}$.     

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.     

Ionic conductivities for poly(ethylene oxide) complexes with lithium salts of monobasic and dibasic acids and blends of poly(ethylene oxide) with lithium salts of anionic polymers

Lithium salts of two polyanionic addition polymers containing alkyl sulphonic acid and perfluoroalkyl carboxylic acid side groups were prepared. Blends of these polymers were formed with poly(ethylene oxide) (PEO). The blend containing alkyl sulphonate units showed some phase separation but this was not observed for the blend containing perfluoroalkyl carboxylate groups. In the latter case a comparatively high conductivity of $\text{～10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}$ cm^?1 at 374 K was obtained. The anionic units in these blends are expected to be virtually immobile. Complexes formed from PEO and the Li-salt of hexafluoroglutaric acid had similar high ionic conductivities and there are grounds for supposing that the anions in these complexes may also be substantially immobilized. In addition, conductivity values were obtained for some PEO complexes containing lithium salts of some monobasic acids and it was found that the complex formed from the Li-salt of the strongest acid gave the highest conductivity ($\text{～4 × 10}{}^{\mathrm{?4}}\text{Ω}{}^{\mathrm{?1}}$ cm^?1 at 373 K for a PEO-LiSO₃CF₃ complex).     

Poly(ethyl acrylate) in dilute solution

Poly(ethyl acrylate) (PEA), solution polymerized in methyl ethyl ketone by free radical initiation, was fractionated and the fractions were characterized by light scattering, viscometry and osmometry. Fractions obtained were in the molecular weight range of 0·3 × 10⁶ to 1·6 × 10⁶ with a polydispersity of 1.40. The following Mark-Houwink relations were established:

$\text{[η]}{}^{\mathrm{<mtext>35°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>acetone</mtext>}}\text{=4·15×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?61}}{}_{\mathrm{W}}$

$\text{[η]}{}^{\mathrm{<mtext>35°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>MEK</mtext>}}\text{=2·03×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?66}}{}_{\mathrm{W}}$

$\text{[η]}{}^{\mathrm{<mtext>39.5°</mtext><mtext>C</mtext>}}{}_{\mathrm{<mtext>n-propanal</mtext>}}\text{=7·89×10}{}^{\mathrm{?2}}\text{M}{}^{\mathrm{0?50}}{}_{\mathrm{W}}$

It was found that n-propanol at 39.5°C was a theta solvent for poly(ethyl acrylate) and that acetone was a poor solvent compared to methyl ethyl ketone. A relation between the molecular dimension and the molecular weight was established. It was observed that the chain dimensions of poly(ethyl acrylate) and poly(butyl acrylate) were considerably larger than poly(ethyl methacrylate) and poly(butyl methacrylate) respectively. The validity of various extrapolation procedures that have been proposed for calculating the unperturbed dimensions have been examined. The steric factor for PEA was 2·16 compared to 2·10 for poly(ethyl methacrylate). Root mean square end-to-end distances were calculated from the Debye-Bueche and Kirkwood-Riseman methods and compared with the experimental values.     

Polyacrylamide in water: molecular weight dependence of 〈R2〉 and [η] and the problem of the excluded volume exponent

A commercial sample of polyacrylamide (CALGON) has been carefully purified, analysed and fractionated. With suitable care, the molecular characterization can be carried out by light scattering and viscosity measurements, without disturbances arising from microgels or aggregates. The molecular weight dependence of the radius of gyration and intrinsic viscosity are given by:

$\text{〈R}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 7.49 × 10}{}^{\mathrm{?}}\text{M}{}^{0.64}\text{(}\text{A}\text{?}\text{)}$

$\text{[η] = 9.33 × 10}{}^{\mathrm{?3}}\text{M}{}^{0.75}\text{(cm}{}^3\text{/g)}$

The value of the exponent ν = 0.64 in the $\text{〈R}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ equation has been cross-checked by a study of the asymptotic behaviour of the scattering envelope. Such a value is higher than that expected in a good solvent (ν = 0.60) and should lead to a higher exponent in the intrinsic viscosity dependence. However, it agrees more closely with the published dependence of sedimentation and diffusion coefficients.     

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).     

Phosphonitrilic chloride: 34. Electrical conductivity of polybisaminophosphazenes

The electrical conductivity of polybisaminophosphazenes investigated over a range of temperatures was found to obey the general relation for semi-conductors. The resistivity decreased or increased when a side group having a high inductive effect or bulky group was linked in the polymers. The electrical conductivity of polybisaminophosphazenes containing primary amine, secondary amine and aromatic amine ranged from 1.3 × 10¹⁰ to $\text{2.8 × 10}{}^{10}\text{Ω-}\text{cm}$, 9.3 × 10¹⁰ to $\text{8.5 × 10}{}^{11}\text{Ω-}\text{cm}$ and above $\text{9.1 × 10}{}^{14}\text{Ω-}\text{cm}$, respectively.     

Synthesis and solution properties of comb polystyrenes

A new method for the synthesis of comb shaped polystyrenes of predetermined structure is described. Silicon-chlorine bonds are introduced into the backbone polystyrene by reaction of SiMe₂Cl₂ with hydrolysed styrene/vinyl acetate copolymers and coupled with polystyryl-lithium in benzene. From a common backbone polymer a series of comb polymers are prepared that have a constant number of branches but vary in branch length. The $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}$ of the whole comb polymers is about 1.3. The comb polymers with high branch density show θ (A₂) temperatures lower than that for linear polystyrene. The radius of gyration at θ (A₂) [〈S²〉_{θ (A2)}] is always larger than calculated from random flight statistics. For comb polymers with 20–30 branches increases with λ^?0.46 where λ is the fraction of polymer in the backbone. The intrinsic viscosities of the comb polystyrenes at θ (A₂) are equal to that of the parent backbone polymer when λ > 0.25 and increase only little when λ becomes equal to 0.1. Similar behaviour is found in toluene. Intrinsic viscosities in cyclohexane at 35°C show a complex pattern because of the θ-temperature variation.     

Small-angle neutron scattering studies of molten and crystalline polyethylene

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

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.     

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.