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 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.     

Small-angle neutron scattering of partially segregated blends of polyethylene and deuteropolyethylene

A previous paper described work in which polyethylene (PEH) blended with 4.3 vol% deuterated polyethylene (PED) was annealed and plastically deformed at different temperatures. The most prominent change resulting from the deformation is a significant reduction in the apparent molecular weight measured from the extrapolated small-angle neutron scattering (SANS) data. The model adopted in the data analysis was based on a heterogeneous distribution of the centres of mass of the labelled (PED) chains which form a two phase system of enriched and depleted regions described by a Debye-like correlation function. A comparison between this model and alternative approaches based on the correlation network and random phase approximation will be delineated. The results from these models lead to the conclusion that for typical melt crystallized samples the centres of mass of the labelled chains are only slightly perturbed from a random distribution. Plastic deformation of the blends tends to lessen the degree of segregation of the PED molecules and the results suggest that a portion of the specimen must undergo a melting and recrystallization mechanism during deformation.     

Small-angle neutron scattering studies of molecular clustering in mixtures of polyethylene and deuterated polyethylene

Studies of the factors governing molecular aggregation in mixed samples of protonated polyethylene (PEH) and deuterated polyethylene (PED) have been made by small-angle neutron scattering. Thermodynamic arguments are given to show that there is a natural tendency for PEH and PED to segregate on crystallizing from the melt. This segregation arises from the shape of the phase diagram of the PEH/PED system, and not from any basic incompatibility of the components. An equilibrium distribution of PED molecules in PEH can be obtained only by cooling very rapidly and quenching in the equilibrium distribution of the melt, or alternatively by cooling extremely slowly, giving the molecules sufficient time to rearrange to a statistical distribution. Because of the very low diffusion rates of the polymer molecules (M_W ～ 100 000), the rates of cooling normally used in practice (>2°C/h) are not sufficiently slow to reach an equilibrium distribution and non-equilibrium crystallization produces partly segregated or clustered distributions. By means of careful control of the cooling rate on crystallization, the molecular weights, concentrations and melting points of the two species, it is possible to prepare samples covering the whole range from virtually phase separated to statistically mixed molecules. Departures from a statistical distribution lead to anomalous features in the SANS patterns, and these features have been used to study the aggregation (clustering) process. Model calculations of the scattering patterns from clustered molecules have been performed which explain all the anomalous features detected in the SANS patterns. These calculations show that the SANS method is extremely sensitive to small deviations from a statistical distribution. The model calculations also provide important indirect evidence that the radius of gyration of the polymer molecule is virtually unchanged on equilibrium crystallization from the unperturbed dimensions measured in the melt.     

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.     

Small-angle neutron scattering from branched epoxide resins

Small-angle neutron scattering experiments in the range of q² from 0.01 to 25 nm⁻² have been carried out on branched epoxide resins based on bisphenol-A at the Institute Laue—Langevin (I.L.L) in Grenoble (q=(4π/λ) sin(θ/2)). Measurements were made with six samples in the range of M_W from 1500 to 19 000 and four concentrations between 1.3 and 10% (w/w) in deuterated diglyme. The results are as follows: (i) The mean square radius of gyration follows a relationship S²_z=4.69×10⁻⁴M^1.20_W (nm²). (ii) In all cases fairly large second virial coefficients A₂ are obtained which, however, decrease strongly with molecular weight. Above M_W=2500, the virial coefficient follows the relationship A₂=1.6M^−0.85_W (mol cm³g⁻²). (ii) The reciprocal particle scattering factor as a function of q² exhibits only a slight upturn and otherwise shows the behaviour of a randomly branched polycondensate. The slight upturn is discussed as being caused by the finite volume of the monomeric unit. Possible reasons for the high exponent in the S²_z versus M_W dependence are briefly discussed.     

Small-angle neutron scattering study of amorphous polycarbonate

Experiments have been performed on deuterated polycarbonate chains with five different molecular weights, randomly dispersed in a protonated polycarbonate matrix. There is evidence for some ester interchange in the melt. This requires that the values of M_w obtained from the SANS data be used. The measured radii of gyration were found to follow the relationship: R_w = βM^a_w, with β = 0.457(9) and α = 0.5. The high value for β compared with that for polystyrene (β = 0.27) is a reflection of the stiffer backbone in polycarbonate.     

Structural characterization of semicrystalline polymer blends by small-angle neutron scattering

A series of phase-separated polyethylene-polypropylene blends, which have undergone different thermal treatments, have been analysed by small-angle neutron scattering (SANS). The coherent scattering from normal hydrogenated blends is virtually zero, but strong contrast may be induced by partial or complete deuteration (labelling) of either phase. Here, the scattering from blends with complete labelling of the polyethylene phase was analysed to provide the domain dimensions by means of a theory due to Debye using an exponential correlation function. By this means the mean chord intercept lengths of both phases were shown to be in the range 1000–10000Å. The scattering from blends with partial labelling of the polyethylene was analysed to give the radius of gyration of the molecules in the polyethylene domains, which was found to be close to that measured in the homopolymer. For melt-quenched blends the deuterated polyethylene was shown to be statistically distributed in the polyethylene phase, whereas for slow-cooled blends, partial segregation of the labelled molecules occurred.     

Small-angle neutron scattering studies on sodium dodecylbenzenesulfonate-tetra-n-butylammonium bromide systems

A phase study was completed on aqueous sodium dodecylbenzenesulfonate (SDBS) and tetra-n-butyl-ammonium bromide (Bu₄NBr) systems, and consolute boundaries were drawn through cloud points. Samples were selected from both miscibility regions [under the lower consolute boundary (LCB) and above the upper consolute boundary (UCB)] for small-angle neutron scattering (SANS) studies. In the first set of experiments, the effect of varying Bu₄NBr concentration on micellular parameters of 100 mM SDBS was studied at 30°C. The pure SDBS micelle has an aggregation number (n _s ) of 51, and the effective charge on the monomer (α) is 0.17. With the addition of Bu₄NBr, the n _s of SDBS micelles increases while α decreases. The system with [Bu₄NBr]=39.5 mM (an above-UCB sample) showed clouding near room temperature (≈29°C) and had a high n _s value (300) and a low α (=0.09). The data indicated that the micelles lose ionic character in the presence of Bu₄NBr. The temperature effect on this sample shows that α remains almost constant, while n _s decreases on heating. A similar effect was observed with samples of lower Bu₄NBr concentration (32 or 25 mM) in the presence of 100 mM SDBS. The same type of temperature effect was seen on a sample of under-LCB region (50 mM SDBS+32 mM Bu₄NBr); the n _s values increased significantly as the LCB was approached. The overall SANS observations suggest that the micelles have low ionic character together with high n _s values (a case of micellar growth) near LCB/UCB.     

Small-angle neutron scattering measurement of block copolymer interphase structure

The notion of an interfacial layer at the domain boundary in block copolymers is reviewed and the possibility of its measurement by small-angle X-ray and small angle neutron scattering discussed. Values of the interfacial layer thickness and its volume fraction have been obtained for a range of styrene-isoprene copolymers. Interfacial layer thickness is not strongly dependent on molecular weight whilst the volume fraction shows a dependence more in line with the theory of Helfand.     

Small-angle neutron scattering by semicrystallized chains: Evaluation of the mean dimensions

The mean dimensions of semicrystallized chains having long crystallized sequences are calculated as functions of the crystallinity. Models of chain incorporated in the monocrystal are defined and their mean dimensions are expressed as functions of the molecular weight of the chain, taking into account the crystalline parameters. The effects of introducing amorphous sequences in the chain are then examined. Finally, the case of a real semicrystallized polymer containing pure amorphous regions is considered. The results are discussed as functions of crystallinity, molecular weight and crystalline parameters of two different polymers: polyethylene and isotactic polystyrene. In particular, it is shown that conformation with long crystallized sequences can lead to a non-variation of the radius of gyration as in Flory's model.     

Small-angle neutron scattering from a polymer coil undergoing stress relaxation

Small-angle neutron scattering measurements have been made on samples of polystyrene in which the stress has been allowed to relax at a constant strain. The radii of gyration parallel and perpendicular to the stretch direction have been measured as a function of time after the strain has been applied. After an initial rapid change, the radii of gyration tend towards asymptotic values which are close to those for the undeformed chain. The deformation appears to behave as if the affine deformation theory holds only for distances separating effective crosslinks. It is proposed that after the initial change in radii of gyration the stress is relieved by reorientation of the chain segments.     

Small-angle neutron scattering study of coal extract solutions in pyridine

Three perdeutero-pyridine extracts of Illinois No. 6 coal were studied with SANS in an effort to: 1. check the reproducibility of the measurements; 2. check the reproducibility of the extractions; and 3. try to measure weight average molecular weights for the non-fractionated extracts. In addition one sample from the Bruceton mine of Pennsylvania was studied to check any dependence on the coal's origin and one silylated sample of an Illinois No. 6 extract was studied to assess the effect of chemical treatment of coals on the average molecular weight. The chemical composition and the number-average molecular weights were obtained for the same samples. Scattering data were observed to be well represented by the Debye theory for a random two phase system with an experimental density-density correlation function described by a correlation length a. The analysis of the data shows that the extraction is a non-reproducible operation and this seems to be due to the heterogeneous nature of coal. In addition the present methods available to obtain molecular weights from the scattering data do not seem to be applicable to coal extracts.     

Small-angle neutron scattering characterization of plastic deformation in amorphous polymers

The direct measurement of coil dimensions resulting from the non-elastic deformation of glassy amorphous polystyrene was undertaken by means of a small-angle neutron scattering technique for various deformation situations. The difference in behaviour between anisotropic glide within a coarse shear band and diffusion-like homogeneous deformation is confirmed on the macromolecular scale.     

Small-angle neutron scattering study on block and gradient copolymer aqueous solutions

The small-angle neutron scattering investigation was carried out on semi-dilute aqueous solutions of block and gradient copolymers comprising pEOVE and pMOVE, pEOVE₃₀₀-block-pMOVE₃₀₀ (Block) and p(EOVE-grad-MOVE)₆₀₀ (Grad). Here, pEOVE and pMOVE denote poly(2-ethoxyethyl vinyl ether) and poly(2-methoxyethyl vinyl ether), respectively, and the numbers indicate the degrees of polymerization. The monomer composition in the Grad had a gradient along the polymer chain. For 20.0 wt% solutions, a microphase-separated structure and physical gelation were observed both in Block and in Grad systems. In the case of the Grad system, a gradual microphase separation took place as a function of temperature via a micellization with a small radius of core, characterized by the “reel-in” process, i.e., a winding of polymer chains to the core of a micelle because of the gradient composition. On the other hand, the Block system underwent a stepwise transition with respect to temperature. The relationship between microphase separation and the rheological behavior is explained from the viewpoint of microscopic structure.     

Autoxidation of semicrystalline polyethylene

Thermal oxidation in linear polyethylene is mainly confined to disordered regions in which scission reactions cause crystallization and eventual deterioration of mechanical properties. Gel formation is negligible at 100°C. As degradation proceeds, comparable changes occur in the intrinsic viscosities of melt and solution-crystallized liner polymers, indicating that chain folds are regularly arranged and are resistant to oxidative scission. Breakdown is much more extensive in branched and crosslinked polymers since crosslinking retards oxidative crystallization and branching increases the volume fraction of substrate ultimately accessible to oxygen.     

Trajectory of polyethylene chains in single crystals by low angle neutron scattering

Measurements of coherent neutron diffraction of oriented single crystals of blends of hydrogenous and deuterated polyethylene have been undertaken in order to study the mutual arrangements of the crystalline ‘stems’ of the same molecule. In the appropriate range of diffraction angle, the scatter is fully consistent with thin lamellae, the planes of which contain the stems. The thickness of these lamellae agrees with that expected for neighbouring stems of one molecule being restricted to the same (110) plane. The density of deuterium atoms in the lamellae is consistent with largely adjacent re-entrant folding; for crystals grown at low supercooling there is a possibility of some segregation according to isotope. Outside the above range of diffraction angle, effects are observed which are attributable to the finite lateral dimensions of the proposed lamellae. At the smallest angles of measurement an artifactual signal attributable to voids can be observed, which can be avoided by suitable sample treatment.     

Small-angle neutron scattering of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers

Small-angle neutron scattering was used to characterize the structure of arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers dissolved in methanol-d4 (CD₃OD). A radial density profile based on a power law functional form provided a good fit to the scattering data. While a model with homogeneous density profiles in the core and shell, respectively, and with a size distribution (a polydisperse core-shell model) also fits the data comparably well, the extra parameters required for this fit are difficult to justify on the basis of the data. In addition, unconstrained fits using the core-shell model failed to converge to values of the overall molecular size and molecular weight which agreed with values determined from independent light scattering measurements which leads to the conclusion that the power law model is a more appropriate function for describing the radial density function of these molecules. The density profile from either model showed that the polystyrene core of the molecules is not collapsed. Values of the second virial coefficient, A₂, have been calculated from Zimm plots and it was found that A₂ decreased as a function of generation to close to zero for the highest generation (i.e. highest molecular weight) polymers. Finally, it was found that the radius of gyration of the polymers increases with the molecular weight according to the scaling relationship, R_g∼M_w^v with v=0.24±0.04.