Small-angle neutron scattering by semicrystalline polyethylene

The angular dependence of the intensity of neutron scattering by deuterated polyethylene chains (PED) dispersed in the protonated host (PEH) in the semicrystalline state has been computed over the scattering range $\text{0 < μ < 0.2}\text{A}\text{?}{}^{\mathrm{?1}}$, where μ = (4π/λ)sin(θ/2), for various morphologies that differ according to the mode of chain re-entry into the crystalline lamellae. The scattering functions vary strongly with the tendency for adjacent re-entry. The intensity in the range $\text{0.04 < μ < 0.10}\text{A}\text{?}{}^{\mathrm{?1}}$ is 30–40% greater for the regularly folded morphology than for the ‘switchboard’ model. Calculations for the latter approximate the experimental results of Schelten et al. Optimum agreement with their scattering intensities, and the chain dimensions and degree of crystallinity as well, is achieved by a statistical model in which the chain preferentially re-enters the crystalline layer with a probability of about 0.7. Re-entry, when it occurs, is not required to be adjacent to the preceding sequence.     

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 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 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 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 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.     

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 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 scattering studies of PVC and PVC blends

Small-angle X-ray and small-angle neutron scattering studies have been carried out on poly(vinyl chloride) (PVC), and blends of PVC with solution-chlorinated polyethylene (SCPE) and poly(butyl acrylate) (PBA). The PVC used was commercial (suspension-polymerized) or bulk-polymerized. The blends of PVC with PBA were prepared by solvent-casting and those with SCPE by in situ polymerization. PVC samples show shoulders in the scattering spectra, presumably due to crystallites, which persist even in samples which have been solvent cast. Blends of PVC with PBA also show a peak but at a higher ‘d’ spacing. The blends with SCPE which were prepared by in situ polymerization show no such peak. This suggests that the method of preparation prevents the formation of crystallites. An increase in scattering of the PBA blends was observed when the samples were heated to the temperature of phase separation. Neutron scattering studies were also carried out using 2% deuterium labelled PVC in PVC and in the blends. In the PVC this showed chain dimensions in good agreement with predicted values. In the blends, dimensions of the same order were obtained, confirming a molecular dispersion of chains in the single phase, but there was an apparent reduction in the chain dimensions. This could be explained by a true reduction in dimensions or a non-zero A₂ value in the blends.     

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 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 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.     

Small-angle light scattering studies of poly(N-vinylcarbazole)

Morphology of PVK samples cast from various solvents (cyclohexanone, tetrahydrofuran, benzene) and crystallized on a glass surface, was studied by means of SALS. Results show existence of rod-like elements forming a morphology with nonrandom correlations of orientations. This morphology is practically independent of crystallization conditions.     

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 and cyclic voltammetry study on electrochemically oxidized and reduced pyrolytic carbon

The electrochemical double layer capacitance and internal surface area of a pyrolytic carbon material after electrochemical oxidation and subsequent reduction was studied with cyclic voltammetry and small-angle neutron scattering. Oxidation yields an enhanced internal surface area (activation), and subsequent reduction causes a decrease of this internal surface area. The change of the Porod constant, as obtained from small-angle neutron scattering, reveals that the decrease in internal surface area is not caused merely by a closing or narrowing of the pores, but by a partial collapse of the pore network.