Neutron scattering and amorphous polymers

During the past ten years neutron scattering has become a much more widely used technique. The use of neutron scattering to study the conformation and dynamics of polymer chains in the bulk amorphous state and in solution is reviewed here. The basic theory of neutron scattering is introduced. The types of instruments which are currently used and the factors affecting neutron scattering experiments are discussed. The following sections are each concerned with a different type of scattering experiment and the information which has been obtained. At the beginning of each of these sections the theory relating to the particular topic under discussion is introduced. The three topics covered by this review are: conformation studies of polymers; dynamics of polymer chains and studies of side group motion in polymers.     

Theory of correlations in partly labelled homopolymer melts

Small-angle neutron scattering by a polymer melt with partly tagged chains is considered. When several types of chain (differently labelled) are present in the system a new long-range correlation effect which modifies the scattering spectrum is predicted. This effect will arise because of the chemical polydispersity of the sample. A general formalism is developed to calculate the scattering intensity and is applied to special cases: diblock and triblock chains. It is shown that even a small chemical polydispersity leads to important long-range fluctuations and modifies the scattering spectrum substantially.     

Determination of the conformation of polymers in the amorphous solid state and in concentrated solution by neutron diffraction

From the coherent neutron scattering on dilute solid solutions of the ordinary polymer within the deuterated polymer, conformation parameters of polymer chains in amorphous solid states can be determined. In this way vitreous poly(methyl methacrylate) (PMMA) has been investigated. The chains form unperturbed coils and the radius of gyration is very near to the corresponding value in dilute solutions of the same polymer in the low molecular θ-solvent butyl chloride. The same principle of measurement has been applied to concentrated solutions of PMMA in D-acetone. The solutions contained 50% polymer, the main part of which (98% and more) was deuterated so that the system was optically dilute for neutron scattering on H-PMMA. A monotonic dependence of the radius of gyration and of thermodynamic parameters on the concentration has been found. A first result is presented for a mixture of two polymers. A dilute solid dispersion of poly(α-methylstyrene) (PMS) within D-PMMA has been investigated at M_w = 250 000. The samples are limpid. The PMS forms micelles of 16 molecules (weight average). The radius of gyration of the micelles, r_z is 170 Å.     

Observation of single chain motion in a polymer melt

Molecular motion of single polymer chains has been investigated in a melt sample of polytetrahydrofuran and compared with results for the same polymer in dilute solution. Using a high resolution neutron scattering technique motion over distances up to 30 Å has been observed with an energy resolution of 0.01 μeV (～10⁷s^?1). The motion of the chains in the melt is described by the Rouse model and a friction factor per segment has been extracted from the data. This compares well with values obtained from viscosity and bulk relaxation measurements on similar polymers.     

Ceramic-reinforced polymers and polymer-modified ceramics

The composites discussed in this review are prepared using techniques similar to those used in the new sol-gel approach to ceramics. Organometallis such as silicates, titanates, and aluminates are hydrolyzed in the presence of polymer chains (for example polysiloxanes and polyimides) that typically contain hydroxyl or amino groups. The functional groups are used to bond the polymer chains onto the silica, titania, or alumina being formed in the hydrolysis, thus forming organic-inorganic composites. When the polymer chains are present in excess, they constitute the continuous phase, with the ceramic-type material appearing as reinforcing particles. When present in smaller amounts, the polymer is dispersed in the continuous ceramic phase, to give a polymer-modified ceramic. Under some conditions, bicontinuous systems are obtained. The composites thus prepared are characterized by electron microscopy, X ray, and neutron scattering intensities, density determinations, and stress-strain and impact-strength measurements.     

Structural, mechanical and osmotic properties of injectable hyaluronan-based composite hydrogels

The osmotic and scattering properties of hyaluronan-based composite hydrogels composed of stiff biopolymer chains (carboxymethylated thiolated hyaluronan (CMHA-S)) crosslinked by a flexible polymer (polyethylene glycol diacrylate (PEGDA)) are investigated and analyzed in terms of the scaling theory. The total pre-gel polymer weight concentration is varied between 0.5 wt.% and 3.2 wt.%, while the mole ratio between the reactive PEG chain ends and the thiolated HA moieties is changed between 0.15 and 1.0. The shear modulus G of the fully-swollen gels exhibits a stronger dependence on pre-gel concentration than on the crosslink density. Osmotic deswelling measurements reveal that the osmotic mixing pressure depends on the weight ratio CMHA-S/PEGDA, and is practically unaffected by the pre-gel concentration. Small-angle neutron scattering observations indicate that the thermodynamic properties of these composite gels are governed by total polymer concentration, i.e., specific interactions between the two polymeric components do not play a significant role.     

Monte Carlo simulations on the effects of nanoparticles on chain deformations and reinforcement in amorphous polyethylene networks

Reinforcing effects in an amorphous polyethylene matrix were estimated for spherical filler particles arranged either on a cubic lattice or randomly in space. Attention was first focused on the effects of the type of arrangement of the particles on the microscopic properties of the polymer chains. Specifically, Monte Carlo rotational isomeric state (MC-RIS) simulations were carried out to predict the effects of the volumes excluded by the filler particles on the configurational distribution functions of the chains, and from these distributions the elastomeric properties of the composites. The calculations were carried out for a range of particle sizes and particle volume fractions. As expected, filler inclusions are found to increase the non-Gaussian behavior of the chains. The results were compared with those from small-angle neutron scattering (SANS) experiments. In the case of arrangement on a cubic lattice, chains dimensions were always found to decrease. In the randomly-dispersed filler arrangements, there were significant increases in chain dimensions relative to the unfilled system in some instances, and the changes were in excellent agreement with the SANS results. The present simulations thus give further encouragement to interpretations of chain deformations in filled systems in terms of volume exclusion effects from the nanoparticle inclusions, including their dispersions and arrangements within polymer matrices.     

Structural investigations of a neutralized polyelectrolyte gel and an associating neutral hydrogel

Small angle neutron scattering (SANS) measurements are used to differentiate the local organization of the polymer chains in two different classes of hydrogel. In neutral polyvinyl alcohol gels, hydrogen bonding gives rise to long range structural perturbations that are superimposed on the underlying chemically cross-linked network, thus producing excess scattering at small values of the scattering vector q. This secondary superstructure causes an increase in the elastic modulus. The intensity scattered by the thermal fluctuations in these gels can be described by an Ornstein-Zernike lineshape and is consistent with the osmotic modulus deduced from macroscopic osmotic and mechanical observations.Strongly charged polyacrylate hydrogels, however, display a qualitatively different scattering response. At low q a power law behavior is observed characteristic of a fractal surface. At intermediate q another component of osmotic origin is visible, which varies as q⁻¹, which indicates that the presence of divalent cations favors linear alignment of the network chains. Acceptable agreement is found between the estimate of the thermal fluctuations deduced from SANS and the results derived from independent osmotic observations.     

Butadiene rubbers: topological constraints and microscopic deformation by mechanical and small angle neutron scattering investigation

Summary Results of stress-strain measurements are reported for butadiene rubbers of varying crosslink density. The fluctuation of the effective tube diameter of the polymer networks was investigated under uniaxial elongation by mechanical measurements as well as by small angle neutron scattering (SANS) which probe the local orientation on a segmental scale. The effect of topological constraints on the microscopic deformation of the butadiene network chains is well described within a tube approach. For the first time, experiments at large deformations and for polydisperse sample are presented. Excellent agreement between the statistical mechanical model and the experimental results is obtained. Received: 20 November 2001 /Revised version: 5 March 2002/ Accepted: 5 March 2002     

Dynamics of polymer molecules using neutron spin—echo

The dynamics of single polymer chains have been investigated in dilute solution and in the melt using the neutron spin—echo technique. In dilute solution the intramolecular motion is described to a first approximation by that for a Rouse chain incorporating hydrodynamic interactions (Zimm). It is characterised by an inverse correlation time which may be normalised by temperature, solvent viscosity and segment size, and which for long chains varies as Q³ at small scattering angles (Q is the change in wavevector on scattering). At very low Q vectors the predicted ‘universal’ regime is observed, but over most of the accessible range chemical structure also becomes important. For short chains, deviations from this Q³ behaviour are associated with overall molecular diffusion. In the melt, chain entanglements come into play and modify the simple Rouse-type motion. The correlation functions are described by a combination of Rouse motion over short distances and times and a long-time slow-motion predicted by the reptation model of melt dynamics.     

Generality of anomalous expansion of polymer chains in supercritical fluids

By using in-situ neutron reflectivity, we have investigated swelling isotherms of solvophilic and solvophobic end-grafted/non-grafted polymer chains on solid substrates in supercritical carbon dioxide and supercritical ethane. It was found that anomalous expansion of the polymer chains associated with excess absorption of the fluid molecules occurs in the large compressible regions of both supercritical fluids (SCFs) regardless of the polymer-fluid interactions. In addition, we found that the excess expansion of the solvophobic polymer chains in both SCFs collapse onto one master curve under the same magnitude of density fluctuations in the fluids. A simple thermodynamic two-state model along with the experimental results proposes that polymer chains are expanded independently of the polymer-fluid interactions to further change solvent density fluctuations around the polymer chains, thereby lowering the free energy of the polymer/SCF systems.     

A new method for data evaluation of small angle neutron scattering experiments and its application to amorphous polycarbonate

Summary The conformation of single chains in bulk polymer materials can be evaluated from coherent neutron scattering on mixtures of normal and deuterated polymers. It is shown that the single-chain structure factor can be also obtained from measurements of highly concentrated mixtures and the procedure of evaluation is described. The application to amorphous polycarbonate demonstrates the advantages of the method.Paper presented at the Colloque Franco-Americain sur la diffusion des rayons X et des neutrons aux petits angles par les polymers, 16. – 19. Septembre 1980, StrasbourgNeutron scattering measurements were carried out at the ILL, Grenoble     

Stress relaxation and hysteresis of nanocomposite gel investigated by SAXS and SANS measurement

The stress relaxation phenomena of nanocomposite gel (NC gels) after uniaxial elongation was investigated by time-resolved small-angle scattering techniques of neutrons and X-rays. Nanocomposite gels consist of clay platelets and poly(N-isopropylacrylamide). It was found that clay oriented instantly and polymer chains were elongated along the stretching direction by elongation, followed by gradual process of peeling-off of adsorbed polymer chains on the clay platelets. When the specimen was held in the deformed state, stress relaxation was observed. This was mainly ascribed to peeling-off of polymer chains. When the strain of the specimen was removed, the polymer chains tended to be adsorbed again to the surface of the clay platelets. The deformation mechanism of NC gels is discussed on the emphasis of the peeling-off and peeling-on process of polymer chains.     

Residual orientation in injection‐moulded plaques of atactic‐polystyrene II: The effect of molecular weight

Injection moulding of polymers is a well‐established technique for the production of increasingly complex articles, and residual molecular orientation is a matter of considerable interest. A single matrix of commercial atactic polystyrene was systematically blended with deuterated polystyrene chains of five different weight fractions and the orientation investigated using small angle neutron scattering (SANS), optical birefringence and thermal shrinkage. The strengths and limitations of the experimental techniques used to measure residual orientation are explored and highlighted the unique contribution of SANS to observe ensemble averaged molecular orientation using deuterated polymers. The residual molecular orientation was found to vary with the molecular weight of the deuterated chains with an increase with increasing molecular weight. The observed correlations lead to a better understanding of the processing parameters that influence the degree of residual orientation on the molecular scale. Such information is valuable in the selection of the polymer matrix, mould design, and processing conditions. POLYM. ENG. SCI., 58:1332–1341, 2018. © 2017 Society of Plastics Engineers     

Phase transition in swollen gels

Summary The temperature dependences of the small-angle neutron scattering (SANS) from solutions and networks of poly (N,N-diethylacrylamide) (PDEAAm), or from the copolymer of DEAAm and 5 mol.% sodium methacrylate (MNa) in deuterated water were measured. In the low-temperature range (T<30°C, expanded state) the SANS curves have features typical of scattering from polymer coils. At elevated temperatures (T>60°C, collapsed state) the character of SANS curves changes, indicating that in both networks and solutions compact globular structures are formed. The presence of MNa (i.e. of charges on the chains) shifts the temperature of the transition range from the expanded to the collapsed state towards higher temperature by 10–15°C.On leave from the Institute of Macromolecular Chemistry, Czechoslovak Academy of Sciences     

Conformation of polymer molecules at solid-liquid interfaces by small-angle neutron scattering

A wide variety of physical-chemical phenomena depend on the behavior of the polymer at solid-liquid interfaces. The feature that distinguishes such phenomena from their small-molecule counterparts is the long-chain structure of the polymer molecules. Just as in solution and the bulk, the conformational statistics of the polymer molecules in the interface is an important determinant of interfacial properties. Conformational statistics of interfacial polymer is expressed in terms a function called the polymer density profile ϕ(Z), which is just the volume fraction of polymer as a function of Z, the distance from the solid surface out into the continuum liquid. There is only one experimental technique that is purported to be able to determine polymer density profiles of polymers confined to the interface between finely divided substrate and dispersant, and that technique is small-angle neutron scattering (SANS). In this paper we present a protocol for the analysis of SANS data on spherical particles with adsorbed polymer for the determination of ϕ(Z). We give an example for nearly-monodisperse chains of poly(n-butyl methacrylate) with a molecular weight of 45,000 tethered to silica spheres with a diameter of 2150 Å. The polymer density profile demonstrates a deep depletion layer next to the surface with a maximum in ϕ(Z) of about 0.7 at about Z = 40 Å. Our experimental ϕ(Z) is compared with various theoretical predictions.     

Potentials with small‐angle neutron scattering technique for understanding structure–property relation of 3D‐printed materials

Carbon fiber (CF)‐embedded acrylonitrile butadiene styrene polymer composites printed on the large‐scale printer at Oak Ridge National Laboratory were investigated by small‐angle neutron scattering to correlate the microstructure of the composites with their mechanical strength. The microstructure of the polymer domains and the alignment of CF were characterized across the interfaces between layers of the hot‐melt extruded material and were compared with CF‐free ABS. The small‐angle neutron scattering data show that the CF‐containing material displays strong anisotropic scatterings suggesting molecular alignment along the printing direction that is not present in the CF‐free ABS. Scattering data analysis across the interfacial layer revealed enhanced molecular alignment along the printing direction near the boundaries and inhomogeneous size distribution of polymer domains upon the addition of CF. We attribute the compromised strength across interfacial layers from CF‐containing material to this inhomogeneous size distribution which prevents effective lateral interaction between layers. POLYM. ENG. SCI., 59:E65–E70, 2019. © 2018 Society of Plastics Engineers     

Molecular dynamics simulation of polymer nanoparticle collisions: orbital angular momentum effects

The collisional dynamics of polymer nanoparticles is investigated using molecular dynamics, with a particular focus on angular momentum effects. Unlike zero impact parameter collisions discussed elsewhere, which are greatly weighted toward sticking collisions, the outcome of collisions with non-zero angular momentum show much greater variability, showing both reactive (where polymer chains are exchanged between particles) and purely scattering trajectories. In the case of inelastic scattering trajectories, the profile for translation to vibration energy transfer is calculated.     

Conformation of oligo(ethylene glycol) grafted polystyrene in dilute aqueous solutions

Temperature induced conformational changes of poly(p-oligo(ethylene glycol) styrene) (POEGS) in aqueous solutions were investigated by small angle neutron scattering (SANS), neutron transmission and dynamic light scattering (DLS). The molecular weight of the polymer studied was 9400 g/mol with a polydispersity index of 1.18 and each repeat unit of the polymer had four ethylene glycol monomer segments. The polymer was water soluble due to the hydrophilicity of the OEG side chains and these solutions showed lower critical solution temperature (LCST) depending on the concentration of the polymer. Measurements of solution behavior were made as a function of temperature in the range of 25-55 °C for three polymer concentrations (0.1 wt%, 0.3 wt%, and 1.8 wt%). Neutron transmission measurements were used to monitor the amount of polymer which precipitated or remained in solution above the cloud point temperature (T_CP). DLS revealed the presence of large clusters in all solutions both below and above T_CP while SANS provided information on the structure and interactions between individual chains. It was found that in the homogeneous region below T_CP the shape of individual polymers in solution was close to ellipsoidal with the dimensions R_a = 37 Å and R_b = 14 Å and was virtually independent of temperature. The SANS data taken for the most concentrated solution studied (1.8 wt%) were fit to the ellipsoidal model with attractive interactions which were approximated by the Ornstein-Zernike function with a temperature-dependent correlation length in the range of 24-49 Å. The collapse of individual polymers to spherical globules with the radius of 15 Å above T_CP was observed.     

Reflection methods for the study of polymer interfaces

The direct study of polymer Interfaces is very difficult. Small angle scattering methods have been most successfully applied to block copolymer Interfaces where the morphology is well known. Other techniques such as electron microscopy, Rutherford back scattering, and forward recoil spectroscopy generally only give resolution of the order of 10 nm. Here we describe two techniques which have only recently been applied to polymer interfaces, neutron reflection, and spectro-scopic ellipsometry. Both reflection techniques examine planar samples and give compositional information in the depth direction. Neutron reflection gives a resolution of 0.5 nm and spectroscopic ellipsometry may give better than 5 nm. We will describe experiments using neutron reflection which measure the inter-facial thickness between two immiscible polymers and experiments using both techniques which measure the interdiffusion of miscible polymers. Other applications and limitations of the techniques will also be discussed.