Crosslink distribution of epoxy networks studied by small-angle neutron scattering

Crosslink distribution of epoxy networks of diglycidyl ether of bisphenol A (DGEBA) cured with stoichiometric amounts of meta-phenylene diamine (mPDA) was examined by small-angle neutron scattering (SANS). A monodisperse DGEBA resin with the smallest molecular weight was used to enhance the crosslink density and to simplify the network structure for deuterium-labelling. Meta-phenylene-d₄ diamine (mPDAd₄) was applied to label definitively the crosslinks. SANS measurements covered a reciprocal space range from 0.016 to 0.220 Å^?1 or, equivalently, real-space distances from 400 to 30 Å. Application of SANS on the deuterium-labelled epoxy networks consistently produces a constant excess intensity over the unlabelled epoxy networks. Since the scattering intensity from total correlation of the network was negligible, as evident from measurements of SANS on the unlabelled epoxy networks and small-angle X-ray scattering on the epoxy networks, the constant excess SANS intensity can only be attributed to a uniform spatial distribution of the amine curing agent. In other words, the crosslinks are distributed uniformly throughout the epoxy network.     

Distribution analyses of multi-modal dynamic light scattering data

A method of data analysis for dynamic light scattering is proposed to evaluate the weight fraction, w(R_h), of a small amount of large aggregates in a dilute solution, where R_h is the hydrodynamic radius. We examined the time-correlation function of scattering intensity for model multi-modal systems, i.e., mixtures of latex solutions having different particle sizes and of polystyrene standard solutions having different molecular weights, by properly taking into account the unknown fractions, w(R_h), and scattering intensities of individual components. We derived an equation to evaluate the weight fractions of the components. The validity of this method was verified by successfully reconstructing the observed correlation functions having fast and slow modes. As a demonstration, the fraction of aggregates in a thermosensitive polymer solution in water was evaluated as a function of temperature.     

Single-chain scattering in heterogeneous block copolymers

Diblock copolymers consisting of polystyrene (S) attached to a polybutadiene (B) block (which is either hydrogenous or perdeuterated) have been synthesized and blended in such a way that the microphase-separated S and B domains have equal scattering-length densities, thus eliminating the component of small-angle neutron scattering (SANS) due to the domain structure. Two samples were studied: one with small spherical polybutadiene microdomains whose size was in essential agreement with calculations assuming equilibrium, and a second one of larger molecular weight in which the sphere size, while larger, was considerably smaller than predicted from equilibrium theory. The SANS spectra of these samples were analysed to give the radii of gyration R_g and molecular weights M_w of the labelled polybutadiene blocks from plots of I^?1versusQ² and least-square fits to the single-chain scattering function proposed by Debye. Results for the first sample agreed with the molecular weight obtained from chromatography and u.v. absorption and with the R_g found in bulk polybutadiene of similar M_w. The SANS estimates of both M_w and R_g for the second sample were anomallously large; these deviations may be due to (a) non-Gaussian conformations of the polybutadiene chains imposed by the nonequilibrium state of the microdomain, or (b) clustering of the deuterated polybutadiene chains within the microdomain due to small isotopic differences in chemical potential, enhanced by the larger M_w. Observations on other systems suggest that the second effect is the dominant one.     

Dynamic light scattering and small-angle neutron scattering studies on phenolic resin solutions

Solution properties of unfractionated phenolic resins prepared by polycondensation of phenol and formaldehyde using oxalic acid as a catalyst were investigated by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The hydrodynamic radius, obtained by DLS experiments with 1 vol % solution in acetone, and the correlation length, ξ, of the Ornstein-Zernike equation, obtained by SANS experiments with 10 vol % solution in tetrahydrofuran, obey a power-law relation as a function of z-average molecular weight estimated by gel permeation chromatography, with scaling exponents of 0.57 and 0.27, respectively. These behaviors are unaffected by polymerization conditions, such as initial phenol-to-formaldehyde molar ratio in the range from 0.9 to 1.5, catalyst concentration with oxalic acid-to-phenol molar ratio from 0.01 to 0.1, and reaction time within the period in which the polymer remains soluble. SANS curves for polymers prepared under different conditions are sufficiently superimposed onto a single curve with the reduced variables, ξ⁻²I(q) and ξq. These results indicate that unfractionated phenolic resins have a self-similar structure with respect to the molecular weight.     

Structural aspects of the LCST phase behavior of poly(benzyl methacrylate) in room-temperature ionic liquid

The structure and lower critical solution temperature (LCST) phase behavior of well-defined poly(benzyl methacrylate) (PBnMA) solution using 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)amide, [C₂mim][NTf₂] ionic liquid (IL) as a solvent have been studied by dynamic light scattering (DLS) and small-angle neutron scattering (SANS) at various temperatures. The SANS profiles observed for fully deuterated IL ([C₂mim]-d₁₁[NTf₂]) containing PBnMA were kept practically unchanged in the temperature range between 298 and 363 K, while they suddenly changed at 363 K. This indicates that the LCST behavior of PBnMA-IL solution is a first-order phase transition, which is consistent with the DLS results. The SANS profiles below 363 K were well represented by the theoretical Debye scattering function with inter-molecular interaction and the radius of gyration, R_g was estimated to be almost constant, i.e., ∼45 Å. The SANS result obtained here was compared with those in aqueous PNIPAm solutions as a typical LCST system, and some differences between IL and aqueous solution systems are pointed out. It is found that thermodynamic quantities (ΔH_demix, ΔS_demix and ΔG_demix) from the homogeneous solution to the phase separation states strongly depend on the solvation of the PBnMA polymer by the IL ([C₂mim] cation and [NTf₂] anion). We propose an LCST phase separation mechanism in the polymer-IL solution.     

Dilute-solution structure of charged arborescent graft polymer

The solutions of charged G1 arborescent polystyrene-graft-poly(2-vinylpyridine) copolymers in methanol-d4 and D₂O were investigated over a dilute concentration range ?=0.005-0.05 (?: mass fraction) using small-angle neutron scattering (SANS). Upon addition of acid (HCl) arborescent graft polymers became charged and a peak appeared in SANS data. The interparticle distance (d_exp) calculated from a peak position corresponded to the expected value (d_uni) for a uniform particle distribution. This indicates the formation of liquid-like ordering due to long-range Coulombic repulsions. The smaller dielectric constant of methanol-d4 resulted in long-range electrostatic repulsions persisting to lower polymer concentration than in D₂O. The slow mode scattering was observed by dynamic light scattering measurements for the same polymer solutions, indicating the presence of structural inhomogeneity in the solutions. Both the peak and slow mode disappeared by addition of NaCl or excess HCl into the solutions due to the screening of electrostatic interactions. The G1 polymer grafted with longer P2VP chains (M_w∼30,000 versus 5000 g mol) formed a gel on addition of HCl. This result reveals that molecular expansion is more significant for arborescent polymers with longer (M_w∼30,000) linear polyelectrolyte branches, resulting in gelation for ?>0.01. Upon addition of NaCl or excess HCl a gel transformed back to a liquid resulted from the screening of electrostatic interactions.     

Poly(ionic liquid)-derived nanoporous carbon analyzed by combination of gas physisorption and small-angle neutron scattering

The preparation of nanoporous carbon materials and their characterization combining small-angle neutron scattering (SANS) with gas physisorption is presented. Carbon with a porous structure and tunable form is obtained here by a salt-templating approach using poly(ionic liquid) as precursor. SANS in combination with contrast matching by deuterated p-xylene was used for a separation of the scattering component deriving from the density fluctuations of the carbon matrix and the inaccessible porosity. The resulting scattering curves could be used for an unambiguous characterization of the pore structure of the materials. SANS curves measured at different partial pressure of the matching agent p-xylene were used for a differential filling of the micro- and mesopores. The analysis using the chord length distribution (CLD) was employed to determine the specific surface area and the pore size at different adsorption steps. The SANS results were in good agreement with the quenched solid density functional theory (QSDFT) analysis of the nitrogen physisorption. By the comparison of both characterization methods the pore shape could be determined. The combination of both SANS and gas physisorption is thus shown to provide a comprehensive characterization of the pore structure of the carbon monoliths throughout the entire pertinent length scale.     

Small-angle neutron scattering characterization of the structure of nanoporous carbons for energy-related applications

We used small-angle neutron scattering (SANS) and neutron contrast variation to study the structure of four nanoporous carbons prepared by thermo-chemical etching of titanium carbide TiC in chlorine at 300, 400, 600, and 800 °C with pore diameters ranging between ∼4 and ∼11 Å. SANS patterns were obtained from dry samples and samples saturated with deuterium oxide (D₂O) in order to delineate origin of the power law scattering in the low Q domain as well as to evaluate pore accessibility for D₂O molecules. SANS cross section of all samples was fitted to Debye-Anderson-Brumberger (DAB), DAB-Kirste-Porod models as well as to the Guinier and modified Guinier formulae for cylindrical objects, which allowed for evaluating the radii of gyration as well as the radii and lengths of the pores under cylindrical shape approximation. SANS data from D₂O-saturated samples indicate that strong upturn in the low Q limit usually observed in the scattering patterns from microporous carbon powders is due to the scattering from outer surface of the powder particles. Micropores are only partially filled with D₂O molecules due to geometrical constraints and or partial hydrophobicity of the carbon matrix. Structural parameters of the dry carbons obtained using SANS are compared with the results of the gas sorption measurements and the values agree for carbide-derived carbons (CDCs) obtained at high chlorination temperatures (>600 °C). For lower chlorination temperatures, pore radii obtained from gas sorption overestimate the actual pore size as calculated from SANS for two reasons: inaccessible small pores are present and the model-dependent fitting based on density functional theory models assumes non-spherical pores, whereas SANS clearly indicates that the pore shape in microporous CDC obtained at low chlorination temperatures is nearly spherical.     

X-ray and neutron scattering studies of poly(ester carbonate)/poly(ethylene terephthalate) alloys

Quenched blends of poly(ester carbonate) (PEC) and poly(ethylene terephthalate) (PET) have a single T_g and behave as single-phase amorphous alloys up to 67% PET. However, small-angle neutron scattering (SANS) data show that the PET molecules are not statistically distributed as classical Gaussian coils in the PEC matrix. In quenched amorphous PEC-rich films (a single phase), PET-rich domains of varying PET concentration appear to be randomly distributed in the PEC matrix, and the excess SANS intensity is attributable to fluctuations in PET concentrations. Wide- and small-angle X-ray scattering data and SANS results show incomplete phase separation of PET and PEC molecules upon annealing. A possible model for annealed blends (two phases) might be domains of folded-chain, crystalline PET with interlamellar amorphous regions composed of a mixture of PET and PEC molecules. These domains are dispersed in the amorphous PEC matrix.     

Phase separation in randomly charged polystyrene sulphonate ionomer solutions

The dynamics of randomly charged polystyrene caesium-sulfonate ionomers in semi-dilute solutions were studied using a combination of dynamic light scattering (DLS), small angle neutron scattering (SANS), and bulk rheology. The samples were studied in toluene solutions where the aggregation of the dipolar groups is favoured. Evidence of aggregation in dilute solution is found using DLS and SANS with both the hydrodynamic and static radius of gyration indicating that there is a contraction of the chains due to intra-chain attractive forces. SANS experiments demonstrate the evolution of the aggregates into a network structure as a function of polymer concentration. The association process is caused by the dipolar attraction between the charged groups and introduces two static correlation lengths in the mesh structure of the network; the standard semi-dilute mesh size (ξ=1.12c^{−0.72±0.03}) and an inhomogeneity length (Ξ=24c^0.58±0.05) due to micro-phase separation. The scaling of the amplitudes of the correlation lengths I₁(0)∼c^{−0.33±0.07} and I₂(0)∼c^2.0±0.4 are consistent with good solvent conditions and micro-phase separation, respectively. An imposed shear causes the break up of the micro-phase separated micellar system with a characteristic yield stress for the Bingham step-like shear thinning.     

Sphere sizes in diblock copolymers: discrepancy between electron microscopy and small-angle scattering results

Five diblock copolymers consisting of polybutadiene spheres in a polystyrene matrix were synthesized and characterized using several techniques, including transmission electron microscopy and small-angle neutron scattering (SANS). The mean radius of the polybutadiene spheres as measured from the electron micrographs was found to be significantly smaller than the SANS value for each of the samples (the average value of $\text{R}{}_{\mathrm{<mtext>EM</mtext>}}\text{R}{}_{\mathrm{<mtext>SANS</mtext>}}$ was 0.77). This discrepancy is greater than can be accounted for by sphere truncation when sectioning the sample for the electron microscope and is believed to be an artifact of the staining procedure.     

Small-angle neutron scattering from symmetric blends of poly(dimethylsiloxane) and poly(ethylmethylsiloxane)

We present results of a small-angle neutron scattering (SANS) study of the structure and thermodynamic properties of symmetric blends of deuterated poly(dimethylsiloxane) (d-PDMS) and poly(ethylmethylsiloxane) (PEMS) as a function of temperature (T) (40≤T≤300 °C) and the molecular weight (M_w) (4700≤M_w≤23,200). The radius of gyration (R_g) of d-PDMS was measured using the high-concentration labeling method and revealed unperturbed chain dimensions at all temperatures regardless of the polymer M_w. The random phase approximation (RPA) fits the data for low M_w blends, however it fails to describe the SANS data for M_w>10,000 g/mol. This observation is explained by the fact that for high M_w blends the correlation length of the concentration fluctuations ξ is always large (ξ>R_g), implying that these blends remain microscopically inhomogeneous at all temperatures studied in this work. At the same time, the low M_w blends are randomly mixed (ξ<R_g) at all T and can reach the ‘ideal mixing’ or Θ condition (χ=0).     

Neutron scattering investigations on the effect of crystallization temperature and thermal treatment on the chain trajectory in bulk-crystallized isotactic polystyrene

Small-angle neutron scattering (SANS) investigations coupled with differential scanning calorimetry (d.s.c.) have been performed on isotactic polystyrene (IPS) samples crystallized in bulk by one of three thermal treatments: crystallization at high supercooling (T_c = 140°C); crystallization at low supercooling (T_c = 200°C); crystallization at T_c = 140°C then annealing at T_an = 180°C. The neutron scattering experiments show that the chain trajectory in the semcrystalline medium varies depending on the molecular weight of the protonated matrix and the crystallization process. The SANS data, interpreted in the light of the d.s.c. measurements and conformational models of the semicrystallized chain, point out in particular that the size of the regularly-folded crystalline sequences (along the 330 plane) increases with chain mobility in the originally amorphous melt. These results are quite consistent with those of previous studies of IPS using bulk-crystallized samples and solution-grown single crystals.     

Multiple scattering in small-angle neutron scattering measurements on polymers

Multiple scattering corrections in small-angle neutron scattering experiments on polymers have been examined. Numerical calculations show that, for typical experimental conditions, the second-order scattering is less than 2% of the first-order scattering for QR_g up to 10.0. An approximate expression is also given for obtaining a rough estimate of the second-order scattering without numerical calculation.     

Shear effects on expanded graphite under uniaxial pressure: An in situ small angle neutron scattering study

In a previous work [1] we elucidated the in situ evolution of the porosity of out-of-plane compressed flexible graphite under uniaxial pressure up to 1000 bar using small-angle neutron scattering (SANS) technique. In order to understand the influence of shear effect on the properties of flexible graphite we study, in the present paper, the in situ behaviour of in-plane compressed flexible graphite under a uniaxial pressure. The sample had a pleated layered structure in which anisotropic SANS patterns revealed a distribution of differently oriented ellipsoid pores. Uniaxial compression generates important shear effects in this kind of sample.We have determined the evolution of the system fractal dimension, pore size distribution and apparent specific surface area with applied pressure which together allow us to describe the meso and macro pore structure evolution. Under pressure, the irreversible collapse and splitting of larger pores into smaller size ones which is characteristic of out-of-plane uniaxial compression [1], is accompanied, in the presence of shear stress components, by an in-plane slipping mechanism giving rise to cracks and consequently to interface formation.     

Interaction of nanogel with cyclodextrin or protein: Study by dynamic light scattering and small-angle neutron scattering

The structure of hydrogel nanoparticles (CHP nanogels), formed by self-aggregation of cholesterol-bearing pullulan (CHP) was studied by dynamic light scattering (DLS) and small-angle neutron scattering (SANS). The interactions between the CHP nanogel and methyl-β-cyclodextrin (CD) or protein (hen egg white) were also investigated. It was revealed by SANS that the nanogels were spherical in shape with a radius of 6.7 nm. The following two functions were disclosed. (1) CHP nanogels were dissociated by the addition of CD and formed inclusion complexes with cholesteryl groups, leading to suppression of hydrophobic interaction between the cholesteryl groups. (2) The nanogel behaved as a molecular chaperone (heat shock protein-like activity) when CHP nanogel was mixed with hen egg white and heated up to 75 °C. The egg white aqueous solutions with CHP nanogel remained transparent while the egg white without CHP nanogel became opaque.     

Phase behaviour and solution properties of sulphobetaine polymers

Aqueous polyelectrolytes have been extensively studied and comprehensively described in numerous books and reviews. In contrast, systematic investigations of aqueous polyzwitterions are few. This paper describes the detailed phase behaviour and solution properties of a homopolymer based upon a recently available sulphobetaine monomer, N-(3-sulphopropyl)-N-methacrylooxyethyl-N,N-dimethyl ammonium betaine (SPE). In addition, such properties are probed at the molecular level by static and dynamic light scattering, as well as laser Raman spectroscopy. Poly[N-(3-sulphopropyl)-N-methacrylooxyethyl-N,N-dimethyl ammonium betaine], P(SPE), of 4.35 × 10⁵M_w shows remarkable phase behaviour. It exhibits both an upper critical solution temperature (UCST) and an ‘apparent inverted’ lower critical solution temperature (LCST), i.e. a 1-phase region flanked by two 2-phase regions. Moreover, the UCST occurs at an order of magnitude lower polymer concentration than predicted by theory or demonstrated by experiment with conventional polymers. The aqueous solubility of (SPE) depends upon polymer molecular weight, as well as the concentration and structure of added salts. ‘Soft’ salt anions and cations are more effective solubilizers than ‘hard’ anions and cations. Furthermore, solutions of P(SPE) display ‘antipolyelectrolyte behaviour’, i.e. viscosities which increase with increasing salt concentrations. Static light scattering experiments indicate that the solvent quality for P(SPE) increases with increasing salt concentration. Dynamic light scattering measurements show that the polymer diffusion coefficients decrease and the chain dimensions increase with increasing salt concentrations. Moreover, laser Raman spectroscopy indicates that the local environment around the zwitterion functionalities is also modified by changes in salt concentration. Based upon such molecular level probes, models have been proposed to account for the P(SPE) phase behaviour and solubility. Thus, P(SPE) is depicted as a collapsed coil in water because of intra-group and intra-chain associations. The unusual phase behaviour of P(SPE) in water is rationalized in terms of a shift from intra- to interinteractions. In turn, NaCl breaks up the intra-associations and promotes polymer solubility.     

Gel-size dependence of temperature-induced microphase separation in weakly-charged polymer gels

The gel-size dependence of microphase separation in weakly-charged gels of N-isopropylacrylamide (NIPA) and 1-vinylimidazole (VI) copolymers has been investigated using swelling measurement, small-angle neutron scattering (SANS), and dynamic and static light scattering (DLS/SLS). It is known that weakly-charged polymer gels undergo microphase separation in a poor solvent as a result of competing interactions involving hydrophobic attraction versus electrostatic repulsion. The microphase separation is characterized by a scattering maximum in SANS intensity functions of which Bragg spacing, Λ, is around 20-30 nm. However, when gel size was reduced to the order of Λ, no microphase separation was observed. Instead, a typical scattering of isolated spherical particles was clearly observed. On the basis of the experimental evidence, we conclude that microphase separation has its own wavelength independent of gel size, and nanometer-order gels, i.e., nanogels, do not undergo microphase separation.     

Deep hydration: Poly(ethylene glycol) Mw 2000–8000 Da probed by vibrational spectrometry and small-angle neutron scattering and assignment of ΔG° to individual water layers

Aqueous solutions of poly(ethylene glycol) (PEG) exhibit some remarkable properties, among which is the small changes in water activity compared to the volumes occupied by the PEG: For example, the water in a 20% mass fraction solution of 6000 Da PEG has an activity of 0.9939. We have investigated PEGs with molecular weights 200, 400, 1000, 2000, 4000, and 8000 Da in the concentration range 1% to 17% mass fraction at neutral pH and with added KCl concentrations of 10 mmol L^?1 in aqueous solutions–conditions near those for promoting protein crystallization. These solutions exhibit a structural change at around 6% mass fraction as seen in the solution viscosities, compressibilities, and infrared spectra. Raman spectroscopy shows that the PEGs remain in the same structural form over the concentration range, and the infrared spectra indicate that the change must be due to a local shift in the water structure. Modeling of the results from small-angle neutron scattering (SANS) on the solutions suggests that the structures of the PEGs in the molecular mass range 2000 Da to 8000 Da are paired in the solution, and the separation distance decreases with increasing PEG concentration. From the structure, it becomes clear that the small effect on water activity occurs because of screening by the more weakly bound outer layers. From the bulk measurement of a_w and with reasonable assumptions, a free energy ΔG° can be assigned to each of the fourth, third, and second hydration layers.     

Cooperative and self-diffusion of polymers in semidilute solutions by dynamic light scattering

The quasielastic light scattering from semidilute solutions of polystyrene in tetrahydrofuran has been measured and we observe two distinct exponential decays separated by several orders of magnitude. The angular dependence of the decay constants is indicative of diffusive processes which we identify with the cooperative diffusion coefficient, D_c and the self diffusion coefficient D_s. It is found that D_c, identified with the fast decay, increases with polystyrene concentration and is independent of molecular weight. However, D_s decreases sharply with concentration and molecular weight. An explanation is given for the light scattering detection of these two diffusion coefficients which is based only on the assumptions inherent in the reptation model. In a limited region of molecular weight and concentration the experimental results appear to be consistent with the predictions of scaling theory.