Single-chain Form Factors Research Articles

Structure of Single-Chain Nanoparticles under Crowding Conditions: A Random Phase Approximation Approach.

The conformation of poly(methyl methacrylate) (PMMA)-based single-chain nanoparticles (SCNPs) and their corresponding linear precursors in the presence of deuterated linear PMMA in deuterated dimethylformamide (DMF) solutions has been studied by small-angle neutron scattering (SANS). The SANS profiles were analyzed in terms of a three-component random phase approximation (RPA) model. The RPA approach described well the scattering profiles in dilute and crowded solutions. Considering all the contributions of the RPA leads to an accurate estimation of the single chain form factor parameters and the Flory-Huggins interaction parameter between PMMA and DMF. The value of the latter in the dilute regime indicates that the precursors and the SCNPs are in good solvent conditions, while in crowding conditions, the polymer becomes less soluble.

Quantifying structure and dynamics of bound and bulk polymer in tailor-made rubber-silica nanocomposites

The dynamics of long polymer chains in the presence of nanoparticles have been investigated. The nanocomposites of interest were inspired by tire industry-like rubber materials and consisted of entangled polyisoprene linear chains mixed with chemically pre-treated silica nanoparticles. Combining rheology, dielectric spectroscopy, and neutron spin echo measurements, we measured the modification of the polymer chain dynamics from bulk state to high filler concentration over a broad range of time and length scales. We show that the end-to-end relaxation does not seem to be impacted, whereas the polymer dynamics is significantly slowed down at a very local scale in the presence of nano-fillers. In addition to this length scale dependent different dynamics, additional Neutron Spin Echo spectroscopy experiments and Small Angle Scattering on labelled polymer chains, irreversibly bound to the filler surface and re-dispersed in a fully deuterated matrix, revealed a negligible dynamical behavior of this particular population of localized chains in the rubber layer. The conformational statistics of these chains is that of self-avoiding walk train within a shell that is thinner than the size of the chain. To the best of our knowledge, this work is the first of its kind which measures the single chain form factor in the bound layer of chemically multi-linked chains to the filler surface.

Structure and Dynamics of Highly Attractive Polymer Nanocomposites in the Semi-Dilute Regime: The Role of Interfacial Domains and Bridging Chains.

Detailed molecular dynamics (MD) simulations are employed to study how the presence of adsorbed domains and nanoparticle bridging chains affect the structural, conformational, thermodynamic, and dynamic properties of attractive polymer nanocomposite melts in the semi-dilute regime. As a model system we have chosen an unentangled poly(ethylene glycol) (PEG) matrix containing amorphous spherical silica nanoparticles with different diameters and at different concentrations. Emphasis is placed on properties such as the polymer mass density profile around nanoparticles, the compressibility of the system, the mean squared end-to-end distance of PEG chains, their orientational and diffusive dynamics, the single chain form factor, and the scattering functions. Our analysis reveals a significant impact of the adsorbed, interfacial polymer on the microscopic dynamic and conformational properties of the nanocomposite, especially under conditions favoring higher surface-to-volume ratios (e.g., for small nanoparticle sizes at fixed nanoparticle loading, or for higher silica concentrations). Simultaneously, adsorbed polymer chains adopt graft-like conformations, a feature that allows them to considerably extend away from the nanoparticle surface to form bridges with other nanoparticles. These bridges drive the formation of a nanoparticle network whose strength (number of tie chains per nanoparticle) increases substantially with increasing concentration of the polymer matrix in nanoparticles, or with decreasing nanoparticle size at fixed nanoparticle concentration. The presence of hydroxyl groups at the ends of PEG chains plays a key role in the formation of the network. If hydroxyl groups are substituted by methoxy ones, the simulations reveal that the number of bridging chains per nanoparticle decreases dramatically, thus the network formed is less dense and less strong mechanically, and has a smaller impact on the properties of the nanocomposite. Our simulations predict further that the isothermal compressibility and thermal expansion coefficient of PEG-silica nanocomposites are significantly lower than those of pure PEG, with their values decreasing practically linear with increasing concentration of the nanocomposite in nanoparticles.

A Novel Method of Extraction of Blend Component Structure from SANS Measurements of Homopolymer Bimodal Blends.

A new method is presented for the extraction of single-chain form factors and interchain interference functions from a range of small-angle neutron scattering (SANS) experiments on bimodal homopolymer blends. The method requires a minimum of three blends, made up of hydrogenated and deuterated components with matched degree of polymerization at two different chain lengths, but with carefully varying deuteration levels. The method is validated through an experimental study on polystyrene homopolymer bimodal blends with . By fitting Debye functions to the structure factors, it is shown that there is good agreement between the molar mass of the components obtained from SANS and from chromatography. The extraction method also enables, for the first time, interchain scattering functions to be produced for scattering between chains of different lengths.

The long-chain dynamics in a model homopolymer blend under strong flow: small-angle neutron scattering and theory

We use small-angle neutron scattering (SANS) measurements to provide a detailed picture of the non-linear dynamics of the long chains in a model polystyrene blend. By a weighted subtraction of SANS measurements from two otherwise identical blends with different deuteration fractions, we isolate the single-chain form factor of the long-chain component of a model blend flowing through a 4 : 1 contraction–expansion flow. Complementary flow-birefringence also provides a measure of chain deformation on finer length-scales. In addition, higher flow Weissenberg numbers than in previous studies on monodisperse melts were achieved, leading to greater anisotropy in the measured single-chain structure factor. The short residence time inside the slit means that the chains are still oriented in the flow direction as they enter the contraction exit, leading to a rapid reversing flow. We compare these data to a simple generalisation of a non-linear tube model. Our model predictions are entirely ab initio, with all model parameters being determined from independent equilibrium measurements. The model shows very good agreement with the experimental data across the full range of length-scales for the contraction entrance and subsequent relaxation within the slit. However, there is conspicuous disagreement between theory and experiments at the contraction exit, in both the SANS and birefringence predictions, which we attribute to the reversing flow that occurs in this region.

An experimentalist's view of the physics of rubber elasticity

An experimentalist's view of the physics of rubber elasticity

Single chain structure in thin polymer films: corrections to Flory’s and Silberberg’shypotheses

Conformational properties of polymer melts confined between two hard structurelesswalls are investigated by Monte Carlo simulation of the bond fluctuationmodel. Parallel and perpendicular components of chain extension, bond–bondcorrelation function and structure factor are computed and compared withrecent theoretical approaches attempting to go beyond Flory’s and Silberberg’shypotheses. We demonstrate that for ultrathin films where the thickness,H, is smaller than the excluded volume screening length (blob size),ξ, the chain size parallel to the walls diverges logarithmically,R2/2N≈b2+clog(N) with c∼1/H. The corresponding bond–bond correlation function decreases like a power law,C(s) = d/sω with s being the curvilinear distance between bonds andω = 1. Upon increasingthe film thickness, H, we find—in contrast to Flory’s hypothesis—the bulk exponentω = 3/2 and, more importantly,a decreasing d(H) that gives direct evidence for an enhanced self-interaction of chain segments reflectedat the walls. Systematic deviations from the Kratky plateau as a function ofH are found for the single chain form factor parallel to the walls in agreement with thenon-monotonic behaviour predicted by theory. This structure in the Kratky plateau might giverise to an erroneous estimation of the chain extension from scattering experiments. For largeH the deviations are linear with the wavevector,q, but are very weak. In contrast, for ultrathin films,H<ξ, very strong corrections (albeit logarithmic inq) are found suggesting a possible experimental verification of our results.

Single-Chain Properties of Polyelectrolytes in Poor Solvent

Using molecular dynamics simulations we study the behavior of a dilute solution of strongly charged polyelectrolytes in poor solvents, where we take counterions explicitly into account. We focus on the chain conformational properties under conditions where chain-chain interactions can be neglected, but the counterion concentration remains finite. We investigate the conformations with regard to the parameters chain length, Coulomb interaction strength, and solvent quality, and explore in which regime the competition between short range hydrophobic interactions and long range Coulomb interactions leads to pearl-necklace like structures. We observe that large number and size fluctuations in the pearls and strings lead to only small direct signatures in experimental observables like the single chain form factor. Furthermore we do not observe the predicted first order collapse of the necklace into a globular structure when counterion condensation sets in. We will also show that the pearl-necklace regime is rather small for strongly charged polyelectrolytes at finite densities. Even small changes in the charge fraction of the chain can have a large impact on the conformation due to the delicate interplay between counterion distribution and chain conformation.

A Small-Angle Neutron and X-ray Contrast Variation Scattering Study of the Structure of Block Copolymer Micelles: Corona Shape and Excluded Volume Interactions

Small-angle neutron and X-ray scattering data have been obtained for micelles of d-polystyrene−polyisoprene (d-PS−PI) of relatively high molecular weight in n-decane. Contrast variation was performed using mixtures of hydrogenated and deuterated decane. Three samples were investigated with d-polystyrene and polyisoprene molar masses of, respectively, 12 000 and 48 000, 40 000 and 40 000, and 40 000 and 80 000. For the two latter samples, the concentration of the polymer was also varied. The data obtained at relatively high resolution were analyzed together with small-angle X-ray scattering data using scattering functions recently derived from Monte Carlo simulations for a model with a spherical core and a corona of semiflexible chains interacting with a hard-core potential. The scattering from the model can be generated by assuming an analytical form of the radial distribution of the corona and an effective single chain form factor of the random-phase approximation type. In the analysis of the experimental scattering data intermicellar interactions were modeled by an effective hard-sphere model. The analysis of the experimental data provides information on shape, aggregation number, polydispersity, core size, core solvation, corona shape/size, and the interactions between the chains in the corona, which are significant for these micelles. The shape of the corona profile depends on the surface coverage of the micelles as well as the curvature of the core−corona interface. For high curvatures the profile is in agreement with a power-law behavior as predicted by scaling theory. For low curvatures the profile is more compact. The profiles and scattering curves are very well reproduced by Monte Carlo simulations based on the parameters for the structures determined in the analysis of the experimental scattering data. The study shows that two parameters are decisive for the profile shape and internal correlations, namely the reduced surface coverage and the curvature.

Heterogeneous structure of poly(vinyl chloride) as the origin of anomalous dynamical behavior

We have investigated the thermal evolution of the structure and the dynamics of poly(vinyl chloride) (PVC) in a wide temperature range. Corroborating earlier findings, small angle neutron scattering revealed the presence of structural heterogeneities. On the other hand, the single chain form factor corresponds to that of Gaussian chains. Gradually with increasing temperature the system becomes homogeneous. A simple description of the heterogeneities in terms of microcrystallites is forwarded. The dynamical behavior of PVC has been investigated combining broadband dielectric spectroscopy (DS) with coherent and incoherent neutron scattering. In a wide temperature range broadband DS facilitated a precise determination of the dynamic response related to the segmental relaxation. Close to the glass transition temperature the line shape strongly deviates from the usual Kohlrausch–Williams–Watts functional form of common glassforming systems. Moreover, the characteristic relaxation time observed by incoherent scattering displays an anomalous dependence on momentum transfer indicating the possible existence of heterogeneities in the sample. Based on the structural and dynamical results, a model is proposed, that considers the coexistence of regions with different dynamical properties leading to a distribution of characteristic relaxation times. The model accounts for the experimental observations, assuming for all regions the same functional form for the α-relaxation. It may be univocally determined from the coherent scattering data at the first static structure peak. The distribution of relaxation times found is compatible with the distribution of only one variable, the glass transition temperature.

Fatty Acid Modified Dendrimers in Bulk and Solution: Single-Chain Neutron Scattering from Dendrimer Core and Fatty Acid Shell

Small-angle neutron scattering (SANS) has been applied to extract the single-chain form factors of the fatty acid (FA) and the dendrimer components in bulk and dilute solution of fatty acid modified poly(propyleneimine) dendrimers (Astramol). The fatty acid chains were covalently or noncovalently linked to the end groups of two generations, G3 and G5. Bulk samples were prepared under contrast match conditions of mixtures of dendrimer-h/FAH and dendrimer-h/FAD to obtain the form factor of the fatty acid components. The solutions were prepared with deuterated fatty acid modified dendrimers in decalin solvent using the contrast match technique. Mixtures of decalin-h and decalin-d were used to match either the dendrimer or FA components. The dendrimer core of both G3 and G5 appears collapsed, without the incorporation of a significant amount of solvent. The G3 FA portion has a size closer to that of the bulk than that of a collapsed FA shell. The G5 dendrimer has the opposite trend.

Conformation of Free Linear Polymer Chains in a Polymer Network

Small angle neutron scattering has been used to measure the radius of gyration of deuterated linear polystyrene at dilute concentration contained in a polystyrene network with different crosslink densities. At each crosslink density, four samples with different linear chain concentrations (less than the overlap concentration) were made. The lower crosslink density samples (Nc >180) remained single phase, while higher crosslink density samples showed evidence of phase separation. Zimm plots were made for all samples which were single phase, and the second virial coefficient was obtained as a function of crosslink density. It was found that the second virial coefficient decreased with increasing crosslink density. Single chain form factors were obtained by extrapolating the scattering data to zero concentration of the linear chain for the single phase samples. A modified Debye equation was used to fit the zero concentration extrapolated scattering data over the entire experimental q range to obtain the radi...

Computer Simulations of the Static Scattering from Model Polymer Blends

To understand the unusual composition and wave vector, q, dependent Flory interaction parameters, χ, obtained from small angle neutron scattering (SANS), we have calculated the three partial structure factors for symmetric binary polymer blends with relatively strong interactions between dissimilar monomers using molecular dynamics simulations. In agreement with past work we find that the radii of gyration of the chains are altered on blending. The following new results emerged from our simulations. The single-chain form factors in the blends follow Gaussian statistics at all distances larger than a monomer diameter, confirming the Flory−de Gennes conjecture that correlations in condensed polymer phases are screened over short length scales. The Rg's deduced from these form factors are in agreement with simulation-determined values and illustrate conclusively that the single chain term in the incompressible random-phase approximation (i-RPA) is altered on blending. The three partial structure factors obtained from the simulations, each of which follows an Ornstein−Zernike behavior, have different q dependences and extrapolate to different values in the thermodynamic limit. The different q dependences can be explained qualitatively by a compressible RPA formalism proposed by Tang and Freed. We then show that any form chosen to combine these partial structure factors into a single total scattering function will, in general, not have a q dependence that is describable by the incompressible RPA. This explains the experimentally observed q dependence of the χ parameter derived from the i-RPA. Finally, a thermodynamic analysis on the zero wave-vector limit of the partial structure factors shows that their absolute values are different from each other due to the effects of density fluctuations, as well as the different partial molar volumes of the two species in the blend. These results serve to emphasize the important role played by compressibility on the scattering obtained from simple polymer mixtures with large excess volumes on mixing.

Measurements of single chain form factors by small-angle neutron scattering from polystyrene blends containing high concentrations of labelled molecules

A series of small angle neutron scattering measurements on blends of normal polystyrene (PSH) and labelled (deuterated) polystyrene (PSD) have been made with concentrations of PSD from 5 to 50 mol %. It is shown that the single chain form factor of the polymer in bulk can be obtained from a single concentration measurement for any concentration of labelled molecules, providing the molecular weights of the parent and labelled molecules are the same and the molecular weight distributions are narrow.