PRISM theory of the structure, thermodynamics, and phase transitions of polymer liquids and alloys

SEB: a computational tool for symbolic derivation of the small-angle scattering from complex composite structures

Analysis of small-angle scattering (SAS) data requires intensive modeling to infer and characterize the structures present in a sample. This iterative improvement of models is a time-consuming process. Presented here is Scattering Equation Builder (SEB), a C++ library that derives exact analytic expressions for the form factors of complex composite structures. The user writes a small program that specifies how the sub-units should be linked to form a composite structure and calls SEB to obtain an expression for the form factor. SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles, solid spheres, spherical shells and cylinders, and many different options for how these can be linked together. The formalism behind SEB is presented and simple case studies are given, such as block copolymers with different types of linkage, as well as more complex examples, such as a random walk model of 100 linked sub-units, dendrimers, polymers and rods attached to the surfaces of geometric objects, and finally the scattering from a linear chain of five stars, where each star is built up of four diblock copolymers. These examples illustrate how SEB can be used to develop complex models and hence reduce the cost of analyzing SAS data.

Correlations in Hard- and Soft-Core Generic Polymer Models

Generic polymer models capturing the chain connectivity and the non-bonded excluded-volume interactions between polymer segments can be classified into hard- and soft-core models depending on their non-bonded pair potential. Here we compared the correlation effects on the structural and thermodynamic properties of the hard- and soft-core models given by the polymer reference interaction site model (PRISM) theory, and found different behaviors of the soft-core models at large invariant degree of polymerization (IDP) depending on how IDP is varied. We also proposed an efficient numerical approach, which enables us to accurately solve the PRISM theory for chain lengths as large as 10⁶.

Surfactant induced gelation of TEMPO-oxidized cellulose nanofibril dispersions probed using small angle neutron scattering

In this work, we studied TEMPO-oxidized cellulose nanofibril (OCNF) suspensions in the presence of diverse surfactants. Using a combination of small angle neutron scattering (SANS) and rheology, we compared the physical properties of the suspensions with their structural behavior. Four surfactants were studied, all with the same hydrophobic tail length but different headgroups: hexaethylene glycol mono-n-dodecyl ether (C₁₂EO₆, nonionic), sodium dodecyl sulfate (SDS, anionic), cocamidopropyl betaine (CapB, zwitterionic), and dodecyltrimethylammonium bromide (DTAB, cationic). Contrast variation SANS studies using deuterated version of C₁₂EO₆ or SDS, or by varying the D₂O/H₂O ratio of the suspensions (with CapB), allowed focusing only on the structural properties of OCNFs or surfactant micelles. We showed that, in the concentration range studied, for C₁₂EO₆, although the nanofibrils are concentrated thanks to an excluded volume effect observed in SANS, the rheological properties of the suspensions are not affected. Addition of SDS or CapB induces gelation for surfactant concentrations superior to the critical micellar concentration (CMC). SANS results show that attractive interactions between OCNFs arise in the presence of these anionic or zwitterionic surfactants, hinting at depletion attraction as the main mechanism of gelation. Finally, addition of small amounts of DTAB (below the CMC) allows formation of a tough gel by adsorbing onto the OCNF surface.

Polymer-mediated self-assembly, dispersion, and phase separation of Janus nanorods

The challenge of stabilizing polymer nanocomposites lies in the fact that nanoparticles tend to phase separate from the polymer melt due to an entropic 'depletion attraction' between nanoparticles. Additionally, composites of polymer and nanorods show a decrease in miscibility with increasing nanorod aspect ratio [U. K. Sankar and M. Tripathy, Macromolecules, 2015, 48, 432-442; U. Erigi, U. Dhumal and M. Tripathy, J. Chem. Phys., 2021, 154, 124903]. In this work, we have studied the structure and phase behaviour of polymer-Janus nanorod mixtures using Polymer Reference Interaction Site Model (PRISM) theory and molecular dynamics simulations. The composite system of polymer and Janus nanorods of two different thicknesses, at various Janus nanorod densities, and for different interaction strengths between polymer and attractive sites of Janus nanorods (ε_pa), is investigated for their miscibility and self-assembly. At low Janus nanorod density, PRISM theory predicts transitions from the entropic depletion-driven contact aggregation of Janus nanorods to a well-dispersed phase to the bridging-driven phase separation of Janus nanorods, with increasing ε_pa. This behaviour is similar to earlier predictions for homogeneous nanorods. However, molecular dynamics simulations do not confirm the bridging-driven phase separation at high ε_pa predicted by PRISM theory. We find that both PRISM theory and molecular dynamics simulations are in agreement in the intermediate and high Janus nanorod density regimes. PRISM theory predicts, and simulations confirm, that at high Janus nanorod densities, the system undergoes a transition from depletion-driven macrophase separation to dispersion to chemical anisotropy-driven self-assembly with increasing ε_pa. The self-assembly at high ε_pa is mediated by the polymer. At intermediate Janus nanorod densities, the usual transition from an entropic depletion-driven macrophase separation to dispersion is predicted at low ε_pa. At high ε_pa, both PRISM theory and molecular dynamics simulations show transition to a state that is simultaneously macrophase separated and microphase separated (self-assembled).

Small angle scattering of diblock copolymers profiled by machine learning

We outline a machine learning strategy for quantitively determining the conformation of AB-type diblock copolymers with excluded volume effects using small angle scattering. Complemented by computer simulations, a correlation matrix connecting conformations of different copolymers according to their scattering features is established on the mathematical framework of a Gaussian process, a multivariate extension of the familiar univariate Gaussian distribution. We show that the relevant conformational characteristics of copolymers can be probabilistically inferred from their coherent scattering cross sections without any restriction imposed by model assumptions. This work not only facilitates the quantitative structural analysis of copolymer solutions but also provides the reliable benchmarking for the related theoretical development of scattering functions.

Anomalous Dynamics in Macromolecular Liquids

Macromolecular liquids display short-time anomalous behaviors in disagreement with conventional single-molecule mean-field theories. In this study, we analyze the behavior of the simplest but most realistic macromolecular system that displays anomalous dynamics, i.e., a melt of short homopolymer chains, starting from molecular dynamics simulation trajectories. Our study sheds some light on the microscopic molecular mechanisms responsible for the observed anomalous behavior. The relevance of the correlation hole, a unique property of polymer liquids, in relation to the observed subdiffusive dynamics, naturally emerges from the analysis of the van Hove distribution functions and other properties.

Long Wavelength Thermal Density Fluctuations in Molecular and Polymer Glass-Forming Liquids: Experimental and Theoretical Analysis under Isobaric Conditions

We establish via an in-depth analysis of experimental data that the dimensionless compressibility (proportional to the dimensionless amplitude of long wavelength thermal density fluctuations) of one-component normal and supercooled liquids of chemically complex nonpolar and weakly polar molecules and polymers follows extremely well a surprisingly simple and general temperature dependence over an exceptionally wide range of pressures and temperatures. A theoretical basis for this behavior is shown to exist in the venerable van der Waals model and its more modern interpretations. Although associated hydrogen-bonding (and to a lesser degree strongly polar) liquids display modestly more complex behavior, rather simple temperature and pressure dependences are also discovered. A new approach to collapse the temperature- and pressure-dependent dimensionless compressibility data onto a master curve is formulated that differs from the empirical thermodynamic scaling approach. As a practical matter, we also find that the dimensionless compressibility scales well as an inverse power law with temperature with an exponent that is system dependent and decreases with pressure. At very high pressures and low temperatures, the thermal liquid behavior appears to approach (but not reach) a repulsion-dominated random close packing limit. All these findings are relevant to our recent theoretical work on the problem of activated relaxation and vitrification of supercooled molecular and polymeric liquids.

Effect of Poly(vinyl butyral) Comonomer Sequence on Adhesion to Amorphous Silica: A Coarse-Grained Molecular Dynamics Study

Modulating a comonomer sequence, in addition to the overall chemical composition, is the key to unlocking the true potential of many existing commercial copolymers. We employ coarse-grained molecular dynamics (MD) simulations to study the behavior of random-blocky poly(vinyl butyral-co-vinyl alcohol) (PVB) melts in contact with an amorphous silica surface, representing the interface found in laminated safety glass. Our two-pronged coarse-graining approach utilizes both macroscopic thermophysical data and all-atom MD simulation data. Polymer-polymer nonbonded interactions are described by the fused-sphere SAFT-γ Mie equation of state, while bonded interactions are derived using Boltzmann inversion to match the bond and angle distributions from all-atom PVB chains. Spatially dependent polymer-surface interactions are mapped from a hydroxylated all-atom amorphous silica slab model and all-atom monomers to an external potential acting on the coarse-grained sites. We discovered an unexpected complex relationship between the blockiness parameter and the adhesion energy. The adhesion strength between PVB copolymers with intermediate VA content and silica was found to be maximal for random-blocky copolymers with a moderately high degree of blockiness rather than for diblock copolymers. We attribute this to two main factors: (1) changes in morphology, which dramatically alter the number of VA beads interacting with the surface and (2) a non-negligible contribution of vinyl butyral (VB) monomers to adhesion energy because of their preference to adsorb to zones with low hydroxyl density on the silica surface.

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Specific effects of antitumor active norspermidine on the structure and function of DNA

We compared the effects of trivalent polyamines, spermidine (SPD) and norspermidine (NSPD), a chemical homologue of SPD, on the structure of DNA and gene expression. The chemical structures of SPD and NSPD are different only with the number of methylene groups between amine groups, [N-3-N-4-N] and [N-3-N-3-N], respectively. SPD plays vital roles in cell function and survival, including in mammals. On the other hand, NSPD has antitumor activity and is found in some species of plants, bacteria and algae, but not in humans. We found that both polyamines exhibit biphasic effect; enhancement and inhibition on in vitro gene expression, where SPD shows definitely higher potency in enhancement but NSPD causes stronger inhibition. Based on the results of AFM (atomic force microscopy) observations together with single DNA measurements with fluorescence microscopy, it becomes clear that SPD tends to align DNA orientation, whereas NSPD induces shrinkage with a greater potency. The measurement of binding equilibrium by NMR indicates that NSPD shows 4-5 times higher affinity to DNA than SPD. Our theoretical study with Monte Carlo simulation provides the insights into the underlying mechanism of the specific effect of NSPD on DNA.

TEMPO-oxidised cellulose nanofibrils; probing the mechanisms of gelation via small angle X-ray scattering

The structure of dispersions of TEMPO-oxidised cellulose nanofibrils (OCNF), at various concentrations, in water and in NaCl aqueous solutions, was probed using small angle X-ray scattering (SAXS). OCNF are modelled as rod-like particles with an elliptical cross-section of 10 nm and a length greater than 100 nm. As OCNF concentration increases above 1.5 wt%, repulsive interactions between fibrils are evidenced, modelled by the interaction parameter νRPA > 0. This corresponds to gel-like behaviour, where G' > G'' and the storage modulus, G', shows weak frequency dependence. Hydrogels can also be formed at OCNF concentration of 1 wt% in 0.1 M NaCl(aq). SAXS patterns shows an increase of the intensity at low angle that is modelled by attractive interactions (νRPA < 0) between OCNF, arising from the screening of the surface charge of the fibrils. Results are supported by ζ potential and cryo-TEM measurements.

Localization switching of a large object in a crowded cavity: A rigid/soft object prefers surface/inner positioning

For living cells in the real world, a large organelle is commonly positioned in the inner region away from membranes, such as the nucleus of eukaryotic cells, the nucleolus of nuclei, mitochondria, chloroplast, Golgi body, etc. It contradicts the expectation by the current depletion-force theory in that the larger particle should be excluded from the inner cell space onto cell boundaries in a crowding media. Here we simply model a sizable organelle as a soft-boundary large particle allowing crowders, which are smaller hard spheres in the model, to intrude across its boundary. The results of Monte Carlo simulation indicate that the preferential location of the larger particle switches from the periphery into the inner region of the cavity by increasing its softness. An integral equation theory is further developed to account for the structural features of the model, and the theoretical predictions are found consistent with our simulation results.

Effective interaction between nanoparticles mediated by a symmetric polymer blend

We analytically study the polymer-mediated (PM) interactions between spherical particles immersed in a symmetric polymer blend. By making use of standard methods of the liquid state theory we have found out a nonconventional mechanism of the PM interactions caused by nonuniformities in the local composition of the polymer blend induced by the particles. The relative significance of the contributions to the PM interaction potential due to the finite compressibility of the polymer blend and its compositional nonuniformity is found to drastically depend on the polymer-to-particle size ratio. In the protein limit of relatively small particles, the mechanism due to the compositional nonuniformity, specific to polymer blends, is shown to play a dominant role in the PM interactions.

Depletion interaction between colloids mediated by an athermal polymer blend

We calculate the immersion energy of a colloid and the potential of the depletion interaction (DI) acting between colloids immersed in an athermal polymer blend. The developed theory has no limitations with respect to the polymer-to-colloid size ratios and polymer densities, covering, in particular, dense polymer blends. We demonstrate that in addition to the standard compressibility-induced mechanism of the DI there exists the mechanism relying on the correlations between compositional fluctuations specific to polymer blends. We quantitatively investigate this "compositional" mechanism of the DI and demonstrate that it causes significant contributions to the effective force acting between colloids. Further we show that relative significance of the contributions to the colloid immersion energy and the depletion potential caused by the above compositional mechanism strongly depends on the mass fractions of the polymer species and their size ratio. We find out that these contributions strongly affect the range of the DI, thus causing a significant increase in the absolute value of the second virial coefficient of the effective potential acting between colloids.

Modeling intra- and intermolecular correlations for linear and branched polymers using a modified test-chain self-consistent field theory

A modified test-chain self-consistent field theory (SCFT) is presented to study the intra- and intermolecular correlations of linear and branched polymers in various solutions and melts. The key to the test-chain SCFT is to break the the translational symmetry by fixing a monomer at the origin of a coordinate. This theory successfully describes the crossover from self-avoiding walk at short distances to screened random walk at long distances in a semidilute solution or melt. The calculations indicated that branching enhances the swelling of polymers in melts and influences stretching at short distances. The test-chain SCFT calculations show good agreement with experiments and classic polymer theories. We highlight that the theory presented here provides a solution to interpret the polymer conformation and behavior under various conditions within the framework of one theory.

Small-Angle X-ray Scattering Demonstrates Similar Nanostructure in Cortical Bone from Young Adult Animals of Different Species

Despite the vast amount of studies focusing on bone nanostructure that have been performed for several decades, doubts regarding the detailed structure of the constituting hydroxyapatite crystal still exist. Different experimental techniques report somewhat different sizes and locations, possibly due to different requirements for the sample preparation. In this study, small- and wide-angle X-ray scattering is used to investigate the nanostructure of femur samples from young adult ovine, bovine, porcine, and murine cortical bone, including three different orthogonal directions relative to the long axis of the bone. The radially averaged scattering from all samples reveals a remarkable similarity in the entire q range, which indicates that the nanostructure is essentially the same in all species. Small differences in the data from different directions confirm that the crystals are elongated in the [001] direction and that this direction is parallel to the long axis of the bone. A model consisting of thin plates is successfully employed to describe the scattering and extract the plate thicknesses, which are found to be in the range of 20-40 Å for most samples but 40-60 Å for the cow samples. It is demonstrated that the mineral plates have a large degree of polydispersity in plate thickness. Additionally, and equally importantly, the scattering data and the model are critically evaluated in terms of model uncertainties and overall information content.

Theory and simulation studies of effective interactions, phase behavior and morphology in polymer nanocomposites

Polymer nanocomposites are a class of materials that consist of a polymer matrix filled with inorganic/organic nanoscale additives that enhance the inherent macroscopic (mechanical, optical and electronic) properties of the polymer matrix. Over the past few decades such materials have received tremendous attention from experimentalists, theoreticians, and computational scientists. These studies have revealed that the macroscopic properties of polymer nanocomposites depend strongly on the (microscopic) morphology of the constituent nanoscale additives in the polymer matrix. As a consequence, intense research efforts have been directed to understand the relationships between interactions, morphology, and the phase behavior of polymer nanocomposites. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level features of the polymer and nanoparticle additives to the resulting morphology within the composite. In this article we review recent theory and simulation studies, presenting briefly the methodological developments underlying PRISM theories, density functional theory, self-consistent field theory approaches, and atomistic and coarse-grained molecular simulations. We first discuss the studies on polymer nanocomposites with bare or un-functionalized nanoparticles as additives, followed by a review of recent work on composites containing polymer grafted or functionalized nanoparticles as additives. We conclude each section with a brief outlook on some potential future directions.

Conformational effect on small angle neutron scattering behavior of interacting polyelectrolyte solutions: a perspective of integral equation theory

We present small angle neutron scattering (SANS) measurements of deuterium oxide (D(2)O) solutions of linear and star sodium poly(styrene sulfonate) (NaPSS) as a function of polyelectrolyte concentration. Emphasis is on understanding the dependence of their SANS coherent scattering cross section I(Q) on the molecular architecture of single polyelectrolyte. The key finding is that for a given concentration, star polyelectrolytes exhibit more pronounced characteristic peaks in I(Q), and the position of the first peak occurs at a smaller Q compared to their linear counterparts. Based on a model of integral equation theory, we first compare the SANS experimental I(Q) of salt-free polyelectrolyte solutions with that predicted theoretically. Having seen their satisfactory qualitative agreement, the dependence of counterion association behavior on polyelectrolyte geometry and concentration is further explored. Our predictions reveal that the ionic environment of polyelectrolyte exhibits a strong dependence on polyelectrolyte geometry at lower polyelectrolyte concentration. However, when both linear and star polyelectrolytes exceed their overlap concentrations, the spatial distribution of counterion is found to be essentially insensitive to polyelectrolyte geometry due to the steric effect.

Depletion forces acting on nanoparticles in confined polymer systems: potential theory

By making use of the developed potential theory, we investigate the polymer-mediated depletion interactions between nanoparticles and hard planar surfaces in the following settings: (i) interaction between two nanoparticles; (ii) interactions between nanoparticle and hard planar surface; (iii) interaction between two nanoparticles in the presence of hard planar surface; and (iv) interaction between nanoparticle and walls of the plane-parallel slab. For each of the listed systems, we have calculated the polymer end density, excess grand potential, and the potential of the depletion forces. On the basis of the obtained results, we have analyzed the effect of the geometric constraints imposed by hard walls on the polymer density structure and the depletion interaction between nanoparticles.

Rheo-SANS studies on shear-thickening/thinning in aqueous rodlike micellar solutions

Shear-induced thickening/thinning phenomena of aqueous rodlike micellar solutions of cetyltrimethylammonium bromide (CTAB) and sodium p-toluene sulfonate (NapTS) were investigated by means of simultaneous measurements of rheology and small-angle neutron scattering (SANS), the so-called Rheo-SANS. The aqueous CTAB/NapTS solutions were classified into five different categories dependent on their flow behavior and micellar structure. By increasing salt concentration and/or shear rates, the micelles underwent morphological transition from (i) spherical or short rodlike micelles to (ii) long rodlike micelles without entanglements, followed by (iii) those with entanglements. These transitions were recognized as changes in flow behavior from Newtonian to shear-thickening and shear-thinning flow, respectively. In the latter two cases, anisotropic SANS patterns appeared around these critical shear rates. The physical meaning of the anisotropic SANS patterns accompanied by shear-thickening flow behavior is discussed in conjunction with other shear-thickening systems.