Resonant soft X-ray scattering in polymer science

Resonant soft X-ray scattering (RSoXS) is an emerging, powerful technique to probe the nano-to-mesoscale structure of polymers and other molecules. It joins together small-angle X-ray scattering (a statistical nanoprobe) with X-ray spectroscopy that brings with it unique chemical and bond-orientation sensitivity. Through over a decade of discovery and development, RSoXS is moving from a niche technique applied to organic electronic thin films to a mature tool applicable to a plethora of polymeric and molecular systems, encompassing new modalities, analyses, and simulation methods. This development promises to deliver increasingly quantitative answers to challenging questions in polymer science as well as expand its usefulness to complementary fields. This review presents a full synopsis of the technique, including background on the theoretical underpinnings, measurement best practices, and examples of recent RSoXS applications and discoveries provided here to accelerate the transition to a broader range of soft matter and polymeric fields.     

Amorphous copolyesters based on bibenzoic acids and neopentyl glycol

High T_g amorphous copolyester thermoplastics were synthesized by incorporating 4,4′‐bibenzoate (4,4′BB) and 3,4′‐bibenzoate moieties into the polyester backbone via melt polycondensation. The high levels of crystallinity typically associated with 4,4′BB containing polyesters were suppressed through copolymerization of ethylene glycol, 1,4‐cyclohexane dimethanol, and neopentyl glycol (NPG) diols. NPG was shown to be highly effective in suppressing crystallization and was used to produce amorphous compositions with T_g’s as high as 129 °C. Diol ratios were determined by ¹H NMR spectroscopy and molecular weights were assessed with inherent viscosity (η_inh). Thermogravimetric analysis showed single‐step weight losses in the range of 395 – 419 °C. Differential scanning calorimetry was used to determine melting points and glass transition temperatures over a wide range of copolyester compositions and identified amorphous compositions. Dynamic mechanical analysis confirmed T_g’s and was used to study β‐relaxations below the T_g. Rheological analysis revealed the effect of NPG structures on shear thinning and thermal stability. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 579–587     

Numerical study of the wrinkling of a stretched thin sheet

A thin sheet clamped at opposite ends and stretched develops wrinkles parallel to the direction of the applied tensile strain due to the hindered Poisson lateral contraction at the clamps. To study this phenomenon, a variational model recently proposed by Puntel, Deseri and Fried is adopted. The relevant energy functional includes bending and membranal contributions and is minimized subject to a constraint on the area of the mid-surface of the sheet. A fourth order partial-differential equation is henceforth obtained and numerically implemented using B-splines. Predictions are obtained concerning the number of wrinkles, critical applied stretches, and scaling relationships for wrinkle amplitude and wavelength. Both a linearized version of the boundary-value problem based on the small-slope approximation and a fully nonlinear one are considered: their results are found to be in good agreement for the whole range of applied stretches taken into account. Comparisons with previous analytical results by Puntel, Deseri and Fried, who used different boundary conditions and an Ansatz on the deflection function are also provided. The numerical results substantially confirm the validity of the analytical predictions. The present work provides then an alternative numerical method for the study of wrinkling in thin sheets and supports the use of analytical and semi-analytical solutions as viable options for specific geometries. Though further investigation, particularly experimental, is still needed, extensive comparisons of the results with other studies available in the literature provide confirmation for the scaling laws and signal that predicted values of the critical stretches may only be accurate for higher length-to-width aspect ratios.     

Photocontrolled Synthesis of n‐Type Conjugated Polymers

Current approaches to synthesize π‐conjugated polymers (CPs) are dominated by thermally driven, transition‐metal‐mediated reactions. Herein we show that electron‐deficient Grignard monomers readily polymerize under visible‐light irradiation at room temperature in the absence of a catalyst. The product distribution can be tuned by the wavelength of irradiation based on the absorption of the polymer. Conversion studies are consistent with an uncontrolled chain‐growth process; correspondingly, chain extension produces all‐conjugated n‐type block copolymers. Preliminary results demonstrate that the polymerization can be expanded to donor–acceptor alternating copolymers. We anticipate that this method can serve as a platform to access new architectures of n‐type CPs without the need for transition‐metal catalysis.     

Sharp-Interface Nematic–Isotropic Phase Transitions without Flow

We derive a supplemental evolution equation for an interface between the nematic and isotropic phases of a liquid crystal when flow is neglected. Our approach is based on the notion of configurational force. As an application, we study the behavior of a spherical isotropic drop surrounded by a radially oriented nematic phase: our supplemental evolution equation then reduces to a simple ordinary differential equation admitting a closed-form solution. In addition to describing many features of isotropic-to-nematic phase transitions, this simplified model yields insight concerning the occurrence and stability of isotropic cores for hedgehog defects in liquid crystals.     

Geometrically-based Consequences of Internal Constraints

When a body is subject to simple internal constraints, the deformation gradient must belong to a certain manifold. This is in contrast to the situation in the unconstrained case, where the deformation gradient is an element of the open subset of second-order tensors with positive determinant. Commonly, following Truesdell and Noll [1], modern treatments of constrained theories start with an a priori additive decomposition of the stress into reactive and active components with the reactive component assumed to be powerless in all motions that satisfy the constraints and the active component given by a constitutive equation. Here, we obtain this same decomposition automatically by making a purely geometrical and general direct sum decomposition of the space of all second-order tensors in terms of the normal and tangent spaces of the constraint manifold. As an example, our approach is used to recover the familiar theory of constrained hyperelasticity.     

A computer simulation of the unwinding of a DNA-like helix

This paper investigates the use of a high-speed computer to simulate the unwinding of DNA. A Langevin equation of motion for the well-known bead-spring statistical macromolecule is written in difference form. An appropriate set of boundary conditions is developed to simulate a helical molecule and the resulting set of rules for the motion of the chain elements is used to produce the strand unwinding. The unwinding appears to proceed via initial end-unwinding followed by progressive unwinding inward. The latter process appears to occur by diffusion of twist outward from the central portion of the macromolecule. A computer simulation, using the Langevin equation, of linear tensile relaxation is compared with the appropriate analytical solution via the Rouse treatment of polymer dynamics, good agreement being obtained. The helical results are compared both with tensile relaxation and with Crothers' (1964) analytical treatment of the unwinding problem, which is analogous to the well-known temperature diffusion problem. The tensile results and Crothers' results are identical in form, and agree quantitatively remarkably closely with the computer-simulated helical unwinding, although the helical unwinding is somewhat slower.Financial support for E.M.S. from the National Institutes of Health is acknowledged. We are also indebted to the National Institutes of Health for grant GM-11916, which supported the cost of the calculations.