Interaction of cylindrical polymer brushes in dilute and semi-dilute solution

Concentration-Driven Self-Assembly of PS-b-PLA Bottlebrush Diblock Copolymers in Solution

Bottlebrush polymers are a class of semiflexible, hierarchical macromolecules with unique potential for shape-, architecture-, and composition-based structure–property design. It is now well-established that in dilute to semidilute solution, bottlebrush homopolymers adopt a wormlike conformation, which decreases in extension (persistence length) as the concentration and molecular overlap increase. By comparison, the solution phase self-assembly of bottlebrush diblock copolymers (BBCP) in a good solvent remains poorly understood, despite critical relevance for solution processing of ordered phases and photonic crystals. In this work, we combine small-angle X-ray scattering, coarse-grained simulation, and polymer synthesis to map the equilibrium phase behavior and conformation of a set of large, nearly symmetric PS-b-PLA bottlebrush diblock copolymers in toluene. Three BBCP are synthesized, with side chains of number-averaged molecular weights of 4500 (PS) and 4200 g/mol (PLA) and total backbone degrees of polymerization of 100, 255, and 400 repeat units. The grafting density is one side chain per backbone repeat unit. With increasing concentration in solution, all three polymers progress through a similar structural transition: from dispersed, wormlike chains with concentration-dependent (decreasing) extension, through the onset of disordered PS/PLA compositional fluctuations, to the formation of a long-range ordered lamellar phase. With increasing concentration in the microphase-separated regimes, the domain spacing increases as individual chains partially re-extend due to block immiscibility. Increases in the backbone degree of polymerization lead to changes in the scattering profiles which are consistent with the increased segregation strength. Coarse-grained simulations using an implicit side-chain model are performed, and concentration-dependent self-assembly behavior is qualitatively matched to experiments. Finally, using the polymer with the largest backbone length, we demonstrate that lamellar phases develop a well-defined photonic band gap in solution, which can be tuned across the visible spectrum by varying polymer concentration.

Rigid-to-Flexible Transition in a Molecular Brush in a Good Solvent at a Semidilute Concentration

The structures of a molecular brush in a good solvent are investigated using synchrotron small-angle X-ray scattering in a wide range of concentrations. The brush under study, PiPOx₂₃₉-g-PnPrOx₁₄, features a relatively long poly(2-isopropenyl-2-oxazoline) (PiPOx) backbone and short poly(2-n-propyl-2-oxazoline) (PnPrOx) side chains. As a solvent, ethanol is used. By model fitting, the overall size and the persistence length as well as the interaction length and interaction strength are determined. At this, the interplay between form and structure factor is taken into account. The conformation of the molecular brush is traced upon increasing the solution concentration, and a rigid-to-flexible transition is found near the overlap concentration. Finally, the results of computer simulations of the molecular brush solutions confirm the experimental results.

Short-Time Dynamics of PDMS-g-PDMS Bottlebrush Polymer Melts Investigated by Quasi-Elastic Neutron Scattering

We have studied the short-time dynamical behavior of polydimethylsiloxane (PDMS) bottlebrush polymers, PDMS-g-PDMS. The samples have similar backbone lengths but different side-chain lengths, resulting in a shape transition. Quasi-elastic neutron scattering was used to observe the dynamical changes inherent to these structural changes. The combination of data from three spectrometers enabled to follow the dynamics over broad frequency and temperature ranges, which included segmental relaxations and more localized motions. The latter, identified as the methyl group rotation, is described by a threefold jump model and shows higher activation energies compared to linear PDMS. The segmental relaxation times, τs, decrease with increasing molecular weight of the side chains but increase with momentum transfer, Q, following a power law, which suggests a non-Gaussian behavior for bottlebrush polymers.

Addressing the challenges of modeling the scattering from bottlebrush polymers in solution

Small-angle scattering measurements of complex macromolecules in solution are used to establish relationships between chemical structure and conformational properties. Interpretation of the scattering data requires an inverse approach where a model is chosen and the simulated scattering intensity from that model is iterated to match the experimental scattering intensity. This raises challenges in the case where the model is an imperfect approximation of the underlying structure, or where there are significant correlations between model parameters. We examine three bottlebrush polymers (consisting of polynorbornene backbone and polystyrene side chains) in a good solvent using a model commonly applied to this class of polymers: the flexible cylinder model. Applying a series of constrained Monte-Carlo Markov Chain analyses demonstrates the severity of the correlations between key parameters and the presence of multiple close minima in the goodness of fit space. We demonstrate that a shape-agnostic model can fit the scattering with significantly reduced parameter correlations and less potential for complex, multimodal parameter spaces. We provide recommendations to improve the analysis of complex macromolecules in solution, highlighting the value of Bayesian methods. This approach provides richer information for understanding parameter sensitivity compared to methods which produce a single, best fit.

Structure, rheology, and microrheology of wormlike micelles made of PB-PEO diblock copolymers

A diblock copolymer made of poly(1,4-butadiene)-block-polyethylene oxide, with a degree of polymerization of the polybutadiene and polyethylene oxide blocks of 37 and 57, respectively, self-assembles in water as worm-like micelles determined by small angle neutron scattering with an average diameter of ∼12.7 nm, a core radius of ∼2.7 nm, a shell radius of ∼3 nm, and an estimated persistence length of >225 nm. Worm-like micelles of almost the same diblock copolymer, but with a smaller polyethylene oxide block (degree of polymerization 45) were also measured. The worm-like micelles were also observed with negative staining using low energy electron microscopy. The boundary between dilute and semidilute regimes was estimated to be ∼0.8 wt%. The viscoelastic spectra at low and intermediate frequencies do not follow the Maxwell model. These micelles do not present the same rheological behavior of worm-like micelle solutions of conventional surfactants. The slow dynamics of the self-assembly explains this uncommon behavior for the system. Any micellar rearrangement is impeded due to the extremely high hydrophobicity of the polybutadiene block; stress mainly relaxes by the reptation mechanism. Using diffusive wave spectroscopy, we measured the mean square displacement of particles in the micellar solution. From the mean square displacement, we obtained G'(ω) and G''(ω) at high frequencies. |G*| exhibits a power law behavior showing the stress relaxation changes as frequency increases, first dominated by the Rouse-Zimm modes and then by the bending modes of the Kuhn segments. This allowed us to estimate the worm-like micelle persistence lengths that depend on the copolymer concentration.

Electrostatic stiffening and induced persistence length for coassembled molecular bottlebrushes

A self-consistent field analysis for tunable contributions to the persistence length of isolated semiflexible polymer chains including electrostatically driven coassembled deoxyribonucleic acid (DNA) bottlebrushes is presented. When a chain is charged, i.e., for polyelectrolytes, there is, in addition to an intrinsic rigidity, an electrostatic stiffening effect, because the electric double layer resists bending. For molecular bottlebrushes, there is an induced contribution due to the grafts. We explore cases beyond the classical phantom main-chain approximation and elaborate molecularly more realistic models where the backbone has a finite volume, which is necessary for treating coassembled bottlebrushes. We find that the way in which the linear charge density or the grafting density is regulated is important. Typically, the stiffening effect is reduced when there is freedom for these quantities to adapt to the curvature stresses. Electrostatically driven coassembled bottlebrushes, however, are relatively stiff because the chains have a low tendency to escape from the compressed regions and the electrostatic binding force is largest in the convex part. For coassembled bottlebrushes, the induced persistence length is a nonmonotonic function of the polymer concentration: For low polymer concentrations, the stiffening grows quadratically with coverage; for semidilute polymer concentrations, the brush chains retract and regain their Gaussian size. When doing so, they lose their induced persistence length contribution. Our results correlate well with observed physical characteristics of electrostatically driven coassembled DNA-bioengineered protein-polymer bottlebrushes.

Rheological and structural properties of complex arabinoxylans from Plantago ovata seed mucilage under non-gelled conditions

Two gel-forming arabinoxylan (AX) fractions with very similar linkage composition and molecular weight distributions have been isolated from Plantago ovata seed mucilage. Both isolated fractions have distinct gel properties attributed to differences in intermolecular hydrogen bonding. This study probes the effect of hydrogen bonding on molecular interactions of P. ovata AX fractions under non-gelled conditions achieved using a mild hydrogen bonding inhibitor, 0.2 M KOH. Chain conformation, relaxation dynamics and interactions between AX molecules are investigated using a combination of rheological techniques and small angle X-ray and neutron scattering. The scattering data confirm similar molecular dimensions and chain rigidity for both fractions, while showing distinct patterns of molecular interactions which result in the formation of a self-associated polymer network. The relationship between molecular associations, chain relaxation time and entanglement behaviour of P. ovata AX solutions are corroborated though the analysis of flow profiles and small amplitude oscillatory shear rheology.

pyPRISM: A Computational Tool for Liquid-State Theory Calculations of Macromolecular Materials

The Polymer Reference Interaction Site Model (PRISM) theory describes the equilibrium spatial-correlations of liquid-like polymer systems including melts, blends, solutions, block copolymers, ionomers, liquid crystalline polymers, and nanocomposites. Using PRISM theory, one can calculate thermodynamic (second virial coefficients, Flory-Huggins χ interaction parameters, potentials of mean force) and structural (pair correlation functions, structure factors) data for these macromolecular materials. Here, we present a Python-based, open-source framework, pyPRISM, for conducting PRISM theory calculations. This framework aims to simplify PRISM-based studies by providing a user-friendly scripting interface for setting up and numerically solving the PRISM equations. pyPRISM also provides data structures, functions, and classes that streamline PRISM calculations, allowing pyPRISM to be extended for use in other tasks, such as the coarse-graining of atomistic simulation force-fields or the modeling of experimental scattering data. The goal of this framework is to reduce the barrier to correctly and appropriately using PRISM theory and to provide a platform for rapid calculations of the structure and thermodynamics of polymeric fluids and nanocomposites.

Loss of bottlebrush stiffness due to free polymers

A recently introduced DNA-bottlebrush system, which is formed by the co-assembly of DNA with a genetically engineered cationic polymer-like protein, is subjected to osmotic stress conditions. We measured the inter-DNA distances by X-ray scattering. Our co-assembled DNA-bottlebrush system is one of the few bottlebrushes known to date that shows liquid crystalline behaviour. The alignment of the DNA bottlebrushes was expected to increase with imposed pressure, but interestingly this did not always happen. Molecularly detailed self-consistent field calculations targeted to complement the experiments, focused on the role of molecular crowding on the induced persistence length lp due to the side chains and the cross-sectional width D of the molecular bottlebrushes. Both the thickness as well as the backbone persistence length drop with increasing protein-polymer bulk concentrations and dramatic effects are found above the overlap threshold. The flexibilisation is more significant and therefore the bottlebrush aspect ratio, lp/D, decreases with protein-polymer concentration. This loss in aspect ratio is yet another argument why molecular bottlebrushes rarely order in anisotropic phases and may explain why bottlebrushes are excellent lubricants.

Structural Evolution of Polylactide Molecular Bottlebrushes: Kinetics Study by Size Exclusion Chromatography, Small Angle Neutron Scattering, and Simulations

Structural evolution from poly(lactide) (PLA) macromonomer to resultant PLA molecular bottlebrush during ring opening metathesis polymerization (ROMP) was investigated for the first time by combining size exclusion chromatography (SEC), small-angle neutron scattering (SANS), and coarse-grained molecular dynamics (CG-MD) simulations. Multiple aliquots were collected at various reaction times during ROMP and subsequently analyzed by SEC and SANS. These complementary techniques enable the understanding of systematic changes in conversion, molecular weight and dispersity as well as structural details of PLA molecular bottlebrushes. CG-MD simulation not only predicts the experimental observations, but it also provides further insight into the analysis and interpretation of data obtained in SEC and SANS experiments. We find that PLA molecular bottlebrushes undergo three conformational transitions with increasing conversion (i.e., increasing the backbone length): (1) from an elongated to a globular shape due to longer side chain at low conversion, (2) from a globular to an elongated shape at intermediate conversion caused by excluded volume of PLA side chain, and (3) the saturation of contour length at high conversion due to chain transfer reactions.

Patchy worm-like micelles: solution structure studied by small-angle neutron scattering

Triblock terpolymers exhibit a rich self-organization behavior including the formation of fascinating cylindrical core-shell structures with a phase separated corona. After crystallization-induced self-assembly of polystyrene-block-polyethylene-block-poly(methyl methacrylate) triblock terpolymers (abbreviated as SEMs = Styrene-Ethylene-Methacrylates) from solution, worm-like core-shell micelles with a patchy corona of polystyrene and poly(methyl methacrylate) were observed by transmission electron microscopy. However, the solution structure is still a matter of debate. Here, we present a method to distinguish in situ between a Janus-type (two faced) and a patchy (multiple compartments) configuration of the corona. To discriminate between both models the scattering intensity must be determined mainly by one corona compartment. Contrast variation in small-angle neutron scattering enables us to focus on one compartment of the worm-like micelles. The results validate the existence of the patchy structure also in solution.

Persistence Length of Dendritic Molecular Brushes

On the basis of mean-field theory, we predict that molecular brushes with dendritic side chains ("dendronized polymers") may exhibit the behavior of semirigid polymers capable of lyotropic odering. The apparent persistence length of these molecular brushes is governed by the interactions between dendritic grafts and may significantly exceed the characteristic brush thickness. Compared to bottle-brushes with linear grafts, manifestation of the induced rigidity in molecular brushes with dendritic branches is expected at smaller degrees of polymerization of the grafts. Under good solvent conditions, the induced rigidity depends solely on the number of side chain monomers per unit length of backbone and the second virial coeffcient of monomer-monomer interactions, irrespective of graft topology.

The Structure of Fluids with Impurities

The influence of dilute impurities on the structure of a fluid solvent is investigated theoretically. General arguments, which do not rely on particular models, are used to derive an extension of the Ornstein–Zernike form for the solvent structure factor at small scattering vectors. It is shown that dilute impurities can influence the solvent structure only if they are composed of ions with significantly different sizes. Non-ionic impurities or ions of similar size are shown to not alter the solvent structure qualitatively. This picture is compatible with available experimental data. The derived form of the solvent structure factor is expected to be useful to infer information on the impurity-solvent interactions form measured scattering intensities.

A fluorescence correlation spectroscopy study of macromolecular tracer diffusion in polymer solutions

We discuss the manner in which the dynamics of tracer polystyrene chains varies with the concentration of matrix polystyrene chains dissolved in toluene. Using fluorescence correlation spectroscopy and theory, it is shown that the cooperative diffusion coefficient of the matrix polystyrene chains can be measured by fluorescence correlation spectroscopy in the semidilute entangled concentration regime. In addition the self-diffusion coefficient of the tracer polystyrene chains can be detected for arbitrary concentrations. The measured cooperative diffusion coefficient is independent of the molecular weight of the tracer polystyrene chains because it is a characteristic feature of the transient entanglement network.