Scattering theory and properties of block copolymers with various architectures in the homogeneous bulk state

Polyurea-Graphene Nanocomposites-The Influence of Hard-Segment Content and Nanoparticle Loading on Mechanical Properties

Polyurethane and polyurea-based adhesives are widely used in various applications, from automotive to electronics and medical applications. The adhesive performance depends strongly on its composition, and developing the formulation-structure-property relationship is crucial to making better products. Here, we investigate the dependence of the linear viscoelastic properties of polyurea nanocomposites, with an IPDI-based polyurea (PUa) matrix and exfoliated graphene nanoplatelet (xGnP) fillers, on the hard-segment weight fraction (HSWF) and the xGnP loading. We characterize the material using scanning electron microscopy (SEM) and dynamic mechanical analysis (DMA). It is found that changing the HSWF leads to a significant variation in the stiffness of the material, from about 10 MPa for 20% HSWF to about 100 MPa for 30% HSWF and about 250 MPa for the 40% HSWF polymer (as measured by the tensile storage modulus at room temperature). The effect of the xGNP loading was significantly more limited and was generally within experimental error, except for the 20% HSWF material, where the xGNP addition led to about an 80% increase in stiffness. To correctly interpret the DMA results, we developed a new physics-based rheological model for the description of the storage and loss moduli. The model is based on the fractional calculus approach and successfully describes the material rheology in a broad range of temperatures (-70 °C-+70 °C) and frequencies (0.1-100 s-1), using only six physically meaningful fitting parameters for each material. The results provide guidance for the development of nanocomposite PUa-based materials.

Double Gyroid Morphologies in Precise Ion-Containing Multiblock Copolymers Synthesized via Step-Growth Polymerization

The double gyroid structure was first reported in diblock copolymers about 30 years ago, and the complexity of this morphology relative to the other ordered morphologies in block copolymers continues to fascinate the soft matter community. The double gyroid microphase-separated morphology has co-continuous domains of both species, and the minority phase is subdivided into two interpenetrating network structures. In addition to diblock copolymers, this structure has been reported in similar systems including diblock copolymers blended with one or two homopolymers and ABA-type triblock copolymers. Given the narrow composition region over which the double gyroid structure is typically observed (∼3 vol %), anionic polymerization has dominated the synthesis of block copolymers to control their composition and molecular weight. This perspective will highlight recent studies that (1) employ an alternative polymerization method to make block copolymers and (2) report double gyroid structures with lattice parameters below 10 nm. Specifically, step-growth polymerization linked precise polyethylene blocks and short sulfonate-containing blocks to form strictly alternating multiblock copolymers, and these copolymers produce the double gyroid structure over a dramatically wider composition range (>14 vol %). These new (AB) _n multiblock copolymers self-assemble into the double gyroid structure by having exceptional control over the polymer architecture and large interaction parameters between the blocks. This perspective proposes criteria for a broader and synthetically more accessible range of polymers that self-assemble into double gyroids and other ordered structures, so that these remarkable structures can be employed to solve a variety of technological challenges.

Ordered Nanostructures in Thin Films of Precise Ion-Containing Multiblock Copolymers

We demonstrate that ionic functionality in a multiblock architecture produces highly ordered and sub-3 nm nanostructures in thin films, including bicontinuous double gyroids. At 40 °C, precise ion-containing multiblock copolymers of poly(ethylene-b-lithium sulfosuccinate ester) n (PESxLi, x = 12 or 18) exhibit layered ionic assemblies parallel to the substrate. These ionic layers are separated by crystalline polyethylene blocks with the polymer backbones perpendicular to the substrate. Notably, above the melting temperature (T m) of the polyethylene blocks, layered PES18Li thin films transform into a highly oriented double-gyroid morphology with the (211) plane (d 211 = 2.5 nm) aligned parallel to the substrate. The cubic lattice parameter (a gyr) of the double gyroid is 6.1 nm. Upon heating further above T m, the double-gyroid morphology in PES18Li transitions into hexagonally packed cylinders with cylinders parallel to the substrate. These layered, double-gyroid, and cylinder nanostructures form epitaxially and spontaneously without secondary treatment, such as interfacial layers and solvent vapor annealing. When the film thickness is less than ∼3a gyr, double gyroids and cylinders coexist due to the increased confinement. For PES12Li above T m, the layered ionic assemblies simply transform into disordered morphology. Given the chemical tunability of ion-functionalized multiblock copolymers, this study reveals a versatile pathway to fabricating ordered nanostructures in thin films.

Nanoscale layers of precise ion-containing polyamides with lithiated phenyl sulfonate in the polymer backbone

Precise polyamide ionomer produces well-defined nanoscale layers.

Sub-3-Nanometer Domain Spacings of Ultrahigh-χ Multiblock Copolymers with Pendant Ionic Groups

We investigated the temperature-dependent phase behavior and interaction parameter of polyethylene-based multiblock copolymers with pendant ionic groups. These step-growth polymers contain short polyester blocks with a single Li⁺SO₃^- group strictly alternating with polyethylene blocks of x-carbons (PESxLi, x = 12, 18, 23). At room temperature, these polymers exhibit layered morphologies with semicrystalline polyethylene blocks. Upon heating above the melting point (∼130 °C), PES18Li shows two order-to-order transitions involving Ia3̅d gyroid and hexagonal morphologies. For PES12Li, an order-to-disorder transition accompanies the melting of the polyethylene blocks. Notably, a Flory-Huggins interaction parameter was determined from the disordered morphologies of PES12Li using mean-field theory: χ(T) = 77.4/T + 2.95 (T in Kelvin) and χ(25 °C) ≈ 3.21. This ultrahigh χ indicates that the polar ionic and nonpolar polyethylene segments are highly incompatible and affords well-ordered morphologies even when the combined length of the alternating blocks is just 18-29 backbone atoms. This combination of ultrahigh χ and short multiblocks produces sub-3-nm domain spacings that facilitate the control of block copolymer self-assembly for various fields of study, including nanopatterning.

Supramolecular Dimerization in a Polymer Melt from Small-Angle X-ray Scattering and Rheology: A Miscible Model System

We present a structural and dynamic study on the simplest supramolecular hetero-association, recently investigated by the authors to prepare architectural homogeneous structures in the melt state, based on the bio-inspired hydrogen-bonding of thymine/diaminotriazine (thy–DAT) base-pairs. In the combination with an amorphous low T_g poly(butylene oxide) (PBO), no micellar structures are formed, which is expected for nonpolar polymers because of noncompatibility with the highly polar supramolecular groups. Instead, a clear polymer-like transient architecture is retrieved. This makes the heterocomplementary thy–DAT association an ideal candidate for further exploitation of the hydrogen-bonding ability in the bulk for self-healing purposes, damage management in rubbers or even the development of easily processable branched polymers with built-in plasticizer. In the present work, we investigate the temperature range from T_g + 20 °C to T_g + 150 °C of an oligomeric PBO using small-angle X-ray scattering (SAXS) and linear rheology on the pure thy and pure DAT monofunctionals and on an equimolar mixture of thy/DAT oligomers. The linear rheology performed at low temperature is found to correspond to fully closed-state dimeric configurations. At intermediate temperatures, SAXS probes the equilibrium between open and closed states of the thy–DAT mixtures. The temperature-dependent association constant in the full range between open and closed H-bonds and an enhancement of the monomeric friction coefficient due to the groups is obtained. The thy–DAT association in the melt is more stable than the DAT–DAT, whereas the thy–thy association seems to involve additional long-lived interactions.

High-χ alternating copolymers for accessing sub-5 nm domains via simulations

Based on molecular dynamics simulations, we designed novel high-χ alternating copolymers (ACPs) for fabricating sub-5 nm domains.

Self-Assembled Structures of Diblock Copolymer/Homopolymer Blends through Multiple Complementary Hydrogen Bonds

A poly(styrene-b-vinylbenzyl triazolylmethyl methyladenine) (PS-b-PVBA) diblock copolymer and a poly(vinylbenzyl triazolylmethyl methylthymine) (PVBT) homopolymer were prepared through a combination of nitroxide-mediated radical polymerizations and click reactions. Strong multiple hydrogen bonding interactions of the A···T binary pairs occurred in the PVBA/PVBT miscible domain of the PS-b-PVBA/PVPT diblock copolymer/homopolymer blend, as evidenced in Fourier transform infrared and 1H nuclear magnetic resonance spectra. The self-assembled lamellar structure of the pure PS-b-PVBA diblock copolymer after thermal annealing was transformed to a cylinder structure after blending with PVBT at lower concentrations and then to a disordered micelle or macrophase structure at higher PVBT concentrations, as revealed by small-angle X-ray scattering and transmission electron microscopy.

Effect of Architecture on Micelle Formation and Liquid-Crystalline Ordering in Solutions of Block Copolymers Comprising Flexible and Rigid Blocks: Rod-Coil vs Y-Shaped vs Comblike Copolymers

Micelle formation of amphiphilic block copolymers of various architectures comprising both flexible and rodlike blocks were studied in a selective solvent via dissipative particle dynamics (DPD) simulations. Peculiarities of self-assembly of Y-shaped (insoluble rigid block and two flexible soluble arms) and comblike (soluble flexible backbone with insoluble rigid side chains) copolymers are compared with those of equivalent rod-coil diblock copolymers. We have shown that aggregation of the rigid blocks into the dense core of the micelles is accompanied by their nematic ordering. However, the orientation order parameter and aggregation number of the micelles are strongly dependent on macromolecular architecture. Relatively small micelles of pretty high nematic order parameter, S₂ ≈ 0.5-0.8, are the features of the Y-shaped and rod-coil copolymer micelles. They are characterized by different responses to the solvent quality worsening. The aggregation number of the rod-coil diblock copolymer micelles increases and that of the Y-shaped copolymer micelles decreases at the solvent quality worsening. However, the order parameter grows in both cases, achieving a maximum value for the Y-shaped copolymer micelles. Herewith, the core elongates. On the contrary, comblike copolymers self-assemble into bigger spherical micelles whose core possesses a lower nematic order of the rods, S₂ ≈ 0.3-0.4. The aggregation number is shown to depend on the length of the combs (on the number of repeating elements in the architecture). Possible physical reasons for such behavior of the systems are discussed.

Interpenetration of polymeric microgels at ultrahigh densities

Soft particles such as polymeric microgels can form ultra-dense phases, where the average center-to-center distance a _s can be smaller than the initial unperturbed particle diameter σ ₀, due to their ability to interpenetrate and compress. However, despite of the effort devoted to microgels at ultrahigh densities, we know surprisingly little about their response to their environment at effective volume fractions ϕ _eff above close packing (ϕ _cp ), and the existing information is often contradictory. Here we report direct measurements of the size and shape of poly(N-isopropylacrylamide) microgels at concentrations below and above ϕ _cp using the zero average contrast method in small-angle neutron scattering. We complement these experiments with measurements of the average interparticle distances using small-angle x-ray scattering, and a determination of the glass transition using dynamic light scattering. This allows us to unambiguously decouple interaction effects from density-dependent variations of the particle size and shape at all values of ϕ _eff . We demonstrate that the microgels used in this study significantly interpenetrate and thus change their size and shape only marginally even for ϕ _eff  ≫ ϕ _cp , a finding that may require changes in the interpretation of a number of previously published studies on the structural and dynamic properties of dense soft particle systems.

Synthesis and Phase Separation Behaviour of High Performance Multiblock Copolymers

The phase separation behaviour of block copolymers of the type (A–B) n(segmented block copolymers, multiblock copolymers) containing segments with different degrees of flexibility was investigated using a stepwise variation of the incorporated blocks A and B. Amorphous/rigid blocks (polysulfone segments) were systematically combined with amorphous/flexible blocks (poly(tetramethylene glycol), semiflexible/nematic blocks (different kinds of aromatic polyesters and poly(ester imides) as well as semicrystalline fluorinated polyester blocks). All multiblock copolymers were synthesized using a conventional transesterification polycondensation in the melt and the polycondensation results are discussed.

The phase separation in the synthesized block copolymers was investigated both experimentally and theoretically. Flory–Huggins interaction parameters of the block copolymers were calculated and used together with mean field calculations in order to understand the phase separation behaviour of all block copolymers correlated to their chemical structure. On the other hand, the onset of phase separation in a series of block copolymers with a systematic variation of block molecular weights was examined experimentally, mainly by DSC and SAXS.

Finally, the question is discussed whether or not the degree of phase separation in the investigated systems determines the properties of the polymers or not. This is for example outlined for the mechanical properties and, in particular, the surface properties of fluorinated block copolymers.

Rapid ordering of block copolymer thin films

Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.

Scattering and Gaussian Fluctuation Theory for Semiflexible Polymers

The worm-like chain is one of the best theoretical models of the semiflexible polymer. The structure factor, which can be obtained by scattering experiment, characterizes the density correlation in different length scales. In the present review, the numerical method to compute the static structure factor of the worm-like chain model and its general properties are demonstrated. Especially, the chain length and persistence length involved multi-scale nature of the worm-like chain model are well discussed. Using the numerical structure factor, Gaussian fluctuation theory of the worm-like chain model can be developed, which is a powerful tool to analyze the structure stability and to predict the spinodal line of the system. The microphase separation of the worm-like diblock copolymer is considered as an example to demonstrate the usage of Gaussian fluctuation theory.

Block copolymers: controlling nanostructure to generate functional materials - synthesis, characterization, and engineering

In this perspective, we survey recent advances in the synthesis and characterization of block copolymers, discuss several key materials opportunities enabled by block copolymers, and highlight some of the challenges that currently limit further realization of block copolymers in promising nanoscale applications. One significant challenge, especially as the complexity and functionality of designer macromolecules increases, is the requirement of multiple complementary techniques to fully characterize the resultant polymers and nanoscale materials. Thus, we highlight select characterization and theoretical methods and discuss how future advances can improve understanding of block copolymer systems. In particular, we consider the application of theoretical/simulation methods to the rationalization, and prediction, of observed experimental self-assembly phenomena. Finally, we explore several next steps for the field and emphasize some general areas of emerging research that could unlock additional opportunities for nanostructure-forming block copolymers in functional materials.

Studying the concentration dependence of the aggregation number of a micellar model system by SANS

We present a small-angle neutron scattering (SANS) structural characterization of n-alkyl-PEO polymer micelles in aqueous solution with special focus on the dependence of the micellar aggregation number on increasing concentration. The single micellar properties in the dilute region up to the overlap concentration ϕ* are determined by exploiting the well characterized unimer exchange kinetics of the model system in a freezing and diluting experiment. The micellar solutions are brought to thermodynamic equilibrium at high temperatures, where unimer exchange is fast, and are then cooled to low temperatures and diluted to concentrations in the limit of infinite dilution. At low temperatures the kinetics, and therefore the key mechanism for micellar rearrangement, is frozen on the experimental time scale, thus preserving the micellar structure in the dilution process. Information about the single micellar structure in the semidilute and concentrated region are extracted from structure factor analysis at high concentrations where the micelles order into fcc and bcc close packed lattices and the aggregation number can be calculated by geometrical arguments. This approach enables us to investigate the aggregation behavior in a wide concentration regime from dilute to 6·ϕ*, showing a constant aggregation number with concentration over a large concentration regime up to a critical concentration about three times ϕ*. When exceeding this critical concentration, the aggregation number was found to increase with increasing concentration. This behavior is compared to scaling theories for star-like polymer micelles.

Perpendicular lamellar-in-lamellar and other planar morphologies in A-b-(B-b-A)2-b-C and (B-b-A)2-b-C ternary multiblock copolymer melts

Ordered planar morphologies in A-b-(B-b-A)2-b-C and (B-b-A)2-b-C terpolymer melts are studied within the framework of the self-consistent field theory for volume fractions of components A, B, and C in the ratio 1:1:2 and the Flory-Huggins interaction parameters satisfying χ(AB) = 2χ(AC). The stable phases turn out to be the disordered, hexagonal, parallel lamellar-in-lamellar L∥ (including the simple lamellar) as well as non-shifted and shifted (L⊥ and SL⊥) perpendicular lamellar-in-lamellar morphologies. Depending on the value of the ratio r = Θ(AB)/Θ(BC), where Θ is a characteristic temperature of the units involved, different sequences of phase transitions are shown to occur. The hexagonal phase is characteristic for r ≅ 1. The L⊥ and SL⊥ morphologies occur at weak and intermediate segregations whereas the L∥ morphology appears for stronger degrees of segregation. For (B-b-A)2-b-C a reduction in r favors the shifted SL⊥ phase over the non-shifted L⊥ one, whereas for A-b-(B-b-A)2-b-C we find re-entrant phase transitions SL⊥ - L⊥. The physics determining the particular phase behavior is discussed.