Polyelectrolyte Block Research Articles

Responses of assembled structures of block polyelectrolytes to electrostatic interaction strength.

In this paper, the responses of assembled behaviors of block polyelectrolytes (PEs) to the strength of electrostatic interactions are studied through molecular dynamic simulations. The results show that the assembled structures closely depend on the electrostatic strength. It should be noted that PE coacervation can outweigh the nucleation of hydrophobic blocks and invert the micelle structures at strong electrostatic strengths, leading to the formation of inverted micelles of PE cores and hydrophobic coronas. In the poor solvent condition for neutral block, diverse anisotropic micelles are presented; candy-like conventional micelles of hydrophobic cores and PE patches coexist with inverted candy-like micelles of PE cores and hydrophobic patches and with Janus micelles of semi-neutral aggregate and semi-PE cluster in the presence of divalent and trivalent counterions. The formation of conventional or inverted micelle is largely determined by the type of micellar fusion, which results from the nucleation competition between electrostatic correlation and hydrophobic interaction. The merge of micelles mediated by hydrophobic attraction leads to conventional hydrophobic cores, and the fusion induced by electrostatic correlations results in PE cores micelles. At strong electrostatic strengths, the PE chains exhibit rich conformations at trivalent counterions, ranging from a fully collapsed state to a rod-like state, and parallel alignment of PE chains is found.

Block Polyelectrolyte Additives That Modulate the Viscoelasticity and Enhance the Printability of Gelatin Inks at Physiological Temperatures.

We demonstrate the utility of block polyelectrolyte (bPE) additives to enhance viscosity and resolve challenges with the three-dimensional (3D) printability of extrusion-based biopolymer inks. The addition of oppositely charged bPEs to solutions of photocurable gelatin methacryloyl (GelMA) results in complexation-driven self-assembly of the bPEs, leading to GelMA/bPE inks that are printable at physiological temperatures, representing stark improvements over GelMA inks that suffer from low viscosity at 37 °C, leading to low printability and poor structural stability. The hierarchical microstructure of the self-assemblies (either jammed micelles or 3D networks) formed by the oppositely charged bPEs, confirmed by small-angle X-ray scattering, is attributed to the enhancements in the shear strength and printability of the GelMA/bPE inks. Varying bPE concentration in the inks is shown to enable tunability of the rheological properties to meet the criteria of pre- and postextrusion flow characteristics for 3D printing, including prominent yielding behavior, strong shear thinning, and rapid recovery upon flow cessation. Moreover, the bPE self-assemblies also contribute to the robustness of the photo-cross-linked hydrogels; photo-cross-linked GelMA/bPE hydrogels are shown to exhibit higher shear strength than photo-cross-linked GelMA hydrogels. Last, the assessment of the printability of GelMA/bPE inks indicates excellent printing performance, including minimal swelling postextrusion, satisfactory retention of the filament shape upon deposition, and satisfactory shape fidelity of the various printed constructs. We envision this study to serve as a practical guide for the printing of bespoke extrusion inks where bPEs are used as scaffolds and viscosity enhancers that can be emulated in a range of photocurable precursors.

Lowest gelation concentration in a complex-coacervate-driven self-assembly system, achieved by redox-RAFT synthesis of high molecular weight block polyelectrolytes.

The objective of this work was to synthesize high molecular weight polyelectrolyte complex (PEC) micelles that are effective in controlling the rheology of aqueous solutions at low concentrations, paving the way for industrial applications of thickeners based on the principle of electrostatic self-assembly. Redox-initiated RAFT (reversible addition-fragmentation chain-transfer) polymerization was used to obtain anionic block polyelectrolytes based on poly(sodium 2-acrylamido-2-methylpropane sulfonate) and poly(acrylamide)-poly(AMPS)-block-poly(AM) (di-block) and poly(AMPS)-block-poly(AM)-block-poly(AMPS) (tri-block), with molecular weights of 237 kDa and 289 kDa and polydispersities of 1.29 and 1.34, respectively. A random poly(AMPS)-co-poly(AM) copolymer was also synthesized for comparison. PEC micelles were obtained upon mixing with cationic poly(N-[3-(dimethylamino)propyl]methacrylamide hydrochloride) - poly(DMAPMA), forming viscoelastic gels at unprecedented low concentrations of <3 wt% for the di-block and <1 wt% for the tri-block, which to date is the lowest demonstrated gelation concentration for a synthetic PEC micelle system. Differences between tri-block and di-block architectures are discussed, with the former being more affected by the addition of salt, which is attributed to percolated network breakdown. The random co-polymer was shown not to be an effective thickener but displayed a surprising lack of phase separation upon coacervation. The assemblies were characterized using dynamic light scattering (DLS) and cryo transmission electron microscopy (cryoTEM), revealing spherical micelles with a diameter of approximately 200 nm for the diblock and a mixture of spherical micelles and network particles for the tri-block PEC micelles. The micelles were not affected by dilution down to a polymer concentration of 7.8 × 10-4% (approx. 0.03 μM). Responsiveness to salinity, pH, and temperature was studied using DLS, revealing a critical NaCl concentration of 1.1 M for the block copolymer micelles.

Toward Effective and Adsorption-Based Antifouling Zipper Brushes: Effect of pH, Salt, and Polymer Design.

The undesired spontaneous deposition and accumulation of matter on surfaces, better known as fouling, is a problematic and often inevitable process plaguing a variety of industries. This detrimental process can be reduced or even prevented by coating surfaces with a dense layer of end-grafted polymer: a polymer brush. Producing such polymer brushes via adsorption presents a very attractive technique, as large surfaces can be coated in a quick and simple manner. Recently, we introduced a simple and scalable two-step adsorption strategy to fabricate block copolymer-based antifouling coatings on hydrophobic surfaces. This two-step approach involved the initial adsorption of hydrophobic-charged diblock copolymer micelles acting as a primer, followed by the complexation of oppositely charged-antifouling diblock copolymers to form the antifouling brush coating. Here, we significantly improve this adsorption-based zipper brush via systematic tuning of various parameters, including pH, salt concentration, and polymer design. This study reveals several key outcomes. First of all, increasing the hydrophobic/hydrophilic block ratio of the anchoring polymeric micelles (i.e., decreasing the hydrophilic corona) promotes adsorption to the surface, resulting in the most densely packed, uniform, and hydrophilic primer layers. Second, around a neutral pH and at a low salt concentration (1 mM), complexation of the weak polyelectrolyte (PE) blocks results in brushes with the best antifouling efficacy. Moreover, by tuning the ratio between these PE blocks, the brush density can be increased, which is also directly correlated to the antifouling performance. Finally, switching to different antifouling blocks can increase the internal density or strengthen the bound hydration layer of the brush, leading to an additional enhancement of the antifouling properties (>99% lysozyme, 87% bovine serum albumin).

Effect of Charged Block Length Mismatch on Double Diblock Polyelectrolyte Complex Micelle Cores.

Polyelectrolyte complex micelles are hydrophilic nanoparticles that self-assemble in aqueous environments due to associative microphase separation between oppositely charged blocky polyelectrolytes. In this work, we employ a suite of physical characterization tools to examine the effect of charged block length mismatch on the equilibrium structure of double diblock polyelectrolyte complex micelles (D-PCMs) by mixing a diverse library of peptide and synthetic charged-neutral block polyelectrolytes with a wide range of charged block lengths (25-200 units) and chemistries. Early work on D-PCMs suggested that this class of micelles can only be formed from blocky polyelectrolytes with identical charged block lengths, a phenomenon referred to as chain length recognition. Here, we use salt annealing to create PCMs at equilibrium, which shows that chain length recognition, a longstanding hurdle to repeatable self-assembly from mismatched polyelectrolytes, can be overcome. Interestingly, D-PCM structure-property relationships display a range of values that vary systematically with the charged block lengths and chemical identity of constituent polyelectrolyte pairings and cannot be described by generalizable scaling laws. We discuss the interdependent growth behavior of the radius, ionic pair aggregation number, and density in the micelle core for three chemically distinct diblock pairings and suggest a potential physical mechanism that leads to this unique behavior. By comparing the results of these D-PCMs to the scaling laws recently developed for single diblock polyelectrolyte complex micelles (S-PCMs: diblock + homopolymer), we observe that D-PCM design schemes reduce the size and aggregation number and restrict their growth to a function of charged block length relative to S-PCMs. Understanding these favorable attributes enables more predictive use of a wider array of charged molecular building blocks to anticipate and control macroscopic properties of micelles spanning countless storage and delivery applications.

Microphase Separation in Neutral Homopolymer Blends Induced by Salt-Doping

Microphase separation in polymeric systems provides a bottom-up strategy to fabricate nanostructures. Polymers that are reported to undergo microphase separation usually include block copolymers or polyelectrolytes. Neutral homopolymers, which are comparatively easy to synthesize, are thought to be incapable of microphase separation. Here, using a minimal model that accounts for ion solvation, we show that microphase separation is possible in neutral homopolymer blends with sufficient dielectric contrast, upon a tiny amount of salt-doping. The driving force for the microphase separation is the competition between selective ion solvation, which places smaller ions in domains with higher dielectric constant, and the propensity for local charge neutrality to decrease the electrostatic energy. The compromise is an emergent length over which microphase separation occurs and ions are selectively solvated. The factors affecting such competitions are explored, including ion solvation radii, dielectric contrast, and polymer fraction, which point to directions for observing this behavior experimentally. These findings suggest a low-cost and facile alternative to produce microphase separation, which may be exploited in advanced material design and preparation.

Stable Water-soluble Polyion Complex Micelles Composed of Oppositely Charged Diblock Copolymers and Reinforced by Hydrophobic Interactions

Polyion complex (PIC) micelles having a hydrodynamic radius of approximately 20 nm were prepared in water by simply mixing a pair of double hydrophilic oppositely charged diblock copolymers composed of a first block containing pendant phosphobetaine groups and a second cationic or anionic styrene-based polyelectrolyte block. The PIC micelles were stable under high salt concentration because the formation of the PIC micelles was driven by both electrostatic and hydrophobic interactions.

Complex pH-Dependent Interactions between Weak Polyelectrolyte Block Copolymer Micelles and Molecular Fluorophores.

Amphiphilic block copolymers with weak polyelectrolyte blocks can assemble stimulus-responsive nanostructures and interfaces. Applications of these materials in drug delivery, biomimetics, and sensing largely rely on the well-understood swelling of polyelectrolyte chains upon deprotonation, often induced by changes in pH or ionic strength. This deprotonation can also tune interfacial interactions between the polyelectrolyte blocks and surrounding solution, an effect which is less studied than morphological swelling of polyelectrolytes but can be just as critical for intended function. Here, we investigate whether the pH-driven morphological response of polyelectrolyte-bearing nanostructures also affects the interactions of these nanostructures with molecules in solution, using micelles of a short-chain polybutadiene-block-poly(acrylic acid) (pBd-pAA) as a model system. We introduce a Förster resonance energy transfer (FRET) approach to probe interactions between micelles and fluorescent molecular solutes as a function of solution pH. As expected, the pAA corona of these pBd-pAA micelles increases in thickness monotonically as a function of pH. However, FRET efficiency, which provides a metric of the spatial proximity of fluorescently labeled micelles and freely diffusing fluorophores, exhibits complex nonmonotonic behavior as a function of pH, indicating that the average separation of micelles and acceptor fluorophores is not strictly correlated with micelle swelling. Dialysis experiments quantify the affinity of fluorophores for micelles as a function of pH, confirming that changes in FRET are driven almost entirely by the pH-dependent affinity of the pAA block for the investigated molecular fluorophores, not simply by a shape change of the pAA corona. This study provides key insights into the interfacial interactions between weak-polyelectrolyte-bearing nanostructures and molecular solutes, of importance for the development of their stimulus-responsive applications.

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions.

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.

RETRACTED: Modular monomers with adjustable solubility: Synthesis of block copolymers for improved photocatalysis by RAFT for the synthesis of atomic nickel co-catalysts

• The loading of Ni on TiO 2 in the prepared composite is in atomic form, and the efficiency of photocatalytic hydrogen precipitation is better than that of the conventional loading method.Adsorption equilibrium process consistent with Langmuir adsorption isotherm and pseudo-second-order kinetics • Modular monomer method allows efficient identification of monomers suitable for RAFT water dispersion polymerization • The "nano-bridge" PMPS-MPS-P ([META + ][PF 6 − ]) plays an important role in the formation of stable Ni-O and Ti-C bonds, and can also influence the formation of Ov through ionic response • Can be modified by defect engineering to manipulate photocatalysts, providing a new idea for similar research directions Using the high incompatibility between the neutral stabilizer body and the block polyelectrolyte to drive phase separation during polymerization-induced self-assembly, a modular approach to systematically adjust ionic monomer/polymer solubility was developed to effectively identify monomers suitable for RAFT aqueous dispersion polymerization, with strong phase separation ability to form worm phases over a wide range of compositions and even at very low solids content. The block copolymer PMPS-MPS-P([META + ][PF 6 − ]), prepared by this method, acts as a "nano bridge" and achieves Ni loading on TiO 2 with the help of sol-gel method + thermal reduction. The atomic loading of Ni on TiO 2 is achieved through strong covalent bonding, metallic bonding and the natural physical intertwining effect of silane coupling agent. Interestingly, it was unexpectedly found that the TiC stable structure generated by this process, the ionization of part of the block polyelectrolyte after the thermal reduction treatment at 773 K and the loading process of Ni all can promote the formation of oxygen vacancy Ov, which facilitates the charge transfer and hydrogen precipitation reaction. It has superior photocatalytic ability and cheaper cost compared to the conventional impregnation dispersion method. These findings provide a new idea to modify the manipulated photocatalysts by defect engineering to achieve efficient photocatalytic efficiency and capability.

Interactions between an Associative Amphiphilic Block Polyelectrolyte and Surfactants in Water: Effect of Charge Type on Solution Properties and Aggregation.

The study of interactions between polyelectrolytes (PE) and surfactants is of great interest for both fundamental and applied research. These mixtures can represent, for example, models of self-assembly and molecular organization in biological systems, but they are also relevant in industrial applications. Amphiphilic block polyelectrolytes represent an interesting class of PE, but their interactions with surfactants have not been extensively explored so far, most studies being restricted to non-associating PE. In this work, interactions between an anionic amphiphilic triblock polyelectrolyte and different types of surfactants bearing respectively negative, positive and no charge, are investigated via surface tension and solution rheology measurements for the first time. It is evidenced that the surfactants have different effects on viscosity and surface tension, depending on their charge type. Micellization of the surfactant is affected by the presence of the polymer in all cases; shear viscosity of polymer solutions decreases in presence of the same charge or nonionic surfactants, while the opposite charge surfactant causes precipitation. This study highlights the importance of the charge type, and the role of the associating hydrophobic block in the PE structure, on the solution behavior of the mixtures. Moreover, a possible interaction model is proposed, based on the obtained data.

The effect of ion pairs on coacervate-driven self-assembly of block polyelectrolytes.

The incorporation of oppositely charged polyelectrolytes into a block copolymer system can lead to formation of microphase separated nanostructures driven by the electrostatic complex between two oppositely charged blocks. It is a theoretical challenge to build an appropriate model to handle such coacervate-driven self-assembly, which should capture the strong electrostatic correlations for highly charged polymers. In this paper, we develop the self-consistent field theory considering the ion paring effect to predict the phase behavior of block polyelectrolytes. In our model, two types of ion pairs, the binding between two oppositely charged monomers and the binding between charged monomers and counterions, are included. Their strength of formation is controlled by two parameters Kaa and Kac, respectively. We give a detailed analysis about how the binding strength Kac and Kaa and salt concentration affect the self-assembled nanostructure of diblock polyelectrolyte systems. The results show that the binding between two oppositely charged blocks provides driven force for microphase separation, while the binding between charged monomers and counterions competes with the polyion pairing and thus suppresses the microphase separation. The addition of salt has a shielding effect on the charges of polymers, which is a disadvantage to microphase separation. The phase diagrams as a function of polymer concentration and salt concentration at different situations are constructed, and the influence of Kaa, Kac, and charged block composition fa is analyzed in depth. The obtained phase diagrams are in good agreement with currently existing experimental and theoretical results.

Modification of the Co-assembly Behavior of Double-Hydrophilic Block Polyelectrolytes by Hydrophobic Terminal Groups: Ordered Nanostructures with Interpolyelectrolyte Complex Domains

We report here the influence of hydrophobic terminal groups from RAFT chain transfer agent 4-cyano-4-[(dodecylsulfanylthiocarbonyl) sulfanyl]pentanoic acid on the co-assembly behavior of two opposi...

Solubilization of Charged Porphyrins in Interpolyelectrolyte Complexes: A Computer Study.

Using coarse-grained dissipative particle dynamics (DPD) with explicit electrostatics, we performed (i) an extensive series of simulations of the electrostatic co-assembly of asymmetric oppositely charged copolymers composed of one (either positively or negatively charged) polyelectrolyte (PE) block A and one water-soluble block B and (ii) studied the solubilization of positively charged porphyrin derivatives (P) in the interpolyelectrolyte complex (IPEC) cores of co-assembled nanoparticles. We studied the stoichiometric mixtures of 137 AB and 137 AB chains with moderately hydrophobic A blocks (DPD interaction parameter ) and hydrophilic B blocks () with 10 to 120 P added (). The P interactions with other components were set to match literature information on their limited solubility and aggregation behavior. The study shows that the moderately soluble P molecules easily solubilize in IPEC cores, where they partly replace PE and electrostatically crosslink PE blocks. As the large P rings are apt to aggregate, P molecules aggregate in IPEC cores. The aggregation, which starts at very low loadings, is promoted by increasing the number of P in the mixture. The positively charged copolymers repelled from the central part of IPEC core partially concentrate at the core-shell interface and partially escape into bulk solvent depending on the amount of P in the mixture and on their association number, . If is lower than the ensemble average , the copolymer chains released from IPEC preferentially concentrate at the core-shell interface, thus increasing , which approaches . If , they escape into the bulk solvent.

Direct synthesis via RAFT of amphiphilic diblock polyelectrolytes facilitated by the use of a polymerizable ionic liquid as a monomer

A novel method to prepare amphiphilic block polyelectrolytes with a strongly hydrophobic block under homogeneous conditions is presented here.

Preliminary evaluation of amphiphilic block polyelectrolytes as potential flooding agents for low salinity chemical enhanced oil recovery

Amphiphilic block polyelectrolytes are known for their remarkable thickening properties in water solution, originating from their ability to self-assemble into large micellar aggregates. This makes them promising flooding agent for chemical enhanced oil recovery (cEOR). However, to the best of our knowledge, they have not yet been directly investigated for this purpose. In this work, a survey of relevant properties for EOR (rheology, filterability and emulsification), and laboratory scale oil recovery experiments, were performed on water solutions of polystyrene-block-poly(methacrylic acid) amphiphilic block polyelectrolytes, and compared with a commercial partially hydrolyzed polyacrylamide (HPAM), to evaluate the real potential in EOR applications for the first time. It was found that the recovery of amphiphilic block copolymers in low salinity brine (0.2% concentration of NaCl) is remarkably higher than that of HPAM at comparable weight concentration and shear viscosity, despite a much lower molecular weight. Effect of salinity and emulsification properties of the studied polymers have also been preliminarily investigated. Our results suggest that the recovery mechanism of these polymers differs from the traditional mechanism of polymer flooding, possibly due to emulsification of the oil. In conclusion, the studied amphiphilic block polyelectrolytes show promise as chemical agents in low salinity polymer flooding.

Putting Ink into Polyion Micelles: Full-Color Anticounterfeiting with Water/Organic Solvent Dual Resistance.

Anticounterfeiting paintings are usually with limited colors and easy blurring and need to be dispersed in an environmentally unfriendly organic solvent. We report a set of water-based polyion micellar inks to solve all these problems. Upon complexation of reversible coordination polymers formed with rare earth metal ions Eu3+ and Tb3+ and the aggregation-induced emission ligand tetraphenylethylene-L2EO4 with oppositely charged block polyelectrolyte P2MVP29-b-PEO205, we are able to generate polyion micelles displaying three elementary emission colors of red (R) (ΦEu3+ = 24%), green (G) (ΦTb3+ = 7%), and blue (B) (ΦTPE = 9%). Full-spectrum emission and white light emission (0.34, 0.34) become possible by simply mixing the R, G, and B micelles at the desired fraction. Strikingly, the micellar inks remain stable even after soaking in water or organic solvents (ethyl acetate, ethanol, etc.) for 24 h. We envision that polyion micelles would open a new paradigm in the field of anticounterfeiting.

Coarse-grained molecular dynamics simulations study of the conformational properties of single polyelectrolyte diblock copolymers

We use coarse-grained molecular dynamics simulations to study a single di block polyelectrolyte chain in solution. We analyze the conformational properties of the chain and localization of counterions as a function of the charge fraction, backbone stiffness, Bjerrum length, and counterion valence. The interplay between the excluded-volume effects and the electrostatic interactions among charged residues leads to variation in block−polyelectrolyte architecture. Our computational findings indicate that varying such system properties lead to nontrivial effects and can be a powerful mechanism to tune the conformational properties of block polyelectrolytes.

Structural Polymorphism of Single pDNA Condensates Elicited by Cationic Block Polyelectrolytes.

DNA folding is a core phenomenon in genome packaging within a nucleus. Such a phenomenon is induced by polyelectrolyte complexation between anionic DNA and cationic proteins of histones. In this regard, complexes formed between DNA and cationic polyelectrolytes have been investigated as models to gain insight into genome packaging. Upon complexation, DNA undergoes folding to reduce its occupied volume, which often results in multi-complex associated aggregates. However, when cationic copolymers comprising a polycation block and a neutral hydrophilic polymer block are used instead, DNA undergoes folding as a single molecule within a spontaneously formed polyplex micelle (PM), thereby allowing the observation of the higher-order structures that DNA forms. The DNA complex forms polymorphic structures, including globular, rod-shaped, and ring-shaped (toroidal) structures. This review focuses on the polymorphism of DNA, particularly, to elucidate when, how, and why DNA organizes into these structures with cationic copolymers. The interactions between DNA and the copolymers, and the specific nature of DNA in rigidity; i.e., rigid but foldable, play significant roles in the observed polymorphism. Moreover, PMs serve as potential gene vectors for systemic application. The significance of the controlled DNA folding for such an application is addressed briefly in the last part.

PNIPAM-b-PDMAEA double stimuli responsive copolymers: Effects of composition, end groups and chemical modification on solution self-assembly

Doubly temperature- and pH-responsive HOOC-poly(N-isopropylacrylamide)-b-poly(2-(dimethylamino)ethyl acrylate)-C12H25 (HOOC-PNIPAM-b-PDMAEA-C12H25) and HOOC-poly(2-dimethylamino)ethyl acrylate)-b-poly(N-isopropylacrylamide)-C12H25 (HOOC-PDMAEA-b-PNIPAM-C12H25) diblock copolymers were successfully synthesized via sequential reversible addition-fragmentation chain transfer (RAFT) polymerization. Hydrophilic COOH groups and hydrophobic C12H25 groups were selectively placed at the chain end of either the thermoresponsive or the pH-responsive block. The amine precursor diblocks were converted to strong, cationic block polyelectrolytes by quaternizing the tertiary amine groups of PDMAEA block with methyl iodide. The self-assembly behavior of amine-based and quaternized diblock copolymers was investigated in aqueous media of varying pH and temperature by utilizing light scattering techniques and fluorescence spectroscopy. The novel diblock copolymers formed nanoassembled structures at temperatures above the nominal lower critical solution temperature (LCST) of the PNIPAM block. However, the amine-based and quaternized block copolymers form loose aggregate structures even at room temperature, due to the existence of the hydrophobic C12H25 terminal groups. Moreover, the solution pH was found to affect the self-assembly behavior of the amine-based diblock copolymers because of the presence of the PDMAEA block.