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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Tutorial: Machine-Learning-Based CREASE-2D Analysis of 2D SAXS Profiles to Characterize Anisotropic Nanostructures in Soft Materials

We present a tutorial to guide users on how to extend the Computational Reverse Engineering Analysis of Scattering Experiments-2D (CREASE-2D) framework to interpret their experimental two-dimensional small-angle scattering (SAS) data from soft materials (e.g., polymers, peptide amphiphiles, biomolecular fibrils). Unlike most traditional SAS analysis approaches, which typically rely on azimuthally averaged onedimensional (1D) profiles, CREASE-2D utilizes the complete 2D scattering profile to reveal information about anisotropy in the structure. In past applications, CREASE has provided insights into complex structural features, including the cross-sectional shapes of assembled nanostructures and dispersity in these features, which are difficult to discern with existing analytical models. While (1D- ) CREASE has been applied to SANS and SAXS data, this tutorial shares the steps for implementing CREASE-2D using an example of a dipeptide solution system, for which we have SAXS data. We present details for these steps involved in using CREASE-2D to interpret SAXS profiles: how to preprocess SAXS data, define relevant structural features, generate three-dimensional real-space structures for specific values of these features, train a machine learning (ML) surrogate model to predict scattering profiles for given structural features, and optimize these features using genetic algorithms (GA). Then, we use these steps to interpret complex 2DSAXS data collected from dipeptide solutions that, in microscopy images, exhibit nanoscale structures that could be elliptical tubes/ flat tapes/cylinders or a combination of these cross sections. Open-source codes, computational hardware, and software requirements, as well as the strengths and limitations of this protocol, are also presented. We expect researchers working with (soft) biomaterials, peptide amphiphiles, amphiphilic polymer solutions, polymer nanocomposites, and blends of particles/polymers will find this CREASE-2D method and this tutorial of use.

CREASE↗
DOE OSTI2025

Surfactant-like peptide gels are based on cross-β amyloid fibrils

Surfactant-like peptides, in which hydrophilic and hydrophobic residues are encoded within different domains in the peptide sequence, undergo facile self-assembly in aqueous solution to form supramolecular hydrogels. These peptides have been explored extensively as substrates for the creation of functional materials since a wide variety of amphipathic sequences can be prepared from commonly available amino acid precursors. The self-assembly behavior of surfactant-like peptides has been compared to that observed for small molecule amphiphiles in which nanoscale phase separation of the hydrophobic domains drives the self-assembly of supramolecular structures. Here, we investigate the relationship between sequence and supramolecular structure for a pair of bola-amphiphilic peptides, Ac-KLIIIK-NH 2 (L2) and Ac-KIIILK-NH 2 (L5). Despite similar length, composition, and polar sequence pattern, L2 and L5 form morphologically distinct assemblies, nanosheets and nanotubes, respectively. Cryo-EM helical reconstruction was employed to determine the structure of the L5 nanotube at near-atomic resolution. Rather than displaying self-assembly behavior analogous to conventional amphiphiles, the packing arrangement of peptides in the L5 nanotube displayed steric zipper interfaces that resembled those observed in the structures of β-amyloid fibrils. Like amyloids, the supramolecular structures of the L2 and L5 assemblies were sensitive to conservative amino acid substitutions within an otherwise identical amphipathic sequence pattern. This study highlights the need to better understand the relationship between sequence and supramolecular structure to facilitate the development of functional peptide-based materials for biomaterials applications.

Das, Abhinaba [Emory University, Atlanta, GA (Unit↗
DOE OSTI2020

Determining population densities in bimodal micellar solutions using contrast-variation small angle neutron scattering

Self-assembly of amphiphilic polymers in water is of fundamental and practical importance. Significant amounts of free unimers and associated micellar aggregates often coexist over a wide range of phase regions. The thermodynamic and kinetic properties of the microphase separation are closely related to the relative population density of unimers and micelles. Although the scattering technique has been employed to identify the structure of micellar aggregates as well as their time-evolution, the determination of the population ratio of micelles to unimers remains a challenging problem due to their difference in scattering power. In this work, using small-angle neutron scattering (SANS), we present a comprehensive structural study of amphiphilic n-dodecyl-PNIPAm polymers, which shows a bimodal size distribution in water. By adjusting the deuterium/hydrogen ratio of water, the intra-micellar polymer and water distributions are obtained from the SANS spectra. The micellar size and number density are further determined, and the population densities of micelles and unimers are calculated to quantitatively address the degree of micellization at different temperatures. Our method can be used to provide an in-depth insight into the solution properties of microphase separation, which are present in many amphiphilic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1997

Molecular Dynamics of Peptide Folding at Aqueous Interfaces

Even though most monomeric peptides are disordered in water they can adopt sequence-dependent, ordered structures, such as a-helices, at aqueous interfaces. This property is relevant to cellular signaling, membrane fusion, and the action of toxins and antibiotics. The mechanism of folding nonpolar peptides at the water-hexane interface was studied in the example of an 11-mer, of poly-L-leucine. Initially placed as a random coil on the water side of the interface, the peptide folded into an a-helix in 36 ns. Simultaneously, the peptide translocated into the hexane side of the interface. Folding was not sequential and involved a 3/10-helix as an intermediate. The folded peptide was either parallel to the interface or had its C-terminus exposed to water. An 11-mer, LQQLLQQLLQL, composed of leucine (L) and glutamine (G), was taken as a model amphiphilic peptide. It rapidly adopted an amphiphilic, disordered structure at the interface. Further folding proceeded through a series of amphiphilic intermediates.

Pohorille, Andrew↗
NASA NTRS2002

The Laboratory Production of Complex Organic Molecules in Simulated Interstellar Ices

Much of the volatiles in interstellar dense clouds exist in ices surrounding dust grains. Their low temperatures preclude most chemical reactions, but ionizing radiation can drive reactions that produce a suite of new species, many of which are complex organics. The Astrochemistry Lab at NASA-Ames studies the UV radiation processing of interstellar ice analogs to better identify the resulting products and establish links between interstellar chemistry, the organics in meteorites, and the origin of life on Earth. Once identified, the spectral properties of the products can be quantified to assist with the search for these species in space. Of particular interest are findings that UV irradiation of interstellar ice analogs produces molecules of importance in current living organisms, including quiriones, amphiphiles, and amino acids. Quinones play a variety of roles including electron transport and are used by all organisms. Studies show that quinones should be made wherever polycyclic aromatic hydrocarbons are irradiated in interstellar ices (Bernstein et al. 2001). Amphiphiles are also made when mixed molecular ices are irradiated. These amphiphiles self-assemble into membrane-walled vesicles when put in liquid water (Dworkin et al. 2001). Ice irradiation can also produce (Bernstein et al. 2002) and destroy amino acids (Ehrenfreund et al. 2001). Many of the same processes thought to make organics in space should yield products highly enriched in deuterium (D) (Sandford et al. 2001). The high D/H ratios in some interstellar species, and the knowledge that many of the organics in primitive meteorites are D-enriched, suggests that such linkages do exist. By using D as a tracer, we expect to learn more about the different chemical processes occurring in space and their relative importance in the production of different organic compounds and delivery to planetary surfaces.

Dworkin, Jason P.↗
DOE OSTI2020

Imaging Supramolecular Morphogenesis with Confocal Laser Scanning Microscopy at Elevated Temperatures

The morphogenesis of supramolecular assemblies is a highly dynamic process that has only recently been recognized, and our understanding of this phenomenon will require imaging techniques capable of crossing scales. Shape transformations depend both on the complex energy landscapes of supramolecular systems and the kinetically controlled pathways that define their structures and functions. We report here the use of confocal laser scanning microscopy coupled with a custom-designed variable-temperature sample stage that enables in situ observation of such shape changes. The submicrometer resolution of this technique allows for real-time observation of the nanostructures in the native liquid environments in which they transform with thermal energy. We use this technique to study the temperature-dependent morphogenic behavior of peptide amphiphile nanofibers and photocatalytic chromophore amphiphile nanoribbons. Furthermore, the variable-temperature confocal microscopy technique demonstrated in this work can sample a large volume and provides real-time information on thermally induced morphological changes in the solution.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Superstructured Biomaterials Formed by Exchange Dynamics and Host–Guest Interactions in Supramolecular Polymers

Dynamic and reversible assembly of molecules is ubiquitous in the hierarchical superstructures of living systems and plays a key role in cellular functions. Recent work from the laboratory reported on the reversible formation of such superstructures in systems of peptide amphiphiles conjugated to oligonucleotides and electrostatically complimentary peptide sequences. Here, a supramolecular system is reported upon where exchange dynamics and host–guest interactions between β-cyclodextrin and adamantane on peptide amphiphiles lead to superstructure formation. Superstructure formation with bundled nanoribbons generates a mechanically robust hydrogel with a highly porous architecture that can be 3D printed. Functionalization of the porous superstructured material with a biological signal results in a matrix with significant in vitro bioactivity toward neurons that could be used as a supramolecular model to design novel biomaterials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Using Aggregation to Chaperone Nanoparticles Across Fluid Interfaces

Abstract Nanoparticles (NPs) transfer is usually induced by adding ligands to modify NP surfaces, but aggregation of NPs oftentimes hampers the transfer. Here, we show that aggregation during NP phase transfer does not necessarily result in transfer failure. Using a model system comprising gold NPs and amphiphilic polymers, we demonstrate an unusual mechanism by which NPs can undergo phase transfer from the aqueous phase to the organic phase via a single‐aggregation‐single pathway. Our discovery challenges the conventional idea that aggregation inhibits NP transfer and provides an unexpected pathway for transferring larger‐sized NPs (>20 nm). The charged amphiphilic polymers effectively act as chaperons for the NP transfer and offer a unique way to manipulate the dispersion and distribution of NPs in two immiscible liquids. Moreover, by intentionally jamming the NP‐polymer assembly at the liquid/liquid interface, the transfer process can be inhibited.

Fu, Yuchen↗
DOE OSTI2023

Using Aggregation to Chaperone Nanoparticles Across Fluid Interfaces

Nanoparticles (NPs) transfer is usually induced by adding ligands to modify NP surfaces, but aggregation of NPs oftentimes hampers the transfer. Here, we show that aggregation during NP phase transfer does not necessarily result in transfer failure. Using a model system comprising gold NPs and amphiphilic polymers, we demonstrate an unusual mechanism by which NPs can undergo phase transfer from the aqueous phase to the organic phase via a single-aggregation-single pathway. Our discovery challenges the conventional idea that aggregation inhibits NP transfer and provides an unexpected pathway for transferring larger-sized NPs (>20 nm). The charged amphiphilic polymers effectively act as chaperons for the NP transfer and offer a unique way to manipulate the dispersion and distribution of NPs in two immiscible liquids. Moreover, by intentionally jamming the NP-polymer assembly at the liquid/liquid interface, the transfer process can be inhibited.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Aqueous Self‐Assembly of Cylindrical and Tapered Bottlebrush Block Copolymers

The self‐assembly of amphiphilic bottlebrush block copolymers (BCPs), featuring backbones densely grafted with two types of side chains, is less well understood compared to linear BCPs. In particular, the solution self‐assembly of tapered bottlebrush BCPs—cone‐shaped BCPs with hydrophilic or hydrophobic tips—remains unexplored. This study investigates eight tapered and four cylindrical bottlebrush BCPs with varied ratios of hydrophobic polystyrene (PS) and hydrophilic poly(acrylic acid) (PAA) side chains, synthesized via sequential addition of macromonomers using ring‐opening metathesis polymerization (SAM‐ROMP). Self‐assembled nanostructures formed in water were analyzed using cryogenic transmission electron microscopy, small‐angle neutron scattering, and dynamic light scattering. Most BCPs generated multiple nanostructures with surface protrusions, including spherical micelles, cylindrical micelles, and vesicles, alongside transitional forms like ellipsoids and semi‐vesicles. Coarse‐grained molecular dynamics simulations supported the experimental findings, which revealed two distinct self‐assembly pathways. The first involved micelle fusion, producing elliptical and cylindrical aggregates, sometimes forming Y‐junctions. The second pathway featured micelle maturation into semivesicles, which developed into vesicles or large compound vesicles. This work provides the first experimental evidence of vesicle formation via semivesicles in bottlebrush BCPs and demonstrates the significant influence of cone directionality on self‐assembly behavior in these cone‐shaped polymeric amphiphiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Hierarchical Self-Assembly Pathways of Peptoid Helices and Sheets

Peptoids (N-substituted glycines) are a class of tailorable synthetic peptidomic polymers. Amphiphilic diblock peptoids have been engineered to assemble 2D crystalline lattices with applications in catalysis and molecular separations. Assembly is induced in an organic solvent/water mixture by evaporating the organic phase, but the assembly pathways remain uncharacterized. We conduct all-atom molecular dynamics simulations of Nbrpe6Nc6 as a prototypical amphiphilic diblock peptoid comprising an NH 2 -capped block of six hydrophobic N-((4-bromophenyl)ethyl)glycine residues conjugated to a polar NH 3 (CH 2 ) 5 CO tail. We identify a thermodynamically controlled assembly mechanism by which monomers assemble into disordered aggregates that self-order into 1D chiral helical rods then 2D achiral crystalline sheets. We support our computational predictions with experimental observations of 1D rods using small-angle X-ray scattering, circular dichroism, and atomic force microscopy and 2D crystalline sheets using X-ray diffraction and atomic force microscopy. Furthermore, this work establishes a new understanding of hierarchical peptoid assembly and principles for the design of peptoid-based nanomaterials.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Computational and Experimental Determination of the Properties, Structure, and Stability of Peptoid Nanosheets and Nanotubes

Peptoids (N-substituted glycines) are a group of highly controllable peptidomimetic polymers. Amphiphilic diblock peptoids have been engineered to assemble crystalline nanospheres, nanofibrils, nanosheets, and nanotubes with biochemical, biomedical, and bioengineering applications. The mechanical properties of peptoid nanoaggregates and their relationship to the emergent self-assembled morphologies have been relatively unexplored and are critical for the rational design of peptoid nanomaterials. In this work, we consider a family of amphiphilic diblock peptoids consisting of a prototypical tube-former (Nbrpm6Nc6, a NH 2 -capped hydrophobic block of six N-((4-bromophenyl)methyl)glycine residues conjugated to a polar NH 3 (CH 2 ) 5 CO tail), a prototypical sheet-former (Nbrpe6Nc6, where the hydrophobic block comprises six N-((4-bromophenyl)ethyl)glycine residues), and an intermediate sequence that forms mixed structures ((NbrpeNbrpm)3Nc6). We combine all-atom molecular dynamics simulations and atomic force microscopy to determine the mechanical properties of the self-assembled 2D crystalline nanosheets and relate these properties to the observed self-assembled morphologies. We find good agreement between our computational predictions and experimental measurements of Young’s modulus of crystalline nanosheets. A computational analysis of the bending modulus along the two axes of the planar crystalline nanosheets reveals bending to be more favorable along the axis in which the peptoids stack by interdigitation of the side chains compared to that in which they form columnar crystals with π-stacked side chains. Here, we construct molecular models of nanotubes of the Nbrpm6Nc6 tube-forming peptoid and predict a stability optimum in good agreement with experimental measurements. A theoretical model of nanotube stability suggests that this optimum is a free energy minimum corresponding to a “Goldilocks” tube radius at which capillary wave fluctuations in the tube wall are minimized.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Polymorphism and Optoelectronic Properties in Crystalline Supramolecular Polymers

Supramolecular polymers can emulate some of the physical properties of covalent polymers but offer new opportunities given the possibility of designing monomers that will form highly ordered assemblies with defined shapes. Internally ordered supramolecular polymers formed through nucleation–elongation self-assembly are well-known but highly crystalline examples which exhibit important properties such as light harvesting, charge transport, and ferroelectricity are not common. We report here on a detailed study of supramolecular polymers formed in water by carboxylated naphtho-p-quinodimethane amphiphiles. We found that supramolecular polymerization of these amphiphiles in aqueous media yields crystalline assemblies with morphologies that included ribbons, helically rolled ribbons, and twisted filaments. This polymorphism was found to be controlled exclusively by repulsive electrostatic interactions controlled by the degree of protonation of the carboxylic head groups which also dictates the nature of supramolecular packing. Substoichiometric amounts of base lead to highly crystalline ribbons due to a decreased surface charge density and less electrostatic repulsion. Increasing deprotonation results in helically rolled ribbons with a different polymorph crystal lattice, whereas excessive deprotonation leads to twisted filaments with maximum surface charge density. Ribbons, helical rolled ribbons, and twisted filaments revealed an increasing red shift in their visible absorption maxima. These crystalline assemblies could be potential candidates for solar energy materials and photocatalytic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Molecular Dynamics Simulation of the Structures, Dynamics, and Aggregation of Dissolved Organic Matter

Dissolved organic matter (DOM) plays a significant role in the transport and transformation of pollutants in the aquatic environment. However, the experimental characterization of DOM has been limited mainly to bulk properties, and the molecular-level interactions among various components of DOM remain to be fully characterized. In this study, we use molecular dynamics (MD) simulations to probe the structural properties of model DOM systems at atomic detail. The 200 ns simulations, validated by available experimental data, reveal processes and mechanisms by which chemical species (cations, peptides, lipids, lignin, carbohydrates, and some low-molecular-weight aliphatic and aromatic compounds) aggregate to form complex DOM. The DOM aggregates are dynamic, consisting of a hydrophobic core and amphiphilic exterior. The lipid tails and other hydrophobic fragments form the core, with hydrophilic and amphiphilic groups exposed to water, making DOM accessible to both polar and nonpolar species. Thus, the lipid component acts as a nucleator, whereas cations (especially Ca 2+ ) connect the molecular fragments on the surface by coordinating with the O-containing functional groups of DOM. The structural details revealed here provide new insights including surface accessible atoms, overall assemblage, and interactions among the molecules of DOM for understanding the kinetics and mechanisms through which DOM interacts with metal and other contaminants.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Solvent-Driven Transformation of Zn/Cd 2+ -Deoxycholate Assemblies

Deoxycholic acid (DOC) is a unique, biologically derived surfactant with facial amphiphilicity that has been exploited, albeit minimally, in supramolecular assembly of materials. Here, we present the synthesis and structural characterization of three hybrid metal (Zn 2+ and Cd 2+ )-DOC compounds. Analysis by single-crystal Xray diffraction reveals the many interactions that are possible between these facial surfactants and the influence of solvent molecules that drive the assembly of materials. These structures are the first metal- DOC complexes besides those obtained from alkali and alkaline earth metals. We isolated polymeric chains of both Cd and Zn (Zn poly -DOC and Cd poly -DOC) from water. Major interactions between DOC molecules in these phases are hydrophobic in nature. Cd poly -DOC exhibits unique P1 symmetry, with complete interdigitation of the amphiphiles between neighboring polymeric chains. Zn 4 -DOC, obtained from methanol dissolution of Zn poly -DOC, features the OZn 4 tetrahedron, widely known in basic zinc acetate and MOF-5 (metal organic framework). We document a solvent-driven, roomtemperature transition between Zn poly -DOC and Zn 4 -DOC (in both directions) by scanning and transmission electron microscopies in addition to small-angle X-ray scattering, powder X-ray diffraction, and infrared spectroscopy. These studies show the methanoldriven transition of Zn poly -DOC to Zn 4 -DOC occurs via an intermediate with no long-range order of the Zn 4 clusters, indicating the strongest interactions driving assembly are intramolecular. On the contrary, water-driven solid-to-solid transformation from Zn 4 -DOC to Zn poly -DOC exhibits crystal-to-crystal transformation. Zn poly -DOC is robust, easy to synthesize, and comprised of biologically benign components, so we demonstrate dye absorption as a proxy for water treatment applications. It favors absorption of positively charged dyes. These studies advance molecular level knowledge of the supramolecular assembly of facial surfactants that can be exploited in the design of organic-inorganic hybrid materials. This research also highlights the potential of solvent for tuning supramolecular assembly processes, leading to new hybrid materials featuring facial surfactants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Impact of Water Extraction on Malonamide Aggregation: A Molecular Dynamics and Graph Theoretic Approach

Solution structure in liquid-liquid extraction affects the efficacy of separation; however, even for simplified organic phases, structural characterization and attribution of aggregation to intermolecular interactions are fundamental challenges. We investigate water uptake into organic phases for two malonamides commonly applied to actinide and lanthanide separations. Extracted water induces reorganization of the amphiphilic extractant molecules, although we find this rearrangement is not strongly manifested in small-angle X-ray scattering making it challenging to probe without methods such as atomistic simulation. Using a graph theoretic approach to define hydrogen bonded water/malonamide aggregates from molecular dynamics simulations, we find evidence of a characteristic aggregate size by water number that results from geometric accommodation of the surrounding malonamide molecules. Furthermore, this implies a degree of size selectivity inherent to these water-in-oil aggregates. Conversely, we find no evidence of a characteristic size of the aggregates with respect to their malonamide number. By defining a separate graphical representation of self-association of the amphiphilic malonamides, we quantify how water affects the local and nonlocal topology of the malonamide network, providing a basis for characterization of the structure and impact of polar solutes in increasingly complex organic phases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Influence of the Nature of Aliphatic Hydrophobic Physical Crosslinks on Water Crystallization in Copolymer Hydrogels

The local environment within a hydrogel influences the properties of water, including the propensity for ice crystallization. Water-swollen amphiphilic copolymers produce tunable nanoscale environments, which are defined by hydrophobic associations, for the water molecules. In this work, the antifreeze properties for equilibrium-swollen amphiphilic copolymers with a common hydrophilic component, hydroxyethyl acrylate (HEA), but associated through crystalline (octadecyl acrylate, ODA) or rubbery (ethylhexyl acrylate, EHA) hydrophobic segments, are examined. Differences in the efficacy of the associations can be clearly enunciated from compositional solubility limits for the copolymers in water (<2.6 mol % ODA vs ≤14 mol % EHA), and these differences can be attributed to the strength of the association. The equilibrium-swollen HEA-ODA copolymers are viscoelastic solids, while the swollen HEA-EHA copolymers are viscoelastic liquids. Cooling these swollen copolymers to nearly 200 K induces some crystallization of the water, where the fraction of water frozen depends on the details of the nanostructure. Decreasing the mean free path of water by increasing the ODA composition from 10 to 25 mol % leads to fractionally more unfrozen water (66–87%). The swollen HEA-EHA copolymers only marginally inhibit ice (<13%) except with 45 mol % EHA, where nearly 60% of the water remains amorphous on cooling to 200 K. In general, the addition of the EHA leads to less effective ice inhibition than analogous covalently crosslinked HEA hydrogels (19.9 ± 1.8%). These results illustrate that fluidity of confining surfaces can provide pathways for critical nuclei to form and crystal growth to proceed.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Coupling of Charge Regulation and Geometry in Soft Ionizable Molecular Assemblies

The size, shape, and charge of structures, such as proteins and amphiphile assemblies, respond in an interconnected manner to solution ionic conditions. Here, we analyze assemblies of an amphiphile (C 16 K 2 ), with two ionizable amino acids [lysine (K)] coupled to a 16-carbon alkyl tail, via small-angle X-ray scattering (SAXS), nonlinear Poisson–Boltzmann theory (nl-PB), and hybrid Monte Carlo-molecular dynamics (MC-MD) simulations. SAXS revealed structural transitions from spherical micelles to cylindrical micelles to bilayers with increasing pH. By combining SAXS-determined structural information and nl-PB, we derived the molecular degree of ionization as a function of pH. The back-calculated titration curves matched the experimental data over an extended pH range, without adjustable parameters. Similarly, the SAXS data on the evolution of spherical micelle structure with ionic strength were combined with nl-PB and MC-MD to derive the bare and effective charges. MC-MD, which considered finite ion sizes, showed that bare and effective charges saturate quickly with increasing salt concentration. Furthermore, the calculated effective charges closely matched results from Zeta-potential measurements. The presented approach has advantages over customary methods for charge regulation, such as the Henderson–Hasselbalch (HH) or Hill models, where molecular ionization/deionization in assemblies is described by effective pKs that are distinct from the pK for isolated molecules. However, these models lack a physical explanation for these pK shifts. By contrast, our approach of combining structural details with an electrostatic model and simulations provides a more intuitive understanding of structure-charge coupling and a framework for understanding charge regulation in many synthetic and biological systems.

ionization↗