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DOE OSTI2026

Effects of Concentration, Salinity and Temperature on the Conformations of Zwitterionic Poly(2-Vinylpyridine- N -Oxide) Chains in Semidilute Solutions Probed by Small-Angle X-Ray and Neutron Scattering

Polyzwitterions, composed of repeating units with equal numbers of anionic and cationic groups, have drawn considerable interest for applications ranging from antimicrobial coatings and antifouling membranes to low-friction interfaces, energy storage media, and actuators. A characteristic feature of many polyzwitterions is the anti-polyelectrolyte effect salt-induced chain expansion in aqueous solution a phenomenon often implicated in their functional behavior. In this study, we investigated the conformational behavior of poly(2-vinylpyridine-N-oxide) (P2VPNO) using smallangle X-ray and neutron scattering (SAXS and SANS). Small-angle X-ray scattering (SAXS) revealed that, in salt-free aqueous solution, P2VPNO adopts an expanded wormlike conformation stabilized by hydration. With increasing concentration, the chains contract due to screening of intrachain excluded-volume interactions, qualitatively consistent with de Gennes’ scaling predictions for neutral polymers. Small-angle neutron scattering (SANS) further demonstrated that P2VPNO exhibits the characteristic anti-polyelectrolyte response to added salt, as observed in many other polyzwitterions. At elevated temperatures, chain flexibility increases, leading to a shorter Kuhn length and reduced radius of gyration. Notably, however, salt-induced chain expansion persists, indicating that the anti-polyelectrolyte effect remains operative under elevated thermal conditions. These findings provide the first experimental evidence of scaling behavior in polyzwitterions, as well as the first observation of their altered antipolyelectrolyte response at elevated temperatures, offering new insights into the solution physics of this important class of polymers.

Conformation↗

DOE OSTI2026

Structural and physicochemical insights into pH-responsive poly(DEAEMA- co -HEMA)-grafted mesoporous silica nanoparticles

Mesoporous silica nanoparticles (SiO 2 ) grafted with responsive polymer shells are versatile hybrid systems. Understanding their three-dimensional organization in the hydrated state remains a significant challenge. Here, in this study, SiO 2 nanoparticles were functionalized with a poly(DEAEMA-co-HEMA) shell via a “grafting-from” polymerization strategy in aqueous media. Successful surface modification was confirmed by FTIR, thermogravimetric analysis, transmission electron microscopy, X-ray photoelectron spectroscopy, N 2 sorption, and ζ-potential, yielding grafting contents of 22% (p1 DEAEMA-co-HEMA ) and 49% (p2 DEAEMA-co-HEMA ). Small-angle neutron scattering (SANS) with solvent contrast variation was employed to elucidate the solution-state core–shell architecture of p1 and p2 hybrids at pH 2, where the grafted polymer shell is protonated and highly hydrated. Near contrast matching of the silica core, theoretically estimated at 58% D 2 O, suppressed the scattering intensity, enhancing sensitivity to the polymer shell. Constrained core–shell ellipsoid modeling across solvent contrasts revealed a systematic increase in shell thickness, overall particle dimensions, and shell anisotropy with increasing grafting content. In solution, the hydrated polymer shells were markedly more extended and structurally anisotropic than suggested by dry-state techniques structural characterization, highlighting the importance of solution-state structural analysis for accurately describing grafted polymer architectures.

Core-shell biomaterials↗

DOE OSTI2026

Investigating Lignin Aggregation and Interactions with Solvents during γ-Valerolactone (GVL) Pretreatment: A Combined Small Angle Neutron Scattering and Molecular Simulations Study

The strong tendency of lignin to aggregate in solution, coupled with limited understanding of how its molecular structure governs this behavior, hinders its effective utilization in biorefineries. Here, in this study, we investigated the solution behavior of lignin extracted from poplar using γ-valerolactone/water (GVL/H2O, 9:1 wt/wt) through combined small-angle neutron scattering (SANS) and molecular dynamics (MD) simulations. Lignin samples obtained at 100 °C (L100) and 120 °C (L120) differed in β–O–4 content, hydroxyl distribution, and S/G ratio, enabling direct assessment of how molecular composition governs solvation and aggregation. SANS showed that L120 formed rigid and elongated cylindrical aggregates at 25 °C that transitioned to more flexible spheroidal structures by 50 °C and remained stable up to 80 °C, whereas L100 adopted globular aggregates that progressively collapsed with increasing temperature. MD simulations reinforced these observations by showing that S-rich (L120-like) oligomers had larger radii of gyration, stronger solvent coordination driven by methoxy groups, and fewer lignin–lignin contacts. In contrast, G-rich (L100-like) oligomers displayed persistent aggregation and lower solubility. Collectively, these results reveal that increased aromatic methoxylation enhances lignin–solvent interactions and suppresses self-association, whereas reduced methoxylation and higher β–O–4 content promote persistent aggregation into colloid-like structures with restricted solvent penetration into the aggregate interior.

biorefinery pretreatment↗

DOE OSTI2026

Quantitative SANS and multi-model analysis of spacer-dependent micellization of urea-based gemini surfactants

The micellization behavior of urea-based cationic gemini surfactants was investigated using small-angle neutron scattering (SANS) with multi-model form factor analysis. A homologous series of surfactants with urea group included in the hydrophobic tail and polymethylene spacers consisting of two to ten methylene units was analyzed using three form factor models: a core–shell ellipsoid and two variants of homogeneous ellipsoids. The results from all models show a consistent trend of the micelle structures, confirming that the spacer length critically influences micellar geometry, aggregation number, and hydration. The surfactant with four CH 2 groups in the spacer formed the largest micelles with the highest aggregation number, while longer spacers led to progressively smaller, more compact aggregates. The shell hydration—quantified as the volume fraction of heavy water within the hydrophilic region—decreased systematically with increasing spacer length due to enhanced hydrophobicity of the headgroup-spacer region. Intermicellar interactions, modeled as screened Coulomb interaction using the rescaled mean spherical approximation (RMSA), revealed the strongest electrostatic repulsion for the case of four methylene groups in the spacer, corresponding to the highest micellar charge and largest interparticle spacing. The observed spacer-dependent trends were robust across all modeling approaches, demonstrating that the spacer length serves as a key structural determinant of self-assembly in this type of urea-based gemini systems. These findings provide insight into the design of gemini surfactants with tailored aggregation behavior for applications in drug delivery, nanostructure templating, and solubilization technologies.

Core–shell ellipsoid model↗

DOE OSTI2026

Controlled Deuteration of Phosphatidylcholine Biosynthetically Produced from Engineered Escherichia coli for SANS Studies

Deuterated phosphatidylcholine (PC) was produced from engineered Escherichia coli (E. coli) BL21 cells grown in deuterated media. The levels of deuteration could be controlled by growing cells in different combinations of deuterated and nondeuterated water, glycerol, and choline, which were analyzed by NMR, mass spectrometric analysis, and small-angle neutron scattering (SANS). By growing cells in deuterium oxide (D2O) in the presence of fully deuterated glycerol and choline, perdeuterated PC (PC-DDD) was produced via this method. The average neutron contrast match points of isolated PC were experimentally determined using SANS. For partially deuterated PC lipids, SANS showed match points of 92 ± 8% D2O for lipids with deuterated fatty acyl chains and glycerol (PC-DDH) and 81 ± 2% D2O for lipids with only deuterated fatty acyl chains (PC-DHH). Our results will benefit SANS studies that utilize deuterated PC lipids as mimetics of lipid bilayers or membrane-like models for structural studies of biomolecular systems.

Zhang, Qiu [ORNL] (ORCID:0000000255064955)↗

DOE OSTI2026

Variable Surface Termination and Ligand Passivation of Lead Sulfide Nanocrystals Synthesized with Excess Lead Chloride

The surface termination and ligand passivation of semiconducting nanocrystals (NCs) impact the stability, optical properties, and self-assembly of NCs. In this work, we definitively characterize the surface of lead sulfide (PbS) NCs synthesized from excess PbCl 2 . With a combination of small-angle neutron scattering (SANS), photoluminescence, and 1D and 2D NMR experiments, we show that the surface termination of PbS NCs depends on the presence of PbCl 2 during ligand exchange. When excess PbCl 2 is removed prior to ligand exchange, PbS[RNH 3 + Cl – ] NCs are obtained, which are terminated by a monolayer of PbCl x on the {100} PbS facet and passivated by oleylammonium chloride ligands. On the other hand, when excess PbCl 2 remains in solution during ligand exchange, lead oleate forms and attaches to the {111} PbS facets of PbS[RNH 3 + Cl – ] NCs, creating PbS@PbCl x NCs. PbS@PbCl x NCs are coated in an epitaxial layer of PbCl x on both the {100} PbS and {111} PbS facets, making them 0.3–0.4 nm larger on average than PbS[RNH 3 + Cl – ] NCs with identical absorption wavelengths. Additionally, PbS@PbCl x NCs have a consistently higher photoluminescence quantum yield and longer photoluminescence lifetimes than PbS[RNH 3 + Cl – ] NCs. This study clarifies the surface structure of PbS NCs synthesized from excess PbCl 2 , highlighting ligand exchange strategies and reconciling observations from across the literature.

Anions↗

DOE OSTI2026

Reparameterizing a Lipid Force Field Using Small-Angle X-ray Scattering to Improve Predictions of Multicomponent Membranes under Organic Solvent Stress

Understanding and predicting properties of lipid-bilayer membranes are essential to elucidating organismal physiology and pathophysiology. Therefore, substantial efforts have been undertaken to derive accurate molecular-mechanics force fields (FF) to allow simulation of their properties; however, much of these past efforts focused on tuning force fields to accurately reproduce the properties of model single-component membranes and not multicomponent or stressed membranes. Here, we tuned the CHARMM36 FF for a simple 2-component model of a Gram-positive bacterium. This updated force field is parametrized against a single condensed-phase property, the small-angle X-ray scattering (SAXS) intensities of the 2-component lipid system, using a version of ForceBalance implemented previously (named ForceBalance-SAS) with SAXS and small-angle neutron scattering (SANS) intensities as optimization targets. After tuning, we observe improved agreement with the experimental SAXS of the membrane under 1-butanol and tetrahydrofuran solvent stresses, with a factor of 10.0 and 7.5 reduction, respectively, in χ 2 , the measure of the discrepancy between experimental and computed SAXS intensities. Furthermore, this reparametrized force field yielded improved agreement between experimental and simulated membrane thicknesses for the pure lipid systems. However, we note limitations in transferability and diagnose the source of such limitations, particularly the need for SANS in addition to SAXS.

Demerdash, Omar N. A. [Oak Ridge National Laborato↗

DOE OSTI2025

Molar-Mass-Dependent Partitioning of Polyethylene in Nanopores of Model Catalyst Supports from Small-Angle Neutron Scattering

Heterogeneous catalysis offers opportunities to enhance valorization of plastic waste via chemical recycling through control of the upcycled product distributions. Minimizing low-value light hydrocarbons is desired; however, fundamental insights into how to control selectivity are lacking. Here we use contrast variation with small-angle neutron scattering (SANS), model perdeuterated polyethylenes (dPEs), and a model liquid hydrocracking product (tetradecane) to quantify polymer partitioning within mesoporous silica (SBA-15). Polyethylene concentration within the mesopores is increased relative to the bulk solution, and this partitioning increases as the temperature increases. However, this polyethylene partitioning is maximized when the radius of gyration of the polymer chains is comparable to the SBA-15 pore size (10 nm). An increased partitioning at higher temperatures is attributed to entropically driven adsorption of PE within the mesopores. There is no observed preferential partitioning of hexatriacontane (a model oligomer) within the mesopores at the temperatures examined. Furthermore, these results suggest that pore size could promote the selective partitioning of polymer species into the mesopores by size. For plastic upcycling, pore-size-dependent partitioning should increase the probability for the reaction of long polymers over oligomeric and small-molecule polyolefin depolymerization products.

Adsorption↗

DOE OSTI2026

Melatonin-Induced Modulation of Cholesterol-Enriched Model Neuronal Membranes

Melatonin, a hormone primarily produced by the brain’s pineal gland, not only regulates circadian rhythms, but also influences the structural and biophysical properties of neuronal membranes. Its amphiphilic nature enables direct incorporation into lipid bilayers and preferential interactions with cholesterol-rich lipid rafts, critical hubs for cellular signaling and membrane organization. Despite increasing recognition of its membrane activity, the molecular basis of melatonin’s interactions with coexisting liquid-ordered (L o ) and liquid-disordered (L d ) phases remains unclear. Here, in this study, we combine small-angle neutron scattering (SANS) and all-atom molecular dynamics simulations to examine model neuronal membranes composed of DSPC, DOPC, POPC, and cholesterol. Our results show that melatonin preserves domain morphology while adopting distinct orientations within the bilayer and at the membrane interface, allowing both lateral and transmembrane bridging across lipid phases. These findings establish the molecular underpinnings of melatonin’s modulation of membrane heterogeneity and provide strong support for its receptor-independent actions.

atomistic simulations↗

DOE OSTI2026

Analysis of Small-Angle Neutron Scattering from Blends of Charged and Neutral Polymers Based on Rod–Coil Random Phase Approximation

Blends of charged and neutral polymers are of interest due to potential applications in rechargeable batteries. In this study, concentration fluctuations in blends of charged poly[lithium 3-(methacryloyloxy)propylsulfonyl-1-(trifluoromethanesulfonyl)imide] (PLiMTFSI) and neutral poly(ethylene oxide) (PEO) were investigated by small-angle neutron scattering (SANS). The scattering data were analyzed in the framework of the random phase approximation (RPA). Since ion dissociation can lead to stiffening, the charged polymers were approximated as rods, while the neutral polymers were assumed to be random coils. This approach works reasonably well at low weight fractions of charged polymers. For blends with higher weight fractions of the charged polymer, concentration fluctuations were highly suppressed, resulting in q-independent coherent structure factors that are inconsistent with the rod-coil RPA.

Lee, Jaeyong↗

DOE OSTI2025

Dynamical Signatures of Thermotoga maritima Maltose-Binding Proteins Affected by Ligand Binding

Functional segregation among protein isoforms depends on the interplay of their overall structures and the molecular dynamics of these structures. Thermotoga maritima maltose-binding protein (tmMBP) isoforms show size-dependent differential binding of maltose and malto-oligomers while maintaining remarkable fold conservation. This differential behavior needs detailed characterization in native-like aqueous conditions to understand the effects of protein dynamics on ligand binding and recognition. Small-angle neutron scattering (SANS), neutron spin echo (NSE) spectroscopy, and dynamic light scattering (DLS) were used in conjunction with previously published computational molecular dynamics (MD) simulations to understand the dynamic behavior of tmMBPs experimentally. SANS provided information on the overall structure of the molecules, while NSE was used to determine the dynamics in the nanosecond time scale. Both tmMBP2 and tmMBP3 have a bidomain architecture linked with a flexible hinge, with the binding pocket sitting in the cleft between the two domains. tmMBP2 and tmMBP3 showed different solution dynamics, with the translational and rotational components dominating the dynamics of both systems, resulting in a clear differentiation of their diffusion pattern. A faster dynamics component was also observed and was attributed to segmental dynamics. Differences observed between the ligand-free (apo) and ligand-bound (holo) states of the two proteins are attributed to conformational entropy. Our results highlight the intricacies of how structure and dynamics can together shape binding to a repertoire of substrates in structurally similar proteins.

Diffusion↗

DOE OSTI2026

Solubilization of PET in binary mixtures of HFIP and DCM

The dissolution of polyethylene terephthalate (PET) is a critical step for a solvent-based process, yet it typically requires highly corrosive or toxic solvents. Here, we investigate the solubilization and conformational behavior of PET in binary mixtures of hexafluoro-2-propanol (HFIP) and dichloromethane (DCM) as a strategy to reduce HFIP usage while maintaining effective dissolution. Small-angle neutron scattering (SANS) measurements reveal that PET remains molecularly dissolved in HFIP/DCM mixtures up to 50 vol% DCM. Analysis of PET chain conformations shows a transition from Gaussian behavior at low HFIP fractions to more swollen chains at intermediate compositions, accompanied by a counter-intuitive minimum in the radius of gyration at 50% HFIP. Complementary SANS measurements of the binary solvents demonstrate that compositional heterogeneity is maximized at this same solvent composition, suggesting a direct coupling between solvent microstructure and polymer dimensions. Molecular dynamics simulations corroborate the experimental findings, revealing solvent domain formation, preferential solvation of PET by HFIP, and a “caging” effect arising from solvent heterogeneity that leads to polymer coil compaction. Together, these results provide molecular-level insight into polymer behavior in mixed solvent systems and establish HFIP/DCM mixtures as a promising, more sustainable solvent platform for the PET post-process.

Arifuzzaman, Arif [ORNL]↗

DOE OSTI2026

Desmearing Bonse–Hart USANS data using Bayesian Gaussian process regression

Ultra-small-angle neutron scattering (USANS) enables access to micrometer-scale structures but is intrinsically affected by strong, anisotropic resolution smearing arising from slit-geometry optics. As a result, recovery of the intrinsic scattering intensity constitutes an ill-posed inverse problem, and commonly used iterative desmearing methods lack rigorous uncertainty quantification. We present a Bayesian desmearing framework for slit-geometry USANS based on Gaussian process regression. In this approach, the scattering intensity is modeled as a smooth random function, and the instrumental point spread function is incorporated explicitly as a forward operator. The resulting formulation yields a closed-form maximum a posteriori solution with well-defined credibility intervals. Computational benchmarks and experimental validation using combined USANS and small-angle neutron scattering (SANS) measurements demonstrate that the framework enables stable desmearing, suppresses experimental noise, and preserves physically meaningful structural features under realistic conditions.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2026

An algebraic convolution formulation for multiple-scattering correction in small-angle neutron scattering

Multiple scattering in small-angle neutron scattering (SANS) redistributes spectral weight and distorts structural interpretation, particularly for thick or strongly scattering samples. We develop a finite-dimensional spectral desmearing framework that corrects multiple scattering without resorting to integral transforms or model-dependent extrapolation. The primary intensity is expanded in an orthonormal basis adapted to the isotropic transverse-momentum measure, under which convolution reduces to a recursive tensor contraction, allowing the Poisson-weighted multiple-scattering series to be evaluated directly in a finite-dimensional basis representation. This formulation yields a stable forward–inverse mapping between apparent and primary spectra. Numerical tests demonstrate convergence under repeated convolution and accurate recovery of the single-scattering intensity. Application to SANS measurements collected at multiple neutron facilities, including the Spallation Neutron Source, the High Flux Isotope Reactor, and the Institut Laue-Langevin, shows the quantitative reconstruction of the underlying primary spectrum across a wide range of transmission conditions, including strongly attenuating samples. Here, the method provides a stable, model-agnostic framework for multiple-scattering correction in SANS and enables consistent structural interpretation across instruments and scattering regimes.

Tung, Chi-Huan [Oak Ridge National Laboratory (ORN↗

DOE OSTI2026

Correlation-aware binning for small-angle neutron scattering via Gaussian-process inference

Binning in small-angle neutron scattering (SANS) is typically performed empirically, with fixed parameters chosen for convenience rather than statistical optimality. Such practices often fail to balance statistical precision and spatial resolution, leading to inconsistencies across instruments and datasets. Here we establish a correlation-aware framework that determines the optimal bin width from first principles by extending the classical Freedman–Diaconis (FD) rule to account for inter-bin correlations with a Gaussian process. In this formulation, the scattering intensity is treated as a smooth stochastic field whose statistical coherence is described by a covariance matrix. Analytical expressions of errors derived from this model yield closed-form criteria that separate the total deviation into contributions from counting noise, aliasing distortion and curvature-dependent correlation effects. Expressed in reduced variables, the resulting dimensionless error surface reveals a continuous transition from the uncorrelated FD regime to the correlation-dominated limit, providing a unified description of noise suppression and resolution control. Because the formulation depends only on the profile characteristics of scattering intensity I(Q), specifically its average intensity and first- and second-order derivatives, it applies generally to any SANS measurement regardless of sample, instrument or geometry. Experimental validation using small- and ultra-small-angle neutron scattering data confirms the predicted scaling behavior, demonstrating that correlation-aware inference systematically reduces mean-squared error and enables information-efficient reproducible data reduction across materials and instruments.

Tung, Chi-Huan [ORNL] (ORCID:0000000221972074)↗

DOE OSTI2025

Toward Thermally Stimuli-Responsive Polymeric Vesicles Fabricated by Block Copolymer Blends for Nanocarriers

Polymeric vesicles, characterized by enhanced colloidal stability, excellent mechanical properties, controllable surface functionality, and adjustable membrane thickness, are extremely useful in nano- and bio-technology for potential applications as nanosized carriers for drugs and enzymes. However, a few preparative steps are necessary to achieve a unilamellar vesicle with a narrow size distribution. Herein, we report the spontaneous formation of unilamellar polymeric vesicles with nanometer sizes (<50 nm), fabricated by simply mixing diblock copolymers (P(EO-AGE)(2K-2K) and P(EO-AGE)(0.75K-2K)) with differing hydrophilic mass fractions in aqueous solutions. Depending on the mixing ratio of block copolymers and the temperature, the block copolymer mixtures self-assemble into various nanostructures, such as spherical and cylindrical micelles, or vesicles. The self-assembled structures of the block copolymer mixtures were characterized by small-angle neutron scattering, resulting in a phase diagram drawn as a function of temperature and the mixing condition. Notably, the critical temperature for the micelle-to-vesicle phase transition can be easily controlled by altering the mixing conditions; it decreases with an increase in the concentration of one of the block copolymers.

block copolymers↗

DOE OSTI2025

Concentration-Driven Slowdown of Chain-Exchange Kinetics in Block Copolymer Micelle Solutions

Here, we investigate the dependence of chain-exchange kinetics on polymer concentration for spherical micelles prepared from a polystyrene-b-poly(ethylene-alt-propylene) (SEP) diblock copolymer ( M n = 75 kDa, Ð = 1.05, and f PS = 0.18) in the PEP-selective solvent squalane. Solutions with concentrations of 15 vol% or more adopt a body-centered-cubic (BCC) packing of micelles, or a dense liquid-like packing (LLP), as confirmed by small-angle X-ray scattering. Concurrently, the mean aggregation number of the micelles grows steadily from about 60 in dilute solution to nearly 200 by 50 vol%. Time-resolved small-angle neutron scattering (TR-SANS) analysis reveals a monotonic and substantial (i.e., more than four orders of magnitude) decrease in the rate of chain exchange as the polymer concentration increases from 1 to 50 vol%. The TR-SANS relaxation functions are analyzed, taking into account both changes in contrast (due to chain exchange) and evolution in the structure factor (due to refinement of micelle packing). The activation energy for chain pullout is extracted using an established model and can be expressed as a linear function of polymer concentration, indicating that, in addition to the enthalpic barrier for extracting the core block, the evolution of micelle characteristics with increasing concentration imposes further constraints on chain exchange. Consistent with a theory of Halperin, these results suggest that the dominant factor reflects steric penalties during core block pullout arising from a reduced interfacial area per chain and associated increased corona crowding, due to the increase in aggregation number. The rate of exchange is independent of whether the micelles adopt a BCC or LLP arrangement, confirming that the rate-limiting step is extraction of the core block.

chemical structure↗

DOE OSTI2026

Signatures of Thermoreversible Associations in X-ray and Neutron Scattering from Dilute Polyzwitterion Solutions

In aqueous solutions of polyzwitterions (PZs), an interplay between dipole–dipole interactions and hydration of zwitterionic groups can lead to thermoreversible associations, which have been difficult to detect in experiments. Here, in this study, we investigated dilute aqueous solutions of poly(1-(3-sulphonatopropyl)-2-vinylpyridinium) (P2VPPS) using small-angle X-ray and neutron scattering (SAXS and SANS) to probe the structure and neutron spin-echo (NSE) spectroscopy to probe dynamics. The SAXS and SANS data show that the correlation length increases with an increase in the concentration of P2VPPS for three different molecular weights. The addition of 0.1 M NaCl to one of the solutions led to almost no dependence of the correlation length on the concentration. Such a concentration dependence of the correlation length suggests the formation of clusters driven by thermoreversible associations in the solutions. The NSE measurements show that the solutions with a larger correlation length display slower relaxation, reflecting the reduced mobility of larger clusters. These results should be considered as signatures of thermoreversible associations in the solutions of P2VPPS. To establish a quantitative link between local structure (clusters) and dynamics in dilute solutions of P2VPPS, we combined a thermoreversible gelation theory for the structure of PZ solutions (Li, S.-F.; Muthukumar, M. Theory of Thermoreversible Gelation and Anomalous Concentration Fluctuations in Polyzwitterion Solutions. J. Chem. Phys. 2024, 161, 024903) with a model for the dynamics of the clusters (generalized Zimm model), developed in this work. Using such a theoretical framework, we have predicted the distribution of clusters in the solutions probed with SANS and SAXS. With the distributions, the generalized Zimm model has been used to extract the diffusion constant of the clusters and their characteristic size from the NSE data, where the latter agrees with the values estimated from the SAXS/SANS data. These findings confirm the presence of thermoreversible associations and establish a quantitative link between local structure (clusters) and dynamics in dilute solutions of P2VPPS. Furthermore, with growing interest in technological applications, this work can provide useful insights into the structural and dynamical properties of other PZ solutions.

field theory↗