Molecular insights into the selective interaction of endocrine-disrupting chemicals with poly(mannuronate) in aqueous systems: a multiscale computational study

Abstract

Estrogens and other steroid hormones, also known as endocrine-disrupting chemicals (EDCs), are emerging contaminants in wastewater effluent due to human activities. Although these compounds play essential roles in medical treatments and modern agriculture, their release into the environment has raised concerns because of their potential ecological and health impacts. The selective removal of EDCs from aqueous environments is a challenge due to competition with water molecules for binding sites. This work presents a systematic computational investigation of the intermolecular interactions and phase equilibria of selected EDCs and water in the presence of poly(mannuronate), a principal component of the brown-algae-derived biopolymer alginate, with the key goal of informing the design of polysaccharide-based materials for water remediation. Atomistic molecular dynamics simulations were coupled with stochastic calculations and extended off-lattice Flory–Huggins theory to assess polymer flexibility, penetrant-polymer coordination numbers, binding energies, and binary phase equilibria. To complement thermodynamic analysis, quantum chemical calculations were performed on representative low-energy configurations. Results showed that both the quantity and spatial positioning of species bound to alginate can be tuned via the relative proportions of guluronate versus mannuronate blocks constituting the polymer, providing a pathway for optimizing binding selectivity. Frontier molecular orbital analysis revealed distinct donor–acceptor characteristics for mannuronate–EDC complexes compared to mannuronate–water systems. These variations result in lower Flory–Huggins interaction parameters and enhanced thermodynamic compatibility of EDCs with the polymer matrix, suggesting preferential association in aqueous environments. Overall, this study provides molecular-level insights into the rational design of materials for the selective removal of EDCs from water systems.

Multiscale simulations reveal how flexible poly(mannuronate) selectively interacts with endocrine-disrupting chemicals (EDCs) over water, providing molecular design principles for tuning alginate block chemistry for wastewater remediation.

1. Introduction

Despite existing experimental and computational research on alginate-based materials for environmental applications, a detailed molecular-level understanding of how specific alginate block chemistries interact with endocrine-disrupting chemicals (EDCs) remains limited. In particular, the electronic structure, intermolecular energetics, and macroscopic thermodynamics compatibility in poly(mannuronate)–EDC systems have not been comprehensively addressed. The current work employed a multiscale computational framework to study the intermolecular interactions and phase behavior of selected EDCs and water with the poly(mannuronate) part of alginate.

EDCs are classified as emerging contaminants (EC), meaning pollutants of growing environmental concern. These compounds are of significant concern due to their association with endocrine and reproductive disorders in both humans and wildlife, especially aquatic organisms.^1,2 Increasing contamination of water bodies has been attributed to the discharge of these agents from pharmaceutical sources via domestic, industrial, and healthcare effluent.³ Reported concentrations in water typically range from 10⁻⁹ to 10⁻⁶ g L⁻¹,^4,5 posing risks to the availability of clean water necessary for commercial and household use. It can be noted that some of these EDCs are endogenous steroid hormones (e.g., estradiol, estrone, estriol, testosterone, and progesterone) that occur naturally but exhibit endocrine-disrupting activity in environmental contexts at trace concentrations, while others (e.g., diethylstilbestrol, ethinylestradiol, and mestranol) are synthetic compounds of pharmaceutical or industrial origin. The ecological and human health consequences of EDC contamination are well-documented, with particular concern for low-dose and non-monotonic dose–response effects that may not follow classical toxicology paradigms.^6,7

A variety of strategies have been investigated to remove or degrade ECs, including adsorption, nanofiltration, reverse osmosis, coagulation, flocculation, and oxidation.⁸ However, each approach presents limitations. For example, activated carbon-based adsorbents such as granular activated carbon (GAC) and powdered activated carbon (PAC) are among the adopted technologies in the removal of emerging contaminants, including EDCs, from drinking water and wastewater.⁹ This is due to their high specific surface area and well-developed pore structure, leading to their adsorption capacity.^10,11 However, the presence of natural organic matter (NOM), dissolved organic carbon, inorganic ions, and competing micropollutants can occupy active adsorption sites, block micropores, or compete with target contaminants for adsorption, thereby reducing adsorption capacity and selectivity.^12,13 Biochar has emerged as a more promising alternative due to its low cost, high surface area, and favorable binding capacity for compounds such as estradiol.^14,15 Although coagulation and flocculation are widely used for removing organic pollutants from wastewater,¹⁶ they are generally less effective for EDC removal.¹⁷ Oxidative treatments show potential for degrading ECs, but they generate harmful by-products.¹⁸ Reverse osmosis can achieve near-complete removal of EDCs;¹⁹ however, its practical application is constrained by high energy demands.²⁰ To overcome these limitations, there is a growing interest in the development of complementary adsorbent materials capable of providing enhanced molecular selectivity, improved regeneration characteristics, and tailored intermolecular interactions. Biopolymer-based adsorbents such as alginate represent one such promising class of materials due to their unique structural morphology.²¹

Mannuronate (M), together with guluronate (G), forms the polysaccharide alginate,²² which is primarily extracted from brown algae. Alginate is a linear copolymer composed of three block types: MM, GG, and alternating MG sequences. MM blocks exhibit flexibility, GG blocks are relatively rigid due to steric hindrance, and MG blocks are the most flexible owing to equatorial-axial linkages.²² Mannuronate repeats in MM blocks that adopt the ⁴C₁ chair conformation with diequatorial substituents, conferring greater linear flexibility and conformational accessibility.²³ Guluronate repeats in GG blocks that predominantly adopt the rigid ¹C₄ chair conformation with diaxial substituents. Alternating MG/GM blocks adopt mixed equatorial-axial conformations that exhibit the greatest conformational flexibility. Owing to its favorable physicochemical properties, alginate is widely used in pharmaceuticals, biomedicine, food products, paper production, and textile printing.²⁴ It is also cost-effective, non-toxic, biocompatible, and capable of reversible sol–gel transitions, making it attractive for diverse applications.²⁵Fig. 1 illustrates the mannuronate repeat unit, which, together with guluronate, constitutes the monomeric structure of alginate.

Fig. 1. Molecular structure of the mannuronate repeat unit, which, together with guluronate, forms the monomers constituting alginate. The atoms are color-coded as follows: grey = carbon, red = oxygen, white = hydrogen. The black arrows indicate the attachment points for polymerization. The carbon atoms are numbered. At the bottom is a scale bar in Å.

Alginate-based systems are also well established in drug delivery applications,^26,27 where polysaccharides are used to encapsulate bioactive agents. Polysaccharides containing complex monosaccharides offer numerous cross-linking sites, enhancing drug encapsulation efficiency and enabling controlled release.²⁸ More recently, alginate has also been explored for the removal of pollutants from aqueous media. Studies have examined its effectiveness in capturing arsenic,²⁹ bisphenol A,³⁰ and estrogenic compounds,³¹ largely due to its sorption capacity and favorable intermolecular binding characteristics.³⁰

In this study, a multiscale computational framework was employed to investigate the intermolecular interactions and phase behavior of selected EDCs and water in poly(mannuronate) systems. Atomistic molecular dynamics simulations were first conducted to determine the cohesive energy density and solubility parameter of poly(mannuronate), enabling identification of the minimum chain length required for a realistic thermodynamic description. Subsequently, stochastic thermodynamic modelling based on the Flory–Huggins approach, combined with density functional theory calculations, was used to develop an integrated multiscale description of poly(mannuronate) interaction with each penetrant molecule. Although the methodology builds upon the previously multiscale framework,³¹ the present work elucidates how alginate block chemistry governs adsorption selectivity. By investigating poly(mannuronate), which exhibits better conformational flexibility than poly(guluronate), this study establishes the molecular mechanism linking polymer structure, intermolecular energies, electronic structure, and macroscopic phase behavior, thereby providing predictive design principles for turning MM/GG block composition in alginate-based adsorbents.

2. Methods

2.1. Calculation workflow

The calculations undertaken in this study are modular and can be divided into three parts: atomistic molecular dynamics simulations (see Section 2.2), atomistic stochastic volume-constraint computations (see Section 2.3), and quantum-chemical calculations (see Section 2.4). The two atomistic components are almost entirely separate, with the molecular dynamics simulations being used to generate an input integer variable (i.e., the polymer chain length suitable for a realistic description on the basis of the cohesive energy density, as outlined in Section 2.2) for a post-processing calculation undertaken to generate phase equilibrium diagrams. Fig. 2 presents a block flow diagram outlining the calculation workflow employed in this study.

Fig. 2. Block flow diagram illustrating the modular nature of the calculation workflow used in this study.

The stochastic volume-constraint calculations are entirely separate from the molecular dynamics calculations and are used to generate mixing energies, coordination numbers, and the Flory–Huggins parameter as a function of temperature. In effect, atomistic molecular dynamics simulations, atomistic stochastic volume-constraint computations, and quantum-chemical calculations are executed in parallel, after which post-processing calculations within the Flory–Huggins framework yield phase equilibria based on the results of the volume-constraint and molecular dynamics computations. The stochastic volume-constraint calculations and the quantum-chemical computations, on their own, yield a range of data of interest for this study, independent of each other and of the molecular dynamics simulations.

2.2. Cohesive energy density from molecular dynamics

This study builds upon previous investigations^31–33 that employed stochastic Monte Carlo simulations^34–36 to sample the configurational space of pollutant-adsorbent systems. Those approaches enabled the evaluation of thermodynamic properties such as mixing energies and coordination numbers, ultimately allowing the construction of phase diagrams. In the present work, all atomistic simulations were performed using the COMPASS force field (version III)³⁷ to describe both inter- and intramolecular interactions, consistent with its successful application in previous studies of EDCs interacting with polymers.^31–33 The COMPASS family of force fields has been developed and validated through fits to quantum-mechanical observables together with experimental liquid and crystal data, and provides explicit partial atomic charges and dispersion terms that facilitate a reasonable description of interactions that are, relatively speaking, weak, such as hydrogen bonding and donor–acceptor coupling.^38,39 The force field has been applied, with acceptable accuracy, to amorphous cellulose and polypropylene–cellulose biocomposites, yielding densities and mechanical properties consistent with experimental values.^40,41 On this basis, the interaction trends reported in this contribution can be taken as a reasonable reflection of physical features rather than force field artifacts.

Amorphous polymer models were generated using the Amorphous Cell module in Materials Studio 2020.⁴² Initial structures were packed to a target density of 1000 kg m⁻³ (comparable to sodium alginate) using a configurational-bias packing algorithm.^43–45 To satisfy the minimum-image convention,⁴⁶ simulation boxes were built with dimensions of at least 28 Å in all directions, ensuring compatibility with a 12 Å cut-off radius for dispersive van der Waals interactions, as adopted in recent work.^36,37,47 The constructed cells were subsequently geometry-optimized using the Smart algorithm^48–50 for 5 × 10³ steps, applying the following convergence criteria:

• Energy – 8.37 × 10⁻⁵ kJ mol⁻¹

• Force – 4.184 kJ mol⁻¹ Å⁻¹

• Displacement – 1.0 × 10⁻⁵ Å

The initial cubic simulation cells generated via this approach were as follows for each polymer chain length (N);

• N = 10 – 30 polymer molecules (6360 atoms)

• N = 20 – 15 polymer molecules (6330 atoms)

• N = 50 – 6 polymer molecules (6312 atoms)

• N = 100 – 3 polymer molecules (6306 atoms)

• N = 200 – 2 polymer molecules (8404 atoms)

• N = 300 – 1 polymer molecule (6302 atoms)

Following optimization, molecular dynamics simulations were carried out using the Forcite module of Materials Studio 2020. The polymer cells were first subjected to simulated annealing in the canonical (i.e., NVT) ensemble using the Berendsen thermostat⁵¹ with a decay constant of 0.1 ps. Annealing was performed over 5 cycles spanning 298–500 K, with five temperature ramps per cycle, for a total duration of 1 ns. After annealing, each system underwent a minimum of 1 ns of molecular dynamics in the canonical NVT ensemble at 298 K using the Berendsen thermostat, followed increments of 2 ns of equilibration in the isothermal–isobaric (NPT) ensemble at 298 K and 100 kPa, employing the Berendsen thermostat and barostat.⁵¹ It was observed that the simulations involving longer polymer chains (N ≥ 50) typically took up to 6 ns of NPT molecular dynamics to achieve equilibrium.

Production simulations were then conducted in the NVT ensemble for 5 ns using the Nosé–Hoover thermostat,^52–55 with configurations sampled every 5 ps. These sampled configurations were used to compute cohesive energy densities. All reported dynamical properties were averaged over configurations obtained from three independent simulation runs. Upon completion of the molecular dynamics simulations, the cohesive energy density CED was determined from the sampled configurations by calculating the ensemble-averaged non-bonded intermolecular energy E_inter^56–61 and dividing by the system volume V:

1

The solubility parameter, δ_p, was obtained as the square root of the cohesive energy density. By examining the dependence of δ_p on the number of repeating units in the polymer chain, the minimum chain length required for a thermodynamically representative model could be identified,⁶² since δ_p typically converges as chain length increases. Convergence within each simulation was assessed by examining the energy of the system, the root mean square deviation (RMSD), and radius of gyration. These results are presented in Fig. 3 and Table 1

Fig. 3. Trajectories of energies for polymer chain lengths N during production runs: (a) N = 10, (b) N = 20, (c) N = 50, (d) N = 100, (e) N = 200, (f) N = 300. Colours are as follows: black = potential energy, blue = kinetic energy, green = non-bond energy, magenta = total energy.

Table 1. Root mean square deviation (RMSD), radius of gyration (r_g), and total energy (E_tot) results for each chain length N. The results are reported as mean ± standard deviation generated during the production runs.

	RMSD (Å)	r g (Å)	E tot (kJ mol−1)
N = 10	0.723 ± 0.050	25.037 ± 0.017	51 839 ± 354
N = 20	0.777 ± 0.048	28.473 ± 0.022	53 253 ± 351
N = 50	0.750 ± 0.043	33.675 ± 0.020	54 320 ± 370
N = 100	0.784 ± 0.053	53.326 ± 0.019	55 009 ± 361
N = 200	0.906 ± 0.076	55.469 ± 0.017	73 492 ± 411
N = 300	0.823 ± 0.052	54.840 ± 0.020	55 209 ± 364

2.3. Stochastic simulations and Flory–Huggins calculations

The mixing behavior and consequently phase equilibria of water and selected EDCs (estradiol, estriol, estrone, ethinylestradiol, diethylstilbestrol, mestranol, testosterone, and progesterone) with poly(mannuronate) were evaluated using a multistage computational strategy. Initially, the geometries of the light penetrant molecules (water and EDCs) and mannuronate monomers were optimized using the Smart algorithm for up to 5 × 10³ steps under the previously defined convergence criteria. During this stage, the attachment sites corresponding to polymer repeating units were specified. In practice, convergence was typically achieved within the first 500 steps.

Subsequently, an extended Flory–Huggins framework^63–65 was applied to determine the mixing energy E_mix, the coordination numbers, and free energies. These quantities were obtained by sampling energetically favorable configurations using the volume constraint method, thereby generating ensemble-averaged thermodynamic properties. After evaluating temperature-dependent interaction parameters, binodal and spinodal curves were constructed using the off-lattice formulation of Flory–Huggins theory, which also enables direct determination of critical points.

For coordination number calculations, 10⁵ cluster samples were generated with 10³ iterations per cluster. Mixing energies were computed from 10⁷, employing an energy histogram bin width of 0.0837 kJ mol⁻¹. All calculations were performed at a reference temperature of 298.15 K. The extended Flory–Huggins technique used in this study is implemented in the Blends module of Materials Studio and has been previously applied to systems involving small penetrant molecules interacting with polymers.^30,31,47,66 This approach enables the construction of binary phase diagrams of water + poly(mannuronate) and EDCs + poly(mannuronate)systems.

Within the extended Flory–Huggins approach,^63–65 the Gibbs free energy change of mixing (ΔG_mix) for a binary system is expressed as:

2

in which ϕ is the volume fraction, N is the degree of polymerization, χ is the Flory–Huggins interaction parameter, and T is the temperature. The appropriate value of N was determined by assessing the convergence of the solubility parameter δ_p with respect to the number of repeating units N following molecular dynamics simulations, as described above. The Flory–Huggins parameter χ is given as derived from the mixing energy E_mix as computed from stochastic simulations:

3

Within the original framework of Flory–Huggins' theory, E_mix was computed using the binding energies E for each pairwise interaction, coupled with the coordination number Z:

4

Each pairwise binding energy E is calculated via averaging over an ensemble of configurations, and the associated coordination number Z is determined using an off-lattice approach. Therefore, eqn (3) ultimately becomes:

5

The Flory–Huggins parameter χ, therefore, possesses an implicit temperature dependence, which gives rise to phase equilibrium diagrams via calculation of the changes in free energy.

It should be emphasized that the formulation of the off-lattice extended Flory–Huggins approach^64,65 relaxes the random-mixing assumption of the original lattice model by sampling energetically favourable configurations under a volume constraint (i.e., excluded volume). Consequently, orientation-dependent and spatially specific interactions, such as hydrogen bonding, are explicitly captured through the atomistic force fields that yield configurationally-resolved binding energies and coordination numbers that appear in eqn (5). Therefore, this extension of Flory–Huggins theory is appropriate for systems in which specific intermolecular interactions are important, despite the bulk thermodynamic character of the resulting interaction parameter χ.

2.4. Quantum chemical calculations

Density functional theory (DFT) as implemented in the DMol³ module of Materials Studio 2020 was used to investigate the electronic structure and interaction energies of mannuronate–EDC complexes. The initial geometries were obtained from low-energy configurations of the stochastic mixing simulations (Section 2.2). The calculations adopted the double numerical polarization (DNP) basis set,⁶⁷ and the exchange–correlation functional employed was the Generalized Gradient Approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE), effective for noncovalent interactions in organic molecular complexes such as those formed between mannuronate and EDCs.⁶⁸ Grimme's DFT-D method was used for dispersion corrections to account for long-range van der Waals interactions, which are important in sorption and polymer interactions.⁶⁹

Geometry optimizations were performed with convergence criteria set to 2 × 10⁻⁵ Ha for total energy charge, 0.004 Ha Å⁻¹ for maximum force, and 0.005 Å for maximum displacement. Following optimization, interaction energies were calculated and corrected for both zero-point vibrational energy (ZPVE) and the counterpoise-corrected (CPC) basis set superposition error (BSSE) to provide more accurate estimates of complex stabilization. Inclusion of ZPVE and BSSE in binding energy calculations can influence the computed interaction energies and need be accounted for to avoid overestimation due to basis set overlap and to capture vibrational contributions to binding.^70,71 ZPVE corrections were obtained from vibrational frequency calculations at the same level of theory, which accounted for vibrational contributions to the total energy.⁷⁰ BSSE corrections were taken into account using the CPC method.⁷²

The final corrected interaction energies E were derived as:

E₀ = E_elec + ZPVE 6

where E_elec is the total electronic energy of the system.

ΔE^cpc = E₀ (conplex) −∑E₀ [mannuronate (EDC) + EDC (mannuronate)] 7

where E₀ [mannuronate (EDC)] is the energy of mannuronate in the presence of the basis function of EDC, while E₀ [EDC (mannuronate)] is the energy of EDC in the presence of the basis function of mannuronate. To obtain a deeper understanding of the physical origin of intermolecular stabilization, electrostatic energy,⁷³ DFT-D dispersion energy,^74,75 Hirshfeld,⁷⁶ and Mulliken⁷⁷ charge analyses were evaluated from the resulting DFT calculations. To further characterize the nature of the intermolecular interactions in real space, reduced density gradient (RDG) and non-covalent interaction (NCI)⁷⁸ analyses were performed using Multiwfn 3.8,^79,80 making use of the formatted checkpoint wavefunctions generated, employing the Gaussian 16 package⁸¹ (B3LYP functional and 6-31g basis set).

3. Results and discussion

3.1. Solubility parameter

Fig. 4 shows the solubility parameter δ_p as a function of polymeric chain length N_p of poly(mannuronate), as derived from the cohesive energy density estimated from dynamical simulations. It is apparent that, as expected, δ_p tends to an asymptotic value with increasing N_p. Similar to previous work,^31,66 one can observe that the solubility parameter converges well before the largest polymer chain length considered in the molecular dynamics simulations. In the present study, convergence to within 2% of the asymptotic value of δ_p was achieved for the range N_p ≥ 50. Hence, a chain length of 50 monomers was used in subsequent extended Flory–Huggins calculations.

Fig. 4. Solubility parameter δ_p of poly(mannuronate) as a function of polymeric chain length N_p. Where they are not visible, the error bars are smaller than the symbols. The lines between the points are guides for the eye. The red horizontal dashed line is the estimated asymptote for N_p → ∞. The dotted red horizontal lines indicate a band of ±2% deviation from the asymptotic value.

It may be noted that the density of simulated poly(mannuronate) at a chain length of 50 monomers was approximately 1.13 g cm⁻³, which is comparable to the value of 1.122 g cm⁻³ obtained for poly(guluronate) in a previous study,³¹ which is also similar to the reported density of 1 g cm⁻³ for commercial alginate.⁸² 50 monomers are evidently sufficient for mannuronate chains, polymer chains 200 monomers long or more were reportedly needed for guluronate,³¹ which can be attributed to the greater flexibility of MM blocks as compared to GG blocks.²²Fig. 5 shows a snapshot of a 50 monomer-long poly(mannuronate) system derived from the molecular dynamics simulations presented in this study.

Fig. 5. Snapshot of an equilibrated poly(mannuronate) simulation cell with a chain length of 50 monomer units. The atoms are color-coded as follows: grey = carbon, red = oxygen, and white = hydrogen. Atoms that are highlighted in pink for the backbone of the polymer chains. The box in the center of this snapshot shows the nominal boundaries of the simulation cell, while a scale bar in Å is shown below.

3.2. Binary phase equilibria

As outlined in Section 2, stochastic atomistic computations were integrated with an extended Flory–Huggins framework to evaluate the phase equilibria for binary mixtures comprising poly(mannuronate) and individual penetrant molecules (water and EDCs). The resulting temperature–composition phase diagrams are shown in Fig. 6.

Fig. 6. Binary phase diagrams for each penetrant molecule with poly(mannuronate) for a chain length of 50 monomer units: (a) water, (b) estradiol, (c) estrone, (d) diethylstilbestrol, (e) mestranol, (f) progesterone, (g) testosterone. The phase diagrams are in terms of temperature T and mole fraction of penetrant species x. The solid lines are the binodal curves, and the dashed lines are the spinodal curves. The red dots are the critical points (i.e., the conditions where the polymer and penetrant species become miscible). The blue triangle refers to data from the literature.⁸³.

The first point to note is that the phase diagrams shown in Fig. 6 are purely for binary phase equilibria between two amorphous phases, and naturally, temperatures associated with other phase changes (such as liquid → vapor) may effectively truncate some phase diagrams at appropriate temperature values. A second point to note is the challenge of presenting a comparison with available experimental data. For estradiol sorption in Fe₃O₄/biochar@sodium alginate beads, a peak capacity of 276.3 mg g⁻¹ was measured,⁸⁴ whilst for ethinylestradiol in activated carbon/sodium alginate beads, a sorption capacity of approximately 0.42 mg g⁻¹ was observed.⁸⁵ In this study, the sorption capacity for estradiol in mannuronate was found to be 28.2 mg g⁻¹, whilst for ethinylestradiol + mannuronate, estradiol + guluronate,³¹ and ethinylestradiol + guluronate,³¹ there was no observed phase equilibria (i.e., complete miscibility/immiscibility).

In practice, alginate serves as an encapsulation material for biologically active compounds (such as in pharmaceutical therapies)⁸⁶ or as a hydrogel support material for adsorbent materials (in environmental remediation, for instance).⁸⁷ This arises due to differences in hydrophobicity/hydrophilicity between steroid hormones and alginate, resulting in low sorption capacity on its own. The disparity between Fe₃O₄/biochar@sodium alginate beads and pure mannuronate (a difference of an order of magnitude) aligns with this aspect. However, it can be noted that there is a favorable comparison in terms of published experimental data for water sorption in alginate⁸³ as shown in Fig. 6(a). The qualitative alignment of expectations for sorption of steroid hormones with alginate, with observations from this study, coupled with quantitative agreement between this study and experimental data for water + alginate, suggests that the force field descriptions of the species in question are generally robust.

When assessing the Connolly surface area or volume, or the ratio of surface area to volume,⁸⁸ no clear physicochemical description among the analyzed compounds permits straightforward grouping according to the number of critical points in partially miscible binary mixtures with poly(mannuronate). The flexibility of chains composed exclusively of mannuronate (M) repeating units may generate a more intricate and nuanced free energy landscape, thereby complicating such categorization. Consequently, for EDCs + mannuronate systems, detailed atomistic-level calculations of penetrant + polymer interactions appear essential for reliable prediction of miscibility and phase behavior. Examination of the intermolecular energy distribution and electronic structure provides more insights in this regard.

3.3. Intermolecular energy distribution

Fig. 7 shows the energy distributions derived from stochastic mixing computations. The potential energy shown in this figure corresponds to the binding energies in eqn (4) and (5). The attractive potential energy for all EDCs with mannuronate is greater than for water with mannuronate, as evidenced by the tendency for the potential energy to take on more negative values for the EDCs than for water. It can be noted that the potential energy distribution for water + mannuronate is comparable to water + guluronate (see ref. 31). There is a broader range of possible potential energies for water + mannuronate compared to water + guluronate, and the intermolecular interactions are generally more attractive for mannuronate than for guluronate. Thereby indicating that the EDCs examined in this study will bind more strongly to MM blocks in alginate than to GG blocks. Hence, to improve the loading of the polymer, both for the purposes of pharmaceutical therapies and water treatment, alginate containing a higher proportion of MM blocks than GG blocks is desirable. This aspect also indicates that the quantity of estradiol, testosterone, etc., bound to alginate chains can be tuned by adjusting the ratio of MM and GG blocks in the polymer.

Fig. 7. Distributions of potential energy E_p in terms of probability density p(E) for each penetrant species with mannuronate: (a) water, (b) estradiol, (c) estriol, (d) estrone, (e) ethinylestradiol, (f) diethylstilbestrol, (g) mestranol, (h) progesterone, and (i) testosterone.

The potential energy curves for water + guluronate and water + mannuronate are extracted and shown together in Fig. 8. As was the case with water + guluronate,³¹ there is a roughly bimodal distribution in terms of the potential energy, as indicated in Fig. 7(a). The two peaks occur at approximately −10 kJ mol⁻¹ and −17 kJ mol⁻¹, which is comparable to the peaks observed for water + guluronate (i.e., −7 kJ mol⁻¹ and −15 kJ mol⁻¹). Overall, it can be noted that water molecules are less restricted in terms of favorable potential energy values of spatial configurations when interacting with mannuronate than with guluronate. This suggests that the steric effects of GG blocks limit water molecules to a narrower range of different configurations that are less energetically attractive than is the case for MM blocks in alginate.

Fig. 8. Potential energy distributions for water + mannuronate and water + guluronate,³¹ expressed in terms of the potential energy E_p and the probability density p(E).

For the EDCs examined in this study, clear differences in potential energy distributions are evident. In the case of mannuronate, the energy distributions are notably narrower, indicating a more limited set of energetically favorable configurations for EDC molecules near mannuronate chains compared with guluronate.

At the same time, the interaction energies are generally more negative, indicating stronger attractions for EDCs with mannuronate than with guluronate, except for ethinylestradiol, which shows similar behavior in both systems. Taken together, these findings suggest that EDC compounds preferentially associate with MM blocks of alginate rather than GG blocks, except in the case of ethinylestradiol.

Furthermore, the energetic landscape around MM blocks appears to promote more well-defined and less variable spatial arrangements of these molecules compared to the broader configurational diversity observed for GG blocks. This feature, and the features described above, also tie into the potential for tuning the carrying or binding capacity of alginate through the proportion of MM and GG blocks.

3.4. Flory–Huggins parameter

The variation of the Flory–Huggins parameter χ with respect to temperature for each penetrant species with poly(mannuronate) is shown in Fig. 9. The Flory–Huggins parameter χ is related to the mixing energy E_mix since χ = E_mix/RT, and so large positive values for χ indicate that the polymer and penetrant molecules may avoid proximity or close contact, whilst for strong solvents it will take on a small or negative value as the polymer chains disperse into the solvent.⁵⁶

Fig. 9. Flory–Huggins parameter χ as a function of temperature for each penetrant species with mannuronate: (a) water, (b) estradiol, (c) estriol, (d) estrone, (e) ethinylestradiol, (f) diethylstilbestrol, (g) mestranol, (h) progesterone, and (i) testosterone.

The results shown in Fig. 9 indicate that estradiol, estriol, estrone, ethinylestradiol, mestranol, and progesterone show a tendency towards miscibility with poly(mannuronate) at ambient conditions (i.e., T ≈ 298 K). In contrast, water, diethylstilbestrol, and testosterone do not display strong miscibility behavior with poly(mannuronate) at ambient conditions. This aligns with previously published observations for EDCs + poly(guluronate),³¹ for which strong miscibility (in terms of the Flory–Huggins parameter χ) was observed for all of estradiol, estriol, estrone, ethinylestradiol, diethylstilbestrol, mestranol, and progesterone. It should also be noted that despite seemingly favorable values for χ, estriol and ethinylestradiol did not exhibit phase splitting with poly(mannuronate).

Although water and alginate are known to be miscible in practice, the relative χ values obtained here suggest that, compared to water, ethinylestradiol and diethylstilbestrol may exhibit comparable or even stronger affinity for poly(mannuronate), though still weaker than that of the other EDC compounds examined. Collectively, these results point toward distinct interaction patterns between MM and GG blocks in alginate and specific EDCs, particularly ethinylestradiol and diethylstilbestrol, indicating that block chemistry plays a critical role in governing miscibility behavior. In summary, the trends observed for χ suggest preferential binding of EDCs with poly(mannuronate) over water, indicating potential selectivity in aqueous system remediation. This aspect is of particular interest if alginate is to be used to bind to EDCs in terms of the proportion and spatial organization of MM, GG, and MG blocks.

It can be noted that the magnitude of computed values for χ extends beyond the range typically observed for small-molecule and well-entangled polymeric systems (i.e., 10⁰–10¹). In practice, alginate is typically used for encapsulation of biologically active compounds, while alginate typically occurs as a hydrogel. The extreme values observed for χ for mannuronate suggest drastic miscibility/immiscibility behaviour for specific pairings. Taken in conjunction with differences observed in previously published results for guluronate,²⁷ this suggests that there may be notable steric and energetic effects for polymeric chains composed of MM, GG, and MG blocks as occur in alginate itself.

3.5. Coordination number

In addition to the binding energy, phase equilibria, and Flory–Huggins parameter, the volume-constraint Flory–Huggins extension methodology also yielded coordination numbers for each binary penetrant-polymer system. The results, provided in Table 2, are used in eqn (4) and (5), and reflect the average number of immediate contacts between polymer and penetrant molecules.

Table 2. Coordination number Z for each penetrant species with mannuronate, as determined from stochastic excluded-volume constraint computations^60,61.

Species i	Z i-mannuronate	Z mannuronate-i
Water	4.800	17.92
Estradiol	11.39	7.540
Estriol	11.49	7.480
Estrone	11.36	7.548
Ethinylestradiol	11.90	7.534
Diethylstilbestrol	11.74	7.566
Mestranol	12.49	7.440
Progesterone	12.09	7.180
Testosterone	11.52	7.194

These values reflect the local packing environment and vary with the size, shape, surface area, and chemical functionality of each penetrant species. The relationship between coordination number and mixing energies directly relates to the Flory–Huggins interaction parameter χ. Recall that Z_{i-mannuronate} reflects the packing of mannuronate around a molecule of penetrant species i, whereas Z_{mannuronate-i} reflects the packing of molecules of penetrant species i around mannuronate. Therefore, on a molecular bases, there are, on average, more mannuronate molecules binding to each EDC molecule than water (at least of the species considered here) by a ratio of approximately 2.4 : 1, with the converse being that when there is available space, there are more water molecules binding to each mannuronate than for the EDCs under consideration by a ratio of about 2.4 : 1. In the former case, this is to be expected as the penetrant species are significantly larger than water and consequently have larger molecular surface areas for mannuronate to bind to. In the latter case, the converse is, of course true.

The surface areas of adjacent molecules are naturally related to intermolecular interactions. If there is more surface area interacting, then the dispersive forces are stronger. If the molecular surfaces are conducive to the occurrence of hydrogen bonding, then, of course, such interactions may occur. Note that alginate is highly hydrophilic, whereas steroid hormones are typically hydrophobic, and so the disparity in coordination numbers (and thus the strength of intermolecular interaction) may vary accordingly. The coordination numbers, taken in conjunction with the pairwise potential energy distributions (see Fig. 7), indicate that there are, to an extent, competing energetic and steric effects underlying the interactions between water + mannuronate and the EDCs + mannuronate. Hence, there may be significant nuance required when assessing the bulk behaviour on the basis of molecular properties alone.

3.6. Quantum chemical analysis through density functional theory

The DFT calculations were performed to provide a molecular-level interpretation of the interaction mechanism inferred from cohesive energy density (CED) and Flory–Huggins interaction parameters. The optimized geometries of mannuronate–EDCs and mannuronate–water complexes are presented in Fig. 10 with HOMO–LUMO orbital localization denoted by the spatial distribution of isosurfaces. Frontier molecular orbital (FMO) analysis clarifies how electronic distributed between mannuronate and EDCs during bonding. The distribution of the FMO in donor–acceptor systems indicates the directionality of electronic interactions, with HOMO localized on electron-rich regions of the donors and LUMO on electron-deficient regions of the acceptors. In computational investigation of molecular complexes and polymers, this molecular orbital-based interpretation is used to understand donor–acceptor interaction in a range of systems, generally correlating with charge transfer propensity and gap narrowing processes.⁸⁹

Fig. 10. HOMO–LUMO isosurfaces of each complex that formed with mannuronate: (a) water, (b) estradiol, (c) estriol, (d) estrone, (e) ethinylestradiol, (f) diethylstilbestrol, (g) mestranol, (h) progesterone, and (i) testosterone.

For the complexes formed between mannuronate and EDCs, the results from Fig. 10 show that the HOMO is predominantly localized on the EDC molecule, while the LUMO is mainly on the mannuronate backbone except for estrone, progesterone, and testosterone. This implies that the EDCs serve as the electron-donor while mannuronate serves as the electron-acceptor, facilitating polarization-driven stability upon binding.⁸⁹ On the other hand, both HOMO and LUMO are mostly localized on EDCs for the mannuronate–estrone (Fig. 10(d)), mannuronate–progesterone (Fig. 9(h)), and mannuronate–testosterone complexes (Fig. 10(i)). This indicates less orbital-mediated coupling and greatly depends on dispersion and hydrogen-bonding interactions rather than substantial orbital hybridization with the polymer backbone.⁹⁰ The mannuronate–mestranol complex (Fig. 9(h)) is an intermediate case because of partial LUMO delocalization onto mannuronate, indicating mixed interaction types. For the mannuronate–water complex (Fig. 9(a) and 12), both HOMO and LUMO remain localized on mannuronate, confirming the lack of significant donor–acceptor interaction with water compared to EDCs.⁹⁰

Fig. 12. Non-Covalent Interaction (NCI) isosurfaces of the optimized mannuronate–EDC complex: (a) water, (b) estradiol, (c) estriol, (d) estrone, (e) ethinylestradiol, (f) diethylstilbestrol, (g) mestranol, (h) progesterone, and (i) testosterone.

As presented in Table 3, the HOMO–LUMO energy gaps of the mannuronate–EDC complexes (3.139–4.292 eV) are reduced relative to those of interacting molecules (3.159–7.812 eV), indicating increased chemical reactivity and successful electronic coupling between the interacting species. This electronic reorganization is consistent with enhanced intermolecular interactions and supports the observed stabilization trends.^89,90

Table 3. HOMO, LUMO, and energy band gap for each of the penetrant species and their complexes. Total interaction energy, Hirshfeld and Mulliken charge transfer, DFT-D dispersion energy, and electrostatic interaction energy.

	HOMO	LUMO	E-Gap (eV)	Total interaction energy (kcal mol−1)	Hirshfeld charge transfer	Mulliken charge transfer	DFT-D dispersion energy (kcal mol−1)	Electrostatic energy (kcal mol−1)
Diethylstilbestrol	−5.016	−1.718	3.298
Estradiol	−5.423	−1.281	4.142
Estriol	−5.427	−1.291	4.136
Estrone	−5.438	−1.886	3.552
Ethinylestradiol	−5.423	−1.281	4.142
Mestranol	−5.370	−1.292	4.078
Progesterone	−5.754	−2.595	3.159
Testosterone	−5.782	−2.590	3.192
Mannuronate	−6.158	−1.812	4.346
Water	−7.169	0.643	7.812
Mannuronate–diethylstilbestrol	−5.030	−1.891	3.139	−2.484	−0.004	−0.014	−41.486	−4931.325
Mannuronate–estradiol	−5.411	−1.861	3.550	−2.668	0.005	0.006	−51.791	−5698.865
Mannuronate–estriol	−5.424	−1.689	3.735	−5.496	0.038	0.053	−55.121	−5620.385
Mannuronate–estrone	−5.422	−1.867	3.555	−2.719	0.007	−0.085	−49.152	−5257.083
Mannuronate–ethinylestradiol	−5.422	−1.915	3.507	−2.319	0.007	0.008	−54.281	−5709.652
Mannuronate–mestranol	−5.393	−1.726	3.667	−11.884	0.077	0.097	−62.630	−5915.460
Mannuronate–progesterone	−5.734	−2.574	3.160	−2.230	−0.031	−0.120	−66.985	−6408.034
Mannuronate–testosterone	−5.756	−2.575	3.181	−3.089	−0.005	−0.100	−63.021	−6005.530
Mannuronate–water	−6.180	−1.888	4.292	0.098	−0.015	−0.005	−14.453	−1709.187

The interaction strength was further quantified through corrected DFT energy, ΔE, calculated as the sum of the electronic energy, ZPVE, and BSSE correction. The results show that mannuronate–EDC complexes are more stable than the mannuronate–water system. This confirms that the electronic complementarity identified by HOMO–LUMO analysis translates into energetic stabilization at the molecular level. The Hirshfeld and Mulliken charge analyses⁹¹ (Table 2) further suggest that complex formation is accompanied by small but measurable charge redistribution. Mestranol and estriol show the clearest positive ligand charges; this suggests partial electron-density donation from the ligand toward mannuronate. Progesterone and testosterone show negative ligand charges, which suggests a different interaction pattern that may likely be dominated more by dispersion and localized electrostatic effects than by simple donor-to-mannuronate charge transfer. Although the absolute charge values obtained from the two partitioning schemes differ, they both support that binding involves measurable but non-covalent electron-density transfer rather than covalent bond formation.

Electrostatic interaction energies calculated (Table 3) reveal that electrostatic attractions have significant contributions to the stabilization of the mannuronate–EDC complexes. This might be from the hydroxyl and carboxyl groups of mannuronate, providing electron-rich oxygen atoms that interact with complementary functional groups of the EDC molecules through hydrogen bonding and dipole–dipole interactions. The results displayed in Table 3 show that complexes exhibiting larger electrostatic stabilization generally show greater charge redistribution in both Hirshfeld and Mulliken analyses,^76,77 indicating that charge transfer and electrostatic attraction are intrinsically coupled during binding. DFT-D dispersion energies (Table 2) show that dispersion forces constitute an important component of the binding mechanism. The DFT-D dispersion is much stronger for EDC complexes (−41.486 to −66.985 kcal mol⁻¹) than for water (−14.453 kcal mol⁻¹). This is an indication that London dispersion interactions contribute substantially to the overall interaction energy. It therefore means that the interaction mechanism is not only governed by HOMO–LUMO orbital alignment, but by the combined effects of electrostatic stabilization, dispersion forces, hydrogen-bonding interactions, and weak donor–acceptor polarization. This provides a basis for the EDCs' stronger interaction energies and supports the lower Flory–Huggins interaction parameters obtained from the thermodynamic modeling.

To further elucidate the binding mechanism and quantitatively identify the non-covalent interaction responsible for stabilization, RDG and NCI analyses^92,93 were performed (Fig. 11 and 12). The RDG scatter plots identify the nature of the intermolecular interactions through the distribution of sign(λ₂)ρ values, while NCI isosurfaces visualize the spatial localization of these interactions. They both provide direct visualization of the energetic contribution. The negative values of sign(λ₂)ρ correspond to attractive hydrogen bonding interactions between mannuronate and the EDC molecules. A broad concentration of scatter points around sign(λ₂)ρ ≈ 0 shows that van der Waals interactions are widespread throughout the binding process, and positive sign(λ₂)ρ values indicate steric repulsion. The NCI isosurfaces support these observations by displaying widespread green surfaces across the intermolecular interface, confirming the dominant contribution of dispersion interactions, and blue regions corresponding to attractive hydrogen bonds. Only small isolated red regions are observed, indicating minimal steric repulsion within the optimized complexes. These observations are consistent with the calculated electrostatic, DFT-D dispersion correction, and negative interaction energy obtained.

Fig. 11. Reduced Density Gradient (RDG) scatter plots of each optimized complex that formed with mannuronate: (a) water, (b) estradiol, (c) estriol, (d) estrone, (e) ethinylestradiol, (f) diethylstilbestrol, (g) mestranol, (h) progesterone, and (i) testosterone.

The molecular-level observations align with the intermolecular energy distribution reported in Section 3.3, where mannuronate–EDC systems show a broad distribution with pronounced negative energies. The accumulation of these favorable configurations leads to reduced ensemble-averaged Flory–Huggins interaction parameters discussed previously, providing a direct mechanistic link between electronic structure, intermolecular energetics, and macroscopic thermodynamics. It is also reflected in the mannuronate–water complex, which has a positive binding energy of 0.098 kcal mol⁻¹ (Table 3) and the highest positive χ values in Fig. 10(a), explaining the high phase separation tendency.

4. Conclusion

This work presents a multiscale computational study of the interactions between poly(mannuronate), a key structural component of alginate, and several endocrine-disrupting chemicals (EDCs), alongside water. The study integrates Flory–Huggins thermodynamic modelling with density functional theory (DFT) calculations and non-covalent interaction analyses. Atomistic molecular dynamics simulations showed that both the cohesive energy density and solubility parameters of poly(mannuronate) reach convergence at polymer chain lengths of about ∼50 monomer units. This behavior reflects the inherent flexibility of MM blocks and establishes a reliable molecular model for subsequent thermodynamic evaluations.

Stochastic simulations combined with an extended Flory–Huggins framework revealed clear differences in intermolecular energy distributions, interaction parameters, and phase equilibria among the penetrant species. Compared with water, EDC molecules exhibited more negative (i.e., more attractive) intermolecular energy distributions and lower Flory–Huggins interaction parameters, indicating stronger thermodynamic affinity for poly(mannuronate). The resulting phase diagrams further underscored compound-specific miscibility trends, highlighting the sensitivity of polymer–penetrant interactions to subtle variations in molecular structure and functional group composition.

To clarify the molecular origins of these thermodynamic trends, DFT calculations were performed. Frontier molecular orbital analysis showed that, in most mannuronate–EDC complexes, the HOMO is primarily localized on the EDC while the LUMO resides on the mannuronate backbone. This distribution is consistent with donor–acceptor interactions that enhance electronic polarization and stabilize the complexes.

In contrast, the mannuronate–water systems, both HOMO and LUMO, remain localized on mannuronate, indicating weaker and less specific interactions. Corrected DFT interaction energies, including zero-point vibrational energy and basis set superposition error corrections, confirmed that mannuronate–EDC complexes are energetically more stable than the mannuronate–water complex. The combined Hirshfeld and Mulliken charge analyses confirmed electron-density redistribution across the adsorption interface, while the combined effects of electrostatic energy and DFT-D dispersion calculations indicated that both hydrogen-bond and long-range van der Waals forces contribute to complex formation. The RDG scatter plots and NCI isosurfaces analyses gave direct real-space visualization of the intermolecular interactions responsible for adsorption.

These molecular-level findings align with the stronger binding tendencies and lower Flory–Huggins parameters observed at the mesoscale. Overall, the results demonstrate that poly(mannuronate) is a promising host material for the selective binding of EDCs in aqueous environments, supporting its potential application in environmental remediation strategies. The results from this study, in conjunction with existing literature on the selection of EDCs under investigation interacting with guluronate, suggest that tailoring the loading capacity of alginate is viable through tuning the relative proportion of MM versus GG blocks in the polymer for optimizing sorption performance. Moreover, the spatial positioning of these EDCs along the polymer chain can be predictably centered on the MM blocks, thus enabling the exploitation of this feature with regard to the addition of, e.g., functional groups or branches to functionally modify the polymer by focusing on MM or GG blocks, depending on the desired outcomes. This suggests that alginate-based materials can be rationally engineered to enhance selectivity toward target contaminants while minimizing competition from water.

It can be noted that the results presented in this contribution can serve as a springboard for future work to investigate the influence of variables such as dissolved salt concentrations, pH, competitive sorption with other organic species, and so on. Accounting for such features could provide a useful link between this study, mesoscale simulations, and laboratory experiments.

Author contributions

Victoria Adeleke: methodology, software, validation, formal analysis, investigation, resources, data curation, writing – original draft, writing – review & editing, visualization. Khalid Osman: writing – review & editing, supervision. Samuel Mugo: writing – review & editing, supervision. Madison Lasich: conceptualization, methodology, software, validation, formal analysis, investigation, resources, data curation, writing – original draft, writing – review & editing, visualization, supervision, project administration.

Conflicts of interest

The authors declare they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

Data for this article (molecular dynamics trajectories and extended Flory–Huggins calculations outputs) are available at the University of KwaZulu-Natal Yabelana repository at https://doi.org/10.25410/ukzn.33465826.