Precursor Solvation in 2-Methoxyethanol/DMI Binary Solvents and Anti-Solvent-Free Film Formation of FA–MA Perovskites

Abstract

The state of a perovskite precursor ink is set by how its solvents coordinate the precursors, yet the roles of individual solvents in green mixtures remain poorly understood. We examine how 2-methoxyethanol (2Me) and 1,3-dimethyl-2-imidazolidinone (DMI) share the solvation of the four precursors of a formamidinium–methylammonium (FA–MA) lead iodide–bromide ink: PbI₂, PbBr₂, FAI and MABr. Cluster–continuum DFT calculations (r²SCAN-3c/SMD) of the exchange of 2Me for DMI in the first solvation shell show that PbI₂ prefers DMI, whereas PbBr₂ and MABr prefer 2Me (+4.9 and +6.3 kJ mol⁻¹ per DMI) and FAI has no clear preference (+2.0 kJ mol⁻¹); in FAI and MABr, 2Me donates O–H···X⁻ hydrogen bonds. A thermodynamic model built on these energies is consistent with 2Me-rich mixtures (about 10–20 vol% DMI) as a tentative compromise. All 2Me/DMI mixtures wet PTAA, with the contact angle falling from 24.7° (2Me) to 13.3° (DMI). Without an anti-solvent (gas quenching only), the 2Me:DMI ink gives on PTAA a film with larger grains in the imaged areas than the DMF:DMSO ink, with the same absorption onset (776 nm) and a similar photoluminescence band. With literature data on blade-coated films, these results support testing 2Me/DMI for anti-solvent-free, large-area processing of FA–MA perovskites.

1. Introduction

Metal halide perovskites are among the most studied materials for solution-processed photovoltaics. Mixed-cation compositions, in which formamidinium (FA⁺) and methylammonium (MA⁺) share the A site and bromide partly replaces iodide, stabilized the perovskite phase of FAPbI₃ and gave n–i–p solar cells with efficiencies above 18% [1]. In 2026, a certified steady-state efficiency of 27.17% was reported for n–i–p cells [2]. Large-area devices lag behind: the latest efficiency tables report 22.1% for a 0.08 m² module and 19.3% for a 0.72 m² module [3]. Reproducible fabrication and scale-up remain difficult, because film formation is sensitive to the state of the precursor solution and to the way the solvent leaves the wet film.

The solvent is an active component of the ink and not only a dissolution medium. In DMF/DMSO inks, DMSO binds PbI₂ strongly and, because of its high boiling point, stays in the wet film, so the film remains undersaturated for a long time and, if left to dry, crystallizes slowly from few nuclei into a rough, incomplete layer. An anti-solvent drip removes DMF and DMSO from the wet film within seconds, raises the supersaturation abruptly and induces dense nucleation of a solvated intermediate, which is converted into the perovskite on annealing [4]; the Lewis-base adduct of PbI₂ with DMSO delays crystallization and improves reproducibility [5]. DMF/DMSO inks therefore need an anti-solvent or an equivalent fast quench, and its application is hard to make uniform over large areas. Precursor solutions are generally colloidal dispersions, and their state controls crystallization kinetics and film morphology [6,7]. How strongly a solvent coordinates Pb²⁺ correlates with its Gutmann donor number [8], and sulfur-donor solvents bind Pb²⁺ more strongly than oxygen-donor solvents [9]; solvated iodoplumbate complexes in DMSO and DMF have been identified by combined DFT and UV–vis studies [10]. A donor-number picture, however, considers only the interaction with Pb²⁺ and ignores hydrogen-bond donation by the solvent. The interaction with the organic cation can also decide which intermediate forms: NMP interacts more strongly than DMSO with formamidinium and stabilizes a FAI–PbI₂·NMP adduct [11]. For FA/MA and I⁻/Br⁻ mixtures, crystallization from DMF and DMSO proceeds through several solvate phases that are set by the composition of the solution [12], and in binary mixtures the most volatile solvent dominates evaporation, so that the solvent ratio at nucleation differs from that in the ink [13].

The need for a fast supersaturation step follows from the LaMer mechanism of nucleation and growth, the framework generally used for perovskite films [14,15]. As the solvent leaves, the solute concentration rises; nucleation starts only when it exceeds a critical supersaturation and stops as soon as the nuclei consume the solute and the concentration falls below it, after which the existing nuclei only grow. A short, sharp burst of nucleation gives many nuclei at once and a dense film of uniform grains, whereas a slow rise spreads nucleation over time and gives few, non-uniform nuclei and incomplete coverage. The anti-solvent drip creates the burst by extracting the solvent abruptly, and gas quenching does so by accelerating evaporation. Where an anti-solvent cannot be applied uniformly, as in large-area coating, the burst has to come from the ink itself, that is, from the volatility of its solvents and from how strongly they bind the precursors, which sets how far the concentration must rise before nucleation. This is why the solvation of the precursors, and not only the film, has to be understood.

The DMF/DMSO pair, the most widely used, has further drawbacks. DMF is toxic, and the DMSO retained in the wet film is the main cause of dewetting of precursor solutions on hydrophobic polymer hole-transport layers such as PTAA in gas-quenching deposition: DMF evaporates first, the DMSO fraction in the wet film rises, and the contact angle approaches that of pure DMSO (45.6° on PTAA), which leaves pinholes [16]. 2-Methoxyethanol (2Me), a more volatile solvent, was introduced for methylammonium lead halide solar cells, where it gave smaller crystals and better surface coverage than DMF [17]. Weakly bonded I⁻ ions and cluster complexes were found in 2Me inks of MAPbI₃, and in FAPbI₃ the cluster ratio was linked to the kinetics of δ-phase formation [18,19]. Combining 2Me with the donor solvent DMI keeps fast drying and adds a carbonyl donor for Pb²⁺. For an ink of (FAPbI₃)_0.95(MAPbBr₃)_0.05, a 2Me/DMI mixture with 75 μL of DMI per mL gave pinhole-free films over more than 100 cm², n–i–p cells of 23.4% and modules of 20.1% efficiency, ahead of DMF/DMSO and 2Me/NMP inks [20]. Desorption measurements showed that DMI is removed completely at 100 °C and leaves the film at a higher temperature than NMP, which points to stronger binding to PbI₂, whereas DMSO remains in the film after 1 h at 100 °C [20].

That work was a process study, and it is still unclear how 2Me and DMI divide their roles among the four components of a FA/MA lead iodide–bromide ink: PbI₂, PbBr₂, FAI and MABr. In contrast to that study, which optimized the ink empirically and evaluated devices, and to DFT studies of precursor solvation in DMSO and DMF [10], we resolve for each of the four precursors separately which solvent occupies the first solvation shell in a 2Me/DMI mixture, and we relate the result to the composition range used in practice. The hydroxyl group of 2Me can donate hydrogen bonds to halide anions, whereas DMI is an aprotic carbonyl donor, so the preferred solvent may differ from one precursor to another. Cluster–continuum models, which combine explicit first-shell solvent molecules with a dielectric continuum [21], are suited to this question. Quantum-chemical interaction energies have also been combined with phase-equilibrium analysis to design mixed solvents in other fields, for example, for the extractive distillation of dimethyl carbonate [22]; here the same idea, a molecular-level description of how the components of a solvent mixture share the interaction with the solute, is applied to the solvation of perovskite precursors. This work concerns the inverted p–i–n architecture, in which the perovskite ink is cast on a hydrophobic hole-transport polymer, here PTAA. The aim is to establish the molecular and processing basis for using 2Me/DMI as a solvent system for anti-solvent-free film formation over large areas. We use cluster–continuum DFT calculations to describe the exchange of 2Me for DMI in the first solvation shell of the four precursors and to derive their relative solubility as a function of the 2Me:DMI ratio, and we complement them with photographs and FTIR spectra of solutions in 2Me/DMI and in the reference solvents, UV–vis spectra, XRD patterns and SEM images of films cast from 2Me:DMI and DMF:DMSO inks on PTAA, PL spectra of films cast on glass, and contact-angle measurements on PTAA. We have not made complete solar cells or large-area films in this work, and statements about devices and large areas rely on literature data, which we state explicitly.

2. Materials and Methods

2.1. Materials

All chemicals were used as received without further purification. Lead(II) iodide (PbI₂, 99.99%) and lead(II) bromide (PbBr₂, 99.99%) were purchased from Tokyo Chemical Industry (TCI; Tokyo, Japan). Poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine] (PTAA, >99%), formamidinium iodide (FAI, >99.5%), methylammonium bromide (MABr, >99%), dimethylformamide (DMF, ≥99.9%), dimethyl sulfoxide (DMSO, ≥99.9%), toluene, anhydrous 2-methoxyethanol (2Me, 99.8%), 1,3-dimethyl-2-imidazolidinone (DMI, ≥99.0%), anhydrous N-methyl-2-pyrrolidone (NMP, 99.5%), methylammonium chloride (MACl, 99.99%), thiourea (≥99.999%, metals basis; Supelco) and poly(methyl methacrylate) (PMMA, Mw ≈ 100,000) were obtained from Sigma-Aldrich (St. Louis, MO, USA).

2.2. Substrate and Film Preparation

Glass substrates coated with indium tin oxide (ITO), 20 mm × 15 mm in size, were cleaned in several steps. First, mechanical cleaning was performed with a 1:10 (v:v) aqueous solution of Hellmanex™ III, followed by ultrasonic cleaning in toluene, acetone, and isopropyl alcohol (IPA) for 10 min each. Substrates were dried under nitrogen flow and treated with UV–ozone (Ossila UV Ozone Cleaner, Ossila Ltd., Sheffield, UK) for 15 min to enhance surface wettability.

A hole transport layer (HTL) was deposited by spin-coating 100 μL of a PTAA solution (1.5 mg mL⁻¹ in toluene) at 6000 rpm for 30 s using a spin coater (Ossila Ltd., Sheffield, UK), followed by annealing at 100 °C for 10 min.

The perovskite precursor solution of composition (FAPbI₃)_0.95(MAPbBr₃)_0.05 was prepared in 2Me:DMI. For 1 mL of ink, PbI₂ (525.6 mg, 1.140 mmol), FAI (196.0 mg, 1.140 mmol), PbBr₂ (22.0 mg, 0.060 mmol), MABr (6.8 mg, 0.061 mmol) and MACl (6.0 mg, 0.089 mmol) were dissolved in 900 μL of 2Me and 76 μL of DMI. The mixture was kept at 60 °C for 30 min, cooled to room temperature and filtered through a 0.45 μm polytetrafluoroethylene (PTFE) syringe filter. After filtration, 17 μL of thiourea (100 mg mL⁻¹ in DMI; 1.7 mg) and 7 μL of poly(methyl methacrylate) (PMMA, 5 mg mL⁻¹ in DMI; 35 μg) were added, and the vial was gently shaken by hand until the additives were fully mixed. The final volume was 900 + 76 + 17 + 7 = 1000 μL; with the DMI introduced by the additive solutions (76 + 17 + 7 = 100 μL), the final solvent composition was 2Me:DMI = 900:100 μL (9:1 v/v); all other binary mixtures used in this work (2Me:NMP, DMF:DMSO and DMF:NMP) also had a volume ratio of 9:1. MACl was included because it stabilizes the intermediate phase and promotes the formation of the α-phase [23], and thiourea because it enlarges the grains, improves crystallinity and reduces pinholes in (FAPbI₃)_0.85(MAPbBr₃)_0.15 films [24].

For film deposition, 100 μL of the solution was spin-coated onto the PTAA layer in two steps: 1000 rpm for 10 s, then 5000 rpm for 60 s. Nitrogen gas quenching at 3 bar (0.3 MPa) was applied from the 10th second of the second step for 40 s, and the gas flow was stopped when the film had turned completely dark brown. The films were then annealed at 130 °C for 30 min. Reference films were prepared from the same precursor composition, with the same additives, dissolved in DMF:DMSO and processed under identical conditions.

2.3. Characterization

2.3.1. Solutions

Perovskite solutions (PVSK, 1 mL) and solutions of the individual precursors (MABr, FAI, PbI₂ and PbBr₂) were prepared at the concentrations of the ink (Section 2.2) in nine solvent systems: the single solvents DMF, DMSO, NMP, 2Me and DMI, and the binary mixtures DMF:DMSO, DMF:NMP, 2Me:DMI and 2Me:NMP. The PVSK solutions were photographed in glass vials. FTIR spectra of the solvents and of all solutions were recorded on an Invenio-S Fourier-transform infrared spectrometer (Bruker Optik GmbH, Ettlingen, Germany) in attenuated total reflectance (ATR) mode over 4000–400 cm⁻¹ at 4 cm⁻¹ resolution. For the analysis, the transmittance T was converted to absorbance, A = −log₁₀(T/T₀), with T₀ the mean transmittance at 2200–2500 cm⁻¹, and the positions of the C=O, C–O, C–H and O–H bands were obtained by fitting a Lorentzian function with a linear baseline to each band. The fit errors are 0.05–0.3 cm⁻¹ for the narrow bands and about 1 cm⁻¹ for the O–H band; each spectrum was recorded once, so the reproducibility between measurements was not tested.

2.3.2. Films

Films were cast from the 2Me:DMI and DMF:DMSO inks as described in Section 2.2. Their absorption spectra were recorded over 550–900 nm on a Shimadzu UV-3600 spectrophotometer (Shimadzu Corporation, Kyoto, Japan) in transmission mode, using films deposited on glass/ITO/PTAA substrates (glass/ITO/PTAA/perovskite); a bare glass/ITO substrate was used as the reference. The spectra were smoothed with a Savitzky–Golay filter (21 nm window, third-order polynomial). The absorption onset was taken as the intersection of the tangent at the steepest point of the absorption edge with the baseline above the edge. Because no direct thickness measurement was made, the thicknesses of the two films were compared through their absorbances: for the same absorption coefficient, the ratio of the film thicknesses equals the ratio of the absorbances at the same wavelength (here 600 nm, corrected for the baseline at 800–830 nm, according to the Beer–Lambert law). This comparison neglects reflection and scattering, and an absolute thickness was not derived. X-ray diffraction (XRD) patterns of the films, deposited on ITO-coated substrates, were recorded on a Rigaku MiniFlex 600 diffractometer (Rigaku Corporation, Tokyo, Japan) with Cu Kα radiation over 2θ = 5–45° in steps of 0.02°. The background was subtracted, and the patterns were smoothed with a Savitzky–Golay filter (9 points, 0.18°; third-order polynomial); peak positions, heights and widths were obtained from pseudo-Voigt fits to the unsmoothed data. The surface morphology of the films was examined with a JSM-IT210 scanning electron microscope (SEM; JEOL Ltd., Tokyo, Japan) in secondary-electron mode under high vacuum, at an accelerating voltage of 8 kV, a working distance of 11.0 mm and a magnification of 8000×; images were acquired with InTouchScope software. Grain sizes were determined from the images shown in the figure by watershed segmentation (Gaussian smoothing, markers from local intensity maxima; scikit-image), excluding grains that touch the image border; the equivalent diameter of each grain, 2(A/π)^1/2 with A the area, was calculated with the scale of the image. For presentation, the images were denoised with a non-local-means filter and their contrast was stretched. Steady-state photoluminescence (PL) spectra were recorded on a FluoTime 300 spectrometer (PicoQuant GmbH, Berlin, Germany) with excitation at 420 nm on films cast from the two inks on bare glass. For presentation, the spectra were smoothed with a Savitzky–Golay filter (7 points, i.e., 12 nm; third-order polynomial) and interpolated with a cubic spline; the peak positions and intensities quoted in the text are the maxima of the unsmoothed spectra.

2.3.3. Wetting

Static contact angles were measured on a KRÜSS DSA25 drop-shape analyzer (KRÜSS GmbH, Hamburg, Germany) by the sessile-drop method at 20.0 °C in air. Drops (2 μL; three per composition) of 2Me/DMI mixtures (2Me:DMI from 10:0 to 0:10 by volume, in steps of 1) were placed on PTAA films prepared as in Section 2.2, and the angle was taken from the fitted drop profile at the moment of contact (0.00 s) as the mean of the left and right angles and of the three drops. The contact angles of the inks themselves (with the dissolved precursors and additives) were not measured.

2.4. Computational Details

All quantum-chemical calculations were performed with ORCA 6.1.1 [25]. Each solvate cluster was treated in three steps. Initial geometries were optimized with GFN2-xTB (xtb version 6.8.0) [26], in the gas phase for lead halides and MABr and in the ALPB implicit model (methanol) for FAI, which prevents N–H···I⁻ proton transfer in the gas phase (no proton transfer occurred in the MABr clusters: N–H ≤ 1.08 Å and H···Br⁻ ≥ 2.05 Å). The geometries were then re-optimized with r²SCAN-3c [27] and the SMD implicit solvation model [28], with the def2 effective core potential on Pb and the continuum parametrized as 2Me for all clusters. The thermal correction to the free energy, (G−E_el), was obtained from GFN2-xTB harmonic frequencies at 298.15 K, with the quasi-RRHO treatment of low-frequency modes [29,30]. For lead halides and the free solvents, the r²SCAN-3c geometry was first re-optimized with GFN2-xTB with tight criteria, and all these structures are minima without imaginary frequencies. For ion pairs, the xTB re-optimization changed the structure qualitatively (a contact ion pair turned into a pair separated by a solvent molecule), so their frequencies were calculated directly at the r²SCAN-3c geometry in ALPB(methanol); the free 2Me and DMI molecules of the ion-pair series were treated in the same way, so that E and G–E_el belong to the same geometry. Small imaginary modes of the ion pairs (|ν| ≤ 50 cm⁻¹; the largest was 37 cm⁻¹) were excluded from the thermal correction. The free energy of each structure is

$$G=E_{{\mathrm{r}}^2\mathrm{SCAN-3c}/\mathrm{SMD}}+{\left(G-E_{\mathrm{el}}\right)}_{\mathrm{GFN2-xTB}}$$

(1)

The first solvation shell was described by explicit solvent molecules and the rest of the medium by a dielectric continuum (cluster–continuum approach [21]). Further details of the protocol are given in Section S1 of the Supporting Information.

2.4.1. Sensitivity Tests

The thermochemical level was tested on 15 representative structures (both solvents; b = 0, 2 and 4 for the four precursors and b = 1 for PbBr₂), which were re-optimized at the r²SCAN-3c/SMD(2Me) level with tight criteria; analytical harmonic frequencies were calculated at the same level (scheme B, Table S1). For PbI₂, PbBr₂ (b = 2, 4) and MABr, scheme B changes ΔG_b by 1.5–4.8 kJ mol⁻¹ relative to the scheme described above (scheme A). For FAI the change is larger (+6 to +20 kJ mol⁻¹, almost entirely from the thermal term), so the magnitude of ΔG_b of FAI depends on the thermochemical level; ΔG₄ of FAI nevertheless remains positive, and the preference for 2Me becomes stronger. In eight of the 15 structures, small imaginary modes remained after the optimization. Displacing the structure along these modes and re-optimizing removed the mode only for MABr at b = 4; in the other seven structures, the optimization returned to nearly the same geometry and modes (−43 to −195 cm⁻¹), which points to numerical noise of the analytical Hessian (integration grid, continuum discretization) and not to true saddle points. Treating these modes as real low-frequency modes changes ΔG_b by at most 5.6 kJ mol⁻¹. Varying the quasi-RRHO cut-off between 50 and 150 cm⁻¹ shifts ΔG_b by at most 2.6 kJ mol⁻¹, whereas pure RRHO changes it by up to 10 kJ mol⁻¹ (Table S2). The sensitivity to the continuum and to the electronic-structure method was tested with single-point calculations at the r²SCAN-3c/SMD(2Me) geometries (Table S3): (a) CPCM [31] instead of SMD; (b) CPCM with the dielectric constant and refractive index of DMI (ε = 37.6, n = 1.472) instead of those of 2Me; and (c) ωB97M-V/def2-TZVP/SMD(2Me) [32,33] for representative species. Changing the continuum from 2Me to DMI alters the exchange energy by at most 1.8 kJ mol⁻¹ per DMI molecule, and ωB97M-V alters it by at most 3.0 kJ mol⁻¹ per DMI molecule, in no case with a change of sign. The difference between SMD and CPCM is larger (up to 6.2 kJ mol⁻¹ per DMI molecule), because CPCM lacks the non-electrostatic terms (cavitation, dispersion, solvent structure) that SMD includes; we regard SMD as the more complete model and treat the difference as a model-type uncertainty. With CPCM the sign changes only for two FAI isomers with |ΔE_b| < 2 kJ mol⁻¹.

2.4.2. Species in Solution

Each precursor was considered separately, as if dissolved alone in the solvent. The species assumed for each follows from the nature of its bonds. PbI₂ and PbBr₂ are polar covalent halides of the soft Lewis acid Pb²⁺, which has a flexible, high coordination number and gains energy by binding donor atoms of the solvent; they were therefore treated as neutral molecular solvate complexes PbX₂(solvent)₄, in which both Pb–X bonds are kept and the solvent donor atoms occupy the remaining coordination sites. In the optimized structures the Pb–X distances remain at 3.10–3.16 Å (Pb–I) and 2.81–2.86 Å (Pb–Br) for every composition (Figure S1b), so the halides stay bound to Pb and are not released as free ions. FAI and MABr, in contrast, are ionic salts, in which cation and halide are held by electrostatic attraction. At the contact distance of about 3.8 Å, this attraction amounts to 1389/(ε·3.8) ≈ 22 kJ mol⁻¹ in 2Me (ε = 16.9) and ≈ 10 kJ mol⁻¹ in DMI (ε = 37.6), several times kT (2.5 kJ mol⁻¹ at 298 K), and the Bjerrum length [34] (33 and 15 Å, Section S2 of the Supporting Information) exceeds the contact distance; in these solvents the ions therefore remain associated as contact ion pairs and not as free solvated ions, and the contact ion pair was taken as the ionic species. Free ions, solvent-separated pairs and iodoplumbate anions (PbX₃⁻, PbX₄²⁻), which form when halide from FAI or MABr is added to PbX₂, were not included, so the model describes each precursor separately and not the complete ink.

2.4.3. Solvate Cluster Models

For PbI₂ and PbBr₂ the coordination bond between Pb²⁺ and the O-donor atom of the solvent is decisive, and strong Lewis bases are needed to dissolve the halides [5,9]. The solvent properties used in the model are collected in Table 1.

Table 1. Properties of 2Me and DMI used in the model (25 °C).

Property	2Me	DMI
Dielectric constant, ε	16.9	37.6
Density, g mL−1	0.965	1.056
Molar mass, g mol−1	76.09	114.15
Pure-liquid concentration, mol L−1	12.68	9.25
Boiling point, °C	124	225
Donor atom	hydroxyl O	carbonyl O
H-bond donor	yes (O–H)	no

Lead halides were modelled as neutral octahedral solvate complexes PbX₂(2Me)_4−b(DMI)_b (X = I, Br; b = 0–4), with the two halides in axial positions and four solvent molecules in the equatorial plane; for b = 2 the cis and trans isomers were calculated separately. FAI and MABr were treated as contact ion pairs (see above and Section S2 of the Supporting Information). Their first solvation shell has four sites (n = 4): two cation sites at N–H groups, to which the solvent O atom binds through N–H···O hydrogen bonds, and two anion sites around the halide, where 2Me binds through O–H···X⁻ hydrogen bonds, whereas aprotic DMI can form only weak C–H···X⁻ contacts. Isomers were calculated separately for each number of DMI molecules at the cation (c = 0–2) and anion (a = 0–2) sites, with b = c + a and statistical weight g = C(2,c)·C(2,a). Free 2Me and DMI molecules were calculated with the same protocol as each series. One starting structure was built with RDKit [35] for each b and (c, a) arrangement, and no systematic conformer search was made. In the GFN2-xTB re-optimization, several contact ion pairs converted spontaneously into pairs separated by a solvent molecule, so solvent-separated ion pairs may also be competitive; the results for FAI and MABr therefore refer to the contact-ion-pair model, and their quantitative reliability is limited by conformational sampling, which was not assessed.

2.4.4. Thermodynamic Model

Solubility in the mixed solvent was derived from ligand-exchange equilibria without calculating the solid phase. For a dissolved species M (PbI₂, PbBr₂, FAI or MABr), the replacement of b molecules of 2Me by b molecules of DMI in the first shell is

$${\mathrm{M}\left(2\mathrm{Me}\right)}_n+b\hspace{0.17em}\mathrm{DMI}\rightleftharpoons {\mathrm{M}\left(2\mathrm{Me}\right)}_{n-b}{\left(\mathrm{DMI}\right)}_b+b\hspace{0.17em}2\mathrm{Me}$$

(2)

with the cumulative free energy of exchange, relative to the all-2Me complex,

$$\Delta G_b=G\left[{\mathrm{M}\left(2\mathrm{Me}\right)}_{n-b}{\left(\mathrm{DMI}\right)}_b\right]-G\left[{\mathrm{M}\left(2\mathrm{Me}\right)}_n\right]+b\left[G\left(2\mathrm{Me}\right)-G\left(\mathrm{DMI}\right)\right]$$

(3)

ΔG_b is thus cumulative; the increment of the b-th exchange is ΔG_b–ΔG_b−1. The number of molecules is conserved, so no standard-state correction is needed. Isomers with the same b are combined by Boltzmann weighting,

$${\beta }_b={\sum }_{i\in b}{g}_i\exp \left(-{\displaystyle \frac{\Delta G_{b,i}}{\mathit{RT}}}\right)$$

(4)

where g_i is the statistical weight, that is, the number of distinct placements of the b DMI molecules on the n sites of the idealized site model. The optimized geometries depart partly from this model (bidentate 2Me, migration of 2Me into the second shell), so g is an approximate combinatorial factor. The concentration of each complex in a saturated solution is

$$c_b\left(\phi \right)=S_{\mathrm{ref}}\hspace{0.17em}{\beta }_b{\left({\displaystyle \frac{C_{\mathrm{DMI}}}{C_{2\mathrm{Me}}}}\right)}^b{a}_{2\mathrm{Me}}^{\hspace{0.17em}n-b}\hspace{0.17em}{a}_{\mathrm{DMI}}^{\hspace{0.17em}b}, S_{\mathrm{sat}}\left(\phi \right)={\displaystyle {\sum }_{b=0}^n}{c}_b\left(\phi \right)$$

(5)

where φ is the volume fraction of DMI, S_ref is the solubility in pure 2Me, C_DMI and C_2Me are the pure-liquid concentrations (Table 1), and a_2Me and a_DMI are the activities of the unbound solvents, found self-consistently from the mass-balance equations (Section S3 of the Supporting Information, Equations (S1) and (S2); Equation (5) is also derived there). DFT gives only relative quantities, so relative solubilities S_sat(φ)/S_sat(0) are reported. The free energies refer to the 1 mol L⁻¹ standard state in the continuum. Because the exchange reaction conserves the number of molecules, the standard-state corrections cancel in ΔG_b, and converting the 1 mol L⁻¹ equilibrium constant to activities relative to the pure liquids gives the factor (C_DMI/C_2Me)^b in Equation (5). Activities refer to the unbound solvents, with the pure liquids as the reference state (a_i = 1) and ideal mixing; the activity coefficient of the solute is taken as unity. Because the solute binds part of the solvent, S_sat(0) is close to, but not identical with, S_ref, and S_ref does not cancel exactly in S_sat(φ)/S_sat(0); all relative values are normalized to S_sat(0) of the same solution. Since no calibration point is available, the calculations of Section 3.3 and Section 3.4 and the speciation in Figure S2 were made in the dilute limit (S_ref = 10⁻⁶ mol L⁻¹), in which the bound solvent is negligible and S_ref cancels exactly; the dependence on S_ref (0.1, 0.5 and 1.0 mol L⁻¹) is shown in Figure S3. The sensitivity to errors in ΔG_b was estimated by shifting it by ±4 kJ mol⁻¹ per DMI molecule. This value is an upper bound of the method errors found in the sensitivity tests above (electronic-structure method ≤3.0 and continuum composition ≤1.8 kJ mol⁻¹ per DMI molecule; quasi-RRHO cut-off ≤2.6 kJ mol⁻¹). The larger SMD–CPCM difference is a model-type uncertainty discussed above, and for FAI the sensitivity to the thermochemical level (up to 20 kJ mol⁻¹ at b = 4, about 5 kJ mol⁻¹ per DMI molecule) exceeds this band. The band represents the method error only; the sampling error (conformers, contact versus solvent-separated ion pairs) and the model assumptions below were not quantified. The model assumes ideal mixing of the solvents and a precipitating solid that is the pure precursor, and it neglects iodoplumbate species (PbX₃⁻, PbX₄²⁻).

3. Results and Discussion

3.1. Structure of the Solvate Clusters

Figure 1 shows the most stable solvate cluster at each step of the exchange series. In PbI₂ and PbBr₂, Pb²⁺ departs from the initial octahedral coordination: part of the 2Me binds Pb through two oxygen atoms (hydroxyl and ether), and another part moves to the second shell and binds the halide through O–H···X hydrogen bonds. In PbI₂ the two iodine atoms change from trans to cis from b = 2 onward, and the mean Pb–I distance increases from 3.10 to 3.16 Å with b (Figure S1b), which indicates that stronger coordination of DMI to Pb weakens the Pb–I bond; the Pb–Br distance hardly changes. In FAI and MABr the cation and anion stay a contact ion pair. DMI first occupies the cation sites (c = b, a = 0 for b ≤ 2), and 2Me keeps O–H···X⁻ hydrogen bonds around the anion; the O–H···Br⁻ distance (2.31–2.35 Å) is markedly shorter than O–H···I⁻ (2.61–2.70 Å) (Figure S1d), so bromide forms stronger hydrogen bonds with 2Me.

Figure 1. Solvate clusters optimized at the r²SCAN-3c/SMD(2Me) level: complexes of (a) PbI₂, (b) PbBr₂, (c) FAI and (d) MABr with b = 0–4 coordinated DMI molecules. The isomer with the lowest free energy is shown for each b; the isomer type for PbX₂ at b = 2 (cis/trans) and the numbers of DMI molecules at the cation and anion sites for FAI and MABr are given below each panel. Solid lines are covalent and Pb–X bonds, dashed lines are Pb–O coordination bonds, and dotted lines are N–H···O and O–H···X⁻ hydrogen bonds.

3.2. Energetics of Ligand Exchange

The cumulative exchange free energies ΔG_b (Figure 2) divide the four precursors into two groups. For PbI₂, ΔG_b is negative and drops quickly for the first two DMI molecules (−22.2 and −33.8 kJ mol⁻¹ at b = 1 and 2); the third and fourth exchanges add almost nothing (cumulative −34.0 and −33.8 kJ mol⁻¹ at b = 3 and 4, increments of −0.2 and +0.2 kJ mol⁻¹). DMI thus displaces 2Me from the first shell of PbI₂, but the effect saturates after the second DMI molecule. At b = 2 the cis isomer is 11.9 kJ mol⁻¹ more stable than the trans isomer. For PbBr₂, FAI and MABr the full-exchange energy is positive (ΔG₄ = +19.6, +8.2 and +25.0 kJ mol⁻¹), so 2Me is the better solvating solvent for PbBr₂ and MABr. For FAI the preference is weak and depends on the thermochemical level: the electronic exchange energy at b = 4 is slightly negative (ΔE₄ = −1.6 kJ mol⁻¹, Table S3), so the positive ΔG₄ comes from the thermal term, which is +8.2 kJ mol⁻¹ in the scheme used here and +28.0 kJ mol⁻¹ with the full r²SCAN-3c/SMD thermochemistry (Table S1).

Figure 2. Free energies ΔG_b (Equation (3)) of the cumulative exchange of 2Me for DMI in the first solvation shell (relative to the all-2Me complex) as a function of the number of coordinated DMI molecules, b: (a) PbI₂, (b) PbBr₂, (c) FAI and (d) MABr. For PbX₂ the cis and trans isomers at b = 2 are shown with different markers; for FAI and MABr the number of DMI molecules at the anion site (a = 0, 1, 2) is shown with different markers. The line connects the Boltzmann-effective values of the isomers at the same b. Negative values indicate that DMI coordination is thermodynamically favored. T = 298.15 K.

For FAI and MABr this follows from the O–H···X⁻ hydrogen bonds that 2Me forms with the halide anion. At b ≤ 2, placing DMI at an anion site is unfavorable: the isomers with a = 1 and a = 2 lie 9.5–14.8 kJ mol⁻¹ (FAI) and 2.1–13.5 kJ mol⁻¹ (MABr) above the a = 0 isomer, whereas placing DMI at a cation site is favorable for FAI (ΔG₂ = −9.7 kJ mol⁻¹ for c = 2, a = 0). The calculations thus show the opposite roles of the two solvents: DMI solvates the cation, and 2Me solvates the anion. Because bromide is a stronger hydrogen-bond acceptor than iodide, the effect is stronger in MABr, whose ΔG_b stays positive for all b.

For PbBr₂ the preference for 2Me may likewise be related to O–H···Br hydrogen bonds (Figure 1b). The value at b = 1 (+36.4 kJ mol⁻¹), however, is higher than that at b = 2 (+13.9 kJ mol⁻¹), which means that the second exchange alone would release 22.5 kJ mol⁻¹ (ΔG₂–ΔG₁), an irregularity unusual for successive exchanges; it is accompanied by a sharp increase in the mean Pb–O distance (Figure S1a). Part of this irregularity is an artifact of the xTB thermal correction: with the full r²SCAN-3c/SMD thermochemistry, ΔG₁ falls to +25.6 kJ mol⁻¹ (Table S1). The remaining irregularity (ΔG₁ > ΔG₂) and the long Pb–O distance suggest that the b = 1 complex is still not the global minimum; no systematic conformer search was made (Section 2.4), so the quantitative PbBr₂ values should be regarded as less certain than those of the other precursors.

3.3. Relative Solubility in the Mixed Solvent

The relative solubility S_sat(φ)/S_sat(0) calculated from Equation (5) and the mass balance is shown in Figure 3. For PbI₂ the solubility rises steeply on adding DMI: in the dilute limit, 10 vol% DMI increases it by a factor of about 1.6·10⁴, φ = 40% gives about 1.3·10⁵, and the curve levels off at about 2·10⁵ near φ = 80%. These values refer to the dilute limit. At realistic concentrations (S_ref = 0.1–1 mol L⁻¹), each dissolved PbI₂ binds four solvent molecules, so the mass balance limits the increase: the solubility rises by a factor of 2–10 at 10 vol% DMI and by 5–25 in the 1:1 mixture (Figure S3); the shape of the curve is unchanged. Because these numbers depend exponentially on ΔG_b, the ±4 kJ mol⁻¹ uncertainty changes them by several orders of magnitude (shaded band in Figure 3a), and the reliable conclusion is the shape of the curve, a steep rise at small DMI fraction followed by saturation, in line with Figure 2. For PbBr₂ and MABr, in contrast, the solubility decreases as DMI is added: in the 1:1 mixture it is about 14–16 times lower than in pure 2Me, and in pure DMI about 10⁴ times (PbBr₂) and 9·10⁴ times (MABr) lower. The solubility of FAI stays nearly constant up to φ ≈ 80% (0.8–1.8 times that in pure 2Me, with a small maximum near the 1:1 mixture) and falls sharply only near pure DMI (about 10² times lower). These variations lie within the ±4 kJ mol⁻¹ band, and with the full r²SCAN-3c thermochemistry the preference of FAI for 2Me is stronger (Table S1), so the reliable conclusion for FAI is that its solubility does not decrease appreciably up to φ ≈ 80%. The solubility limit of PbI₂ is therefore expected at low DMI fractions and that of the other three precursors at high DMI fractions. The distribution of solvate complexes (Figure S2) shows the mechanism: in PbI₂ the all-2Me complex disappears at a very small DMI fraction, PbI₂(2Me)₂(DMI)₂ dominates between φ ≈ 2% and 56%, PbI₂(2Me)(DMI)₃ between 57% and 86%, and the full DMI complex above 86%; in PbBr₂ and MABr the all-2Me complex dominates up to φ ≈ 90%, and mixed complexes appear only in a narrow range near pure DMI; in FAI the mixed complex with two DMI molecules at the cation and two 2Me molecules at the anion is the main species from φ ≈ 16% to 98%. In a mixed solvent the two solvents together thus create the optimal solvation environment for FAI.

Figure 3. Relative saturation solubility S_sat(φ)/S_sat(0) of the precursors as a function of the DMI volume fraction φ, calculated with Equation (5) and the mass balance: (a) PbI₂, (b) PbBr₂, (c) FAI and (d) MABr. The solid line is calculated with the computed ΔG_b; the shaded band is the range obtained by shifting ΔG_b by ±4 kJ mol⁻¹ per DMI molecule (method error, Section 2.4). The curves are calculated in the dilute limit (S_ref = 10⁻⁶ mol L⁻¹); for realistic concentrations see Figure S3. The upper axis gives the 2Me:DMI volume ratio.

3.4. Overall Solvation Preference and Tentative Composition Range

The full-exchange free energy per DMI molecule, ΔG_n/n (Figure 4), summarizes the four precursors: −8.4 kJ mol⁻¹ for PbI₂ and +4.9, +2.0 and +6.3 kJ mol⁻¹ for PbBr₂, FAI and MABr. With the ±4 kJ mol⁻¹ uncertainty, the sign is unchanged for PbI₂, PbBr₂ and MABr (for PbBr₂ the error bar ends close to zero), whereas the value for FAI lies within the error band, so FAI shows no clear preference for either solvent. The calculations point to a trade-off: PbI₂ needs only a small DMI fraction, because its gain saturates after two DMI molecules, whereas the solubility of PbBr₂ and MABr falls steadily as DMI is added and that of FAI stays nearly constant up to φ ≈ 80%. A 2Me-rich mixture is therefore expected to suit all four precursors best. The composition range of about 10–20 vol% DMI that follows from the model is not a prediction: the calculated solubilities depend exponentially on ΔG_b, and without an experimental solubility as a calibration point (Section S3 of the Supporting Information), the absolute limits cannot be derived. We use the range only as a consistency check. The empirical optimum of 75 μL of DMI per mL of ink (7.5 vol%) reported for blade-coated films of the same composition [20], and the ink used here (Section 2.2; 10 vol% DMI, 76 μL per mL before the additive solutions), lie at or slightly below the lower edge of this range, so the agreement is only approximate. Two further limitations apply. The ink contains 1.14 M PbI₂ and only about 0.9 M DMI, that is, fewer than one DMI molecule per PbI₂, so the dilute-limit picture, in which DMI is in large excess over the solute, does not apply directly (Figure S3). PbBr₂ and MABr, whose solubility decreases with DMI, are present at only about 0.06 M each, so they are far from their solubility limits in a 2Me-rich mixture. The range should therefore be regarded as tentative.

Figure 4. Full-exchange free energy per DMI molecule, ΔG_n/n (n = 4); error bars are ±4 kJ mol⁻¹ (method error, Section 2.4). A negative value indicates that DMI is preferentially solvating, a positive value that 2Me is.

3.5. Dissolution of the Precursors in 2Me/DMI and Reference Solvents

To test whether the 2Me/DMI mixture can hold the precursors in solution, perovskite solutions in green and conventional solvents were photographed (Figure 5). Besides 2Me:DMI and DMF:DMSO, the series contains two NMP-containing mixtures as controls: NMP is the Lewis-base co-solvent that was benchmarked against DMI in 2Me-based inks [20], it binds the formamidinium cation and stabilizes a FAI–PbI₂·NMP adduct [11], and DMF:NMP is its counterpart in the DMF-based pair. Comparing 2Me:NMP with 2Me:DMI, and DMF:NMP with DMF:DMSO, separates the effect of the co-solvent from that of the main solvent (2Me or DMF), and the single solvents show the contribution of each component. All solutions, including those based on 2Me, DMI, 2Me:DMI and 2Me:NMP, are clear and show no visible turbidity or precipitate, so the green solvents keep the precursors in solution, with no visible undissolved material, at the concentration of the ink (about 1.2 M Pb). The 2Me:DMI solution is pale yellow, like the DMF:DMSO reference, whereas the NMP-containing solutions (Figure 5d,i) are a deeper yellow-orange; this difference was not investigated here.

Figure 5. Photographs of perovskite precursor solutions in different solvents: (a) DMF, (b) DMSO, (c) DMF:DMSO, (d) NMP, (e) DMF:NMP (conventional formulations); (f) 2Me, (g) DMI, (h) 2Me:DMI, (i) 2Me:NMP (alternative and green formulations).

3.6. FTIR Spectra of the Precursor Solutions

Figure 6 compares the spectrum of the 2Me:DMI binary solvent with those of solutions containing MABr, FAI, PbI₂ and PbBr₂. The spectra show the C=O stretch of DMI near 1683 cm⁻¹, the C–O stretching bands of 2Me at 1120–1050 cm⁻¹ and the broad O–H band of 2Me near 3400 cm⁻¹, so both solvents remain available as donors in the mixture. The spectra of the conventional solvents and of the other formulations are given in Figures S4–S6 and are dominated by the same kind of solvent bands: ν(C=O) near 1660 cm⁻¹ for DMF and NMP, ν(S=O) near 1050 cm⁻¹ for DMSO and ν(O–H) near 3400 cm⁻¹ for 2Me. The DFT results predict that the carbonyl oxygen of DMI binds Pb²⁺ and the N–H groups of FA⁺ and MA⁺, and that the hydroxyl group of 2Me hydrogen-bonds to halide anions. In the harmonic r²SCAN-3c/SMD(2Me) spectra of representative clusters (Table S4), the C=O stretch of DMI shifts by only −3 to −13 cm⁻¹ relative to free DMI (b = 4 complexes: −5.5 cm⁻¹ for PbI₂, −13.2 for PbBr₂, −2.6 for FAI and −4.0 for MABr), and the O–H stretch of 2Me by −120 to −420 cm⁻¹ because of O–H···X⁻ hydrogen bonding. The calculated frequencies are harmonic and unscaled, and only shifts relative to the free solvent are used.

Figure 6. FTIR spectra of the 2Me:DMI binary solvent and of solutions containing the precursors (MABr, FAI, PbI₂ and PbBr₂): (a) 4000–400 cm⁻¹ (offset vertically), (b) C=O stretching region and (c) O–H stretching region of the absorbance spectra normalized to the band maximum. The arrow in (b) marks the shoulder of the FAI solution near 1715 cm⁻¹ and that in (c) the enhanced low-wavenumber side of the O–H band.

The measured band positions are given in Table 2. The C=O band of DMI lies at 1682.8 cm⁻¹ in 2Me:DMI, and it shifts by −0.7 cm⁻¹ on adding MABr, by −0.6 cm⁻¹ on adding PbBr₂ and not at all (0.0 cm⁻¹) on adding PbI₂. The C–O and C–H bands of the solvent move by 0.8 cm⁻¹ or less. Only the FAI solution shows a larger change in the C=O region: the band is shifted by −3.2 cm⁻¹ (to 1679.6 cm⁻¹), is slightly broader and has an additional shoulder near 1715 cm⁻¹ (Figure 6b). The shift agrees with the calculated value for FAI (−2.6 cm⁻¹), but the shoulder is most probably the C=N stretching band of FA⁺, which lies in the same region and would distort the position of the C=O band, and a shift of 3 cm⁻¹ is below the resolution of the measurement (4 cm⁻¹); we therefore do not treat it as evidence of coordination. For PbI₂ and PbBr₂, for which the largest shifts are calculated (−5.5 and −13.2 cm⁻¹), none is observed. The calculated values refer to complexes in which DMI occupies all four sites, whereas the band measured is an average over all DMI molecules, bound and free, in a mixture that contains 90 vol% of 2Me, so the shifts are expected to be much smaller; this is consistent with the observation but does not allow us to test the calculated values.

Table 2. Positions of the main IR bands of 2Me:DMI and of its solutions of the precursors, from Lorentzian fits (cm⁻¹), and their shifts relative to 2Me:DMI in parentheses. The fit errors are 0.05–0.3 cm⁻¹; the resolution of the measurement is 4 cm⁻¹.

Band	2Me:DMI	+MABr	+FAI	+PbI2	+PbBr2
C=O, DMI	1682.8	1682.2 (−0.7)	1679.6 (−3.2)	1682.8 (0.0)	1682.2 (−0.6)
C–O, 2Me	1121.0	1120.9 (−0.2)	1120.3 (−0.7)	1121.0 (0.0)	1120.9 (−0.1)
C–O, 2Me	1062.8	1062.8 (0.0)	1062.4 (−0.4)	1062.3 (−0.5)	1062.7 (−0.1)
C–H	2875.8	2876.1 (+0.3)	2876.4 (+0.6)	2876.5 (+0.7)	2875.7 (−0.1)

The O–H band of 2Me (maximum near 3400 cm⁻¹) shows a clearer change: its low-wavenumber side (3000–3250 cm⁻¹) is stronger in all four solutions than in 2Me:DMI (Figure 6c). At 3100 cm⁻¹ the absorbance, normalized to the band maximum, is 0.14 for 2Me:DMI and rises to 0.22 (MABr), 0.26 (PbI₂), 0.29 (PbBr₂) and 0.44 (FAI). This is the direction expected for O–H···X⁻ hydrogen bonds, and for PbI₂ and PbBr₂ it cannot be caused by N–H groups. However, the N–H stretching bands of FA⁺ and MA⁺ absorb in the same region, and water taken up by the hygroscopic salts, whose content was not determined, also increases the absorbance there, so the change cannot be assigned to coordination quantitatively. The spectra thus show qualitative changes in the C=O and O–H regions in the direction predicted by the calculations, apart from the missing shifts for PbX₂, but they are single measurements, the shifts are at or below the resolution, and they are not used as independent evidence for the calculated coordination pattern. The spectra also show that the solvents remain chemically intact and that no new strong bands other than those of the cations appear when the precursors are dissolved.

3.7. Optical and Structural Properties of the Films

The absorption spectra of the perovskite films prepared from the 2Me:DMI and DMF:DMSO inks are compared in Figure 7. Both films have the absorption onset at 776 nm (1.60 eV; tangent method, Section 2.3), the steepest part of the edge at 760 nm and the same low background above 800 nm, so the choice of solvent does not change the position of the edge. The 2Me:DMI film absorbs more strongly at shorter wavelengths, with a steep rise below 570 nm, and shows weak shoulders near 575, 645, 665 and 685 nm that are absent from the DMF:DMSO spectrum. Stronger absorbance was likewise found for films from 2Me inks with an optimized DMI content [20]. A higher absorbance can reflect a thicker or more strongly scattering film. The shoulders are not features of a single-phase three-dimensional perovskite edge; they may come from additional absorbing species, such as residual intermediate or lower-dimensional phases, or from optical interference in the film, and their origin is not resolved by these data. Because of this, no conclusion on film quality is drawn from the absorption spectra beyond the position of the band edge. The absorbance of the 2Me:DMI film at 600 nm (baseline-corrected) is about 1.25 times that of the DMF:DMSO film (1.31 and 1.05), so, if the absorption coefficients are equal, the 2Me:DMI film is about 25% thicker, which accounts at least in part for its stronger absorbance. The thickness was not measured directly (profilometry or cross-sectional SEM), and the comparison neglects reflection and scattering. The XRD patterns (Figure 8) are discussed below.

Figure 7. UV–vis absorption spectra of perovskite (PVSK) films prepared from the 2Me:DMI and DMF:DMSO inks. The dashed line marks the absorption onset at 776 nm.

Figure 8. XRD patterns of perovskite films cast from the DMF:DMSO and 2Me:DMI inks (background subtracted, smoothed as described in Section 2.3): (a) 10–45° with the reflections of the cubic perovskite phase indexed and those of ITO marked; (b) the PbI₂ (001) reflection.

The XRD patterns of the two films (Figure 8a) show the reflections of the cubic α-phase of the perovskite at 14.1°, 20.0°, 24.5°, 28.4°, 31.8°, 40.6° and 43.1° (indexed as (100), (110), (111), (200), (210), (220) and (300) of a cubic cell) and those of the ITO substrate at 30.2° and 35.0°. Both films also contain residual PbI₂, with its (001) reflection at 12.7° (Figure 8b); the height ratio of the PbI₂ (001) and perovskite (100) reflections is 0.10 for the film from DMF:DMSO and 0.17 for that from 2Me:DMI, so the 2Me:DMI film contains somewhat more PbI₂ (a semi-quantitative comparison of peak heights, which also depend on film thickness and preferred orientation). The ratio of the (200) and (100) heights is the same in both films (0.74 and 0.73), so the orientation of the grains does not differ appreciably. The full width at half maximum of the (100) reflection is 0.19° for DMF:DMSO and 0.22° for 2Me:DMI; XRD therefore does not indicate larger crystalline domains in the 2Me:DMI film, although the width also depends on the instrument and on microstrain and is not converted into a crystallite size here. Weak reflections at 8.3°, 10.1°, 21.3° and 23.3°, which we have not assigned, are present in both patterns, and a reflection at 29.1° is present only in the pattern of the DMF:DMSO film. The origin of the absorption shoulders in Figure 7 is not explained by the XRD patterns. One pattern of each film is shown.

Steady-state PL spectra of films cast on glass from the two inks are compared in Figure 9. Both films show a single emission band with a maximum at 796 nm for 2Me:DMI and 792 nm for DMF:DMSO and with the same width (full width at half maximum about 57 nm). The maxima lie at longer wavelengths than the absorption onset at 776 nm, and the 4 nm difference between the films is small, so the solvent system does not change the emission band of the absorber appreciably, in agreement with the identical absorption edge. The peak intensity of the 2Me:DMI film is about 11% higher than that of the DMF:DMSO film. This difference is not evidence of fewer non-radiative losses: PL intensity also depends on film thickness, surface roughness and light out-coupling, and one film of each type was measured, and the 2Me:DMI film is estimated to be about 25% thicker. The films were measured on glass and not on PTAA, and no time-resolved PL or PL with transport layers was recorded, so carrier lifetimes are not discussed.

Figure 9. Steady-state PL spectra of perovskite films cast from the DMF:DMSO and 2Me:DMI inks on glass. The spectra were smoothed as described in Section 2.3.

3.8. Wetting of PTAA by 2Me/DMI Mixtures

Figure 10 and Table S5 show the contact angle of the 2Me/DMI mixtures on PTAA (drop profiles in Figure S7). All compositions wet PTAA well, with angles between 24.7° for pure 2Me and 13.3° for pure DMI. The angle decreases monotonically as the DMI content rises. The largest single change occurs at the first addition of DMI (24.7° to 21.7° at 10 vol%); beyond this the angle falls almost linearly, by 0.6–1.5° per 10 vol% of DMI, and the total change over the whole range is 11.4°. For comparison, DMSO, DMF and NMP give 45.6°, 25.6° and 12.0° on PTAA [16] (a different PTAA film, so the values are comparable only in trend): pure DMI wets PTAA about as well as NMP and 2Me about as well as DMF, whereas DMSO wets it much worse.

Figure 10. Contact angle of 2Me/DMI mixtures on PTAA as a function of the DMI volume fraction. The shaded band marks the 10–20 vol% DMI range that is consistent with the calculations as a tentative compromise for dissolving all four precursors (Figure 3).

In the tentative composition range suggested by the calculations (10–20 vol% DMI), the contact angle changes only from 21.7° to 21.0°, a difference of 0.7° that is probably within the experimental uncertainty (the scatter of the three drops is not reported), so wetting does not discriminate between compositions inside this range; it only shows that none of them suffers from poor wetting. The wetting behavior also changes during drying, which is what matters in gas-quenching deposition: the volatile 2Me (boiling point 124 °C) leaves the wet film first and the DMI fraction (boiling point 225 °C) rises, so the contact angle is expected to fall towards that of pure DMI. In DMF:DMSO the opposite happens: DMF leaves first, and the angle approaches that of DMSO, the poorest wetting solvent [16]. A high DMI content, although it favors wetting, slows drying and may retain solvent in the film, so a mixture with 10–20 vol% DMI appears to be a reasonable compromise. The measurements were made with the solvent mixtures alone; the dissolved precursors can change the angle and the surface tension, which were not determined. The contact angles of the inks themselves were not measured. The two inks contain the same precursors at the same concentrations and the same additives and differ only in the solvent system, so a difference in wetting is expected to originate mainly from the solvent; the effect of the dissolved salts on surface tension and viscosity, however, was not verified in either solvent system, and the wetting argument therefore rests on the solvent mixtures and on literature data for DMF:DMSO.

3.9. Film Morphology and Choice of the Reference Solvent

3.9.1. Choice of the Two Systems

Films were cast from 2Me:DMI and DMF:DMSO only, although nine solvent systems (five single solvents and four binary mixtures) were examined in solution. DMF:DMSO was taken as the reference because inks of this type are the basis of the solvent-engineering route [4,5], and in a direct comparison of inks with the same (FAPbI₃)_0.95(MAPbBr₃)_0.05 composition, 2Me/DMI gave the highest efficiency (23.45%) ahead of DMF/DMSO (22.73%) and 2Me/NMP (22.29%) [20]. NMP-containing mixtures were not taken to the film stage because the 2Me/NMP ink has a narrower processing window and a lower efficiency than 2Me/DMI [20], and DMF:NMP still contains the toxic DMF and is therefore not a green alternative. Single solvents were not taken to the film stage because the calculations show that neither 2Me nor DMI alone is the best solvent for all four precursors (Section 3.4), which is the reason for combining them; the single-solvent solutions served only to show the contribution of each component. The solution results do not separate the remaining formulations: all solutions are clear (Figure 5), the FTIR bands of the solvent change by 4 cm⁻¹ or less on adding the precursors (Figure 6), and the films from 2Me:DMI and DMF:DMSO have the same absorption onset at 776 nm (Figure 7). Both inks therefore give absorbers with the same band edge, so a difference between the films can be attributed to the solvent system and not to a different composition.

3.9.2. Morphology

Figure 11 compares the films. The film from DMF:DMSO (Figure 11a) consists of small, closely packed grains of about 0.4–1 μm, with clusters of bright elongated particles a few hundred nanometers long in some areas. The film from 2Me:DMI (Figure 11b) is built from larger grains of about 0.6–2 μm with well-defined boundaries and without such particles. Both films are continuous in the imaged areas and no pinholes are seen in either, so the images show a difference in grain size and not in coverage; the homogeneity was assessed visually only. The composition of the bright particles was not determined. A burst of nucleation gives many small grains, and slower nucleation gives fewer, larger ones (Section 1), so the different grain sizes may reflect different nucleation behavior of the two inks, but the present data do not resolve this. The wetting results point in the same direction: all 2Me/DMI mixtures wet PTAA (Figure 10), whereas DMSO is the poorest wetting solvent of the DMF/DMSO pair on PTAA, and dewetting caused by the DMSO fraction left in the wet film leads to pinholes in gas-quenching deposition [16]. The DMF:DMSO film imaged here shows no pinholes, so the SEM images neither show nor exclude this effect; the contact angles of the inks themselves were not measured, and one area of each film was imaged. Both inks contain the same additives (MACl, thiourea and PMMA), so the difference cannot be attributed to them. Together, the DFT, wetting and SEM results indicate that, under the same gas-quenching conditions, the 2Me:DMI ink gives on PTAA a film of larger grains than the DMF:DMSO ink in the imaged areas, which supports the use of a 2Me-rich mixture as a green alternative. Grain sizes were measured on the two images shown in Figure 11 (Section 2.3): the mean equivalent grain diameter is 0.64 ± 0.17 μm for DMF:DMSO (473 grains) and 0.81 ± 0.22 μm for 2Me:DMI (294 grains), with medians of 0.62 and 0.79 μm; the distributions are given in Figure S8. The values refer to one area of each film, the grains are not independent samples of the film, and the automatic segmentation splits some large grains in the 2Me:DMI image, which lowers its mean, so the difference of about 25% should be read as an estimate for the imaged areas and not as a statistical result for the films. The ranges quoted above are read from the scale bars of the images shown; the statistics above and the ranges differ because the ranges describe the visible spread of grain sizes and not their mean.

Figure 11. Top-view SEM images (secondary electrons, 8000×) of perovskite films cast from (a) DMF:DMSO and (b) 2Me:DMI on PTAA. Scale bars, 2 μm. The images were denoised (non-local-means filter) and their contrast was stretched; no other processing was applied.

3.10. Implications for Large-Area, Anti-Solvent-Free Processing

Large-area coating places requirements on the ink that the results above address in part. First, the ink must stay dissolved at a high concentration. The 1.2 M inks in 2Me:DMI are clear (Figure 5), and the calculations explain why some DMI is needed and why only a little: DMI raises the solubility of PbI₂ (by orders of magnitude in the dilute limit and by about 2–25 times at realistic concentrations, Figure S3), with most of the gain from the first two DMI molecules (Figure 2a and Figure 3a), whereas a 2Me-rich solvent keeps PbBr₂, FAI and MABr in solution (Section 3.4). The calculations give this trend and not the exact composition, because absolute limits need a solubility calibration point that DFT cannot supply (Section S3 of the Supporting Information). The composition rests on experiment: in blade-coated films of the same composition, 25–50 μL of DMI per mL of ink gave pinholes because DMI was too little to retard nucleation, 125 μL gave defective films, and the optimum was 75 μL [20]. The DMI content therefore cannot be reduced without limit; the workable range is narrow and is of the order of 10 vol% DMI, consistent with the direction of the calculated trend but not derived from it.

Second, the wet film must spread completely. All 2Me/DMI compositions wet PTAA (Figure 10), and the film from 2Me:DMI is continuous and built from larger grains than the DMF:DMSO film (Figure 11). Third, the intermediate formed after solvent extraction must survive the time that large-area coating takes before annealing. For 2Me/DMI, no δ-phase and no growth of PbI₂ were found after 5 min in ambient air before annealing, whereas the DMF/DMSO intermediate (diethyl ether quenching) degraded to PbI₂ and the 2Me/NMP intermediate formed δ-phase [20]. This stability is consistent with the preference of PbI₂ for DMI found here (Figure 2a). DMI nevertheless leaves the film completely at 100 °C within about 10 min, whereas DMSO remains after 1 h [20].

Fourth, no anti-solvent is needed. Our films were formed by nitrogen gas quenching alone, and 2Me/DMI inks have been processed by air-flow-assisted blade coating, again without an anti-solvent, into films over more than 100 cm² and modules of 20.1% efficiency [20]. Gas quenching can possibly be reduced further. During natural drying, nucleation in 2Me/DMI starts after about 1 min and the intermediate forms over 1–5 min [20], and 2Me is volatile, so a 2Me-rich ink with the lowest DMI content that still dissolves PbI₂ might crystallize even without quenching, which would remove the main equipment requirement of the method. This is a hypothesis: it was not tested here, our films were gas-quenched, and low DMI contents led to fast, inhomogeneous crystallization under air quenching [20]. Films cast with systematically reduced DMI content, with and without quenching, on blade- or slot-die-coated areas, and the resulting solar cells, are the experiments that would decide it. We also note that 2Me is itself a hazardous solvent (a reproductive toxicant) that needs closed handling, so the benefit of the 2Me/DMI system lies in its processing (no anti-solvent, a volatile main solvent, complete removal of DMI at 100 °C) and not in the absence of hazard.

4. Conclusions

Cluster–continuum DFT calculations show that DMI and 2Me play different roles in the solvation of the four precursor components of a FA/MA lead iodide–bromide ink. PbI₂ prefers DMI, with most of the stabilization gained from the first two DMI molecules, whereas PbBr₂ and MABr prefer 2Me and FAI shows only a weak preference that depends on the thermochemical level. In FAI and MABr, 2Me occupies the anion sites through O–H···X⁻ hydrogen bonds, while DMI preferentially solvates the cation. A thermodynamic model built on these free energies predicts that the solubility of PbI₂ rises steeply and then saturates on adding DMI, while the solubility of PbBr₂ and MABr falls and that of FAI stays nearly constant up to φ ≈ 80%, so that a 2Me-rich mixture is expected to be the best compromise for a single ink; the composition range of about 10–20 vol% DMI is a consistency check with experiment and not a prediction. All 2Me/DMI mixtures wet PTAA (21–22° at 10–20 vol% DMI). Without an anti-solvent (gas quenching only), the 2Me:DMI ink gives on PTAA a continuous film of larger grains than the DMF:DMSO ink in the imaged areas, with the same absorption onset (776 nm) and a similar PL band (maxima at 796 and 792 nm); no pinholes were found in either film in the imaged areas. XRD shows the cubic α-phase in both films, with somewhat more residual PbI₂ in the 2Me:DMI film (PbI₂ (001)/perovskite (100) height ratio 0.17 against 0.10) and no larger crystalline domains; the 2Me:DMI film is estimated to be about 25% thicker from the absorbance. Combined with literature data on blade-coated films and modules, these results support 2Me:DMI as a solvent system for anti-solvent-free, large-area processing, with a narrow, 2Me-rich composition range set by PbI₂ solubility on one side and by the solubility of the other precursors and the nucleation rate on the other. The calculations give relative solubilities only, assume ideal mixing of the solvents and use a continuum parametrized for 2Me; the uncertainty from conformational sampling and from the contact-ion-pair model was not quantified. Large-area films, solar cells and modules, films with reduced DMI content with and without gas quenching, and the contact angles of the inks remain to be reported.