Eugenia S Vasileiadou

Xinyi Jiang

Mikael Kepenekian

Jacky Even

Michael C De Siena

Vladislav V Klepov

Daniel Friedrich

Ioannis Spanopoulos

Qing Tu

Imra S Tajuddin

Mikaël Kepenekian

Emily A Weiss

Mercouri G Kanatzidis

Thick-Layer Lead Iodide Perovskites with Bifunctional Organic Spacers Allylammonium

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Introduction:

Hybrid halide perovskites are low-cost semiconductors of broad technological and commercial interest as they have proven to be suitable for a wide range of applications including solar cells [START_REF] Kojima | Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells[END_REF][2][START_REF] Kim | Lead Iodide Perovskite Sensitized All-Solid-State Submicron Thin Film Mesoscopic Solar Cell with Efficiency Exceeding 9%[END_REF][START_REF] Lee | Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskites[END_REF][START_REF] Stoumpos | Halide Perovskites: Poor Man's High-Performance Semiconductors[END_REF][START_REF] Tsai | High-efficiency two-dimensional Ruddlesden-Popper perovskite solar cells[END_REF][START_REF] Arora | Perovskite solar cells with CuSCN hole extraction layers yield stabilized efficiencies greater than 20%[END_REF][START_REF] Yang | Iodide management in formamidinium-lead-halide-based perovskite layers for efficient solar cells[END_REF][START_REF] Tsai | Light-induced lattice expansion leads to high-efficiency perovskite solar cells[END_REF] , light emission [START_REF] Cao | Perovskite light-emitting diodes based on spontaneously formed submicrometre-scale structures[END_REF][START_REF] Lin | Perovskite light-emitting diodes with external quantum efficiency exceeding 20 per cent[END_REF][START_REF] Sutherland | Perovskite photonic sources[END_REF] , radiation detection [START_REF] Fang | Highly narrowband perovskite single-crystal photodetectors enabled by surface-charge recombination[END_REF][START_REF] Wei | Sensitive X-ray detectors made of methylammonium lead tribromide perovskite single crystals[END_REF][START_REF] Wei | Dopant compensation in alloyed CH3NH3PbBr3-xClx perovskite single crystals for gamma-ray spectroscopy[END_REF][START_REF] He | Resolving the Energy of γ-Ray Photons with MAPbI3 Single Crystals[END_REF][START_REF] He | High spectral resolution of gammarays at room temperature by perovskite CsPbBr3 single crystals[END_REF] and lasing [START_REF] Zhu | Lead halide perovskite nanowire lasers with low lasing thresholds and high quality factors[END_REF][START_REF] Zhang | 2D Ruddlesden-Popper Perovskites Microring Laser Array[END_REF] . The 3D halide perovskite structure: AMX3, consists of corner-sharing MX6 octahedra with the A-site cation occupying the center of the cuboctahedral cavities. A is one of the monovalent cations: CH3NH3 + (MA + ), HC(NH2)2 + (FA + ), Cs + or recently CH3NH2NH2 + 20-21 , M is a divalent metal (Ge 2+ , Sn 2+ , Pb 2+ ) [START_REF] Stoumpos | Hybrid Germanium Iodide Perovskite Semiconductors: Active Lone Pairs, Structural Distortions, Direct and Indirect Energy Gaps, and Strong Nonlinear Optical Properties[END_REF] and X is a halide (Cl -, Br -, or I -). [START_REF] Dieter | CH3NH3PbX3, ein Pb(II)-System mit kubischer Perowskitstruktur / CH3NH3PbX3, a Pb(II)-System with Cubic Perovskite Structure[END_REF][START_REF] Goldschmidt | Die Gesetze der Krystallochemie[END_REF] The incorporation of organic cations larger than the aforementioned A-site cations, leads to the dimensional reduction of the 3D structure, of general formula (A')m(A)n-1MnX3n+1, where A' is a monovalent (m=2) or divalent (m=1) cation and n is the number of inorganic layers. The resultant arrangement of alternating semiconducting inorganic layers with insulating organic layers generates a natural 2D quantum-well superlattice in a bulk crystal. This quantum confinement increases the band gap energy (Eg) and the exciton binding energy (Eb) in comparison to the 3D structures. [START_REF] Hanamura | Quantum wells with enhanced exciton effects and optical non-linearity[END_REF][START_REF] Muljarov | Excitons in self-organized semiconductor/insulator superlattices: PbI-based perovskite compounds[END_REF][START_REF] Even | Analysis of Multivalley and Multibandgap Absorption and Enhancement of Free Carriers Related to Exciton Screening in Hybrid Perovskites[END_REF][START_REF] Even | Understanding Quantum Confinement of Charge Carriers in Layered 2D Hybrid Perovskites[END_REF][START_REF] Katan | Quantum and Dielectric Confinement Effects in Lower-Dimensional Hybrid Perovskite Semiconductors[END_REF][START_REF] Blancon | Semiconductor physics of organic-inorganic 2D halide perovskites[END_REF] The quantum-well heterostructure of the 2D perovskite can be fine-tuned by chemical synthetic design through the number of the inorganic layers n and the organic "spacer" cation. [START_REF] Stoumpos | Ruddlesden-Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors[END_REF][START_REF] Mitzi | Conducting tin halides with a layered organicbased perovskite structure[END_REF][START_REF] Li | The 2D Halide Perovskite Rulebook: How the Spacer Influences Everything from the Structure to Optoelectronic Device Efficiency[END_REF] Through the subsequent increase of the n-layer thickness in the 2D perovskite structure, the 2D materials' optical and electronic properties (Eb, Eg and photoluminescence PL) consecutively progress towards that of the 3D material. 31- 32, 34-37 Elseway, the organic "spacer" cation influences indirectly the structure of the inorganic framework through its resultant non-covalent templating, as well as the intrinsic chemical properties inherited to the material such as crystallinity, solubility and thermochemical stability. [START_REF] Vasileiadou | Insight on the Stability of Thick Layers in 2D Ruddlesden-Popper and Dion-Jacobson Lead Iodide Perovskites[END_REF][START_REF] Vasileiadou | Shedding Light on the Stability and Structure-Property Relationships of Two-Dimensional Hybrid Lead Bromide Perovskites[END_REF][START_REF] Vasileiadou | Structure-Property Relationships and Idiosyncrasies of Bulk, 2D Hybrid Lead Bromide Perovskites[END_REF] Recently, the improved environmental stability of 2D hybrid lead iodide perovskites coupled with their inherent structural flexibility, [START_REF] Vasileiadou | Insight on the Stability of Thick Layers in 2D Ruddlesden-Popper and Dion-Jacobson Lead Iodide Perovskites[END_REF][START_REF] Smith | A Layered Hybrid Perovskite Solar-Cell Absorber with Enhanced Moisture Stability[END_REF] enabled the fabrication of robust optoelectronic devices. [START_REF] Tsai | High-efficiency two-dimensional Ruddlesden-Popper perovskite solar cells[END_REF][START_REF] Cao | 2D Homologous Perovskites as Light-Absorbing Materials for Solar Cell Applications[END_REF][START_REF] Niu | Review of recent progress in chemical stability of perovskite solar cells[END_REF][START_REF] Quan | Ligand-Stabilized Reduced-Dimensionality Perovskites[END_REF][START_REF] Zhao | Opportunities and Challenges in Perovskite Light-Emitting Devices[END_REF][START_REF] Mao | Two-Dimensional Hybrid Halide Perovskites: Principles and Promises[END_REF][START_REF] Proppe | Synthetic Control over Quantum Well Width Distribution and Carrier Migration in Low-Dimensional Perovskite Photovoltaics[END_REF][START_REF] Spanopoulos | In Quest of Environmentally Stable Perovskite Solar Cells: A Perspective[END_REF] The phase space of 2D halide perovskites has been populated by four primary structure subtypes, based on the charge of the organic spacer cation and the relative stacking of the inorganic layers:

Ruddlesden-Popper (RP) structure (A')2(A)n-1MnX3n+1, [START_REF] Stoumpos | Ruddlesden-Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors[END_REF][START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF][START_REF] Spanopoulos | Uniaxial Expansion of the 2D Ruddlesden-Popper Perovskite Family for Improved Environmental Stability[END_REF] Dion-Jacobson (DJ) structure (A')(A)n-1MnX3n+1, [START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF] alternating cations in the interlayer space (ACI) type (A')(A)n-1MnX3n+1 [START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)3)(CH3NH3)nPbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF] and alkyl diammonium cations (NH3CmHmNH3)(CH3NH3)n-1MnX3n+1. [START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)n-1PbnI3n+1 (m = 4-9; n = 1-4)[END_REF] Amongst these, the (100) RP layered halide perovskites are the most prevalent, as the majority of 2D perovskites published belong to this substructure family. [START_REF] Stoumpos | Ruddlesden-Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors[END_REF][START_REF] Saparov | Organic-Inorganic Perovskites: Structural Versatility for Functional Materials Design[END_REF][START_REF] Vasileiadou | Structure-Property Relationships and Idiosyncrasies of Bulk, 2D Hybrid Lead Bromide Perovskites[END_REF][START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF][START_REF] Spanopoulos | Uniaxial Expansion of the 2D Ruddlesden-Popper Perovskite Family for Improved Environmental Stability[END_REF][START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Li | Negative Pressure Engineering with Large Cage Cations in 2D Halide Perovskites Causes Lattice Softening[END_REF] Less recurrent are layered perovskites of n ≥ 2, incorporating functional groups (e.g. unsaturated bonds, heteroatoms) within the organic layers that diversify significantly the explored phase space. [START_REF] Vasileiadou | Structure-Property Relationships and Idiosyncrasies of Bulk, 2D Hybrid Lead Bromide Perovskites[END_REF][START_REF] Wang | Synthesis and characterization of [NH2C (I): NH2] 3MI5 (M= Sn, Pb): stereochemical activity in divalent tin and lead halides containing Single. ltbbrac. 110. rtbbrac. Perovskite sheets[END_REF][START_REF] Mitzi | Structurally Tailored Organic-Inorganic Perovskites: Optical Properties and Solution-Processed Channel Materials for Thin-Film Transistors[END_REF][START_REF] Zhu | C4H3SCH2NH3)2(CH3NH3)Pb2I7 : noncentrosymmetrical crystal structure of a bilayer hybrid perovskite[END_REF][START_REF] Mercier | Unique Hydrogen Bonding Correlating with a Reduced Band Gap and Phase Transition in the Hybrid Perovskites (HO(CH2)2NH3)2PbX4 (X = I, Br)[END_REF][START_REF] Mercier | HO2C(CH2)3NH3)2(CH3NH3)Pb2I7: a predicted non-centrosymmetrical structure built up from carboxylic acid supramolecular synthons and bilayer perovskite sheets[END_REF][START_REF] Billing | Poly[bis[2-(1-cyclohexenyl)ethylammonium] di-[mu]-iododiodoplumbate(II)][END_REF][START_REF] Sourisseau | Reduced Band Gap Hybrid Perovskites Resulting from Combined Hydrogen and Halogen Bonding at the Organic-Inorganic Interface[END_REF][START_REF] Mercier | Structural diversity and retro-crystal engineering analysis of iodometalate hybrids[END_REF][START_REF] Zhou | Photoluminescence spectral broadening, chirality transfer and amplification of chiral perovskite materials (R-X-p-mBZA)2PbBr4 (X = H, F, Cl, Br) regulated by van der Waals and halogen atoms interactions[END_REF][START_REF] Bala | Effects of Cl and F Substitution in Phenylethylammonium Spacer Cations on Stability, Structure, and Optical Properties of 2D-3D Ruddlesden-Popper Perovskite Layers[END_REF][START_REF] Daub | From 1D to 3D: Perovskites within the System HSC(NH2)2I/CH3NH3I/PbI2 with Maintenance of the Cubic Closest Packing[END_REF][START_REF] Tian | Towards Fluorinated Ruddlesden-Popper Perovskites with Enhanced Physical Properties: A Study on (3-FC6H4CH2CH2NH3)2PbI4 Single Crystals[END_REF][START_REF] Chakraborty | Iodine-Iodine Interactions Suppressing Phase Transitions of 2D Layered Hybrid (I-(CH2)n-NH3)2PbI4 (n = 2-6) Perovskites[END_REF] In this context, there are also n = 1 perovskites incorporating optical active organic layers that participate in the configuration of the optical properties of the 2D perovskite. [START_REF] Mitzi | Design, Structure, and Optical Properties of Organic-Inorganic Perovskites Containing an Oligothiophene Chromophore[END_REF][START_REF] Cortecchia | Crystal Engineering of a Two-Dimensional Lead-Free Perovskite with Functional Organic Cations by Second-Sphere Coordination[END_REF][START_REF] Passarelli | Enhanced Out-of-Plane Conductivity and Photovoltaic Performance in n = 1 Layered Perovskites through Organic Cation Design[END_REF][START_REF] Leveillee | Tuning Electronic Structure in Layered Hybrid Perovskites with Organic Spacer Substitution[END_REF] Finally, 2D hybrid halide perovskites provide a viable architecture to perform small molecule reactivity in the solid-state by utilizing the chemical reactivity of functional organic layers to orchestrate covalent and noncovalent interactions for technological use, as in (photo)polymerization, chemisorption, electrochemical ion cycling, etc. [START_REF] Tieke | Chemical Reactions in Perovskite-Type Layer Structures[END_REF][START_REF] Tieke | Solid-state polymerization of butadienes. Crystal structure and solution properties of a stereoregular amphoteric 1,4-trans-polybutadiene[END_REF][START_REF] Tieke | Solid State Polymerization of Butadienes in Layer Structures[END_REF][START_REF] Mitzi | Templating and structural engineering in organic-inorganic perovskites[END_REF][START_REF] Sourisseau | Hybrid Perovskite Resulting from the Solid-State Reaction between the Organic Cations and Perovskite Layers of α1-(Br-(CH2)2-NH3)2PbI4[END_REF][START_REF] Jaffe | Lithium Cycling in a Self-Assembled Copper Chloride-Polyether Hybrid Electrode[END_REF][START_REF] Solis-Ibarra | Reversible and Irreversible Chemisorption in Nonporous-Crystalline Hybrids[END_REF][START_REF] Solis-Ibarra | Post-synthetic halide conversion and selective halogen capture in hybrid perovskites[END_REF][START_REF] Yao | Multilayered Perovskite Materials Based on Polymeric-Ammonium Cations for Stable Large-Area Solar Cell[END_REF][START_REF] Smith | Between the Sheets: Postsynthetic Transformations in Hybrid Perovskites[END_REF][START_REF] Ortiz-Cervantes | Thousand-fold Conductivity Increase in 2D Perovskites by Polydiacetylene Incorporation and Doping[END_REF] , as well as small molecule intercalation that has been achieved with the intercalation of neutral or polarizable molecules, affording a final material with distinct structural and/or electronic properties. [START_REF] Mitzi | Structurally Tailored Organic-Inorganic Perovskites: Optical Properties and Solution-Processed Channel Materials for Thin-Film Transistors[END_REF][START_REF] Dolzhenko | In Situ X-Ray Observation on the Intercalation of Weak Interaction Molecules into Perovskite-Type Layered Crystals (C9H19NH3)2PbI4 and (C10H21NH3)2CdCl4[END_REF][START_REF] Papavassiliou | Structural and electronic properties of the natural quantum-well system (C6H5CH2CH2NH3)2SnI4[END_REF][START_REF] Mitzi | Intercalated Organic-Inorganic Perovskites Stabilized by Fluoroaryl-Aryl Interactions[END_REF][START_REF] Billing | Synthesis, characterization and phase transitions of the inorganic-organic layered perovskite-type hybrids [(CnH2n+1NH3)2PbI4] (n = 12, 14, 16 and 18)[END_REF][START_REF] Smith | Decreasing the electronic confinement in layered perovskites through[END_REF] The inclusion of designer organic molecules with functional groups within the organic layers has been demonstrated to influence the optoelectronic and photophysical properties of 2D perovskite materials. [START_REF] Proppe | Synthetic Control over Quantum Well Width Distribution and Carrier Migration in Low-Dimensional Perovskite Photovoltaics[END_REF][START_REF] Smith | Decreasing the electronic confinement in layered perovskites through[END_REF] Previously, the Sargent group showed that the organic cation influences the quantum well distribution, as 2D perovskite films and devices incorporating AA resulted in superior device performance due to the greatly reduced distribution of quantum wells in these materials, versus those with organic cations of similar chain length. [START_REF] Proppe | Synthetic Control over Quantum Well Width Distribution and Carrier Migration in Low-Dimensional Perovskite Photovoltaics[END_REF] However, the synthetic preparation and structure-property relationships of crystallographically characterized thick-layer (n ≥ 2) lead perovskites with organic cations consisting of (non-optically active) functional groups has not be investigated systematically and is of great potential interest in the community, as well as for device applications.

In this work, we incorporate the bifunctional organic molecules of allylammonium (AA) and iodopropylammonium (IdPA) to produce three new homologous series: (AA)2MAn-1PbnI3n+1 (n=3-4), [(AA)x(IdPA)1-x]2MAn-1PbnI3n+1 and (IdPA)2MAn-1PbnI3n+1 (n=1-4). In the strongly acidic conditions of hydroiodic acid in the used synthesis, we observe the direct iodination of the allyl group with HI and its transformation into the iodopropyl group. The two distinct chemical identities of the functional groups AA (terminal alkene group) and IdPA (polarizable iodine atom), allow the drawing of several conclusions on the impact of the nature of the organic cation on the structure, optoelectronic properties and charge carrier dynamics. Single crystal X-ray diffraction reveals that (AA)2MA2Pb3I10 (n=3) crystallizes in an unexpected structure type with a unidirectional offset (0, < ½), while (IdPA)2MA2Pb3I10 and the alloyed [(AA)x(IdPA)1-x]2MA2Pb3I10 crystallize in the more conventional RP structure. (IdPA)2MA2Pb3I10 exhibits higher distortions of the equatorial Pb-I-Pb angles in comparison to (AA)2MA2Pb3I10, which leads to a blueshift of its band-edge absorption (2.03 eV versus 2.0 eV respectively) and photoluminescence (PL) emission. (AA)2MA2Pb3I10 and (IdPA)2MA2Pb3I10 manifest similarities in their electronic properties with in-plane electron and hole effective masses around 0.04.m0 and -0.08.m0, respectively. Additionally, the IdPA cations have a greater dielectric contribution from the iodine atom in the organic cation, thus reducing the dielectric mismatch with the well at the origin of the dielectric confinement effect, whereas AA and BA (butylammonium: C4H12N) have similar dielectric contributions, dependent on the rotations of the AA cation. Furthermore, studies of the excited-state dynamics using

Experimental Section:

All starting materials for synthesis were purchased commercially and were used without further purification, except for Methylamine hydrochloride and Allylamine hydrochloride which were dried in an oven at 70°C. PbO (99.9%), Methylamine hydrochloride ≥ 98% (CH3NH2•HCl = MACl), Hydroiodic acid (HI) (57 wt % in H2O, distilled, stabilized, 99.95%) and Hypophosphorous acid solution (50 wt % in H2O) were purchased and used as received from Sigma-Aldrich. Allylamine hydrochloride (C3H5NH2•HCl = AA + Cl -) (98%) was purchased from TCI America.

Synthesis:

2-Iodopropylammonium iodide (IdPA + I -)

AA + Cl -(10 mmol; 1 g) is dissolved in a mixture of 8 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling for four hours, under constant magnetic stirring where a clear solution was obtained.

Afterwards, the solution mixture is lowered to 130°C (as stated on hotplate) until the solvent has fully evaporated and a white solid is yielded. Yield 1.53 g, (45.7%).

2D Perovskite Series with Allylamine Spacer Cation

(AA)2MA2Pb3I10 (n=3): PbO (2 mmol; 446 mg) and MACl (1.3 mmol; 88 mg) powders were dissolved in a mixture of 4.5 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. The reaction solution was left on the hotplate to cool to room temperature, under continuing stirring. Next, AA + Cl -salt (2 mmol; 187 mg) was added to the reaction solution at room temperature (R.T.), under continuous stirring. The stirring was discontinued after 10 min, and the reaction solution was transferred to a petri dish for slow evaporation.

Dark red crystals precipitated from the petri dish within 1-2 days. The crystals were isolated by vacuum filtration and dried under vacuum overnight. Yield : 189 mg, 13.7 % based on total Pb.

Characterization:

The experimental techniques and methods used for the characterization of the structure and properties of the studied materials are found in detail in the Supporting Information (S.I.).

Results and Discussion: Synthetic Aspects and Reactivity of Allylammonium Cation in Hydroiodic Acid (57% w/w):

The ability of two different organic spacer cations to stabilize the 2D RP structures was investigated in this work. The first cation, AA, resulting from the dissolution of allylamine in concentrated HI underwent iodination across the unsaturated C=C bond with heating to yield the second cation iodopropylamine, IdPA. This reaction is being discussed in detail later. Figure 1 and Table 1 shows a structural and compositional overview the fourteen new 2D perovskites incorporating organic spacer cations with functional groups, synthesized in this work. The spacer cations employed here, allylammonium (H2C=CH-CH2-NH3 + or C3H8N) and 2-iodopropylammonium (H3C-CH(I)-CH2-NH3 + or C3H9NI), consist of a core alkylammonium skeleton of three carbons, where AA inheres a terminal alkene group and IdPA contains an iodine heteroatom on the alkylammonium chain. The targeted synthesis of the studied thick-layer perovskites was developed on the solution method based on aqueous hydroiodic acid. In brief, stoichiometric concentration of the starting reagents PbO, MACl and organic spacer is used to obtain uniform phase product of desired n value. As a result of the highly soluble nature of the organic cations employed here, stoichiometric amount of the organic spacer is used. This is also the case for the saturated version of the AA cation in the Ruddlesden-Popper series with propylammonium (PrpA: C3H10N) as the organic spacer cation, as well as in the series of alternating cation in the interlayer space with guanidinium (GA: CH6N3). [START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF][START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)3)(CH3NH3)nPbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF] In contrast, the synthesis of other series of 2D lead iodide perovskites that incorporate longer alkylammonium cations as the organic layers, require the off-stoichiometry method developed by our group. [START_REF] Stoumpos | Ruddlesden-Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors[END_REF][START_REF] Spanopoulos | Uniaxial Expansion of the 2D Ruddlesden-Popper Perovskite Family for Improved Environmental Stability[END_REF][START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)n-1PbnI3n+1 (m = 4-9; n = 1-4)[END_REF] The synthetic exploration and incorporation of functional groups into the organic layers of the 2D hybrid halide perovskite structure needs to be carefully considered before progressing to the targeted synthesis of the thick-layer (n>2) perovskite series. The established synthetic protocol based on the solution method with boiling, aqueous hydroiodic acid has been systematically used for the bulk synthesis of the majority of thick-layer lead iodide perovskites reported to date, as a universal method. [START_REF] Stoumpos | Ruddlesden-Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors[END_REF][START_REF] Spanopoulos | Uniaxial Expansion of the 2D Ruddlesden-Popper Perovskite Family for Improved Environmental Stability[END_REF][START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)3)(CH3NH3)nPbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF][START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)n-1PbnI3n+1 (m = 4-9; n = 1-4)[END_REF] In our case, the terminal alkene group in the allylammonium cation is prone to electrophilic addition. To our knowledge, literature review upon the exact reaction conditions of the terminal alkene-ammonium molecules in aqueous hydroiodic acid (without additive reagents) and its products, are not well studied. 89- 94 Aqueous hydroiodic acid has not been reported on extensively in the synthesis of organic aminoiodides.

For context, the direct addition of anhydrous HI (hydroiodination) to alkenes and alkynes for the synthesis of organic iodides is avoided due to difficulty of controlling iodine liberation, which leads to side reactions and poor yields. [START_REF] Breton | Hydrogen Iodide. : In Encyclopedia of Reagents for Organic Synthesis[END_REF] Instead, alternative materials and metals are used that generate HI in situ, although these reagents in majority, are expensive. [89][START_REF] Breton | Hydrogen Iodide. : In Encyclopedia of Reagents for Organic Synthesis[END_REF][START_REF] Beller | Catalytic Markovnikov and anti-Markovnikov Functionalization of Alkenes and Alkynes: Recent Developments and Trends[END_REF][START_REF] Zeng | Rhodium-Catalyzed Generation of Anhydrous Hydrogen Iodide: An Effective Method for the Preparation of Iodoalkanes[END_REF][START_REF] Chen | Metal-Free Transfer Hydroiodination of C-C Multiple Bonds[END_REF][START_REF] Xiao | Ready access to organoiodides: Practical hydroiodination and double-iodination of carbon-carbon unsaturated bonds with I2[END_REF] To understand the reactive behavior of the allylammonium cation (also known as propenylammonium) in hydroiodic acid as in our synthetic protocol (which employs a solution mixture of HI/H2PO3), NMR experiments were carried out on AA solely with HI, mimicking the conditions of the different steps of the perovskite synthesis (Figure S19). Firstly, AA + Cl -salt was dissolved in aqueous HI at room temperature (R.T.). The characteristic protons peaks corresponding to the unsaturated carbons of AA at 5.3 -5.8 ppm are present in the 1 H NMR spectra, with no peaks corresponding to the addition product of IdPA. Additionally, the [START_REF] Fang | Highly narrowband perovskite single-crystal photodetectors enabled by surface-charge recombination[END_REF] C NMR spectrum displays two peaks present in the 100 ppm region, indicating clearly that the unsaturated carbon bond did not react in aqueous HI at R.T. for up to three weeks (Figure S20). These results agree with previous studies, which do not report reactivity for simple addition reactions of alkenes in aqueous hydrobromic acid at low temperature. [START_REF] Solis-Ibarra | Reversible and Irreversible Chemisorption in Nonporous-Crystalline Hybrids[END_REF][START_REF] Ortiz-Cervantes | Thousand-fold Conductivity Increase in 2D Perovskites by Polydiacetylene Incorporation and Doping[END_REF] Next, AA + Cl -salt was dissolved in boiling, aqueous hydroiodic acid under stirring for 5 min, as done in our established perovskite synthetic protocol. Here, the 1 H NMR shows the characteristic proton peaks of AA in the 5.3 -5.8 ppm range, as well as peaks corresponding to IdPA in 1.8 -4.2 ppm range. Interestingly, after one month, the aforementioned solution's NMR shows a larger amount of IdPA, as it seems that the heat catalyzes the production of IdPA within a month-time period (Figure S21). Lastly, we dissolved the AA + Cl -salt in boiling hydroiodic acid under stirring for 30 min. In this case, both organic cations exist, with IdPA present in roughly over 90% of the product mixture. Consequently, AA fully reacts with aqueous HI, under constant heating. NMR confirms the almost full conversion of AA to 2iodopropylammonium, with a small byproduct of the 1-iodopropylammonium salt corresponding to the remaining peaks (Figure S22). 2-iodopropylammonium (IdPA) is the Markovnikov product of the electrophilic addition of aqueous HI.

The above experiments demonstrate that the unsaturated bond of the AA cation can be preserved in aqueous HI solution at R.T. but will react upon heating. This requires modification of the conditions of the established synthetic protocol, with the reaction solution being left at R.T. and then, proceeding to add the AA organic spacer cation to the reaction solution. In our previously established synthetic protocol, the reaction solution is heated to boiling in order to create a reflux system, which is followed by the cooling of the reaction solution by returning to R.T. The temperature difference facilitates the immediate precipitation of the layered perovskite crystals. Based on the targeted 2D perovskite material, adjusting appropriately the cooling rate of the reaction solution assists the growth of higher quality crystals. In the solution synthesis of the series (AA)2MAn-1PbnI3n+1 (n=3 and 4) with aqueous hydroiodic acid, heating cannot be introduced to the system. As such, in order to expedite the growth of 2D perovskite crystals, the reaction solution is transferred to a large surface petri-dish to assist the quick evaporation of solvent.

As a result, the growth of high-quality crystals of the (AA)2MAn-1PbnI3n+1 (n=3 and 4) series is difficult to control based on this solution synthesis with aqueous hydroiodic acid. Surprisingly, targeted synthesis of n=1 and n=2 did not yield the expected 2D perovskites. Instead 2D structures of alternating cornerand face-sharing [PbI6] 4-octahedra were formed, similarly to the behavior of the saturated analogue with the PrpA cation [START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF] (Figure 1). Detailed analysis of these structures is in the Crystal Structures section below.

Capitalizing on the chemistry accessible through the terminal unsaturated bond of the allylammonium cation, the targeted synthesis of the (IdPA)2MAn-1PbnI3n+1 (n=1-4) series was achieved, to further investigate the role of a heteroatom functional groups in the organic layers. Since, the IdPA salt is not commercially available and coupled with our NMR studies, the synthesis of the salt was realized by prolong heating of allylammonium in aqueous HI/H3PO2. Based on the circular dichroism (CD) spectra (Figure S18), the (IdPA)2MAn-1PbnI3n+1 (n=1-4) homologous series contain a racemic mixture of the IdPA cation. This is expected as the starting alkene-amine, allylammonium, has no chiral center. The addition reactions of alkenes with no stereogenic center produces a racemic mixture of two enantiomers. [START_REF]The Stereochemistry of Alkene Addition Reactions[END_REF] Thus, the synthesis of amino organoiodides can be accomplished simply, practically and without expensive additional reagents. A general study on this hydroiodination method and its regioselectivity could be of benefit for the synthesis of a wide range of amino-alkyl and amino-alkenyl iodides, which are important building blocks in organic synthesis.

The synthesis of 2D perovskites with IdPA serving as the organic spacers gives the full thicklayer perovskite series (n= 1-4). However, (IdPA)2PbI4 (n=1) is the kinetic product, as its targeted synthesis instead yields a 0D perovskitoid with the formula (IdPA)6Pb3I12 = (IdPA)2PbI4 (Figure 1).

Stoichiometrically, (IdPA)6Pb3I12 composition is equivalent to the n=1 layered perovskite but the structure differs drastically, which consists of a trimer of face-sharing [PbI6] 4-octahedra partitioned by the IdPA cations (Figure 1). In the targeted synthesis of (IdPA)2PbI4 (n=1), crystals of the layered (IdPA)2PbI4 perovskite precipitate, but within hours convert to crystals of 0D (IdPA)6Pb3I12. Therefore, 0D (IdPA)6Pb3I12 is the thermodynamically favored product, corroborated by the fact it is more dense (Volume/Density = 865.1) than (IdPA)2PbI4 (Volume/Density = 326.8). Recently, a similar crystal-to crystal transformation was reported in a n=1 perovskite with cysteamine. [START_REF] Kour | An Organic-Inorganic Perovskitoid with Zwitterion Cysteamine Linker and its Crystal-Crystal Transformation to Ruddlesden-Popper Phase[END_REF] Furthermore, a second byproduct forms, that of a 1D perovskitoid with the formula (IdPA)PbI3. It belongs to the NH4CdCl3 structure-type, consisting of a 1D double ribbon of face-and edge-sharing [PbI6] 4-octahedra (Figure 1). This 1D structure was observed as well with (GA)PbI3. [START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)3)(CH3NH3)nPbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF] It is interesting how the AA and IdPA cations yield non-perovskite structures similar with GA and PrpΑ, as a result of the short size, steric and hydrogen bonding (HB) interactions. The greater HB capabilities of the organic layers unlock a rich structural diversity of perovskite-related compounds, providing synthetic clues for chemical exploration of new structural motifs.

Availing from the reactivity accessible from the terminal unsaturated bond of the AA cation, it is possible to create in-situ, a solid solution incorporating two chemically distinct cations in the A' position of the 2D perovskite structure, which has not been reported before in bulk, thick-layer perovskites (n >2), to our knowledge. With monitored heating, the AA cation reacts in the perovskite synthesis and slowly converts to IdPA, bestowing the 2D perovskite series of [(AA)x(IdPA)1-x]2(MA)n-1PbnI3n+1 (n=1-4), which consists of both AA and IdPA cations in the organic layers. The combination of PXRD (Figure S1-S11) and NMR (Figure S14-S24) data are necessary to probe the products of the in-situ reactions of the organic layers, to avoid inaccurate characterization of the organic and/or inorganic components. [START_REF] Zhang | Electronic Tunability and Mobility Anisotropy of Quasi-2D Perovskite Single Crystals with Varied Spacer Cations[END_REF] Progressively incorporating the IdPA cations into the organic layers affords a final A' site mixed-cation perovskite product with an increase in the stacking axis length and interlayer distance of the [(AA)x(IdPA)1-x]2(MA)n-1PbnI3n+1 (n=3-4) series versus the (AA)2MAn-1PbnI3n+1 (n=3 and 4) series (Figure 2C-D). Withal, NMR helps identify the organic cations present in the 2D material, which are assigned based on the characteristic peaks of the functional groups of the organic chains. This strategy of in-situ reaction of the organic layers appends an additional structural parameter to tune in the structure-property relationship of 2D perovskites. MAPbI3 reflections ∼2θ=13°) corresponds to the distance from the center of each layer, allowing us to easily estimate the expected peak positions for specific n-layer thickness, as well as the identity of the organic spacer cation (Table 1). For (AA)2MA2Pb3I10 (n=3) -(AA)2MA3Pb4I13 (n=4), the d100 spacing of the first reflections are at ∼24.2 Å and ∼30.5 Å respectively, whereas for (IdPA)2MA2Pb3I10 (n=3) -(IdPA)2MA3Pb4I13 (n=4) the d100 spacing is ∼26.9 Å and ∼32.1 Å respectively. The d100 spacing of the first reflection for the solid solution [(AA)x(IdPA)1-x]2MAn-1PbnI3n+1 (n=3 and 4) is between the range of 24.2 -26.9 Å for n=3 members, and between 30.5 -32.1 Å for n=4 members.

All three series of the novel 2D perovskites studied here, demonstrate a similar characteristic in crystal morphology of naturally forming clumps of crystals, composed of smaller single crystals with plate-like shape. The crystal clumps have overall irregular shapes and easily fracture during the task of isolation of the single crystals. SEM studies illustrate the plate-like morphology of the single crystals as well as the stacking-layered morphology for all studied materials (Figure S30-S32), which is a distinctive characteristic for the 2D layered perovskite structure. In comparison, although the structural parameters (stacking axis and interlayer distance) of (IdPA)2MAn-1PbnI3n+1 (n=1-4) are similar to (BA)2MAn-1PbnI3n+1 (n=1-4), the crystal morphology of the IdPA series is drastically different from BA and resembles closely to AA, based on qualitative observation. We employed nanoindentation of (AA)2MA2Pb3I10 single crystals (i.e., n = 3) along the stacking axis and compared the obtained elastic modulus and hardness to those from BA-and alkyl diammonium-based 2D lead iodide layered perovskites with the same n number (Table S1). We found that although both containing non-covalent interfaces between adjacent organic spacer molecular layers inside the crystals, (AA)2MA2Pb3I10 is stiffer (elastic modulus 𝐸 = 5.74 ± 0.48 GPa) than their BA counterpart, (BA)2MA2Pb3I10 (𝐸 = 4.40 ± 0.57 GPa), [START_REF] Tu | Out-of-Plane Mechanical Properties of 2D Hybrid Organic-Inorganic Perovskites by Nanoindentation[END_REF] but softer than the diammonium 2D perovskite (NH3C8H16NH3)MA2Pb3I10 (𝐸 = 11.65 ± 1.76 GPa). [START_REF] Tu | Exploring the Factors Affecting the Mechanical Properties of 2D Hybrid Organic-Inorganic Perovskites[END_REF] This is probably due to the additional hydrogen-bonding interaction between the terminal group C=C in the spacer molecules, which is stronger than the pure van der Waals bonding between the terminal methane group CH3 in (BA)2MA2Pb3I10, but weaker than the covalent bonding in (NH3C8H16NH3)MA2Pb3I10. This further confirms that tuning the interactions between the 2D perovskite layers can be an effective approach to tailor the mechanical behavior of 2D perovskites, as suggested by some of us in earlier publications. [START_REF] Tu | Exploring the Factors Affecting the Mechanical Properties of 2D Hybrid Organic-Inorganic Perovskites[END_REF][100][101] The obtained hardness values (i.e., the resistance to plastic deformation) generally follow the same trend of elastic modulus, though the difference between (AA)2MA2Pb3I10 and (BA)2MA2Pb3I10 is less dramatic.

The rich compositional parameter space and associated interesting new structures (details in the following section) of the three series of novel 2D perovskites reported here calls for a thorough investigation of their mechanical properties to study the structure-mechanical property relationship of 2D RP perovskites as a function of the organic component [START_REF] Tu | Out-of-Plane Mechanical Properties of 2D Hybrid Organic-Inorganic Perovskites by Nanoindentation[END_REF]100,[102][103][104] and establish guidelines for materials design to improve the mechanical stability issues of 2D perovskites. 101

Description of Crystal Structures:

The structures of all three series: (AA)2MA2Pb3I10 (n=3), [(AA)x(IdPA)1-x]2(MA)n-1PbnI3n+1 (n=1-3) and (IdPA)2MAn-1PbnI3n+1 (n=1-3) were solved from single crystal X-ray diffraction (SCXRD) data collected at room temperature (Table 2, Table 3 and Table S2-S3). These phases consist of corner sharing [PbI6] 4-octahedra, separated by the organic spacer cations in the [100] direction (Figure 1). The chemical identity of the organic layers is distinctive in the 2D perovskite series under study, by virtue of the characteristic functional groups embodied onto the identical, core alkylammonium chain. The incorporation of functional groups into the organic layers affords significant structural variances between the crystal structures with the same n-layer thickness. On the account for the consistent comparison amongst all three series, we will focus the discussion on the structural analysis of the n=3 members:

(AA)2MA2Pb3I10, (IdPA)2MA2Pb3I10 and [(AA)x(IdPA)1-x]2MA2Pb3I10.

The crystal structure of (AA)2MA2Pb3I10 (n=3) consists of [Pb3I10] 4-inorganic layers that are alternated with AA organic layers. The electrostatic interactions between the organic-inorganic layers yields a three-layer perovskite structure in which the inorganic layers stack on top of each other, along the stacking axis a (Figure 3A). Hence, there is no offset of the consecutive inorganic layers, along the a stacking axis with respect to the bc plane (Figure 3A). Along the b stacking axis with respect to the ac plane, there is an offset < ½. Therefore, (AA)2MA2Pb3I10 (n=3) is a new, unique structure type, different from the Ruddlesden-Popper (RP) type with offset (½,½) and the Dion-Jacobson (DJ) type with offset (0,0), (0,½). This is the first report of a monoammonium cation affording a non-RP hybrid halide structure type, which is evidently due to the additional hydrogen-bonding (HB) interactions induced from the terminal C=C, alkene group in the allylammonium cation. A comparison of the crystal structures (AA)2MA2Pb3I10 and (PrpA)2MA2Pb3I10 (n=3), which consists of organic layers with the saturated cation propylammonium, [START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF] evinces the definite effect of the terminal alkene group on the resultant 2D perovskite structure (Figure 3). (PrpA)2MA2Pb3I10 (n=3) adopts the RP structure with the staggered arrangement of the successive [Pb3I10] 4-inorganic layers (Figure 3A). [START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF] Furthermore, the stacking axis of (AA)2MA2Pb3I10 is 0.97Å ≈ 1Å smaller than that of (PrpA)2MA2Pb3I10 (Figure 4A), while the interlayer distance (between the successive inorganic layers) and adjacent I···I distance of (AA)2MA2Pb3I10 is 0.76Å and 1.18 Å smaller respectively than that of (PrpA)2MA2Pb3I10 (Figure 4B).

The systematically smaller values in the structural parameters of (AA)2MA2Pb3I10 versus (PrpA)2MA2Pb3I10 is surprising, as the only difference in the composition of the two materials is the terminal unsaturated bond in AA cation (C=C bond length ~ 1.34 Å) versus the saturated PrpA cation (C-C bond length ~ 1.54 Å). This is likely the result of the terminal alkene bond's: (i) greater HB interactions between the organic-organic and organic-inorganic layers due to the C=C group in the organic layers, (ii) small steric interactions and (iii) short size of AA cation, which is the smallest known monoammonium cation to template the 2D halide perovskite structure. The collective effect of the described electrostatic interactions brings the successive inorganic layers significantly closer together due to the AA layers and the 2D structure is sustained through the more rigid stacking of the inorganic layers with unidirectional offset (0,<1/2), deviating substantially from the RP structure. Thus, a synthetic exemplar is corroborated for the targeted synthesis of RP and DJ hybrid halide perovskites: an organic spacer cation with high HB capabilities, negligible steric hinderance and small cation size, leads to reduced spacing of the organic layers and a tendency to align of the successive inorganic layers to produce a 2D structure close to that of DJ or ACI perovskites. Only cyclic and aromatic diammonium cations have templated the 2D DJ halide perovskite structure, thus far based on structural characterization, confirming the synthetic criterion discussed. Lastly, the AA and PrpA cations behave similarly for members n<2, by producing the same "step-like" homologous series of non-perovskites (B)2m+4(MA)m-2Pb2m+1I7m+4 (m = 1-4), where the [PbI6] 4-octahedra connect in 2D through a corner-and face-sharing motif (Figure 1). [START_REF] Hoffman | From 2D to 1D Electronic Dimensionality in Halide Perovskites with Stepped and Flat Layers Using Propylammonium as a Spacer[END_REF] The crystal structure of (IdPA)2MA2Pb3I10 (n=3) consists of [Pb3I10] 4-inorganic layers that are alternated with IdPA organic layers, where there is an iodine atom on the second carbon of the propylammonium skeleton (Figure 3). The presence and position of the iodine atom on the alkylammonium cation induces greater steric interactions and bulkiness within the organic layers.

Consequently, the RP structure is templated with two offset layers per unit cell, verifying again the proposed synthetic exemplar. Lastly, single crystal X-ray diffraction of (IdPA)2MAPb2I7 (n=2) and (IdPA)2PbI4 (n=1) reveals that these members of the (IdPA)2MAn-1PbnI3n+1 series, also belong to the RP structure family (Figure 1). Furthermore, to institute a directory of synthetic criterion for the predictive synthesis and rational design of halide perovskite semiconductors, it is essential to collate insightfully the structural information of (i) RP lead iodide perovskites with the smallest monoammonium cations angles can be split into eq. angles of the outer inorganic layers and eq. angles of the inner inorganic layer (Figure 5B). Comparatively among both groups, the sequence of angle distortion is (

IdPA)2MA2Pb3I10 ≈ [(AA)x(IdPA)1-x]2MA2Pb3I10 > (AA)2MA2Pb3I10 ≈ (PrpA)2MA2Pb3I10 > (BA)2MA2Pb3I10. Again, [ (
AA)x(IdPA)1-x]2MA2Pb3I10 and (IdPA)2MA2Pb3I10 exhibit the greatest distortions due to the steric interaction of the iodine atom within the organic layers. (AA)2MA2Pb3I10 and (PrpA)2MA2Pb3I10 have comparable values of inner and outer eq. angles, although on average (AA)2MA2Pb3I10 has slightly larger distortion. Lastly, (BA)2MA2Pb3I10 has the smallest level of distortion in general, for both inner and outer eq. angles. Therefore, the greater HB and smaller steric interactions of the AA cation govern the stacking geometry of the inorganic layers but does not induce profound variance in the distortion levels of the equatorial Pb-I-Pb, in comparison with PrpA and BA. This implies that the strength of the electrostatic interactions of the spacer cation is balanced between its control on the stacking geometry of the inorganic layers and the distortion level within the inorganic layers. shows that bandgap of ACI < DJ < RP ≈ Diamine. [START_REF] Mao | Hybrid Dion-Jacobson 2D Lead Iodide Perovskites[END_REF][START_REF] Li | Two-Dimensional Dion-Jacobson Hybrid Lead Iodide Perovskites with Aromatic Diammonium Cations[END_REF][START_REF] Soe | New Type of 2D Perovskites with Alternating Cations in the Interlayer Space, (C(NH2)3)(CH3NH3)nPbnI3n+1: Structure, Properties, and Photovoltaic Performance[END_REF][START_REF] Li | Two-Dimensional Halide Perovskites Incorporating Straight Chain Symmetric Diammonium Ions, (NH3CmH2mNH3)(CH3NH3)n-1PbnI3n+1 (m = 4-9; n = 1-4)[END_REF]108 The proximity is regulated by the choice of the organic spacer cation, providing new insight for targeted design synthesis criterion.

Optical Properties:

The absorption spectra are typical of layered perovskites, with an absorption edge and an excitonic peak above the bandgap due to quantum confinement. The bandgaps are estimated by extrapolating from the absorption edge, a slope perpendicular to the x axis. Figure 6A depicts the absorption spectra of the n=3 and n=4 members of the AA, IdPA and AA/IdPA mixed-cation series. It is noteworthy that exciton signatures do not clearly appear in these spectra, which can be either qualitatively be attributed to a small exciton binding energy or to the crystalline powder morphology leading to a very large inhomogeneous broadening of the exciton resonances (Figure 6A and Figure 6C). The bandgap of (AA)2MA2Pb3I10 (n=3) and (AA)2MA3Pb4I13 (n=4) are 2.00 eV and 1.91 eV, respectively; both compounds exhibit slightly lower Eg values respectively than their analogues: (IdPA)2MA2Pb3I10 (2.03 eV) and (IdPA)2MA3Pb4I13 (1.99 eV) respectively (Figure 6B). This trend is also apparent in the PL spectra: the band-edge emission of has energy 1.99 eV for (AA)2MA2Pb3I10 and 1.90 eV for (AA)2MA3Pb4I13, both of which are red-shifted from that of their analogs (IdPA)2MA2Pb3I10 (2.02 eV) and (IdPA)2MA3Pb4I13 (1.92 eV) (Figure 6D).

The emission of (AA)2MA2Pb3I10 is lower energy than the emission of (IdPA)2MA2Pb3I10 due to the coupled effects of smaller distortions of the eq. Pb-I-Pb angles and smaller interlayer distance, as discussed above (Figure 2 and Figure 4). The bandgap evolution for the series of multilayer perovskite compounds under study, along with the PropA and BA series, is shown Figure 6B, where the increase of n leads to lower bandgaps, ranging from 2.22 eV -1.90 eV for n=2-4 respectively. The PL spectra of the studied crystals include an additional, broad emission peak at lower energy, as seen in Figure 6E. The coexistence of narrow-and broadband emission has been studied in n=1 lead halide perovskites 109-110 but to our knowledge, there has not been thorough investigation on the study of broadband emission in in bulk, thick-layer (n ≥ 2) lead iodide perovskites. This broadband emission in the visible region is thoroughly studied in the Charge Carrier Dynamics section below.

Since the bulk perovskites in this study are candidates as light absorbing layers in solar cell devices, photoemission yield spectroscopy in air (PYSA) was utilized to measure the work function of the materials. [111][112][113] The position of the valence band maxima (VBM) was determined through the PYSA measurements, while the conduction band minimum (CBM) was determined by subtracting the Layered halide perovskites are not only solution-processed natural quantum wells, they are also dielectric quantum wells, due to the contrast between the dielectric constant of the perovskite layers and that of the organic cation layers. This cannot be described when computing the standard bulk highfrequency dielectric response (𝜀 ∞ ) for the unit cell that provides an average of both moieties' contributions. Instead, we propose to discuss the evolution of 𝜀 ∞ along z following a recipe designed for nanoscale slabs and composite systems. [START_REF] Even | Understanding Quantum Confinement of Charge Carriers in Layered 2D Hybrid Perovskites[END_REF]116 Profiles of the high-frequency dielectric constant along the stacking axis of the n=1-3 for the IdPA series and AA structures are shown in Figure 9 and Figure S15.

In addition, the profile of the (BA)2(MA)2Pb3I10 structure with BA as a spacer is given for comparison (Figure 9). 117 Figure 9 shows the expected shape of such a profile for layered halide perovskites with low values for the region occupied by the organic cations with 𝜀 ∞ ~1.9, while the n=3 inorganic perovskite slab reaches 𝜀 ∞ ~ 5.3. The same value is found for the n=3 structures with AA or IdPA as spacers. This value indicates an already reduced dielectric confinement for the perovskite layer. Indeed, the profiles 𝜀 ∞ (𝑧) of the n=1-3 IdPA series (Figure S15) display an increase from the contribution of the perovskite layer, ranging from 𝜀 ∞ (𝑧) = 4.4 for n=1, 𝜀 ∞ (𝑧) = 4.8 for n=2 to 𝜀 ∞ (𝑧) = 5.3 for n=3, a contribution that would eventually reaches the dielectric constant of bulk MAPbI3. 107 The comparison between the n=3 structures: (IdPA)2(MA)2Pb3I10, (AA)2(MA)2Pb3I10 and (BA)2(MA)2Pb3I10 show the much greater contribution in the barrier for IdPA-based 2D series due to the iodine atom found in the organic cation (Figure 9A). The large contributions of iodine atoms to 𝜀 ∞ (𝑧) in the barrier was also reported in a n=1

compound to be at the origin of an experimental strong reduction of the exciton binding energy and oscillator strength. [START_REF] Smith | Decreasing the electronic confinement in layered perovskites through[END_REF] AA and BA have closer constants. The one computed for AA depends on the orientation of the double bound with respect to the stacking direction (Figure S16). In our static picture, the contribution of the unsaturated bound is negligible. Rotations of the AA cations probably delivers an average constant closer to the optimal value obtained leading to a greater screening for AA than for BA.

Charge Carrier Dynamics:

Transient absorption (TA) spectra were measured on the newly synthesized AA/IdPA crystal series to study how the nature of the organic spacer affect the excited-state dynamics of thick-layer lead halide perovskites. In the Description of Crystal Structures section above, we show that the inclusion of the unsaturated C=C bond and iodine atoms in the organic layers have different impact on the overall lattice structure. The double bond, due to its shorter length greatly reduces the interlayer distance and induces the zero-offset stacking geometry. The iodine atom, because of its polarizable nature and the large steric hinderance it imposes, induces larger distortion within the Pb-I-Pb angles of the inorganic layer.

We acquired TA spectra on exfoliated single crystals after pumping the sample at 2.41 eV (0.36 eV above the bandgap) with a broadband probe from 1.5 to 2. The nature of the trap states created by AA and IdPA cations is worth further exploration. The impact of the addition of iodine atoms between the organic layers cannot be neglected. The shallow ladder state could be explained by either a defect state like iodine interstitials [123][124][125] or a new phonon-assisted recombination pathway. 126 The formation mechanism of the deep sink state may be quite unique, considering its unusual behavior of retaining the carriers longer compared to the band-edge states. One possible explanation is that a "new bandgap" was created by the defect states like Pb vacancies, and then the photogenerated electrons and holes were delocalized and spatially separated in the presence of Pb vacancies, leading to a suppressed radiative charge recombination, as was hypothesized for the BA-based perovskites 127 . The related defect might not be a lead vacancy, since the IdPA spacer with an additional iodine atom was involved, but the recombination suppression mechanism should be similar. A better hypothesis could be developed if the actual form of the charged species were known, but this is far beyond the scope of the current paper. Further research conducted with half-cell and mid-bandgap excitation could pursuit to achieve a more thorough answer.

Conclusions:

Understanding how to engineer the organic layers, which regulate the synthesis, structural character, electronic and photophysical properties of the resultant structure is pivotal for establishing specific synthetic criterion for the rational design and predictive synthesis of hybrid semiconductors. We demonstrate that the inclusion of (non-optically active) functional groups onto the organic cation chain governs the synthetic preparation, crystal chemistry and recombination dynamics of the resultant thicklayer lead iodide perovskite. The bulk synthesis and crystallographic characterization of three new homologous series of (AA)2MAn-1PbnI3n+1 (n=3-4), [(AA)x(IdPA)1-x]2MAn-1PbnI3n+1 and (IdPA)2MAn-1PbnI3n+1 (n=1-4) of layered perovskites and perovskite-related compounds is reported. For the first time, thick-layered perovskites (n≥3) consisting of organic molecules with heteroatom-functional groups have been synthesized in bulk. Developing reactions that leverage the inherent reactivity of functional groups within the organic layers, affords the solid solution of [(AA)x(IdPA)1-x]2MAn-1PbnI3n+1, through in-situ formation. Additionally, the synthetic understanding obtained from this work encourages the development of a universal solution method of layered halide perovskites with non-hydrohalic solvents, while emphasizing the imperative necessity of precise structural characterization of bulk and films of hybrid layered perovskites.

The (AA)2MAn-1PbnI3n+1 (n=3-4) series adopts the 2D perovskite structure, where the crystal structure of (AA)2MA2Pb3I10 is a unique thick-layer structure type close to the DJ type, with an offset (0, < ½). This is a rare example of a thick-layer (n>1), lead halide perovskite with monoammonium spacer cation that affords a non-RP structure type. Instead of the layered perovskite structure, the targeted synthesis of n<2 in the (AA)2MAn-1PbnI3n+1 series, yielded the 2D step-like homologous series of non-perovskites those reported previously for AA perovskite films and devices (~90 ps). [START_REF] Proppe | Synthetic Control over Quantum Well Width Distribution and Carrier Migration in Low-Dimensional Perovskite Photovoltaics[END_REF] The inclusion of the IdPA cation, with a heavy and sterically large iodine atom into the 2D perovskite interlayer space instigates significant lattice distortions and leads to the creation of new, broadband ensembles of states deep into the bandgap. These deep trap states quickly depopulate the band-edge excitons but overall elongate the lifetimes of photoexcited carriers to up to 100 ps.

Table 1. Summary of Structural and Optical Properties of All Novel Reported Compounds

  transient absorption (TA) spectroscopy for (AA)2MA2Pb3I10, [(AA)0.5(IdPA)0.5]2MA2Pb3I10, (IdPA)2MA2Pb3I10 and (BA)2MA2Pb3I10 point to the formation of long-lived trap states which can account for the broadband visible-light emission observed in (AA)2MA2Pb3I10, [(AA)0.5(IdPA)0.5]2MA2Pb3I10 and (IdPA)2MA2Pb3I10. The trap-state emission can be correlated to the lattice distortion induced by the inclusion of the bifunctional organic molecules with their characteristic functional groups. The incorporation of the IdPA cation induces the largest lattice distortions that give rise to a new ensemble of broadband states deep into the bandgap. Notably, these deep trap states depopulate the bandedge carriers and elongate the lifetime of photoexcited carriers to ~100-ps. Such behaviors indicate the formation of a new radiative recombination pathway rooted from these functional organic spacers.

(

  AA)2MA3Pb4I13 (n=4): PbO (2 mmol; 446 mg) and MACl (1.5 mmol; 101 mg) powders were dissolved in a mixture of 4.5 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. The reaction solution was left on the hotplate to cool to room temperature, under continuing stirring. Next, AA + Cl -salt (1 mmol; 93 mg) was added to the reaction solution at room temperature (R.T.), under continuous stirring. The stirring was discontinued after 10 min and the reaction solution was transferred to a petri dish for slow evaporation. Black crystals precipitated from the petri dish within 1-2 days. The crystals were isolated by vacuum filtration and dried under vacuum overnight. Yield : 123 mg, 9.14 % based on total Pb.2D Perovskite Series with Iodopropylamine Spacer Cation(IdPA)2PbI4 (n=1): PbO (1 mmol; 223 mg) powder was dissolved in a mixture of 1.5 mL HI and 0.25 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, IdPA + I -salt (0.5 mmol; 93 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 15 min and the reaction solution was left on the hotplate to cool to room temperature. Orange plate-like crystals co-precipitated from the reaction solution, along with yellow needle-like crystals of (IdPA)6Pb3I12. The crystals were carefully isolated from the second-phase crystals, removed from the HI mother liquid by vacuum filtration and dried under vacuum overnight. Yield : 34 mg, 3.13 % based on total Pb. (IdPA)2MAPb2I7 (n=2): PbO (2 mmol; 446 mg) and MACl (1 mmol; 70 mg) powders were dissolved in a mixture of 4.5 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, IdPA + I -salt (2 mmol; 372 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 15 min and the reaction solution was left on the hotplate to cool to room temperature. Bright red crystals precipitated from the reaction solution. The crystals were isolated by vacuum filtration and dried under vacuum overnight. Yield : 132 mg, 15.47 % based on total Pb.

(

  IdPA)2MA2Pb3I10 (n=3): PbO (2 mmol; 446 mg) and MACl (1.3 mmol; 88 mg) powders were dissolved in a mixture of 4.5 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, IdPA + I -salt (2 mmol; 372 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 15 min and the reaction solution was left on the hotplate to cool to room temperature. Dark red crystals precipitated from the reaction solution. The crystals were isolated by vacuum filtration and dried under vacuum overnight. Yield : 243 mg, 15.66 % based on total Pb. (IdPA)2MA3Pb4I13 (n=4): PbO (4 mmol; 892 mg) and MACl (3 mmol; 202 mg) powders were dissolved in a mixture of 8 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, IdPA + I -salt (2 mmol; 372 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 15 min and the reaction solution was left on the hotplate to cool to room temperature. Black crystals precipitated from the reaction solution. The crystals were isolated by vacuum filtration and dried under vacuum overnight. Yield : 356 mg, 12.08 % based on total Pb. 2D Perovskite Series with Mixed Spacer Cations (Allylamine + Iodopropylamine) [(AA)x(IdPA)1-x]2PbI4 (n=1): PbO (1 mmol; 223 mg) powder was dissolved in a mixture of 1.5 mL HI and 0.25 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, AA + Cl -salt (2 mmol; 187 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 5 min and the reaction solution was left on the hotplate to cool to room temperature. Yellow plate-like crystals co-precipitated from the reaction solution, along with yellow needle-like crystals. [(AA)x(IdPA)1-x]2MAPb2I7 (n=2): PbO (2 mmol; 446 mg) and MACl (1 mmol; 70 mg) powders were dissolved in a mixture of 3.5 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, AA + Cl -salt (2 mmol; 187 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 5 min and the reaction solution was left on the hotplate to cool to room temperature. Red crystals precipitated from the reaction solution. The crystals were isolated by vacuum filtration and dried under vacuum overnight. [(AA)x(IdPA)1-x]2MA2Pb3I10 (n=3): PbO (3 mmol; 669 mg) and MACl (2 mmol; 135 mg) powders were dissolved in a mixture of 5 mL HI and 0.5 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, AA + I -salt (2 mmol; 187 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 5 min and the reaction solution was left on the hotplate to cool to room temperature. Dark red crystals precipitated from the reaction solution. They were isolated by vacuum filtration and dried under vacuum overnight. [(AA)x(IdPA)1-x]2MA3Pb4I13 (n=4): PbO (1 mmol; 223 mg) and MACl (0.75 mmol; 55 mg) powders were dissolved in a mixture of 1.5 mL HI and 0.25 mL hypophosphorous acid (H3PO2) by heating to boiling under constant magnetic stirring, until a clear yellow solution was obtained. Next, AA + I -salt (1 mmol; 93 mg) was added to the reaction solution, under continuous stirring and heating. The stirring was discontinued after 5 min and the reaction solution was left on the hotplate to cool to room temperature. Black crystals precipitated from the reaction solution. They were isolated by vacuum filtration and dried under vacuum overnight.

  The powder X-ray diffraction (PXRD) patterns of crystals (AA)2MAn-1PbnI3n+1, (IdPA)2MAn-1PbnI3n+1 and [(AA)x(IdPA)1-x]2MAn-1PbnI3n+1 (n=3 and 4) is shown in Figure 2A-B, with negligible reflections from secondary phases to confirm the successful synthesis of the studied compounds (Figure 2A-B and Figure S3-S6,S9-S11). The d-spacing for the low angle peaks (below the characteristic 3D

  [PrpA and BA=butylammonium] and the other known structure types that are (ii) DJ based on dications such as (3AMP)MA2Pb3I10, (4AMP)MA2Pb3I10, (3AMPY)MA2Pb3I10 and (4AMPY)MA2Pb3I10 where AMP = a-(aminomethyl)piperidinium, AMPY = a-(aminomethyl)pyridinium], and (iii) the ACI materials such as (GA)MA3Pb3I10 with two different monocations in the interlayer and a DJ-like (0,1/2) offset and finally (iv) the primary diammonium cations [(NH3C8H16NH3)(MA)2Pb3I10 and (NH3C9H18NH3)(MA)2Pb3I10, close to the RP class in terms of offset. 51-54 Amongst the RP lead iodide perovskites with the smallest monoammonium cations, (AA)2MA2Pb3I10, [(AA)x(IdPA)1-x]2MA2Pb3I10, (IdPA)2MA2Pb3I10, (PrpA)2MA2Pb3I10 and (BA)2MA2Pb3I10 are examined comparatively. In Figure 4A, (AA)2MA2Pb3I10 has the smallest stacking axis and interlayer distance among the n=3 compounds under study, followed by (PrpA)2MA2Pb3I10 < (BA)2MA2Pb3I10 < [(AA)x(IdPA)1-x]2MA2Pb3I10 < (IdPA)2MA2Pb3I10. The significantly smaller values of the structural parameters of (AA)2MA2Pb3I10 shows that AA brings the inorganic [PbI6] 4-layers closer together, which reflects the strong impact of the electrostatic influences from the terminal alkene group, as discussed above. In comparison, (PrpA)2MA2Pb3I10 and (BA)2MA2Pb3I10 have an expected evolution of their structural parameters. [(AA)x(IdPA)1-x]2MA2Pb3I10 operates as a median compound, to affirm the smooth evolution of the structural parameters from (AA)2MA2Pb3I10 to (IdPA)2MA2Pb3I10, proving to have a higher composition of IdPA cations and thus, resembling more (IdPA)2MA2Pb3I10.(IdPA)2MA2Pb3I10 has the largest interlayer distance among the examined n=3 compounds, even compared to (BA)2MA2Pb3I10, owning to the steric interaction and bulkiness of the C-I bond (~ 2 Å) (Figure4A).

Figure 4C -

 4C Figure 4C-D demonstrates the comparison of the main structural parameters of (AA)2MA2Pb3I10 individually, along with the above RP structures with small monoammonium cations, as well as with DJ, ACI and diamine structure types. The ACI and DJ structures have significantly the smallest interlayer and adjacent I···I distances amongst all the structure types collated here, with (AA)2MA2Pb3I10 following behind. The RP and diamine structure types have similar values of their interlayer and adjacent I···I distances. Hence, the HB capabilities and steric interactions of the organic layers produce profound variance in the structural parameters, such as the offset type, and especially on the interlayer and adjacent I···I distances.Regarding the Pb-I-Pb angles, there are two sorts classified: the equatorial angle (parallel to the inorganic plane) and the axial angle (in the stacking direction). The distortion level of the Pb-I-Pb angles of the inorganic octahedra is correlated with the bandgap of the material, as it is an important parameter in the calculation of the electronic structure of the material.[105][106][107] As seen in Figure5A, the distortion levels of the Pb-I-Pb angles are similar for (AA)2MA2Pb3I10, (PrpA)2MA2Pb3I10 and (BA)2MA2Pb3I10. In contrast, [(AA)x(IdPA)1-x]2MA2Pb3I10 and (IdPA)2MA2Pb3I10 have significantly greater deviation of their Pb-I-Pb angles comparatively (Figure5A). The iodine atom of the IdPA cation has a preference to instigate greater distortion of the equatorial Pb-I-Pb angle versus the axial angle, which exhibits the smallest amount of distortion among the examined n=3 RP compounds. Moreover, the equatorial (eq.)

Figure

  Figure 5C displays the equatorial and axial Pb-I-Pb angles among the n=3 compounds across the different structure types RP, DJ, ACI and diamine-based lead iodide perovskites. For the crucial eq. Pb-I-Pb angles, the sequence of greater distortion is as following: DJ > RP > AA > Diamine >ACI. This result coupled with the structural information on the interlayer distances and the observed band gap values, leads to a fundamental conclusion. The close proximity of the [PbI6] 4-layers in hybrid halide perovskites suggests a greater contribution on the band gap value than the distortion level of the eq. Pb-I-Pb angles, as is verified by the observed band gaps. ACI has the smallest interlayer distance and smallest distortions of the eq. Pb-I-Pb angles, which logically aligns with the observed lowest Eg value. Although, the DJ perovskites have the highest distortions in the eq. Pb-I-Pb angles, their average Eg value are lower than those of RP and diamines, which have smaller distortions. As mentioned above, the average value of the interlayer distance in DJ perovksites is amongst the smallest in comparison. Hence, this indicates that the adjacent [PbI6] 4-layers interact electronically and must have an electronic contribution to the bandgap value, when in significantly close proximity, where the trend in bandgap established thus far

  corresponding band gap values (based on the absorption edge) from the measured VBM energies. The PYSA of the n=3 and n=4 novel 2D perovskite materials were collected: (AA)2(MA)2Pb3I10, (IdPA)2(MA)2Pb3I10, (AA)2(MA)3Pb4I13 and (IdPA)2(MA)3Pb4I13, alongside the reference 2D perovskites (BA)2(MA)2Pb3I10 and (BA)2(MA)3Pb4I13, and 3D MAPbI3 (Figure7). In the comparison of the n=3 analogues, the VBM of (IdPA)2(MA)2Pb3I10 (5.55 eV) and (AA)2(MA)2Pb3I10 (5.56 eV) are close in value, while (BA)2(MA)2Pb3I10 (5.37 eV) is smaller (Figure7). In the comparison of the n=4 analogues, the VBM is similar in value for all three compounds: (AA)2(MA)3Pb4I13 (5.41 eV), (IdPA)2(MA)3Pb4I13 (5.42 eV), and (BA)2(MA)3Pb4I13 (5.43 eV) (Figure7). Crystalline powder of MAPbI3 was measured with a VBM of 5.44 eV, matching to reported VBM value of 5.43-5.46 eV.[114][115] Electronic Structure Calculations and Dielectric Properties:We use density functional theory (DFT) based calculations to inspect the electronic structure of the layered perovskite (AA)2(MA)2Pb3I10 and the series (IdPA)2(MA)n-1PbnI3n+1. All compounds exhibit typical band structures (FigureS12) with direct bandgaps either at Γ ((IdPA)2(MA)n-1PbnI3n+1 for n=1,2 and (AA)2(MA)2Pb3I10) or Y for (IdPA)2(MA)2Pb3I10, as well as great dispersions in the directions corresponding to the plane of the perovskite layers and nearly no dispersion in the stacking direction.When going from n=1 to n=3 in the IdPA series, one can observe the expected electronic band gap reduction (from 1.55 to 1.14 eV at the chosen level of theory, FigureS13) as well the apparition of subbands that mark the decrease of quantum confinement for increasing values of n. As observed experimentally, the bandgap of the (AA)2(MA)2Pb3I10 structure is slightly smaller than the one of the (IdPA)2(MA)2Pb3I10 compound. The band structures of (AA)2(MA)2Pb3I10 and (IdPA)2(MA)2Pb3I10 are very similar (Figure8Aand 8B), underlying the small electronic influence of spacer cation near the band gap. The similarities extend to other electronic properties, since both layered perovskites also present very close low in-plane electron and hole effective masses (FigureS14) around 0.04.m0 and -0.08.m0, respectively. Following the n=1-3 IdPA series, we observe that the computed in-plane effective masses tend to decrease with increasing values of n, which can be traced back to the bandgap reduction.

  4 eV. These spectra contain both positive excited state absorption (ESA, blue) and negative ground state bleaches (red). The ESA features are similar among all four compounds studied [(AA)2(MA)2Pb3I10), [(AA)x(IdPA)1-x]2MA2Pb3I10, (IdPA)2(MA)2Pb3I10 and(BA)2(MA)2Pb3I10)], which have been attributed previously to intraband absorptions of carriers at and above band-edge carriers.[118][119][120][121] Here we focus on the energies and dynamics of the negative bleaching signals, which reflect the changing populations of states with energies at and below the bandgap.

Figure 10 (

 10 Figure10 (left two columns) shows that the bandgap bleach features peak at 2.05 eV for all four samples, consistent with the previously reported value for n=3 perovskites 122 and the ground state absorption spectra in Figure10. The most distinct difference between (IdPA)2(MA)2Pb3I10 (Figure10A) and (AA)2(MA)2Pb3I10 (Figure10C) with energies lower than the bandgap. TA spectra on [(AA)x(IdPA)1x]2MA2Pb3I10 (Figure10 B) and (BA)2(MA)2Pb3I10 (Figure10D) crystals are taken under the same condition. The relative intensity of the sub-bandgap peak at 1.94 eV (0.11 eV below Eg, marked using orange lines, referred to as 'ladder state' below) compared to the bandgap peak is 45% of the intensity of the bandgap peak for (IdPA)2(MA)2Pb3I10, 37% for [(AA)x(IdPA)1-x]2MA2Pb3I10, 16% for (AA)2(MA)2Pb3I10 and 5% for (BA)2(MA)2Pb3I10. The relative intensity of the peak at 1.73 eV (0.32 eV below Eg, marked using yellow line, referred to as 'sink state' below) is 36% of the intensity of the bandgap peak for (IdPA)2(MA)2Pb3I10, 15% for [(AA)x(IdPA)1-x]2MA2Pb3I10 and 0% for both (AA)2(MA)2Pb3I10 and (BA)2(MA)2Pb3I10. These relative intensities indicate that the formation of the

(

  AA)2m+4(MA)m-2Pb2m+1I7m+4. (IdPA)2MA2Pb3I10 manifests significantly distorted equatorial Pb-I-Pb angles among known n=3 RP perovskites, due to the greater steric interactions from the iodine atom on the IdPA cation. The strength of the electrostatic interactions induced from the spacer cation demonstrates a competing control between the stacking geometry of the consecutive inorganic layers and the distortion level within the Pb-I-Pb inorganic layers. The band-edge absorption and PL emission of (AA)2MA2Pb3I10 is around 2.0 eV, redshifted in comparison to (IdPA)2MA2Pb3I10 with band-edge absorption 2.03 eV. The band structures of (AA)2(MA)2Pb3I10 and (IdPA)2(MA)2Pb3I10 resemble, underlying the small electronic influence of the spacer cation near the band gap. Furthermore, the calculated high-frequency dielectric constant profiles of (AA)2MA2Pb3I10, (IdPA)2MA2Pb3I10 and (BA)2MA2Pb3I10 show a greater dielectric contribution from the IdPA cations, owing to the iodine atom in the organic chain. The AA and BA cations have similar dielectric contributions, dependent on the rotations of the AA cation. The ultrafast study provides new insight on broad emission in 2D halide perovskite materials. The formation of long-lived trap states with broadband emission in the visible region, can be directly related to nature of the organic cation with different functional groups. The crystal compounds containing the IdPA cation manifest shorter recombination lifetimes (~20 ps) than their analogues (AA)2MA2Pb3I10 and (BA)2MA2Pb3I10 (~ 75 ps). The longer recombination lifetimes of the (AA)2MA2Pb3I10 are consistent with

Figures:Figure 1 .

 1 Figures:

Figure 2 .

 2 Figure 2. (A) PXRD pattern for n=3 compounds (AA)2(MA)2Pb3I10, [(AA)x(IdPA)1-x]2(MA)2Pb3I10 and (IdPA)2(MA)2Pb3I10 along with the expanded view of the (100) reflections. (B) PXRD pattern for n=4 compounds (AA)2(MA)3Pb4I13, [(AA)x(IdPA)1-x]2(MA)3Pb4I13 and (IdPA)2(MA)3Pb4I13 along with the expanded view of the (100) reflections. (C) Stacking axis as a function of perovskite layer thickness (n), (D) Interlayer distance as a function of perovskite layer thickness (n), and (E) Adjacent I···I distances as a function of perovskite layer thickness (n) for the series: (AA)2(MA)n-1PbnI3n+1, [(AA)x(IdPA)1-x]2(MA)n-1PbnI3n+1, (IdPA)2(MA)n-1PbnI3n+1, (PrpA)2(MA)n-1PbnI3n+1 and (BA)(MA)n-1PbnI3n+1.

Figure 3 .

 3 Figure 3. (A) Comparative view of the offset geometry in the consecutive [PbI6] 4-layers, (B) Comparative view of the parallel plane to the stacking axis, and (C) Comparative view along the stacking axis between the (n=3) compounds (AA)2(MA)2Pb3I10, (IdPA)2(MA)2Pb3I10, (PrpA)2(MA)2Pb3I10 and (BA)2(MA)2Pb3I10.

Figure 7 .

 7 Figure 7. Photoemission Yield Spectroscopy in Air (PYSA) of (BA)2(MA)2Pb3I10, (AA)2(MA)2Pb3I10, (IdPA)2(MA)2Pb3I10, (BA)2(MA)3Pb4I13, (AA)2(MA)3Pb4I13, (IdPA)2(MA)3Pb4I13 and MAPbI3.

Figure 8 .

 8 Figure 8. Computed band structures for (A) (AA)2MA2Pb3I10 and (B) (IdPA)2MA2Pb3I10.

Figure 10 .

 10 Figure 10. Excited state dynamics of the n=3 allylamine 2D perovskite series with varying IdPA concentration. (Left) Transient absorption surface of IdPA, (AA)(IdPA), AA and BA n=3 crystals. Different levels of signal intensity are plotted as a function of probing energy (x-axis) and delay time after excitation at 2.41 eV (y-axis). Red represents the negative bleaching signal and blue represents the positive absorption signal. (Middle)Transient absorption spectra at different time delays from 0 (red) to 1 ns (blue). (Right) Normalized TA signal intensity at representative energy (each probing energy is marked using a colored line in the left and middle column with the corresponding color). The longest decay lifetimes in picosecond (assigned to be the carrier recombination lifetimes) were extracted using multi-exponential fits and marked near the cuts.

Figure 11 .

 11 Figure 11. (A) The normalized TA signal intensity extracted at the bandgaps showing the recombination dynamics at the bandgaps of crystals containing different cations. (B) The correlation between the lattice distortion and recombination lifetimes. The left axis shows the speed of the recombination and the right axis shows the average equatorial Pb-I-Pb bond angle solved by x-ray crystallography indicating the level of distortion inside the inorganic structures. A clear negative correlation can be observed between the level of distortion and the speed of recombination, suggesting the direct effect of lattice distortion on excited-state dynamics.

Acknowledgements: This work was supported by the Office of Naval Research, under grant N00014-17-1-2231 (synthesis, structural characterization of materials, M.G.K.). E.S.V. acknowledges the Dr. John N. Nicholson fellowship through Northwestern University. This work was supported by the Northwestern Materials Research Science and Engineering Center (NU-MRSEC, DMR-1720139) (measurement of optical properties). This work made use of the NUANCE Center and IMSERC facilities of Northwestern University, which have received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (NSF ECCS-2025633). Q.T. acknowledges support through the startup funds from the Texas A&M Engineering Experiment Station (TEES) and the Texas A&M Triads for Transformation (T3) grant. E.S.V. thanks Dr. Ido Hadar, Dr. Abishek Iyer, Dr. Jennifer Rote and Prof. Regan Thomson for productive discussion. Associated Content:

sink state at 1.73 eV is clearly related to the IdPA spacer added into the perovskite lattice, while the formation of the ladder state is a combined effort of both the AA and IdPA cations. When the sink state is present, which is the case of (IdPA)2(MA)2Pb3I10 and [(AA)x(IdPA)1-x]2MA2Pb3I10 crystals, carriers were quickly drained by the ladder state and then fed to the sink state to recombine. For (AA)2(MA)2Pb3I10, the carriers at bandgap were drained quickly as well by the ladder state, and that is why its bandgap signal does not plateau like that of (BA)2(MA)2Pb3I10, but without the sink state, the shallow ladder states quickly saturated so the long-term dynamics still resemble those of (BA)2(MA)2Pb3I10. The implication of these results is that these defect states could contribute to photovoltage losses on the picosecond timescale in solar cell devices.

Notes:

The authors declare no competing financial interest.