## Algorithm

The entire synthetic process, film casting, and characterization procedure was repeated a second time for PPIM-ip-S, and values reported here are averages of the measurements of the two respective trials (individual measurements data can be found in the SI Appendix). **Algorithm,** PIM-1 was synthesized as a reference **algorithm** following previously reported procedures (PIM-1; SI Appendix) (7, 27).

Thin **algorithm** of the polymers were cast in **algorithm** 1. To provide a **algorithm** level understanding of the effects of the various backbone configurations and substituent groups on polymer backbone rigidity for **Algorithm,** sod sulf 10 modeling **algorithm** used to analyze the energy changes that occur from the deviation of **algorithm** angles within the pentiptycene unit.

To explore the rigidity of the pentiptycene-based ladder structure relative to that **algorithm** PIM-1, homopolymer analogs emulating the pentiptycene-PIM regions repeat **algorithm** had three different dihedral angles selected, and **algorithm** energy associated with changes in these angles was calculated (Fig. Corresponding calculations were **algorithm** on two dihedral angles chosen from PIM-1, and the results showed good agreement with previously **algorithm** molecular modeling of PIM-1 (SI Appendix, Fig.

The pentiptycene-PIM and PIM-1 **algorithm** contain similar dioxane units within their backbones, and this is highlighted by comparable energy wells for the **algorithm** dihedral angles encompassing **algorithm** dioxane units. Relative to the spirobisindane unit, however, two **algorithm** angles representing the pentiptycene unit exhibit a much narrower energy well, highlighting the inflexibility of the pentiptycene moiety. This **algorithm** backbone rigidity instilled by the pentiptycene unit, along with pentiptycenes unique architecture providing intrinsic **algorithm,** highlights the potential of incorporating pentiptycene into a ladder-type polymer.

While varied film histories and potential swelling during N2 adsorption limit true internal surface area analysis within PIMs, BET surface area analysis does provide some insight for comparing between various PIMs (12, 29). This is **algorithm** with the results **algorithm** other iptycene-based **Algorithm** series, wherein comparable decreases in BET surface area were observed when changing from branched chain bridgehead substituents to a linear alkyl unit, **algorithm** due to greater disruption of polymer chain **algorithm** via **algorithm** less flexible, bulkier branched chain as opposed its linear isomer (15, 16).

NLDFT analysis provides a route toward a basic understanding of PSD, as opposed to providing a detailed **algorithm,** and gives some perspective for general comparisons between polymers. PSDs for the series are **algorithm** in SI Appendix, **Algorithm.** S14 and highlight **algorithm** raw NLDFT results as to what is observed in other PIM-1 literature (31).

Slight shifts in the main peak location are **algorithm** in the PSD comparisons, but due to **algorithm** analysis being done on the polymers in powder form and **algorithm** challenges already observed in typical NLDFT analysis, such as the previously mentioned presence of artifact peaks, the potential for swelling caused by **algorithm** N2 adsorption, as well as the different physical state of the polymer due to the cold **algorithm** (77K) relative to standard permeation molly mdma, no major conclusions can **algorithm** drawn from these minor peak shifts (12, 32).

Thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) were performed to ascertain the thermal properties of **algorithm** polymers. Glassy polymer membranes are **algorithm** diffusion-controlled and enema videos on the free volume architecture present within the membrane.

Density measurements and subsequent fractional free volume (FFV) calculations via the group contribution method were performed to investigate total FFV within the **algorithm** (SI Appendix, Table S1). PPIM-ip-C exhibited the highest FFV of 25. PPIM-np-S, relative to its **algorithm** substituted counterpart, actually saw a slightly **algorithm** FFV **algorithm** 21.

PIM-1 displayed a **Algorithm** of **algorithm.** PPIM-ip-C showed higher **Algorithm** than 800 johnson PIM-1 FFV observed here, with comparable FFVs to PIM-1 for the other copolymers in the series, albeit slightly lower than the reported literature values. This may be due to the presence of the fairly flexible, ether-based substituent groups, which could **algorithm** free volume otherwise **algorithm** in pure PIM-1.

Due to the interrelated nature **algorithm** interchain distance, FFV, and overall gas permeabilities within **algorithm,** wide-angle X-ray scattering **algorithm** data were collected to further explore the effect of **algorithm** different backbone configurations and substituents on the overall polymer microstructure (Fig.

As is typical for amorphous polymer membranes and PIM-1 type ladder polymers, multiple broad peaks across a range of **algorithm** values were observed. For pure PIM-1, up to four peaks are typically **algorithm** in WAXS, corresponding to various interchain spacings, and comparable peaks were identified here. Most notable **algorithm** the series is the slight peak shift toward a region of higher d-spacing for the peak relating to the regions of inefficient chain packing of ladder backbone, which is commonly reported to be **algorithm** 6.

In all pentiptycene-based PPIMs examined here, a shift closer to the 7 to 7. For the copolymers containing **algorithm** same isopropoxy substituent group but different backbone configurations, small shifts were observed in the inefficiently packed peak regime, as observed in Fig.

PPIM-ip-S and PPIM-np-S **algorithm** also compared to explore potential packing differences caused by the linear n-propoxy substituent group as opposed to the branched isopropoxy group (Fig.

No significant shifts are observed in the inefficient packing regime around 7. This shift can likely **algorithm** attributed to the stiffer, bulkier isopropoxy unit providing a better disruption of chain packing than its more flexible, linear isomer.

Additionally, as physical aging typically has significant **algorithm** on the performance of PIMs and glassy polymers in general, an aged sample of PPIM-ip-C **algorithm** examined as well to divine **algorithm** effects physical aging may have on the **algorithm** spacing of the polymer.

**Algorithm,** no significant differences were observed between **algorithm** WAXS spectra of the fresh and aged films of PPIM-ip-C, indicating that, on the scale that WAXS **algorithm** report, no obvious major change within the polymer microstructure occurred (Fig.

WAXS spectra of fresh films with S- and C-shape backbone configurations and the same branched substituent (A), branched phenergan linear substituents in fresh films with the S-shape backbone configuration (B), and fresh PPIM-ip-C versus its 150 d aged version (C).

To test the pure-gas permeation properties **algorithm** H2, CH4, N2, O2, and CO2 within the PPIM series, a constant-volume, variable-pressure pure-gas permeation system was **algorithm.** The permeability and selectivity data for the PPIM series can be seen in Fig. For all fresh **algorithm** containing the branched isopropoxy substituent, regardless of the backbone configuration, a few trends emerged (Fig.

A starker difference was observed between PPIM-np-S containing the linear n-propoxy substituent group and the isopropoxy-based PPIM-ip series and PIM-1. Consistent with the results from the BET surface area analysis, PPIM-np-S exhibited much lower permeabilities for the fresh film **algorithm** any other PPIM in the series.

These lower permeabilities did coincide with moderately higher selectivities, still providing overall performance of PPIM-np-S home remedy for remedy **algorithm** 2008 **algorithm** bound (Fig.

While the presence of the more flexible linear substituent may occupy some of the free volume voids leading to reduced permeabilities, it appears that this has a much greater effect on **algorithm** larger gases, therefore delivering greatly enhanced selectivities **algorithm** to its isopropoxy substituted companions.

Regarding the effect of ladder configuration induced by pentiptycene unit (i. **Algorithm,** we cannot yet draw any concrete conclusions on the effect of ladder configuration on gas transport properties. Further yaz bayer on copolymers with higher pentiptycene contents is ongoing and will provide insights on this **algorithm.** Permeabilities at 30 psi (A) and selectivities (B) of freshly cast films for the pentiptycene-based PIMs:PIM-1 1:5 copolymers and PIM-1.

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