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655d1092dbd7c8b54bbca93d | 4 | X-ray diffraction (XRD) measurements (θ/2θ) were performed using a Rigaku Smartlab xray diffractometer with a Cu Kα source operating at 40 kV and 150 mA. XRD patterns were collected over the range of 5° to 60° 2θ. A channel-cut Ge (220) double-bounce monochromator was used on the copper source side to strip the Kα2 and Kβ X-ray lines. Measurements were done at room temperature and under ambient conditions. Single crystals were laid flat on the sample XRD holder so that diffraction patterns were acquired from the larger area surfaces. |
655d1092dbd7c8b54bbca93d | 5 | Root mean squared (RMS) surface roughness analysis was performed using a Bruker ContourX-500 3D Optical Profilometer equipped with dual color LED illumination (white light and 532 nm green light), automated objective turret with 2.5×, 5×, 10×, 20×, and 50× objective apertures, and additional internal 0.5-2× zoom lens (for a maximum of 100×). RMS surface roughness measurements were acquired via phase shift interferometry using the 532 nm illumination source in order to achieve sub-angstrom resolution. Measurements were acquired with the 10× objective and 1× internal zoom lens (xy pixel size of ~790 nm). 1×1 mm area maps were constructed by stitching 6 separate images together with ~20% overlap with neighboring images. |
655d1092dbd7c8b54bbca93d | 6 | The chemical composition of a ~1 cm 2 cleaved piece of as-grown MAPbBr3 was analyzed using a Thermo Scientific Escalab xi + X-ray Photoemission Spectrometer (XPS) equipped with a monochromatic X-ray source with an Al anode producing characteristic X-rays with photon energy of 1487 eV. The XPS spectrum was measured at the crystal surface that was in contact with the glass substrate during growth propagation. A survey scan was measured along with high resolution scans of Pb 4f, O 1s, N 1s, Br 3d, and C 1s core levels to evaluate the MAPbBr3 chemical composition on the sample surface. All spectra were collected without the use of a flood gun to neutralize the sample. |
655d1092dbd7c8b54bbca93d | 7 | The XPS data was analyzed using CasaXPS processing software. All MAPbBr3 XPS spectra were calibrated to the adventitious carbon on the sample surface used as a charge correction reference peak region with peak centered adjusted to 284.8 eV. The O 1s, C 1s, and Br 3d5/2 3d3/2 high-resolution spectra backgrounds were treated with Tougaard function, a linear function was used for N 1s, and the core level Pb 4f7/2 4f5/2 background was modeled with a Shirley function. |
655d1092dbd7c8b54bbca93d | 8 | Most of the synthetic peak models used a LA line shape-a numeric convolution of a Lorentzian with a Gaussian. Select peaks were modeled with the product of a Lorentzian and Gaussian (GL) to achieve a lower residual standard deviation. Quantification of atomic concentration was calculated from a spectra formed by merging high-resolution core-level peaks, and integrating peak regions then normalizing the individual core level signal area to the total peak area yielding atomic percentage. |
655d1092dbd7c8b54bbca93d | 9 | Energy dispersive x-ray spectroscopy (EDS) was performed using a Zeiss Gemini 500 scanning electron microscope (SEM) operating at 20 keV which was equipped with an Oxford Instruments X-Max 80 detector. The spectrum was collected on the crystal surface that was in contact with the glass slide during growth. The atomic concentration was calculated using Oxford Instrument NanoAnalysis AZtec (Version 6.0) software. |
655d1092dbd7c8b54bbca93d | 10 | Variable angle spectroscopic ellipsometry was carried out using an RC2 ellipsometer (JA Woollam). Reflection measurements were collected from 50-80° at 5° increments for wavelengths 200-2500 nm. Optical dispersion data analysis of the raw ellipsometry data was performed using CompleteEASE v6.55 (JA Woollam). An Agilent Cary 5000 UV-VIS-NIR spectrometer was used to collect the transmission intensity of the crystal at normal incidence from 200-2500 nm. |
655d1092dbd7c8b54bbca93d | 11 | A comparison of example MAPbBr3 optical properties (refractive index, n, and extinction coefficient, k) reported in the literature is shown in Figure . The optical dispersions compared in Figure represent the optical properties of MAPbBr3 grown using different antisolvent, hydrothermal, and ITC The magnitude of the Δn and Δk in Figure is unexpected assuming controlled MAPbBr3 growth processing conditions and appropriate post-growth handling procedures. However, changes due to processing dependencies and surface or bulk material degradation have been shown to change the chemical composition and crystalline structure of MAPbX3 that directly impact the associated optical properties. Process-induced effects are known to generate lattice defects and dopant impurities while material degradation generally occurs due to unprotected, prolonged ambient air and moisture exposure under variable temperature fluctuation. Defects and impurities within the crystalline lattice (such as lead or halide vacancies or interstitials) and surface degradation (such as oxidation) also affect the resulting optical properties of MAPbBr3 primarily due to changes to the band gap (chemical composition), electron-hole pair recombination dynamics, and/or associated absorption/emission behavior. Additionally, as mentioned above, inaccurate modeling assumptions and the resulting robustness of the optical dispersion data analysis can potentially contribute to variability in the derived n and k (discussed in Section 3.3). |
655d1092dbd7c8b54bbca93d | 12 | While a ≥0.1 change in n and k for any material can result in significant optical device design discrepancy challenges, the Δk = 0.35 below the band edge in Figure is of specific concern for these representative MAPbBr3 and expected PSC solar radiation absorption. Given a bandgap of ~539 nm, it is expected that k should rapidly approach zero at this wavelength and below. However, this is not the case for most reported values of k, except for Choi and coworkers. Here, again, the large Δk for MAPbBr3 is likely due to differences in material surface quality (e.g., oxidation, doping, and/or surface roughness) in addition to inadequate optical dispersion data analysis to derive the reported values. Furthermore, the differences in the crystallographic face orientation responses reported by Tao and coworkers are likewise unexpected given MAPbBr3 is not considered a birefringent material (exhibiting neither uniaxial or biaxial optical anisotropy). When solar radiation interacts with a planar thin-film solar cell, the response of the light through a given device architecture is determined by the optical properties and thicknesses of each layer in the PSC stack. Here, we use an illustrative single junction planar solar cell architecture (five layers excluding the substrate) to demonstrate the impact of variable active layer perovskite n and k inputs on the modeled PSC optical performance: (i) encapsulating substrate, (ii) front contact, (iii) electron transport layer, (iv) active absorbing layer, (v) hole transport layer, and (vi) back contact. For simplicity, we use a similar device architecture as reported by Ball et al. (see Figure ) with MAPbBr3 as the active layer. Here, the substrate is glass (infinite modeled thickness), the front contact is fluorine-doped tin oxide (FTO, 420 nm thick), the electron transport layer is titanium dioxide (TiO2, 41 nm thick), the active absorbing layer is MAPbBr3 (492 nm thick), the hole transport layer is 2,2',7,7'-tetrakis-(N,N-di-4-methoxyphenylamino)-9,9'- spirobifluorene (Spiro-OMeTAD, 253 nm thick), and the back contact is gold (Au, 30 nm thick). |
655d1092dbd7c8b54bbca93d | 13 | The optical properties for non-MAPbBr3 device material layers can be found in Ref. [31]. absorptance with respect to the other material layers in the given device configuration. Figure shows the difference in optical absorptance between optimized and unoptimized MAPbBr3 active layer thickness PSC designs, PSC ΔA% = Optimized PSC A% -Unoptimized PSC A%, (Eq. 1) |
655d1092dbd7c8b54bbca93d | 14 | Optical profilometry was used to measure the quality of the crystal surface grown at the glass slide interface. Figure shows a contour plot of a 1×1 mm 2 area of the crystal surface. The surface roughness (root mean square height, Sq) of this area is ~3 nm, indicating that the crystal surface is optically smooth and free of major defects. It is presumed that any defects observed on the crystal surface are imparted from the glass surface that the crystal was grown on. The normalized X-ray diffraction patterns of our MAPbBr3 crystal match the simulated diffractogram produced from MAPbBr3 in the Pm3m space group in Figure . No impurity peaks are present in the measured diffractogram and the MAPbBr3 diffraction peaks are indexed to the (100) crystallographic plane and multiples of (100), showing strong preferred orientation of the top crystal surface in the 〈100〉 crystallographic direction. The MAPbBr3 surface XPS spectra depict typical surface chemistry characteristics of a sample exposed to ambient atmosphere with an oxygen concentration of about 10.4 at.% and adventitious carbon at about 66 at.%. Merged high-resolution XPS spectra of the MAPbBr3 sample surface, inset table of peak position, integrated peak area, and atomic percentage are shown in Figure . A survey XPS scan of all measured elements from the surface of the MAPbBr3 sample is provided in Figure . The decomposition of the Pb 4f spectra (Fig. ) is modeled by component peaks with binding energy in the range of a native Pb oxide (4f7/2 ≈ 138.4 and 4f5/2 ≈ 143.3 eV) and Pb 2+ binding energy of (4f7/2 ≈ 137.6 and 4f5/2 ≈ 142.6 eV). The O 1s core-level peak is modeled (residual STD = 0.582) with four synthetic component peaks (Figure ) with lowest energy component peak having a binding energy comporting with that of Pb oxide at ≈ 530.6 eV. EDS was also performed to investigate the chemical composition deeper into the bulk of the crystal (Figure ). The expected 1:3 ratio of Pb:Br was found from EDS (Table ) confirming that only a thin layer of the surface is oxidized while the bulk of the crystal is pure lead halide perovskite. |
655d1092dbd7c8b54bbca93d | 15 | Spectroscopic ellipsometry is a useful characterization technique to support the development of high-quality perovskite materials and PSCs. When performing spectroscopic ellipsometry, a known incident polarization state of light interacts with the perovskite sample surface (bulk material) and the reflected (transmitted) light is analyzed to determine the change in amplitude ratio (Ψ) and phase (Δ). From this characterization approach, the fundamental optical properties can be derived including the refractive index (n), extinction coefficient (k), dielectric functions (ε1 and ε2), and absorption coefficient (α). These interrelated optical properties play a crucial role toward the optimization and resulting efficiency of engineered PSCs. However, inadequate sample preparation, modeling assumptions, and optical dispersion data analysis can lead to an inaccurate derivation of perovskite optical properties (see Section 3.1 and Figure ). As a result, to ensure proper characterization of complex index materials using spectroscopic ellipsometry, it is often necessary to employ more rigorous optical dispersion data analysis methods (discussed here) and quantify associated process-dependent material structure-property relationships (see Section 3.2). |
655d1092dbd7c8b54bbca93d | 16 | Variable angle spectroscopic ellipsometry was used to measure our MAPbBr3 single crystal in a wavelength range of 210-2500 nm. These data contain changes to the amplitude ratio (Ψ, Figure ) and phase (Δ, Figure ) difference between the p-and s-reflection coefficients of the polarized incident light, but often do not provide necessary sensitivity to low absorption coefficients of a given material (i.e., α <100 cm -1 ). As a result, absorptance characteristics (especially with very fine spectral features observed for MAPbBr3) can be under approximated from spectroscopic ellipsometry characterization alone. However, appending spectroscopic ellipsometry data (Figure ) with transmission intensity data (200-2500 nm, Figure ) can provide the necessary optical absorption information to properly derive the optical properties of MAPbBr3 for both normal and anomalous optical dispersion. Furthermore, in some cases, this appended modeling approach can help improve the accuracy of the analysis and reduce uncertainties in the optical property derivation. As a result, our approach eliminates and/or corrects parameter correlations or insensitivity that could have occurred from optical dispersion data analysis using ellipsometry data alone. It is important to note that our experimentally appended optical analysis essentially yields the effective optical properties of our single crystal MAPbBr3, given the subtle oxidation at the surface of the single crystal due to the processing/handling conditions employed (see Figure ). A separate oxide layer was assessed in the optical dispersion data analysis for comparison, but resulted in negligible influence (i.e., little change to the mean squared error, MSE, of the fits) to the derived optical properties. As such, an oxide layer was not included here for simplicity of illustration. However, the influence of the oxide layer is captured in our experimentally appended optical dispersion data analysis (i.e., the impact on optical transmission is captured). Given the minimal surface oxidation, we consider these effective optical properties a close approximation of fully stoichiometric MAPbBr3. This appended modeling approach is necessary for MAPbBr3 to improve anomalous optical dispersion sensitivity to the bandgap transition regime as well as lower-order spectral overtones. |
655d1092dbd7c8b54bbca93d | 17 | Here, spectral overtones refer to the presence of other optically absorbing species in the perovskite material. While some have suggested perovskites are nearly transparent in the infrared regime this is not the case for hybrid organic-inorganic perovskites. Although not phenomenologically quantified with respect to material species and optical absorption mechanics, in the case of MAPbBr3, the MA moieties represent compositional species that contribute to the optical absorptance peaks below the band edge. For example, we observe spectral overtone features beginning at ~1050 nm that continue to longer wavelengths shown in the transmission intensity spectra in Figure . To generate a robust derivation of MAPbBr3 optical properties, it is necessary to include these anomalous optical dispersion characteristics at, above, and below the bandgap in the optical dispersion data analysis. To our knowledge, no complementary modeling methodology has been reported for MAPbX3; however, this characterization approach has been demonstrated for other complex index thin films with anomalous optical dispersion. In part, the lack of such complementary analysis for MAPbBr3 to date may be due to limited single crystal material/surface quality and sample size dimensions necessary to generate low scattering transmission intensity spectra. |
655d1092dbd7c8b54bbca93d | 18 | We use a Kramers-Kronig consistent basis-spline (B-spline) model to facilitate our appended optical dispersion data analysis. The B-spline function is a piecewise polynomial function that consists of multiple segments, each of which is defined by a set of control points and the polynomial degree. This analysis method results in a smooth and continuous function across the modeled segments, which can then be adjusted to fit the experimental data using conventional optimization algorithms. The B-spline formalism was used here to fit both the experimental spectroscopic ellipsometry and transmission data (Figure ). The modeled results in Figure show reasonable profile fits of the fine spectral features above and below the bandgap for MAPbBr3. By comparison, fitting fine spectral features is not easily done using a conventional general oscillator model approach (e.g., Gaussian, Lorentz, Tauc-Lorentz, Cody-Lorentz, or Tanguy formalisms). Our spectroscopic ellipsometry and transmission intensity appended modeling approach with a Kramers-Kronig consistent high resolution B-spline fit yields a rigorous optical dispersion data analysis of single crystal MAPbBr3. |
655d1092dbd7c8b54bbca93d | 19 | The optical properties derived from our analysis are shown in Figure . These optical dispersion curves provide well-approximated spectral characteristics at, above, and below the bandgap for MAPbBr3. At the scales shown in Figure , the influence of the MA overtones below the bandgap are not depicted well. Figure shows a logarithmic y-axis scale for k, which shows the fine features of the MA overtone anomalous optical dispersion. These data illustrate another advantage of employing spectroscopic ellipsometry and transmission intensity data appended optical dispersion analysis. Reflection mode spectroscopic ellipsometry alone typically does not offer sufficient sensitivity for the derived optical constants below ~10 -3 . However, by including transmission intensity data in the analysis, we improve optical property derivation sensitivity to with a logarithmic y-axis scale to show the sharp band edge transition and MA overtones captured using our experimentally appended optical dispersion data analysis method. ). Here, the MAPbBr3 layer exhibits the greatest peak absorptance above 539 nm followed by FTO and Au. MAPbBr3 exhibits the lowest absorptance below 539 nm; however, there is parasitic absorptance from all other layers at these wavelengths. PSC Design II layer absorptance yields very similar results to PSC Design I, except there is a small peak increase in the MAPbBr3 layer absorptance for Design II below 539 nm. Despite optimizing for MAPbBr3 layer absorptance in the device, the minimal increase in absorptance is due to the fixed thicknesses for all other layers in the design. This is primarily due to the FTO layer exhibiting greater parasitic absorptance above and below the bandgap, with Au contributing next to the most parasitic absorptance below the MAPbBr3 bandgap. |
655d1092dbd7c8b54bbca93d | 20 | To further maximize MAPbBr3 layer absorptance and minimize parasitic absorptance by non-active layers in the PSC device, we optimize MAPbBr3 layer absorptance while permitting changes to FTO and Au layer thicknesses. The impact of permitting the parameterization of just these three layers in the device is shown in Figure . Here, a noticeable increase in peak MAPbBr3 absorptance below the bandgap is observed along with a considerable decrease in parasitic absorptance across all wavelengths above 400 nm (the arbitrarily selected target wavelength cutoff of the MAPbBr3 optimization for the PSC design). We evaluated the performance of the PSC device with parameterization of all layer thicknesses; however, little improvement was observed between PSC Design III and an all-layer thickness parameterization design (not shown). Overall, PSC Design III suggests it is possible to carry out PSC design iterations constrained by physical thickness limits of the non-active layers, for instance, in order to maintain electronic performance of the contact and electron/hole transport layers while optimizing overall optical performance. |
655d1092dbd7c8b54bbca93d | 21 | The optical performance of a given PSC in practice also includes the angle of the incident of light, which will be strongly influenced by the design. Figure show the total absorptance for the respective PSC designs from 0-90° AOI as a function of wavelength, where 0° represents the incident light normal to the device interface. PSC Designs I and II show very similar AOI performance with a noticeable increase in parasitic absorptance below the band edge at ~50° AOI. This increase in parasitic optical absorptance originates as a result of each individual layer material optical properties and is a direct artifact of the PSC device design (layer thicknesses of the nonactive layers within the PSC). PSC Design III in Figure shows no such spectral artifact at ~50° AOI and an improvement in device optical absorptance at and below the MAPbBr3 bandgap as a function of AOI, which further demonstrates the need to optimize the optical performance of selected material layers in a given PSC. By selectively expanding the design optimization, Design III shows that the MAPbBr3 layer absorptance can be strategically improved, parasitic absorptance by the other device layers can be decreased at all wavelengths, and total device optical performance can be refined up to high angles of incidence. |
655d1092dbd7c8b54bbca93d | 22 | Overall, these modeled PSC designs demonstrate the critical influence of accurate optical property determination in order to further improve the optical performance of modeled PSC devices. Most influential for these illustrative planar thin film device designs is capturing MAPbBr3 optical behavior at the band edge transition and below. Also present in each of these designs (Table and Figure ) is the influence of the MA overtones of MAPbBr3. It is also important to note that the influence of these spectral features at the reported layer thicknesses (Table ) are subtle but not negligible, and these can impact optical performance below the bandgap. Such material optical characteristics have the potential to yield unexpected optical or device behavior if unaccounted for in the given PSC optical coating design (i.e., R, T, and A including the performance at different angles of incidence). The impact of such features will become more significant with increased MAPbBr3 layer thicknesses due to an increase in solar radiation attenuation. |
67da38ba6dde43c9085d5857 | 0 | Molecular symmetry significantly affects organic compounds' phase transition temperature (Tm and Tb) and solubility. As a general rule , crystals of symmetrical molecules have higher melting temperatures but are less soluble than crystals of less symmetrical molecules with similar structures. A prevalent explanation is based on Gibbs free energy at the thermal equilibrium regarding the relationship between the enthalpy (ΔH), entropy (ΔS), and phase transition temperature. The higher temperature implies the smaller ΔS because the enthalpy is usually related to the molecular interactions such as the ionic, polar, and hydrogen bond interactions. Isomers have the same functional groups; thus, the enthalpy should be equal. Hence, entropy dominates the difference of isomers' phase transition temperature. Walden showed that the average entropy of melting for many "coal tar" derivatives, which consist mainly of aromatic hydrocarbons, is constant, 13.5 cal/(deg•mol) . In contrast, for small spherical molecules, it is 3 cal/(deg•mol) . The boiling entropy of non-hydrogenbonding organic compounds generally follows Trouton's rule, 88 J/(deg•mol) - . However, conventional thermodynamics infers that molecules have a large degree of rotational and conformational freedom in both the liquid and the gas; the entropy associated with changes in these parameters upon boiling is small. Conversely, liquid molecules gain tremendous translational freedom upon entering the gas phase. The entropy of boiling is almost entirely the result of this increase in translational motion. In contrast, the entropy of melting is primarily due to rotational and conformational factors and only slightly due to translational factors. Therefore, the factor of molecular symmetry gradually faints in the studies of boiling entropy. Instead, Joback quantified the contributions of functional groups to the enthalpy to predict the boiling point and solubility. After that, this method dominated the studies on the boiling point. - The intimate connection between molecular symmetry and melting temperature is quantified by Yalkowsky et al. . A high enthalpy of melting implies considerable bonding energies. Molecular symmetry may contribute to tighter crystal packing via shape-cohesion effects. The molecular rotational symmetry number (σ) is introduced to express the impact of molecular symmetry on the entropy of melting: the number of indistinguishable positions that can be obtained by rigidly rotating the molecule about its center of mass. The greater the molecular rotational symmetry number, the higher the probability of the molecule being in the correct orientation. In the solid phase, the symmetry of a molecule results in a residual amount of molar entropy of magnitude Rlnσ above that of a similar but non-symmetrical molecule. Consequently, the difference in entropy between the liquid and solid phases will be negligible for the more symmetrical molecule. This, in turn, means that symmetry in a molecule reduces the entropy gained upon melting for that compound (ΔSm). Either of the two effects listed above, not to mention a combination of the two, would result in a higher melting temperature for a symmetrical molecule over a non-symmetrical one. |
67da38ba6dde43c9085d5857 | 1 | ∆𝑆 𝑚 = 56.5 -𝑅𝑙𝑛𝜎 (J K -1 mol -1 ) (1) The significant intuitive appeal of the above explanation comes from its conceptual and numerical arguments being valid and entirely consistent. However, the same account fails to explain a widespread observation: Symmetrical molecules, which, as a general rule, do have higher melting temperatures, quite often have greater melting entropies than their less symmetrical isomers. Therefore, Gilbert introduced the effect of "entropy-enthalpy compensation" into Eq. 1, namely that ΔSm is dependent upon the enthalpy of melting ΔHm. `Flexible' molecules (potentially multi-conformational) tend to yield higher values of ΔSm for a given ΔHm than `rigid' ones. |
67da38ba6dde43c9085d5857 | 2 | Another effort to combine the molecular symmetry into the phase transition temperature is to pursue theoretical consistency. , - Within a homologous series, adding a substituent that increases internal cohesive forces also increases densities, boiling points, heat of vaporization, refractive indexes, and surface tensions. However, the melting points are the outstanding exceptions, which behave idiosyncratically. The lack of molecular symmetry in the functional group contribution equations is considered a reason. |
67da38ba6dde43c9085d5857 | 3 | Although significant progress has been made in predicting the physical properties of organic compounds, some fundamental problems still exist. First, it is hard to correlate the functional group contribution and the molecular symmetry number with thermodynamic properties such as pressure and temperature. For example, the Clausius-Clapeyron equation indicates pressure impacts on the phase transition temperatures. Second, determining the functional group contribution and symmetry number is arbitrary. For example, the symmetry number of CH4 is designated as 12 because it has 4 C3 rotational axes. However, nine symmetry operations should be degenerated in the energy level. Moreover, the symmetry number of monoatomic gas is designated to 200. In contrast, the symmetry number of entirely asymmetrical molecules CHXYZ (X, Y, and Z denote different atoms or groups except for H) is 1. It is beyond common sense that the spin of an atom can contribute so much entropy. Moreover, it seems inverse to the order of entropy, reflecting the diversity of molecular configurations. Third, the geometric symmetry of mass distribution is solely selected without any reasoning. However, in quantum theory, the symmetry of orbits is vital to the reactions , and spectroscopy , . Therefore, it is essential to assess the definition of molecular symmetry and the quantitating approach based on the principle of straightforward and reasonable. |
67da38ba6dde43c9085d5857 | 4 | In our previous papers, we reported a series of inferences based on a new thermodynamic theory: the state equation of real gas , gas solubility and gas-liquid interfacial tension , the specific heat capacity of real gas , the equilibrium distance of molecular interaction , and the state equation at isotherm . The new thermodynamics is founded on the revised thermodynamic laws: defining the heat with the first law and system work with the second law. It was verified to qualify as a basic principle of thermodynamics. Therefore, this paper will address molecular symmetry and entropy connected with the third law. |
67da38ba6dde43c9085d5857 | 5 | As shown in Fig. , a linear regression perfectly fits the curve of 𝑌~1 𝑇 with a coefficient of determination R 2 =1 from M.P. to the critical temperature (Tc). Here, it should be noted that the maximum value of R 2 is 1. R 2 =1 indicates that the fitting is perfect. As R 2 deviates from 1, the smaller the fitting, the worse. Since the coefficient R in the figures duplicates the gas constant, D 2 will be used instead of R 2 in the context. Therefore, Eq. 2 may be altered by Eq. 4. |
67da38ba6dde43c9085d5857 | 6 | 1) The effects of atomic/molecular mass and molecular interactions on the A and D 2 values are not observed; however, they are significant on the B value. The series of inert gases in Fig. exemplifies the mass impact. B values of NF3 and NH3 in Fig. exhibit the effects of molecular interactions. |
67da38ba6dde43c9085d5857 | 7 | 2) A and D 2 significantly correlate to molecular symmetry. A symmetric molecule gives a much smaller A, and in most cases, D 2 =1 or 0.9999, whereas an asymmetric molecule gives an inverse. For example, cyclopropane is symmetric; thus, A=3.7396, D 2 =1. In contrast, propane is asymmetric; therefore, A=5.0709, D 2 =0.9974. As a result, A and D 2 may be the criteria for assessing the molecule's symmetry. 3) As shown in Fig. , in the cases of smaller D 2 , e.g., NF3: D 2 =0.999, the linear regression can proceed in different temperature intervals to gain D 2 →1 as possible. It is natural and rational because, for asymmetric molecules, the packing status of molecules in a liquid may be affected by the temperature. For example, as the temperature increases from M.P. to Tc, NF3: A decreases from 5.7103 to 3.6213, while B (absolute value) decreases from 1566.7 to 1317.8 K. |
67da38ba6dde43c9085d5857 | 8 | Since A and B represent the difference of packing status between gas and liquid, the more significant value indicates that the packing is tighter in liquid, provided that the packing status in gas is entirely random. Hence, as the molecular motion slows down at a lower temperature, it is rational that the packing becomes tight, thereby giving the more significant values of A and B. This result indicates that A and B vary along with the temperature variation. The linear regression over the whole range of temperature from M.P. to Tc gives the averaged A and B values. D 2 =1 is just a signal of tiny variation. 4) The same configuration exhibits a different symmetry according to A and D 2 . For example, the configuration of both NH3 and NF3 is a tetrahedron with a vertex occupied by an unbonded p orbital. However, the averaged A and D 2 of the two molecules are quite different. D 2 =0.9998 exhibits that NH3 is close to a symmetric molecule, while D 2 =0.999 indicates that the symmetry of NF3 is inferior. However, an inverse conclusion is drawn from the A values (NH3: A=4.8459; NF3: A=4.1011). Therefore, we have to utilize the interval value. In the 85-97.5K interval, the linear regression of NF3 gives A=5.7103. Comprehensively, it is concluded that the symmetry of NH3 is superior to that of NF3. Fortunately, the assessment is consistent in the pairs of H2O and H2S and CH4 and CF4. For H2O, A=5.3322, D 2 = 0.9998; H2S: A=3.6898, D 2 = 0.9999, whilst for CH4, A=2.9519, D 2 =1; CF4: A=4.0262, D 2 = 0.9997. Accordingly, the symmetry of H2S and CH4 is better than that of their counterparts. It indicates that the unbonded p orbital, e.g., 2p of the Fluorine atom, and its size, e.g., 3p of the Sulfur atom, impact the molecule's symmetry. This result suggests that the symmetry of the molecular orbital, rather than the conventional mass symmetry , is proper to be a criterion for accessing molecule symmetry. However, the sign symmetry of the molecular orbital in Woodward and Hoffmann's rule should be excluded. As a result, set D 2 → 1 as possible, A is solid for assessing the molecule's symmetry, though, in most cases, the averaged A is reliable enough. |
67da38ba6dde43c9085d5857 | 9 | Figure , Curves of Y ~1/T and the results of linear regression of some representative gases Figure summarizes the average A values of small molecules. It is striking that some asymmetric molecules, e.g., CO, exhibit better symmetry than those symmetric molecules, for instance, CO2, under the theory of mass symmetry. It supports the suggestion of molecular orbital symmetry. Fig. shows the average A values of hydrocarbon molecules. Four linear relationships are observed. For example, except for CH4, the straight-chain alkanes with an even number of carbons and those with an odd number of carbons stand on a straight line, respectively. It reflects the better symmetry of alkanes with an even number of carbons. However, cyclo-C4F8 does not fall on the line composed of CH4, cyclopropane, etc. Combining the higher A values of fully fluorinated alkanes indicates that the effects of unbonded p orbitals of Fluorine are significant. A striking observation is that the A value of propene equals that of propane, while the spot of benzene overlaps that of cyclohexane. It is beyond the anticipation provoked by the symmetry of a double bond. 𝑅 is the entropy change of evaporation (ΔSv), A must be an item reflecting the entropic contribution of symmetry operations because the item of long-distance kinetic energy is set to 3/2. Moreover, the conventional mass symmetry is not suitable for describing the variations of A and D 2 . Therefore, the shapes of atomic/molecular orbitals are worthy of discussion. |
67da38ba6dde43c9085d5857 | 10 | Given that the description of the quantum theory is correct, for instance, the outer atomic orbital of inert gas (excluding He) at the ground state is s 2 p 6 , and the p orbital shields the s orbital. Fig. exhibits the shape of atomic/molecular orbits and the number of symmetry operations. |
67da38ba6dde43c9085d5857 | 11 | As shown in Fig. , using Argon as an example of inert gases, the operation number, n, of p 6 atomic orbital is 6+1 (1 denotes E operation). Assuming that each operation contributes 1/2 RT to either the rotational kinetic energy or the entropy of the ensemble, n/2=3.5 is close to the A value of Ar, 2.9104. This means that 0.5896 RT remains in the liquid, assuming that a molecule in the gas state is entirely free and owns all the operation numbers. It turns into rotational and translational energy in the liquid state, even though most operations are restricted due to the dense packing of molecules. Similarly, for Ne, Kr, and Xe, the values of n/2-A are 0.9492, 0.5896, 0.586, and 0.5822, respectively. It implies that the smaller the atom, the more energy remains. In other words, the larger the atom, the tighter the packing in the liquid. It is consistent with the density variation. |
67da38ba6dde43c9085d5857 | 12 | As we try to correlate the number of symmetry operations to A, it should be emphasized that a default prerequisite is n/2 > A. Otherwise, RT/2 of each operation must be adjusted case by case to fit A. Although the choice is arbitrary, we choose the former, namely that n/2>A is the prerequisite in the following discussion. |
67da38ba6dde43c9085d5857 | 13 | As shown in Fig. , in contrast to the concept of mass symmetry, N2 (A=3.1403, D 2 =0.9999) is more symmetric in comparison with O2 (A=3.2418, D 2 =0.9994) and F2 (A=3.5235, D 2 =0.9994). In addition, CO (A=3.2879, D 2 =0.9999) is also symmetric. For N2, n=6, i.e. 1C4+4C2+E, but A=3.1403. Therefore, an additional symmetry operation should be found. Conventionally, two π bonds are considered rigid. However, the σ bond's rotation must be included to ensure n/2>A. A σ bond rotation supplies two operations: a cross of p orbitals of two N atoms and a C2 of cross. Hence, n = 8 for N2. The twist of two π bonds is also acceptable, but we must endow a twist operation with RT. Comparatively, a σ bond rotation is a better choice universal to other molecules. As mentioned above (Fig. ), the C-C π bond in the ethylene and benzene ring does not exhibit symmetric superiority compared to ethane and cyclohexane. Hence, if the σ bond in ethylene and benzene could rotate freely as in ethane and cyclohexane, the similar A values could be rationally interpreted. Moreover, CO2 (A=4.2768, D 2 =1) should have more than nine symmetry operations. Only two σ bond rotations can supply so many symmetry operations. Those analyses are consistent with the oscillating structure of the π bond, namely that two bonded electrons may immigrate to one of the bonded atoms. CO is similar to N2 because a spare O p 2 orbital can form a π bond with a vacant C p 0 . Therefore, n=8, satisfying A=3.2879. Similarly, for CO2, immigrating one pair of spare O p 2 electrons between C and O increases the number of operations. |
67da38ba6dde43c9085d5857 | 14 | For O2, as shown in Fig. , n=6. However, Fig. exhibits that the maximum A=4.2336 corresponds to n≥9. O2 has two spare O p 2 orbitals. Since the kinetic energies of all electrons are equal, apart from a σ bond, the molecular structure oscillates O p 4 ↔ O p 2 , by which an additional 5 operations are obtained. Therefore, n=11 for O2. |
67da38ba6dde43c9085d5857 | 15 | Figure , Orbital symmetry of some molecules As shown in Fig. , H2O and H2S are asymmetric molecules in terms of the geometric symmetry of mass. However, H2S acts as a symmetric molecule. A=3.6898 corresponds to n ≥ 8. It is likely ascribed to the large 3sp 3 hybridized orbital of S, relative to the small 1s orbital of H. Two H-S bonds do not destroy the tetrahedral symmetry of the sp 3 hybridized orbital (see CH4, n=8), though it inevitably deforms. Hence, n=8 is possible. |
67da38ba6dde43c9085d5857 | 16 | In contrast, H2O in ice is abnormal . A breakpoint is found at M.P. due to the abrupt decrease of density, and A=9.2823 corresponds to n≥19 below M.P. It is hard to get so many symmetry operations from H2O in gas. Meanwhile, such a large A (>9) is only found in the longer alkanes (C > 4) near M.P. Moreover, it is rare even in alcohols, i.e., methanol, ethanol, propanol, and isopropanol. Therefore, two causes are possible. The first is that migrating two hydrogen atoms among the four vertices of an O sp 3 tetrahedron increases the operation number. The second is that the complex forms due to the strong H-bonds at the temperature below M. P. |
67da38ba6dde43c9085d5857 | 17 | Like H2S, NH3 looks like a symmetric molecule with A=4.832 and D 2 =0.9999. This implies that the volume of N 2sp 3 hybridized orbitals is much larger than that of the H1s orbital; thus, the tetrahedral symmetry remains major. However, even though a tetrahedron gives n=8, it doesn't satisfy A. Hence, considering the packing of molecules, the immigration of H among the four vortexes of a tetrahedron is a kind of freedom, provided that immigration is forbidden in liquid because another NH3 occupies the vacant orbital via the hydrogen bond. By this means, n=11 is obtained for NH3. Such an approach is also for H2O. Form M.P. to B.P. of H2O, A=5.9334 corresponds to n≥12, while above B.P., A=5.1168. As shown in Fig. , since there are two spare sp 3 hybridized orbitals in H2O, two H atoms can immigrate between two spare orbitals. It produces 6 additional operations. Therefore, n = 14 for H2O. |
67da38ba6dde43c9085d5857 | 18 | Figure , Y via reciprocal T of some asymmetric molecules However, NF3 (A=4.1011, D 2 =0.999) exhibits asymmetry due to the unbonded three occupied F sp 3 hybridized orbitals. As shown in Fig. , near M.P., A=5.7103 corresponds to n≥12. The tetrahedron possibly collapses. Therefore, the symmetry operations should be a molecule C3, with three migrations and the contribution from the rotation of three F sp 3 hybridized orbitals. Since each F atom has a C3, the total operations should be 9, i.e., molecule C3×F atom C3. Subtracting a C3, n=13 for NF3. |
67da38ba6dde43c9085d5857 | 19 | Due to molecular orbitals' application, CF4 exhibits a symmetry different from CH4. As shown in Fig. , n=8 for a tetrahedron, in addition to 4 rotations of σ bond, thus n= 4 molecule C3×4 F C3 -4 molecule C3 + 3 molecule C2×4 F C3-3 molecule C2 = 22, namely that CF4 has 22 operations, n=22. However, since a fluorine atom is bigger than a carbon atom, in addition to the three big sp 3 orbitals of each fluorine atom, the rotation of the σ bond may be restricted. Something like the synergistic rotation may exist. It may reduce by half the number of operations. Hence, CF4 gives A=4.6377 near M.P., corresponding to n=10. In contrast, SF6 exhibits an excellent symmetry with the average A=4.2976 and D 2 =0.9999, corresponding to n ≥ 9. In the theory of mass symmetry, it is an octahedron consisting of 8 equilateral triangles formed by the d 2 sp 3 hybridized orbitals of a sulfur atom. However, according to the theory of this paper, for the best status, it should be a regular tetradecahedron with three vertices of vacant d orbitals. Accordingly, it is hard to scale the symmetry. |
67da38ba6dde43c9085d5857 | 20 | As shown in Fig. , the similarity of ethylene and ethane, propane and propene, and cyclohexane and benzene in the A values strikes the common knowledge of molecular structure. Unlike the rotatable σ bond, a C-C π bond is usually recognized as a rigid and symmetric bond; thereby, as an example, benzene should have exhibited excellent symmetry relative to cyclohexane. However, as shown in Fig. , the difference in the A values is not as significant as anticipated. A cyclohexane molecule is commonly recognized as a soft regular-hexagon frame that the conformations of chair type and boat type can form due to the rotation of C-C σ bonds. In contrast, a benzene molecule is a rigid regularhexagonal pie fixed by a grand π bond. Therefore, the operation number of a benzene ring should be figured out readily, i.e., n = 12 (1C2+3C3+1C6+6C2+E). Correspondingly, above B.P., A=4.3072 corresponds to n=9, while below B.P., A=5.2 corresponds to n=11. However, for cyclohexane, the max. n = 7 (3 boat types×1 C2 + 3 chair types×1C2 +E). It needs additional symmetry operations. Based on effective packing and entropy, the mirror operation can be added to the operations of cyclohexane under the condition that it does not overlap the rotation operation. By this means, n=3 boat types × (1 C2 + 1 σ 2 ) + 3 chair types × (1C2 +1 σ 2 ) +E =13. Unfortunately, such a treatment is not suitable for ethylene. Therefore, as mentioned above, for N2, etc., π bonds must be rotatable to satisfy n/2≥A. There are only 3 C2 operations for CH2=CH2, but the max is A=5.1978, corresponding to n≥11. In contrast, ethane has the operations of 3C3+9C2+3C2+E=16, thus the max. A=6.2299 is proper. |
67da38ba6dde43c9085d5857 | 21 | As shown in Fig. , alcohols have a large average A, generally >7. Near their M.P., A=8.1776, 9.0645, 8.7631, and 8.8537 correspond to methanol, ethanol, n-propanol, and isopropanol. For those molecules, symmetry is out of the question. It is too complicated. The diversity of conformations or the number of freedoms should concern the molecules' packing and entropy. |
67da38ba6dde43c9085d5857 | 22 | As a summary of the section, the first attempt to connect the entropy of phase transition with the symmetry of atomic/molecular orbitals is successful. Compared with the mass distribution theorem, this method is operable with rational results. For example, the symmetry of inert gas atoms gives the operation number n = 1 in the theoretical frame of the geometric symmetry of atomic mass distribution. Meanwhile, for an asymmetric molecule CHXYZ where X, Y, and Z are different atoms, the operation number is also n = 1. Hence, it is not distinguishable in the symmetry. However, based on the shape and size of molecular orbitals, the symmetries of the above two molecules are distinguishable with different rational A values. |
67da38ba6dde43c9085d5857 | 23 | In our previous paper , it was pointed out that Tc is the temperature corresponding to x2 = 60~70%, a maximum value that a gas system enables to keep the thermal equilibrium by the heat exchange cycle. Here, Tc * is the theoretical temperature at x2 = 1. It corresponds to Pc* . However, in this paper, R•B is the heat delivered by, theoretically, complete liquefication of 1 mole gas. |
67da38ba6dde43c9085d5857 | 24 | Eq. 8 can never be zero unless T=Tc*. It is similar to the definition of internal energy in the conventional thermodynamics. As discussed above, for a symmetric molecule, 𝐻 𝑣 ∅ is constant, irrespective of temperature and pressure. However, for an asymmetric molecule, B is different due to the different packing status of molecules in the liquid at various temperatures. Hence, ∆𝐻 𝑣 ∅ is variable. However, the variation is generally slight except for water below M.P. For example, in Fig. (9) Reminiscent of the pressure at saturation, 𝑙𝑛𝑃 -𝑙𝑛𝑃 𝑐 * = 𝑙𝑛𝑥 2 (10) Thus, provided that A and ∆𝐻 𝑣 ∅ are independent to the temperature, |
67da38ba6dde43c9085d5857 | 25 | ) is almost the same value, 85~88 J/(K•mol) , , for various kinds of liquids at their boiling points. Although it is based on the Gibbs potential ∆G = 0, ∆𝐻 𝑣 ∅ and Tb are measured independently. Hence, ∆S 𝑣 may be comparable to the data in Tab. 1-4. Tab. 5 shows the results. As shown in Tab. 5, Trouton's entropy is only found in some long-chain alkanes, benzene, and toluene. An interesting observation is that the entropy of small molecules calculated from Gibbs's potential is almost two-fold the entropy calculated in this paper. For example, this paper gives the entropy of 36.7 J/(K•mol) to Ar, whereas Trouton's entropy is 74.9 J/(K•mol). Gibbs's potential suggests the minimum ΔG at equilibrium. It is correct, but it doesn't mean ΔG=0. The second law of thermodynamics implies that the spontaneous process is irreversible. Indeed, the exothermic heat of liquefaction is not equal to the endothermal heat of evaporation. Since the surroundings must keep the isolation of an isolated system, it pays more energy than the exhausted energy from an isolated system. Similarly, it may be inferred that Walden's entropy of fusion should also have been overestimated. |
67da38ba6dde43c9085d5857 | 26 | In the above discussion, helium is not mentioned because its behavior is weird. It should be noted that the data on helium-4 in the technical note has been adopted. By comparison with the data in the NIST Chemistry WebBook, it is found that WebBook digested the technical note data from 2.18 to 5.20 K. As shown in Fig. , at first, it is disturbing in mathematics that the Y•T~T curve is not a straight line, in contrast to so-far concerned other gases, in which both Y~1/T and Y•T~T curves are straight lines, and also the linear regressions give similar results. Moreover, A is negative. For example, 4.22-5.20 K, A=0.3009; 3.2-4.22 K, A=0.0152; 2.05-3.2 K, A=-0.4843; 1.05-2.05 K, A=-0.8058; 0.8-1.05 K, A=-1.3004. It means that the entropy of a liquid or solid is more significant than that of a gas at the same temperature. |
67da38ba6dde43c9085d5857 | 27 | Liquid helium is a superfluid with zero viscosity, which flows without losing kinetic energy. - When stirred, superfluid forms vortices that rotate indefinitely. The viscosity of superfluid helium can be understood in the classical two-fluid model, where only the normal fluid contributes to the viscous response. The abrupt drop in the mobility of electrons leads to a change in the solvation structure: the electron becomes localized and forms a sizeable spherical cavity (''bubble'') in the medium. However, it is hard to imagine that the positively charged nuclei are dissolved in the negatively charged electrons. From the viewpoint of orbital symmetry, the following atomic orbital shape change is depicted in this paper. As shown in Fig. , assuming that the shape of helium in gas is elliptic, whereas in the interval 4.2-5.2 K, the shape is spherical, we get n=2 for gas and n=1 for liquid. After that, the shape of helium in liquid changes as the temperature decreases. In addition, the mobility of helium in liquid is enhanced as the temperature decreases. Hence, A values become negative. In H2 and D2, A decrease is also observed as the temperature decreases. As shown in Fig. , for H2, A=1.48 in the region of Tc, but A=0.79 in the area of M.P. As for D2, the decrement of A is decreased considerably to 0.2. It implies that the mass of nuclei may relieve the particularity. On the other hand, comparing the Y•T~T curves of He-4 (Fig. ) and H2, it is observed that if extrapolating the temperature to 0 K, the H2 curve might exhibit a similar shape to He. That is to say, increasing entropy near 0 K is possibly expected for all the gases. |
67da38ba6dde43c9085d5857 | 28 | It is rational that the mobility of electrons decreases near 0 K . However, the assumption must be clarified that the positively charged nuclei dissolve in a solvent of the negatively charged electrons . Such an assumption implies that the electron and nucleus are electroneutral, which is consistent the results reported in our previous paper . |
67da38ba6dde43c9085d5857 | 29 | In the paper, linear regressions of 𝑅 as the condensation entropy, it is observed that the entropy is about half of the entropy derived from Gibbs's free energy, i.e., ∆G = 0. This result indicates that Gibbs's theorem is disputable, namely that the reversibility is impossible according to the second law of thermodynamics. Indeed, the exothermic heat of liquefaction is not equal to the endothermal heat of evaporation. Clausius-Clapeyron equation is derived from the exothermic heat equations. Helium-4 superfluid abnormally exhibits a continual entropy increase in liquid as T decreases from 3.5 to 0.8 K. A similar finding in the linear regression curve of H2 as the temperature approaches 14 K, proposes that the entropy increase in liquid is a common phenomenon as the temperature approaches 0 K. |
64ecf53cdd1a73847fb7654c | 0 | Sustainability and the circular economy have become cornerstones of corporate strategy. Today's products must satisfy the needs of engineering, marketing, business, regulation, and consumer preference while also being sustainable. Design decisions rely on eco-design and green chemistry principles, life cycle assessments (LCA), and related methods to reduce a product's environmental impact. Plastics and their pollution challenge current approaches in the design of sustainable products. Materials are selected principally by balancing tradeoffs between environmental impact categories, such as greenhouse gas (GHG) emissions and water usage during production. However, environmental persistence, defined as the time a plastic item lasts in the environment as pollution, is missing from the selection criteria (e.g., in LCA ). |
64ecf53cdd1a73847fb7654c | 1 | While plastics do break down in the environment, estimates of the environmental lifetimes of plastic products have only recently been made. These estimates vary widely and range from months to decades or longer. Biotic and abiotic processes act to fragment, degrade, transform, modify, assimilate, and mineralize plastics. The efficiency and selectivity of these processes depend on environmental conditions, the type of plastic, and the functionality and geometry of the product, i.e., on features of product design. Thus, an opportunity exists to consider environmental breakdown in the design of plastic products. Because some plastic products will inevitably enter the environment as pollution, regardless of waste management strategies, it is necessary to confront their persistence. |
64ecf53cdd1a73847fb7654c | 2 | With the understanding that more persistent materials pose greater potential threats to ecosystems and human health, environmental persistence is a fundamental principle of regulatory frameworks. Therefore, considering persistence during product design by selecting materials that quickly break down when leaked into the environment presents an opportunity to minimize risks to ecosystems and human health. Recently collected data on environmentally realistic plastic degradation rates catalyze this thinking. Here, we aggregate concepts learned from the past decades of plastic pollution research and integrate them into established material selection practices, formulating a novel eco-design framework for minimizing the environmental impacts of plastic pollution. |
64ecf53cdd1a73847fb7654c | 3 | Selecting appropriate materials is critical for engineers, industrial designers, and architects to create functional and aesthetically pleasing products. According to Ashby, the problem of choosing the "best" material can be framed as a collection of design requirements (i.e., functions, objectives, and constraints) for which material indices (MIs) can be determined and optimized. |
64ecf53cdd1a73847fb7654c | 4 | Complementary to this, we define environmental lifetime as the time it takes for an item's mass to reduce to zero because of degradative processes. Accordingly, we propose that persistence can be included in material selection by considering the design objective to minimize environmental lifetime at end-of-use. Much like other MIs (Table , Section S1), we developed an approach to derive MIs for environmental lifetime by i) defining the appropriate objective equation and ii) substituting relationships for the initial geometry of the item specified by the design constraints. |
64ecf53cdd1a73847fb7654c | 5 | To demonstrate the approach, consider the design of a stiff beam (Figure ). A typical function for a beam is to support a load without sagging. Rather than minimize the beam's mass or cost, the design objective for persistence is to minimize the beam's environmental lifetime at end-of-use. The design constraints on the beam define the loading conditions, amount of tolerable deflection, and geometry. The free, unconstrained variables are the choice of material and some geometric features. To derive an MI for persistence, we first defined the objective equation by solving a degradation rate equation, establishing a mathematical relationship between environmental lifetime and the geometry of the beam. |
64ecf53cdd1a73847fb7654c | 6 | The uniform degradation rate of a plastic item in the environment can be defined as the differential mass loss per unit time ( 𝑑𝑚 𝑑𝑡 ), equal to the product of the surface area (𝐴 𝑠 ) of the item and the density (𝜌) and specific surface degradation rate (𝑘 𝑑 ) of the item's material (Equation ). |
64ecf53cdd1a73847fb7654c | 7 | Thus, minimizing 𝑡 𝐿 requires minimizing 𝑏 0 and maximizing 𝑘 𝑑 . However, this relationship is incomplete. The predefined design constraints dictate 𝑏 0 . From beam theory (Section S2), 𝑏 0 can be defined in terms of the tolerable deflection (𝛿) of the beam, the beam's initial length (𝑙 0 ), the supported load (𝐹), the loading and support configuration (𝐶 1 ), and the Young's modulus (𝐸) of the beam's material (a measure of a material's resistance to elastic deformation) (Equation ). |
64ecf53cdd1a73847fb7654c | 8 | Grouping the terms for material properties expressed in Equation 4, the MI for minimizing the persistence of a beam with a solid square cross-section is 1 𝑘 𝑑 𝐸 1/4 . Notably, this MI implies that minimizing the beam's environmental lifetime requires considering a material's kd and E. Using reported values for kd and E of several plastics, functionally equivalent beams made from polycaprolactone (PCL) and polyhydroxyalkanoates (PHA) could be the least persistent, followed by cellulose diacetate (CDA), polyamide (PA), and polyurethane (PUR) (Figure ). |
64ecf53cdd1a73847fb7654c | 9 | In practice, products cannot solely be designed to minimize persistence at end-of-life; products must satisfy multiple, often competing, design objectives. Using literature data for several plastics, we calculated MIs to optimize a beam with a solid square cross-section in terms of financial (cost) and sustainability metrics (embodied GHG emissions and environmental lifetime). The choice of material had much greater effects on environmental lifetime than on cost or embodied GHG emissions. The median MIs for cost or embodied GHG emissions spanned less than one order of magnitude. In contrast, the MI for environmental lifetime spanned nearly three (Figure ). were lower, and PA, PHA, and PUR were higher than polyolefins). These same materials, though, had properties that reduced the MI for environmental persistence (i.e., shorter lifetimes than polyolefins). While MIs are helpful, they cannot, on their own, quantify the tradeoffs between competing design objectives. To address this, value functions can be used to systematically weigh the relative value of any given combination of MIs by forming a compound objective for optimization. Value functions are defined by converting the performance (e.g., mass, energy, time) to value (e.g., monetary value or cost) using exchange constants (e.g., price per kg). |
64ecf53cdd1a73847fb7654c | 10 | Because plastic products can persist in the environment as pollution, their impact is cumulative every year they remain. Therefore, we propose that the cost of plastic pollution (𝐶 𝑃 ) i.e., its value, can be defined as a performance-exchange constant pair of environmental lifetime and the cost of plastic pollution per mass of material per year in the environment. Accordingly, the cost of plastic pollution is realized as the product of the exchange constant (𝛼 𝐿 ) and the integrated mass over a product's environmental lifetime (Equation ), where 𝑚 is the instantaneous mass of the product from when it first entered the environment (𝑡 = 0) to when it is completely degraded (𝑡 = 𝑡 𝐿 ). |
64ecf53cdd1a73847fb7654c | 11 | For the value of 𝛼 𝐿 we propose using the economic cost of plastic pollution, estimated to be between $3300 and $33000 per metric ton of marine plastic per year (2011 $USD). This term underestimates the total cost of plastic pollution, as it only considers the toll on marine ecosystems, not the complete biosphere. To acknowledge that not every item leaks into the environment, we adjusted 𝐶 𝑃 by multiplying by the total fraction of plastic leaking into the environment (𝜒 𝑃 ) and by the fraction with which a given type of item would contribute to the total amount of leaked plastic (𝑓 𝑃 ). Presently, society, not the manufacturer, bears the cost of plastic pollution, requiring discussions of policies for extended producer responsibility to acknowledge this cost. |
64ecf53cdd1a73847fb7654c | 12 | For most geometries (those that retain the same morphology as they degrade), Equation 5 can be approximated by Equation 6 where 𝑚 0 is an item's initial mass, and 𝑛 is a dimensionless 'shape factor' (𝑛 is 1 for films, 2 for solid cylinders and beams, and 3 for spheres) (Section S3). |
64ecf53cdd1a73847fb7654c | 13 | Currently, billions of disposable coffee cup lids are used annually of which a fraction become pollution, accounting for ~5% of plastic debris in nearshore waters. Thus, any savings from their environmental impact can yield significant benefits. In this section, we use our framework to evaluate which on-the-market lid material reduces the environmental impact the most and determine which next-generation plastics are best and thus warrant adoption. |
64ecf53cdd1a73847fb7654c | 14 | Today, disposable coffee cup lids are made from PLA, PP, or PS (Figure ); which material "best" reduces environmental impact, however, is non-obvious. Comparing MIs for several environmental impact categories included in LCAs indicated that of the three materials, PP was the best. PP minimized MIs for GHG emissions and water usage (Figure ). Ironically, PP is one of the most abundant types of plastic found in marine garbage patches. Calculated value as the sum of the cost of material and the social cost of CO2 per 1000 lids expressed in 2016 $USD for PP, PS, and PLA ranged from $9.17 to $10.72 for PP, $11.61 to $16.46 for PS, and $6.99 to $11.60 for PLA (Figures ). Thus, overall, no material was much better than another. Though abridged, the result is not expected to change, given that conventional LCA impact categories trend well with GHG emissions. Lid design should account for persistence. Of the three materials, PS was optimal for environmental lifetime (Figure ). Including persistence (cost of plastic pollution) could increase the cost per 1000 lids expressed in 2016 $USD for PLA and PP to over $200 while increasing the cost for PS to ~$20. Our analyses suggest that PS may be the least impactful of the three materials on the market for disposable lids. |
64ecf53cdd1a73847fb7654c | 15 | Our metric provides an opportunity not only to compare materials in use but also to identify less environmentally impactful alternatives. CDA, PBAT, PBS, and PHA are championed by many as alternative, more sustainable, degradable plastics for making consumer products. Comparing MIs, disposable lids made of CDA or PHA could provide more than an order of magnitude better performance for environmental lifetime while being comparable in other categories (Figure ). PBAT and PBS were worse than current plastics for nearly all MIs (Figure ). This result underscores the idea that bio-based, biodegradable, or compostable plastics are not a panacea for addressing the environmental impacts of plastics. Instead, our results suggest that a more nuanced understanding is needed, whereby some biobased plastics are robust alternatives (i.e., CDA and PHA), and others appear to exacerbate the problem (i.e., PBAT and PBS). |
64ecf53cdd1a73847fb7654c | 16 | Notably, without accounting for persistence, the incentive to switch to these alternative plastics is weak, given their increased cost and limited reductions in GHG emissions (if at all) compared to current plastics (Figures ). However, adopting alternatives could be incentivized by the value gained by reducing the cost of plastic pollution. Savings to the cost of pollution per 1000 lids from switching to CDA or PHA compared to current plastics were estimated to range from $1.46 to $220.01 and -$0.40 to $220.49, respectively (Figure ). Given the billions of lids consumed annually, these savings could translate to societal benefits of hundreds of millions of dollars for this item. |
64ecf53cdd1a73847fb7654c | 17 | Additionally, several studies were conducted using closed-system bottle incubations, which can lack environmental relevance because the plastic in question is used as the sole nutrient source of carbon. Results of these studies often report much faster degradation rates than those from more realistic mesocosm and field experiments (Table ). Moreover, the few reports of kd pale compared to the vast number of plastic formulations contributing to the large variability across plastic types. For example, in the case of PHAs (Figure ), kd values span nearly two orders of magnitude. Consequently, while PHAs could be materials with the least cost of pollution (Figure ), they could also be some of the more costly choices. In the case of PA, only one study has measured kd (Table ), making any estimate of PA lifetime and cost of pollution highly uncertain. Such tremendous variability and uncertainty pose significant challenges to material selection. |
64ecf53cdd1a73847fb7654c | 18 | Moreover, while some studies demonstrate that kd represents the mineralization of plastic to carbon dioxide, dissolution to dissolved organic carbon, or assimilation to biomass, 14 many studies present no evidence of complete or partial transformation. This poses challenges in knowing whether kd represents the chemical degradation (depolymerization) of the polymer or merely the physical degradation (disintegration) to microplastics. Regardless of the degradation process, the impacts of any degradation products released from plastic items must also be considered. Finally, a key challenge is that the molecular and microstructural features underpinning polymer degradation 46 also control many other polymer properties (e.g., Young's modulus). Of the studies reporting data sufficient to calculate kd, less than half included characterization of any physical and mechanical properties or provided enough details to determine them after the fact. Because the environmental lifetime of an item can depend on kd and other material properties, making effective material selection decisions will require reporting comprehensive details of material properties along with kd. |
64ecf53cdd1a73847fb7654c | 19 | The metric we propose for minimizing environmental lifetime applies to mitigating terrestrial plastic pollution and waste destined for landfill or composting, although similar data limitations exist for kd in these environments. Overall, a greater understanding of the environmental controls (e.g., sunlight exposure, temperature, nutrients, microbial communities) and structureproperty-formulation relationships governing plastic degradation will improve predictions of kd and resulting lifetime and cost of pollution estimates. |
64ecf53cdd1a73847fb7654c | 20 | Plastics are polymers modified with organic and inorganic additives, constituting their formulation. Various compounds added to plastics or included in them as non-intentionally added substances can facilitate or inhibit the environmental degradation of plastics. For example, antioxidants and ultraviolet light stabilizers are added to plastics to protect them from thermal degradation during processing and photochemical degradation during outdoor use. Because plastics are typically thermally processed, most plastic products contain antioxidants, which can prolong plastic lifetimes compared to additive-free plastics. Other additives can intentionally (e.g., pro-oxidants, photocatalysts, enzymes, or microbes ) or inadvertently (e.g., pigments , catalyst residues, and unsaturated bonds 21 ) enhance degradation. Additionally, the amount of polymer used to make a product can be reduced using fillers, thereby reducing lifetimes in proportion to the amount of filler used. While additives may prove helpful for reducing environmental lifetimes, their potential harm to human health and the environment must also be appreciated. Moreover, the intrinsic toxicity of plastic will require an MI to inform design decisions. Ecocompatible plastics must be made from ecocompatible polymers and ecocompatible additives. |
64ecf53cdd1a73847fb7654c | 21 | A product's degradation rate is controlled by material and geometry (i.e., surface area). It should be standard practice for engineers to use topology optimization techniques and additive manufacturing to design and fabricate products that maximize surface area and thus minimize environmental lifetime. Such strategies have already begun to be applied to some single-use items (e.g., cutlery ) by redesigning them to remove structurally unnecessary material. Latticefilled or foamed structures also achieve this objective. In particular, foamed items may have added benefits by keeping them in conditions more favorable to degradation because of their positive buoyancy and, thus, exposure to sunlight. Addressing the plastic pollution crisis will This limited specificity in accreditation criteria is reflected in practice. For example, a review of 24 undergraduate material science and engineering programs (with or without ABET accreditation) across researchintensive universities (R1) in North America demonstrated that eco-design might only be taught within ~30% of material selection courses (Data S1). Thus, ~70% of engineers may enter the workforce without receiving mandatory curricular instruction on the environmental impact of materials and their tradeoffs. Incorporating our novel metric and others (e.g., for microplastic formation ) into material selection and design courses thus represents an opportunity to train the next generation of engineers about eco-design and close the sustainability gap in materials education. Local communities have already begun regulating single-use plastic products (e.g., bans on straws, grocery bags, and bottles). Yet often, consumers are without recommendations for products made from alternative materials. Like product designers, consumers need strategies for making the "best" material selection choices for the environment. We recommend implementing a simple, quantitative persistence label for plastic products that can complement existing eco-labels (e.g., Energy Star) to inform consumers about the persistence of plastic materials in the environment. |
64ecf53cdd1a73847fb7654c | 22 | Globally, negotiations for an international plastics treaty are underway. The eco-design framework presented herein for mitigating environmental persistence should be considered part of the resolution. Material indices provide quantitative metrics for benchmarking materials during the design process that could be integrated with other sustainability metrics to define regulatory criteria in policy. |
674df0837be152b1d0b45ecf | 0 | Photoswitches, e.g. molecules that undergo reversible changes in their structure and properties upon irradiation with light, offer promising opportunities of steering the conversion of optical-into mechanical energy through powered nanoscale motions. In particular, the combination of photoswitching with controlled directional motion, referred to as light-driven molecular motors, enables fascinating prospects in nanotechnology and molecular engineering. Notable examples of photoswitch-driven nanodevices and molecular machines include the light-control of surface wettability, optoelectronics such as light-powered electrical switches, chemical sensing, and photosensitive medicine. Especially for biological-and material science applications that do not tolerate high-energy input, the absorption of visible light by the photoswitchable chromophores is particularly desirable. Apart from the long-known azobenzenes, a recently emerging class of photoswitches is given by indigoids and particularly hemithioindigo (HTI) (Scheme 1). These compounds feature such desired low-energy absorption bands for electronic excitations together with a good thermal bi-stability, and chemical durability along the switching process. Consequentially, HTIs have found their way into a plethora of applications including molecular machines such as motors, gears, or tweezers, as well as photoresponsive catalysis, supramolecular chemistry, molecular computing, or photopharmacology. Further chemical modifications have been employed to enable HTI attachment to metal surfaces, or to tailor selfassembly. The photoreactions of hemithioindigo-based molecules were extensively studied in the past by both, experimental and theoretical investigations . In the most straight- forward cases, these molecules undergo torsional deformation of the double bond upon visible light excitation, and thus form Z and E isomers after relaxation to the electronic ground state. However, more complex bond rotations of HTIs in the excited state have also been developed recently, notably concomitant single and double bond rotation as initially propsed by Liu and Asato, the Hula Twist photoreaction, or a single bond rotation. Moreover, the kinetics and type of photoreaction depends on the specific environment, such as the choice of the solvent. Both, the groups of de Vivie-Riedle and Maurer found that the photoinduced doublebond isomerization (DBI) in unsubstituted hemithioindigo (scheme 1) is largely characterized by dihedral rotation around the central -C=C-bond. Moreover, depending on stilbene substitution, the molecule may undergo an early-stage pyramidalization for the transition from the bright S1-state to the dark, reactive S2-state with more electron rich arenes requiring less pyramidalization. However, Yang et al. showed by nonadiabatic molecular dynamics simulations that the reactive DBI pathways of hemithioindigo are defined by conical intersections dominated by dihedral torsion with a rather weak degree of pyramidalization. 50 As can be seen by the multitude of HTI applications mentioned above, suitable functionalization of these molecular photoswitches is key for developing more complex and capable functions in the future. For a truly rational design of such advanced capabilities, in-depth mechanistic understanding of the photochemistry of HTIs and the effect of the functionalization is required -both at the electronic and the molecular scale. From the perspective of theory, such characterization may be provided by timedependent density functional theory (TD-DFT) calculations and more sophisticated multireference methods to study the electronic states, whereas molecular dynamics (MD) simulations offer the investigation of atomic motion using classical Newtons dynamics. The key hurdle to MD investigations is however given by the need to appropriately describe the forces and energies of the atomic interactions -both in the electronic ground state and after photoactivation. While the most accurate approach would call for a fully quantum treatment of both electronic and vibrational degrees of motion, the computational costs of such modelling are quite considerable. As a consequence, only models of a few selected degrees of freedom could be subjected to full quantum dynamics simulations at the current state of the art. |
674df0837be152b1d0b45ecf | 1 | Molecular photoswitches including HTI are highly sensitive to the environment and it is of critical importance to understand the details of solvent effects or HTI embedding in molecular assemblies such as self-assembled monolayers. We therefore advocate for explicit solvent models and extended statistical sampling -which implies 10,000s of atoms sized simulation systems and 100 ns scale dynamics runs, respectively. This calls for computationally efficient approaches that largely replace quantum mechanical (QM) calculations by molecular mechanics (MM). This may be accomplished by multistate force-fields to specifically describe Born-Oppenheimer potential energy profiles at a given electronic state. The latter are routinely available for the ground state, however for photoswitches we also need specific force-fields for describing the modification of the atomic forces upon electronic excitation. As a minimum requirement, at least the most relevant excited state, typically the adiabatic S1, needs to be mimicked by a tailor-made MM interaction potential. |
674df0837be152b1d0b45ecf | 2 | To model the photoinduced excitation process, multi-state force-fields may be connected to surface-hopping approaches that implement transition probabilities based on QM calculations. In a QM/MM fashion, the underlying QM system is often limited to the photoswitch molecule, whereas embedding effects (solvent, local aggregates etc.) are efficiently described by MM approaches. On the other hand, once the electronic state has changed we may investigate photoswitch relaxation from straight-forward MD simulation using the S0/S1/... -specific MM force-fields. This enables the investigation of geometry changes from Newtons dynamics rather than imposing minimum energy pathways. Moreover, the interplay with the embedding environment is assessed from explicit atomic movement of the nearby molecules. |
674df0837be152b1d0b45ecf | 3 | In what follows, we develop S0/S1 -specific MM force-fields for the parent HTI and demonstrate the analysis of solvent effects from detailed MD simulations. Apart from the underlying energetics, a particular focus is dedicated to statistical sampling. This enables also assessing entropic and kinetic effects -which we argue are becoming of increasing relevance with the increasing complexity encountered in photoswitches and their derived molecular machines in particular. |
674df0837be152b1d0b45ecf | 4 | Unless otherwise noted, all quantum chemical calculations were carried out using Kohn-Sham density functional theory (DFT) as implemented in the ORCA 5.0.4 quantum chemistry software package using the B3LYP exchange-correlation functional in combination with the def2-TZVP basis set and the def2/J auxiliary basis. Dispersion was treated by Grimme's D3 dispersion correction including the Becke-Johnson damping function. Acceleration of the calculations was achieved by applying resolution of identity approximation and chain of spheres exchange. To assess the nature of stationary points, the vibrational frequencies of all optimized geometries were calculated by applying the harmonic oscillator approximation. From this, we ensure the absence of imaginary frequencies for identifying minimum energy configurations on the potential energy surface. |
674df0837be152b1d0b45ecf | 5 | All molecular mechanics force field parameters -except for the new terms -were derived from the General AMBER Force Field (GAFF) 2.2.20 suite, as released with the Amber22 software package. Atomic partial charges were obtained by the restricted electrostatic potential (RESP) method fit. The corresponding electrostatic potential was obtained from the DFT optimized structures using a Hartree-Fock calculation on a 6-31G** basis as implemented in Gaussian16. Consequently, the RESP charges were generated using Antechamber. Molecular dynamics simulations were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) using a time step of 1.0 fs. |
674df0837be152b1d0b45ecf | 6 | Temperature and pressure were controlled by applying the Nosé-Hoover thermostatbarostat algorithm as implemented in LAMMPS using relaxation constants of 0.1 ps and 1.0 ps for temperature and pressure, respectively. Non-bonded short-range interactions were cut off at a distance delimiter of 12 Å. To account for long-range Coulomb interactions, the particle-particle particle-mesh Ewald approach was utilized. |
674df0837be152b1d0b45ecf | 7 | All molecular dynamics simulations in explicit solvation boxes were preceded by 10 ns of NpT equilibration of the bulk solvent, followed by additional 10 ns runs after insertion of the HTI molecule. Apart from the gas phase, photoswitching was investigated in nhexane and dimethyl sulfoxide (DMSO) using cubic, 3D-periodic simulation models of 508 and 991 solvent molecules, respectively. For each isomer, Z and E, parallel systems were prepared and propagated for 50 ns in the NpT ensemble to provide volume relaxation. While 2 ns were found necessary for equilibration, the occurrence profiles of the torsion angle in the different states were derived from the remaining sketches of 48 ns. We then fixed the box volume to the mean volume of the NpT equilibration run and performed an additional NVT run of 50 ns, taking snapshots at every 10 ps. This provided 5,000 structures referring to the (solvated) Z-and Estructures in the S0 state that were used as the starting structures for investigating photoexcitation to S1. The trajectories of the actual switching events were propagated in the NVE ensemble, using an initial 20 ps run in the S1 state and then instantaneously switching back to the S0-FF to produce additional 5 ps NVE runs that describe the S1 → S0 switching, respectively. |
674df0837be152b1d0b45ecf | 8 | Based on parallel series of 2×5,000 switching trajectories created in this manner, the probability of (S0 → S1 → S0) relaxation to the S0-E state was scrutinized by committor analyses referring to the atomic coordinates of the model systems at the moment when switching the force field according to the S1 → S0 transition. For each of the geometric features investigated, occurrence profiles were sampled using 20 equidistant bins within the observed minimum and maximum values, respectively. On the basis of this discrimination, conditional committor probabilities are sampled and subjected to a sigmoid fit using a logistic regression classifier as implemented in Scikit-learn version 1.5.0. 80 Prior to model training, the feature sets were recentered and rescaled using the StandardScaler from the Scikit-learn library. No penalty was added to the logistic regression model. |
674df0837be152b1d0b45ecf | 9 | The torsion profile of the core HTI molecule features two (local) energetic minima in each, the S0 and S1 states, respectively (figure ). Using unrestrained geometry optimization from DFT calculations, we prepared reference models of these key structures. The underlying S0/S1 type minimum energy structures of HTI are used for computing the atomic partial charges of the MM models. Starting from the DFT-relaxed S0-E and S1-syn structures, rigid scans of the -C=Ctorsion were performed in parallel runs. While such rigid scans are particularly useful for parameterization of the torsion potentials without interference from lateral movements, we suggest the fully relaxed minimum energy configurations S0-Z/E and S1-syn/anti for benchmarking our MM models. |
674df0837be152b1d0b45ecf | 10 | In turn, electronic excitation manifests in changes in the atomic partial charges and the -C=C-torsion potential as a minimum to finding appropriate MM models. While the actually relevant electronic excitation describing photoswitching refers to the adiabatic S1 state, a simple numerical trick in the DFT calculations is to first characterize the more stable T1 state, which corresponds to the lowest non-relativistic energy eigenstate for a total electron spin of 1, followed by subtracting two times the exchange potentials to yield the S1 energy. On this basis, numerically robust scans of torsional degrees of freedom and valence angles can be performed to parametrize the MM potentials. The underlying rigid scans require sterically reasonable starting points -which we picked from the DFT-relaxed S0-E and S1-syn (actually T1-syn) structures, respectively. |
674df0837be152b1d0b45ecf | 11 | To this end, the explicit atomic structures used for computing the S1-state torsion profile do not fully match those of the S0-state based scan, albeit featuring the same torsion angle θ. In fig. , the conical intersection is prepared by matching the MM-based S1 profile to the MM-based S0 torsion barrier. In TD-DFT, the conical intersection prevents numerical assessment of S1 energies for the HTI structures near θ = 90° as already demonstrated by Plötner and Dreuw. To assess the energy shift between T1 and S1, we instead used the S0-Z and S0-E configurations at 90°, which showed offsets of 2•ΔEexchange = 0.80 and 0.74 eV, respectively. Our excited-state MM models fitted to the T1-based DFT energies of the torsion profile, are thus suggested to use a constant shift of 0.77±0.03 eV to mimic the corresponding S1-states. |
674df0837be152b1d0b45ecf | 12 | Before looking into the actual Z→E isomerization process, we characterized the underlying local energy configurations by separate MD simulations in the NpT ensemble (50 ns at T=300K). Figure shows the occurrence profiles h(θ) of the -C=Ctorsion angle θ, for i) HTI in the gas phase, solvation in ii) n-hexane and iii) DMSO, both at ambient conditions, respectively. As a consequence of the large torsion barrier in the S0-state, two separate profiles were derived for the Z-and E-conformers, respectively, using parallel MD runs. On this basis, the average energy difference in S0-Z and S0-E conformers was found as 0. given by the S0-Z conformer, and Boltzmann statistics at 300K would predict at most 1.4 % population of the S0-E conformer. |
674df0837be152b1d0b45ecf | 13 | Based on the relaxed S0-Z and S0-E configurations (in vapor, hexane and DMSO) as discussed above, we now look into the photoexcitation to S1 by means of MD simulation. For this, 2×5000 randomly depicted snapshots were taken from NVT runs for each isomer, subjected to instantaneous switching to the S1-MM model, and propagation from MD simulations. Relaxation in the S1 state was monitored in the NVE ensemble to avoid artificial damping of the kinetics by the thermostat algorithm. |
674df0837be152b1d0b45ecf | 14 | Sampling averages from the (each) 5000 pathways collected for the S0-Z and S0-E starting points, respectively, we produced time-dependent profiles of the -C=C-torsion angle (fig. , see also supplementary information S3.1). The different relaxation dynamics are best seen from contrasting S0-Z/E → S1 in vapor to HTI photoswitching in solution, respectively. In the former, 0/180° → 90° deformation of the -C=C-torsion angle is observed on the fs scale, however leading to strong vibrations of the entire HTI molecule -and thus re-visiting the Z/E type configurations. In turn, after energy dissipation from the torsion degree of freedom to molecular vibration, we find convergence to the S1 state within about 10 ps. On the other hand, in solution the torsional motion is slowed by nearby solvent molecules. This damps HTI vibrations significantly and convergence to the equilibrium S1 state is found at the 5 and 15 ps scale in hexane and DMSO, respectively. Statistics of the vertical energy difference between the S0-and the S1-state are reported in the supplementary information S3, whereas the electronic decay from S1-states is discussed in the following. From comparing the evolution of photoswitching pathways starting from S0-Z and S0-E, we argue that upon 20 ps propagation in the S1 state, our MD simulations converged to S1 type configurations. Using the endpoints of these 2×5000 trajectories, we switched our MM model back to the S0 state to mimic the electronic decay to the ground state. In all solvent scenarios, we find the HTI molecules to lock into either S0-Z or S0-E configurations within only a few picoseconds of NVE simulation runs (fig. ). While evolution to the S0-Z state is preferred over all solvent scenarios, the observed Z/E ratio after completing the photoswitching cycle differs significantly. Indeed, the probability of finding S0-Z conformers (which was found as 55. collected for the S1→S0 transition runs. To this end, the probability of HTI relaxation to the E-isomer p(S1→S0-E) is assumed as the reaction coordinate. While mathematically exact, it however provides little help for our actual understanding of the underlying mechanisms. This motivates the formulation of structural descriptors of which we created a small series of candidates from intuition. |
674df0837be152b1d0b45ecf | 15 | To benchmark the suitability of a given descriptor x as a trigger for enhancing/diminishing Z-E isomerization by photoexcitation, we elucidate its performance in predicting the 'mathematical reaction coordinate' p(S1→S0-E,x). The latter refers to the above-described statistics of p(S1→S0-E) -which was devised as a function of x, that is the value of the given descriptor at the instant of the electronic decay S1→S0 (implemented by switching of the MM models). This target function is approximated by a sigmoid-type fit function p(x) according to: |
674df0837be152b1d0b45ecf | 16 | Inspired by the fitting of logistic regression classifiers, two parameters A and ω are used to best approximate our target function, namely p(S1→S0-E,x) as sampled from the corresponding occurrences observed from our MD runs. To this end, parameter A controls p(𝑥 = 〈𝑥〉) -which is reflected by the overall average of p(S1→S0-E). In turn, the parameter ω indicates how sharply the sigmoid shape of p(x) depends on the actual value x of the descriptor. This allows interpreting ω in terms of the suitability of a given descriptor model. For example, a poorly chosen descriptor that does not correlate at all with p(S1→S0-E,x) will essentially provide random numbers as inputs to p(x). The corresponding fit will thus show ω = 0 and p(S1→S0-E,x) = p(S1→S0-E) is a constant. |
674df0837be152b1d0b45ecf | 17 | For HTI switching in vacuum, only the DBI torsion angle 𝜃-C=Ccould be identified as a significant descriptor for triggering relaxation to S0-Z versus S0-E from the S1-state. In fig. , this is indicated by a well-defined sigmoid shape of the fitted function p(x) for predicting the committor probability p(S1→S0-E,x). For comparison, we also show the fitting of eq. 3 in case of using the SBR torsion angle 𝜃=C-Cas a putative descriptor. In this case, we indeed find ω=0 and a rather indifferent approximation of p(S1→S0-E,x) = constant. A more subtle picture is however observed for HTI photoswitching in solution. While the 𝜃-C=Cangle is still of central importance for Z-E isomerization, we identified two solvent coordinates as additional descriptors for predicting our committor analyses. |
674df0837be152b1d0b45ecf | 18 | Indeed, to study the influence of explicit solvent molecules on the photoswitching, we defined focal points (FPs) representing key features of the HTI geometry and sampled their distance to nearby solvent atoms. For this, we computed the center-of-geometry of the phenyl ring (Ph) and suggested its geometric center between the C 7 / S atoms of HTI as FP-PhC 7 / FP-PhS sites to elucidate the coordination of nearby solvent molecules (fig. ). To discriminate these solvation effects, we suggest four prototype cases depending on the minimum solvent distances to FP-PhC ). |
674df0837be152b1d0b45ecf | 19 | To resolve this apparent contradiction, we sampled the nearest-neighbor solvent arrangement a) at the moment of the electronic transition S1→S0 and b) after 200 fs relaxation dynamics in the S0-state (fig. ). For HTI solvation in hexane, such before/after analysis of nearby solvent atom distribution clearly shows the steric hindering effect: solvent atoms close to FP-PhC 7 are shoved aside during the hinge motion of the phenyl ring while the solvent on the opposing side of the stilbene moiety is following this motion. In stark contrast to this solvation mechanism, the coordinating DMSO molecule moves concertedly with the stilbene moiety to keep the hydrogenbonding pattern upright. Hence, the lower extend of steric hindrance experienced for HTI switching in DMSO may be related to a less dense solvation of the phenyl ring (fig. ) and the concerted rotation motion of DMSO coordinating the stilbene moiety (fig. ). |
674df0837be152b1d0b45ecf | 20 | In parallel to the photoinduced double bond isomerization described above, we also studied possible rotation of the stilbene moiety around the =C-C-single bond from the series of S0→S1→S0 transition trajectories. While SBR is readily observed in hemithioindigo chromophores with asymmetrically substituted phenyl rings , it cannot be resolved experimentally for the unsubstituted HTI due to the chemically Apart from the overall amount of kinetic energy gained from S1→S0 switching in the molecular mechanics models -which is indeed largest for configurations θ-C=C-= 90° -the chance of triggering SBR surely depends on the way that the excess kinetic energy is being dissipated. In solution, such dissipation involves both the HTI and nearby solvent species. In turn, HTI switching in the gas phase does permit energy dissipation to other molecules and thus leads to particularly strong enhancement of the vibrations within the HTI itself. Indeed, we found a significantly higher SBR quantum yield of 28.3 % in gas phase. This is in line with a 'hot ground state' picture in which the HTI molecule in vapor retains high kinetic energy after leaving the excited state whilst HTI in solution undergoes energy dissipation with a few picoseconds (see also supplementary information S4). |
64e4bfbf3fdae147fa9b3948 | 0 | The efficient light-absorbing metasurface can be engineered as a 2D material with a metal-dielectric(insulator)-metal (MIM) structure consisting of top layer of metallic nanoparticles, a nano-thin spacer on a metal base layer. The underlying metal base layer suppresses light transmission and, with a top-pattern of metallic nanoparticles, suppresses overall light reflection from the MIM structure . Such metamaterial realizes a highly efficient light absorption at the designed wavelength and acts as a photo-thermal conversion device . Interestingly, electromagnetic field calculations have revealed that the optical absorption and scattering coefficients are equivalent under the anti-reflective condition when metasurfaces are constructed with metallic materials commonly used at the plasmon resonance of gold (Au), silver (Ag), and copper (Cu) bands . It was experimentally determined that the emissivity of MIM metasurface does not reach 100% even if the reflection spectrum shows a completely anti-reflective condition (transmittance T =0, reflectance R=0). This means that light is not fully absorbed in completely anti-reflective conditions and thermal radiation is not reaching 100%. To achieve the "true perfect absorption and true perfect radiation,", control of the absorption and scattering cross sections σ abs,sca , respectively, hold the key role. For conventional MIM metasurfaces that are made of Au, σ abs are equal to σ sca at the minimum anti-reflection condition. It was demonstrated earlier that by control of σ abs and σ sca using multi-layer Au-Si nano-discs, the response of MIM structure can be divided into the peaks of σ abs and σ sca . We have realized a perfect-absorber/emitter using MIM structures by intricate tune of absorbtion via scattering of MIM structures by increasing σ abs in respect to σ sca 8, 9 . This was achieved by increasing a thickness of Cr film used as an adhesive layer between the Au and dielectric layers, hence, favoring the absorbance contribution. |
64e4bfbf3fdae147fa9b3948 | 1 | For thermal emitters at a designed IR-band, choice of materials for MIM patterns becomes important since more emission can be obtained at elevated temperatures. In this regard, when Au and Cr are stacked and heated, Cr will quickly diffuse into Au, destroying the MIM structure and degrading optical properties. Therefore, we focused on searching for homogeneous metallic materials with strong absorption. We propose to use high entropy alloys (HEA), which are, by a narrow definition, metallic materials in which five or more metallic elements are alloyed in the same atomic number ratio. It has the characteristic of maximizing the configuration entropy of the metallic material . The configuration entropy S can be written as: |
64e4bfbf3fdae147fa9b3948 | 2 | where R is the gas constant, N is the number of possible compositions. In conventional two-component alloys, the configuration entropy is R ln 2 ∼ 0.69R, but when the alloy becomes a five-component, the configuration entropy is ∼ 1.61R. The HEA material is defined by S > 1.5R, where a middle entropy alloy has 1.0R < S < 1.5R and a low entropy alloy S < 1.0R. In the case of normal two-component alloys, a phase separation usually occurs without enthalpically unfavorable alloying due to low configuration entropy. The phase formation is thermodynamically guided by the Gibs free energy of mixing ΔG = ΔH -T ΔS defined by the enthalpy ΔH and ΔS entropy parts at temperature T . In contrast, when the configuration entropy is increased, even under enthalpically unfavorable conditions, entropy acts as a driving force and a single-phase alloy forms (it is similar to the surfactant to oil/water emulsion formation). It has been reported that HEA conversion improves the mechanical strength of metals . Several reports on HEA using precious metals, including Kitagawa et al. and others , have reported that HEA has a greater catalytic effect than stand-alone palladium or platinum. However, up to now, HEA has not been adapted to optical devices based on optical/plasmonic properties. |
64e4bfbf3fdae147fa9b3948 | 3 | Recently, alloys have been attracting attention as plasmon resonance materials, e.g., Au, Ag, and Cu alloys were made . We obtained, for the first time, the complex permittivity ε ≡ (n + iκ) 2 of a metallic tri-metal alloy made of Au, Ag, and Cu at different mixing ratios and used those alloys for their plasmonic function (n is the refractive index, and κ is extinction). We also found that forming alloys with Au and Pd improves the hydrogen response and enables the construction of optical hydrogen sensors. In optical applications based on plasmon resonance, it is crucial to determine the complex refractive index (n + iκ) of metallic materials. This is essential for electromagnetic field calculations, including numerical methods, e.g., finite differences time domain (FDTD) calculations which provide exact numerical solutions of Maxwell's equations. However, it is known that when an alloy is formed, its complex permittivity becomes different. It is not accurate to use the arithmetic mean of the constituent part to describe the alloy . In addition, the permittivity changes because of the size and defects (grain boundaries, stacking faults, dislocations, porosity) depending on the film's deposition conditions. Therefore, evaluating the permittivity of a film deposited under the exact same conditions used for nano-particles top layer of MIM is always required, and ε has to be determined experimentally. |
64e4bfbf3fdae147fa9b3948 | 4 | In this study, we constructed a MIM metasurface using a HEA made of Au, Ag, Cu, Pd, and Pt. Reflectance spectra were experimentally determined, and the corresponding cross sections for the reflection, absorption, and scattering contributions were modeled by FDTD. These results can be extended with anticipation of the high efficiency of photo-thermal energy conversions. |
64e4bfbf3fdae147fa9b3948 | 5 | Metasurface fabrication was performed as described elsewhere in more detail ? In short, 5 nm Cr and 200 nm Au were thermal deposited on a silicon substrate first. After depositing 5 nm Cr, set of samples with SiO 2 layers from 100 nm to 500 nm (with a 100 nm step) were deposited by electron-beam (EB) evaporation. After, an electron beam lithography (EBL) resist was spin-coated, and EBL exposure was performed to define the top-layer metallic nanostructures. After development, Cr 5 nm and various metals were deposited, and lift-off followed. Five metal alloys target were purchased (Tanaka Precious Metal Co., Ltd.) to form HEA by sputtering. |
64e4bfbf3fdae147fa9b3948 | 6 | Microspectroscopy was used for spectral characterization of meta-surface MIM structures, which had a footprint with a 300μm cross-section. A Fourier transform infrared (FT-IR) spectrometer and a microscope unit (FTIR-6000 and IRT-1000, JASCCO) were used to measure the reflection spectra in the mid-infrared region. Film of Au of 350 nm thickness was used for the reflection reference, with 98% reflectance in the entire mid-infrared area. |
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