Odd-even Effect Research Articles

Special odd-even effects of electron transport through quantum-dot molecules with side-coupled Majorana zero modes

Special odd-even effects of electron transport through quantum-dot molecules with side-coupled Majorana zero modes

Enhanced Low-Density Silicone Foams Blown by Water-Hydroxyl Blends.

Water, alcohols, diols, and glycerol are low-cost blowing agents that can be used to create the desired silicone foam structures. Although their combined use can be beneficial, it remains unclear how it affects the physical properties of the resulting materials. We conducted a comparative study of these hydroxyl-bearing blowing agents in fumed silica- and mica-filled polymer composite systems for simultaneous blowing and crosslinking to obtain a low-density, uniform porosity and superior mechanical properties. The foams were optimized for a uniform open-pore structure with densities ranging from 75 to 150 kg‧m-3. Varying the diol chain length (Cn) from one to seven carbons can alter the foam density and structure, thereby enhancing the foam tensile strength while maintaining a low density. Replacing 10 mol% of water with 1,4-butanediol decreased the density by 26%, while increasing the specific strength by 5%. By combining glycerol and water blowing, the resulting foams exhibited a 30% lower apparent density than their water-blown analogs. The results further showed that Cn > 4 alkane chain diols had an odd-even effect on the apparent density and cell wall thickness. All foamable compositions had viscosities of approximately 7000 cSt and curing times below 2 min, allowing for quick dispensing and sufficient time for the foam to cure in semi-industrial volumes.

Monoisotopic targets production from atomic and molecular positive ion implantation in a tandem accelerator at low energies

We produced monoisotopic targets of 13C and 28,29Si with 1015−16 atoms/cm2 areal density by ion implantation in different matrices at the Accelerator Mass Spectrometry (AMS) facility in Mexico. The tandem accelerator terminal voltage was set at the lowest achievable value (200 kV) that yield beams with energy of 435 keV. It is possible to do ion implantation at lower energies in our facility through the use of molecular beams, so in this work we looked for, and successfully found, bound positively charged molecular beams, although with very low intensity. We inject 235 keV molecules into the charge of exchange canal (argon) of our tandem accelerator and detected the survival fraction of C2,3,4 molecules in 1+ and 2+ charge states or above. Our results showed that some molecules remain bound, with one or more electrons missing, after being forced through a low density gas stripper at relatively high energy. In the production process of negative molecular fluxes in the Source of Negative Ions by Cesium Sputtering (SNICS) we found an odd-even effect in their intensity that we understand as the coupling between the fragment size distribution of a dynamic fragmentation of graphite by cesium impact and the electron affinity of the molecules with n-carbon atoms. The availability of these kind of high energy molecular beams opens the door for discovery both in the study of the physics of negative and positive molecular ions.

Degradable and Recyclable Polyesters from Multiple Chain Length Bio- and Waste-Sourceable Monomers.

Monomers sourced from waste or biomass are often mixtures of different chain lengths; e.g. catalytic oxidation of polyethylene waste yields mixtures of dicarboxylic acids (DCAs). Yet, polyesters synthesized from such monomer mixtures have rarely been studied. We report polyesters based on multiple linear aliphatic DCAs, present in chain length distributions that vary in their centers and ranges. We demonstrate that these materials can adopt high-density polyethylene-like solid state structures, and are ductile (e.g. Et 610 MPa), allowing for injection molding, or film and fiber extrusion. Melting and crystallization points of the polyesters show no odd-even effects as dipoles cannot favorably align in the crystal, similar to traditional odd carbon numbered, long-chain DCA polyesters. Biodegradation studies of 13C-labelled polyesters in soil reveal rapid mineralization, and depolymerization by methanolysis indicates suitability for closed-loop recycling.

Excited-State Odd-Even Effect in Through-Space Interactions.

The odd-even effect is a fantastic phenomenon in nature, which has been applied in diverse fields such as organic self-assembled monolayers and liquid crystals. Currently, the origin of each odd-even effect remains elusive, and all of the reported odd-even effects are related to the ground-state properties. Here, we discover an excited-state odd-even effect in the through-space interaction (TSI) of nonconjugated tetraphenylalkanes (TPAs). The TPAs with an even number of alkyl carbon atoms (C2-TPA, C4-TPA, and C6-TPA) show strong TSI, long-wavelength emission, and high QY. However, the odd ones (C1-TPA, C3-TPA, C5-TPA, and C7-TPA) are almost nonexistent with negligible QY. Systematically experimental and theoretical results reveal that the excited-state odd-even effect is synthetically determined by three factors: alkyl geometry, molecular movability, and intermolecular packing. Moreover, these flexible luminescent TPAs possess tremendous advantages in fluorescent information encryptions. This work extends the odd-even effect to photophysics, demonstrating its substantial importance and universality in nature.

The s-p Nonhybrid Nature Causes Adaptive Superatomic States of Bismuth Clusters.

We report a joint experimental and theoretical study on the stability and reactivity of Bin+ (n = 5-33) clusters. The alternating odd-even effect on the reaction rates of Bin+ clusters with NO is observed, and Bi7+ finds the most inertness. First-principles calculation results reveal that the lowest energy structures of Bi6-9+ exhibit quasi-spherical geometry pertaining to the jellium shell model; however, but the Bin+ (n ≥ 10) clusters adopt assembly structures. The prominent stability of Bi7+ is associated with its highly symmetric structure and superatomic states with a magic number of 34e closed shell. For the first time, we demonstrate that the unique s-p nonhybrid feature in bismuth rationalizes the stability of Bi6-9+ clusters within the jellium model, by filling the 6s electrons into the superatomic orbitals (forming "s-band"). Interestingly, the stability of 18e "s-band" coincides with the compact structure for Bin+ at n≤9 but assembly structures for n ≥10, showing an accommodation of the s electrons to the geometric structure. The atomic p-orbitals also allow to form superatomic orbitals at higher energy levels, contributing to the preferable structures of tridentate binding units. We illustrate the s-p nonhybrid nature accommodates the structure and superatomic states of bismuth clusters.

XFEL Microcrystallography of Self-Assembling Silver n-Alkanethiolates.

New synthetic hybrid materials and their increasing complexity have placed growing demands on crystal growth for single-crystal X-ray diffraction analysis. Unfortunately, not all chemical systems are conducive to the isolation of single crystals for traditional characterization. Here, small-molecule serial femtosecond crystallography (smSFX) at atomic resolution (0.833 Å) is employed to characterize microcrystalline silver n-alkanethiolates with various alkyl chain lengths at X-ray free electron laser facilities, resolving long-standing controversies regarding the atomic connectivity and odd-even effects of layer stacking. smSFX provides high-quality crystal structures directly from the powder of the true unknowns, a capability that is particularly useful for systems having notoriously small or defective crystals. We present crystal structures of silver n-butanethiolate (C4), silver n-hexanethiolate (C6), and silver n-nonanethiolate (C9). We show that an odd-even effect originates from the orientation of the terminal methyl group and its role in packing efficiency. We also propose a secondary odd-even effect involving multiple mosaic blocks in the crystals containing even-numbered chains, identified by selected-area electron diffraction measurements. We conclude with a discussion of the merits of the synthetic preparation for the preparation of microdiffraction specimens and compare the long-range order in these crystals to that of self-assembled monolayers.

Self-Consistent Calculation of Nuclear Charge Radii in K Isotopes

Fully self-consistent study of the charge radii in Ca region is exemplified by the calculation in the long chains of K isotopes. The neutron-deficient and neutron-rich nuclei with pairing in both neutron and proton sectors, as well as the (semi-) magic nuclei around the closed neutron shells at N = 20, 28, 32 are treated within the Energy Density Functional (EDF) approach with the Fayans functional DF3-a. The performance of the DF3-a is analysed in describing the odd-even staggering effects found both in previous and in more recent CERN-ISOLDE experiments for 36–52K isotopes.

A study on (n, α) reaction cross sections using a new empirical systematic

In this article, we report a new empirical formula for quick calculation of cross sections of (n, α) reactions with 14–15 MeV neutrons. Cross sections are analysed in terms of the compound nucleus model. A systematic trend for 14–15 MeV neutrons is found in the variation of (n, α) reaction cross sections with the parameters (N − Z + 1), (En+Q)0.5 and N/Z. The empirical relation between the cross sections and these parameters has been obtained, which give fairly good fits with the experimental data. We have also investigated the odd-even effects on (n, α) cross sections considering binding energy systematic of the shell model. The present formula is very useful in predicting of the (n, α) cross sections, where the measurements are not available as well as in testing new experimental data.

Lateral dipole moments induced by all-cis-pentafluorocyclohexyl groups cause unanticipated effects in self-assembled monolayers

All-cis-hexafluoro- and all-cis-pentafluoro-cyclohexane (PFCH) derivatives are new kinds of materials, the structures and properties of which are dominated by the highly dipolar Janus-face motif. Here, we report on the effects of integrating the PFCH groups into self-assembled monolayers (SAMs) of alkanethiolates on Au(111). Monolayers with an odd (eleven) and even (twelve) number of methylene groups were characterized in detail by several complementary experimental tools, supported by theoretical calculations. Surprisingly, all the data show a high similarity of both kinds of monolayers, nearly lacking the typically observed odd-even effects. These new monolayers have a packing density about 1/3 lower than that of non-substituted alkanethiolate monolayers, caused by the bulkiness of the PFCH moieties. The orientations of the PFCH groups and the alkyl chains could be determined independently, suggesting a conformation similar to the one found in the solid state structure of an analogous compound. Although in the SAMs the PFCH groups are slightly tilted away from the surface normal with the axial fluorine atoms pointing downwards, most of the dipole moments of the group remain oriented parallel to the surface, which is a unique feature for a SAM system. The consequences are much lower water contact angles compared to other partly fluorinated SAMs as well as rather moderate work function values. The interaction between the terminal PFCH moieties results in an enhanced stability of the PFCH-decorated SAMs toward exchange reaction with potential molecular substituents in spite of the lower packing density of these films.

Bottom-Up Synthesis of Crystalline Covalent Organic Framework Nanosheets, Nanotubes, and Kippah Vesicles: An Odd-Even Effect Induction.

Few-layer organic nanosheets are becoming increasingly attractive as two-dimensional (2D) materials due to their precise atomic connectivity and tailor-made pores. However, most strategies for synthesizing nanosheets rely on surface-assisted methods or top-down exfoliation of stacked materials. A bottom-up approach with well-designed building blocks would be the convenient pathway to achieve the bulk-scale synthesis of 2D nanosheets with uniform size and crystallinity. Herein, we have synthesized crystalline covalent organic framework nanosheets (CONs) by reacting tetratopic thianthrene tetraaldehyde (THT) and aliphatic diamines. The bent geometry of thianthrene in THT retards the out-of-plane stacking, while the flexible diamines introduce dynamic characteristics into the framework, facilitating nanosheet formation. Successful isoreticulation with five diamines with two to six carbon chain lengths generalizes the design strategy. Microscopic imaging reveals that the odd and even diamine-based CONs transmute to different nanostructures, such as nanotubes and hollow spheres. The single-crystal X-ray diffraction structure of repeating units indicates that the odd-even linker units of diamines introduce irregular-regular curvature in the backbone, aiding such dimensionality conversion. Theoretical calculations shed more light on nanosheet stacking and rolling behavior with respect to the odd-even effects.

13C Nuclear Magnetic Resonance Investigations of Molecular Mesogens with a Terminal Phenyl Ring Linked via a Spacer: Odd-Even Effect.

A set of mesogens considered as model molecules to the technologically important twist-bend (NTB) nematogens are investigated. They consist of a three-ring core connected to a phenyl ring via a flexible spacer and displayed enantiotropic nematic and smectic C mesophases. In such systems, odd or even number of atoms present in the spacer could influence the orientation of the terminal phenyl ring and thus have a bearing on designing the NTB phase, considered as intermediate between the nematic and the cholesteric phases. One-dimensional (1D) and two-dimensional (2D) 13C NMR spectra have been recorded in the liquid crystalline phases and the alignment-induced chemical shifts (AIS) and the 13C-1H dipolar couplings obtained. The order parameters of the phenyl rings reveal features relatable to the odd/even number of atoms of the flexible spacer and the type of linkage. The AIS plots of the phenyl rings of the even spacer-based mesogen showed the usual behavior for all of the phenyl rings with a decrease in AIS with increasing temperature. However, for the odd-spacer mesogens, unusual behaviors are noted for the terminal phenyl ring. Thus, two of the mesogens showed an increase of AIS in the smectic C phase that continued till the middle of the nematic phase temperature range, followed by a decrease. The other two odd-spacer mesogens also showed different behaviors. These observations indicate that the terminal phenyl ring is oriented at an angle with respect to the long molecular axis for the odd-spacer mesogens that changes as a function of temperature. The angles have been found to depend on the nature of the atom/group connecting the spacer to the terminal ring and the spacer length. Thus, the present study provides critical information on the design of the odd dimers that are recognized to generate fascinating NTB mesophases.

Designing Long and Highly Conducting Molecular Wires with Multiple Nontrivial Topological States.

Molecular one-dimensional topological insulators (1D TIs), described by the Su-Schrieffer-Heeger (SSH) model, are a new class of molecular electronic wires whose low-energy topological edge states endow them with high electrical conductivity. However, when these 1D TIs become long, the high conductance is not sustained because the coupling between the edge states decreases with increasing length. Here, we present a new design where we connect multiple short 1D SSH TI units linearly or in a cycle to create molecular wires with a continuous topological state density. Using a tight-binding method, we show that the linear system gives a length-independent conductance. The cyclic systems show an interesting odd-even effect, with unit transmission in the topological limit, but zero transmission in the trivial limit. Furthermore, based on our calculations, we predict that these systems can support resonant transmission with a quantum of conductance. We can further expand these results to phenylene-based linear and cyclic 1D TI systems and confirm the length-dependent conductance in such systems.

Effect of Metal Coordination on Two-dimensional Assemblies in Curcumin Derivatives

Two-dimensional (2D) structures of Cu(II)-coordinated curcumin derivatives were revealed by scanning tunneling microscopy at the solid/liquid interface. The Cu(II)-coordination resulted in the formation of dimerized structure, which was different from the pristine curcumin derivatives. The appearance and disappearance of 2D structure modulation due to odd-even effect were dependent on the number of alkyl chain substituents. In addition, the appearance of the odd-even was found to be maintained before and after the Cu(II) coordination. Scanning tunneling microscopy observations revealed the two-dimensional (2D) structures of Cu(II)-coordinated curcumin derivatives at the solid/liquid interface. The dimerized structure was formed due to Cu(II) coordination, and the 2D structure of metallated curcumin derivatives were different from the pristine ones. Appearance of odd-even effect was dependent on the alkyl chain substituents, and was maintained before and after the Cu(II) coordination.

Z_{2} Spin Liquids in the Higher Spin-S Kitaev Honeycomb Model: An Exact Deconfined Z_{2} Gauge Structure in a Nonintegrable Model.

The higher spin Kitaev model prominently features the extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although it is not exactly solvable. It remains an open question regarding the physical meaning of these conserved quantities in the higher spin model. In this Letter, by introducing a Majorana parton construction for a general spin-S we uncover that these conserved quantities are exactly the Z_{2} gauge fluxes in the general spin-S model, including the case of spin-1/2. Particularly, we find an even-odd effect that the Z_{2} gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z_{2} gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z_{2} gauge charges of the integer spin model, on the other hand, could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.

Examination of machine learning for assessing physical effects: Learning the relativistic continuum mass table with kernel ridge regression* *Supported by the National Natural Science Foundation of China (11875075, 11935003, 11975031, 12141501, 12070131001), the China Postdoctoral Science Foundation under (2021M700256), the State Key Laboratory of Nuclear Physics and Technology, Peking University (NPT2023ZX01, NPT2023KFY02), and the President's Undergraduate Research Fellowship (PURF) of

The kernel ridge regression (KRR) method and its extension with odd-even effects (KRRoe) are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory. With respect to the binding energies of 9035 nuclei, the KRR method achieves a root-mean-square deviation of 0.96 MeV, and the KRRoe method remarkably reduces the deviation to 0.17 MeV. By investigating the shell effects, one-nucleon and two-nucleon separation energies, odd-even mass differences, and empirical proton-neutron interactions extracted from the learned binding energies, the ability of the machine learning tool to grasp the known physics is discussed. It is found that the shell effects, evolutions of nucleon separation energies, and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods, although the odd-even mass differences can only be reproduced by the KRRoe method.

The α-particle clustering and half-lives of the newly discovered 207,208Th decay chains within relativistic-Hartree-Bogoliubov approach

The structural and decay properties of the ground state of recently discovered neutron-deficient 207Th and remeasured 208Th isotopes Yang et al. (2022) [26] is examined using the Relativistic-Hartree-Bogoliubov (RHB) formalism using the DD-ME2 parameter set within the preformed cluster-decay model (PCM). The relativistic medium-dependant R3Y so-called DD-R3Y NN potentials are for the first time used to obtain the nucleus-nucleus potential as input into the PCM. The penetration probability is calculated using the WKB approximation, and the preformation probability (Pα) is estimated using our newly derived formula, which is based on parameters well known to influence the α -particle radioactivity. A close correlation is observed between the α-preformation factor and the crucial role of the pairing correlation in the α-decay process. Furthermore, the Pα values for the even-even nuclei are generally found to be of higher magnitude than those for the odd-A nuclei. Our results further affirm that the odd-even staggering effect on the Qα values and its accompanying effects on other observables such as the charge radii and the decay half-lives, which can be largely attributed to the pairing correlation and Pauli blocking of the unpaired valence nucleons.

Synthesis, Solution, and Solid State Properties of Homological Dialkylated Naphthalene Diimides-A Systematic Review of Molecules for Next-Generation Organic Electronics.

This systematic study aimed at finding a correlation between molecular structure, solubility, self-assembly, and electronic properties of a homological series of N-alkylated naphthalene diimides (NDIs). NDIs are known for their n-type carrier mobility and, therefore, have potential in the field of organic electronics, photovoltaics, and sensors. For the purpose of this study, nine symmetrical N,N'-dialkylated naphthalene diimides (NDIC3-NDIC11) were synthesized in the reaction of 1,4,5,8-naphthalenetetracarboxylic dianhydride with alkylamines ranging from propyl- to undecyl-. The NDIs were characterized by spectroscopic (NMR, UV-Vis, FTIR), microscopic, and thermal methods (TGA and DSC), and X-ray diffraction (XRD). Our experimental study, extensively referring to findings reported in the literature, indicated that the NDIs revealed specific trends in spectroscopic and thermal properties as well as solubility and crystal morphology. The solubility in good solvents (chloroform, toluene, dichlorobenzene) was found to be the highest for the NDIs substituted with the medium-length alkyl chains (NDIC5-NDIC8). Systematic FTIR and XRD studies unraveled a distinct parity effect related to the packing of NDI molecules with odd or even numbers of methylene groups in the alkyl substituents. The NDIs with an even number of methylene groups in the alkyl substituents revealed low-symmetry (P1-) triclinic packing, whereas those with an odd number of carbon atoms were generally monoclinic with P21/c symmetry. The odd-even parity effect also manifested itself in the overlapping of the NDIs' aromatic cores and, hence, the π-π stacking distance (dπ-π). The odd-numbered NDIs generally revealed slightly smaller dπ-π values then the even-numbered ones. Testing the NDIs using standardized field-effect transistors and unified procedures revealed that the n-type mobility in NDIC6, NDIC7, and NDIC8 was 10- to 30-fold higher than for the NDIs with shorter or longer alkyl substituents. Our experimental results indicate that N,N'-alkylated NDIs reveal an optimum range of alkyl chain length in terms of solution processability and charge transport properties.

The effect of position of (-)-menthyl on the mesomorphic and photoisomerization behavior in azobenzene chiral liquid crystals

As the mesomorphic type of liquid crystals could be largely altered by the molecular chirality, we herein explored the effect of position of chiral (-)-menthyl on the mesomorphic and photoisomerization behavior in azobenzene liquid crystals. By modifying the position of chiral (-)-menthyl in the menthol based liquid crystal compounds through gradually increasing the alkyl chain length of the dicarboxylic spacer, seven new chiral liquid crystal compounds 4-(4-menthyloxy-n-oxoalkanoyloxy)-4′-(4-ethoxybenzoyloxy) azobenzene MnAZO2B (n = 2–8) were prepared. A combination of analysis methods was conducted to systematically investigate their structures, mesophase behaviors and optical properties. The length and parity of the flexible spacers has a dramatic influence on the mesomorphic behaviors, and an odd-even effect is observed for these chiral liquid crystal compounds.

Chain-Length Induced Structural Polymorphism for two-dimension self-assembly

Structural polymorphism obtained through the 2D self-assembly which was made use of the chain-ength induced, has has aroused wide concern. On the one hand, owing to its significance meaning in crystal engineering, on the other hand, it has a broad application prospect in nano science and technolog.The assembly of symmetric 2, 7-bis (n-alkoxy) -9-fluorenone(F-OCn) with varying lengths of peripheral alkyl chains dissolved in homologous acids was investigated. The size and shape of molecules and the structure and position of substituents were critical factors that regulate the equilibrium of the interaction and formation of self-assembled patterns. Useing altered the symmetry and chain-length of the molecular structure, the self-assembly morphology and cellular properties can be predicted. The self-assembled strcture displayed the assembly of F-OCn (11-14). “S” shaped and alternating phases are the thermodynamic stable states. The competition between van der Waals forces from the interdigital alkyl chains and van der Waals forces between molecule-substrate takes effect. The vdW forces between the molecule-substrate was predominant when n varies from 15 to 18. The observation of the chain-length effects and odd-even effects showed that: F-OCeven developed from a loose-and close-packed patterns to a dislocated zigzag patterns.Self-assembled morphology of F-OCodd evolved from a well-distributed trimer monolayer to the dislocated zigzag pattern.These researches offers insight into the structural diversity by regulating the alkyl side chain-length and odd-even effects on two-dimension self-assembly and the construct a new molecular materials.