Intermolecular Collisions Research Articles

A multiscale stochastic particle method based on the Fokker-Planck model for nonequilibrium gas flows

The Fokker-Planck (FP) model characterizes the intermolecular collisions as continuous stochastic processes in velocity space. Compared to the Direct Simulation Monte Carlo (DSMC) method, which is grounded in the Boltzmann equation, the stochastic particle method based on the FP model, referred to as the SP-FP method, demonstrates a relative improvement in computational efficiency. However, the traditional SP-FP method, utilizing operator splitting scheme, encounters analogous limitations to DSMC, thereby limiting the application of large temporal-spatial discretization for simulating near-continuum and continuum flows. In this study, two critical advancements are introduced to improve the traditional SP-FP method. First, the exact integration scheme of the ellipsoidal-statistical FP (ESFP) model is derived, enabling the replication of the theoretical solutions for homogeneous relaxation with any time step. Furthermore, leveraging the integration scheme of the ESFP model, we propose a Multiscale Stochastic Particle (MSP) method. The MSP method quantifies the numerical errors stemming from the operator splitting scheme and corrects them in the relaxation step. This capability allows the MSP method to be employed with larger temporal-spatial discretization for inhomogeneous problems, achieving second-order accuracy while retaining implementation simplicity. Application of the MSP method to various benchmark problems, including Couette flow, Fourier flow, Poiseuille flow, Sod tube flow, Lid-driven cavity flow, and flow through a slit, demonstrates its promise for simulating multiscale nonequilibrium gas flows with high computational efficiency and accuracy.

Effect of sugar or sugar alcohol with different spatial structures on the stability of paclitaxel/HS15/Tween80 micelles: Based on micellization thermodynamics

Paclitaxel (PTX) is clinically recommended for the treatment of breast, ovarian and non-small cell lung cancer. This study delves into the impact of sugars (mannose or glucose) and sugar alcohols (mannitol or sorbitol) with varying spatial structures on the interfacial and thermodynamic behavior of the PTX/HS15/Tween80 micellar system. The research reveals that the presence of OH groups in sugars and sugar alcohols enhances hydrogen bonding force between surfactant and water, altering the critical micelle concentration (CMC) in solution and the surfactant’s arrangement at the interface, thus facilitating micelle formation and enhancing system stability. Dynamic light scattering (DLS) results show that the particle size of the PTX/HS15/Tween80 system is 11.69 nm, with micellar size showing a positive correlation with additive concentration. Sugar alcohols exhibit a more pronounced effect on increasing micelle size compared to sugars. Molecules featuring outward-facing OH groups demonstrating a greater ability to facilitate the formation of smaller micelle than those with inward-facing groups, emphasizing the influence of spatial structural differences. Stability experiments demonstrate that light transmission remains above 97 % in the system for 8 h after the addition of sugar, and the relative absorbance of PTX is maintained above 97 % within 6 h. Results from FD-B21 fluorescence probe release further confirm the positive impact of sugars and sugar alcohols on the stability of PTX/HS15/Tween80 micelles, highlighting stability differences based on molecules with distinct spatial structures. When OH groups on sugar or sugar alcohol molecules are more oriented in the same direction, intramolecular hydrogen bonds are formed, reducing spatial resistance and promoting the formation of micellar with smaller particle sizes. This process enhances physical stability by reducing inter-molecular collisions. In summary, the presence of sugars and sugar alcohols promotes micelle formation and boosts system stability, offering valuable insights for enhancing the stability of drug-loaded micelles.

Heterogeneous CuS QDs/BiVO4@Y2O2S Nanoreactor for Monitorable Photocatalysis.

Exploration of multifunctional integrated catalysts is of great significance for photocatalysis toward practical application. Herein, a 1D confined nanoreactor with a heterogeneous core-shell structure is designed for synergies of efficient catalysis and temperature monitoring by custom encapsulation of Z-scheme heterojunction CuS quantum dots/BiVO4 (CuS QDs/BiVO4) and Y2O2S-Er, Yb. The dispersed active sites created by the QDs with high surface energy improve the mass transfer efficiency, and the efficient electron transport channels at the heterogeneous interface extend the carrier lifetime, which endows the nanoreactor with excellent catalytic performance. Meanwhile, real-time temperature monitoring is realized based on the thermally coupled levels 2H11/2/4S3/2→4I15/2 of Er3+ using fluorescence intensity ratio, which enables the monitorable photocatalysis. Furthermore, the nanoreactor with a multidimensional structure increases effective intermolecular collisions to facilitate the catalytic process by restricting the reaction within distinct enclosed spaces and circumvents potential unknown interaction effects. The design of multi-space nanoconfined reactors opens up a new avenue to modulate catalyst function, providing a unique perspective for photocatalytic applications in the mineralization of organic pollutants, hydrogen production, and nitrogen fixation.

Aerodynamic Analysis of Deorbit Drag Sail for CubeSat Using DSMC Method

Reducing space debris is a critical challenge in current space exploration. This study focuses on designing a drag sail for CubeSat models and examining their aerodynamic properties using the direct simulation Monte Carlo (DSMC) method. The analysis encompasses the aerodynamic performance of intricate three-dimensional shapes with varying sail dimensions at orbital altitudes of 125 km, 185 km, 300 km, and 450 km. Additionally, free molecular flow (FMF) theory is applied and compared with the DSMC findings for both a flat-plate model and the CubeSat. The results reveal that FMF accurately predicts the drag coefficient at altitudes of 185 km and above, while significant discrepancies occur at lower altitudes due to increased inter-molecular collisions. This study also suggests that the drag sail substantially enhances the CubeSat’s drag force, which effectively reduces its deorbiting time.

In-depth understanding of the effects of different molecular weight pullulan interacting with protein and starch on dough structure and application properties

This work clarified the positive effects of pullulan on dough structure and application properties varied with its molecular weight. Pullulan with different molecular weights were introduced into dough system to explore their intervention effects on structural and technological properties of dough as well as physical and digestion properties of biscuits. Results showed that HPL (pullulan with molecule weight of 100– 300 kDa) could increase the intermolecular collisions, prompt the protein aggregation and limit the water migration in dough system, resulting in an integrate, continuous and dense network structure of the gel with strengthened elasticity and weakened extensibility, which caused an increase in biscuit thickness, hardness and crispness. On the contrary, LPL (pullulan with molecule weight of 3– 100 kDa) could go against the formation of stable and elastic dough through breaking down cross-linkage between protein and starch so as to provide biscuits with decreased hardness and crispness during baking. Both HPL and LPL delayed starch pasting and retrogradation process while HPL had the stronger retarding effect on starch digestibility of biscuits than LPL. These findings dedicated to a better understanding of pullulan function in dough system and provide suggestions for fractionation applications of pullulan in food field.

Nonequilibrium statistical mechanics of money/energy exchange models

Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in econophysics and in chemistry classrooms: the money game, in which players exchange money randomly in a process that resembles elastic intermolecular collisions in a gas, giving rise to the Boltzmann distribution of money owned by each player. Although this model offers a pedagogical example that demonstrates the origins of Boltzmann statistics, such demonstrations usually rely on computer simulations. In fact, a proof of the exponential steady-state distribution in this model has only become available in recent years. Here, we study this random money/energy exchange model and its extensions using a simple mean-field-type approach that examines the properties of the one-dimensional random walk performed by one of its participants. We give a simple derivation of the Boltzmann steady-state distribution in this model. Breaking the time-reversal symmetry of the game by modifying its rules results in non-Boltzmann steady-state statistics. In particular, introducing ‘unfair’ exchange rules in which a poorer player is more likely to give money to a richer player than to receive money from that richer player, results in an analytically provable Pareto-type power-law distribution of the money in the limit where the number of players is infinite, with a finite fraction of players in the ‘ground state’ (i.e. with zero money). For a finite number of players, however, the game may give rise to a bimodal distribution of money and to bistable dynamics, in which a participant’s wealth jumps between poor and rich states. The latter corresponds to a scenario where the player accumulates nearly all the available money in the game. The time evolution of a player’s wealth in this case can be thought of as a ‘chemical reaction’, where a transition between ‘reactants’ (rich state) and ‘products’ (poor state) involves crossing a large free energy barrier. We thus analyze the trajectories generated from the game using ideas from the theory of transition paths and highlight non-Markovian effects in the barrier crossing dynamics.

Collision-broadening of vibration-inversion-rotation ammonia spectral lines in Q(J)-branch at 6.2 µm by cavity ring-down spectroscopy

In this experimental investigation, collision broadening effects on the Q(J)-branch vibration-inversion-rotation spectral lines of ammonia (NH3) within the fundamental ν4 asymmetric bending vibrational band in the 6.2 µm mid-IR region are reported. A continuous-wave external-cavity quantum cascade laser coupled with a high-sensitive cavity ring-down spectrometer was employed to selectively probe 10 transitions in high-resolution, including few inversion doublets of gaseous NH3. Pressure-broadening coefficients, γNH3-Xi (Xi = He, Ar, N2, O2, zero-air) in cm−1 atm−1, characterizing the collision interaction between NH3 and various external perturbing gases, including helium, argon, nitrogen, oxygen, and zero-air, were determined at room temperature (296 K). Mean collision times and optical collision diameters of each collision partner were explored to gain deeper insight into the perturber-induced collision dynamics. This investigation elucidates the intricate intermolecular interactions and collision phenomena induced by various foreign perturbers with NH3, with potential implications for future spectroscopic and atmospheric research of this polyatomic molecule.

On an Efficient Solution of the Boltzmann Equation Using the Modified Time Relaxed Monte Carlo (MTRMC) Scheme

The study proposes a new method called MTRMC to simulate flow in rarefied regimes, which are important in various industrial and engineering applications. This new method utilizes a modified collision function with smaller number of inter-molecular collisions, making it more computationally efficient than the widely used direct simulation Monte Carlo (DSMC) method. The MTRMC method is used to analyze the flow over a flat nano-plate at various free stream velocities, ranging from low to supersonic speeds. The results are compared with those from DSMC and time relaxed Monte Carlo (TRMC) schemes, and the findings show that the MTRMC method is in good agreement with the standard schemes, with a significant reduction in computational expense, up to 51% in some cases.

Transmission probability of gas molecules through porous layers at Knudsen diffusion

Gas flow through layers of porous materials plays a crucial role in technical applications, geology, petrochemistry, and space sciences (e.g., fuel cells, catalysis, shale gas production, and outgassing of volatiles from comets). In many applications the Knudsen regime is predominant, where the pore size is small compared to the mean free path between intermolecular collisions. In this context common parameters to describe the gas percolation through layers of porous media are the probability of gas molecule transmission and the Knudsen diffusion coefficient of the medium. We show how probabilistic considerations on layer partitions lead to the analytical description of the permeability of a porous medium to gas flow as a function of layer thickness. The derivations are made on the preconditions that the molecule reflection at pore surfaces is diffuse and that the pore structure is homogenous on a scale much larger than the pore size. By applying a bi-hemispherical Maxwell distribution, relations between the layer transmission probability, the half-transmission thickness, and the Knudsen diffusion coefficient are obtained. For packings of spheres, expressions of these parameters in terms of porosity and grain size are derived and compared with former standard models. A verification of the derived equations is given by means of numerical simulations, also providing evidence that our analytical model for sphere packing is more accurate than the former classical models.

Effect of demineralization on waste tire pyrolysis char physical, chemical characteristics and combustion characteristics

Waste tire carbon black particles (CBp) are the main pyrolysis products of waste tires (WT), and CBp is difficult to use directly. This work mainly focuses on the physicochemical and combustion characteristics of demineralized CBp (DCBp) to explore the resourceful utilization of CBp resources in large quantities. This work also provides a comprehensive comparison with CBp and other carbon-based solid fuels. The results show that most of the minerals in CBp can be removed by chemical demineralization treatment (Ash content of DCBp <0.11 %). DCBp has a more developed pore structure than CBp. The deashing process affects the degree of loosening and stacking of the graphitic carbon microcrystalline structure, and the relative content of oxygen-containing functional groups in CBp to a minor extent. The deashing process leads to a decrease in the relative strength of the cross-linked stable structure and an increase in the disordered structure of carbon in CBp. The volatile fraction to fixed carbon ratio of DCBp is only 0.0467, and a large number of catalytic alkali metal elements and alkaline earth metal elements are removed in the demineralization process, which makes the early combustion of DCBp more difficult. As the combustion reaction proceeds, the internal pores of the particles are opened, and the micropores and mesopores in DCBp provide a larger surface area for the reaction. In addition, the decrease in the relative strength of the cross-linked stable structure and increases in the disordered structure of carbon can increase the intermolecular collision frequency during the combustion process, thus improving the burnout characteristics of DCBp. The above results indicate that DCBp has the potential to be used as fuel for large-scale resource utilization.

Hölder regularity of the Boltzmann equation past an obstacle

AbstractRegularity and singularity of the solutions according to the shape of domains is a challenging research theme in the Boltzmann theory. In this paper, we prove an Hölder regularity in for the Boltzmann equation of the hard‐sphere molecule, which undergoes the elastic reflection in the intermolecular collision and the contact with the boundary of a convex obstacle. In particular, this Hölder regularity result is a stark contrast to the case of other physical boundary conditions (such as the diffuse reflection boundary condition and in‐flow boundary condition), for which the solutions of the Boltzmann equation develop discontinuity in a codimension 1 subset (Kim [Comm. Math. Phys. 308 (2011)]), and therefore the best possible regularity is BV, which has been proved by Guo et al. [Arch. Rational Mech. Anal. 220 (2016)].

The Amorphous Carbon Thin Films Synthesized by Gas Injection Magnetron Sputtering Technique in Various Gas Atmospheres

This work presents the potential for using pulsed gas injection to produce amorphous carbon films. In this experiment, the frequency of injecting small amounts of gas was used to control the pressure amplitudes, thus achieving the conditions of plasma generation from stationary, through quasi-stationary, to pulsed oscillations of pressure. In addition, we used various gases and their mixtures, an alternative to argon. In the experiment, we studied the energy state of the plasma. The films were examined for phase and chemical composition, surface morphology, and optical and mechanical properties. We determined low-frequency pulsed gas injections to be conditions favorable for C(sp3)−C(sp3) bond formation. The plasma generated by gas injections is better ionized than that generated by static pressure. Pulsed conditions favor the plasma species to retain their kinetic energy, limiting the probability of intermolecular collision events. Since helium has a relatively high ionization energy, it is a practical addition to sputtering gas because of the increasing sp3 content in the films. The electrons created by helium ionization improve the plasma’s ionization degree.

Geometrical and temperature impact on elucidation of intermolecular interactions for the binary mixtures of morpholine with aliphatic esters by thermodynamic, FTIR and DFT study

Abstract In this investigation, the binary solutions of morpholine (MP) with tert-butyl acetate (TBA), iso-butyl acetate (IBA), butyl acetate (BA) and butyl acrylate (BAC) were prepared for the densities (ρ) and speeds of sound (u) measurements at T = (303.15, 308.15, 313.15 and 318.15) K over the entire composition range and at atmospheric pressure (P = 0.1 MPa). From these data, excess thermodynamic properties such as excess molar volume ( V m E ${V}_{m}^{E}$ ), excess isentropic compressibility ( κ S E ${\kappa }_{S}^{E}$ ) and excess speeds of sound ( u E ${u}^{E}$ ) were calculated to elucidate the strength and types of intermolecular interactions between the component molecules. Redlich-Kister (RK) equation and Prigogine–Flory–Patterson (PFP) theory was applied to correlate the excess parameters and excess volumes, respectively. Further, intermolecular free length theory and collision frequency theory were used to correlate the speed of sound data. Shifting of bands (δν), bond length and hydrogen bond strength between the atoms were calculated from the experimental FTIR and DFT theoretical studies. The systematic increasing order of the intermolecular hydrogen bond strength between the two atoms in the studied binary systems as follows: TBA &gt; IBA &gt; BA &gt; BAC.

Performance characterization and kinetic analysis of atmosphere-breathing electric propulsion intake device

An atmosphere-breathing electric propulsion (ABEP) system is designed to capture and compress the rarefied atmosphere through an intake device in very-low-Earth-orbit (VLEO). This study numerically characterizes the intake performance according to the design parameters, including the geometry of the tapered chamber, gas-surface interaction (GSI) models, surface temperature, aspect ratio, and sizing. The design of grid ducts is examined for different gaps, lengths, and yaw angles. The influence of intermolecular collisions is also investigated. The diffuse GSI model is chosen as a realistic model at VLEO due to the adsorption of atomic oxygen. The direct simulation Monte Carlo method is employed to calculate the capture efficiency, compression ratio, particle flow rate, and number density as the four indicators of intake performance. The flow conditions are obtained using the NRLMSISE-00 model, with a target altitude range of 180–220 km. In addition, a comprehensive design is proposed and the related propellant characteristics are investigated using kinetic analysis. Multi-modality is found in the particle velocity distribution, which implies non-equilibrium of the ABEP propellant.

Non-Markovian collisional dynamics probed with laser-aligned molecules

The Markov, as well as the secular, approximations are key assumptions that have been widely used to model decoherence in a large variety of open quantum systems, but, as far as intermolecular collisions are considered, very little has been done in the time domain. In order to probe the limits of both approximations, we here study the influence of pressure on the alignment revivals (echoes) created in properly chosen gas mixtures (HCl and ${\mathrm{CO}}_{2}$, pure and diluted in He) by one (two) intense and short laser pulse(s). Experiments and direct predictions using molecular-dynamics simulations consistently demonstrate, through analyses at very short times $(&lt;15 \mathrm{ps})$ after the laser kick(s), the breakdown of these approximations in some of the selected systems. We show that the nonadiabatic laser-induced molecular alignment technique and model used in this paper directly provide detailed information on the physical mechanisms involved in the collisional dissipation. Besides this ``fundamental'' interest, our findings also have potential practical applications for radiative heat transfer in planetary atmospheres and climate studies. Indeed, short time delays in the dipole autocorrelation function monitoring the light absorption spectrum correspond to large detunings from the optical resonances in the frequency domain, thus influencing the atmospheric transparency windows. Furthermore, the fact that the approach tested here for linear rotors can potentially be applied to almost any gas mixture (including, for instance, nonlinear and/or reacting molecules) further strengthens and broadens the perspectives that it opens.

Understanding the Reaction Kinetics and Microdynamics between Methylimidazole and Alkyl Thiocyanate for Ionic Liquid Synthesis through Experiments and Theoretical Calculation

Ionic liquids (ILs) are usually prepared via the Menshutkin SN2 reaction. Herein, the effects of the alkyl chain length of the substrate on the reaction kinetics and microdynamics between 1-methylimidazole (MIm) and alkyl thiocyanate (RSCN, R = methyl, ethyl, and butyl groups) for the preparation of thiocyanate-based ILs were analyzed by time-dependent Fourier transform infrared (FTIR) spectroscopy, classical molecular dynamics (MD) simulation, and ab initio molecular dynamics (AIMD) simulation. Experimental results show that the longer chain length of thiocyanate leads to a significantly slower rate constant and much higher activation energy. The rate constant of the MIm/BuSCN system is reduced by a factor of 21 fold compared to that of the MIm/MeSCN system at 330 K. The activation energy of the MIm/BuSCN system is increased by 27.5 kJ/mol in the MIm/MeSCN system. Metadynamics calculations in the explicit solvent offer a consistent trend for transition state energy barrier with experiments. MD simulations indicate that the long alkyl chain of thiocyanate results in a weaker spatial distribution of reaction sites as well as slower diffusion and reorientation, which can reduce the intermolecular collision probability. Hopefully, the insights from this work would guide the industrial synthesis of ILs.

Atomistic insight into the effects of electrostatic fields on hydrocarbon reaction kinetics.

Reactive Molecular Dynamics (MD) and Density Functional Theory (DFT) computations are performed to provide insight into the effects of external electrostatic fields on hydrocarbon reaction kinetics. By comparing the results from MD and DFT, the suitability of the MD method in modeling electrodynamics is first assessed. Results show that the electric field-induced polarization predicted by the MD charge equilibration method is in good agreement with various DFT charge partitioning schemes. Then, the effects of oriented external electric fields on the transition pathways of non-redox reactions are investigated. Results on the minimum energy path suggest that electric fields can cause catalysis or inhibition of oxidation reactions, whereas pyrolysis reactions are not affected due to the weaker electronegativity of the hydrogen and carbon atoms. MD simulations of isolated reactions show that the reaction kinetics is also affected by applied external Lorentz forces and interatomic Coulomb forces since they can increase or decrease the energy of collision depending on the molecular conformation. In addition, electric fields can affect the kinetics of polar species and force them to align in the direction of field lines. These effects are attributed to energy transfer via intermolecular collisions and stabilization under the external Lorentz force. The kinetics of apolar species is not significantly affected mainly due to the weak induced dipole moment even under strong electric fields. The dynamics and reaction rates of species are studied by means of large-scale combustion simulations of n-dodecane and oxygen mixtures. Results show that under strong electric fields, the fuel, oxidizer, and most product molecules experience translational and rotational acceleration mainly due to close charge transfer along with a reduction in their vibrational energy due to stabilization. This study will serve as a basis to improve the current methods used in MD and to develop novel methodologies for the modeling of macroscale reacting flows under external electrostatic fields.

Collision-induced Hopf-type bifurcation reversible transitions in a dual-wavelength femtosecond fiber laser.

Collisions refer to a striking nonlinear interaction process in dissipative systems, revealing the particle-like properties of solitons. In dual-wavelength mode-locked fiber lasers, collisions are inherent and periodic. However, how collisions influence the dynamical transitions in the dual-wavelength mode-locked state has not yet been explored. In our work, dispersion management triggers the complex interactions between solitons in the cavity. We reveal the smooth or Hopf-type bifurcation reversible transitions of dual-color soliton molecules (SMs) during the collision by the real-time spectral measurement technique of time-stretch Fourier transform. The reversible transitions between stationary SMs and vibrating SMs, reveal that the cavity parameters pass through a bifurcation point in the collision process without active external intervention. The numerical results confirm the universality of collision-induced bifurcation behavior. These findings provide new insights into collision dynamics in dual-wavelength ultrafast fiber lasers. Furthermore, the study of inter-molecular collisions is of great significance for other branches of nonlinear science.

Insight into synergistic enhancement of photothermal catalytic hydrogen production by plasmonic Au-NP/TiO2 in the presence of glycerol

Using glycerol that is by-product in biodiesel production for hydrogen production represents a promising way to utilize solar energy to recycle energy contained in waste resources. In this work, Au nanoparticles are synthesized on TiO2 nanoparticles (Au-NP/TiO2) for photothermal catalytic hydrogen production in the presence of glycerol. Particular attention is paid to the enhancement mechanism of the loaded plasmonic Au nanoparticles and their synergistic effect on hydrogen evolution. It is demonstrated that the local electromagnetic field at the contact interface between Au and TiO2 in relation to radiative relaxation of local surface plasmon resonance (LSPR) is greatly enhanced for efficient separation of electrons and holes. The thermal effect caused by non-radiative relaxation of LSPR not only enhances intermolecular collisions between reactant molecules through thermolization, but also increases the carrier concentration to generate more free radicals. The apparent activation energy also dramatically decreases. Because of these synergistic effects, the photothermal catalytic hydrogen production rate is greatly improved. This work not only deepens the understanding of the LSPR contribution to photothermal catalytic hydrogen production, but also demonstrates the promising potential in recycling the by-product from biodiesel industries to produce hydrogen.

Fully quantum calculations of the line shape parameters for 1-0 P(22) and P(31) lines of CO perturbed by He or Ar.

This work reports the full quantum calculations of the spectral line shape parameters for the P(22) line of 13CO and the P(31) line of 12CO in the fundamental band perturbed by He or Ar from 20 to 1000K for the first time. The generalized spectroscopic cross sections of CO-He/Ar indicate that the Dicke narrowing effect competes with the pressure broadening effect. The pressure broadening can be explained by the dynamic behaviors of intermolecular collisions. The intermolecular inelastic collisions contribute more than 95% to the pressure broadening in both CO-He and CO-Ar systems at high temperatures. Regarding the state-to-state inelastic contributions to pressure broadening, the maximum contribution out of the final state of a given line is close to that out of the initial state. The Dicke narrowing effect influences the line shape profile significantly at high temperatures, which suggests that it is indispensable for reproducing the spectral line profile. With the Dicke narrowing effect, the calculated pressure-broadening coefficients and spectral intensity distribution are in good agreement with the available experimental observations.