Nucleation Rate Research Articles

Anthropogenic Extremely Low Volatility Organics (ELVOCs) Govern the Growth of Molecular Clusters Over the Southern Great Plains During the Springtime

AbstractNew particle formation (NPF) often drives cloud condensation nuclei concentrations and the processes governing nucleation of molecular clusters vary substantially in different regions. The growth of these clusters from ∼2 to >10 nm diameters is often driven by the availability of extremely low volatility organic vapors (ELVOCs). Although the pathways to ELVOC formation from the oxidation of biogenic terpenes are better understood, the mechanistic pathways for ELVOC formation from oxidation of anthropogenic organics are less well understood. We integrate measurements and detailed regional model simulations to understand the processes governing NPF and secondary organic aerosol formation at the Southern Great Plain (SGP) observatory in Oklahoma and compare these with a site within the Bankhead National Forest (BNF) in Alabama, southeast USA. During our two simulated NPF event days, nucleation rates are predicted to be at least an order of magnitude higher at SGP compared to BNF largely due to lower sulfuric acid (H2SO4) concentrations at BNF. Among the different nucleation mechanisms in WRF‐Chem, we find that the dimethylamine (DMA) + H2SO4 nucleation mechanism dominates at SGP. We find that anthropogenic ELVOCs are critical for explaining the growth of particles observed at SGP. Treating organic particles as semisolid, with strong diffusion limitations for organic vapor uptake in the particle phase, brings model predictions into closer agreement with observations. We also simulate two non‐NPF event days observed at the SGP site and show that low‐level clouds reduce photochemical activity with corresponding reductions in H2SO4 and anthropogenic ELVOC concentrations, thereby explaining the lack of NPF.

Seed-Assisted Hydrothermal Synthesis of Monodispersed Au@C Core–Shell Nanostructures for Enhancing Thermal Diffusivity of Water-Based Nanofluids

Au@C core–shell nanostructures (Au@C-NS) were synthesized through a low-temperature seed-assisted hydrothermal approach using glucose as carbon source. The material characterization and chemical analysis confirm that the synthesis method allows to obtain uniform core–shell nanostructures constituted by a crystalline metal core and an amorphous carbon shell. Depending on the synthesis conditions, their average size ranges from 146 nm to 342 nm with relative standard deviation as low as 7 %. It is proposed that the characteristic monodispersity results due to a high nucleation rate of the carbon phase at the liquid–solid interface. The obtained monodisperse Au@C-NS were used to prepare water-based nanofluids with superior heat transport properties. The thermal lens analysis shows that the thermal diffusivity of Au@C nanofluids is 9.5 % and 31.3 % higher than their Au nanofluids counterparts and pure water, respectively, at particle concentration of 285 × 1011 ml−1. Phonon-related interactions at the metal cores and carbon shells interfaces are proposed as the heat transport mechanism behind the thermal diffusivity enhancement of the Au@C water-based nanofluids.

Flow-based nonperturbative simulation of first-order phase transitions

We present a flow-based method for simulating and calculating nucleation rates of first-order phase transitions in scalar field theory on a lattice. Motivated by recent advancements in machine learning tools, particularly normalizing flows for lattice field theory, we propose the “partitioning flow-based Markov chain Monte Carlo (PFMCMC) sampling” method to address two challenges encountered in normalizing flow applications for lattice field theory: the “mode-collapse” and “rare-event sampling” problems. Using a (2+1)-dimensional real scalar model as an example, we demonstrate the effectiveness of our PFMCMC method in modeling highly hierarchical order parameter probability distributions and simulating critical bubble configurations. These simulations are then used to facilitate the calculation of nucleation rates. We anticipate the application of this method to (3+1)-dimensional theories for studying realistic cosmological phase transitions.

Nucleation and phase transition of decagonal quasicrystals.

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely, the nullspace-preserving saddle search method. In particular, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and multi-step modes of symmetry breaking or recovery in the phase transition from DQC, where the multi-step modes are more probable.

An analysis of the synthesis, crystal structure, optical, spectroscopic, mechanical, self-focusing, and third-order nonlinear optical properties of Kojic acid single crystals

A single, excellent crystal of Kojic acid (KA) was developed utilising the traditional approach of gradual evaporation in a solution-growing procedure. A variety of characterisation techniques were utilised to evaluate the characteristics of the crystals generated. Single crystal x-ray diffraction (SXRD) was utilised to identify the crystal structure. The crystalline arrangement of the KA crystal was confirmed using a powder x-ray diffraction (PXRD) analysis. Experiments with UV–vis spectrometers revealed that the KA crystal has a lower wavelength at which it blocks UV light but has outstanding light transmission throughout the visible spectrum. The KA single crystal has an energy band gap (Eg) of 2.5 eV. The Z-scan method was used to examine the third order susceptibility, nonlinear refraction, and nonlinear absorption coefficient of the synthesised KA crystal. The dielectric characteristics and AC conductivity were examined, with a particular emphasis on their connection to resistance at room temperature. The presence of appreciable levels of kojic acid was confirmed by energy-dispersive spectrometry. The crystal’s thermal behaviour was investigated using differential thermal analysis (DTA) and thermogravimetric (TG) methods. The nucleation parameters and controlled nucleation rate were calculated using normal theoretical research methods.

Global modeling of aerosol nucleation with a semi-explicit chemical mechanism for highly oxygenated organic molecules (HOMs)

Abstract. New particle formation (NPF) involving organic compounds has been identified as an important process affecting aerosol particle number concentrations in the global atmosphere. Laboratory studies have shown that highly oxygenated organic molecules (HOMs) can make a substantial contribution to NPF, but there is a lack of global model studies of NPF with detailed HOM chemistry. Here, we incorporate a state-of-the-art biogenic HOM chemistry scheme with 96 chemical reactions to a global chemistry–climate model and quantify the contribution to global aerosols through HOM-driven NPF. The updated model captures the frequency of NPF events observed at continental surface sites (normalized mean bias changes from −96 % to −15 %) and shows reasonable agreement with measured rates of NPF and sub-20 nm particle growth. Sensitivity simulations show that compared to turning off the organic nucleation rate, turning off organic initial growth results in a more substantial decrease in aerosol number concentrations. Globally, organics contribute around 45 % of the annual mean vertically integrated nucleation rate (at 1.7 nm) and 25 % of the vertically averaged growth rate. The inclusion of HOM-related processes leads to a 39 % increase in the global annual mean aerosol number burden and a 33 % increase in cloud condensation nuclei (CCN) burden at 0.5 % supersaturation compared to a simulation with only inorganic nucleation. Our work predicts a greater contribution of organic nucleation to NPF than previous studies due to the semi-explicit HOM mechanism and an updated inorganic NPF scheme. The large contribution of biogenic HOMs to NPF on a global scale could make aerosol sensitive to changes in biogenic emissions.

Nucleation of multi-species crystals: methane cleatrate hydrates, a playground for classical force models

Nucleation and growth of methane clathrate hydrates is an exceptional playground to study crystallisation of multi-component, host-guest crystallites when one of the species forming the crystal, the guest, has a higher concentration in the solid than in the liquid phase. This adds problems related to the transport of the low concentration species, here methane. A key aspect in the modelling of clathrates is the water model employed in the simulation. In previous articles, we compared an all-atom force model, TIP4P/Ewald, with a coarse grain one, which is highly appreciated for its computational efficiency. Here, we perform a complementary analysis considering three all-atoms water models: TIP4P/Ewald, TIP4P/ice and TIP5P. A key difference between these models is that the former predicts a much lower freezing temperature. Intuitively, one expects that to lower freezing temperatures of water correspond to lower water/methane–methane gas–clathrate coexistence ones, which determines the degree of supercooling and the degree of supersaturation. Hence, in the simulation conditions, 250 K (500 atm, and fixed methane molar fraction), one expects computational samples made of TIP4P-ice and TIP5P, with a similar freezing temperature ( T f ∼ 273 K), to be more supersaturated with respect to the case of TIP4P-Ew ( T f ∼ 245 K), and crystallisation to be faster. Surprisingly, we find that while the nucleation rate is consistent with this prediction, growth rate with TIP4P-ice and TIP5P is much slower than with TIP4P-Ew. The latter was attributed to the slower reorientation of water molecules in strong supercooled conditions, resulting in a lower growth rate. This suggests that the freezing temperature is not a suitable parameter to evaluate the adequacy of a water model.

Theoretical Investigation into Polymorphic Transformation between β-HMX and δ-HMX by Finite Temperature String

Polymorphic transformation is important in chemical industries, in particular, in those involving explosive molecular crystals. However, due to simulating challenges in the rare event method and collective variables, understanding the transformation mechanism of molecular crystals with a complex structure at the molecular level is poor. In this work, with the constructed order parameters (OPs) and K-means clustering algorithm, the potential of mean force (PMF) along the minimum free-energy path connecting β-HMX and δ-HMX was calculated by the finite temperature string method in the collective variables (SMCV), the free-energy profile and nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations, and the temperature effect on nucleation was also clarified. The barriers of transformation were affected by the finite-size effects. The configuration with the lower potential barrier in the PMF corresponded to the critical nucleus. The time and free-energy barrier of the polymorphic transformation were reduced as the temperature increased, which was explained by the pre-exponential factor and nucleation rate. Thus, the polymorphic transformation of HMX could be controlled by the temperatures, as is consistent with previous experimental results. Finally, the HMX polymorph dependency of the impact sensitivity was discussed. This work provides an effective way to reveal the polymorphic transformation of the molecular crystal with a cyclic molecular structure, and further to prepare the desired explosive by controlling the transformation temperature.

Numerical simulation of condensation of supercritical water gasification products in a supersonic nozzle

The clean and efficient separation of supercritical water gasification products (SCWGP) has emerged as a significant challenge in supercritical water gasification technology. This paper proposes the use of a supersonic nozzle for the condensation and separation of H2 and CO2 from SCWGP, leveraging the high-pressure characteristics of these products. By establishing a flow model and a condensation model for the supersonic nozzle, the effects of inlet pressure and inlet temperature on the condensation process are analyzed. The analysis reveals that the latent heat released during condensation causes an abnormal distribution of pressure and temperature within the nozzle. When the inlet pressure of the nozzle is increased from 7.0 to 9.0 MPa, the liquid phase mass fraction at the outlet rises from 5.3 × 10−3 to 0.056. Similarly, when the inlet temperature is lowered from 300.0 to 290.0 K, the liquid phase mass fraction at the outlet also rises from 5.3 × 10−3 to 0.058. The increase in inlet pressure leads to the condensation location shifting toward the throat by ∼8.5 × 10−3 m⋅MPa−1, while the impact of inlet temperature is approximately −2.3 × 10−3 m⋅K−1. The nucleation rate in the nozzle is always concentrated in a small region.

Microgalvanic cell-mediated green synthesis of Cu2O nanocubes with (100) facets for boosting dopamine hydrochloride sensing performance

Despite numerous efforts have been made on exploring the preparation, properties and application of Cu2O nanocrystal, there is still a lack of a facile and green synthesis strategy to obtain well-defined Cu2O nanocubes (NCs). And exploration of the superior low-index lattice plane of Cu2O in electrochemical sensing is also inadequate. Herein, we proposed a Ni(OH)2-mediated in-situ synthetic strategy for the preparation of Cu2O NCs enclosed by low-index facets with simple procedure, mild temperature and low energy-consumption. The Ni(OH)2 sites not only facilitated the contact between Cu2+ and the substrate Ni foam (NF), but also can combine with the NF to act as a primary battery to regulate the nucleation and growth rate of Cu2O (100) facets. Benefiting from the high ratio of exposed electroneutral (100) lattice planes of nanocubes, the Cu2O NCs formed on Ni(OH)2-abundant Ni Foam (Cu2O NCs/NFEO) exhibited a wide linear range (3.25–1178.8 μM), a low detection limit (1.86 μM) and a high sensitivity (900 μA mM−1 cm−2) in dopamine hydrochloride (DAH) electrochemical sensing. This work expects to provide more clues about the relationship between different dominant low-index facets of Cu2O NCs and electrochemical sensing performance towards DAH, and thereby contributes to the development of functional materials based on Cu2O nanocrystals with desirable facets.

Spontaneous continuous multiple jump of condensate droplets on superhydrophobic surface with hierarchical micro-nano structures

When two or more droplets coalesce on a superhydrophobic surface, the released surface energy will partially convert into kinetic energy, resulting in droplet jump from substrate surface. In this paper, a kind of superhydrophobic surface with hierarchical papillary micro-nano structures was fabricated to facilitate droplets coalescence-induced jump. The surface is easy to prepare without complex process. Different from single jump, a kind of spontaneous continuous multiple jump was observed on this kind of superhydrophobic surface. The influences of continuous multiple jump on condensation nucleation rate and water collection rate are investigated and a theoretical model is adopted to determine energy conversion efficiency of continuous multiple jump. The results find that continuous multiple jump makes large droplets to move spontaneously, and improves performance of superhydrophobic surface to maintain dropwise condensation even under a high subcooling. With condensing, the continuous multiple jump becomes more frequent. The average condensation nucleation rate is 303 % higher than those of surfaces without hierarchical micro-nano structures. The water collection rate on superhydrophobic surface is 2 times higher than those without hierarchical micro-nano structures. The energy conversion efficiency of continuous multiple jump is two times higher than that of single jump. This study provides a potential direction for heat transfer enhancement of condensation and self-cleaning.

Magnesium-Induced Rapid Nucleation of Tetrahydrofuran Hydrates.

Hydrates are ice-like crystalline structures of hydrogen-bonded water molecules that trap a guest molecule. Hydrates have several applications, including carbon sequestration, gas separation, desalination, etc. A classical major challenge associated with artificial hydrate formation is the very long induction time to nucleate hydrates. This has spurred the development of multiple chemical, mechanical, and electrical strategies to promote nucleation. Presently, we discover that magnesium can significantly promote the nucleation of tetrahydrofuran (THF) hydrates. While magnesium has been recently shown (by our group) to promote the formation of carbon dioxide hydrates (gas-liquid system), this study discovers that the benefits of magnesium extend to liquid-liquid hydrate systems as well. Experiments show that magnesium reduces the induction time for THF hydrate nucleation with deionized (DI) water and saltwater by six and eight times, respectively. Magnesium-induced nucleation rate enhancements for hydrate formation with DI water and saltwater were 12 and 99 times, respectively. Importantly, we demonstrate near-instantaneous nucleation when magnesium is introduced after the hydrate-forming system reaches suitable thermodynamic conditions. We conduct statistically significant measurements of nucleation and XPS analysis to identify the underlying mechanisms responsible for nucleation. We discuss multiple phenomena at play, including chemical and mechanistic promotion pathways. The formation of hydrogen bubbles and the presence of magnesium ions in solution are seen as important to magnesium-based nucleation promotion. Importantly, very low amounts of Mg are consumed in this process unlike in traditional chemical promotion techniques. Overall, our discovery can enable on-demand nucleation of liquid-liquid hydrate systems, which is critical to the development of several applications.

Towards enhanced elevated-temperature mechanical properties by regulation of eutectic structure in Al-Cu-Si alloys solidified under super-gravity field

High volume fraction of tri-phase eutectic structure is challenging to obtain in ternary alloys through conventional methods. Currently, we reported that super-gravity solidification can be utilized to obtain high-volume fraction Al-Al2Cu-Si tri-phase eutectic structure in Al-Cu-Si alloys. The refinement of the eutectic structure can be detected mainly due to the enhancement of mass transfer, affecting the nucleation rate and growth of eutectic phase in the Al-Cu-Si eutectic system. Interestingly, the refined Al2Cu and Si eutectic structures are stable even up to 300 °C thermal exposure without obvious coarsening, contributing to the enhancement of elevated-temperature mechanical properties (∼268.8±8.8 MPa at 300 °C), which is ∼51.9 % higher than those solidified under normal gravity field (∼177.0±1.9 MPa). The refinement and homogeneous distribution of more Al-Al2Cu-Si tri-phase eutectic structures provide better stress dispersion, favoring crack initiation and propagation within the tri-phase eutectics, resulting in a transition from brittle fracture to ductile fracture mode.

Fokker-Planck equation for the crystal-size probability density in progressive nucleation and growth with application to lognormal, Gaussian and gamma distributions

The Fokker Planck (FP) equation for the probability density function (PDF) of crystal size in phase transformations ruled by progressive nucleation and growth, has been derived. Crystals are grouped in sub-sets, we refer to as τ-crystals, where τ is the birth time of the set. It is shown that the size PDF is the superposition of the PDF of the crystal sub-sets (τ-PDFs), with weight given by the nucleation rate. The growth and diffusion coefficients entering the FP equations are estimated as a function of both τ-PDFs and nucleation rate. The functional form of these coefficients is studied for solutions of the FP equation for τ-crystals given by the lognormal, Gaussian and gamma distributions. For the first two distributions, the effect of fluctuations, nucleation rate and growth rate, on the shape of the distribution has been investigated. It is shown that for an exponential decay of the fluctuation term, the shape of the PDF is mainly governed by both the time constant for nucleation and the strength of the fluctuation. It is found that τ-PDFs given by the one-parameter gamma distributions are suitable to deal with KJMA (Kolmogorov Johnson Mehl Avrami) compliant phase transformations, where the fluctuation term is proportional to crystal size. The connection between the FP equation for the size PDF and the evolution equation for the density of crystal populations is also discussed.

Study on the influence factors of the grain growth type of micro-nano silver powders prepared by liquid-phase reduction method

Abstract The preparation was carried out by liquid-phase reduction method with AgNO3 as the oxidizing agent, ascorbic acid (C6H8O6) as the reducing agent, and polyvinyl pyrrolidone (PVPK30) as the dispersing agent. The effects of silver nitrate concentration, ascorbic acid concentration, PVPK30 concentration, solution PH value before and after the reaction, and the temperature of reaction on average particle size (D50), dispersity, and particle size uniformity of silver particles were investigated by orthogonal experiment L18 (36) with six factors and three levels. The spheroid-like silver particles with good dispersity of 400-600nm and the spheroid-like silver particles with suitable particle size uniformity of 80-100nm were successfully prepared by optimal experiments. The results of the orthogonal experiment show that the molar ratio of the reducing agent to the oxidizing agent plays a decisive role in the type of grain growth. The crystal nucleus will coagulate and grow at a higher molar ratio (⩾1.05). With the increase in molar ratio, the nucleation rate is higher, the grain growth rate is faster, and the size of silver particles is smaller.

Regulation of nucleation and crystallization for blade-coating large-area CsPbBr3 perovskite light-emitting diodes

Metal halide perovskite light-emitting diodes (PeLEDs) and large-area perovskite color conversion layers for liquid crystal display exhibit great potential in the field of illumination and display. Blade-coating method stands out as a highly suitable technique for fabricating large-scale films, albeit with challenges such as uneven nucleation coverage and non-uniformity crystallization process. In this work, we developed an in-situ characterization measurement system to monitor the perovskite nucleation, and crystallization process. By incorporating formamidine acetate (FAAc) into perovskite precursor solutions, the nucleation rate and nuclei density of perovskite were increased, leading to more uniform nucleation. In addition, we inserted a layer of [2-(9H-carbazol-9-yl)ethyl] phosphonic acid above the poly(9-vinylcarbazole) hole transport layer. This layer acts as an anchor for the perovskite nano-crystal nuclei formed in the precursor, enhancing the steric hindrance of the solute and subsequently slowing down the crystal growth rate, thereby improving crystal quality. Based on these improvements, large-area perovskite nano-polycrystalline films with significantly improved uniformity and enhanced photoluminescence quantum yield were obtained. A small-area PeLED (2 mm × 2 mm) with a maximum external quantum efficiency of 25.91% was realized, marking the highest record of PeLED prepared by blade-coating method to date. An ultra-large-area PeLED (5 cm × 7 cm) was also prepared, which is the largest PeLED prepared by the solution method reported so far.

Crystallization ripening and erosion of calcium oxalate under the effect of bacteria and a polymer materials surface.

As typical examples of pathological biomineralization, urinary stones and stent encrustation have been associated with bacteria, yet the underlying mechanisms remain unclear. In this study, the effect of Gram-negative Escherichia coli and Gram-positive Staphylococcus aureus on the nucleation and growth of calcium oxalate crystals both in solution and on material surfaces in vitro was investigated. Both bacteria can promote calcium oxalate crystallization, and E. coli shows a prominent ability to boost the nucleation and growth rate. Interestingly, we discovered an Ostwald ripening phenomenon after the initial nucleation on the material surfaces, where larger particles emerge upon the disappearance of small nuclei particles, evident in the case of S. aureas. Over an extended period of time, erosion and disintegration of the crystals was observed when bacteria were involved. Based on these understandings, we developed a new functional surface by synthesizing an antibacterial polypeptoid in-house and utilizing polyurethane as the substrate material. This surface exhibits a synergistic effect that inhibits the formation of calcium oxalate crystals. This study helps to elucidate the role of bacteria in calcium oxalate biomineralization and supports further development of treatment approaches such as anti-encrustation polymer materials.

Molecular recognition characteristics of co-assembled peptides on atomically flat graphite surfaces

Molecular recognition, involving the binding of two or more molecules, is widely found in multiple disciplines. It plays a crucial role in driving specific molecular functionalization or biological activities such as antigen–antibody interactions. Recently, the molecular recognition of single peptides self-assembly at interfaces has been widely investigated since their broad applications in biosensors and bioelectronics. However, the recognition characteristics of peptide-peptide co-assembly on solids has not been investigated yet, which provides a basis for potential multi-probes biosensing or structure-intermingled functionalized bioelectronic applications. Here, we explored the molecular recognition characteristics of co-assembled peptides on two-dimensional (2D) layered nanomaterials, specifically graphite. Our findings showed distinct surface characteristics of peptide co-assembly in comparison to the independent peptides self-assembly. Peptide co-assembly exhibited the nucleation and growth heterogeneities with reduced nucleation and growth rates, dominated by a diffusion-limited step as confirmed via carrying out the sequential-assembled experiments. Moreover, molecular dynamics simulation reveals a slowdown binding process of co-assembled peptides to graphite. Furthermore, the misattachment of one peptide to arrays of another types of peptide with distinct structural ordering orientations severely postponed peptide elongation. Therefore, our work provides valuable insight into the fundamental surface characteristics of two co-assembled peptides as they specifically recognize graphite surface via undergoing continuous surface behaviors from binding to diffusion until final ordering process. The formation of co-assembled peptide patterns on 2D layered nanomaterials incorporates multiple functions enabling to provide potential applications in intermingled peptide-based biosensing or bioelectronic nanodevices.

Microstructure and corrosion properties of CrMnFeCoNi high entropy alloy coating by temperature field-assisted laser cladding

The CrMnFeCoNi high entropy alloy coatings were prepared on the surface of Q345 steel using a temperature field-assisted laser cladding process, and the effects of the applied temperature field on the cladding coatings were studied. The microstructures and corrosion morphologies of the coatings were observed, and the elemental distribution, hardness, effective elastic modulus, electrochemical corrosion performance, and corrosion products of different coatings were analyzed. The results show that the porosity of the HEA coatings prepared with a temperature field is reduced to below 50 % of the initial level. The microstructure of the coating changed, with the nanoindentation hardness of the coating increasing by up to 0.55 GPa, enhancing the mechanical properties. Among all the coatings, the coating prepared at 250 °C temperature field exhibited the best corrosion resistance, with corrosion potential and current density of −0.27 V and 0.15 μA/cm2, respectively, improving the corrosion potential by 0.1 V and reducing the current density by 1.08 μA/cm2 compared to the sample prepared at room temperature. After incorporating the temperature field, the stability of the passive film on the coating during corrosion improved, and the nucleation rate of pitting decreased. Therefore, incorporating an appropriate temperature field during laser cladding can effectively enhance the overall performance of the CrMnFeCoNi HEA coating.

Numerical investigation of non-equilibrium condensation of carbon dioxide from a gas mixture of carbon dioxide and argon in a supersonic nozzle under cryogenic conditions

This study involved a numerical investigation of the homogeneous nucleation of CO2 from a CO2–Ar gas mixture in a supersonic nozzle with a throat size of 2.11 mm, a total pressure of 61.15 kPa, and a total temperature of 293.15 K. The flow conditions covered the cryogenic temperature range (∼75 K). Therefore, the surface tension of the clusters was calculated using the Tolman–Tanaka correction, and nucleation growth was evaluated considering both free molecular and continuum regimes. Numerical simulations were conducted for a wide range of CO2 mole fractions (3%–39%). In particular, the effect of the CO2 mole fraction on the condensation-shock position—approximately the Wilson point—was investigated. For 3%, 12%, 24%, and 39%, the condensation shock occurred at 0.048, 0.043, 0.046, and 0.054 m from the throat, respectively. When the mole fraction was low (≤10%), the condensation-shock position moved downstream as the mole fraction decreased. This trend was attributed to a lower nucleation rate. In contrast, when the mole fraction was high (≥10%), the condensation-shock position moved downstream as the mole fraction increased. This was because the CO2 equilibrium pressure rose more rapidly than the CO2 vapor pressure as the mole fraction increases.