An EMB apparatus was used to investigate the dynamics and kinetics of butanol interactions with graphite and nopinone surfaces. The experimental setup, described in detail elsewhere (Kong et al., 2012, 2014a; Johansson et al., 2017), comprises a three-chamber, differentially pumped beamline. Pulsed molecular beams are generated from a gas mixture of helium and butanol vapor, formed by passing helium through a liquid butanol reservoir. The pulsed molecular beam, generated at 120 Hz with a 50 % duty cycle, passes through a 1 mm skimmer to produce a collimated, low-density flow before entering the environmental chamber. The ∼16 ms inter-pulse delay exceeds the residence time of fast-desorbing species, ensuring that the scattering kinetics of each pulse could be observed independently (Kong et al., 2021). However, in the case of the thin nopinone coating, a minor population of butanol molecules with much longer residence times enables gradual buildup of a condensed butanol layer during prolonged exposure.

The low-pressure environment ensures that observed desorption kinetics reflect intrinsic surface processes rather than gas-phase diffusion, re-collision, or re-adsorption effects. While atmospheric uptake occurs under ambient pressure, the same surface-controlled rate constants govern gas-particle exchange and are explicitly required inputs for kinetic multilayer aerosol models. The EMB approach therefore provides mechanistic and quantitative constraints on interfacial processes that operate under atmospheric conditions.

While the molecular beam has a narrow and directed energy distribution, the observed dynamics are governed by rapid energy accommodation at the surface. The dominance of thermal desorption indicates efficient redistribution of the incident energy, such that the system largely loses memory of the initial velocity distribution. The extracted kinetic parameters therefore reflect intrinsic surface-controlled processes and are transferable to atmospheric conditions.

Mass spectra show dominant peaks at m/z= 31 (CH₂OH⁺), 41 (C₂HO⁺), and 56 (C₄H8+) for monomers, and m/z= 75 (C₄H₁₀OH⁺) for clusters. A weak broad signal near m/z= 75 is attributed to protonated cluster ions ([2 BuOH + H]⁺), consistent with the presence of small clusters (typically dominated by dimers to tetramers and with a distribution also covering larger clusters) in the beam under the employed stagnation and temperature conditions. Both monomers and clusters travel with an average velocity of ∼1600 m s⁻¹. The pulsed beam strikes the target surface at a 45° incidence angle inside the environmental chamber, and the outgoing flux is detected using a rotatable, differentially pumped quadrupole mass spectrometer (QMS) for time-of-flight (TOF) analysis. Ions generated by electron impact in the QMS are collected by a multi-channel scaler with a 10 µs dwell time. Highly oriented pyrolytic graphite (HOPG, 12×12 mm, grade ZYB; Advanced Ceramics Corp.) was used as the substrate and cleaned at 600 K before and after each experiment.

Nopinone surfaces were prepared by dosing vapor-phase (1R)-(+)-nopinone (98 %, Sigma-Aldrich) through a precision leak valve onto the substrate. The nopinone thick layer was grown to a thickness of approximately 1 µm. The thickness of the nopinone thick layer was determined by 670 nm laser interferometry, with an estimated uncertainty of approximately ±5 %–10 %, arising mainly from the refractive index of the condensed film and fringe resolution. In contrast, the thin nopinone coating was below the optical detection limit of ∼8 nm and was therefore characterized using helium scattering attenuation, which provides a sensitive and reproducible measure of surface coverage (Johansson et al., 2020).

The TOF distributions were analyzed to resolve the kinetics and dynamics of butanol interactions with nopinone surfaces. Upon impact, incident molecules may undergo either inelastic scattering (IS) or trapping followed by thermal desorption (TD). Incident butanol clusters are likely to trap on the surface promoted by efficient energy transfer to cluster and surface modes (Svanberg et al., 1995; Tomsic et al., 2001). A cluster may remain intact after adhering to the surface, or split into smaller cluster fragments that either remain on the surface or, with low probability, leave the surface in connection with the initial collision process (Andersson et al., 1997). Clusters that remain bound to the surface will eventually dissociate and ultimately desorb as monomers (Någård and Pettersson, 1998; Kong et al., 2021). The butanol flux from the surface is thus dominated by butanol molecules that leave the surface by either IS or TD, and both components were included in the fitting analysis. Nonlinear least-squares fitting was employed to deconvolute the IS and TD contributions. The IS component was represented by a velocity-dependent function (Arumainayagam and Madix, 1991), 1IISυt=Ciυ(t)4exp⁡-υt-υ‾2kBTISm2, where Ci is a scaling parameter, υ is the velocity calculated from the molecular arrival time, υ‾ is the average velocity, kB is the Boltzmann constant, m is the molecular mass of butanol, and TIS is a free parameter representing the IS velocity spread.

The TD distributions are each a combination of two components: (i) a velocity distribution that relates desorption to molecular excitation based on the surface temperature, 2ITD1υt=Cjv(t)4exp⁡-υt2kBTsm2, and (ii) a distribution related to the desorption rates, 3ITD2=Cje-kt, where Cj is a free scaling factor, Ts is the surface temperature, k is the fitted desorption rate coefficient, and t is time. ITD1 shows the velocity spread of the TD flux, and ITD2 accounts for the exponential decay of ToF distributions. Thus, the TD distributions are calculated as a convolution of these two components. Although both IS and TD components were included in the fitting analysis, only two distinct TD channels (fast and slow) were identified and resolved from the experimental data.

MD simulations were performed to characterize the collisions of butanol clusters with solid nopinone surfaces. The GROMOS force field, optimized for small molecules in condensed phases (Horta et al., 2016), was used to model the nopinone crystal and implemented in the GROMACS package (Van Der Spoel et al., 2005) Molecular topologies were generated using the Automated Force Field Topology Builder (ATB) database (Malde et al., 2011; Stroet et al., 2018). Since the default ATB GROMOS charges do not reproduce melting behavior, a new set of charges was derived from ab initio calculations. Restrained Electrostatic Potential (RESP) point charges (Bayly et al., 1993) were fitted to replicate the electrostatic potential of an isolated nopinone molecule calculated at the BLYP-D3/6-31++G^** level of theory.

The equations of motion were integrated using the leap-frog algorithm (Stephan et al., 2019) with bond constraints applied via the LINCS method (Hess et al., 1997), allowing a 2 fs time step. Short-range interactions were truncated at 1.8 nm, and long-range electrostatics were treated with the particle mesh Ewald (PME) method (Essmann et al., 1995). The system temperature was controlled using the velocity-rescale (V-rescale) thermostat (Bussi et al., 2007) with a coupling time of 0.1 ps. The nopinone crystal structure was based on X-ray diffraction data by Palin et al. (2008), obtained from the Cambridge Structural Database (Groom et al., 2016).

An infinite crystal was generated by replicating the unit cell along all three dimensions. After energy minimization with the steepest-descent algorithm, the crystal was equilibrated in the NPT ensemble at 200 K for 10 ns, resulting in a simulation box containing approximately 100 000 atoms with dimensions 10.68×16.88×6.59 nm. To model surface slabs, the crystal was cleaved between nopinone bilayers to expose the most energetically favorable surface. Three slabs of different thicknesses, 4 layers (∼ 2.8 nm), 6 layers (∼ 3.5 nm), and 15 layers (∼ 9 nm), were prepared to represent thin and thick coatings observed experimentally.

In real atmospheric environments, the thickness of organic coatings on soot particles varies widely, ranging from sub-nanometer patchy films on freshly emitted soot to continuous layers of tens or even hundreds of nanometers on heavily aged particles (Li et al., 2024; Ahern et al., 2016; Zhang et al., 2008). In the present simulations, the slab thicknesses are chosen to capture the transition from substrate-influenced, thin coatings to bulk-like organic layers, rather than to reproduce the full atmospheric thickness range. The thinner slabs represent a low-coverage regime where substrate effects remain important, whereas the thicker slab corresponds to a regime in which the organic layer effectively screens the substrate. The box was extended by 10 nm in the z-direction to prevent image interactions, and each slab was equilibrated in the NPT ensemble at 200 K for 10 ns.

Butanol clusters consisting of 10 molecules were modeled using the same GROMOS force field (Horta et al., 2016) and RESP charges (Bayly et al., 1993). Stable cluster configurations were first obtained from equilibrated simulations at 298 K. Cluster-surface collisions were then simulated at 200 K with an incident kinetic energy of 0.45 eV (corresponding to 1606 m s⁻¹) and an incidence angle of 45° relative to the surface normal. Butanol clusters were decoupled from the thermostat during impact to avoid artificial damping of dynamics. Initial lateral (x,y) positions were randomized 1 nm above the surface, and 30 independent trajectories were performed for each slab thickness to ensure statistical significance.

To connect the experimentally observed surface desorption kinetics to an atmosphere-relevant framework, we describe gas uptake using a minimal surface-kinetic parameterization. The effective uptake coefficient, γeff, is expressed as the competition between surface incorporation and thermal desorption: 4γeffT=αkinckinc+kdesT, where α is the surface accommodation coefficient, kinc is an effective incorporation rate into the particle or condensed overlayer, and kdes(T) represents the effective desorption rate of the slow TD channel. The desorption rate is parameterized using an Arrhenius expression, kdesT=A⋅exp⁡(-Ea/(kB⋅T)), with effective Arrhenius parameters extracted from Fig. S3 in the Supplement for HOPG and the nopinone thick coating. These parameters represent multi-step, cluster-mediated delayed desorption rather than a single elementary barrier. For the thin nopinone coating, no slow TD channel is observed experimentally; therefore, no Arrhenius description is applied, and this case is treated as a kinetic limit with γeff≈α. The parameter space is explored by scanning temperature and incorporation timescales (τinc= 1/kinc), enabling regime mapping without invoking detailed multilayer or diffusion-resolved models.

The distinct fast and slow TD channels identified above provide a direct basis for interpreting heterogeneous uptake in kinetic terms. To translate the experimentally resolved desorption kinetics into an atmosphere-relevant description of gas-particle exchange, the effective uptake coefficient, γeff, is evaluated as the outcome of competition between surface incorporation and thermally activated delayed desorption.

Figure 6 illustrates how γeff transitions between kinetically controlled and desorption-limited regimes as a function of temperature and the characteristic surface incorporation timescale. In the thin-coating limit, γeff approaches the surface accommodation coefficient (α) and remains nearly temperature independent, reflecting rapid energy dissipation and efficient incorporation that suppress the slow TD channel entirely. This behavior corresponds to a kinetic retention regime in which surface residence times are sufficiently long that desorption no longer limits uptake.

In contrast, uptake on HOPG and on the nopinone thick layer exhibits a pronounced decrease in γeff with increasing temperature. This trend directly reflects the emergence of the slow TD channel, for which thermally activated delayed desorption increasingly competes with incorporation as temperature rises. The similar temperature dependence observed for HOPG and the thick organic layer is consistent with their comparable Arrhenius parameters and indicates a shared, desorption-controlled uptake regime.

These results highlight that equilibrium partitioning represents a limiting case rather than a general description of gas-particle exchange. When surface residence times are finite, uptake is governed by kinetic competition between incorporation and desorption, and coating morphology can shift particles between fundamentally different regimes. Thin organic films promote kinetic retention by suppressing delayed desorption, whereas thicker, more ordered coatings restore desorption-limited behavior. Importantly, the simple kinetic formulation employed here reproduces the experimentally observed distinctions between thin and thick coatings while remaining directly compatible with heterogeneous uptake parameterizations used in aerosol dynamics and chemical transport models.

Classical MD simulations were performed to investigate the interactions between butanol clusters and nopinone surfaces. The nopinone crystal structure was constructed based on experimental X-ray diffraction data (Palin et al., 2008), which reveal a bilayer arrangement in which functional groups are oriented inward within each bilayer (Fig. S5a). Weak van der Waals forces between bilayers maintain the overall structural cohesion of the crystal. The melting point of bulk nopinone is 260 K (Palin et al., 2008), and therefore, at the simulation temperature of 200 K, the nopinone slabs remain crystalline.

Figure S5 presents simulation snapshots at key stages of a butanol cluster colliding with a 15-layer nopinone slab, representing the interaction between the butanol molecular beam and a nopinone surface. Initially, a 10-molecule cluster is positioned 1 nm above the surface (Fig. S5a). Within 15–30 ps of impact, one molecule reflects from the surface (Fig. S5b, c), while the remaining molecules divide into two fragments that adsorb onto the surface (Fig. S5d, e). These fragments remain bound over the next ∼ 2 ns and reorganize into stable surface clusters (Fig. S5f, g). Molecules located in the cluster interior are strongly bound and resistant to direct desorption, whereas those at the periphery are more weakly bound and can either desorb directly or undergo a two-step process involving detachment followed by monomer desorption.

A non-reflective collision pathway was also observed (Fig. S6b–e), in which the incident cluster remains largely intact but splits into two fragments. The smaller fragment, composed of three butanol molecules, is loosely bound to the nopinone surface and readily undergoes TD. Both reflective and non-reflective behaviors were observed for nopinone slabs of 4-layer (∼ 2.8 nm) and 6-layer (∼ 3.5 nm) thickness. These contrasting outcomes suggest that differences in surface structure may modulate cluster stability and desorption behavior, an effect examined in detail below using the structural analysis in Fig. 7.

The nopinone surface is predominantly terminated by well-ordered hydrocarbon groups, rendering the carbonyl functionalities largely inaccessible to hydrogen bonding. Occasional rotation of surface molecules by 180° about one of the molecular axes exposes hydroxyl groups that act as surface defects, introducing localized hydrophilicity and disrupting the otherwise nonpolar surface. These defect sites play a key role in mediating the adsorption and desorption dynamics of impinging butanol clusters by providing transient hydrogen-bonding or dipole-dipole interaction sites that enhance molecular trapping.

As shown in Fig. 7a, the radial distribution functions (RDFs) reveal clear structural differences among nopinone slabs of varying thickness. The 4-layer slab exhibits a rightward shift and broadening of RDF peaks, indicative of weaker intermolecular packing and increased structural disorder resembling a pre-melted or amorphous-like surface. In contrast, the 6- and 15-layer slabs display sharper, well-defined peaks characteristic of a solid-like crystalline organization. This progressive increase in molecular order with thickness implies that thinner coatings have higher densities of surface defects and greater morphological heterogeneity.

These structural variations translate directly into the experimentally observed desorption behavior. The increased disorder and defect density in thinner coatings enhance molecular accommodation, leading to efficient trapping of butanol clusters and suppression of the slow TD channel. In contrast, the more ordered and corrugated surface of the nopinone thick layer reduces the availability of stable adsorption sites, resulting in less efficient energy dissipation and enhanced delayed desorption, consistent with the strong slow TD signal observed experimentally.

Figure 7b shows that the reflection probability of butanol molecules within a cluster decreases systematically with decreasing slab thickness, confirming that disordered, defect-rich surfaces promote collisional energy loss and adsorption. Together, these simulation results provide a molecular-level explanation for the experimental findings. The thin, partially disordered nopinone coatings contain a higher density of flexible or defect sites that efficiently dissipate collisional energy and promote transient hydrogen-bonding interactions, leading to stabilization of condensed butanol overlayers. In contrast, the thicker, crystalline-like nopinone thick layers present more rigid, well-ordered hydrocarbon terminations that limit energy accommodation and reduce the availability of binding sites, thereby favoring cluster breakup and delayed desorption. The underlying graphite substrate in the thin-coating regime may further enhance adsorption by providing additional π-OH or defect-mediated interactions accessible through the incomplete nopinone layer, reinforcing the stronger retention observed experimentally.