Second inflection point of supercooled water surface tension induced by hydrogen bonds: A molecular-dynamics study.

Surface tension of supercooled water is a fundamental property in various scientific processes. In this study, we perform molecular dynamics simulations with the TIP4P-2005 model to investigate the surface tension of supercooled water down to 220 K. Our results show a second inflection point (SIP) in the surface tension at temperature TSIP ≈ 267.5 ± 2.3 K. Using an extended IAPWS-E functional fit for the water surface tension, we calculate the surface excess internal-energy and entropy terms of the excess Helmholtz free energy. Similar to prior studies [Wang et al., Phys. Chem. Chem. Phys. 21, 3360 (2019); Gorfer et al., J. Chem. Phys. 158, 054503 (2023)], our results show that the surface tension is governed by two driving forces: a surface excess entropy change above the SIP and a surface excess internal-energy change below it. We study hydrogen-bonding near the SIP because it is the main cause of water's anomalous properties. With decreasing temperature, our results show that the entropy contribution to the surface tension reaches a maximum slightly below the SIP and then decreases. This is because the number of hydrogen bonds increases more slowly below the SIP. Moreover, the strengths and lifetimes of the hydrogen bonds also rise dramatically below the SIP, causing the internal-energy term to dominate the excess surface free energy. Thus, the SIP in the surface tension of supercooled TIP4P-2005 water is associated with an increase in the strengths and lifetimes of hydrogen bonds, along with a decrease in the formation rate (#/K) of new hydrogen bonds.

Effects of molecular size and orientation on the interfacial properties and wetting behavior of water/n-alkane systems: a molecular-dynamics study.

Molecular dynamics simulations (MD) are performed to study the interfacial structure/tension and wetting behavior of water/n-alkane systems (water/nC5 to water/nC16 where nCx = CxH(2x + 2)). In particular, we study complete-to-partial wetting transitions by changing the n-alkane chain length (NC) at a constant temperature, T = 295 K. Simulations are carried out with a united-atom TraPPE model for n-alkanes and the TIP4P-2005 model of water. Simulation results are in excellent agreement with the initial spreading coefficients and contact angles calculated using experimental values of the surface and interfacial tensions. In addition, it has been determined that water/(nC5-nC7) and water/(nC8-nC16), respectively, exhibit complete and partial initial wetting modes. Simulations show that the interfacial structures of water/(nC5-nC7) are different from water/(nC8-nC16) systems. In the latter, water preferentially orients near the interface to increase the number of hydrogen bonds and the charge and mass densities. Moreover, the orientation of n-alkane molecules at water/(nC8-nC16) interfaces has a long-range persistence, resulting in layered structures that increase with NC. In addition, simulation results of the orientational order parameter Sz show alignment behavior of the n-alkane molecules with respect to the interfaces. Simulations predict that the central segments of n-alkane are strongly packed in the interfaces while the end segments (methyl groups) form smaller peaks in the outer edge of the layer. This observation confirms the "horseshoe" or "C-shaped" structure of n-alkane molecules in the water/n-alkane interfaces. At constant temperature, the interface widths of both water and the n-alkanes decrease with increasing n-alkane molecular length. These results suggest that increasing the n-alkane chain length affects the water/n-alkane interfacial properties in a manner similar to that of cooling.

The effects of methanol clustering on methanol-water nucleation.

The formation of subcritical methanol clusters in the vapor phase is known to complicate the analysis of nucleation measurements. Here, we investigate how this process affects the onset of binary nucleation as dilute water-methanol mixtures in nitrogen carrier gas expand in a supersonic nozzle. These are the first reported data for water-methanol nucleation in an expansion device. We start by extending an older monomer-dimer-tetramer equilibrium model to include larger clusters, relying on Helmholtz free energy differences derived from Monte Carlo simulations. The model is validated against the pressure/temperature measurements of Laksmono et al. [Phys. Chem. Chem. Phys. 13, 5855 (2011)] for dilute methanol-nitrogen mixtures expanding in a supersonic flow prior to the appearance of liquid droplets. These data are well fit when the maximum cluster size imax is 6-12. The extended equilibrium model is then used to analyze the current data. On the addition of small amounts of water, heat release prior to particle formation is essentially unchanged from that for pure methanol, but liquid formation proceeds at much higher temperatures. Once water comprises more than ∼24 mol % of the condensable vapor, droplet formation begins at temperatures too high for heat release from subcritical cluster formation to perturb the flow. Comparing the experimental results to binary nucleation theory is challenged by the need to extrapolate data to the subcooled region and by the inapplicability of explicit cluster models that require a minimum of 12 molecules in the critical cluster.

Molecular dynamics study of wetting of alkanes on water: from high temperature to the supercooled region and the influence of second inflection points of interfacial tensions.

To explore the wetting behavior of alkanes on bulk water interfaces, molecular dynamics (MD) simulations were carried out for united-atom PYS alkane models, and for SPC/E and TIP4P/2005 water models over a wide temperature range. The MD results at each temperature were used to find (1) the surface tension of the alkanes (octane, nonane) and water, and (2) the interfacial tensions of the alkane-water systems. These quantities were then used to calculate the spreading coefficient (S) and contact angle (θc) for each alkane on water. At higher temperatures, the contact angle of octane and nonane on water is found to behave in accord with conventional expectations, i.e., it decreases with increasing temperature for both water models as each system approaches the usual high-temperature transition to perfect wetting. At lower temperatures, we found an unusual temperature dependence of S and θc for each PYS alkane on SPC/E water. In contrast to conventional expectations, θc decreases with a decrease in the temperature. For octane-SPC/E water, this unusual behavior of θc occurs due to the presence of second inflection points (SIP) in the vapor-water and the octane-water interfacial tensions, whereas the SIP effect is much less important for the nonane-water system. The unusual temperature dependence of θc observed for nonane on SPC/E water is also found for nonane on TIP4P/2005 water. On the other hand, such unusual wetting behavior has not been observed in the PYS octane-TIP4P/2005 water system, except possibly for the two lowest temperatures studied.

Confined phase separation of aqueous-organic nanodroplets.

Nano-confined supercooled water occurs frequently in aqueous-organic aerosol nanodroplets that are ubiquitous in the atmosphere and in many industrial processes such as natural gas refining. The structure of these nanodroplets is important because it influences droplet growth and evaporation rates, nucleation rates, and radiative properties. We used classical molecular dynamics (MD) simulations to study the structures of binary water-butanol nanodroplets for several temperatures and droplet sizes. Water-butanol cross interactions are calculated using a Lennard-Jones (LJ) potential with non-bonded specific parameters adjusted to reproduce the experimentally observed mutual solubilities of water-butanol at 295 K. To compare with the results of the density functional theory (DFT) of aqueous-organic nanodroplets [Phys. Chem. Chem. Phys., 2006, 8, 1266-1270], we focus on T = 250 K. Our simulations show three different nanodroplet structures depending on the butanol concentration. For low concentrations, we observe a core-shell (CS) structure in which a butanol shell completely wets a water-rich core. For high concentrations, a well-mixed (WM) structure occurs as the water and the butanol become fully miscible. For intermediate concentrations of butanol, we find a distinct phase-separated Russian Doll-Shell (RDS) structure. This RDS structure consists of a roughly ellipsoidal water-rich droplet partially wetted by a well-mixed water/butanol convex lens (RD) and this lens-on-sphere structure is coated by a thin shell of butanol. We also examined the stability of our RDS structure at a higher temperature and found that at 295 K, the RDS structure had transformed into a well-mixed droplet, presumably due to the increase in the mutual solubility of water and butanol. Finally, we performed calculations using classical density functional theory for conditions that should favor the RDS structure. The results closely resembled those found using MD.

The structure of D2O-nonane nanodroplets.

We study the internal structure of nanometer-sized D2O-nonane aerosol droplets formed in supersonic nozzle expansions using a variety of experimental techniques including small angle X-ray scattering (SAXS). By fitting the SAXS spectra to a wide range of droplet structure models, we find that the experimental results are inconsistent with mixed droplets that form aqueous core-organic shell structures, but are quite consistent with spherically asymmetric lens-on-sphere structures. The structure that agrees best with the SAXS data and Fourier transform infra-red spectroscopy measurements is that of a nonane lens on a sphere of D2O with a contact angle in the range of 40°-120°.

Monomer, clusters, liquid: an integrated spectroscopic study of methanol condensation.

We have combined static pressure, spectroscopic temperature, Fourier transform infrared spectroscopy (FTIR), and small angle X-ray scattering (SAXS) measurements to develop a detailed picture of methanol condensing from a dilute vapor-carrier gas mixture under the highly supersaturated conditions present in a supersonic nozzle. In our experiments, methanol condensation can be divided into three stages as the gas mixture expands in the nozzle. In the first stage, as the temperature decreases rapidly, small methanol n-mers (clusters) form, increase in concentration, and evolve in size. In the second stage, the temperature decreases more slowly, and the n-mer concentrations continue to rise. Thermodynamic and FTIR experiments cannot, however, definitively establish if the average cluster size is constant or if it continues to increase. Finally, when the vapor becomes supersaturated enough, liquid droplets form via nucleation and growth, consuming more monomer and reducing the concentration of clusters. At the point where liquid first appears, cluster formation has already consumed up to 30% of the monomer. This is significantly more than is predicted by a model that describes the vapor phase as an equilibrium mixture of methanol monomer, dimer, and tetramer. An energy balance suggests that a significant fraction of the cluster population is larger than the tetramer, while preliminary SAXS measurements suggest that these clusters contain, on average, 6 monomers.

Nucleation rates of methanol using the SAFT-0 equation of state.

Classical and nonclassical calculations of nucleation rates are presented for methanol, an associating vapor system. The calculations use an equation of state (EOS) that accounts for the effects of molecular association based on the statistical association fluid theory (SAFT). Two forms of classical nucleation theory (CNT) were studied: a Gibbsian form known as the P-form and the standard or S-form. CNT P-form calculations and nonclassical gradient theory (GT) calculations were made using the SAFT-0 EOS. Calculated rates were compared to the experimental rates of Strey, et al. [J. Chem. Phys. 1986, 84, 2325-2335]. Very little difference was found between the two forms of CNT for either the temperature (T) or supersaturation (S) dependence of the rates. Nucleation rates based on GT showed improved T and S dependence compared to CNT. The GT rates were also improved by factors of 100-1000 compared to CNT. Despite these improvements, GT does not describe the reported T and S dependence of the nucleation rates. To explore this further, the GT and experimental rates were analyzed using Hale's scaled model [J. Chem. Phys. 2005, 122, 204 509]. This analysis reveals an inconsistency between the predictions of GT, which scale relatively well, and the experimental data, which do not scale. It also shows that the measured rate data have an anomalous T and S dependence. A likely source of this anomaly is the inadequate thermodynamic data base for small cluster properties that was used originally to correct the raw rate data for the effects of association.

CH(3)CH(2)OD/D(2)O binary condensation in a supersonic Laval nozzle: Presence of small clusters inferred from a macroscopic energy balance.

We determined the heat released in the condensing flow of a CH(3)CH(2)OD/D(2)O/carrier gas mixture (EtOD/D(2)O for brevity) through a supersonic Laval nozzle by integrating the equations for supersonic flow with condensation, using the static pressure, temperature, and mole fractions of EtOD and D(2)O monomers [S. Tanimura, B. E. Wyslouzil, M. S. Zahniser, et al., J. Chem. Phys. 127, 034305 (2007)] as inputs. By considering the depletion of the monomer species, the deviation of the pressure from the isentropic value, and the heat released, we estimated that approximately 10% of the EtOD molecules are present as pure clusters (dimer to tetramer) upstream of the onset point of condensation. In contrast, clustering was not detected when only pure EtOD was present under the same conditions (temperature and the partial pressure of EtOD) for which clustering was observed in the EtOD/D(2)O flow. This suggests that the formation of EtOD clusters is facilitated by D(2)O in the EtOD/D(2)O flow. A comparison of the heat released to the flow and the expected heat of dissociation of the EtOD/D(2)O droplets suggests that small EtOD clusters persist downstream of the onset point. Both upstream and downstream of the onset point of condensation, the concentration of these clusters in the nozzle is higher than that expected at equilibrium. A possible mechanism for the overabundance of pure EtOD clusters is that they form in the mixed EtOD/D(2)O particles (droplets or clusters) and evaporate from them.

Small angle X-ray scattering measurements probe water nanodroplet evolution under highly non-equilibrium conditions.

Our in situ small angle X-ray scattering (SAXS) measurements yield an unprecedented and detailed view of rapidly evolving H(2)O nanodroplets formed in supersonic nozzles. The SAXS experiments produce spectra in a few seconds that are comparable to small angle neutron scattering (SANS) spectra requiring several hours of integration time and the use of deuterated compounds. These measurements now make it possible to quantitatively determine the maximum nucleation and growth rates of small droplets formed under conditions that are far from equilibrium. Particle growth is directly followed from about 10 micros to 100 micros after particle formation with growth rates of approximately 0.2 to 0.02 nm micros(-1). The peak H(2)O nucleation rates lie between 10(17) and 10(18) cm(-3) s(-1).

Volumes of critical bubbles from the nucleation theorem.

A corollary of the nucleation theorem due to Kashchiev [Nucleation: Basic Theory with Applications (Butterworth-Heinemann, Oxford, 2000)] allows the volume V(*) of a critical bubble to be determined from nucleation rate measurements. The original derivation was limited to one-component, ideal gas bubbles with a vapor density much smaller than that of the ambient liquid. Here, an exact result is found for multicomponent, nonideal gas bubbles. Provided a weak density inequality holds, this result reduces to Kashchiev's simple form which thus has a much broader range of applicability than originally expected. Limited applications to droplets are also mentioned, and the utility of the p(T,x) form of the nucleation theorem as a sum rule is noted.

A structural phase diagram for model aqueous organic nanodroplets.

Our density functional theory calculations predict that model aqueous organic nanodroplets have either well mixed or core-shell structures, depending on the state of the metastable binary vapor and that, furthermore, there is a broad transition region in the phase diagram where both structures can occur at the same vapor state.

Experimental evidence for internal structure in aqueous-organic nanodroplets.

The spatial distribution of species within an aerosol droplet influences how it interacts with its environment. Despite the ubiquity of multicomponent nanodroplets in natural and technological aerosols, there are no published measurements of their internal structure. Here, we report the first experimental results for structure in aqueous organic nanodroplets based on small angle neutron scattering by high number density aerosols. For H(2)O-n-butanol droplets, fitting of the diffraction patterns confirms the picture of an aqueous core containing approximately 3 mol% alcohol covered by a shell of densely packed alcohol molecules.

Kinetics of binary nucleation of vapors in size and composition space.

We reformulate the kinetic description of binary nucleation in the gas phase using two natural independent variables: the total number of molecules g and the molar composition x of the cluster. The resulting kinetic equation can be viewed as a two-dimensional Fokker-Planck equation describing the simultaneous Brownian motion of the clusters in size and composition space. Explicit expressions for the Brownian diffusion coefficients in cluster size and composition space are obtained. For characterization of binary nucleation in gases three criteria are established. These criteria establish the relative importance of the rate processes in cluster size and composition space for different gas phase conditions and types of liquid mixtures. The equilibrium distribution function of the clusters is determined in terms of the variables g and x. We obtain an approximate analytical solution for the steady-state binary nucleation rate that has the correct limit in the transition to unary nucleation. To further illustrate our description, the nonequilibrium steady-state cluster concentrations are found by numerically solving the reformulated kinetic equation. For the reformulated transient problem, the relaxation or induction time for binary nucleation was calculated using Galerkin's method. This relaxation time is affected by processes in both size and composition space, but the contributions from each process can be separated only approximately.

Nucleation rates of water and heavy water using equations of state.

The original formula of Gibbs for the reversible work of critical nucleus formation is evaluated in three approximate ways for ordinary and heavy water. The least approximate way employs an equation of state to evaluate the pressure difference between the new and old phases. This form of the theory yields a temperature dependence for the nucleation rate close to that observed experimentally. This is a substantial improvement over the most commonly used (and most approximate) form of classical theory.

Nucleation near the spinodal: limitations of mean field density functional theory.

We investigate the diverging size of the critical nucleus near the spinodal using the gradient theory (GT) of van der Waals and Cahn and Hilliard and mean field density functional theory (MFDFT). As is well known, GT predicts that at the spinodal the free energy barrier to nucleation vanishes while the radius of the critical fluctuation diverges. We show numerically that the scaling behavior found by Cahn and Hilliard for these quantities holds quantitatively for both GT and MFDFT. We also show that the excess number of molecules Deltag satisfies Cahn-Hilliard scaling near the spinodal and is consistent with the nucleation theorem. From the latter result, it is clear that the divergence of Deltag is due to the divergence of the mean field isothermal compressibility of the fluid at the spinodal. Finally, we develop a Ginzburg criterion for the validity of the mean field scaling relations. For real fluids with short-range attractive interactions, the near-spinodal scaling behavior occurs in a fluctuation dominated regime for which the mean field theory is invalid. Based on the nucleation theorem and on Wang's treatment of fluctuations near the spinodal in polymer blends, we infer a finite size for the critical nucleus at the pseudospinodal identified by Wang.