Alkanes are common in nature and are frequently used in various applications in chemical industries [1
]. While it’s not feasible to list all scientific and technological areas that involve alkanes, a few examples can provide a useful perspective on how the study of alkanes at the molecular scale can have a significant impact across many sectors of science and the economy. In particular, we wish to highlight that alkanes frequently occur in heterogeneous systems, composed of many molecules and phases at a wide range of pressures and temperatures. Petroleum is composed overwhelmingly of hydrocarbons and often a significant portion are alkanes [2
]. The process of refining and cracking crude oil entails an examination of alkane behavior in numerous environments and conditions [2
]. Methane and other small hydrocarbons occur in Earth’s atmosphere and are consequential greenhouse gases [3
]. Alkanes are much more reactive than CO2
, however, so they have far shorter lifetimes in the atmosphere [3
]. Their reactivity is important for their use in synthetic organic chemistry as well as linked to their hypothesized roles in the natural formation of complex organic molecules particularly in abiotic conditions. Venturing beyond Earth, these molecules are common in many extraterrestrial environments, comprising a significant portion of some planetary surfaces and atmospheres [5
]. Many of these examples feature complex mixtures of molecules, so the use and evaluation of robust, transferable force fields for such systems is an opportunity to look at more realistic systems without the need for time consuming parameterization or slower simulation protocols. Additionally, they often serve as the first molecules introduced in organic chemistry courses. Beyond pedagogical convenience, they are also important models of the driving forces underlying the behavior of hydrophobic molecules, particularly as they relate to biological questions, like protein folding [8
], protein-protein interactions [8
], lipid structure and dynamics [11
], and other topics. As such, their behavior provides context for the properties of hydrophobic molecules and is relevant for understanding a diverse set of natural and technological processes.
Despite their apparent simplicity and ubiquitous prevalence, alkanes remain a frequent topic of inquiry. Here we focus on normal alkanes, n-alkanes, which are hydrocarbon molecules with a linear chain of fully saturated carbon atoms. These molecules have general molecular formulas of the form CH3
or more compactly Cn
, where n is the number of carbon atoms in the molecule. The structure of n-alkanes was the topic of some of the first X-ray diffraction studies of aliphatic molecules in liquids [14
]. These studies helped establish and inform our understanding of molecular structure, like bond lengths, angles, and dihedral angles. Many of the small n-alkane liquids have received significant attention. For example, Habenschuss et al. used X-ray diffraction to study the structure of liquid methane [15
]. Despite methane itself appearing spherically symmetric in X-ray experiments, intermolecular structural correlations revealed distributions indicative of tetrahedral molecular symmetry [15
]. Similar studies have been reported for ethane [16
], propane [17
], n-butane [18
], n-pentane [19
], and so on. A common thread through these studies is that n-alkanes have increasing molecular flexibility with length and present richly complicated intermolecular structures. These studies go beyond understanding just the structure of the molecule itself but reveal correlations between multiple molecules. This permits the elucidation of solvation structure when n-alkanes are used as the solvent. Additionally, it has permitted the exploration of processes like solvation and desolvation of solutes, wetting and dewetting of surfaces, nucleation, etc. Indeed, in this work, we are particularly interested in the intermolecular structure of alkane liquids as a path to understand the thermodynamics of these systems. This liquid structure provides a new perspective on n-alkanes as solvents, but also on features specific to liquid phase behavior.
There have been numerous molecular simulation studies of n-alkanes, both examining their specific properties and as model systems to evaluate force fields and other aspects of simulation protocols [9
]. Density is frequently presented, because it is straightforward to determine, a holistic measure of force field performance, and typically unambiguously comparable with experimental results. Many force fields, developed with different philosophies and parameterized using many different strategies, have been shown to accurately reproduce experimental densities for these systems [9
]. Many force fields are specifically tuned to reproduce the density at some state point for the system of interest, but general force fields are constructed to on average provide adequate description of molecular interactions so that thermodynamic and dynamic behavior is suitably reproduced. As such, density serves as an important test of the performance of a molecular model.
In this work, we perform molecular dynamics simulations to examine the density and radial distribution functions of pure n-alkane liquids, from methane to pentadecane, to understand similarities and differences in the local structure of these liquids. We are specifically interested in the variation of liquid structure as the number of carbon atoms in the alkane increases. We find that there are several signatures of convergence with respect to chain length, depending on the property examined. This set of molecules is known to have trends in many thermodynamic properties with increasing n, which are often used to understand how intermolecular forces and molecular size affect thermodynamic properties (indeed they are often presented in general and organic chemistry to help new students understand relationships between molecule structure and emergent properties). Further, while this study does not directly consider mixtures, the convergence of properties for pure n-alkanes can be used to anticipate the onset, or conversely the breakdown, of ideal solution principles in mixtures.
The density and
are often viewed as important evaluations of the quality of a molecular model, especially the non-bonded terms. Figure 1
shows the density of each n-alkane at the normal (1 bar) boiling point. Figure 2
compares the simulations reported here with experimental densities via a parity plot. Table 2
from our simulations compared with experimental values.
Structure of the liquids is evaluated using radial distribution functions. In Figure 3
, we examine the radial distribution functions between all carbon atoms within a system. Further, in Figure 4
, we examine the local structure around specific carbon atoms. These compare the structure around the terminal carbon with all other carbon atoms (Figure 4
a), around the second carbon from the end (Figure 4
b), around the third carbon from the end (Figure 4
c), and so on. Both ends of each alkane are symmetric, so neither are shown. Only the longest alkane, pentadecane, has an interior carbon that is eight bonds from a terminal carbon, so it is the only molecule in Figure 4
We examined the free energy and entropy of binding in Figure 5
. The free energy of binding is calculated from the maximum value in the radial distribution functions shown in Figure 3
. The entropy of binding is determined from the free energy of binding in Figure 5
a as well as the analysis of another simulation 10 K below the boiling point of the molecule. Figure 5
a is the average free energy binding a carbon from a molecule in the liquid, so we also examine n ΔGbind
in Figure 6
, as a measure of the total average binding free energy holding each molecule in solution.
We have found that GAFF2 with charges parameterized with RESP reproduces liquid densities at the normal boiling point of n-alkanes from methane to pentadecane within an average deviation of 2%. All deviations in density are positive but deviations in are more complex. is overestimated for short alkanes but the increase with chain length is too small so it is underestimated for long alkanes. This suggests that revisiting the parameterization of aliphatic molecules could be a way to improve this force field for these types of molecules. We examine the local structure and resulting thermodynamics and show that the shortest n-alkanes have a distinct liquid structure, but based on radial distribution functions, the series is found to converge to similar distribution functions for longer alkane chains. Further, we found that the molecular structure around terminal carbon atoms depends sensitively on the chain length, but interior carbon atoms have a more uniform local solvation structure. Finally, we found that the binding free energy between carbon atoms becomes less favorable with increasing chain length. The longer alkanes have more carbon atoms “holding” onto each other, so the net free energy holding molecules in the condensed phase does not necessarily become less favorable.
This study supports using GAFF2 to model these systems, despite the disparity in some cases between the environments and physical conditions envisioned when the force field was developed. There are undeniably specialized force fields [22
] or even less empirical methods like ab initio molecular dynamics that can be used for these systems, but there are advantages to GAFF2. The diverse range of molecules that can be described by GAFF2, or conversely the difficulty of parameterizing new molecules or functional groups within the framework of more sophisticated force fields, makes GAFF2 a useful tool for atypical molecules. Additionally, since GAFF2 employs relatively simple functional forms, it can feasibly consider larger systems, which are often beyond practical limits for more computationally intensive methods. Therefore, approaches like those that we have presented here are an important tool for studying complex, heterogeneous systems like those where alkanes often occur.