Transfer of non-ionic surfactants across the water-oil interface: A molecular dynamics study

Colloids and Surfaces A: Physicochem. Eng. Aspects 506 (2016) 20–31

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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa

Transfer of non-ionic surfactants across the water-oil interface: A molecular dynamics study Tsvetan Krasimirov Zahariev, Alia Vitali Tadjer, Anela Nikolova Ivanova ∗ Laboratory of Quantum and Computational Chemistry, Faculty of Chemistry and Pharmacy, Sofia University, 1 James Bourchier Blvd., 1164 Sofia, Bulgaria

h i g h l i g h t s

g r a p h i c a l

a b s t r a c t

• Adsorption at and transfer of alkanols across water-oil interfaces are modelled. • Umbrella sampling simulations are performed to determine free energy profiles. • A new method for estimation of free energy group contributions is proposed. • A detailed analysis of free energy curves demonstrates specificity of functional groups impact.

a r t i c l e

i n f o

Article history: Received 9 April 2016 Received in revised form 6 June 2016 Accepted 7 June 2016 Available online 7 June 2016 Keywords: Water-alkane interfaces n-Alkanols Adsorption Interfacial transfer Molecular dynamics simulations Free energy calculations

a b s t r a c t Compounds able to adsorb at the interface of two immiscible liquids are of high importance for numerous chemical, physical and biological processes. Deeper understanding of the interfacial phenomena in such systems can contribute significantly to the rational practical application of small amphiphiles in electrochemistry, extraction, stabilization of emulsions, and drug design. Particularly interesting are the oil-water formulations, where the aqueous and the hydrophobic phases tend to express different molecular structure and characteristics under identical conditions. Surfactant behaviour in such environments is known to differ distinctly from the one observed in bulk water or oil or at the gas-liquid interface. It has been demonstrated that the free energy of adsorption and transfer of amphiphiles across water-oil interfaces can be decomposed into specific contributions of molecular fragments. The models developed so far do not provide information about the specifics of the functional groups contributions. To elaborate further on this topic, classical molecular dynamics simulations, combined with umbrella sampling calculations and weighted histograms method analysis are applied to reconstruct the free energy profile for several water-oil-amphiphile models along a relocation coordinate normal to the interface. Normal pentane, hexane, and heptane are chosen as models of the hydrophobic liquids and three short-chained normal alcohols—as low-molecular-weight amphiphiles. Gibbs energies of transfer and adsorption, as well as the average contributions per unit of elongation of the alkyl chain, are estimated and compared

∗ Corresponding author. E-mail addresses: [email protected]fia.bg (T.K. Zahariev), [email protected]fia.bg (A.V. Tadjer), [email protected]fia.bg (A.N. Ivanova). http://dx.doi.org/10.1016/j.colsurfa.2016.06.003 0927-7757/© 2016 Elsevier B.V. All rights reserved.

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to experimental data and empirical results. The experimental trends of all quantities are reproduced correctly. Some quantitative differences are discussed. A detailed analysis of the free energy change vs. position of alcohol molecules shows that the transfer process can be decomposed into several stages. Such more precise stratification of the interfacial region is employed to determine and rationalize the free energy contributions of the separate alkanol functional groups. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Adsorption of non-ionic surfactants at and transfer across the water-oil interface are less well understood than those at the airwater interface. Despite the common nature of the driving force for surface activity in both types of environments, there is a certain distinction between the thermodynamic and the structural characteristics of the processes at the two types of interfaces [1]. The behaviour of surfactants at the water-air and water-oil interface has been studied both theoretically and experimentally in the recent years [2–4] because of the importance of such phenomena for industrial, electrochemical and pharmaceutical applications [5,6]. Most of these applications involve the formation of monomolecular layers of amphiphilic species at the interfaces [7] or the incorporation of surfactants into certain amphiphilic environments, for example cell membranes [8,9]. Detailed knowledge of the energetics of the processes of adsorption at and transfer across hydrophilic-hydrophobic liquid interfaces enables the design of new surfactant or amphiphilic species with specific inherent properties, such as hydrophobicity, dipole moment, or conformational flexibility. A correct theoretical representation of these processes would allow such understanding. Theoretical elucidation of the process of adsorption and transfer of non-ionic surfactants with alkyl tails at/across the water-oil interface has been attempted at several levels of sophistication. An important starting point for its interpretation has been the rule of Traube [10], which paved the way for the concept that free energies of adsorption and transfer could be represented as a linear combination of hydrophobic and hydrophilic group contributions. Later, Langmuir [11] interpreted this rule as a linear dependence of the standard adsorption free energy on the number of methylene groups in the molecule. More recent statistical analysis followed by thermodynamic modeling of experimentally determined water-oil partition coefficients and adsorption constants of non-ionic surfactants [1,12], termed the mechanistic model further on, demonstrated that methylene groups in a hydrocarbon alkyl chain have similar contributions to the free energy of transfer, which are larger for water-oil interfaces than for water-air surfaces. Another angle of looking at the phenomena at aqueous interfaces with non-polar substances is by employing the so-called ‘hydrophobic effect’ [13], which may be described by contemporary hydrophobic solvation theories. The phenomenon is rooted in the strong affinity of water molecules to form hydrogen bonds, which are lost when hydrophobic or amphiphilic compounds are introduced. This provides a qualitative explanation of the adsorption, aggregation and amphiphile relocation processes at the water-air surface: they result in a decreased number of water molecules involved into hydrophobic hydration, i.e., the entropy of the system is increased. In an oil phase, hydrophilic compounds and amphiphiles could participate in similar processes, yet the driving force is different: uncompensated electrostatics of charged or polarized fragments. A quantitative description of all interactions mentioned above is not simple and requires a detailed model for molecular solvation mechanisms and solute structure. Several

more elaborate theories have been developed on the basis of statistical mechanics equations and have been tested by molecular simulations [14–17]. They are mostly based on the division introduced by Pratt and Chandler [18] that the free energy of solvation can be decomposed into a cavity formation and an intermolecular attraction term. The latter could be evaluated from radial distribution functions, while the former is not so easily calculated. The Scaled Particle Theory (SPT1 ) [14] gives an analytical expression for this term needed to arrange the hydration shell of a hard sphere that does not interact with the solvent based on the radius of the cavity. This approach has a limited applicability, as its main strength could be expressed in determination of the effective van der Waals diameter of the water molecule ␴ww [19]. An information theory (IT2 ) approach [20], introduced by Hummer [21–23], relies on estimation of the probability of finding n water oxygen centres inside a randomly positioned observation volume of size and shape corresponding to the solvent-excluded volume of the solute. It can be evaluated on the basis of information available from simulations, such as water density, radial distribution function, and isothermal compressibility. This theory provides a good qualitative explanation of the hydrophobic effect manifestation and its temperature dependence, yet it does in some aspects contradict experiment. Moreover, like SPT, it does not enable detailed microscopic insight into the hydration shell formation and structure. In order to fill this gap, the Quasi-Chemical Theory (QCT3 ) has been developed [17]. In its framework, the formation of a cavity is treated as an equilibrium process, described by an equilibrium constant. Determination of the excess chemical potential of a solute is then calculated from these equilibrium constants and from the local density of the solvent. Such an approach provides more insight into the thermodynamic origin of formation of hydration structures. It also allows taking into account correlation effects that are manifested during solvation of non-spherical structures. A generalized view of the solvation processes at present is that surfactant behaviour in different liquid environments is a result of the specific molecular packing and the balance of hydrophobic-hydrophilic solute-solvent interactions [24,25]. The models mentioned in the previous paragraph are referred to as molecular theories below. A third approach for theoretical description of adsorption at and transfer across water-oil interfaces of non-ionic surfactants is the computational modelling. It is gaining momentum but at present there is a limited number of applications to the particular process. Molecular dynamics (MD) simulations of small hydrophobic compounds (including short-chained alkanols from C1 to C6 ) and their behaviour in water-oil systems have revealed that the nonpolar liquids contained larger amounts of the solutes than water [2,3,26–30]. In addition, reconstruction of the free energy profile A(z) for transfer of amphiphiles along the interface normal has been reported. The obtained curves are smooth functions of the coordinate perpendicular to the interface. Constant values of the

1 2 3

SPT—Scaled Particle Theory. IT—Information Theory. QCT—Quasi-Chemical Theory.

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free energy (plateaus) are observed in the regions corresponding to bulk water and oil, while the positions close to the interface are characterized by a potential well with energy lowering of ca. −23.73 kJ mol−1 relative to bulk water and −17.50 kJ mol−1 with respect to bulk oil (hexane) for hexanol [28]. For short-chain alkanols (propanol) Patel and co-workers [3] have reported values of −6.69 kJ mol−1 relative to water and −20.82 kJ mol−1 with respect to oil (hexane). These results enabled the determination of the standard Gibbs energies of adsorption at the water-hexane interface and transfer from bulk water to bulk hexane. It has also been observed that upon elongation of the alkyl chain in the alcohol it became more hydrophobic, i.e., the Gibbs energy of transfer between water and oil lowered with each CH2 -group. While homologues from C1 to C4 tend to be more hydrophilic, normal alcohols with higher number of carbon atoms prefer the hydrophobic medium. Comparison between the main concepts in the molecular and the mechanistic approach indicates that the empirical findings can be rationalized in more detail by computational simulations. Therefore, the aim of the present paper is to describe the behaviour of simple amphiphiles during their relocation from bulk to interfacial water and oil phases and then to bulk oil by atomistic molecular dynamics computations and to provide more in-depth interpretation of the process at molecular level with details not reported before. The current work differs from the previous ones [3,28] in several aspects: longer-chain alkanols (pentanol, heptanol) are included, the influence of the particular type of molecules forming the oil phase is systematically checked, and more exhaustive and methodical analysis of the free energy curves is carried out. 2. Thermodynamics of adsorption and transfer The process of transfer between the aqueous and the oil phase is characterized by the Gibbs energy Gw o , the enthalpy Hw o , and the entropy Sw o of transfer of the surfactant. For an ideal solution, the chemical potentials w and o of the surfactant in the aqueous and in the oil phase are: w

 =

w 0

w

o

+ RT ln c ;  =

o0

o

+ RT ln c .

(1)

Here, cw and co are the bulk concentrations of the amphiphile in water and in oil. The standard potentials 0 w and 0 o are equal (within the accuracy of the calculations) to the free energies Gcalc w and Gcalc o of a surfactant molecule in the respective phase (Eq. (2)), which can be obtained from MD simulations [28,29,31]. Based on the condition that the chemical potentials of the surfactant in both phases should be equal (w = o ) at equilibrium, one easily obtains the relation between the Gibbs energy of transfer Gw o to the standard chemical potentials and to the partition coefficient PC : o o w Gw = o0 − w 0 = Gcalc − Gcalc , o Gw

i w = i0 − w = Gcalc − Gcalc , 0

Ea = CH3 + (n − 1) CH2 + A − o ˛⊥ .

(3)

(o−i)

Ga

i o = i0 − o0 = Gcalc − Gcalc ,

(4)

where the superscript “i” denotes the respective quantities at the interface.

(5)

Here,  o denotes the tension characterizing the pure interface, ˛⊥ is the cross-sectional area of the hydrocarbon chain with length n, CH3 is the contribution of the terminal methyl group to the standard adsorption free energy of the alkanol, while CH2 and A are respectively the average free energy change per methylene group and the adsorption free energy of an arbitrary head-group during water-to-oil translocation. Using the thermodynamic parameters from Eq. (5) and including a correction for the loss of rotational potential energy, Slavchov and Ivanov [1,35] derived an expression for the variation of the free energy with the coordinate normal to the interface A(z):

A (z) =

co = −RT ln w = −RT ln PC . c

(w−i)

Experimentally, free energies of adsorption can be measured from extrapolating the concentration dependence of surface pressure or surface tension to infinite dilution. There are free energy data for n-pentanol, n-hexanol, and n-heptanol at the water-alkane interface extracted from tensiometric measurements [33]. Within the contemporary mechanistic model (a synopsis is given in the Supplementary Material and complete derivation can be found in Ref. 1) the process of transfer of non-ionic surfactants (n-alkanols from C4 to C18 [1] and ethylene glycols from C3 to C5 and from E1 to E4 [34]) from bulk water across the interface to bulk oil is quantified by the water-oil partition coefficient. It is expressed by the ratio of the water-to-interface adsorption constant (Ka w ) and the interface-to-oil desorption constant (Kd o ) defined in a specific manner. The expression for the adsorption free energy Ea (defined in a particular way) is then transformed to:

(2)

Eq. (3) can be used to estimate Gw o experimentally. This has been done by performing interferometric measurements for the transfer of n-pentanol, n-hexanol, and n-heptanol from water to three oils – octane, dodecane, and hexadecane [32]. The respective energies of adsorption from each of the bulk phases to the interface can be calculated in a manner similar to Eq. (2) from MD simulation data: Ga

Fig. 1. Excess free energy variation for transfer of an alkyl-tail surfactant molecule from bulk water to the water-air interface.

⎧ ⎪ ⎨ ⎪ ⎩

0, Ea − kT ln 2 − |CH2 | ∞,

z , lCH2

z ≤ −nlCH2 −nlCH2 < z < 0; z ≥ 0.

⎫ ⎪ ⎬ ⎪ ⎭

(6)

where A(z) is the excess free energy of the system, CH2 is the average contribution to the adsorption free energy of a single methylene group, and lCH2 is the diameter of the latter. This is illustrated graphically in Fig. 1. To evaluate the analytical A(z) dependence (Eq. (5)) for a given surfactant, one needs to determine the specific thermodynamic parameters CH3 , CH2 , A , and ˛⊥ . In the work of Slavchov et al. [1] the parameters are adopted from experimental data [36–39]. However, they may be evaluated independently from molecular simulations. Estimation of  of the different functional groups is one of the aims of the present study. Also, an attempt is

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Fig. 2. Models of the n-alkanol homologues (left) and an example of the periodic box used in the simulations (right); carbon atoms are coloured in cyan, oxygen atoms – in red, and hydrogens – in white. A space-filling model of the alkanol shows its initial placement in the box; two of the coordinate system axes are denoted – z is always normal to the water-oil interface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

made to clarify the origin of this change in the chemical potential per group during interfacial transfer. CH2 = ∂G/∂n is the central parameter of interest and is a measure of the hydrophobicity of the methylene group. Since its value depends on the phases that serve as media for the relocation processes, it should be different in magnitude for water-air or water-oil systems. A wide selection of experimental methods has been applied to estimate this parameter. Experiments for water-air interfaces [1,31] confirm the original result of Traube: CH2 ≈ kT ln3 ≈ −1.099 kT. On the other hand, it has been proven that for water-oil interfaces the change of the chemical potential is larger [1,34,40–42]. Different studies report numbers of the same order of magnitude with relatively minor span: from −1.39 kT to −1.45 kT (Table S1 of the Supplementary material). An interesting observation is made by Manabe et al. [40], namely, CH2 , obtained for normal alkanols from ethanol to hexanol yield an average value of −1.44 kT. Slavchov et al. [12,34] found values −1.04 kT for water-air surface and −1.39 kT for water-oil (dodecane) interface. At present, these results could be considered the most accurate ones, as the data set that was used was significantly larger than the ones in the preceding studies. The specific target of the current study is to simulate with MD the processes of adsorption at and transfer of simple nonionic amphiphiles across the water-oil interface. Evaluation of the free energy profiles for several simple species would allow obtaining more detailed information and eventually correlating the free energy change to thermodynamic and structural parameters of the model systems, estimating from molecular simulations some of the terms in Eqs. (5) and (6). 3. Molecular models and computational methods 3.1. Model systems Non-ionic surfactants are considered appropriate model systems to transfer across the water-oil interface, since the electrostatic component of the intermolecular and intramolecular interactions is weaker than for the ionic ones and will not mask the influence of finer effects. Two typical groups of non-ionic surfactants are the normal alkanols (Cn H2n+1 OH) and the alkyloligoethylene glycol ethers (Cn Em ). The low-molecular-weight members of the first group are widely applied anaesthetics that affect such significant biological processes as membrane fusion [43] or the modulation of the receptor activity [8]. Therefore, three representatives, namely, n-pentanol, n-hexanol, and n-heptanol, are chosen as model amphiphiles. The model systems used in the present study consist of periodic boxes with repeating water and oil slabs. Half of each box volume is filled with explicit water molecules and the other half

– with explicit alkane molecules. The placement of the slabs is illustrated in Fig. 2. Three normal low-molecular-weight alkanes – pentane, hexane and heptane, are chosen to represent different oil phases. The molecular models used to simulate these liquids have been reported in a previous work [44]. The oil layers contain between 250 and 350 alkane molecules. The water phase is built of ca. 2200 molecules. In the initial configurations one alkanol molecule is placed in the aqueous bulk phase (Fig. 2). The structural parameters of the nine simulated model systems are listed in Table S2 of the Supplementary material. Periodic boundary conditions are applied in all directions. 3.2. MD parameters and equilibrium simulations All MD simulations are performed with the GROMACS 4.5.2 and GROMACS 4.6.5 packages [45]. The molecular mechanics force field AMBER99 [46] is employed for the alkanes and alkanols and the model TIP4P [47] – for water. The statistical ensemble is NPT where the system temperature is rescaled at every 0.1 ps and the system pressure – at every 5 ps. Constant temperature of 298 K and pressure of 1 bar are maintained with the Berendsen thermostat and barostat [48]. Long-range electrostatics is estimated with РМE [49]; non-bonded and short-range electrostatic interactions are truncated at 1.2 nm and 1.4 nm, respectively, with a switch function activated at 0.2 nm less than the cut-off distance. The algorithm LINCS [50] is used to constrain the length of the hydrogen-containing bonds in alkanes and alkanols and SETTLE [51] is applied for holonomic constraints of water. Long-range corrections (LRC) for energy and pressure are calculated at each time step. After an equilibration stage, trajectories of length 50 ns are generated and analysed statistically including frames taken at every 1 ps. The same MD parameters are applied also during the free energy simulations. 3.3. Free energy calculations To simulate the free energy profile along the transition coordinate (in all systems coinciding with the z axis), the Umbrella sampling (US) procedure is applied [52,53]. In order to sample initial configurations for the US simulations, the n-alkanol molecule is pulled with constant force of 250–300 kN [54] along the transition coordinate from the water bulk towards the alkane slab for 1 ns. The frame at time 50 ns from the equilibrium MD runs is used as the starting configuration. During the pulling runs the molecule passes several times through the whole length of the box. The generated trajectory is then used to extract initial frames for the US windows spaced at intervals of 0.08–0.1 nm along z. For each window, a harmonic restraint is applied to the distance along the z coordinate between the center of mass (COM) of the alcohol and the

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Fig. 3. (Top) Relative free energy profiles for transfer of the alkanols from water to oil (pentane to heptane from left to right) along the z-coordinate of the periodic box. The minima of the curves correspond to z = 0; (bottom) Mass density profiles of water and alkanes with notation of the equimolecular dividing surfaces showing coincidence of the interface position with the minima of the PMF curves.

water subphase. This distance is selected as the transfer coordinate and is increased from 0 to 4 nm at steps of 0.08 nm between the centres of the neighboring windows, which corresponds to 45–50 windows and complete transfer of the alkanol from the aqueous to the oil phase. The force constant of the restraining potential is set to 1500 kJ mol−1 nm−2 [54]. 1 ns equilibration and 10 ns productive runs are generated for each window to accumulate data for the statistical processing. To estimate the free energy along the relocation coordinate, WHAM [55,57] analysis is carried out. The obtained potential of mean force (PMF) profiles, corresponding to the free energy variation during the alkanol transfer across the interface, are plotted and analysed in detail in order to obtain the thermodynamic parameters of interest. The intramolecular degrees of freedom of the alkanol molecules are kept fixed to the all-trans conformation throughout all stages of the free energy simulations by applying a harmonic potential with a force constant of 150 kJ mol−1 nm−2 for the hydrocarbon fragment and 175 kJ mol−2 nm−2 for the OH group along x and y, and 3 kJ mol−1 nm−2 for all atoms in the molecule along z. The orientation of the alcohol molecule is also fixed – its OH group always points towards the water phase. The imposed restraints lead to a fixed all-trans conformation and an orientation of the molecular long axis normal to the interface. This geometry is selected for two reasons: (i) it allows unequivocal definition of individual group contributions to the free energy changes during the molecule relocation in the model systems (Section 4.3); (ii) comparison to the findings of the mechanistic model described above is straightforward. This structural approximation does not result in significant inaccuracy of the obtained results because the all-trans geometry and the perpendicular orientation of the alcohol towards the interface are statistically the most probable ones (detailed justification of the representability of the amphiphile model is provided in the Supplementary material, Figs. S1, S2, and in Ref. [58]). The Umbrella sampling procedure is applied to all 9 model systems. In 8 of those convergence and window overlap were sufficient

to extract a smooth free energy profile. In the case of the model system water-hexane-heptanol the obtained profile was not credible due to poor positioning and overlap of the windows, which could not be improved after several attempts. Therefore, this system is excluded from the analysis. 4. Results and discussion 4.1. Free energy profiles The simulated potentials of mean force, which reflect the free energy variation, are usually represented as function of the centerof-mass position of the alkanol along the z-coordinate, which is the transfer coordinate. However, in the studied systems the minimum of the curve does not match the position of the alkanol COM. Therefore, it is more convenient to draw the free energy profiles as functions of the position of the alkanol ‘hydrophilic-lipophilic center’ (HLC, defined after inspection of the atomic charge distribution as the center of the O C distance along z), which coincides with the minimum of the curve for all models. On the ordinates, the relative free energy is given, which is obtained by subtracting the lowest energy for a given system from every other energy value for this system. The results are shown in Fig. 3. It is evident that because of the similar structure of the solutes the profiles follow identical patterns. The energetics is also not influenced by the type of the oil, which is due to the very similar characteristics of the three liquids [44]. The minima of the curves (z = 0) correspond to the approximate positions of the equimolecular dividing surfaces (Fig. 3, bottom). The left plateaus in the graphics correspond to the free energy of an alkanol dissolved in the water phase, while the right ones – to complete immersion of the solute in the alkane oil. Comparison of the curves corresponding to the individual models leads to several important conclusions. The location of the free energy minima at the interface reproduces the expected energy

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Table 1 Free energies of alkanol adsorption from water (Gɑ (w−i) ) and from oil (Ga (o−i) ) and of transfer between the two bulk slabs (Gw o ) estimated from the MD simulation data (calc); statistical errors are obtained by the bootstrap procedure [56,64]. Empirical values (emp) from measurements at 20 ◦ C are provided for comparison [32,33]. Deviations between calculated and empirical data (␦G = 100 × |[G(calc) − G(emp)]/G(emp)|) are also included. Oil

Alkanol

G(w−i) [kJ mol−1 ] calc

n-C5 H12

n-C6 H14

n-C7 H16

Oil

C5 H11 OH C6 H13 OH C7 H15 OH C5 H11 OH C6 H13 OH C7 H15 OH C5 H11 OH C6 H13 OH C7 H15 OH

−24.93 ± 1.24 −28.79 ± 8.65 −34.94 ± 2.66 −23.00 ± 1.25 −26.88 ± 1.91 – −23.29 ± 1.92 −26.63 ± 2.87 −31.25 ± 2.66 Alkanol

G(o−i) [kJ mol−1−1 ] empa

␦G[%]

calc

−27.82 −31.56 −34.44

10.39 9.62 −1.43 17.32 17.42 – 16.28 18.52 10.19

−17.24 ± 4.04 −16.85 ± 10.32 −17.14 ± 5.04 −16.90 ± 1.93 −17.28 ± 2.49 – −15.50 ± 3.21 −16.39 ± 4.06 −17.27 ± 3.23

n-C6 H14

n-C7 H16

C5 H11 OH C6 H13 OH C7 H15 OH C5 H11 OH C6 H13 OH C7 H15 OH C5 H11 OH C6 H13 OH C7 H15 OH

␦G[%]

−23.64 −24 −23.71

27.07 29.79 27.71 28.51 28 – 34.43 31.71 27.16

Gw o [kJ mol−1 ] calc

n-C5 H12

empa

−7.69 ± 2.76 −11.94 ± 3.13 −17.80 ± 3.24 −6.10 ± 1.35 −9.59 ± 1.08 – −7.79 ± 1.73 −10.24 ± 1.31 −13.98 ± 1.18

empb

␦G[%]

−4.01 to −4.83 −6.74 to −7.50 −10.11 to −10.85

91.77 77.15 76.06 52.12 42.28 – 94.26 51.93 38.28

a The oil is dodecane; the reported values correspond to standard state of 1 mN m−1 surface tension, unity mole fraction of the alkanol in the oil, and unity ratio of adsorption layer thickness vs. molar volume of the oil. b The two given values for each system are from two measurements – octane (left) and dodecane (right); the experimental errors fall between 0.05 and 0.15 kJ mol−1 ; change of the oil from dodecane to hexadecane results in variations of the data within the error; standard state is the same as above.

preference for adsorption of the amphiphiles. The relative energy of the two plateaus reveals that the three alkanols dissolve favourably in hydrophobic solvents, which is in accordance with previous theoretical findings [3,28] and with the partition coefficients of these alcohols [32,40,59]. The curves are almost identical for the different solutes. More specifically, the transfer from the interface to the bulk oil phase is insensitive to the type of oil or alkanol whereas the adsorption from water depends on the specificity of the alcohol. A possible explanation is that the energetics of the transfer process is a balance between the hydration and dehydration interactions of the alkanol hydroxyl group in the two liquid phases. This has already been commented in the works of Pohorille and co-workers [28] and Patel and co-workers [3]. Moreover, in accordance with the results reported by these two research groups (Table S3), the relative free energies corresponding to immersion into bulk water are higher for the alcohols with longer chains. This comparison confirms that the free energy profiles in this work are a correct representation of the actual systems. The width of the potential well, which can be estimated from the distance between the two plateaus at its termini, is expanding slightly with elongation of the hydrophobic tail of the alkanol. This expansion for the alkanols with longer chain is due to the fact that the longer alkyl chains start penetrating the interfacial area at distances, which are farther apart from the dividing surfaces. Since the geometry of the alkanols is fixed in an all-trans conformation, linear contributions of the similar functional groups to the overall length of the molecule (calculated as the difference between the z-coordinates of the terminal atoms) can be assumed. Then, extension of the alkanol by a single methylene group should widen the potential well by a constant increment. If the distance between the points separating the water and oil bulk regions from the interfacial layers (Fig. S4) is plotted against the number of carbon atoms in the alkanol, this would allow determination of the effective length of one methylene group. An example is shown in Fig. S4 with plots for the pentane-water-alkanol and heptanewater-alkanol systems. The respective estimates for the effective

length of one methylene group, obtained from this analysis, are 0.14 nm and 0.11 nm. Due to the limited dataset the statistical accuracy is not high. Yet, the average is 0.125 ± 0.02 nm, which deviates insignificantly from the crystallographic result of 0.126 nm [60] and is used further on for lCH2 (Eq. 6). 4.2. Free energies of adsorption and transfer The data in Fig. 3 enable estimation of the free energies of adsorption from water (Gɑ (w−i) ) or from oil (Gɑ (o−i) ) to the interface and also of the free energy of transfer from water to oil (Gw o ). Eqs (4) and (2) were used for the purpose. To obtain the free energy values for the two bulk phases (Gcalc w and Gcalc o ), the G(z) data from the respective bulk regions of the PMF profiles were averaged: from z = −2.0 nm to z −1 nm for water and from z 0.6 nm to z = 1.25 nm for oil (Fig. 3). These points correspond to the amphiphile entering the interfacial slab at one of the intervals ends and to its HLC being located in the middle of each bulk slab at the other end. The free energy value at the minimum of each PMF curve, i.e., the relative free energy at the interface, was used as Gcalc i in Eq. (4). The results are given in Table 1. Comparison between the theoretical and the empirical (obtained from interferometric and tensiometric experiments [32,33]) results shows the same trends, namely, that adsorption of the alkanols at the water-oil interface is favourable from energetic point of view. For all systems Gɑ (w−i) is more negative than Ga (o−i) , which means that desorption from the interface to water is more difficult than to oil. Considering also the negative values of the free energy of transfer from water to bulk oil confirms the observation made above that solvation of the three alkanols in oil is more preferable than in water. This coincides with experimental solubility data for these compounds in the two types of solvents [28,61,62]. Both theoretical and experimental values of Gɑ (w−i) and Gw o become more negative upon elongation of the alkanol hydrophobic tail. Consequently, the molecular models reproduce properly

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the enhanced hydrophobic character of the longer-chain alcohols. The numerical estimates of Gɑ (w−i) deviate from the empirical ones by 2–18% (0.5–4.9 kJ mol−1 with mean statistical error of ca. 2 kJ mol−1 ). This mismatch can be explained with the positional restraints applied on the alkanols, which result in higher energy barriers for the intramolecular degrees of freedom [63] and do not permit more compact geometry of the alkanol in the aqueous phase. This effect has been demonstrated for the first time by Pohorille and Benjamin who carried out MD simulations of p-n-pentylphenol at the water-vacuum interface [57]. They have shown that very close to the interface restraints were not essential because the amphiphiles were mainly in extended conformation. However, the influence was stronger when the surfactants were in bulk water where the hydrophobic effect required minimum volume of the solvated amphiphile. In order to determine the influence of the restraints on the free energy profiles in the systems studied herein, a pulling + Umbrella sampling simulation was carried out for the model water-pentanepentanol without conformational restrictions on the alcohol. The energy barriers were lowered by 2–4 kJ mol−1 . This means that the influence of the restraints is comparable to the deviations between theoretical and experimental free energies. It is also noteworthy that the results obtained in this study are very close to values from MD simulations reported earlier [3,28]. The adsorption free energy Gɑ (w−i) for the system water-hexanehexanol of Pohorille and co-workers (Table S3) differs only by about 2 kJ mol−1 from our estimates and by ca. 8 kJ mol−1 from the experimental results of Aveyard et al. [33] (Table 1), which indicates that the current assessments are a slight improvement over the existing simulations with non-polarizable force fields. The reason for the larger deviation of the data of Pohorille and co-workers may be sought in the shorter runs for the umbrella sampling windows (0.5–2.0 ns) and in the larger separation of the windows. The differences of the calculated Gɑ (o−i) from the empirical estimates are more substantial (27–34%). They correspond to absolute deviations of 6–8 kJ mol−1 with mean statistical error of ∼3 kJ mol−1 . Several reasons for that can be outlined. First, the employed force field does not take explicitly into account the molecular polarizability. As a result, the electrostatic interactions in the systems are not utterly precise. This drawback is compensated in the aqueous phase by the atomic charges of the water molecules, which are fit in a way, which takes into account the polarizability implicitly. However, such adjustments are not made in the force field for the alkanes. Second, the imposed positional restraints on the alkanols in directions x and y do not allow the molecules to orient in a more advantageous way with respect to the interface. Analysis of the pure water-alkane interfaces has shown that the alkyl tails there are tilted at ca. 30◦ (Fig. S5), while in the umbrella sampling simulations the angle to the interface is fixed at 90о . These two factors explain the observed dissimilarities. Comparison of the experimental data to previous theoretical estimates of Gɑ (o−i) shows a systematic difference between the simulations and the measurement techniques. The values of this quantity extracted from the PMF profiles of Pohorille and coworkers and Patel and co-workers (Table S3) vary in the range 18–21 kJ mol−1 . It is important to specify that the upper bound is for short-chain hydrophilic alcohols (methanol, ethanol) and the lower bound is for n-hexanol and is very similar to the estimates in the current study. Our data come from larger statistical samples and narrower windows but are based on smaller number of conformations and orientations than in the previous reports [3,28]. Possible reasons for the mismatch may also originate from the processing of the experimental data or from the approximations made during the MD simulations. The theoretical estimates can be improved quantitatively by using larger models (in terms of

thickness of the water and oil slabs), longer simulations with nonadditive force fields, and relieved positional restraints. However, the current data are already semi-quantitative and serve well the purpose of the study. The theoretical estimates of Gɑ (o−i) reproduce the experimental trends. There is no change of the adsorption free energies from the oil upon elongation of the alkyl chains of alkanols or alkanes. This is an indication that the main contribution to the free energy of adsorption stems from the electrostatic and H-bonding interactions of the hydroxyl group, while the coupling between alkyl chains of various length is analogous. The MD-calculated free energies of transfer from water to oil are more negative than the empirical ones. The relative differences vary from 38 to 92% but the absolute deviations are within 3–5 kJ mol−1 , which is almost entirely within the statistical accuracy (Table 1). The trend of Gw o upon alkyl chain elongation is reproduced correctly. It should be noted that there is no systematic accumulation of error for any of the theoretically evaluated parameters. Based on that and on the discussion so far, it may be concluded that the employed atomistic model describes adequately the adsorption and transfer of the selected amphiphiles across the water-alkane interface. Some specific parameters of this process are evaluated next, including values for the enthalpy and entropy of transfer (see the Supplementary material, Figs. S6 and S7). 4.3. Effective contributions of the functional groups The main purpose of the study is determination of CH2 in Eq. (6) from the MD simulation outcome. The data for Gɑ (w−i) from Table 3 can be used in a linear fit of the dependence introduced by Duclaux and Traube: Ga = Go + nCH2 (Fig. S8). An alternative approach to obtain the free energy contributions from the separate functional groups of the alkanols is to estimate the derivative ∂A(z)/∂z in the PMF regions between −1.0 nm and −0.25 nm, where the profiles are linear (Fig. 3). According to Eq. (6), this derivative should satisfy the relation:

∂G CH2 . = lCH2 ∂z

(7)

Therefore, the chemical potential contribution of a single group is calculated as follows: CH2 =

∂G lCH2 , ∂z

(8)

where the derivative of the free energy is evaluated from a linear fit (details are given in the Supplementary material, Fig. S9) of the G(z) data in the above-mentioned intervals. It needs to be stressed that the obtained values of  include also the effect of the terminal methyl and hydroxyl groups on the free energy changes. So, they should be regarded as average shares per functional group of the alkanols and not solely per methylene group. Both methods were implemented to obtain estimates of CH2 . The results are listed in Table 2. The two approaches yield similar results. The values achieved for each of the three alkanols by differentiation (Eq. (8)) deviate from the ones extracted from experimental data by ∼0.04 kT units on average. The smallest deviation is 1.44% and the largest one is 16.55%, which shows that the overall agreement is very good. The usage of adsorption energy values (Fig. S8) leads to results that are somewhat overestimated relative to experiment but this is not unexpected given the systematically higher adsorption energies (Table 1). Overall, both methods can be applied to obtain estimates for  of the functional groups from molecular simulations. Differentiation of the PMF, however, allows specificities of the particular system to be captured.

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27

Table 2 Estimates for the chemical potential change per single functional group obtained using Eq. (8) (denoted as calc) and by a linear fit of the adsorption free energy Gɑ (w−i) data as a function of the chain length (fit). ␦1 ␮CH2 and ␦2 ␮CH2 are the respective deviations from the mechanistic model values (emp) extracted from Slavchov et al. [1,12] and Grozev et al. [34]. Oil

Alkanol

␮CH2 [kT]

C5 H11 OH C6 H13 OH C7 H15 OH C5 H11 OH C6 H13 OH C7 H15 OH C5 H11 OH C6 H13 OH C7 H15 OH

n-C5 H12

n-C6 H14

n-C7 H16

calc

fit

emp

␦1 ␮CH2 [%]

␦2 ␮CH2 [%]

−1.37 ± 0.05 −1.31 ± 0.45 −1.54 ± 0.02 −1.41 ± 0.34 −1.34 ± 0.27 – −1.34 ± 0.19 −1.62 ± 0.20 −1.48 ± 0.14

−2.02 ± 0.27

−1.39 ± 0.03

1.44 5.76 10.79 1.44 3.60 – 3.60 16.55 6.47

45.32

–

−1.61 ± 0.15

–

15.83

Table 3 Chemical potential variation of the functional groups () of pentanol for transfer between bulk water and interfacial water (␣), from interfacial water to the ISR (␤), from the ISR to the interfacial oil (␥), and from the interfacial to the bulk hydrocarbon layer (␦) scaled to identical z increment and averaged for the three oils.  [kJ mol−1 ]

CH3 CH2 (a) CH2 (b) CH2 (c) CH2 (d) OH

␣

␤

␥

−0.13 ± 0.05 −0.30 ± 0.04 −0.35 ± 0.06 −0.40 ± 0.19 −0.39 ± 0.22 −0.48 ± 0.22

−0.11 ± 0.39 0.04 ± 0.41 −0.22 ± 0.09 −0.12 ± 0.07 −0.02 ± 0.02 0.04 ± 0.06

−0.29 ± 0.20 −0.28 ± 0.08 −0.20 ± 0.02 −0.06 ± 0.05 −0.02 ± 0.04 0.09 ± 0.05

It is evident from the data that there is no systematic trend of ␮CH2 for the different model systems – it varies in the same narrow range irrespective of the oil or of the alkanol. This corresponds to the findings within the mechanistic model. The reason for the maximum 10–15% of discrepancy should be sought in the differences between the simulations and the mechanistic model. Despite its pragmatically developed base and good parametrization, the model of Slavchov and Ivanov has some limitations and so do the MD simulations. The interface in the mechanistic model is represented as a two-dimensional surface, while there should be a perturbed-density layer with non-zero thickness (as evidenced from the mass density profiles, Figs. 3 and S3), which is characterized by specific properties and molecular ordering. The statistical accuracy of the values extracted from MD, on the other hand, would depend on the quality of the PMF. Neither the mechanistic model, nor the simulations take into account any conformational changes in the molecular structure of the alkanols. Results from MD simulations of p-n-pentylphenol at the watervapour interface [57], however, have shown that the orientation and conformation of the alkyl chain depended to some extent on the position of the surfactant with respect to the water surface. Also, in the simulation profiles for water-oil systems, the PMF curve is smooth and does not indicate any sudden jumps as in Fig. 1. Therefore, it is hard to determine a constant parameter for the surface area vacation in Eq. (6). A good explanation of these effects is given by the molecular theories of solvation [14–17]. Even though quite accurate, the two methods suggested for calculation of  provide only average contributions to the free energy change of each functional group from the alkanols. In order to understand better the specifics of CH2 , a more detailed partitioning of the transfer process is needed. The contribution of a single methylene (functional) group to the free energy change may be regarded as an average of the shares of all groups because they are correlated. One option to obtain it is to analyse the free energy profile on the basis of the positions of the individual functional groups corresponding to a certain z-position of the solute molecule, i.e., to a definite free energy of the system. The purpose of this analysis is to develop the phenomenological concept based on the classical

␦ 0.13 ± 0.08 0.21 ± 0.05 0.28 ± 0.12 0.32 ± 0.04 0.22 ± 0.12 0.54 ± 0.32

␣+␤

␣+␤+␥

−0.24 ± 0.39 −0.25 ± 0.45 −0.57 ± 0.15 −0.52 ± 0.17 −0.41 ± 0.23 −0.45 ± 0.23

−0.53 ± 0.21 −0.53 ± 0.37 −0.77 ± 0.17 −0.58 ± 0.23 −0.43 ± 0.23 −0.36 ± 0.18

␣+␤+␥+␦ −0.40 ± 0.26 −0.32 ± 0.40 −0.49 ± 0.22 −0.26 ± 0.19 −0.21 ± 0.27 0.18 ± 0.20

Gibbs representation of the liquid–liquid interface and the assumption that all functional groups of a certain type contribute equally to the free energy changes in the system. Our extension is based on two foundations: (1) each functional group could make a specific contribution, depending on its intramolecular position, and (2) during its translocation, the target molecule enters regions of varying density, where the effective intermolecular potential (both electrostatic and non-electrostatic) applied on it depends on the distance from the interface. Both theoretical and experimental studies indicate that the water-oil interfaces that are molecularly sharp (immiscible) [65], at the molecular level are actually characterized by intrinsic width of a perturbed-density layer broadened by capillary waves [66]. A realistic model of the solute relocation processes would then include three basic steps: (1) transfer from the bulk to the interfacial water layer; (2) transfer from the interfacial water to the interfacial oil layer; (3) transition from the interfacial to the bulk oil region. Reconsidering the sharp interface often accepted in thermodynamics leads to the idea of an intermediate step between (2) and (3), which is in fact the insertion of the solute in the region between the immiscible fluids, i.e., between the equimolecular dividing surfaces of water and alkane (termed below inter-surfaces region or ISR). According to our estimates the magnitude of this separation is ca. 0.1 nm and since it permits accommodation of a functional group, which will be in a different environment than in the interfacial slabs, was included as a separate step. It is reasonable to assume a priori that the contribution of each step to the free energy change is different in magnitude. Therefore, shares of the separate functional groups should depend on their position along z and a characteristic change of the chemical potential could be attributed to all four regions of the PMF profile. Splitting the transfer process into four sub-processes leads to four different free energies for each discrete transition. For simplicity, the transfer from bulk to interfacial water is denoted by ␣, subsequent relocation to the ISR – by ␤, ␥ is assigned to penetration into the interfacial oil slab, and ␦ – to transition to the bulk hydrocarbon. To estimate the change of free energy per single functional group, it is convenient to make comparison of the free energy values at four fixed positions along the relocation

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Fig. 4. Part of the free energy profile for the system water-pentane-pentanol in the interval of z-coordinates corresponding to a relocation of the alcohol molecule from the bulk water slab to the interfacial region (left). Dotted lines represent the positioning of the HLC of the molecule equivalent to stepwise relocation of functional groups towards the interface (right). The discrete step of coordinate changes z is of the same order as lCH2 , which provides the disposition of a single functional group at the border between the bulk and the perturbed water layer. hw and ho denote the equimolecular dividing surfaces determined from density curves fit (Fig. 3).

coordinate, which indicate the formal boundary points dividing the four regions (Fig. S3). Taking into account the respective positions of all separate functional groups allows the formulation of a system of linear equations (see the Supplementary material), which should be solved to obtain the group contributions to . Given the position restraints imposed on the n-alkanols, it is easy to reconstruct the coordinates of all atoms, corresponding to a certain displacement of the HLC from its initial position. As a consequence, it is possible to choose points on the free energy profiles that correspond to discrete steps of translocation of the separate functional groups between the four parts of the interface. Graphical representation of such a translocation for the pentanewater-pentanol model system is displayed in Fig. 4. The evaluation of G, when each of the 6 functional groups is located at a z-coordinate corresponding to one of the dividing surfaces, allows some discretization of the free energy dependence. Since this is done for each dividing surface, it results in 24 G values for pentanol (4m for an arbitrary alkanol, where m is the number of functional groups in the molecule) corresponding to a different displacement of each functional group from the bulk water slab. The geometry of the alcohol is kept fixed, which means that from the value of the z-coordinate of a single group the positions of all other groups could be recalculated. They show in which sub-layer each functional group is located when G(z) has a certain value. Linear combinations of the obtained 24 free energies yield the  contributions of the 6 functional groups to each elementary step of the transfer process. This procedure is given in more detail in the Supplementary material (Tables S4–S7) using the system water-pentane-pentanol as an example. It is applied to all PMF profiles of the water-alkane-pentanol and water-alkane-hexanol systems to allow taking into account the specificity of the local environment on  and assessment of the statistical accuracy. The raw outcome is listed in Tables S8–S13 of the Supplementary material. The data for  there, however, are obtained for the various functional groups from free energy differences spanning unequal z intervals, which render them incomparable. In order to trace more accurately the changes for the separate molecular fragments, all  values are scaled to identical z variation of 0.01 nm, which is the smallest interval used in the calculations. The data scaled and averaged over all water-alkane combinations for the two alkanols are presented in Tables 3 and 4.

The parameters for each group are combined in three overall transition chemical potentials. The first one (˛ + ˇ) is mostly hypothetical and is the energy for transferring the group from bulk water to the interface ISR. The second one (˛ + ˇ + ) is the transfer energy of the functional group from bulk water to the interfacial oil W -I = ˛ + ˇ +  and the third one (˛ + ˇ +  + ı) is the transfer energy of the group between the two bulk phases: W -O = ˛ + ˇ +  + ı . In accordance with the initial assumption that the value of  is different for each step, it can be seen that it is specific to the position of the group along the molecular chain and among the elementary steps of the transfer process. Entering the interfacial aqueous layer is beneficial for all functional groups. Maximum  have the inner methylene groups CH2 (c) and CH2 (d) and the hydroxyl group in pentanol and the outer methylene groups CH2 (a) and CH2 (b) of hexanol. At the same time, larger ˛ values of the selected groups are accompanied by higher standard errors, while the estimates for CH2 (c), CH2 (d) and OH groups are varying in smaller intervals. To some extent, the two sets of data for the three fragments mentioned above are similar, since the upper boundaries of the error in pentanol yield a value that is close to the one obtained with the lower boundaries of the errors in hexanol: ∼0.20–0.25 kJ mol−1 nm−1 . Such a deviation is comparable to the averages obtained for the rest of the methylene groups. It also corresponds to the picture described by the molecular theories of solvation – the basic contribution comes from the lower work for cavity formation in the interfacial slab [2,24]. Finally, it should be mentioned that correlations exist between the functional groups because of the overlap of their hydration shells, i.e., some water molecules hydrate more than one functional group. On average, each methylene group lowers its free energy less in hexanol than in pentanol when entering interfacial water. The only stable (i.e., unchanging) value is that of CH2 (b). ˇ for pentanol and hexanol vary but for this stage the fluctuations of the interface influence the results because some of the functional groups are solvated both by water and by alkane molecules. A common observation is that the ISR is unfavourable for the hydroxyl group of the two alcohols, which is interpreted with a partial loss of ability to form hydrogen bonds. Except for the CH2 (a) group in the pentanol molecule, the estimates for all hydrocarbon groups are negative, which indicates that the transition from perturbed water to the ISR region is favourable in general. The sta-

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29

Table 4 Chemical potential variation of the functional groups () of hexanol for transfer between bulk water and interfacial water (␣), from interfacial water to the ISR (␤), from the ISR to the interfacial oil (␥), and from the interfacial to the bulk hydrocarbon layer (␦) scaled to identical z increment and averaged for the three oils. ␮ [kJ mol−1 ]

CH3 CH2 (a) CH2 (b) CH2 (c) CH2 (d) CH2 (e) OH

␣

␤

␥

␦

␣+␤

␣+␤+␥

␣+␤+␥+␦

−0.17 ± 0.03 −0.26 ± 0.05 −0.35 ± 0.06 −0.22 ± 0.11 −0.21 ± 0.04 −0.19 ± 0.08 −0.11 ± 0.10

−0.33 ± 0.11 −0.42 ± 0.16 −0.42 ± 0.10 −0.25 ± 0.06 −0.16 ± 0.06 −0.02 ± 0.05 0.06 ± 0.02

−0.34 ± 0.06 −0.35 ± 0.04 −0.42 ± 0.15 −0.15 ± 0.02 −0.08 ± 0.02 −0.05 ± 0.03 0.08 ± 0.05

−0.05 ± 0.14 0.19 ± 0.05 0.30 ± 0.05 0.37 ± 0.01 0.25 ± 0.08 0.11 ± 0.08 0.31 ± 0.36

−0.49 ± 0.15 −0.69 ± 0.13 −0.77 ± 0.17 −0.47 ± 0.08 −0.37 ± 0.09 −0.21 ± 0.13 −0.05 ± 0.09

−0.82 ± 0.18 −1.03 ± 0.10 −1.20 ± 0.31 −0.62 ± 0.06 −0.45 ± 0.12 −0.26 ± 0.11 0.04 ± 0.10

−0.87 ± 0.23 −0.83 ± 0.14 −0.90 ± 0.26 −0.25 ± 0.06 −0.20 ± 0.08 −0.14 ± 0.04 0.35 ± 0.46

tistical errors are comparable for both alkanes, except for the CH3 and CH2 (a) groups in the pentanol molecule, which are greater in magnitude than the mean values. This makes the latter quite fluctuating. It is also noteworthy that the value of ˇ is typically more negative for the groups closer to the terminal CH3 fragment and less negative for the ones that are closer to the OH group. Overall, this translocation step is less advantageous for the groups closer to the polar head. Locating the functional groups in the perturbed oil layer is also a preferential process because  are negative for all alkyl groups. The only exception is OH with positive  . The small magnitude of the latter is due to the fact that even after traversing ho , the polar head still feels the electrostatic field of the water molecules. There is an energy ‘jump’ after CH2 (b) in the two alkanols indicating that insertion into the interfacial oil is more favourable for the three terminal functional groups than for the rest of the alkyl chain, irrespective of its length. ı characterizing the transition from interfacial to bulk oil are positive. The only exception is the small negative ı of hexanol methyl group but there the statistical error is significant. This possibly favourable contribution may stem from the small work needed to incorporate only one group among the alkane molecules, the rest of the alkanol still being in the less dense interfacial layer. It should be noted here that ı of the remaining methylene functional groups are very similar in pentanol and hexanol, which reflects the invariance towards the oil also at functional groups level. All the explanations are, of course, conditional to some extent, since the differences between  of the various groups are of the same order as the average thermal energy and can be regarded as comparable to the statistical error. Nevertheless, they are guidelines for the contributions of the separate functional groups. The processes discussed so far are the elementary steps of the overall adsorption and transfer. Therefore, it is more correct to analyse the cumulative free energy changes for several consecutive elementary steps (the last three columns of Tables 3 and 4). Overall, the transition from bulk water to the interfacial ISR is preferential for all functional groups. The same is valid for transfer to the perturbed oil except for the hydroxyl group of hexanol. The transfer between the two bulk phases is favourable for all alkyl functional groups but not for the polar head. Plausible reason for the latter is the loss of hydrogen bonds and electrostatic attraction with the water molecules. The calculated average changes of CH2 for transfer from bulk water to bulk oil estimated as group contributions (Tables S8, S9) are lower in magnitude than the values from PMF data fits (Table 2). Much closer are the mean CH2 to ˛ and (˛+ˇ) (Tables S8, S9). In fact, the minimum of G(z) (ca. −0.02 nm from the position of the HLC) corresponds to full solvation of the hydrophobic tail of pentanol or the methylene groups of hexanol in the perturbed oil region. Finally, it needs to be mentioned that all PMF wells have finite width of ca. 0.5 nm. This means that the fits to experimental data register statistical averages on various molecular placements within the adsorption layer, which could be

combinations of the contributions obtained above. Another important factor is the smooth density variation in the interfacial layers. There, the intermolecular interactions might also change gradually, which is neglected in the group-wise analysis. Nevertheless, the above partitioning of the PMF data is a successful first attempt to distinguish specificities at the molecular level during the adsorption and interfacial transfer process of simple non-ionic surfactants. As mentioned in the Introduction, the solvation of molecular species can be divided into two effects – the work needed to form the cavity, in which the solute is to be placed, and the attraction potential energy between the dissolved particle and the solvent molecules. Application of this concept to adsorption and transition processes [24] shows that in the perturbed layers the work needed to form a cavity of a given size is much less than in the bulk regions. The lesser number of solvent molecules could influence also the average potential energy of attraction. An accurate description of these phenomena for particles with non-spherical geometry requires a model that not only distributes quantitatively the contributions of individual structural fragments but also allows inclusion of specific correlation effects that stem from the solvent intermolecular structure. Such analysis is envisaged in a next stage of the study, where the parameters estimated in this work will be implemented further as analytical expressions in terms of molecular interactions. 5. Conclusions Classical Molecular dynamics simulations, combined with the Umbrella Sampling method and WHAM technique, are implemented to recreate in a systematic way the standard free energy changes during translocation of a set of single normal alkanol molecules across water-alkane interfaces. In order to obtain a more general perspective, the procedure is applied to three similar series of water-alkane-alkanol model systems, each containing one of the following homologues: n-pentanol, n-hexanol, or n-heptanol and explicitly described n-pentane, n-hexane or n-heptane liquid oil phase. The obtained data are used to validate the computational strategy by estimating the standard Gibbs free energies of adsorption and transfer and comparing them to empirical estimates. Overall, a good qualitative representation of the curves and the order of magnitude of the quantities is achieved. The observed discrepancies (up to 30%) can be attributed to the non-polarizable nature of the force field and to the constrained amphiphile geometry. A novel method based on differentiation of the free energy profile is suggested as a tool to estimate the free energy changes per single functional group of the alkanols. It is demonstrated that such an approach reproduces the empirical values [1,12,35] with high accuracy (1–10%) and exceeds in terms of precision the classical fitting of the adsorption free energy. Finally, the amphiphiles translocation across the fluid interface is analysed in more detail by introducing several formal substeps characterized by specific positions of the separate alkanol functional groups relative to the interface. It is demonstrated that the value of  attributed to

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each functional group depends on its position along the coordinate normal to the interface and at the same time can vary according to its place in the alkanol molecule. The obtained results clearly reflect the predicted inhomogeneity of group contributions. Therefore, the analysis can be viewed as an extension of the existing empirical models [1,11,34,40–42] and should be developed in the future towards finding a relationship with the molecular solvation modelling. This could elucidate further the interaction balance and the molecular ordering in the studied systems. 6. Supplementary material The following data is available as Supplementary material: histograms of the distributions of torsion angles C C C C and C C C O in the molecule of n-heptanol from MD simulations without conformational restraints on the alkanol (Fig. S1); probability distribution of the angle formed between the hydrophobic tail of the n-heptanol molecule and the z-axis of the coordinate system (Fig. S2); experimental estimates of the free energy contribution per single methylene group (Table S1); composition of the water-alkane-alkanol model systems (Table S2); estimates of the free energy of adsorption and transfer obtained from similar studies by other authors (Table S3); mass density profiles along the zcoordinate in the pure water-alkane model systems (Fig. S3); linear fits of the potential well width dependence dz = f [n(C)] (Fig. S4); zcomponent of the orientational order parameter of the alkyl chains at the interfaces water-pentane, water-hexane, and water-heptane (Fig. S5); values of the electrostatic and van-der-Waals interaction energies between the alkanol and each of the two solvents, standard enthalpy and entropy of transfer of an alkanol molecule between bulk water and oil (Figs. S6 and S7), and a detailed description of their determination from simulation data; linear fit for the Gɑ (w−i) = f [n(C)] dependence (Fig. S8); notes on the fits of the linear regions of the PMF profiles (Fig. S9); detailed description of the estimation procedure used in the group-wise analysis of the free energy profile for the water-alkane-alkanol systems and the data obtained thereof (Tables S4–S13).

[4]

[5] [6]

[7] [8] [9] [10] [11] [12]

[13] [14] [15] [16]

[17] [18] [19] [20] [21] [22]

[23] [24]

Acknowledgements Project DVU-90/2010 of the National Science Fund of Bulgaria provided partial financial support. T. Z. is grateful to the Bulgarian Ministry of Education and Science for a “Science and Business” fellowship. Dr. Radomir Slavchov is acknowledged for enticing us into addressing this problem, for suggesting Eqs. (12) and (13) as implementation of the differential method, and for the critical discussions of the results. The authors are thankful to Dr. Vesselin Kolev and Dr. Ilsoo Kim for thorough proofreading and commenting on the manuscript. Appendix A. Supplementary data

[25]

[26]

[27] [28]

[29]

[30] [31]

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.colsurfa.2016.06. 003.

[32] [33]

References [1] R.I. Slavchov, S.I. Karakashev, I.B. Ivanov, Ionic surfactants and ion-specific effects: adsorption, micellization, thin liquid films, in: L. Römsted (Ed.), Surfactant Science and Technology: Retrospects and Prospects, CRC Press-Taylor and Francis, LLC, 2013. [2] A. Pohorille, M. Wilson, Excess chemical potential of small solutes across water–membrane and water–hexane interfaces, J. Chem. Phys. 104 (1996) 3760–3773. [3] Y. Bauer, D.J. Meninger, J.E. Davis, S.J. Patel, Phase-transfer energetics of small-molecule alcohols across the water–hexane interface: molecular

[34]

[35]

[36] [37]

dynamics simulations using charge equilibration models, Mol. Graphics Model. 29 (2011) 876–887. G. Catanoiu, E. Carey, S.R. Patil, S. Engelskirchen, C. Stubenrauch, Partition coefficients of nonionic surfactants in water/n-alkane systems, J. Colloid Interface Sci. 355 (2011) 150–156. A.J. Bard, L.R. Faulkner, Electrochemical Methods: Fundamentals and Applications, Wiley, New York, 1980. S. Haslam, S.G. Croucher, C.G. Hickman, J.G. Frey, Surface second harmonic generation studies of the dodecane/water interface: the equilibrium and kinetic behaviour of p-nitrophenol and tri-n-butyl phosphate, Phys. Chem. Chem. Phys. 2 (2000) 3235–3245. Phase Transfer Catalysis, in: C.M. Starks, C.L. Liotta, M. Halpern (Eds.), Chapman & Hall, New York, 1994. J. White, Membrane fusion, Science 258 (1992) 917–924. H.R. Petty, Molecular Biology of Membrane Structure and Function, Plenum Press, New York, 1993. J. Traube, Ueber die Capillaritätsconstanten organischer Stoffe in wässerigen Lösungen, Liebigs Ann. 265 (1891) 27–55. I. Langmuir, The constitution and fundamental properties of solids and liquids. II. Liquids, J. Am. Chem. Soc. 39 (1917) 1848–1906. R.I. Slavchov, I.M. Dimitrova, I.B. Ivanov, Cohesive and non-cohesive adsorption of surfactants at liquid interfaces, in: R.G. Rubio, Y.S. Ryazantsev, V.M. Starov, G.X. Huang, A.P. Chetverikov, P. Arena, A.A. Nepomnyashchy, A. Ferrús, E.G. Morozov (Eds.), Without Bounds: A Scientific Canvas of Nonlinearity and Complex Dynamics, Springer-Verlag, Berlin, 2013. J.N. Israelachvili, Intermolecular and Surface Forces, 3rd ed., Academic Press, New York, 2011. F.H. Stillinger, Structure in aqueous solutions of nonpolar solutes from the standpoint of scaled-particle theory, J. Solut. Chem. 2 (1973) 141–158. R.A. Pierotti, A scaled particle theory of aqueous and nonaqueous solutions, Chem. Rev. 76 (1976) 717–726. G. Hummer, Sh. Garde, A. García, A. Pohorille, L. Pratt, An information theory model of hydrophobic interactions, Proc. Natl. Acad. Sci. U. S. A. 93 (1996) 8951–8955. L.R. Pratt, R.A. LaViolette, Quasi-chemical theories of associated liquids, Mol. Phys. 94 (1998) 909–915. L.R. Pratt, D. Chandler, Theory of the hydrophobic effect, J. Chem. Phys. 67 (1977) 3683–3704. H.S. Ashbaugh, L.R. Pratt, Scaled particle theory and the length scales of hydrophobicity, Rev. Mod. Phys. 78 (2006) 159–178. E.T. Jaynes, R.D. Rosenkrantz, in: Papers on Probability, Statistics and Statistical Physics, Reidel, Dordrecht, 1983. G. Hummer, S. Garde, Cavity expulsion and weak dewetting of hydrophobic solutes in water, Phys. Rev. Lett. 80 (1998) 4193–4196. G. Hummer, S. Garde, A.E. García, M.E. Paulatis, L.R. Pratt, The pressure dependence of hydrophobic interactions is consistent with the observed pressure denaturation of proteins, J. Phys. Chem. B 102 (1998) 10469–10482. G. Hummer, S. Garde, A.E. García, L.R. Pratt, New perspectives on hydrophobic effects, Chem. Phys. 258 (2000) 349–370. L.R. Pratt, A. Pohorille, Hydrophobic effects and modeling of biophysical aqueous solution interfaces, Chem. Rev. 102 (2002) 2671–2692. L.R. Pratt, R.A. LaViolette, M.A. Gomez, M. Gentile, Quasi-chemical theory for the statistical thermodynamics of the hard-sphere fluid, J. Phys. Chem. B 105 (2001) 11662–11668. T. Chang, L. Dang, Molecular dynamics simulations of CCl4-H2O liquid–liquid interface with polarizable potential models, J. Chem. Phys. 104 (1996) 6772–6783. A. Pohorille, P. Cieplak, M.A. Wilson, Interactions of anesthetics with the membrane-water interface, Chem. Phys. 204 (1996) 337–345. A. Pohorille, M.A. Wilson, C. Chipot, Interaction of alcohols and anesthetics with the water-hexane interface: a molecular dynamics study, Prog. Colloid Polym. Sci. 103 (1997) 29–40. A. Pohorille, M.H. New, K. Schweighofer, M.A. Wilson, Insights from computer simulations into the interactions of small molecules with membranes, in: D. Deamer (Ed.), Membrane Permeability: 100 Years Since Ernst Overton, Current Topics in Membranes, Academic Press, San Diego, 1999. L. Pratt, G. Hummer, Simulation and Theory of Electrostatic Interactions in Solution, American Institute of Physics, New York, 1999. P. Kralchevsky, D. Danov, The standard free energy of surfactant adsorption at air/water and oil/water interfaces: theoretical vs. empirical approaches, Colloid J. 74 (2012) 172–185. R. Aveyard, R.W. Mitchell, Distribution of n-alkanols between water and n-alkanes, Trans. Faraday Soc. 65 (1969) 2645–2653. R. Aveyard, B.J. Briscoe, Adsorption of n-alkanols at alkane/water interfaces, J. Chem. Soc. Faraday Trans. 1 68 (1972) 478–491. N.A. Grozev, T.G. Tosheva, I.M. Dimitrova, R.I. Slavchov, Adsorption and partitioning of nonionic surfactants at water|oil interfaces, Bulg. J. Chem. 2 (2013) 25–35. I.B. Ivanov, K.D. Danov, D. Dimitrova, M. Boyanov, K.P. Ananthapadmanabhan, A. Lips, Equations of state and adsorption isotherms of low molecular non-ionic surfactants, Colloids Surf. A 354 (2010) 118–133. T. Smith, Monolayers on water: I. A theoretical equation for the liquid expanded state, J. Colloid Interface Sci. 23 (1967) 27–35. W. Hückel, Theoretical Principles of Organic Chemistry, vol. II, Elsevier, Amsterdam, 1958.

T.K. Zahariev et al. / Colloids and Surfaces A: Physicochem. Eng. Aspects 506 (2016) 20–31 [38] A.I. Kitaigorodskii, Organic Chemical Crystallography, Consultant Bureau, Moscow, 1961. [39] M.J. Schick, Non-ionic Surfactants: Physical Chemistry, Marcel Dekker, New York, 1987. [40] M. Manabe, M. Koda, K. Shirama, Partition coefficients of alkanols and polyoxyethylene alkyl ethers in dodecane-water system at 25 ◦ C, Bull. Chem. Soc. Jpn. 48 (1975) 3553–3556. [41] M. Manabe, H. Kawamura, G. Sugihara, M. Tanaka, Transfer of homologous alkanols from water to fluorocarbon and hydrocarbon surfactant micelles, Bull. Chem. Soc. Jpn. 61 (1988) 1551–1555. [42] R. Villalonga, Interfacial tensions and partition coefficients in water and n-heptane systems containing n-alkanols, alkylketones, alkylamides, and alkylmonocarboxylic acids, J. Colloid Interface Sci. 90 (1982) 539–542. [43] D. Goodsell, The Machinery of Life, Springer, New York, 1993. [44] Ts. K. Zahariev, R.I. Slavchov, A.V. Tadjer, A.N. Ivanova, Fully atomistic molecular-mechanical model of liquid alkane oils: computational validation, J. Comput. Chem. 35 (2013) 776–788. [45] D. van der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E. Mark, H.J.C. Berendsen, Force field benchmark of organic liquids: density, enthalpy of vaporization, heat capacities, surface tension, isothermal compressibility, volumetric expansion coefficient, and dielectric constant, J. Comput. Chem. 26 (2005) 1701–1718. [46] W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz Jr., D.M. Ferguson, D.C. Spellmeyer, T. Fox, J.W. Caldwell, P.A. Kollman, A second generation force field for the simulation of proteins, nucleic acids, and organic molecules, J. Am. Chem. Soc. 117 (1995) 5179–5197. [47] (a) J. Jorgensen, J.D. Madura, R.W. Impey, M.L. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys. 79 (1983) 926–935; (b) W.L. Jorgensen, J.D. Madura, Monte Carlo simulation of differences in free energies of hydration, Mol. Phys. 56 (1985) 1381–1392. [48] H.J.C. Berendsen, J.P.M. Postma, W.F. Van Gunsteren, A. Dinola, J.R. Haak, Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81 (1984) 3684–3690. [49] U. Essmann, L. Perera, M.L. Berkowitz, T. Darden, H. Lee, L.G. Pedersen, A smooth particle mesh Ewald method, J. Chem. Phys. 103 (1995) 8577–8593. [50] B. Hess, H. Bekker, H.J.C. Berendsen, J.G.E.M. Fraaije, LINCS: a linear constraint solver for molecular simulations, J. Comput. Chem. 18 (1997) 1463–1472. [51] S. Miyamoto, P.A. Kollman, Settle: an analytical version of the SHAKE and RATTLE algorithm for rigid water models, J. Comput. Chem. 13 (1992) 952–962. [52] G.M. Torrie, J.P. Valleau, Nonphysical sampling distributions in monte carlo free-energy estimation: umbrella sampling, J. Comput. Phys. 23 (1977) 187–199.

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[53] D. Frenkel, B. Smith, Understanding Molecular Simulation, Academic Press, San Diego, 2002. [54] Both the value of the pulling force and of the force constant during the umbrella simulations were varied in a number of preliminary tests in order to assign the optimal magnitudes for our model systems. In the case of the pulling simulations, the chosen external force was meant to provide a constant, relatively low relocation velocity that would lead to a smooth passing of the alkanol molecule through the oil and water slabs. The optimal value of the force constant, on its part, should guarantee steep increase of the respective umbrella potential outside the boundaries of the selected ‘window’. A typical value for 0.2 nm spacing is 1000 kJ mol−1 nm−1 . In our case, the spacing between the windows is somewhat smaller, which corresponds to a larger force constant, used to enhance the sampling in the narrower windows. [55] A.M. Ferrenberg, R.H. Swendsen, Optimized Monte Carlo data analysis, Phys. Rev. Lett. 63 (1989) 1195–1198. [56] Sh. Kumar, J.M. Rosenberg, D. Bouzida, R.H. Swendsen, P.A. Kollman, The weighted histogram analysis method for free-energy calculations on biomolecules, J. Comput. Chem. 13 (1992) 1011–1021. [57] J.S. Hub, B.L. de Groot, D. van der Spoel, g wham—a free weighted histogram analysis implementation including robust error and autocorrelation estimates, J. Chem. Theory Comput. 6 (2010) 3713–3720. [58] A. Pohorille, I. Benjamin, Structure and energetics of model amphiphilic molecules at the water liquid-vapor interface: a molecular dynamic study, J. Phys. Chem. 97 (1993) 2664–2670. [59] D.R. Lide (Ed.), CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 2005, Internet Version http://www.hbcpnetbase.com. [60] C. Tanford, The Hydrophobic Effect, Wiley, New York, 1980. [61] D.J. Giesen, C.J. Cramer, G.G. Truhlar, A semiempirical quantum mechanical solvation model for solvation free energies in all alkane solvents, J. Phys. Chem. B 99 (1995) 7137–7146. [62] A.C. Chamberlin, C.J. Cramer, D.G. Truhlar, Predicting aqueous free energies of solvation as functions of temperature, J. Phys. Chem. B 110 (2006) 5665–5675. [63] Free Energy Calculations, in: C. Chipot, A. Pohorille (Eds.), Springer Verlag, Berlin, New York, 2007. [64] B. Efron, Bootstrap methods: another look at the jackknife, Ann. Stat. 7 (1979) 1–26. [65] A. Tikhonov, D. Mitrinovic, M. Li, Z. Huang, M. Schlossman, X-ray reflectivity study of alkane-water interfaces, J. Phys. Chem. B 104 (2000) 6336–6339. [66] A. Pohorille, M.A. Wilson, Viewpoint 9—molecular structure of aqueous interfaces, J. Mol. Struct. (THEOCHEM) 284 (1993) 271–298.