In Silico Prediction of the Thermodynamic Equilibrium of Solute

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In silico prediction of the thermodynamic equilibrium of solute partition in multiphase complex fluids: A case study of oil-water microemulsion Mattia Turchi, Qiong Cai, and Guoping Lian Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b01513 • Publication Date (Web): 23 Jul 2019 Downloaded from pubs.acs.org on July 27, 2019

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In silico prediction of the thermodynamic equilibrium of solute partition in multiphase complex fluids: A case study of oil-water microemulsion Mattia Turchi, †, ‡, Qiong Cai‡, Guoping Lian†, ‡

†

Unilever Research Colworth, Colworth Park, Sharnbrook, Bedfordshire MK44 1LQ, UK,

‡Department

of Chemical and Process Engineering, University of Surrey, Guildford GU27XH, UK

Corresponding author:

Guoping Lian, Tel.: +44 1234 222741; Fax: +44 1234 222410. Email: [email protected]

Abstract Multiphase complex fluids such as micelles, microemulsions and dispersions are ubiquitous in product formulations of foods, pharmaceuticals, cosmetics, and fine 1 ACS Paragon Plus Environment

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chemicals. Quantifying how active solutes partition in the microstructure of such multiphase fluids is necessary for designing formulations that can optimally deliver the benefits of functional actives. In this paper, we at first predict the structure of a heptane/butanol/sodium dodecyl sulfate (SDS) droplet in water that self-assembled to form a microemulsion through the MD simulation and subsequently investigate the thermodynamic equilibrium of solute partitioning using COSMOmic. To our knowledge, this is the first time that the MD/COSMOmic approach is used for predicting solute partitioning in a microemulsion. The predicted partition coefficients are compared to experimental values derived from retention measurements of the same microemulsion. We show that the experimental data of droplet-water partition coefficients (Kdroplet/w) can be reliably predicted by the method that combines MD simulations with COSMOmic.

Introduction

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There is significant interest in recent years in predicting solute partitioning in multiphase materials such as emulsions and dispersions. Particularly in the design of product formulations, understanding the partitioning behaviour of solutes in such multiphase microstructures is crucial for ensuring the optimal delivery of benefits and efficacy of functional actives. Solute partitioning in multiphase complex formulations can be determined by experimental methods such as gas chromatography, high performance liquid chromatography1–3 and electrochromatography3,4. However, these experimental methods are often quite expensive and time consuming. In-silico methods for predicting thermodynamic equilibrium can be used as an alternative. Several in-silico models have been reported in recent years for predicting solute partitioning in model solvent systems. For example, EPI (Estimation Programs Interface) fragments method and Abrahams descriptors have been extensively applied for predicting the partition coefficient of octanol/water, Ko/w5,6. These models require certain fitting to experimentally measured partition coefficients, thus making them applicable only to systems for which sufficient experimental data of partition coefficients

are

available.

Group

contribution

(UNIQUAC Functional-group Activity Coefficients)

models are


such

powerful

as

UNIFAC

methods

for

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predicting partition coefficients in mixed fluids7–9. These models use functional groups of molecules to calculate the activity coefficient of each component in a liquid mixture. Partition coefficients are then calculated as the ratio of activity coefficients of solutes in the miscible solvent systems. Most recent versions of UNIFAC10 hold parametrizations for a relevant number of atom groups that allow the prediction of partition coefficients for several solvent systems. On the downside, there is still a lack of parameters for characterizing some of the most common surfactant systems, such as sodium dodecyl sulfate (SDS) anionic surfactant. An alternative to the above mentioned semi-empirical methods is the “conductor-like screening model for real solvents”, the so-called COSMO-RS11–13 method. As a quantum chemistry based thermodynamics method, the COSMO-RS theory uses the screening charge density on the surface of solute molecules to determine the chemical potential of solute species in pure and/or mixed liquids. Based on the chemical potential, the activity coefficients of solutes in the solvent mixtures are computed and the partition coefficients between two solvents are then computed as the ratio of the activity coefficients of the solute molecules in each of the two solvent systems. The surface charge densities of solute molecules are computed through quantum chemical 4 ACS Paragon Plus Environment

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calculations and can be obtained for surfactant molecules of interest, making this method applicable to structured fluids such as micelles and microemulsions. The standard way in which partition coefficients are calculated with the COSMO-RS theory is by means of a pseudo-phase approach, where the solvent mixtures are homogeneous. This particular feature makes this method suitable for partition coefficients predictions in relatively simple systems in which the inhomogeneity of molecular assembly can be neglected. However, in more complex systems, such as micelles and microemulsions, inhomogeneity of the molecular assembly has to be taken into account. COSMOmic14 method is an extension of the COSMO-RS theory for inhomogeneous systems. In the COSMOmic approach, the screening charge density of molecules in structured molecular assemblies are explicitly computed at atomistic scale. The atomistic level molecular assembly of liquid structure can be achieved by performing molecular dynamics (MD) simulations. The method that combines MD with COSMOmic has been proven to accurately predict partition coefficients of not only homogeneous fluids such as octanol-water15 but also structured fluids of micelles containing anionic, cationic and zwitterionic surfactants and surfactants mixtures16–21. 5 ACS Paragon Plus Environment

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In this paper, we extend the combined MD/COSMOmic approach to investigate the partition coefficients of solutes in a heptane/butanol/sodium dodecyl sulfate (SDS) in water microemulsion. The SDS/butanol/heptane in water microemulsion has a wide range of applications22 in separation science, such as: chiral separation of enantiomeric analytes23–25, separation of highly hydrophobic compounds26,27, partition coefficients

determination28–30,

biomembrane

permeability

and

lipophilicity

determination3,31. Ishihama et al.4 showed that solute partitioning in this microemulsion is different from that in octanol/water and micellar systems but similar to that in gelphase liposome systems. In this work, MD simulations are performed to obtain a heptane/butanol/SDS in water droplets, at the same concentration range reported by Ishihama et al4 . The partition coefficients of 14 chemicals between the simulated droplets and water are subsequently predicted using COSMOmic. To our knowledge, this is the first work that applies the combined MD/COSMOmic approach for predicting solute partitioning of oil in water microemulsion system. The predicted partition coefficients are compared with available experimental data and there is a good agreement, suggesting the combined MD/COSMOmic method is a good way for predicting the thermodynamic equilibrium of solutes in multi-phase complex fluids. 6 ACS Paragon Plus Environment

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Methods Experimental dataset for partition coefficients

Experimental data for heptane/butanol/SDS in water droplet and water partition coefficients were derived from the work by Ishihama et al.4 who used microemulsion electrokinetic chromatography (MEEKC) for the measurement of the retention factor of a number of solutes in heptane/butanol/SDS/water microemulsion at pH = 7 and at T = 298.15 K. The measurements were carried out following the guideline of Abraham

et al31. The microemulsion contains 1.44% (w/w) SDS, 6.49% (w/w) butanol and 0.82% (w/w) heptane. By using the phase diagrams from the work of Van Nieuwkoop et al.32, where the phase behaviour of the SDS/butanol/heptane/water system was studied, it can be confirmed that oil in water microemulsions are formed at the above concentrations. The 3D phase diagram of Figure 1 shows that for the above concentrations of SDS, butanol and heptane in water, the considered formulation falls in the region of oil in water microemulsion, which is the smallest hatched region in the far right side of the diagram. 7 ACS Paragon Plus Environment

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Figure 1: 3D phase diagram for the SDS, butanol, heptane and water quaternary system.

From the measured retention factor, Ishihama et al.4 derived the experimental values of enthalpy ∆Htransf and entropy ∆Stransf for the transfer of 14 solutes from the water phase to the droplet phase (Table 1). Using equation (1), we can calculate the Gibbs free energy of transfer (∆Gtransf) and derive the logarithm of the solute partition coefficients between the droplet phase and the water phase (K droplet/w).


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(1)

∆Gtransf = ∆Htransf ―T∆Stransf

Log (Kdroplet/w) =

∆Gtransf ―2.303RT

(2)

Additionally, available experimental values of heptane/water partition coefficients for the considered solutes dataset were collected from the work of Abraham et al.33 (Table 1). These experimental values allow us for a comparison between droplet/water and heptane/water partition coefficients and to unveil the different partitioning behaviour of solutes in these two solvent systems.

Table 1: Enthalpy (ΔH transf), Entropy (ΔS transf) and Gibbs free energy (ΔG transf) for the transfer of 14 solutes from water to the heptane/butanol/SDS in water droplets and the derived droplet/water partition coefficients. ΔH transf

ΔS transf

ΔG transf

Log K droplet/w

Log K heptane/w

(Joule/mol)

(Joule/mol*K)

(Joule/mol)

(mol/mol)*

(mol/mol)**

resorcinol

-4300

5.4

-5909

1.03

-3.18

p-methoxyphenol

-5000

8.6

-7563

1.32

n.a.

phenol

-4800

10.7

-7989

1.40

-0.01

p-nitroaniline

-9300

-3

-8406

1.47

-0.29

nitrobenzene

-3100

22.3

-9745

1.71

2.36

o-cresol

-8900

3

-9794

1.72

0.99

m-cresol

-8200

6.3

-10077

1.77

0.55

p-cresol

-8800

4.1

-10022

1.77

0.71

p-nitroanisole

-8300

8

-10684

1.87

n.a.

p-chlorophenol

-14400

-6.9

-12344

2.16

0.52

p-ethylphenol

-11900

2.1

-12526

2.19

1.15

Solutes


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2-naphthol

-16500

-9.5

-13669

2.39

1.22

toluene

-12400

3.9

-13562

2.38

3.76

p-propylphenol

-15200

-1.5

-14753

2.59

1.77

*Data reproduced from Ishihama et al.4 Experimental values for the heptane/water partition coefficients.

**Data collected from Abraham et al33.

Molecular dynamic (MD) simulation The starting configuration of heptane, butanol and SDS molecules for MD simulations was

generated

through

the

PACKMOL-18.169

(http://www.ime.unicamp.br/~martinez/packmol) package34. The PACKMOL software allows for placing the molecules within a desired simulation box. 26 SDS molecules, 449 butanol molecules and 41 heptane molecules were randomly placed by PACKMOL in a 4 nm × 4 nm × 4 nm periodic box. The system was then solvated with 21607 water molecules and the box volume was increased to 8 nm × 8 nm × 8 nm to contain the water molecules. 26 sodium counterions were added to neutralize the SDS charged molecules for ensuring the electro-neutrality of the whole molecular system. The number of molecules for the four components matched the microemulsion composition of 1.44% w/w SDS, 6.49% w/w n-butanol, 0.82% w/w n-heptane and 91.25% w/w water as reported by Ishihama et al.4. Using the PACKMOL generated


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configuration,

MD

simulations

were

performed

using

GROMACS

5.1.135

(ftp://ftp.gromacs.org/pub/gromacs/gromacs-5.1.1.tar.gz). GROMACS is widely used for molecular simulations and trajectory analysis of

biological systems such as

proteins36–39, surfactants40,41 and lipid systems42–45. The CHARMM36 force field46 was used for SDS, n-butanol and n-heptane molecules and the TIP3P force field was used for water molecules. The CGenFF47 software was used for including the atomic structure and atom connections in the CHARMM36 force field library for butanol compound. The system was relaxed in order to minimize the internal energy with the steepest descent algorithm implemented in GROMACS. After the energy minimization step, a short simulation of 600 ps was carried out in the constant-temperature, constant-volume (NVT) ensemble. The Nose-Hoover48 thermostat with a coupling constant of τt = 1 ps was used for maintaining the temperature at a constant value of T = 298.25 K. The leap-frog integrator was used for the integration of the equation of motion. The Verlet cutoff scheme was employed and the short-range electrostatic cutoff and the short-range van der Waals cutoff were set at 1.2 nm. The Particle Mesh Ewald method49,50 was used for the long-ranged electrostatic interactions and long range dispersion corrections for energy and pressure were applied. The LINCS 11 ACS Paragon Plus Environment

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algorithm51 was used for constraining the bonds of hydrogens. The final simulation was run in the constant-temperature, constant-pressure (NPT) ensemble for 40 ns whilst the coordinates were saved in every 100 ps. The Nose-Hoover thermostat with a coupling constant of τt = 1 ps was used for maintaining the temperature at a constant value of T = 298.25 K and the Parrinello-Rahman52 barostat with a coupling constant of 𝜏𝑝 = 1 𝑝𝑠 was used for maintaining the pressure at a constant value of P = 1 bar. At the end of the 40 ns run, the density of the system reached 995.435 Kg/m3 and a spherical droplet is formed, containing the SDS/butanol/heptane molecules surrounded by water molecules.

MD simulations have also been performed for a bigger system by doubling the number of molecules (52 SDS, 898 butanol, 82 heptane and 43214 water), with the aim of investigating the droplet size effect. This system will thereafter be referred as the “big” system, whilst the system of 26 SDS, 449 butanol, 41 heptane and 21607 water molecules will be referred as the “small” system. The starting configuration for the big system was chosen after considering the spherical assembly obtained with the first MD simulation of the small system. In this big system, PACKMOL was used for placing


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heptane molecules within a sphere of 30 Å radius and butanol and SDS molecules within a spherical shell of 25 Å to 50 Å. The system was then inserted in a cubic box of 12 nm × 12 nm × 12 nm to contain the water molecules. 52 sodium counterions were added to neutralize the SDS charged molecules for ensuring the electroneutrality of the whole molecular system. The energy minimization and equilibration steps as well as the production run of 40 ns were subsequently performed, following the same procedure used for the small system. At the end of the 40 ns run, the density of the system was found to be 998.121 Kg/m3 and a spherical droplet containing the SDS/butanol/heptane molecules surrounded by water molecules is formed.

The self-assembled droplets formed at the end of the MD simulation were extracted together with a thin shell of water molecules, using an in-house code written in Biopython53 package. Figure 2 (a) and (b) show the small droplet and the big droplet with water molecules removed and Figure 2(c) and (2d) are the droplets a the thin shell of water molecules included. The molecular assembly of the droplets including the thin shell of water molecuels is then fed into COSMOmic for deriving the partition coefficients of solutes.


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COSMOmic: a COSMO-RS based software

In the COSMO-RS theory, the chemical potential of a solute X within its surrounding solvent is computed from the screening charge density on the surface of molecules using the Conductor-like Screening Model for Real Solvent (COSMO-RS). Detailed description of COSMO-RS method can be found elsewhere11–13. Briefly, with the COSMO-RS theory, solute molecules are treated as if embedded in a dielectric medium via a molecular surface or “cavity”. The charge distribution of the embedded molecules polarizes the dielectric medium (source charge). The response of the medium is described by the generation of screening charges on the cavity surface. The cavity surface is discretized into fine elements, called segments. Each surface segment is associated with its underlying atom and is characterized by its area 𝑎𝑖 and its screening charge density (SCD) 𝜎𝑖. Charge densities are calculated through Quantum Chemical calculations. In this work, 𝜎𝑖 values for solute and microemulsion molecules (water, heptane, butanol and SDS), were computed using the density functional theory (DFT) with the Becke-Perdew54,55 (BP) functional, the triple-zeta valence polarization56,57 (TZVP) basis set and the resolution of identity58 (RI) 14 ACS Paragon Plus Environment

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approximation. A full geometry optimization was used for all solute molecules, while single point calculations were used for microemulsion molecules. Quantum chemical calculations

were

carried

out

using

Turbomole

7.359

package

(http://www.turbomole.com). Details about parameters needed for performing DFT quantum chemical calculations can be found in the Turbomole user manual (http://www.cosmologic.de/files/downloads/manuals/TURBOMOLE-UsersManual_70.pdf). COSMO-RS theory was first implemented for homogenous fluid mixtures

in

COSMOtherm

software

package13

(http://www.cosmologic.de/files/downloads/manuals/COSMOtherm_Manual.pdf). COSMOmic is a new extension of the COSMO-RS theory for solutes in complex objects such as micelles and bio membranes as long as the molecular assembly of the complex objects is known.

COSMOmic

19.0

(http://www.cosmologic.de)

is

used

in

this

work

(http://www.cosmologic.de/files/downloads/manuals/COSMOmic_Manual.pdf), along with the COSMO-RS parameter file BP_TZVP_19.ctd. In COSMOmic, the spherical geometry of the input droplets was discretized into 30 layers along the radius, the last layer was exclusively composed by water molecules. Jakobtorweihen et al.60 showed 15 ACS Paragon Plus Environment

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how COSMOmic predictions are unaffected by the layers size as long as the size is less than 0.2 nm. The probability distribution of the surface segments corresponds to a specific charge density σ-profile 𝑝𝑗(𝜎,𝑟), where 𝑗 denotes the layer of the extracted sphere and 𝑟 is the radius to the centre of the droplet (including the water shell). The probability to find solute 𝑋𝑖 in the 𝑗 layer is evaluated by integrating 𝑝𝑗(𝜎,𝑟) over the surface of solute 𝑋𝑖. Details about COSMOmic can be found elsewhere14.


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a

b

c

d

Figure 2: Self assembled heptane/butanol/SDS in water droplets by MD simulation. (a): small system of heptane enclosed in SDS and butanol; (b) big system, (c). small system with a thin shell of water molecules, as input for COSMOmic,(d) big system with a thin shell of water molecules. Water molecules are colored in ice-blue, butanol molecules in yellow, SDS molecules in green and heptane molecules in red.

Results and Discussion The droplet characteristics


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The heptane/butanol/SDS in water droplets obtained after 40 ns of MD simulation are shown in Figure 2 (a) and (b). The centre of mass (COM) of the droplet ensemble, is calculated by GROMACS, using the built-in gmx-traj functionality. Subsequently, the density profiles of water, butanol and SDS molecules relative to the COM are calculated and shown in Figure 3(a) and (b). For the small system, the density profiles of all the droplet phase components start to approach zero at radius higher than 25 Å , as shown in Figure 3 (a). Within this radius, 25 SDS molecules, 41 heptane molecules and 169 butanol molecules are included. For the big system, the density profiles of all the droplet phase components start to approach zero at radius higher than 32 Å, as shown in Figure 3 (b). Within this radius, 37 SDS molecules, 64 heptane molecules and 264 butanol molecules are included. The point at which the water density profile intersects with the butanol density profile is found to be at r droplet = 25 Å and at r droplet = 32 Å , respectively for the small and the big systems. Thus, these are chosen as the radius of the droplets. Additionally, the radius of gyration for SDS molecules was computed in order to evaluate the mean radius of the SDS molecule assembly, following the criteria suggested by Bogusz et al.61:


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Rsds =

5 3Rgyration

(3)

The value of R sds can be used to estimate the droplet radius, assuming that butanol molecules at the droplet/water interface are located at a similar distance to the COM as the SDS ones. The calculated values of R sds = 25.3 Å for the small system and R sds =

32.5 Å for the big one are in good agreement with the selected droplet radii of 25

Å and 32 Å. Similar droplets radii were found in a recent study on Soybean oil/Tween 80 in water microemulsion by Moghaddasi et al.62 Figure 4 (a) shows the number of butanol molecules within 25 Å

radius of the droplet COM as a function of the

simulation time, for the small system. In the starting configuration, all butanol molecules were placed within a 40 Å × 40 Å × 40 Å box. As the simulation proceeds, the number of butanol molecules within the 25 Å radius rapidly decreased in the first 5 ns, showing some butanol molecules diffused out and away from the region. The average number of butanol molecules within the 25 Å radius of the droplet remained at around 169, as the simulation time further increased. Figure 4 (b) shows the number of butanol molecules within 32 Å from the COM of the big droplet. In the starting configuration all butanol molecules were placed within a spherical shell from 25 Å to


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50 Å radii. As the simulation proceeded the number of butanol molecules within 32 Å radius rapidly increased in the first 5 ns, showing some butanol molecules diffusing from outside towards the interface of the droplet. The average number of butanol molecules within 32 Å radius then remained constant at around 264 molecules for the rest of the simulation. This shows how the droplet assemble is independent of the starting configuration. Similar values for the number of butanol molecules in a quaternary oil-in-water microemulsion were found by Lang et al.63 With the small system, by subtracting the 169 molecules in the droplet from the total 449 butanol molecules in the system, one can infer the number of the butanol molecules in the bulk water phase to be 280. The concentration of the 280 butanol molecules in the surrounding bulk phase of the 21119 water molecules was calculated to be 𝑐𝑏𝑢𝑡= 0.055g/g. Similarly, for the big system, a total of 634 butanol molecules are in the bulk water phase and accordingly the concentration of butanol in water is equal to 𝑐𝑏𝑢𝑡= 0.060g/g. These values are comparable to the experimentally determined butanol solubility of 0.077 g/g64 indicating that the water bulk phase is close to be saturated with butanol. The slightly lower butanol concentration in the bulk water could be caused by over counted water molecules near the interface. 20 ACS Paragon Plus Environment

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0.35 0.3

a

0.4 Heptane SDS Water

0.25 0.2 0.15 0.1

b

SDS

0.35

Butanol

number density (Å -3)

0.4

number density (Å -3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.05

Butanol Heptane

0.3

Water

0.25 0.2 0.15 0.1 0.05

0

0

0 5 10 15 20 25 30 35 40 45 50 55 60 65

0

distance from the oil droplet com (Å)

5

10

15

20

25

30

35

40

distance from the oil droplet com (Å)

Figure 3: Density profiles for SDS (dashed and dotted line), butanol (dashed line), heptane (dotted line) and water (solid line) to COM, for the small system (a) and the big system (b). Vertical solid lines indicate the droplets radii.


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350

a Number of butanol molecules

350

Number of butanol molecules

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300 250 200 150 100 50

b

300 250 200 150 100 50 0

0 0

20000

0

40000

Simulation time (ps)


Figure 4: The number of butanol molecules within 25 Å radius of centre of mass of the simulated droplet, along the simulation time, for the small system (a) and within 32 Å for the big system (b). The dotted line shows the average number of butanol molecules within the selected radii, along the simulation time.

The shape of the droplet can be analysed by considering the eccentricity (e) defined as follows:

𝑒=1―

𝐼𝑚𝑖𝑛 𝐼𝑎𝑣𝑔

(4)

Where 𝐼𝑚𝑖𝑛 is the principal moment of inertia with the smallest magnitude and 𝐼𝑎𝑣𝑔 is the average of the three moment of inertia. The eccentricity value is related to the asymmetry of the formed droplet. In the case of e = 0, the droplet is a perfect sphere; values greater than 0 indicate a deviation from the spherical shape towards an elliptical


Page 23 of 52

one. The SDS/butanol/heptane in water droplet shape as a function of the MD simulation time, for the small system, is shown in Figure 5 (a). The average value of eccentricity along the simulation time as represented by the dotted line in Figure 5(a) was found to be e = 0.121. For the big system, the eccentricity profile of the droplet along the simulation time is given in Figure 5 (b). In this case, the average value is found to be equal to 0.356. Luft et al.65 reported that for a rhamnolipid/decane oil in water microemulsion, the oil/surfactant ratio affects the droplet shape. In particular droplets with a higher oil/surfactant ratio are characterized by a more oblate shape. In our case the heptane/SDS ratio for the big and the small systems are 1.73 and 1.64 respectively, suggesting the shape of the big system is more oblate (e = 0.356) than the small system (e = 0.121). This agrees with the finding of Luft et al.

a

0.25

0.7

b

0.6

0.2

Eccentricity

0.5

Eccentricity

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.15 0.1

0.4 0.3 0.2

0.05

0.1 0

0 0

20000

Simulaton time (ps)

40000

0


20000


40000

65

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Figure 5: Eccentricity profile for the butanol/heptane/SDS in water droplets along the MD simulation time, for the small system (a) and the big system (b). The dotted line shows the average eccentricity values, along the simulation time.

Probability distribution of terminal atoms within the droplet

The formed droplet is also characterized in terms of probability distribution of the distance of some reference atoms from the droplet COM. Atoms belonging to hydrophilic and hydrophobic groups within the radius of 25 Å and 32 Å, respectively for the small and the big systems were selected for carrying out this analysis. The sulfur atom of the SDS hydrophilic group (S), the terminal carbon atom of the SDS carbon chain (C12), the oxygen atom of the butanol hydrophilic group (O), the terminal carbon atom of the butanol carbon chain (C4) and the two terminal carbon atoms of heptane (C1 and C7) were chosen as reference atoms. Selected atoms are showed in Figure 6. Figure 7(a) and 7(b) show the probability distributions of reference atoms at the end of the MD simulations, for the small and the big systems.


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Figure 6: Atoms belonging to hydrophilic and hydrophobic groups that were selected for carrying out the probability distribution. Terminal carbon atoms are highlighted in blue, oxygens of the hydrophilic groups in red and sulfur atom of the SDS hydrophilic group in yellow.

0.14

0.12

A

SDS_S BUT_C1 HEPT_C1 SDS_C12 BUT_O HEPT_C7 water

0.12 0.10 0.08 0.06 0.04

B

SDS_S SDS_C12 BUT_C4 HEPT_C1 HEPT_C7 BUT_O water

0.1

Probability (Å-1)

0.16

Probability (Å-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.08 0.06 0.04 0.02

0.02

0

0.00

0

0 Distance 10 to droplet 20 center30of mass 40 (Å)

10

20

30

40

Distance to droplet center of mass (Å)

Figure 7: Probability distribution of reference atoms at 40 ns of MD simulation, for the small system (a) and the big system (b).


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Terminal atoms of heptane (HEPT_C1 and HEPT_C7 in Figure 7(a) and 7(b)) have almost identical probability distribution, the mean of which is found to be ~ 13.12 Å for the small system and ~ 16.85 Å for the big system. This confirms the fact that the heptane molecules are located in the inner core of the droplet and that the heptane molecules, being non-polar, have no preferential orientation towards the water phase. The terminal carbon atoms of the SDS molecule (SDS_C12 in Figure 7(a) and 7(b)) have the mean of probability distribution at 12.55 Å for the small system and 20.13 Å for the big system. As expected for both systems the hydrophobic part of the SDS molecule is oriented towards the oil phase.

However, for the small system the

distribution of SDS_C12 atoms overlaps with those of HEPT_C1 and HEPT_C7, while for the big system the C12_SDS distribution is more shifted towards the droplet interface. This is probably due to the slightly higher heptane/SDS ratio for the big system. A higher number of heptane molecules per number of SDS molecules makes the core of the droplet more hydrophobic and in turn the oil part of the droplet becomes more disconnected from the interface, constituted by amphiphilic molecules (SDS and butanol). The sulphur atoms of SDS (SDS_S in Figure 7a and 7b) have the mean of the probability distribution at 22.12 Å for the small system and at 29.19 Å for the big 26 ACS Paragon Plus Environment

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system, hence the hydrophilic part of the SDS molecule is oriented towards the bulk water phase. For the oxygen atoms of butanol (BUT_O in Figure 7a and 7b), the mean of the probability distribution is at 22.36 Å for the small system, which is almost equal to the one of the sulphur atoms. For the big system the BUT_O atoms the mean is at 26.53 Å, therefore the BUT_O distribution does not overlap with the SDS_S distribution. This confirms an overall shifting of SDS molecules towards the water phase. For the terminal butanol carbon atoms (BUT_C1 in Figure 7(a) and 7(b)), the mean of the distribution is at 20.53 Å for the small system and 23.71 Å for the big one, indicating that the butanol molecules are located at the oil-water interface. The location of butanol molecules proves the role of the co-surfactant component (butanol) in stabilizing the emulsion. The stabilizing effect is even more evident for the big system, in which the distributions of butanol atoms are in between the ones of SDS and heptane and the co-surfactant bridges the oil and the surfactant compounds.

Figures 8 and 9 show the evolution of the average distances of the reference atoms to the droplet centre of mass, respectively for the small and the big systems. For the small system all atoms have similar average positions at the beginning of the simulation, ranging between 18 and 21 Å. This is because with the starting 27 ACS Paragon Plus Environment

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configuration all butanol, heptane and SDS molecules were inserted randomly in a box of 40 Å × 40 Å × 40 Å. As the simulation progressed, the sulphur atoms shifted towards the droplet centre and at the end of 40 ns MD simulation, the average distance reached the final value of 12.55 Å. C12 terminal carbons of SDS molecule moved outwards and approached the final value of 22.12 Å at 40 ns. C4 and O atoms of butanol molecule moved slightly outwards and reached an average distance from the centre of mass of 20.53 Å and 22.36 Å respectively. C1 and C7 terminal carbon atoms of heptane molecule rapidly moved inwards from the initial positions in the first 5 ns of the simulation and approached a final value of around 13 Å. For the big system the starting configuration space was set up by placing heptane molecules within a sphere with radius 30 Å and butanol and SDS molecules within a spherical shell of 25 Å < r < 50 Å. The average positions at the start were 38.5 Å for SDS_C12 and 40.1 Å for SDS_S atoms, 36.4 Å for both BUT_O1 and BUT_C4, 34.1 Å for HEPT_C1 and 35.2 Å for HEPT_C7. In the first 5 ns of the simulation, the distance of all the reference atoms to the droplet centre of mass rapidly decreased. Distance profiles for HEPT_C1 and HEPT_C7 stabilized around a final value of 17 Å, for SDS_S around 29 Å, for


Page 28 of 52

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SDS_C12 around 21 Å, and around 24 Å and 27 Å for BUT_C4 and BUT_O, respectively.

30

25

average distance (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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20

15

10

5 0

5000

10000

15000

20000

25000

30000

35000

40000


Figure 8: Average distances of reference atoms from the droplet COM, for the small system: green lines were used for SDS molecule, red lines for heptane and yellow lines for butanol.


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33

average distance (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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28

23

18

13 0

5000

10000

15000

20000

25000

30000

35000

40000

Simulation time(ps)

Figure 9: Average distances of reference atoms from the droplet COM, for the big system: green lines were used for SDS molecule, red lines for heptane and yellow lines for butanol.

Accessible surface area for the droplet components

The accessible surface area (ASA) gives an insight on the relative area of each component (heptane, butanol, SDS) of the simulated droplets that interacts with the


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water phase. The ASA is calculated by removing all water molecules and rolling a probe molecule around the droplet surface. A probe of radius 1.4 Å was chosen to mimic water molecules66. The accessible surface area was computed with the built-in GROMACS

function,

gmx-sasa

(http://manual.gromacs.org/documentation/5.1/onlinehelp/gmx-sasa.html). In Figure 10 (a) and (b), the probability distribution of molecular ASA for each component (heptane, butanol, SDS) of the small and big droplets is reported. For the small system, the average molecular ASA for heptane, butanol and SDS correspond to 194.1 Å2, 144.1 Å2, 446.5 Å2, respectively. By multiplying the average molecular area for the number of molecules, respectively for all the heptane, butanol and SDS molecules within the droplet radius of 25 Å, we can estimate the total ASA to be 7958.1 Å2, 24064.7 Å2 and 11162.87 Å2, respectively. For the big system the average ASA for heptane, butanol and SDS are: 163.3 Å2, 109.1 Å2 and 483.9 Å2, respectively. Similarly, the total ASA for heptane, butanol and SDS is 10451.2 Å2, 28802.4 Å2 and 17904.3 Å2, respectively. This shows that heptane molecules are well protected from the water phase, while butanol and SDS assemble at the diffusive interface and thus screen the oil phase from the water bulk phase. Those values for ASA are in 31 ACS Paragon Plus Environment

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accordance with previous studies from

Luft et al.65 for the Rhamnolipid/decane

0.01 0.009

a

Probability (Å 2) -1

0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0 0

microemulsion

0.01

system.

200

400

Acessible surface area (Å2)

600

b

0.008

Probability (Å 2) -1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 52

0.006 0.004 0.002 0 0

200

400

Acessible surface area (Å2)

600

Figure 10: Probability distribution of ASA for butanol (dashed), SDS (dotted and dashed) and heptane (dotted) molecules, for the small system (a) and the big system (b).

Droplet/water partition coefficients


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The droplet/water partition coefficients of the 14 solutes measured by Ishihama et al.4 have been predicted using COSMOmic and compared with the experimental values. The 14 solute compounds adopted for this study are listed in Table 2. Entropy and enthalpy data for the 14 solutes were reported by Ishihama et al.4 for the simulated heptanes/butanol//SDS in water microemulsion system, from which the droplet/water partition coefficients were obtained. The comparison between the predicted and the experimentally measured partition coefficient was made by using root mean square error 1 n

(RMSE).

RMSE

is

n

∑i = 1(logKdroplet/w,predicted ― logKdroplet/w,exp),

defined where

as:

logKdroplet/w,predicted

RMSE = is

the

logarithmic of predicted, logKdroplet/w,exp is the logarithmic of the experimental values and n is the number of compounds in the analysed dataset. Droplet/water partition coefficients have been also compared to heptane/water partition coefficients, in order to investigate how the partitioning behaviour changes from the homogeneous bulk system of heptane to the inhomogeneous system of heptane/butanol/SDS in water microemulsion. Figure 11 (a) and (b) show the comparison between predicted droplet/water partition coefficients and experimental values of the 14 compounds belonging to the compound classes of polyaromatics, aromatics, ammines, esters and 33 ACS Paragon Plus Environment

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phenols, for the small system and the big system. The central solid diagonal line represents a perfect agreement between the experimental data and the predicted values. The two side lines above and below the solid diagonal line represent a ± 0.5 discrepancy from the central diagonal line in the logarithmic scale. The central diagonal line and the two side diagonal lines are drawn, to allow the examination of how well (or bad) the predicted partition coefficients compare with the experimental values. The predicted and experimental values for the droplet/water partition coefficients are listed in Table 2. The RMSE is equal to 0.41 and to 0.43 for the small and the big system respectively. As shown in Figure 11, most of the predicted values agreed well with the experiment data, having an accuracy within 0.5 in the logarithmic scale. The RMSE values are in line with previous studies on octanol-water67, micellar systems16,21,68 and lipid systems17,69,70. Only the partition coefficient for p-nitroaniline was severely underpredicted, with an error considerably higher than 0.5 in the logarithmic scale. This is expected given the previously reported inability of COSMORS in predicting the properties for secondary and tertiary amines accurately. The comparison with the heptane/water system is shown in Table 2 and in Figure 12. Experimental values for the droplet/water partition coefficients and the heptane/water 34 ACS Paragon Plus Environment

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ones are significantly different. Figure 12 shows that none of the data points fall within the ± 0.5 discrepancy region, suggesting that the partitioning behaviour of solutes in the homogeneous bulk phase of heptane is significantly different from the inhomogeneous heptane/butanol/SDS in water microemulsion. As the heptane bulk phase is a more lipophilic environment than the SDS/butanol/heptane in water droplet, non-polar compounds of the dataset such as toluene and nitrobenzene show considerably higher heptane/water partition coefficients compared to droplet/water ones. On the contrary, the rest of the solute compounds are composed by polar groups such as the hydroxyl group for phenols, cresols and 2-naphthol and the amine group for p-nitroanisole, therefore these compounds show significantly lower heptane/water partition coefficients than the droplet/water ones.


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3

a Log K droplet/w (predicted)

3

Log K droplet/w (predicted)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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2

1

b

2

1

phenols aromatics polyaromatics amines

0 0

1

2

Log K droplet/w (experimental)

ethers

0

3

0

1 (experimental) 2 Log K droplet/w

3

Figure 11: Comparison of predicted droplet/water partition with experimental data (calculated from the free energy reported by Ishihama et al.4) for heptane/butanol/SDS in water

microemulsion. The small system (a) and the big system (b) .

Table 2: List of experimental and predicted values for the heptane/butanol/SDS in water droplet partition coefficients.

Class

Solutes resorcinol pmethoxyphenol

phenols

aromatics

Log (K droplet/w)

Log (K heptane/w)

(exp) *

(exp) **

small

big

1.04

-3.18

0.70

0.58

n.a.

1.07

1.01

1.33

Log (K droplet/w) (pred)

phenol

1.40

-0.01

1.01

0.92

p-chlorophenol

2.16

0.52

1.69

1.58

p-ethylphenol

2.20

1.15

1.83

1.79

p-propylphenol

2.59

1.77

2.30

2.28

nitrobenzene

1.71

2.36

1.46

1.53

o-cresol

1.72

0.99

1.49

1.46

m-cresol

1.77

0.69

1.41

1.36

p-cresol

1.76

0.61

1.42

1.34


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toluene

2.38

3.76

1.85

1.92

amines

p-nitroaniline

1.47

-0.29

0.38

0.40

ethers

p-nitroanisole

1.87

n.a.

1.53

1.58

polyaromatics

2-naphthol

2.40

1.16

1.78

1.76

*Experimental data are derived from the reported free energy values of Ishihama et al4. **Experimental data for the heptane/water partition coefficients collected from Abraham et al33 are listed for comparison .

4 phenols aromatics

Log K heptane/w (experimental)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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amines

3

polyaromatics

2

1

0 0

1

2

3

4

Log K droplet/w (experimental)

Figure 12: Comparison of experimental values for the heptane/water partition coefficients and the heptane/butanol/SDS in water droplet/water partition coefficients.


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Conclusions Solute partitioning in the microstructure of multiphase fluids, such as micelles, emulsions and dispersions, is an important thermodynamic property for designing product formulations with optimal delivery. Experimental measurements for solute partition coefficients in complex product formulations are expensive and time consuming, whereas the majority of in-silico methods are only applicable to homogenous fluid systems. In recent years the method that combines MD simulations to COSMO-RS theory has been used for predicting micelle/water partition coefficients. In this paper the performance of this in-silico approach was tested for the prediction of solute partition coefficients in an inhomogeneous heptane/butanol/SDS in water microemulsion. MD simulations were used for modelling the self-assembling of two different sized heptane/butanol/SDS in water droplets. Subsequently the selfassembled heptane/butanol/SDS in water droplets were used in COSMOmic for the prediction of the droplet/water partition coefficients. The predicted droplet/water partition coefficients were compared directly with the experimental values for a dataset of 14 chemicals. The comparison showed a good agreement of the prediction with the


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experimental data for both the simulated systems, yielding a RMSE = 0.41for the small and a RMSE = 0.43 for the big one.

The combined MD/COSMOmic approach is shown to be reliable for predicting heptane/butanol/SDS in water droplet partition coefficients. The dependency of partitioning properties on temperature and pH can be also evaluated with the MD/COSMOmic approach. It can be foreseen that with the rapid development of MD simulation with replica exchange at constant pH71,72 and temperature73–75, these combined in-silico approach will represent a valid low-cost alternative to experiments. The main limitation of the method is the time required for the MD simulations, which increases with the size and complexity of the molecular assembly. Coarse grained simulations with subsequent back-mapping to the atomistic scale76 can be investigated and tested in combination with COSMOmic for speeding up the prediction.

Acknowledgement


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The authors appreciate the financial support provided by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 675251. Computational resources have been provided by Unilever Research & Development Port Sunlight Laboratory.


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