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Colloids and Surfaces A

journal homepage: www.elsevier.com/locate/colsurfa

Structural and interfacial properties of the CO2-in-water foams preparedwith sodium dodecyl sulfate (SDS): A molecular dynamics simulation study

José G. Parraa,⁎, Héctor Domínguezb, Yosslen Arayc,1, Peter Izad,h, Ximena Zaratee,g,Eduardo Schottf,g

aUniversidad de Carabobo, Facultad Experimental de Ciencias y Tecnología, Dpto. De Química, Lab. De Química Computacional (QUIMICOMP), Edificio de Química,Avenida Salvador Allende, Bárbula, Venezuelab Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, México, DF, 04510, Mexicoc Facultad de Ciencias, Universidad de Ciencias Aplicadas y Ambientales, UDCA, Campus Universitario Norte, Bogotá, Colombiad Escuela Superior Politécnica del Litoral, ESPOL, Departamento de Física, Campus Gustavo Galindo km 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuadore Theoretical and Computational Chemistry Center, Instituto de Ciencias Químicas Aplicadas, Facultad de Ingeniería, Universidad Autónoma de Chile. Avenida Pedro deValdivia 425, Santiago, ChilefDepartamento de Química Inorgánica, UC Energy Research Center, Facultad de Química y de Farmacia, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860,Macul, Santiago, ChilegMillenium Nuclei on Catalytic Processes towards Sustainable Chemistry (CSC), Chileh Center of Research and Development in Nanotechnology, CIDNA, Escuela Superior Politécnica del Litoral, ESPOL, Km 30.5 vía Perimetral, Campus G. Galindo,Guayaquil, Ecuador

G R A P H I C A L A B S T R A C T

A R T I C L E I N F O

Keywords:FoamsMolecular interactionInterface coverageSurfactants

A B S T R A C T

Structural characteristics, interfacial distribution and molecular interactions of the components of the CO2(gas)/SDS/water/SDS/CO2(gas) systems as a function of the CO2(gas)/water interface coverage by the SDS surfactantto different amounts of the CO2 were studied with molecular dynamics simulations and the NVT ensemble.Initially, the repulsive nonbonding parameter between the water oxygen and CO2 oxygen was adjusted to im-prove the prediction of the solvation free energy, solubility of the CO2 gas in water and the behavior of theCO2(gas)/SDS/water/SDS/CO2(gas) systems at molecular level. Our results show that the stability of the studied

https://doi.org/10.1016/j.colsurfa.2019.123615Received 24 May 2019; Received in revised form 11 June 2019; Accepted 25 June 2019

⁎ Corresponding author.E-mail address: jgparra2@uc.edu.ve (J.G. Parra).

1 In memoria of the Doctor Yosslen Aray.

Colloids and Surfaces A 578 (2019) 123615

Available online 27 June 20190927-7757/ © 2019 Elsevier B.V. All rights reserved.

T

foams can be improved incrementing of the vapor/water interface coverage with the SDS surfactant and theamount of CO2 in the system. With the highest interface coverage, the sulfate group has a molecular array morecompact at the interface. Furthermore, CO2 gas have a reduction of the diffusion across of the hydrocarbonchains to the water layer with an increment of the number of CO2 molecules in the system, indicating a behaviormore hydrophobic of the CO2 gas. The tendencies obtained of the simulations are consistent with the reportedexperimental results.

1. Introduction

Foams are dispersed systems of a gas in a liquid, which are ther-modynamically unstable, however, they can be kinetically stabilized bysurfactants, nanoparticles and polymers [1–3]. These systems presentdifferent self-destructive processes such as liquid drainage, Ostwaldripening and bubble coalescence [2,3]. Foams have been used in severalindustrial applications such as mineral flotation [4], enhanced oil re-covery (EOR) technique [5] and detergency [6]. For instance, in pet-roleum industry, EOR techniques use carbon dioxide (CO2) as foamingagent with different types of surfactants to design CO2-in-water (C/W)foams in extraction process [7–11]. Generally, due to the high viscosityof the CO2-in-water (C/W) foams, gas mobility is reduced by improvingsweep efficiency in oil reservoirs [12–14].

In these studies, there are several factors that could affect foamsstability such as concentration and types of surfactants, presence ofadditives, temperature and pressure among others. All these featureshave been evaluated to explain their effects on the behavior of the CO2-in-water (C/W) foams [10–16].

Surfactants are responsible of foamability and foam stability whenthey are absorbed at the gas/liquid interface [3,17]. In particular, theSodium Dodecyl Sulfate (CH3(CH2)11OSO3

−Na+, SDS) has been used inthe preparation of CO2-in-water (C/W) foams due to its high capacity toreduce the surface tension and produce high volume of foams that arewidely used in oil reservoirs [18–21]. However, it has been observedthat CO2-in-water (C/W) foams prepared with SDS are less stablecompared with those foams prepared with the same surfactant and withother gases such as N2 and O2 [20,22]. Therefore, studying the factorsthat affect the stability of the CO2-in-water (C/W) foams is a topic thatneeds to be addressed.

At the molecular level, Molecular Dynamic (MD) simulations havebeen employed to explore the behavior of SDS surfactant at the water/oil interface, the properties of CO2-in-water (C/W) foams and surfactantfilms located at the air/water interface using different force field types[19,22–26]. Also, in other investigations, the interfacial behavior of theCO2 in water and brine have been evaluated by means of MD simula-tions [27–29]. At the same time, the determination of the solubility anddiffusivity properties of CO2 in water have been carried out using thecombination of different force field with MD simulations [30].

Also, MD simulations have been used to study foams prepared withSDS where gas concentration and surface coverage (surface area permolecule) are constant. For instance, Li et al. [22] studied the behaviorof the foam as function of the molecular array of the surfactantmonolayer at the interfacial region, the molecular interaction betweenthe gases and the hydrophilic group, and gas diffusion across themonolayer.

Furthermore, experimentally, SDS presents the capacity to generatehigh volume of CO2-in-water foams [21]. However, these foams havepoor stability and very short lifetime, where the phenomena of liquiddrainage, coalescence of bubbles, and rupture of the films have beenobserved widely when these systems are used in petroleum industryapplications [7–11]. Therefore, to understand at molecular level thebehavior of the CO2-in-water foams prepared with the SDS surfactant,and to determine the factors that can improve their stability, we havedeeply studied, the interfacial distribution, structural properties andmolecular interactions of the components of the CO2(gas)/SDS/water/SDS/CO2(gas) systems using MD simulations. Herein, the propertieswere determined as function of the CO2(gas)/water interface coverageby the SDS surfactant and also as function of the amount of CO2 in thesystem.

2. Potential energy models and computational details

The GROMOS53A6 force field [31] was applied for describing theCO2 and SDS molecules in the MD simulations. The total energy, Etotal,includes the valence terms and nonbonding interaction terms, whichare defined by the Eqs. 1 and 2 [31]:

∑ ∑

∑

= − + −

+ + +

= =

=−

E K r r K θ θ

K δ m ϕ

14

( ) 12

(cos( ) cos( ))

(1 cos( )cos( )) E

N

b o

N

θ o

N

ϕ n n n

totaln 1

2 2 2

n 1

2

n 1non bonding

b θ

ϕ

(1)

∑ ∑= ⎛

⎝⎜ − ⎞

⎠⎟ +E

Cr

Cr

q qε r

12 64πε

1i j

onon-bonding

pairs(i,j)

ij

ij

ij

ij pairs(i,j) 112 6 (2)

In the Eq. 1, Kb, Kθ and Kφ terms are the parameters associated tothe bond distances (r and ro), angles between atoms (θ and θo) andtorsional dihedral angle (φn), respectively. The δn and mn terms arephase shift and multiplicity of the torsional dihedral angle. In the Eq. 2,the C12ij and C6ij terms are the parameters of the van der Waals in-teractions that depend on the atom types separated by a rij distance. TheC12ij and C6ij parameters are obtained from C12ii, C12jj, C6ii and C6jjparameters of each atom type, with the following combination rule[31]:

= =C C C C C12 12 12 ,C6 6 6ij ii jj ij ii jj (3)

In the electrostatic interactions, the εo and ε1 terms are the dielectricpermittivity of vacuum and relative permittivity of the medium inwhich the atoms are embedded. Finally, qi and qj are the charges of theatoms separated by a rij distance.

The bonded parameters of SDS and CO2 molecules were generated

Table 1Bonding and nonbonding parameters of the GROMOS53A6 force field for the CO2 used in the simulations.

Nonbonding Bonding

C6ij (carbon) 2.3582×10−3 kJ mol-1 nm6 KCO 3.2508×107 kJ mol−1 nm-4

C12ij (carbon) 4.9743×10−6 kJ mol-1 nm12 rCO 0.1170 nmC6ij (oxygen) 2.2789×10−3 kJ mol-1 nm6 KOCO 500 kJ mol−1

C12ij (oxygen) 7.4705×10−7 kJ mol-1 nm12 θOCO 180.0°qCarbon +0.752eqOxygen −0.376e

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from the Automated Force Field Topology Builder server (ATB, http://compbio.biosci.uq.edu.au/atb) [33]. Nonbonding parameters weretaken from the GROMOS53A6 parameter set [31] contained in theGromacs software (version 5.0.2) [34,35]. Final charges of the mole-cules were obtained by the method described in the ATB paper [33].Table 1 shows the bonding and nonbonding parameters of the GRO-MOS53A6 force field for the CO2 molecule obtained from the ATBserver [33].

Water was described with the Single Point Charge (SPC) model[32], which is a very good model to assess the solvent properties such asdensity and self-diffusivity in the bulk phase. In the SPC model, theOeH distance is 0.100 nm and the HeOeH angle is 109.47 degreeswith a unique nonbonding interaction between the oxygen sites. Non-bonding parameters and atomic charges in SPC model areσ(O)= 0.317 nm, ε(O)= 0.650 kJ/mol, qhydrogen = +0.4100e andqoxygen = −0.8200e.

The initial molecular geometries of the SDS, CO2 and water mole-cules were constructed using the Avogadro software [36] and the mo-lecular geometries are shown in Figure S4 in the supporting informa-tion. Afterwards, all the systems were constructed using the genbox,genconf and editconf tools of the GROMACS software (version 4.5.4)[34,35].

To calculate the solvation free energy of CO2 in water, the systemwas constructed placing a CO2 molecule in the center of a periodic boxof dimensions 3.098 nm x 3.098 nm x 3.098 nm with 999 water mole-cules. At the same time, the bilayer model was used in the constructionof the CO2(gas)/water/CO2(gas) and CO2(gas)/SDS/water/SDS/CO2(gas) systems, which is based on the Jang and Goddard [22,37] andZhao et al. [26] methods. In this part, a box of dimensions 3 nm x 3 nm x5 nm with 1500 water molecules was constructed with the genbox tool.Then, this water layer was located in the middle of a box in the z axiswith dimensions 3 nm x 3 nm x 120 nm based in the same procedureused by Boek et al. [27]. Afterwards, for the construction of theCO2(gas)/water/CO2(gas) system, CO2 layers were placed on both sidesof the water layer. A total of 11, 16, 22, 30 and 44 CO2 molecules wereused for the construction of the layers. In turn, CO2(gas)/SDS/water/SDS/CO2(gas) systems were constructed using SDS monolayers with ahexagonal close packing with 14, 18 and 23 molecules which corre-spond to interface coverages of 64, 50 and 39 Å2/molecule (occupiedarea per molecule of SDS surfactant). These correspond to unsaturated,saturated and oversaturated interface with SDS molecules, respectively.The gas vapor pressure was calculated using the ideal gas equation,vacuum volume of the box and temperature of 300 K. In the systems,the CO2 layers contain 11, 44 and 80 molecules, which represent CO2

pressures equivalent to 0.10MPa, 0.35MPa and 0.64MPa. The con-tribution to the pressure due to the water molecules present in thevapor phase was not considered.

A total of nine CO2(gas)/SDS/water/SDS/CO2(gas) systems weresimulated with periodic boxes whose dimensions were 3 nm x 3 nm x120 nm using the same procedure used by Boek et al. [27]. An example

of the initial and final configurations of the CO2(gas)/SDS/water/SDS/CO2(gas) systems are shown in Fig. 1. SDS molecules are located per-pendicular to the interface along the z axis. The hydrophilic group is incontact with the water and the CO2 molecules are located in the ex-tremes of the hydrocarbon chains. The molecular construction of thesystems is based in the schematic representation suggested by Johnstonet al. [11a] and Li et al. [11c] that show a structural array of the CO2-in-water (C/W) foams obtained of experimental results, where the CO2

molecules are being encapsulated by an interfacial layer of SDS sur-factants.

Previously, the repulsive nonbonding interaction parameter be-tween the water oxygen and CO2 oxygen were reparametrized using thesolvation free energy of the CO2 in water. This was performed to im-prove the combination of the SPC and GROMOS53A6 force fields in thedescription of the CO2(gas)/SDS/water/SDS/CO2(gas) systems and theaffinity of the CO2 in water. In this case, solvation free energy of theCO2 in water was computed by means of MD simulations in the NPTensemble with the GROMACS software (version 5.0.2) [34,35] usingthe thermodynamic integration approach [38,39]. In this approach, thefree energy difference between two states A and B, ΔGAB, is defined bythe Eq. 4:

∫==

=λΔG dH( )

dλABλ 0

λ 1

(4)

Where the H term is the energy of the system between neighboringλ values and λ term is the parameter of coupling between two states Aand B. In the state A (λ=0), the solute is decoupled to the solvent. Onthe other hand, in the state B (λ=1), the solute is completely em-bedded in the solvent. In GROMACS, the Bennett's Acceptance Ratio(BAR) method [40] was used for the estimation of the free energy ofsolvation. Initially, the system was minimized with the steepest descentalgorithm [41] and the final configuration was equilibrated with a MDsimulation of 2 ns in the NPT ensemble at 300 K and 1 atm. Afterwards,the system was split with different points of λ (λ equal 0.0, 0.2, 0.4, 0.6,0.7, 0.8, 0.9, 1.0). Then, MD simulations of 5 ns in the NPT ensemble byeach value of λ was carried out employing the accurate leap-frog sto-chastic dynamics integrator [42] at 300 K y 1 atm. The temperature wascontrolled with the v-rescale thermostat [43] with a relaxation timeconstant of 0.2 ps and the pressure with the Parinello-Rahman barostat[44,45] with a time constant for coupling equal to 5 ps. In the system,the bond lengths were constrained using the LINCS algorithm [46].Periodic boundary conditions were applied in all directions. The leap-frog algorithm [47] was used with a time step of 2 fs and the energieswere obtained every 1.0 ps. The van der Waals potential was performedwith a soft-core potential [48]. The parameters for the soft-core po-tential were: sc-power equal 1, sc-sigma equal to 0.34 and sc-alphaequal to 0.5. The Particle Mesh Ewald (PME) method [49] was em-ployed for the electrostatic interactions. Finally, trajectories werestored each 1000 fs. These simulations were carried out by triplicate.

Fig. 1. Snapshot of the CO2(gas)/SDS/water/SDS/CO2(gas) system. (a) Initial configuration of the system and (b) final configuration obtained after the simulation.The system has SDS monolayers and CO2 layers in the extremes. The length of the box in the z axis was of 120 nm.

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The results of the reparameterization of the repulsive nonbonding termbetween the water oxygen and CO2 oxygen using the solvation freeenergy of the CO2 in water are shown and discussed in the section S1 ofthe supporting information. The new repulsive nonbonding parameterbetween the water oxygen and CO2 oxygen is used in the description ofthe CO2(gas)/SDS/water/SDS/CO2(gas) systems and the determinationof the affinity of the CO2 in water.

At the same time, the interfacial and structural properties of theCO2(gas)/water/CO2(gas) and CO2(gas)/SDS/H2O/SDS/CO2(gas) sys-tems were determined using MD simulations and the NVT ensemblewith a time step of 1 fs. First, a process of minimization using thesteepest descent algorithm [41] was carried out and then, a 25 ns of MDsimulation were performed to obtain the used trajectories in the ana-lysis. In these simulations, the temperature was controlled with the v-rescale thermostat [43] with a relaxation time constant of 0.1 ps. Thebond lengths were constrained using the LINCS algorithm [46]. Peri-odic boundary conditions were used in the xyz directions. The leapfrogalgorithm [47] was used with a time step of 1 fs and the coordinates,velocities and energies were obtained every 1.0 ps. The non-bondedpotential was performed with a cutoff distance at 1.25 nm for theLennard-Jones interactions. The Particle Mesh Ewald (PME) method[49] was employed for the long-range electrostatic interactions. Tra-jectories were stored each 1000 fs. Graphs were plotted using GRACEsoftware [50] and the images were created using PyMOL [51] and VMD[52]. To verify that the studied CO2(gas)/SDS/water/SDS/CO2(gas)systems are in equilibrium, the variance of the total energy of thesystems was monitored along the simulations being invariable after ofthe 5 ns. The simulations were carried out by triplicate.

3. Results and discussion

3.1. Structural properties of the SDS surfactant, CO2 and water

With the density profiles along the Z axis of the components presentin the system is possible to evaluate the distribution of molecules in thenormal direction to the interface. The number densities of water, CO2

and the different components of the SDS surfactant (sulfate hydrophilicgroup, carbon chains and Na+ ion) were separately determined. In allcases, density profiles were determined with the number density sym-metrized over the two interfaces along the z axis with respect to thecenter of the system, where solely an interface is shown for better vi-sualization. Fig. 2 shows the concentration profiles of the SDS, CO2 andwater species present in the systems for interface coverage equal to0.64 nm2 by part of the SDS to different CO2 pressures. The rest of thedensity profiles obtained using different occupied area per molecule ofSDS surfactant equals to 0.64 nm2, 0.50 nm2 and 0.39 nm2 (these

correspond to unsaturated, saturated and oversaturated interface) todifferent CO2 pressure are shown in Figure S5 in the supporting in-formation.

The position of the GDS in the CO2(gas)/SDS/water/SDS/CO2(gas)systems was determined fitting the values of the interfacial densityprofile of the water to the hyperbolic tangent function defined by theEq. 5. In all systems, the interfacial region is well-defined. Indeed, weconsider that the interfacial region begin when the water density is a 90per cent of the bulk density and finalize in the position of the GDS in theaxis Z (see Fig. 2).

At the same time, the distribution of the SDS surfactant is in goodagreement with the array of the anionic surfactants at the vapor/waterinterface and also obtained in other investigations [22,25]. The sulfatehydrophilic group penetrates the water layer and the hydrocarbonchains are located in the vapor phase. The Na+ ions are located in thewater layer very close to the sulfate hydrophilic groups. Also, The Na+

ions are good solvated by the water molecules and the number densityprofiles demonstrate that the sulfate hydrophilic groups and Na+ arepreferentially closer at the interfacial region of the water layer.

In all systems, the water molecules are distributed in the bulk phase,interfacial region and vapor phase. At the interfacial region, watermolecules solvate the sulfate hydrophilic groups and the Na+ ions ofthe SDS surfactants.

Afterwards, in order to characterize the interfacial region, we de-termine the interfacial width of the interface of the studied systemsapplying the 10–90 criteria [22,37] on the water density profiles. Fig. 3shows interfacial width of the CO2(g)/SDS/water/SDS/CO2(g) systemsas function of the CO2 pressure to different interfacial coverages of theSDS surfactant. Herein, the variation of the interfacial width as functionof the CO2 pressure allows evaluating the effect of the CO2 on the in-terfacial film.

Without the presence of CO2 molecules, the interfacial width of thevacuum/SDS/water/SDS/vacuum systems with interfacial coveragesequal to 0.64 nm2, 0.50 nm2 and 0.39 nm2 were 9.40 Å, 9.52 Å and10.69 Å, respectively. These magnitudes indicate that the increment ofthe interfacial width is due to an increase of the concentration of thesulfate hydrophilic groups and Na+ ions of the SDS surfactant presentat the vapor/water interface. This same behavior was observed also byJedlovszky et al. [53] when they studied the variation of interfacialwidth as function of SDS surface concentration at the vacuum/waterinterface.

In presence of CO2 molecules and with the lower interface coverages(occupied area per molecule of SDS surfactant equal to 0.64 nm2 and0.50 nm2), the interfacial width of the CO2(gas)/SDS/water/SDS/CO2(gas) systems increase considerably with the CO2 pressures of0.10MPa and 0.35MPa. However, with a CO2 pressure equivalent to

Fig. 2. Number density profiles of the SDS, water and CO2 species in the systems with an interface coverage of 0.64 nm2. The CO2 pressure is equal to (a) 0.10MPaand (b) 0.64MPa. The Gibbs Dividing Surface (GDS) is located in the water density profile at the half of its value in the bulk phase.

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0.64MPa, the interfacial widths with lower interface coverages suffer aslight reduction. On the other hand, with the higher interface coverage(occupied area per molecule of SDS surfactant equal to 0.39 nm2), theinterfacial width increases slightly with the CO2 pressure in comparisonwith the other two interface coverage. Also, this property with thehighest interface coverage varies very few with an increment of CO2

pressure (from 12.41 Å to 13.32 Å when the pressure varies from0.10MPa to 0.35MPa).

These tendencies suggest that the CO2 molecules are located at theinterface to low interface coverages (occupied area per molecule of SDSsurfactant equal to 0.64 nm2 and 0.50 nm2). In this case, the sulfatehydrophilic groups are more separated from each other at the interfaceallowing that the CO2 molecules coexist with a higher number of watermolecules at the interface, which generate an increment of the inter-facial width as result of the CO2 pressure. This behavior indicates thatCO2 molecules can migrate from the interface toward the water bulk.Instead, when the CO2 pressure is equivalent to 0.64MPa, CO2 mole-cules coexist preferentially with the hydrocarbon chains of the SDSsurfactants present in the monolayer, which produce a reduction of theinterfacial width. This suggests that an increment of the pressure re-duces the liquid water drainage and increase the lifetime of the CO2-in-water foam prepared with the SDS surfactant. Experimentally, Wanget al. [20] found that the foaming volume and half-life for CO2 foamsprepared with SDS increase as function of the pressure.

In the system with the high interface coverage (occupied area permolecule of SDS surfactant equal to 0.39 nm2) and CO2 pressure of0.35MPa and 0.64MPa (Figs. 4(b) and 4(c)), the tendency of the in-terfacial width indicate that the CO2 molecules have difficulty to coexistwithin the ordering compact and rigid of the hydrophilic part of theSDS surfactant at the vapor/water interface, and therefore, the inter-facial width is affected very little with an increment of CO2 pressure(see Fig. 3).

Here, CO2 molecules are concentrating in the hydrocarbon chains ofthe surfactant monolayer (see Figures S5(g), S5(h) and S5(i) in thesupporting information). Based on this behavior, we suggest that thestability of a CO2-in-water foam prepared with SDS surfactant can befavored with a high concentration of surfactant located at the inter-facial region of the system (oversaturated interface with SDS surfac-tant). At the same time, the concentration of CO2 molecules that coexistwith the hydrocarbon chains of the SDS surfactants in the vapor phaseincrement with the CO2 pressure (see Fig. 4(c) and Figure S5(i) in thesupporting information). This same behavior was found for the rest ofthe interface coverage (see figures S6(a)-(c) and S7(a)-(c) in the sup-porting information).

Additionally, making a comparison between the systems with thesame interface coverage but different CO2 pressure, we observe that thehydrocarbon chains density profiles are most affected to the highest andlowest interface coverage (0.39 nm2 and0.64 nm2, respectively). Thiscan be visualized in Figures S5(a)-(c) and S5(g)-(i) of the supportinginformation. These density profiles are more expanded along of the zaxis with the increment of the CO2 pressure, which indicate that thehydrocarbon chains of the SDS monolayer are more extended in thenormal direction to the interface. Instead, for the interface coverageequal to 0.50 nm2, the system with the CO2 pressure of 0.35MPa hasthe density profile more expanded along of the z axis (see Figure S3(e)in the supporting information). In all cases, these results suggest that anincrement of the CO2 pressure favor the formation of channels betweenthe extended hydrocarbon chains of the SDS surfactant that allow mi-gration of the CO2 molecules toward the interface.

To verify the SDS tail extension, the average molecular orientationof the hydrocarbon chains of the SDS surfactants was determined usingthe order parameter [54]. Order parameter along the z axis (Sz) is de-fined by Eq. 5:

=S θ12

(3cos ( )-1)z2

(5)

In this Eq. 5, the θ term is the angle between the vector parallel to

Fig. 3. Interfacial width of the CO2(g)/SDS/water/SDS/CO2(g) systems ob-tained in function of the variation of the CO2 pressure.

Fig. 4. Snapshots of the final configuration of the water/SDS/CO2 systems for an occupied area per molecule of SDS equal to 0.39 nm2. The CO2 pressure in thesystems were (a) 0.10MPa, (b) 0.35MPa and (c) 0.64MPa, respectively.

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the z axis and the molecular axis associate to the hydrocarbon chains ofthe SDS surfactants, which is defined as the vector from the carbonlinked to the hydrophilic group (Cn-1) and Cn+1. Sz order parameter isequal to -1/2 when the hydrocarbon chain of the surfactant is parallelto the interface, 1 when the chain is perpendicular to the interface andzero in the case of an isotropic orientation [55,56]. Fig. 5 shows themolecular orientation along the z axis of the hydrocarbon chains of theSDS surfactants as a function of the CO2 pressure and interface cov-erage. In circles, the Sz order parameter of the hydrocarbon chains ofthe SDS surfactants without the presence of CO2 molecules in the sys-tems are shown in Figs. 5(a)-5(c). Herein, the carbon atom C1 of thehydrocarbon chain is linked to the sulfate group. The tendency of thegraphs suggest that the hydrocarbon chains present a vertical disposi-tion in the carbon atoms that are closer to the interfacial region (fromcarbon atom C1 to C4, from carbon atom C1 to C7 and from carbonatom C1 to C9 for the surface coverage equal to 0.64 nm2, 0.50 nm2 and0.39 nm2, respectively). Instead, the last carbon atoms located in theextreme of the hydrocarbon chains have an isotropic orientation, in-dicating that SDS surfactant molecules do not have the same tilt angle.

Also, we have observed that the Sz order parameter is increasingwith an increment of the interface coverage (values of 0.1915, 0.2504and 0.3611 for the surface coverage equal to 0.64 nm2, 0.50 nm2 and0.39 nm2 in the carbon atom C1, respectively), which suggest that thehydrocarbon chains of the SDS surfactants is more vertical in themonolayer with the higher interface coverage equal to 0.39 nm2.Furthermore, the values of the Sz order parameter of the hydrocarbonchain of the SDS surfactant without the presence of CO2 molecules arelower than 0.2. These values are similar to the reported in other systemswith the SDS surfactant [55–58].

The studied systems with the presence of CO2 molecules, the Szorder parameter of the hydrocarbon chains of the SDS surfactants iswidely affected (see Figs. 5(a), 5(b) and 5(c)). With an increment of theCO2 pressure, the Sz order parameter is increasing in the same order,which indicate that the presence of CO2 molecules help to the verticalorientation with respect to the interface of the hydrocarbon chains ofthe SDS surfactants. This effect is much more visible when the CO2

pressure is equivalent to 0.64MPa and for the surface coverages thatcorrespond to the values of 0.50 nm2 and 0.39 nm2. These results cor-roborate that in the saturated and oversaturated interface with a SDSmonolayer, the hydrocarbon chain of this surfactant have an orienta-tion almost perpendicular with respect to the interfacial region, whichgenerate the formation of channels that can allow the migration of theCO2 molecules from the vapor phase to the interfacial region. Thisbehavior has been obtained in other work [19,59]. At the same time,

these results are consistent with those obtained using the density pro-files mentioned above, where the hydrocarbons chains are more ex-tended with an increment of the CO2 pressure.

Finally, the stability of the CO2-in-water (C/W) foams prepared withSDS surfactant depend of the compact packing of the surfactant filmthat reduce the liquid drainage and the CO2 diffusion from the vaporphase toward the water bulk. In this case, above results suggest that thesystem with the highest interface coverage and CO2 pressure (occupiedarea per molecule of SDS surfactant equal to 0.39 nm2 and pressure of0.64MPa) can have the highest stability, where the CO2 moleculescoexist with the hydrocarbon chains of the SDS monolayer. However,with the highest interface coverage of 0.39 nm2, CO2 molecules havedifficulty to go through the ordering compact and rigid of the hydro-philic part of the SDS surfactant at the vapor/water interface. Tocomplement these phenomena, the molecular interaction between thesulfate hydrophilic group with the water and CO2 molecules is dis-cussed in the section 3.3.

3.2. Molecular interaction between the sulfate group, water and CO2

To analyze the water-sulfate group, CO2-sulfate group andwater−CO2 interactions, the Radial Distribution Functions (RDFs, g(r))of these pairs were determined over the last 10 ns of the simulationsusing certain atom in specific.

For the water-sulfate group interaction, the RDFs between the threeoxygens (OM) linked to the sulfur of the sulfate group and water oxygen(OW) were determined as function of the interface coverage and CO2

pressure (see Fig. 6).In Figs. 6(a)-(c), RDFs of the OMeOW pair shows three peaks lo-

cated at 0.188 nm (first peak), 0.332 nm (second peak) and 0.412 nm(third peak). The intensity and position of the first peak indicate thestrong hydrogen bond interaction that exist between the sulfate groupand water in the first hydration shell, whose thickness is taken at thedistance of the position of the first minimum in the RDFs, which islocated at 0.260 nm. Furthermore, the heights of the first peak suggestthat the sulfate hydrophilic group have a high influence on the watermolecules that are around them in the interfacial region. The secondpeaks at 0.332 nm suggest the formation of a second hydration shell dueto the electrostatic interaction between the hydrated sulfate group andwater molecules near of the first hydration shell. Here, the second hy-dration shell has an extension from 0.260 nm to 0.378 nm. Finally, thethird peaks located at the position 0.412 nm show the formation of athird hydration shell generated by a weak molecular interaction, whichis extended to 0.488 nm. The formation of these hydration shells allows

Fig. 5. The Order parameter of the hydrocarbon chain of SDS with occupied areas per molecule equal to (a) 0.64 nm2, (b) 0.50 nm2 and (c) 0.39 nm2.

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predicting that the sulfate group can be extended into the water layer,which is consistent with the hydrophilic nature of the SDS surfactant.This behavior has been reported in other investigations [24,25].

Afterwards, the effect of CO2 pressure on the molecular interactionbetween the sulfate group and water was evaluated (see Figs. 6(a), 6(b)and 6(c)). In all cases, for a given interface coverage, the increment ofCO2 pressure reduce very little the height of the three peaks present inthe RDFs of the OMeOW pair (For example, for the surface coverageequal to 0.39 nm2, intensities of the first peak were 31.55, 30.04 and28.84 for the CO2 pressure of 0.10MPa, 0.35MPa and 0.64MPa, re-spectively). The rest of the values can be observed in the Table S4 in thesupporting information. This indicate that the interaction between thesulfate hydrophilic group and water in the interfacial region is slightlyaffected by the presence of CO2 molecules located at the interface andtherefore CO2 pressure reduce the number of hydrated water moleculesaround the sulfate hydrophilic group.

Also, sulfate group−CO2 interaction was evaluated using the RDFs.In this case, RDFs between the oxygen atom (OM) of the sulfate groupand CO2 carbon atom was determined in all the studied systems (seeFig. 7(a)-7(c)).

In Fig. 7(a)-(c), RDFs of the OMeC pair shows two peaks located at0.294 nm (first peak) and 0.518 nm (second peak), where these valuescorrespond to average positions. The position of the first peak located at0.294 nm means that the CO2 molecules interact with the sulfate grouppreviously hydrated with the water molecules. Therefore, the CO2

molecules can be located between the first and the second hydrationshell of water that are around the sulfate hydrophilic group. Instead, theposition of the second peak located at 0.518 nm indicate that a group ofCO2 molecules are located after the third hydration shell of water that isaround the sulfate hydrophilic group.

At the same time, the height of the first peak of the RDFs associate tothe OMeC pair change with the CO2 pressure for the different interfacecoverages (see Fig. 7(a)-(c) and Table S5 in the supporting informa-tion). For the interface coverages whose values are 0.50 nm2 and0.39 nm2, the height of the first peak decrease with an increment of theCO2 pressure, so the interaction between the sulfate group and CO2 isweaker with an increment of the CO2 pressure. However, for the in-terface coverage equivalent to 0.64 nm2, where the sulfate group aremore separated each other at the interfacial region, the variation of theheight of the first peak with respect to the CO2 pressure was anomalous.In this case, the interaction more favorable between the sulfate groupand CO2 was obtained for the CO2 pressure equal to 0.35MPa.

Also, to a given CO2 pressure, the height of the first peak decreasewith an increment of the interface coverage, which means that thecompact packing and rigid of the sulfate groups at the interfacial regionincrement the repulsion between the sulfate groups and CO2 molecules.

Here, the sulfate groups are closer at the interface and these phenomenareduce the migration of the CO2 molecules from the vapor phase to theinterfacial region.

Additionally, molecular interaction between the water and CO2 wasdetermined using the RDFs between the CO2 carbon atom (C) and wateroxygen (OW) as function of the interface coverage and CO2 pressure(see Fig. 8). In all the systems, RDFs of the CeOW pair show a peaklocated at 0.410 nm with a minimum located at 0.540 nm, which isconsistent with the value of 0.380 nm that was obtained by Panhuiset al. [60] using a nonpolarizable force field for the CO2 in combinationwith the water SPC-E model. The height of this peak suggests that exista weak nonbonding interaction between the CO2 and water molecules.

Furthermore, the height of the peak of the C-OW pair decrease withan increment of the CO2 pressure for all the interface coverages, whichindicate a reduction of the interaction between the CO2 and water.Instead, for the interface coverage equivalent to 0.64 nm2, the max-imum peak has almost the same value when the CO2 pressures are0.35MPa and 0.64MPa, respectively.

Experimentally, the CO2 becomes more lipophilic with an incrementof the pressure [20,22]. Therefore, the reduction of the intensity of thepeak with an increment of the CO2 pressure suggests that CO2 mole-cules show a behavior more hydrophobic with an increment of the CO2

pressure. Because of that, CO2 molecules are concentrating in the hy-drocarbon chains of the SDS monolayer (see Figs. 5(b) and 5(c)), whichsuggest that the interaction of CO2 molecules with water decrease whenthe CO2 pressure increase (see Fig. 8).

Fig. 6. RDFs between the sulfate group and water as function of the CO2 pressure and interface coverage of the SDS. Occupied areas per molecule of SDS surfactantare equal to (a) 0.39 nm2, (b) 0.50 nm2 and (c) 0.64 nm2.

Fig. 7. RDFs between the sulfate group and CO2 as function of the CO2 pressureand interface coverage by the SDS surfactant. Occupied areas per molecule ofSDS surfactant correspond to (a) 0.39 nm2, (b) 0.50 nm2 and (c) 0.64 nm2.

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These results demonstrate that the CO2-in-water foams preparedwith SDS surfactant have an increment in the lifetime when the inter-face coverage is high (occupied area per molecule of SDS surfactantequal to 0.39 nm2 and 0.50 nm2) and the surfactant film has a mole-cular array more rigid and compact of the hydrophilic part at the in-terfacial region, which avoid that the CO2 molecules migrate from thevapor phase towards the water bulk. Moreover, an increment of the CO2

pressure can help to the stability of CO2-in-water foams, as result of theincrement of the hydrophobic nature of the CO2. This tendency at levelmolecular is consistent with the behavior experimental obtained byWang et al. [20] in the study of the stability of CO2 foams at highpressure. In this case, molecular interaction of the hydrocarbon chain ofthe SDS with the CO2 in the surfactant film is more favorable (seeFig. 4(b) and 4(c)). Also, the results suggest that the CO2-in-water foamsprepared with SDS surfactant at low surface coverage have the lowestlifetime and stability.

3.3. Diffusion of the CO2 in the studied CO2(gas)/SDS/water/SDS/CO2(gas) systems

Dynamics properties of the CO2 were determined using the meansquare displacements (MSD) in the studied systems. In GROMACS, theMSD can be determined using Eq. 6 [34,35]:

∑= −=

tN

r t rMSD( ) 1 | ( ) (0)|N

i ii 1

2

(6)

In this equation, N corresponds to the number of molecules orparticles, and ri(t) is the position of the particles at time t. In this case, Nvaries as function of the number of CO2 molecules present in the sys-tems and MSD was determined along the z axis of the simulated system.Figure 10 shows the MSD of the CO2 for different interface coveragesand CO2 pressures.

The dynamics of the diffusion of the CO2 from the vapor phase to-wards the bulk water play a fundamental role in the lifetime of CO2-in-water foams prepared with SDS. Consequently, we have discussed thatthe CO2 molecules coexist in the region of the hydrocarbons chainswhen the CO2 pressure increase. Results of MSD are consistent withthose obtained with the molecular interaction between the CO2 andwater pair, and between the sulfate group and CO2 pair. Here, CO2

molecules have a reduction of the diffusion and mobility across of thehydrocarbon chains towards the water bulk with an increment of theCO2 pressure and surface coverage (see Figs. 9(a), 9(b) and 9(c)). Infact, in all interface coverages, the mobility of the CO2 molecules ismore favorable for the pressure of 0.10MPa, and therefore, these mo-lecules have a high diffusion towards the bulk water.

At the same time, these results suggest that the reduction of the MSDwith the increment of the CO2 pressure is due to the increase of themolecular interaction between the hydrocarbon chains and CO2 mole-cules, which indicate an increment of the hydrophobic nature of theCO2 molecules with the increase of the gas pressure in all the systems.As result of this, the MSD complement the factors mentioned above thathelp to improve the stability of the CO2-in-water foams prepared withSDS surfactant.

4. Conclusions

Interfacial distribution, structural characteristics and molecular in-teractions of the components present at the CO2(gas)/SDS/water/SDS/CO2(gas) systems were determined as function of the interface coverageby the SDS surfactant for different CO2 pressures by means of moleculardynamics simulation. The density profiles demonstrate that the sulfatehydrophilic group penetrate the water layer and the hydrocarbonchains are located in the vapor phase. In fact, the hydrocarbon chainsare more extended with an increment of the CO2 pressure. In othercontext, CO2 molecules coexist in high proportion with the hydro-carbons chains with an increment of the CO2 pressure in the CO2(gas)/SDS/water/SDS/CO2(gas) systems.

The RDFs of the sulfate hydrophilic group-water pair suggest thatthe sulfate hydrophilic group increment the molecular interaction withthe water as function of the interface coverage presenting three hy-dration shell. At the same time, the RDFs of the sulfate group−CO2 pair

Fig. 8. RDFs between the water and CO2 as function of the CO2 pressure andinterface coverage by the SDS surfactant. Occupied areas per molecule of SDSsurfactant correspond to (a) 0.39 nm2, (b) 0.50 nm2 and (c) 0.64 nm2.

Fig. 9. Mean square displacement of the CO2 molecule for different surface coverages. Occupied areas per molecule of SDS surfactant are (a) 0.64 nm2, (b) 0.50 nm2

and (c) 0.39 nm2.

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indicate that the molecular interaction between the sulfate hydrophilicgroup and CO2 is reduced with an increment of the CO2 pressure.Moreover, RDFs of water−CO2 pair demonstrate that the molecularinteraction between the water and CO2 is reduced with the increment ofthe CO2 pressure, which means that the CO2 is more hydrophobic withan increase of the pressure.

The CO2-in-water foams prepared with SDS surfactant can improveits stability with a high interface coverage (occupied area per moleculeof SDS surfactant of 0.39 nm2 and 0.50 nm2) when the surfactant filmhave a molecular array more rigid and compact of the hydrophilic partat the interfacial region, reducing the diffusion of the CO2 moleculesfrom the vapor phase towards the bulk water. Moreover, with an in-crease of the CO2 pressure in the CO2-in-water foams, CO2 moleculescoexist with the hydrocarbon chain of the SDS which suggest that theCO2 molecules have a behavior more hydrophobic. This behavior isconsistent with the experimental results obtained for these foams. Atthe same time, the results indicate that the CO2-in-water foams with thelower interface coverage for different CO2 pressures have a minor sta-bility.

Declarations of interest

None.

Acknowledgment

Professor José G. Parra acknowledges financial support from theMaterials Science Institute, Universidad Nacional Autónoma de México,México, DF, 04510, by the short research visit. The authors thank theprovided supported by FONDECYT1161416 and Millennium ScienceInitiative of the Ministry of Economy, Development and Tourism-Chile,grant Nuclei on Catalytic Processes towards Sustainable Chemistry(CSC).

Appendix A. Supplementary data

Supplementary material related to this article can be found, in theonline version, at doi:https://doi.org/10.1016/j.colsurfa.2019.123615.

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