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Mechanism of foam destruction by antifoams: a molecular dynamics study† Fengfeng Gao,a Hui Yan,b Qiwei Wangc and Shiling Yuan*a In enhanced oil recovery (EOR), the micro-oil droplet heavily affected the stability of foam and prevented foam flooding. In this paper, the oil bridge-stretching mechanism of foam rupture was described through molecular dynamics with the aim of providing supplements to the experiments at the molecular level. Two important phenomena for foam rupture have been pointed out by the simulation. One is about the pseudoemulsion film, representing the stability of the oil–water–air three phase interface. The bound water connecting the headgroups of the surfactant through strong H-bonding interactions played a vital role in the stability of the pseudoemulsion film. These water molecules could hinder the disappearance of the water phase in the pseudoemulsion film. The additional energy barrier, which was influenced by the surfactant concentration, also played a vital role in preventing the destruction process. The other factor is about the oil bridge, which appeared after the destruction of the pseudoemulsion film. The external horizontal force stretched the bridge resulting in the destruction of the bridge. The process was decided
Received 10th May 2014, Accepted 16th June 2014
by the properties of the oil molecules. In the simulation, the stretching force was divided into three stages
DOI: 10.1039/c4cp02038c
the second equilibrium force, which stretched the middle of the oil bridge so that it became thin, was vital
including the initial increasing force, the middle equilibrium force and the final decreasing force. Especially to the foam rupture. The concentration and properties of the oil molecules were the crucial factors for
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foam rupture. The simulated results offer important supplements to experiments.
1. Introduction Foam is a typical thermodynamically unstable gas–liquid system,1 which is widely used in fire-fighting, personal care, polymeric foam insulation and so on.2,3 However, in some industrial cases, foam is undesirable. Excessive foam can hamper industrial processes.4 In those conditions, eliminating undesired foam becomes crucial. In experiments, microscopic solid particles, oil droplets, and their combination, are widely used as typical ‘‘antifoams’’,5 and these antifoams pre-disperse in the foam solution to prevent producing excessive foam.2 In recent years, many experimental techniques, including X-ray reflection,6 resonance Raman scattering,7 and interfacial rheology,8 have been explored to investigate the properties of foams. These experiments have provided much information about the characters of foam films. At the same time, several mechanisms of foam rupture have been reported. By a high
speed video camera, the bridge-stretching mechanism (Fig. 1) has been suggested to explain the process of foam destruction in the presence of antifoams.2,9 This mechanism unambiguously shows that an antifoam globule could enter the Plateau Borders (PBs) and be compressed by the foam walls. This behavior compels the antifoam globule to enter into the film and form an oil bridge in
a
Key laboratory of Colloid and Interface Chemistry, Shandong University, Jinan 250100, China. E-mail: [email protected]; Fax: +86 531 88564464; Tel: +86 531 88365896 b College of Pharmacy, Liaocheng University, Liaocheng 252059, China c Geological Scientific Research Institute of Shengli Oilfield Company, SINOPEC, Dongying 257015, China † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4cp02038c
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Fig. 1
A sketch of the bridge-stretching mechanism.
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the middle of the foam film. In most conditions, capillary pressures can stabilize the water–oil–vapor three phase interface of the oil bridge. However, uncompensated capillary pressures will stretch the bridge in the radical direction with time evolution, which eventually results in film rupture.9,10 A diagram of the bridge-stretching mechanism, evolving from the work of Denkov,2 is shown in Fig. 1. When an oil globule acting as antifoam approaches the PBs, an asymmetric oil–water–air film appears9 (Fig. 1b). The film was defined as a pseudoemulsion film by Wasan,11 and its stability is very important to the foam film. The stability of a pseudoemulsion film is disturbed by compressive forces from the foam walls. If the compressive force is too small to affect the pseudoemulsion film, foam films are steady; otherwise, the foam films could rupture quickly.12 The formation and rupture of the pseudoemulsion film are the necessary step to film destruction.10 The factor deciding the stability of a pseudoemulsion and preventing the antifoam from emerging on the solution surface is called the entry barrier.10 Many experiments have unambiguously showed that the entry barrier is one of the crucial factors for evaluating foam stability.13–15 High entry barriers can prevent oil globules from entering foam films. While, low entry barriers make antifoams enter foam films easily and induce foam rupture quickly. The entry barrier is also used to explain how an antifoam affects the stability of a pseudoemulsion film.16 When the pseudoemulsion film is destroyed, an oil bridge is formed between the surfaces of the two foams (Fig. 1c). For the oil bridge, even a small perturbation is able to induce the bridge from the equilibrium position to unsteady. What’s worse, the perturbation will result in the whole rupture of the foam film (Fig. 1d).13 In experiments, capillary pressures, which can balance the oil–water and oil–air interfaces, are crucial to the stability of the oil bridge. If the capillary pressure is uncompensated, it will stretch the bridge with time (Fig. 1c) and give rise to rupture of the foams.9 Based on previous concepts,13–15 the bridge-stretching mechanism provides new explanations for foam destruction. However, due to the limitations of experimental techniques, details of the foam destruction mechanism, especially at the molecular level, are still not explicit to scientists. A complete understanding of the mechanism of foam rupture needs the assistance of theoretical research. Steered molecular dynamics (SMD) has been proved to be an effective method to investigate the behavior of a system toward a special phenomenon, which might not be realized by conventional molecular dynamics (MD).17 In SMD, an external force can perturb the equilibrium of a system and further give rise to displacements in the simulations.18 In this paper, SMD will be used to simulate the process of foam rupture and supply important information for experiments at the molecular level. The current work is divided into three parts. First, the character of the foam was investigated. Second, the entry barrier,
Table 1
which determines the stability of the pseudoemulsion film and the formation of the oil bridge, was discussed. Third, the stretching force to the oil bridge was studied. The force led to foam rupture directly. Using the SMD method, molecular level information about the bridge-stretching mechanism was obtained, which is helpful as it supplements experiments.
2. Simulation section 2.1
The construction of the foam film
In the crude oil industry, the layer of spread oil on a film surface plays an important role in foam rupture.13,19 Therefore, a typical foam film was constructed. In our simulation, the surfactant, sodium polyoxyethylene alkylether carboxylate (AEC), which has been widely used in oilfields, was selected.20 A dodecane (C12) molecule acted as the pre-dispersed oil molecule.21 To construct the foam film, a water layer, whose size was about 16 4 4 nm3, was built. Then 160 surfactants and 160 dodecane molecules were scattered randomly on each side of the water layer. In order to maintain neutrality in the simulation box, 320 sodium ions were added to the water solution. Then the Z axis of the box was extended to 20 nm to minimize interactions between periodic replicas. The constructed foam film was considered as System I (Fig. S1, ESI†). In crude oil conditions, some molecules with surface activities can adsorb on the surface of an oil globule to form an emulsified oil globule. Hence, one globule containing 60 C12 molecules and 10 AEC molecules, as an antifoam, was put in the water phase of the foam films (System I) to simulate foam rupture. The system was defined as System II (Fig. S2, ESI†). In many experiments, the concentration of the surfactant can seriously affect foam rupture. Thus, a low concentration AEC was introduced, and the system was called System III (Fig. S3, ESI†). All the systems and corresponding labels are listed in Table 1. 2.2
Simulation details
All simulations were put in GROMACS 4.0.5. The interatomic interactions were calculated according to the parameters and potential functions of the GROMOS 53a6 force field.22 The standard potential model of molecular mechanics was used: X 2 X 2 u rN ¼ ki li li;0 þ ki yi yi;0 bonds
þ
þ
angles
X Vn ð1 þ cosðno gÞÞ 2 torsions N X N X i¼1 j¼iþ1
" ! 6 # sij 12 sij qi qj 4eij þ rij rij rij
Summaries of simulated systems
System label
Water number
AEC number
C12 number
Na+ number
Emulsified oil globule
Box size (nm3)
Simulation pattern
I II III
8400 7300 7300
320 320 160
320 320 320
320 320 320
0 1 1
16 4 20 16 4 20 16 4 20
10 ns MD SMD 10 ns MD + SMD SMD
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The first three terms represent the bond interactions, which consist of bond, angle and torsion interactions, respectively; the last terms are the van der Waals and Coulombic interactions, which are defined as nonbonding interactions. In this force field, a united-atom description was used for the AEC and C12 molecules. The coordinates and parameters of the AEC molecule and C12 were taken from ProDRG,23 and their charges were obtained by Dmol3.21,24 Detailed descriptions are in the ESI.† In the simulation, water was described by the simple point charge (SPC) model.25 Sodium came from the work of Lyubartsev et al.26 Periodic boundary conditions were applied in the x, y, and z directions in all simulation systems. The cut-off of the Lennard-Jones interactions was 1.2 nm. Bond lengths were constrained using the LINCS algorithm.27 The Particle Mesh Ewald (PME) method was employed for the longrange electrostatic interactions.28 For the three systems, different molecule dynamics methods were used. System I used the steepest descent method to minimize the initial configurations. Then 10 ns NVT Ensemble at 298 K was carried out. For Systems II and III, the simulations were inaccessible on the time scale of conventional MD. Therefore, the SMD method was applied to study the particular phenomena. In the SMD systems, the foam films are pulled to the center of the antifoam along the Z-axis using a constant of 500 kcal mol1 nm2 and a pulling rate of 0.005 nm ps1. The external force was calculated directly from the SMD trajectory within acceptable error.18,29 During all simulations, the time step was 2 fs, and the trajectories were kept every 10 ps. Trajectories were visualized using VMD 1.8.5.30 In the experiments, two kinds of forces on the foam film were noticed in the bridge-stretching mechanism. One is the force coming from the film walls on two sides, and the other is the force due to the perturbation of capillary pressures in the foam film. The former is considered as the force applied along the vertical direction of the film which compels the antifoam to enter into the film (Fig. 1b), and the latter is the one along the horizontal direction which stretches the oil bridge to cause foam rupture (Fig. 1c). In our work, the key point is how to apply the SMD method to mimic the two types of forces on the foam film.
3. Results and discussion 3.1
Structure of AEC foam films (System I)
System I was used to investigate the character of the foam films. The energy profile of the system is flat during the last 5 ns (Fig. S4, ESI†), indicating that a steady AEC foam film containing the pre-dispersed oil C12 molecules is formed. Because of their amphiphilic properties, the AEC molecules form an orderly array at the interface. Their headgroups are attracted by the water and the alkyl chains are drawn toward the vacuum. Due to their hydrophobicity, C12 molecules twist with the AEC alkyl chains (Fig. 2b). To study the array of the AEC molecules, we named the oxygen atoms of polyoxyethylene as Oa, Ob, and Og, respectively (Fig. 2c). Fig. 2a reveals the density profile of water
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Fig. 2 (a) Density of water and oxygen atoms of polyoxyethylene. (b) A sketch of the foam films. The AEC molecules are grey and the pink represents the C12 molecules, which stand for the pre-spread oil. The blue is the trapped water, the red is the bulk water and the CPK model is the bounded water. The hydrogen bonds are shown in green. (c) Sketch of the AEC monomer. (d) MSD of the bulk, bounded, and trapped water.
molecules and oxygen atoms along the Z direction. The peaks of selected atoms denote where they locate in the foam film. The ‘‘10–90’’ rule is commonly used to define the thickness of a complicated interface.31,32 In this paper, the distance from 10% to 90% of the water density represents the thickness of the liquid–vapor interface, and the distance between the two 90% of the density is taken as the water phase. The divide is shown in Fig. 2a. The oxygen atoms of polyoxyethylene are all in the liquid–vapor interface, however, the headgroups of AEC are in the bulk water. Comparing with the positions of the oxygen atoms, the peak of Oa is closer to the bulk water than Ob and Og. The difference suggests that Oa has inserted deep into the water phase and the two other oxygen atoms are on the periphery of the interface. For the AEC molecules, the connected water can be divided into three kinds according to their location (Fig. 2b). The first is the bound water (shown in CPK model), which binds with the headgroups of the surfactant molecules through strong H-bonding interactions. Actually, the bound water is favorable for the stability of the foam film,33 which can prevent outside factors from affecting the foam. In many experiments, the decreasing number of bound water will give rise to foam film rupture easily, especially in drainage. The second is trapped water (displayed in blue), which is located among the alkyl chains of the surfactant or C12 molecules. These molecules move through the hydrophobic space, and they also increase the strength of the interface film. The other kind is bulk water, which constitutes the water phase.
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The properties of the water diffusion process can be characterized by a useful tool, mean square displacement (MSD).34 The equation of MSD is shown as follows:32 * + N 1X 2 MSDðtÞ ¼ jri ðtÞ ri ð0Þj N i¼1 where N is the number of water molecules in the system, ri(t) represents the position of water molecule i at time t. It is clear that MSD shows the motion of molecules compared with their original position, and the value is related to the diffusion coefficient (D) using the Einstein relation: Da ¼
Na D E 1 dX lim ½ri ðtÞ ri ð0Þ2 6Na t!1 dt i¼1
where d is the dimension of the space, and ri(t) and ri(0) are the coordinates of the ith particle at time t and 0, respectively. The diffusion coefficients of the water molecules in the three regions were calculated by a linear fit to the corresponding MSD over the last 100 ps, which are shown in Fig. 2d. The data indicate that water molecules in the bound region are less mobile than the trapped and bulk water. It is easy to understand that the H-bonding interactions between the headgroups and water molecules constrain the mobility of the bound water. The affinity of the bound water and the AEC molecules proves that the bound water plays an important role in the stability of the foam film. The diffusion coefficient of trapped water is slightly larger than that for the bound water and much lower than that for the bulk water. The behavior of trapped water implies that the hydrophobic alkyl chains restrict the freedom of the trapped water. 3.2 From the pseudoemulsion film to the oil bridge (Systems II and III) On the base of System I, an emulsified C12 droplet (as antifoam) is put in the water phase of the film foams to construct System II. It is used to investigate the destruction of the pseudoemulsion film and the formation of the oil bridge. While the emulsified oil droplet is protected by AEC molecules, the antifoam stays in the film stably unless external forces are added to the film walls along the vertical direction. The added forces, quantified by the SMD method, are used to mimic the droplet compression process. 3.2.1 Pseudoemulsion film. On account of the emulsified oil droplet in the water phase, one pseudoemulsion film is formed (Fig. 3a). The stability of the pseudoemulsion film can affect the foam film heavily.9,12 To destroy the pseudoemulsion film, the external forces drive the water molecules out of the pseudoemulsion film. As mentioned above, the water in the pseudoemulsion film is mainly bound water. This moves to the bulk water driven by the compressive forces. Once the water phase in the pseudoemulsion film disappears, an oil bridge begins to form. Eventually, an oil bridge structure replaces the pseudoemulsion film in the foam film. Fig. 3 shows the destruction course of the pseudoemulsion film. In the simulation, we are more interested in the water
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Fig. 3 (a) The pseudoemulsion film in the foam film. (b) The initial structure of the pseudoemulsion film. Structure at (c) 50 ps, (d) 150 ps, and (e) 300 ps. (f) The oil bridge. The green is the oil globule, the yellow is the emulsified surfactants, and the other details are as in Fig. 2.
molecules of the pseudoemulsion film. For the foam films, the thickness of the pseudoemulsion film is kept at about 8.5 Å (Fig. 3a). As shown in Fig. 1, the SMD method was applied to the foam films to mimic the compression forces from two film walls in the experiment. The forces compel the films to get close to the oil globule at the given pulling rates along the vertical direction. At that time, the water is gradually excluded during this compression process. To investigate the behavior of water, some water molecules in the CPK model are taken as examples in Fig. 3. At the beginning, the water in the pseudoemulsion film is bound with the headgroups of the surfactant (Fig. 3b) due to the strong H-bonding interactions. Because of the additional force, the AEC molecules in the foam films come to the oil droplet with the bound water (Fig. 3c). With increasing force, the headgroups of the surfactant are expelled into two parts to around the oil droplet, and the bound water also divides into two parts (Fig. 3d). Ultimately, the antifoam molecules interact with the surfactant in the foam films (Fig. 3e) through hydrophobic interactions, which leads to the disappearance of the pseudoemulsion film completely and the appearance of the oil bridge (Fig. 3f). 3.2.2 Entry barrier. The disappearance of the pseudoemulsion film is impacted by whether the antifoam enters into the foam films or not. In fact, the dominating factor for the oil globule entering the film is called the entry barrier.2 This is influenced by the properties of oil globule and the concentration of the surfactants. In the simulation, the external forces were quantized by SMD, which is helpful for the investigation of the entry barrier. The forces are shown in Fig. 4a and summarized by the equation:35 -
-
-
F(t) = k(vt (r(t) r0)n) where k is the constant of the force, v is the pulling velocity, n is the normal of the pulling direction, r0 is the initial position and r(t) is the position at time t. The total forces along the vertical direction applied to the surfactant layers are displayed in Fig. 4b. System III with a low AEC concentration was used to investigate the effect of the concentration on the entry barrier. For the two systems, the external
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Fig. 4 (a) Sketch of the external forces on the foam walls along the vertical direction. For details refer to Fig. 3. (b) The total forces of two different foam systems in different concentrations.
forces increase with time evolution (Fig. 4b). At the same time, the film walls approach the oil globule gradually. However, the repulsion between the films and oil globule prevents the film walls from moving. With the force increasing, the repulsion is overcome and the water in the pseudoemulsion film is excluded gradually. When the surfactant molecules contact the oil globule, the force reaches a maximum. At that time, the pseudoemulsion film disappears and the oil bridge is formed (Fig. 3f). The critical point in Fig. 4b corresponds to the entry barrier in the experiment. The peak of the force in System II is about 2100 kJ mol1 nm1, while that for System III is about 900 kJ mol1 nm1. The different force peaks indicate that the concentrations of surfactant can affect the repulsion forces. The bigger the repulsion force, the more stable the pseudoemulsion film is, and the more difficult it is to form the oil bridge. Comparing the force curves of Systems II and III, a low concentration has a lower peak value. This may be attributed to the repulsion of the surfactant foam films and the emulsified antifoams. The low AEC concentration system has weak repulsion to the antifoam, which is favorable for the foam films close to the oil globule, and tends to reduce the stability of the foam film. In the simulation, regardless of which system, the antifoam couldn’t enter into the foam films unless the entry barrier was overcome. The conclusions agree with the experiments.16 In a word, the entry barrier plays a vital role in the disappearance of the pseudoemulsion film. 3.3
From the oil bridge to foam rupture
With the disappearance of the pseudoemulsion film, a hydrophobic region in the middle of the foam film (Fig. 3f) is formed, which is named the oil bridge.2 Due to the same phenomenon occurring for Systems II and III, System II was taken as the example. Because the SMD perturbs the system artificially, 10 ns molecular dynamics was used to bring the final structure into equilibrium. In experiments, capillary pressures at the oil–water and oil–air interfaces play important roles in balancing the oil bridge. However, the uncompensated capillary pressures affect the oil bridge seriously. The stretching of the bridge in a radial direction, as a result of uncompensated capillary pressures, led to the eventual formation of a thin, unstable oil film in the bridge center.2 To mimic the stretch process of the oil bridge, horizontal forces were added to System II. In this simulation, the changes to the oil bridge are observed obviously. According to experiments,
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Fig. 5 Sketches of the oil bridge after (a) 0 ps, (b) 40 ps, (c) 180 ps, and (d) 240 ps, and (e) the total force in the SMD simulation. The emulsified AEC molecules are displayed in yellow and CPK was used to token the end-point of the oil bridge. For all other details refer to Fig. 2.
the middle of the oil bridge becomes thin and the bridge is unstable due to horizontal forces. Eventually, the oil bridge ruptures because of excessive stretching. The corresponding sketches and total force are shown in Fig. 5. Fig. 5 displays the total force of the system which varies with time evolution and can be approximately divided into three stages. In the first 40 ps (Stage I), some surfactants adsorb to the antifoam globule and their tails intertwine with the oil molecules through hydrophobic interactions. With the help of the external force, the oil bridge is stretched in the horizontal direction. However, the strong hydrophobic interactions of the oil molecules prevent perturbation of the oil bridge. Therefore, the total force of the system increases to overcome the hydrophobic interactions. We think that the hydrophobic interactions between the surfactant tails and oil molecules are the first key factor for the stability of the oil bridge. The hydrophobic interactions can affect the magnitude of force. At this stage, the force increases with time evolution. However, it is difficult to observe an evident change of aggregated structure from the initial structure (Fig. 5a) to the end of increasing force (Fig. 5b). At Stage II (from 40 ps to 180 ps), the force fluctuates within a range. That means that the oil bridge is in a stretched equilibrium in the system. In other words, the external forces equal the hydrophobic interactions between the oil molecules. At this stage, the bridge is stretched in the horizontal direction and the center of the bridge becomes thin. This process is decided by the character of the oil molecules. We think that the hydrophobic interactions among the oil molecules is the second key factor for the stability of the oil bridge. If the hydrophobic interactions of the oil molecules are strong enough to counteract the external force, the stretching process will last long time. If not, the stretching course is short. Though the oil bridge is stretched by strong added force with time evolution, the bridge is not
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able to rupture. Instead, the oil bridge is always stretching in the dynamic equilibrium. With the stretching, the strength of the oil bridge is affected and the diameter expands spontaneously. This behavior induces the center of the bridge to be thin (Fig. 5c). Comparing Fig. 5b (40 ps) and Fig. 5c (180 ps), a variation is clearly obtained. Once the force added exceeds the hydrophobic interactions among the oil molecules, the bridge will be destroyed. The third stage represents the oil bridge rupture (Fig. 5c and d). In this stage, the force profile of the system decreases almost in a straight line, indicating that the excessive stretching causes the hydrophobic interactions of the oil bridge to weaken. At about 240 ps, the oil bridge destructs (Fig. 5d). The three-stage model based on the total force change adequately explains the course of the oil bridge rupture. From this discussion, we can conclude that the reason for the foam rupture under excessive stretching is mainly due to the hydrophobic interactions, which are decided by the properties of the oil molecules.
4. Conclusion The bridge-stretching mechanism (Fig. 1) of foam rupture is considered as reasonable to explain the process of foam rupture. In this paper, we focus on the simulation of air–water boundary conditions at the nanometer level and give the details of the rupture mechanism of foam films. In the foam films, the surfactants are adsorbed at the air–water interface intertwined with the pre-dispersed oil molecules through hydrophobic interactions. The bound water of the surfactants plays a vital role in the stability of the foam films. It can prevent the destruction of the pseudoemulsion film, which is the necessary step for the bridge-stretching mechanism. The entry barrier is also an important factor to decide the emergence of the antifoam appearing on the solution surface. Thus, an external force (Fig. 1b) is added to overcome the entry barrier. As the external force increases, the bound water is taken into the bulk water with the surfactant molecules. The behavior gives rise to the disappearance of the pseudoemulsion film and the formation of the oil bridge. Then the stretching forces in the horizontal direction perturb the stability of the oil bridge seriously and cause the bridge to rupture. In the SMD simulation, the stretching force is quantified and divided into three stages. First, the force increases gradually to overcome the hydrophobic interactions of the oil molecules. At this stage, the force is not large enough to affect the bridge seriously. Second, the force stretches the bridge in the dynamic equilibrium and gives rise to the center of bridge becoming thin. Thus, the hydrophobic interactions in the oil bridge become weak. Finally, the bridge ruptures under the excessively stretching. The three stages explain the process of the oil bridge destruction in detail at the molecular level. The hydrophobic interactions, decided by the properties of the antifoam, play a vital role in the destruction of the oil bridge. The simulations support the experiments and will aid the control of the foam volume.
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Acknowledgements We gratefully appreciate the financial support form NSFC Project (No. 21173128) and Key NSF Project of Shandong province (No. ZR2011B0003).
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30 W. Humphrey, A. Dalke and K. Schulten, J. Mol. Graphics, 1996, 14, 33. 31 S. S. Jang, S. T. Lin, P. K. Maiti, M. Blanco, W. A. Goddard III, P. Shuler and Y. C. Tang, J. Phys. Chem. B, 2004, 108, 12130. 32 E. Z. LI, Z. P. Du and S. L. Yuan, Sci. China: Chem., 2013, 56, 773. 33 S. L. Yuan, L. X. Ma, X. Q. Zhang and L. Q. Zheng, Colloids Surf., A, 2006, 289, 1. 34 H. G. Sun, W. Chen, H. Sheng and Y. Q. Chen, Phys. Lett. A, 2010, 374, 906. 35 D. Q. Zhang, J. Gullingsrude and J. A. McCammon, J. Am. Chem. Soc., 2006, 128.
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Mechanism of foam destruction by antifoams: a molecular dynamics study† Fengfeng Gao,a Hui Yan,b Qiwei Wangc and Shiling Yuan*a In enhanced oil recovery (EOR), the micro-oil droplet heavily affected the stability of foam and prevented foam flooding. In this paper, the oil bridge-stretching mechanism of foam rupture was described through molecular dynamics with the aim of providing supplements to the experiments at the molecular level. Two important phenomena for foam rupture have been pointed out by the simulation. One is about the pseudoemulsion film, representing the stability of the oil–water–air three phase interface. The bound water connecting the headgroups of the surfactant through strong H-bonding interactions played a vital role in the stability of the pseudoemulsion film. These water molecules could hinder the disappearance of the water phase in the pseudoemulsion film. The additional energy barrier, which was influenced by the surfactant concentration, also played a vital role in preventing the destruction process. The other factor is about the oil bridge, which appeared after the destruction of the pseudoemulsion film. The external horizontal force stretched the bridge resulting in the destruction of the bridge. The process was decided
Received 10th May 2014, Accepted 16th June 2014
by the properties of the oil molecules. In the simulation, the stretching force was divided into three stages
DOI: 10.1039/c4cp02038c
the second equilibrium force, which stretched the middle of the oil bridge so that it became thin, was vital
including the initial increasing force, the middle equilibrium force and the final decreasing force. Especially to the foam rupture. The concentration and properties of the oil molecules were the crucial factors for
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foam rupture. The simulated results offer important supplements to experiments.
1. Introduction Foam is a typical thermodynamically unstable gas–liquid system,1 which is widely used in fire-fighting, personal care, polymeric foam insulation and so on.2,3 However, in some industrial cases, foam is undesirable. Excessive foam can hamper industrial processes.4 In those conditions, eliminating undesired foam becomes crucial. In experiments, microscopic solid particles, oil droplets, and their combination, are widely used as typical ‘‘antifoams’’,5 and these antifoams pre-disperse in the foam solution to prevent producing excessive foam.2 In recent years, many experimental techniques, including X-ray reflection,6 resonance Raman scattering,7 and interfacial rheology,8 have been explored to investigate the properties of foams. These experiments have provided much information about the characters of foam films. At the same time, several mechanisms of foam rupture have been reported. By a high
speed video camera, the bridge-stretching mechanism (Fig. 1) has been suggested to explain the process of foam destruction in the presence of antifoams.2,9 This mechanism unambiguously shows that an antifoam globule could enter the Plateau Borders (PBs) and be compressed by the foam walls. This behavior compels the antifoam globule to enter into the film and form an oil bridge in
a
Key laboratory of Colloid and Interface Chemistry, Shandong University, Jinan 250100, China. E-mail: [email protected]; Fax: +86 531 88564464; Tel: +86 531 88365896 b College of Pharmacy, Liaocheng University, Liaocheng 252059, China c Geological Scientific Research Institute of Shengli Oilfield Company, SINOPEC, Dongying 257015, China † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4cp02038c
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Fig. 1
A sketch of the bridge-stretching mechanism.
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the middle of the foam film. In most conditions, capillary pressures can stabilize the water–oil–vapor three phase interface of the oil bridge. However, uncompensated capillary pressures will stretch the bridge in the radical direction with time evolution, which eventually results in film rupture.9,10 A diagram of the bridge-stretching mechanism, evolving from the work of Denkov,2 is shown in Fig. 1. When an oil globule acting as antifoam approaches the PBs, an asymmetric oil–water–air film appears9 (Fig. 1b). The film was defined as a pseudoemulsion film by Wasan,11 and its stability is very important to the foam film. The stability of a pseudoemulsion film is disturbed by compressive forces from the foam walls. If the compressive force is too small to affect the pseudoemulsion film, foam films are steady; otherwise, the foam films could rupture quickly.12 The formation and rupture of the pseudoemulsion film are the necessary step to film destruction.10 The factor deciding the stability of a pseudoemulsion and preventing the antifoam from emerging on the solution surface is called the entry barrier.10 Many experiments have unambiguously showed that the entry barrier is one of the crucial factors for evaluating foam stability.13–15 High entry barriers can prevent oil globules from entering foam films. While, low entry barriers make antifoams enter foam films easily and induce foam rupture quickly. The entry barrier is also used to explain how an antifoam affects the stability of a pseudoemulsion film.16 When the pseudoemulsion film is destroyed, an oil bridge is formed between the surfaces of the two foams (Fig. 1c). For the oil bridge, even a small perturbation is able to induce the bridge from the equilibrium position to unsteady. What’s worse, the perturbation will result in the whole rupture of the foam film (Fig. 1d).13 In experiments, capillary pressures, which can balance the oil–water and oil–air interfaces, are crucial to the stability of the oil bridge. If the capillary pressure is uncompensated, it will stretch the bridge with time (Fig. 1c) and give rise to rupture of the foams.9 Based on previous concepts,13–15 the bridge-stretching mechanism provides new explanations for foam destruction. However, due to the limitations of experimental techniques, details of the foam destruction mechanism, especially at the molecular level, are still not explicit to scientists. A complete understanding of the mechanism of foam rupture needs the assistance of theoretical research. Steered molecular dynamics (SMD) has been proved to be an effective method to investigate the behavior of a system toward a special phenomenon, which might not be realized by conventional molecular dynamics (MD).17 In SMD, an external force can perturb the equilibrium of a system and further give rise to displacements in the simulations.18 In this paper, SMD will be used to simulate the process of foam rupture and supply important information for experiments at the molecular level. The current work is divided into three parts. First, the character of the foam was investigated. Second, the entry barrier,
Table 1
which determines the stability of the pseudoemulsion film and the formation of the oil bridge, was discussed. Third, the stretching force to the oil bridge was studied. The force led to foam rupture directly. Using the SMD method, molecular level information about the bridge-stretching mechanism was obtained, which is helpful as it supplements experiments.
2. Simulation section 2.1
The construction of the foam film
In the crude oil industry, the layer of spread oil on a film surface plays an important role in foam rupture.13,19 Therefore, a typical foam film was constructed. In our simulation, the surfactant, sodium polyoxyethylene alkylether carboxylate (AEC), which has been widely used in oilfields, was selected.20 A dodecane (C12) molecule acted as the pre-dispersed oil molecule.21 To construct the foam film, a water layer, whose size was about 16 4 4 nm3, was built. Then 160 surfactants and 160 dodecane molecules were scattered randomly on each side of the water layer. In order to maintain neutrality in the simulation box, 320 sodium ions were added to the water solution. Then the Z axis of the box was extended to 20 nm to minimize interactions between periodic replicas. The constructed foam film was considered as System I (Fig. S1, ESI†). In crude oil conditions, some molecules with surface activities can adsorb on the surface of an oil globule to form an emulsified oil globule. Hence, one globule containing 60 C12 molecules and 10 AEC molecules, as an antifoam, was put in the water phase of the foam films (System I) to simulate foam rupture. The system was defined as System II (Fig. S2, ESI†). In many experiments, the concentration of the surfactant can seriously affect foam rupture. Thus, a low concentration AEC was introduced, and the system was called System III (Fig. S3, ESI†). All the systems and corresponding labels are listed in Table 1. 2.2
Simulation details
All simulations were put in GROMACS 4.0.5. The interatomic interactions were calculated according to the parameters and potential functions of the GROMOS 53a6 force field.22 The standard potential model of molecular mechanics was used: X 2 X 2 u rN ¼ ki li li;0 þ ki yi yi;0 bonds
þ
þ
angles
X Vn ð1 þ cosðno gÞÞ 2 torsions N X N X i¼1 j¼iþ1
" ! 6 # sij 12 sij qi qj 4eij þ rij rij rij
Summaries of simulated systems
System label
Water number
AEC number
C12 number
Na+ number
Emulsified oil globule
Box size (nm3)
Simulation pattern
I II III
8400 7300 7300
320 320 160
320 320 320
320 320 320
0 1 1
16 4 20 16 4 20 16 4 20
10 ns MD SMD 10 ns MD + SMD SMD
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The first three terms represent the bond interactions, which consist of bond, angle and torsion interactions, respectively; the last terms are the van der Waals and Coulombic interactions, which are defined as nonbonding interactions. In this force field, a united-atom description was used for the AEC and C12 molecules. The coordinates and parameters of the AEC molecule and C12 were taken from ProDRG,23 and their charges were obtained by Dmol3.21,24 Detailed descriptions are in the ESI.† In the simulation, water was described by the simple point charge (SPC) model.25 Sodium came from the work of Lyubartsev et al.26 Periodic boundary conditions were applied in the x, y, and z directions in all simulation systems. The cut-off of the Lennard-Jones interactions was 1.2 nm. Bond lengths were constrained using the LINCS algorithm.27 The Particle Mesh Ewald (PME) method was employed for the longrange electrostatic interactions.28 For the three systems, different molecule dynamics methods were used. System I used the steepest descent method to minimize the initial configurations. Then 10 ns NVT Ensemble at 298 K was carried out. For Systems II and III, the simulations were inaccessible on the time scale of conventional MD. Therefore, the SMD method was applied to study the particular phenomena. In the SMD systems, the foam films are pulled to the center of the antifoam along the Z-axis using a constant of 500 kcal mol1 nm2 and a pulling rate of 0.005 nm ps1. The external force was calculated directly from the SMD trajectory within acceptable error.18,29 During all simulations, the time step was 2 fs, and the trajectories were kept every 10 ps. Trajectories were visualized using VMD 1.8.5.30 In the experiments, two kinds of forces on the foam film were noticed in the bridge-stretching mechanism. One is the force coming from the film walls on two sides, and the other is the force due to the perturbation of capillary pressures in the foam film. The former is considered as the force applied along the vertical direction of the film which compels the antifoam to enter into the film (Fig. 1b), and the latter is the one along the horizontal direction which stretches the oil bridge to cause foam rupture (Fig. 1c). In our work, the key point is how to apply the SMD method to mimic the two types of forces on the foam film.
3. Results and discussion 3.1
Structure of AEC foam films (System I)
System I was used to investigate the character of the foam films. The energy profile of the system is flat during the last 5 ns (Fig. S4, ESI†), indicating that a steady AEC foam film containing the pre-dispersed oil C12 molecules is formed. Because of their amphiphilic properties, the AEC molecules form an orderly array at the interface. Their headgroups are attracted by the water and the alkyl chains are drawn toward the vacuum. Due to their hydrophobicity, C12 molecules twist with the AEC alkyl chains (Fig. 2b). To study the array of the AEC molecules, we named the oxygen atoms of polyoxyethylene as Oa, Ob, and Og, respectively (Fig. 2c). Fig. 2a reveals the density profile of water
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Fig. 2 (a) Density of water and oxygen atoms of polyoxyethylene. (b) A sketch of the foam films. The AEC molecules are grey and the pink represents the C12 molecules, which stand for the pre-spread oil. The blue is the trapped water, the red is the bulk water and the CPK model is the bounded water. The hydrogen bonds are shown in green. (c) Sketch of the AEC monomer. (d) MSD of the bulk, bounded, and trapped water.
molecules and oxygen atoms along the Z direction. The peaks of selected atoms denote where they locate in the foam film. The ‘‘10–90’’ rule is commonly used to define the thickness of a complicated interface.31,32 In this paper, the distance from 10% to 90% of the water density represents the thickness of the liquid–vapor interface, and the distance between the two 90% of the density is taken as the water phase. The divide is shown in Fig. 2a. The oxygen atoms of polyoxyethylene are all in the liquid–vapor interface, however, the headgroups of AEC are in the bulk water. Comparing with the positions of the oxygen atoms, the peak of Oa is closer to the bulk water than Ob and Og. The difference suggests that Oa has inserted deep into the water phase and the two other oxygen atoms are on the periphery of the interface. For the AEC molecules, the connected water can be divided into three kinds according to their location (Fig. 2b). The first is the bound water (shown in CPK model), which binds with the headgroups of the surfactant molecules through strong H-bonding interactions. Actually, the bound water is favorable for the stability of the foam film,33 which can prevent outside factors from affecting the foam. In many experiments, the decreasing number of bound water will give rise to foam film rupture easily, especially in drainage. The second is trapped water (displayed in blue), which is located among the alkyl chains of the surfactant or C12 molecules. These molecules move through the hydrophobic space, and they also increase the strength of the interface film. The other kind is bulk water, which constitutes the water phase.
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The properties of the water diffusion process can be characterized by a useful tool, mean square displacement (MSD).34 The equation of MSD is shown as follows:32 * + N 1X 2 MSDðtÞ ¼ jri ðtÞ ri ð0Þj N i¼1 where N is the number of water molecules in the system, ri(t) represents the position of water molecule i at time t. It is clear that MSD shows the motion of molecules compared with their original position, and the value is related to the diffusion coefficient (D) using the Einstein relation: Da ¼
Na D E 1 dX lim ½ri ðtÞ ri ð0Þ2 6Na t!1 dt i¼1
where d is the dimension of the space, and ri(t) and ri(0) are the coordinates of the ith particle at time t and 0, respectively. The diffusion coefficients of the water molecules in the three regions were calculated by a linear fit to the corresponding MSD over the last 100 ps, which are shown in Fig. 2d. The data indicate that water molecules in the bound region are less mobile than the trapped and bulk water. It is easy to understand that the H-bonding interactions between the headgroups and water molecules constrain the mobility of the bound water. The affinity of the bound water and the AEC molecules proves that the bound water plays an important role in the stability of the foam film. The diffusion coefficient of trapped water is slightly larger than that for the bound water and much lower than that for the bulk water. The behavior of trapped water implies that the hydrophobic alkyl chains restrict the freedom of the trapped water. 3.2 From the pseudoemulsion film to the oil bridge (Systems II and III) On the base of System I, an emulsified C12 droplet (as antifoam) is put in the water phase of the film foams to construct System II. It is used to investigate the destruction of the pseudoemulsion film and the formation of the oil bridge. While the emulsified oil droplet is protected by AEC molecules, the antifoam stays in the film stably unless external forces are added to the film walls along the vertical direction. The added forces, quantified by the SMD method, are used to mimic the droplet compression process. 3.2.1 Pseudoemulsion film. On account of the emulsified oil droplet in the water phase, one pseudoemulsion film is formed (Fig. 3a). The stability of the pseudoemulsion film can affect the foam film heavily.9,12 To destroy the pseudoemulsion film, the external forces drive the water molecules out of the pseudoemulsion film. As mentioned above, the water in the pseudoemulsion film is mainly bound water. This moves to the bulk water driven by the compressive forces. Once the water phase in the pseudoemulsion film disappears, an oil bridge begins to form. Eventually, an oil bridge structure replaces the pseudoemulsion film in the foam film. Fig. 3 shows the destruction course of the pseudoemulsion film. In the simulation, we are more interested in the water
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Fig. 3 (a) The pseudoemulsion film in the foam film. (b) The initial structure of the pseudoemulsion film. Structure at (c) 50 ps, (d) 150 ps, and (e) 300 ps. (f) The oil bridge. The green is the oil globule, the yellow is the emulsified surfactants, and the other details are as in Fig. 2.
molecules of the pseudoemulsion film. For the foam films, the thickness of the pseudoemulsion film is kept at about 8.5 Å (Fig. 3a). As shown in Fig. 1, the SMD method was applied to the foam films to mimic the compression forces from two film walls in the experiment. The forces compel the films to get close to the oil globule at the given pulling rates along the vertical direction. At that time, the water is gradually excluded during this compression process. To investigate the behavior of water, some water molecules in the CPK model are taken as examples in Fig. 3. At the beginning, the water in the pseudoemulsion film is bound with the headgroups of the surfactant (Fig. 3b) due to the strong H-bonding interactions. Because of the additional force, the AEC molecules in the foam films come to the oil droplet with the bound water (Fig. 3c). With increasing force, the headgroups of the surfactant are expelled into two parts to around the oil droplet, and the bound water also divides into two parts (Fig. 3d). Ultimately, the antifoam molecules interact with the surfactant in the foam films (Fig. 3e) through hydrophobic interactions, which leads to the disappearance of the pseudoemulsion film completely and the appearance of the oil bridge (Fig. 3f). 3.2.2 Entry barrier. The disappearance of the pseudoemulsion film is impacted by whether the antifoam enters into the foam films or not. In fact, the dominating factor for the oil globule entering the film is called the entry barrier.2 This is influenced by the properties of oil globule and the concentration of the surfactants. In the simulation, the external forces were quantized by SMD, which is helpful for the investigation of the entry barrier. The forces are shown in Fig. 4a and summarized by the equation:35 -
-
-
F(t) = k(vt (r(t) r0)n) where k is the constant of the force, v is the pulling velocity, n is the normal of the pulling direction, r0 is the initial position and r(t) is the position at time t. The total forces along the vertical direction applied to the surfactant layers are displayed in Fig. 4b. System III with a low AEC concentration was used to investigate the effect of the concentration on the entry barrier. For the two systems, the external
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Fig. 4 (a) Sketch of the external forces on the foam walls along the vertical direction. For details refer to Fig. 3. (b) The total forces of two different foam systems in different concentrations.
forces increase with time evolution (Fig. 4b). At the same time, the film walls approach the oil globule gradually. However, the repulsion between the films and oil globule prevents the film walls from moving. With the force increasing, the repulsion is overcome and the water in the pseudoemulsion film is excluded gradually. When the surfactant molecules contact the oil globule, the force reaches a maximum. At that time, the pseudoemulsion film disappears and the oil bridge is formed (Fig. 3f). The critical point in Fig. 4b corresponds to the entry barrier in the experiment. The peak of the force in System II is about 2100 kJ mol1 nm1, while that for System III is about 900 kJ mol1 nm1. The different force peaks indicate that the concentrations of surfactant can affect the repulsion forces. The bigger the repulsion force, the more stable the pseudoemulsion film is, and the more difficult it is to form the oil bridge. Comparing the force curves of Systems II and III, a low concentration has a lower peak value. This may be attributed to the repulsion of the surfactant foam films and the emulsified antifoams. The low AEC concentration system has weak repulsion to the antifoam, which is favorable for the foam films close to the oil globule, and tends to reduce the stability of the foam film. In the simulation, regardless of which system, the antifoam couldn’t enter into the foam films unless the entry barrier was overcome. The conclusions agree with the experiments.16 In a word, the entry barrier plays a vital role in the disappearance of the pseudoemulsion film. 3.3
From the oil bridge to foam rupture
With the disappearance of the pseudoemulsion film, a hydrophobic region in the middle of the foam film (Fig. 3f) is formed, which is named the oil bridge.2 Due to the same phenomenon occurring for Systems II and III, System II was taken as the example. Because the SMD perturbs the system artificially, 10 ns molecular dynamics was used to bring the final structure into equilibrium. In experiments, capillary pressures at the oil–water and oil–air interfaces play important roles in balancing the oil bridge. However, the uncompensated capillary pressures affect the oil bridge seriously. The stretching of the bridge in a radial direction, as a result of uncompensated capillary pressures, led to the eventual formation of a thin, unstable oil film in the bridge center.2 To mimic the stretch process of the oil bridge, horizontal forces were added to System II. In this simulation, the changes to the oil bridge are observed obviously. According to experiments,
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Fig. 5 Sketches of the oil bridge after (a) 0 ps, (b) 40 ps, (c) 180 ps, and (d) 240 ps, and (e) the total force in the SMD simulation. The emulsified AEC molecules are displayed in yellow and CPK was used to token the end-point of the oil bridge. For all other details refer to Fig. 2.
the middle of the oil bridge becomes thin and the bridge is unstable due to horizontal forces. Eventually, the oil bridge ruptures because of excessive stretching. The corresponding sketches and total force are shown in Fig. 5. Fig. 5 displays the total force of the system which varies with time evolution and can be approximately divided into three stages. In the first 40 ps (Stage I), some surfactants adsorb to the antifoam globule and their tails intertwine with the oil molecules through hydrophobic interactions. With the help of the external force, the oil bridge is stretched in the horizontal direction. However, the strong hydrophobic interactions of the oil molecules prevent perturbation of the oil bridge. Therefore, the total force of the system increases to overcome the hydrophobic interactions. We think that the hydrophobic interactions between the surfactant tails and oil molecules are the first key factor for the stability of the oil bridge. The hydrophobic interactions can affect the magnitude of force. At this stage, the force increases with time evolution. However, it is difficult to observe an evident change of aggregated structure from the initial structure (Fig. 5a) to the end of increasing force (Fig. 5b). At Stage II (from 40 ps to 180 ps), the force fluctuates within a range. That means that the oil bridge is in a stretched equilibrium in the system. In other words, the external forces equal the hydrophobic interactions between the oil molecules. At this stage, the bridge is stretched in the horizontal direction and the center of the bridge becomes thin. This process is decided by the character of the oil molecules. We think that the hydrophobic interactions among the oil molecules is the second key factor for the stability of the oil bridge. If the hydrophobic interactions of the oil molecules are strong enough to counteract the external force, the stretching process will last long time. If not, the stretching course is short. Though the oil bridge is stretched by strong added force with time evolution, the bridge is not
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able to rupture. Instead, the oil bridge is always stretching in the dynamic equilibrium. With the stretching, the strength of the oil bridge is affected and the diameter expands spontaneously. This behavior induces the center of the bridge to be thin (Fig. 5c). Comparing Fig. 5b (40 ps) and Fig. 5c (180 ps), a variation is clearly obtained. Once the force added exceeds the hydrophobic interactions among the oil molecules, the bridge will be destroyed. The third stage represents the oil bridge rupture (Fig. 5c and d). In this stage, the force profile of the system decreases almost in a straight line, indicating that the excessive stretching causes the hydrophobic interactions of the oil bridge to weaken. At about 240 ps, the oil bridge destructs (Fig. 5d). The three-stage model based on the total force change adequately explains the course of the oil bridge rupture. From this discussion, we can conclude that the reason for the foam rupture under excessive stretching is mainly due to the hydrophobic interactions, which are decided by the properties of the oil molecules.
4. Conclusion The bridge-stretching mechanism (Fig. 1) of foam rupture is considered as reasonable to explain the process of foam rupture. In this paper, we focus on the simulation of air–water boundary conditions at the nanometer level and give the details of the rupture mechanism of foam films. In the foam films, the surfactants are adsorbed at the air–water interface intertwined with the pre-dispersed oil molecules through hydrophobic interactions. The bound water of the surfactants plays a vital role in the stability of the foam films. It can prevent the destruction of the pseudoemulsion film, which is the necessary step for the bridge-stretching mechanism. The entry barrier is also an important factor to decide the emergence of the antifoam appearing on the solution surface. Thus, an external force (Fig. 1b) is added to overcome the entry barrier. As the external force increases, the bound water is taken into the bulk water with the surfactant molecules. The behavior gives rise to the disappearance of the pseudoemulsion film and the formation of the oil bridge. Then the stretching forces in the horizontal direction perturb the stability of the oil bridge seriously and cause the bridge to rupture. In the SMD simulation, the stretching force is quantified and divided into three stages. First, the force increases gradually to overcome the hydrophobic interactions of the oil molecules. At this stage, the force is not large enough to affect the bridge seriously. Second, the force stretches the bridge in the dynamic equilibrium and gives rise to the center of bridge becoming thin. Thus, the hydrophobic interactions in the oil bridge become weak. Finally, the bridge ruptures under the excessively stretching. The three stages explain the process of the oil bridge destruction in detail at the molecular level. The hydrophobic interactions, decided by the properties of the antifoam, play a vital role in the destruction of the oil bridge. The simulations support the experiments and will aid the control of the foam volume.
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Acknowledgements We gratefully appreciate the financial support form NSFC Project (No. 21173128) and Key NSF Project of Shandong province (No. ZR2011B0003).
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