Revisiting the Thermodynamics of Water Surfaces and the Effects of

Feb 3, 2016 - It is common knowledge that surfactants lower the surface tension of water. The typical textbook explanation of this phenomenon is that ...
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Revisiting the Thermodynamics of Water Surfaces and the Effects of Surfactant Head Group Dan Hu,† Amirhossein Mafi,†,‡ and Keng C. Chou*,† †

Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z3, Canada

‡

S Supporting Information *

ABSTRACT: It is common knowledge that surfactants lower the surface tension of water. The typical textbook explanation of this phenomenon is that the force of attraction between surfactant and water molecules is less than that between two water molecules; hence the surface contraction force decreases in the presence of surfactants; however, this common description, based on the strength of intermolecular interactions, is overly simplified because it ignores an important thermodynamic function: the surface entropy of water. Here we report separate measurements of water’s surface enthalpy and surface entropy in the presence of nonionic, zwitterionic, anionic, and cationic surfactants. While all of these surfactants decreased the surface enthalpy of water by 50−70%, the surface entropy of water could drop to near-zero or even negative values for ionic surfactants. Studies of this zero-entropy state of water surface using phase-sensitive sum-frequency generation (SFG) vibrational spectroscopy and molecular dynamics (MD) simulations suggested that the zero-entropy state of the water surface was associated with surfactant-induced ordering of water molecules and enhanced hydrogen bond formation at the water surface. Both effects reduce water molecules’ degrees of freedom for motion and thus lower the surface entropy of water. The ability of a surfactant to decrease the surface entropy of water is in the order ionic > zwitterionic > nonionic. For all surfactant head groups surface entropy plays a critical role in determining the surface tension of water. The description of water’s surface tension is not complete without considering its surface entropy.

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INTRODUCTION Besides mercury, water has the highest surface tension among all common liquids: Water’s surface tension is 72 mN/m compared with ethanol’s 22 mN/m and heptane’s 20 mN/m.1 The high surface tension is due to the rather strong hydrogen bonding between water molecules. A typical textbook description for the origin of surface tension is illustrated in Figure 1.2 While a molecule in the bulk liquid experiences attractive force from all directions, a molecule at the surface experiences a net inward force. This force always tends to

minimize the surface area of the liquid. By definition, the energy required to increase the liquid surface is the surface tension. In the presence of surfactants (green colored in Figure 1), the surface tension of water decreases because the surfactant−water and surfactant−surfactant interactions are weaker than the water−water interactions. Although this description has offered a simple picture to understand the surface tension and the effect of surfactants, it has ignored an important thermodynamic function of water: entropy. Water has the lowest entropy among all common liquids. The entropy of liquid water is 70 J/(mol·K) compared with ethanol’s 161 J/(mol·K) and heptane’s 328 J/(mol·K).1 The low entropy of water is also due to the strong hydrogen bonding between water molecules. In the Boltzmann’s statistical formulation, entropy is related to the freedom of motion: entropy S = k·ln(Ω), where k is the Boltzmann’s constant and Ω is the number of possible microstates in which a system can be found. The more freedom the molecules have to occupy different microstates, the higher the entropy. On average, each liquid water molecule has 3 to 3.5 hydrogen bonds.3−5 Therefore, the possible motions of water molecules in the bulk liquid are relatively constrained, resulting in a low number of possible microstates, that is, a low entropy state. On the contrary, water molecules at the surface have significantly

Figure 1. Scheme of the attractive forces commonly used to explain the origin of surface tension. While the forces (red arrows) on an inner molecule are balanced, a molecule at the surface experiences a net inward force. In the presence of surfactants (green spheres with tails), the intermolecular attractive forces at the surface are weakened, and the surface tension consequently decreases. © XXXX American Chemical Society

Received: November 30, 2015 Revised: January 28, 2016

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DOI: 10.1021/acs.jpcb.5b11717 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

Table 1. Surface Tension, γ, Surface Entropy, SS, −TSS, and Surface Enthalpy, HS, of Water at T = 293 K with Various Surfactants at Their CMC surfactant pure water C12E4 (nonionic) DDAPS (zwitterionic) SDS (anionic) DTAC (cationic)

γ (mN/m)

SS (mN/m·K)

−TSS (mN/m)

HS (mN/m)

± ± ± ± ±

0.15 ± 0.02 0.10 ± 0.02 0.07 ± 0.02 0.04 ± 0.02 −0.02 ± 0.02

−44 ± 6 −29 ± 6 −20 ± 6 −12 ± 6 6±6

117 ± 6 59 ± 6 62 ± 6 52 ± 6 36 ± 6

72.7 30.2 41.6 40.6 41.6

0.2 0.2 0.2 0.2 0.2

Sample Preparation. Sodium dodecyl sulfate (>99%), dodecyltrimethylammonium bromide (>99%), 3-(N,N-dimethyldodecylammonium propanesulfonate (>99.5%), and tetraethylene glycol monododecyl ether (>98%) were purchased from Sigma-Aldrich. Water used for solution preparation was obtained from a Millipore system (resistivity >18.2 MΩ·cm). MD Simulation. We implemented a molecular dynamics simulation using GROMACS 5.0.28−10 in the canonical ensemble, in which the number of particles, the box volume, and the temperature are kept constant. To describe the behavior of the surfactant molecules (SDS), we used the allatom force field parameters as provided by Shen and Sun for AMBER-type potential equations.11 The SPC/E model was applied to describe the behavior of the water molecules.12 The simulation box had dimensions of 4 × 4 × 40 nm3. Initially a slab of 4 nm × 4 nm × 16 nm was filled with 8567 water molecules. This slab of water was placed at the center of the simulation box, and a vacuum of approximately 12 nm depth was at both sides of the water slab. Then, 36 SDS molecules were randomly distributed on each side of the water interface using the PACKMOL13 package such that the headgroup pointed toward the water. A surface coverage of 0.44 nm2/ molecule was created, corresponding to the surface coverage of SDS at its critical micelle concentration (CMC). To maintain electronic neutrality of the system, 72 water molecules were randomly replaced with the 72 Na+ counterions that came with the SDS molecules. The same system configuration without surfactant molecules was used to simulate the neat water/air interface for comparison with the surfactant/water interface. The steepest descent energy minimization was conducted to prepare the system for dynamic simulation. The system temperature was maintained at 293 K using V-rescale thermostat with temperature constant, τT, equal to 0.1 ps.14 All bonds, including water OH bond, were constrained by SHAKE algorithm with a tolerance of 10−4.15 The LennardJones interactions were truncated at a cutoff radius of 1.2 nm. Unlike-atom interactions were computed using standard Lorentz−Berthelot combination rules.16,17 Periodic boundary conditions were applied to all three directions. Particle mesh Ewald (PME) algorithm with real cutoff radius of 1.2 nm and grid spacing of 0.12 nm was used to consider the long-range columbic interactions.18 The simulation was carried out for 120 ns with time steps of 2 fs for integration of the equations of motion. The system took 100 ns to reach its equilibrium state; therefore, the last 20 ns were used for analysis. The visualizations were made by VMD 1.9.1.19

more freedom for rotational and translational movements. Therefore, the entropy of the surface is higher than that in the bulk. While surface tension is the most popular measure to study the water surface and the effect of surfactants, the surface entropy of water has been largely ignored. The thermodynamic definition of surface tension (γ) is the Gibbs free energy per unit area, which is a function of surface enthalpy (HS) and surface entropy (SS): γ = HS + T·SS where T is the temperature of the system. In the current study, we measured HS and SS separately to gain a better understanding of the water surface. Additionally, surface vibrational spectra obtained by phasesensitive SFG vibrational spectroscopy were correlated to the measured macroscopic thermal dynamics functions, and MD simulations were carried out to gain deeper insight into the properties of the water surface.

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METHODS

Surface Tension Measurements. The surface tension of water was measured at 20 °C by the Wilhelmy plate method. Each measurement was repeated at least three times for every solution. The temperature dependence of the surface tension was obtained by changing the system temperature (T) between 15 and 25 °C. The surface entropy of water presented in Table 1 was calculated using the slope: SS = −(Δγ/ΔT). Because the Δγ was very small, a larger ΔT was needed to measure an accurate Δγ. Because SS was not strongly dependent on the temperature, a ΔT of 10 °C was not the dominating error of the measured SS presented in Table 1. In the current study, the uncertainty in the measured surface tension (±0.2 mN/m) was the dominating error. Phase-Sensitive SFG. A femtosecond Ti-sapphire laser (2 mJ/pulse at 1 kHz) was used to pump an optical parametric amplifier (TOPAS, Coherent, USA) to generate a femtosecond IR beam. The IR beam and a narrowband picosecond 800 nm beam were aligned in a collinear optical path previously described by Shen and coworkers.6 A reference SFG beam was obtained by focusing the IR and picosecond 800 nm beams into a quartz crystal with a thickness of 50 μm. The IR, picosecond 800 nm, and reference SFG beams were then focused again on the sample. The reference SFG and the SFG generated at the sample went through a time-delay, a polarizer, a bandpass filter, a lens, and a monochromator, and then the interference pattern of SFG was recorded by a charge-couple device (CCD) camera. The Im(χ(2)) spectra were obtained following the methodology described previously by Tahara and his coworkers.7 The polarization combination used in this study was SSP (spolarized SFG, s-polarized 800 nm, and p-polarized IR). The incident angle was 60°. The energies of the 800 nm and IR beams were ∼10 μJ/pulse and ∼5 μJ/pulse, respectively. The spot size on the sample was ∼300 μm. Each spectrum presented in the paper was an average over 20 min. All SFG spectra were measured at 20 °C.

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RESULTS AND DISCUSSION The decrease in water’s surface tension is highly dependent on the concentration and the type of the surfactant. Typically, surfactants are classified according to their head groups: nonionic, zwitterionic, anionic, and cationic. The insets in Figure 2 show the molecular structures of four model B

DOI: 10.1021/acs.jpcb.5b11717 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

To study the nature of this extremely low entropy state of the water surface, we used phase-sensitive SFG to probe the molecular ordering and orientation at the water surface in the presence of these four surfactants. In contrast with the conventional SFG spectroscopy, which only measures the amplitude of the second-order nonlinear susceptibility |χ(2)|, phase-sensitive SFG measures the spectra of the imaginary χ(2), Im(χ(2)), which reveals both the ordering (the amplitude of peaks) and orientations (the sign of peaks) of surface molecules.7,26,27 Figure 3 shows the Im(χ(2)) spectra of the

Figure 2. Surface tension of water surface with various concentrations of C12E4 (◆), DDAPS (▲), SDS (■), and DTAC (●). The insets are the molecular structures of the surfactants.

surfactants used in the current study: tetraethylene glycol monododecyl ether (C12E4) (nonionic), 3-(N,N-dimethyldodecylammonium) propanesulfonate (DDAPS) (zwitterionic), sodium dodecyl sulfate (SDS) (anionic), and dodecyltrimethylammonium chloride (DTAC) (cationic). To eliminate possible tail-length effects, all surfactants used in the current study have the same tail length of 12 carbons. As shown in Figure 2, the surface tension of water typically has little change at a low surfactant concentration ( 0) produces a positive contribution to Δγ, which counteracts the enthalpy term. Experimentally, the surface entropy of water can be measured using the thermodynamic identity S S = −

( ∂∂Tγ )T ,P ,

25

Figure 3. (a) Phase-sensitive SFG spectra of various surfactants on water at their CMCs. The peaks near 2875 and 2930 cm−1 are the CH3 symmetric stretch and the Fermi resonance, respectively. The CH peaks appear negative when the CH3 pointing upward.29 (b) Corresponding SFG spectra of water. The OH peaks appear negative when the OH bonds pointing downward and positive when the OH bonds pointing upward.

water surface in the CH and OH regions near the CMCs of the four surfactants. As expected, the CH spectra of the surfactants in Figure 3a are similar, which agrees with measurements using neutron reflection, showing that the surface coverage of these surfactants is similar (42−55 Å2/molecule).20−24,28 In contrast, the OH spectra of water shown in Figure 3b are dramatically different. In an OH spectrum, the Im(χ(2)) can be positive or negative, depending on the sign of the average OH projection with respect to the surface normal: A positive peak indicates water molecules with the hydrogen pointing toward the air (up) and a negative peak indicates the hydrogen pointing down.26 The ionic surfactants SDS and DTAC induced a much more ordered water structure at the surface, as indicated by the magnitudes of the SFG peaks. The opposite charges carried by SDS and DTAC flipped the water molecules such that their dipoles point in opposite directions, as indicated by the sign of the peaks. In thermodynamics, an ordered state has a lower entropy. Therefore, the extremely low entropy state of the water surface in the presence of SDS or DTAC is associated with the ordered water structure induced by the charged surfactant. MD simulations were carried out to gain a further molecularlevel understanding of the low-entropy water surface. SDS was chosen for MD simulations because it is the most studied surfactant with well-tested force fields. Figure 4a shows the final configuration of SDS and water molecules after 120 ns of energy optimization. Figure 4b shows the average orientation of water’s dipoles ⟨cos θ⟩ as a function of depth (z), where the surface normal of water is defined as θ = 0. Figure 4b shows

and subsequently

the surface enthalpy can be calculated using HS = γ + T·SS. The measured values of water’s HS and SS for various surfactants at their CMCs are summarized in Table 1. While the surfactants decreased the surface enthalpy by ∼50−70%, water’s surface entropy could drop to near zero or even a negative value for the ionic surfactants. Because surface entropy is a surface excess property, zero surface entropy indicates that the motions of molecules near the surface of water have become as constrained as those in the bulk water. C

DOI: 10.1021/acs.jpcb.5b11717 J. Phys. Chem. B XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry B

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.5b11717. Hydrogen bond calculations, radial distribution functions of water’s oxygen atoms with respect to oxygen atoms of water and SDS, and definition of the orientation angle. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 1-604-8225850. Author Contributions

SFG spectroscopy and surface tension measurements were carried out by D.H. MD simulation was performed by A.M. All authors participated in data interpretation and writing of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the Institute for Oil Sands Innovation at the University of Alberta, the Natural Sciences and Engineering Research Council of Canada, and the Canada Foundation for Innovation. We thank Dr. Murray R. Gray for his support with this project. A.M. is supported by the Four Year Doctoral Fellowship awarded by the Department of Chemical and Biological Engineering in the University of British Columbia.

Figure 4. (a) Structures of water and SDS in the MD simulation. (b) Water dipole order parameter ⟨cos θ⟩, where water’s surface normal is defined as θ = 0. (c) Average number of hydrogen bonds per water molecule versus the depth.

that in the absence of SDS surface water molecules are preferentially ordered over a depth of only 1 nm (blue curve). In the presence of SDS, the ordered water structure propagates over 5 nm into water surface (red curve). Additionally, the MD simulation shows that adsorption of SDS on the water surface promotes the formation of hydrogen bonds (HBs) near the water surface. Figure 4c shows that the average number of HBs for each water molecule is ∼3.2 in the bulk water. (The definition of HB is described in the Supporting Information.) At the pure water surface, the averaged number of HBs per water molecule can be as low as 2 because the water molecules at the top layer have a limited number of neighbors available for HB formation. In the presence of SDS, the number of HBs increased to ∼2.5. The increased number of HBs also contributes to the reduction of entropy as the degrees of freedom decrease. Overall, both the increase in the ordering of water molecules and the formation of additional HBs lead to a lower surface entropy.

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REFERENCES

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CONCLUSIONS We studied the surface entropy of water and the effects of four different surfactants by separately measuring the enthalpy and entropy of the water surface. All surfactants induced a significant surface entropy decrease that counteracts the enthalpic effect. Interestingly, both the anionic and cationic surfactants lowered the surface entropy of water to near-zero. SFG vibrational spectroscopy showed that this low entropy state of the water surface was associated with the surfactantinduced ordering of surface water molecules. Additionally, MD simulation indicated that ionic surfactants promoted the formation of hydrogen bonds near the water surface. Both effects lead to the reduction of water’s surface entropy, which plays a critical role in determining the surface tension of water. D

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