Liquid−Liquid Interfaces of Semifluorinated Alkane Diblock

16012

J. Phys. Chem. B 2008, 112, 16012–16020

Liquid-Liquid Interfaces of Semifluorinated Alkane Diblock Copolymers with Water, Alkanes, and Perfluorinated Alkanes† Flint Pierce,*,§ Mesfin Tsige,⊥ Dvora Perahia,§ and Gary S. Grest‡,# Department of Chemistry, Clemson UniVersity, Clemson, South Carolina 29634, Department of Physics, Southern Illinois UniVersity, Carbondale, Illinois 62901, and Sandia National Laboratories, Albuquerque, New Mexico 87185 ReceiVed: June 24, 2008; ReVised Manuscript ReceiVed: August 20, 2008

The liquid-liquid interface between semifluorinated alkane diblock copolymers of the form F3C(CF2)n-1(CH2)m-1CH3 and water, protonated alkanes, and perfluorinated alkanes are studied by fully atomistic molecular dynamics simulations. A modified version of the OPLS-AA (Optimized Parameter for Liquid Simulation All-Atom) force field of Jorgensen et al. has been used to study the interfacial behavior of semifluorinated diblocks. Aqueous interfaces are found to be sharp, with correspondingly large values of the interfacial tension. Due to the reduced hydrophobicity of the protonated block compared to the fluorinated block, hydrogen enhancement is observed at the interface. Water dipoles in the interfacial region are found to be oriented nearly parallel to the liquid-liquid interface. A number of protonated alkanes and perfluorinated alkanes are found to be mutually miscible with the semifluorinated diblocks. For these liquids, interdiffusion follows the expected Fickian behavior, and concentration-dependent diffusivities are determined. I. Introduction Processes at liquid-liquid interfaces govern a large variety of phenomena from cell membrane dynamics to chemical reactions1,2 to recent technological innovations such as bottomup assemblies of nanoparticles to form functional materials.3 The embedded nature of the interfaces and the small length scales on which interfacial fluctuations often occur result in limited understanding of the structure and dynamics of these interfaces. The current study uses fully atomistic molecular dynamic simulations to investigate the structure of semifluorinated alkanes (SFAs) at the interface with polar and nonpolar solvents. The significance of semifluorinated alkanes lies in their current and potential applications including eye surgery as a retinal tamponade as well as in burn treatment and blood substitution due to their biocompatibility.4-7 As each of these applications occurs within the liquid state and involves interfaces between SFAs and other materials, a clear characterization of SFAs in such circumstances is needed. An additional aspect of SFAs and other semifluorinated polymers is their potential use as interface-responsive materials, a feature that arises from the different interfacial behavior of the fluorinated and protonated segments. When the chemical or physical environment (i.e., contacting substance or temperature, respectively) of these substances is altered, they can respond through segregation of either the fluorinated or protonated segments to the interface and interfacial-induced molecular alignment that provide a driving force for a reversal in the enhancement of one block component over the other. † Part of the “Karl Freed Festschrift”. * To whom correspondence should be addressed. E-mail: fpierce@ clemson.edu. § Clemson University. ⊥ Southern Illinois University. # Sandia National Laboratories. ‡ E-mail: [email protected].

Most studies of interfacial behavior to date have focused on liquid-vapor interfaces. Experimental, computational, and theoretical studies have shown that the structure and dynamics are strongly affected by the interaction of the molecules at the interface. These studies have captured a variety of characteristics from interfacial composition and orientation to capillary waves in a wide variety of systems from Lennard-Jones particles to water and a number of short-chain molecules. Several studies have explored the bulk and interfacial properties of SFAs.4,7-20 To date, only a few have dealt with specific interactions between SFAs and other liquids, including investigations of liquidsupported monolayers of SFAs12,21-27 as well as the solubility of SFAs in a small set of alkanes, perfluorinated alkanes, and other fluorinated molecules.9,11,12,15 This study focuses on liquid-liquid interfaces of semifluorinated alkane diblock copolymers (SFAs) of the form F3C(CF2)n-1(CH2)m-1CH3 with hydrophobic (alkanes and perfluorinated alkanes) and hydrophilic (water) liquids. SFAs are one class of potentially responsive materials in which protonated and fluorinated blocks, in addition to being hydrophobic to different degrees, are also mutually phobic. Recent computational studies include characterizations of liquid-vapor interfacial properties of protonated alkanes,28-34 perfluorinated alkanes,35 and semifluorinated alkanes.18,20 In contrast, liquidliquid interfaces are less understood, despite their importance in biological and biochemical systems and a host of technical applications.36 The embedded nature of the liquid-liquid interface has made experimental characterization a challenge.36 Despite such difficulties, a number of liquid-liquid interfaces, often aqueous interfaces of linear alkanes or other hydrophobic molecules, have been studied experimentally37-40 or via computer simulation.29,41-50 Our studies of SFAs at the liquid-vapor interface have shown that the interface is fluorine-rich, not fully fluorinated, and independent of the fraction of fluorine on the chain. The interfacial energies are affected by small amounts of fluorine at the interface.20 We determined the liquid density, surface

10.1021/jp805574f CCC: $40.75  2008 American Chemical Society Published on Web 10/25/2008

Liquid-Liquid Interfaces of SFA Diblock Copolymers

J. Phys. Chem. B, Vol. 112, No. 50, 2008 16013 and C16H34, the components are found to be miscible, and interdiffusion occurs,4 as seen in Figure 1b. These differences in SFA behavior at the interface with other liquids is studied in detail in the current work. This paper is organized as follows. In section II, the simulated liquid-liquid interfaces are described, including the interaction potentials used in this study. Section III focuses on the interfacial properties for aqueous interfaces of SFAs, protonated alkanes, and perfluorinated alkanes. SFA interfaces with protonated alkanes and perfluorinated alkanes are explored in section IV. Results are summarized in section V. II. Simulation Model and Methodology A. Interatomic Potentials. SFAs, protonated alkanes, and perfluorinated alkanes have been modeled using the fully atomistic OPLS-AA potential of Jorgensen et al.51-53 The OPLSAA potential is comprised of the following terms

Utot ) Ubond + Uang + Utor + Uvdw + Ucoul

(1)

The direct bonding (Ubond) and angle bending (Uang) terms are harmonic. The torsional (dihedral) term has the form Figure 1. Liquid-liquid interfaces. (a) (left) C8F17C8H17(lower)/ H2O(upper) at 375 K (SFA F: gray, H: white; H2O O: dark gray, H: white) at t ) 7.1 ns. The equilibrium interface is sharp, indicating immiscibility. (b) (right) C8F17C8H17(lower)/C16H34(upper) at 375 K (SFA same as a; protonated alkane H: black) at t ) 7.2 ns. The components are miscible, and the interfacial region continues to broaden with time, as discussed in section IV. The dimensions of the simulation cell for both are Lx )46 Å, Ly )46 Å, and Lz )300 Å, though only 100 Å in the z-direction is shown.

tension, liquid-vapor interfacial enhancement, and orientation of molecules near the liquid-vapor interface for a wide range of SFA lengths and compositions, using two different fully atomistic potentials, the OPLS-AA potential of Jorgensen et al.51-53 and a modified version of Borodin’s exp-6 potential.20,54,55 The OPLS-AA potential provided results in good agreement with known experimental values of liquid density and surface tension while overestimating the melting point of certain perfluorinated alkanes and SFA. The exp-6 potential also provided results that are in excellent agreement with experiment while, in certain cases, underestimating their melting points. The atomic-level detail used in these potentials was found necessary for an accurate description of the interfacial properties of SFAs, especially the surface tension.18,20 This was the first computational study, to our knowledge, that accurately reproduced surface tension values for a large range of SFA systems. The current study focuses on the liquid-liquid interface. Due to the large number of systems investigated, we present results only for the OPLS-AA potential.51-53 OPLS-AA was chosen over exp-6 in part since the interaction parameters for both protonated and perfluorinated alkanes with SPC/E water are known. On the basis of our previous study, we expect similar results for the exp-6 potential. Liquid-liquid interfaces of linear SFA with a number of liquids including water, protonated alkanes, and perfluorinated alkanes are considered. Specifically, aqueous interfaces of C8F17C8H17, hexadecane (C16H34), and perfluorohexadecane (C16F34) are studied in order to compare the interaction of SFAs with water to that of protonated alkanes and perfluorinated alkanes. Sharp interfaces are formed with a correspondingly high interfacial tension. One such interface, between C8F17C8H17 and H2O, is displayed in Figure 1a. However, in other cases, such as the interface of C8F17C8H17

Utor )

∑ kncosn φijkl

(2)

n

where φijkl is the dihedral angle and kn are dihedral parameters which depend on the identity of the four atoms involved. Recent work by Padua56 has provided the necessary dihedral terms at the junction of the protonated and fluorinated blocks to describe the SFA. The nonbonded potential between atoms is composed of a Lennard-Jones (LJ) and electrostatic potential51,52

[( ) ( ) ]

Unb(rij) ) Uvdw + Ucoul ) 4ij

σij rij

12

-

σij rij

6

+ kcoul

qiqj rij (3)

where ij and σij are the LJ well depth and diameter for atoms i and j and qi and qj are their partial charges. Geometric mixing rules are used for all LJ interactions between unlike atoms; ij ) (ij)(1/2) and σij ) (σiσj)(1/2), except for a 25% reduction in the H-F interaction energy as discussed by Song57 and Escobedo and Chen19 and used in our previous work.20 This reduction was found necessary to accurately describe solution behavior of protonated alkanes with perfluorinated alkanes.19 Nonbonded interactions are calculated for all atomic pairs on different molecules as well as between atoms on the same molecule separated by three or more bonds. The interaction is reduced by a factor of one-half for atoms separated by only three bonds. Four distinct atom types are used to describe SFA within this framework, fluorinated carbon, protonated carbon, fluorine, and hydrogen. The full set of OPLS-AA parameters is given by Pierce et al.20 Water has been modeled using the standard SPC/E parameter set.58 This model integrates easily with the OPLS-AA potential used for SFA and has been used in a number of previous liquid-liquid interface simulations.46,50 The SPC/E water model provides surface tension values closer to experimental values than most of the three- and four-point nonpolarizable water models, including several variations of TIP3P and TIP4P, with TIP4P-Ew providing only marginal improvement.59

16014 J. Phys. Chem. B, Vol. 112, No. 50, 2008 Distance cutoffs were not used for either the Coulomb or the r-6 portion of the LJ potential. Rather, an explicit Ewald summation technique34,60-63 was used to calculate these longrange interactions. This eliminated the need to use tail corrections for the interfacial tensions.34,35,64,65 For these long-range terms, a real-space to Fourier-space crossover distance of 12 Å was used for all simulations. The r-12 term in the LJ potential was cut off at 12 Å since it decays sufficiently rapidly. No tail correction or long-range summation technique was required for this term. B. Building the Interfaces. Simulated systems were constructed by joining two previously equilibrated20 film samples with thicknesses of 50 to 70 Å in a single periodic simulation box, as shown in Figure 1. The x and y extent of the simulation box was approximately the same as the film thickness. For hexadecane, perfluorohexadecane, and SFA with n + m ) 16, which were used for most of these studies, this corresponded to 200 molecules, while for hexane and C48H98, 800 and 100 molecules were used, respectively. Water films contained 3537 molecules. Thick films were required in order to achieve bulklike conditions at the center of each film and separation of liquid-vapor interfacial effects from those at the liquid-liquid interface. The choice of film thickness was confirmed by the presence of a plateau in the mass density profile at the center of each film. Mass densities in these plateau regions closely matched available experimental liquid densities. Each film had two interfaces, a liquid-liquid interface at which it contacted the other material and a liquid-vapor interface on the opposing side of the film, as shown in Figure 1. A gap of roughly twice the film thickness was left above the liquid-vapor interface of each film in order to prevent interaction of the two liquidvapor interfaces across the z periodic boundary. C. System Evolution. All simulations were performed under NVT conditions. The equations of motion were integrated using a velocity-Verlet algorithm with a 1 fs time step. A Langevin thermostat with a 100 fs damping time was used to regulate the system temperature. Most systems were simulated for a range of temperatures between 375 and 600 K. All results for aqueous interfaces are time-averaged over a period of 5-10 ns, discarding a minimum of 0.5 ns for equilibration. Extending the equilibration times past 0.5 ns was not observed to have any appreciable effect on simulation results. For the SFA-alkane interface, the runs were 8-18 ns, depending on the diffusivity D. Soon after the simulation commenced, the small gap between the two liquids created by placing the interfaces together was closed, and contact between the two liquids was made, regardless of their mutual phobicity. III. Water Interfaces A. Interfacial Composition. Both the protonated and fluorinated block components of SFAs as well as protonated alkanes and perfluorinated alkanes are hydrophobic.37,49,66-68 The few studies that have addressed contact between SFA and water have explored Langmuir monolayers of SFAs at the water/ air interface.12,21,22,24-27 The equilibrium conformation of the SFA monolayer predominantly shows the protonated block immersed in water and the fluorinated block in air,12,21,24-27 though in a few cases, antiparallel H-F surface domains have been observed.22 These monolayer studies cannot discern whether such a conformation is a result of the reduced hydrophobicity of the protonated block or the reduced liquid-vapor surface tension of the fluorinated blocks since each molecule in the monolayer experiences both effects. In order to analyze the relative hydrophobicity of the SFA blocks, this study focuses on aqueous

Pierce et al.

Figure 2. Atomic number density profiles at the C8F17C8H17/H2O interface at (a) 375 (top) and (b) 450 K (bottom). Insets: Atomic number density profiles for H and F at the C8F17C8H17/vapor interface at 375 and 450 K.

interfaces of SFA thick films. For comparison, interfaces of water with protonated and perfluorinated hexadecane were also examined. 1. F and H Density Profiles at the SFA-Water Interface. The results of our previous study of SFA at the liquid-vapor interface show an enhancement of F over H in the interfacial region, even for minimally fluorinated alkane diblocks, due to the reduced surface tension of fluorinated groups.20 Here, we expose SFA to water and find that this trend is reversed at the SFA-water interface, as shown in Figure 2a for C8F17C8H17 and H2O at 375 K. There is an enhancement of hydrogen and protonated carbons in this narrow interfacial region (2-4 Å), in agreement with the results for Langmuir monolayers of SFAs at the water-air interface.12,21,22,24-27 The inset of Figure 2a shows the density profiles of hydrogen and fluorine at the SFA-vapor interface, clearly indicating an increased fluorine content in this region. The fluorine enhancement at the SFA liquid-vapor interface has been effectively decoupled from the hydrogen enhancement at the SFA-water interface, which we can now attribute to the reduced hydrophobicity of the protonated blocks over the fluorinated ones. To our knowledge, this is the first study of this responsive property of SFAs. Density profile results for 450 K are shown in Figure 2b. Hydrogen enhancement at the water interface is increased at higher temperatures. At higher temperatures, it is entropically favorable for the more flexible protonated block to extend further into the water interface than the stiffer fluorinated block. We also observe this at the liquid-vapor interface20 where, at higher temperatures, these entropic effects begin to overcome the local phase segregation of fluorinated and protonated blocks, bringing the hydrogen density closer to that of the fluorine despite the fluorine block’s lower surface tension. Scaled mass density profiles are shown in Figure 3 for the aqueous interfaces of C16H34, C16F34, and C8F17C8H17 at 450 K for comparison. Protonated and perfluorinated alkane interfaces

Liquid-Liquid Interfaces of SFA Diblock Copolymers

Figure 3. Mass density profiles (scaled by the bulk density Fbulk) for the aqueous interfaces of C16H34, C16F34, and C8F17C8H17 at 450 K. Error bars in the density are smaller than 0.05 g/cm3.

J. Phys. Chem. B, Vol. 112, No. 50, 2008 16015

Figure 5. Histograms of interfacial residence times for carbons at the C16H34/H2O interface at 350 (circles), 375 (squares), and 450 K (triangles).

TABLE 1: Interfacial Tensions and Widths ∆ of Protonated Alkanes, Perfluorinated Alkanes, and SFAs with Water for L| ) 46 Å

Figure 4. Ratio of the number of protonated to fluorinated carbons residing at the C8F17C8H17/H2O interface for a range of times at several temperatures. Inset: Ratio at the C8F17C8H17 liquid-vapor interface at 375 K.

with water have the same characteristic sharpness of immiscible liquid-liquid37,68 interfaces as that seen for the SFA. For the perfluorinated alkane, we observe small oscillations near the interface. These oscillations are the result of molecular alignment in the interfacial regions. A similar effect was observed for SFA at the liquid-vapor interface and found to decrease as temperature increased.20 At 450 K, significant molecular ordering is possible only for the perfluorinated alkane, leading to the observed oscillations in the density. This temperature is well above that required to see density oscillations in the protonated alkane and SFA. Similar effects have been observed for protonated alkanes and SFAs at lower temperatures. 2. Residence Times. The relative enhancement of a component in an interfacial region can also be observed through its increased residence time in that region. Figure 4 shows ratios of the number of protonated to fluorinated carbons residing in the C8F17C8H17/H2O interfacial region for a range of times at temperatures varying from 350 to 500 K. The interfacial region is defined as the z-range over which the diblock mass density varies from 10 to 90% of the mass density at the center of the sample (essentially the bulk value). Ratios near 1 indicate little or no enhancement of protonated or fluorinated carbons, while values greater than 1 indicate enhancement of protonated carbons in the region. While little enhancement is observed at 350 K, enhancement of protonated carbons increases with temperature, in good agreement with the enhanced hydrogen densities. Similar results for C8F17C8H17 at its liquid-vapor interface at 375 K are shown for comparison in the inset of Figure 4. Ratios of less than 1 here indicate that the fluorinated

substance

temperature (K)

interfacial tension (uncertainty) (mN/m)

∆substance (Å)

∆H2O (Å)

C16H34 C16H34 C16H34 C16F34a C16F34a C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17

350 375 450 450 500 350 375 400 450 475 500

57.9(1.1) 53.8(1.7) 39.5(0.7) 29.2(2.8) 22.1(2.3) 55.0(1.9) 48.8(1.1) 47.2(1.3) 39.1(2.5) 34.7(2.0) 31.9(1.0)

1.41 1.62 2.49 2.49 3.50 1.34 1.49 1.65 2.33 3.19 3.04

1.59 1.75 2.51 2.53 3.53 1.57 1.76 1.96 2.48 3.16 3.03

a

C16F34 crystallizes below 450 K.

carbons persist at the interface longer than protonated carbons, also in agreement with the enhanced fluorine density at the interface. For SFAs, alkanes, and perfluoroalkanes, there is an average rise in residence time with increasing temperature, a result of the increase in the interfacial width with temperature, as demonstrated for protonated carbons in the C16H34/H2O interface in Figure 5. B. Interfacial Tension. The interfacial tension is a measure of the energy cost of creating additional surface contact area between two liquids. The interfacial tension is calculated from the ensemble averages of the pressure in each of the three principal directions (x, y, z) via the Kirkwood-Buff equation69

γlv,L + γll + γlv,B )

∞ [p⊥(z) - p|(z)]dz ∫ -∞

γll ) L⊥(〈p⊥〉 - 〈p|〉) - (γlv,A + γlv,B)

(4) (5)

where p⊥ ) pz and p| ) (1/2)(px + py), L⊥ is the sum of the slab thicknesses of the two liquids in contact, and γlv,A and γlv,B are the liquid-vapor surface tensions of the two liquids. Our calculations incorporate SFA, alkane, and perfluorinated alkane surface tensions calculated by Pierce et al.20 and water surface tensions determined by in’t Veld et al.63 Table 1 summarizes interfacial tensions for our simulations of n-hexadecane, nperfluorohexadecane, and C8F17C8H17 aqueous interfaces. The data are plotted in Figure 6. Such high values for the interfacial tension between water and hexadecane are consistent with the findings of Goebel and Lunkenheimer.37 For the alkane and SFA, the interfacial tension is a linearly decreasing function of

16016 J. Phys. Chem. B, Vol. 112, No. 50, 2008

Figure 6. Interfacial tensions of protonated hexadecane, perfluorohexadecane, and C8F17C8H17 with H2O as a function of temperature.

Pierce et al.

Figure 8. Interfacial width ∆ versus T/γ for C16H34/H2O (C16H34: filled circles; H2O: filled squares) and C8F17C8H17/H2O (C8F17C8H17: open circles; H2O: open squares) interfaces.

and four-point nonpolarizable water models. SPC/E has the advantage over these other models of having surface tensions more in line with experiment, as mentioned previously. Discrepancies in the temperature coefficient do not originate from liquid-vapor surface tensions of the SFA, alkane, and perfluorinated alkane as these were found to agree well with experimental values.20 C. Interfacial Widths. The large interfacial tensions of the aqueous interfaces correspond to sharp, well-defined liquid-liquid interfaces, as seen in Figures 2 and 3. The interfacial width of the liquid-liquid interface is extracted from error function fits to the density profiles44,59

[ (

) ]

F(z) 1 z0 - z 1 ) erf +1 F0 2 √2 ∆

(6)

where z0 is the position of the interface, ∆ is the interfacial width, F(z) is the density at a distance z from the center of the sample, and F0 is the equilibrium liquid density. Density profiles are well-described by error function fits, as can be seen in Figure 7 for both the SFA and water.44,59 Table 1 displays results for interfacial widths as calculated from these fits for both SFA, protonated alkane, or perfluorinated alkane and water at the liquid-liquid interface for L| ) 46 Å, where L2| ) Lx · Ly is the interfacial area. The interfacial width is a combination of two components, the intrinsic interfacial width ∆0, and a temperature-dependent component, ∆cap, due to capillary waves44,59,74-78 Figure 7. Density profiles of C8F17C8H17 (top) and H2O (bottom) and error function fits near the C8F17C8H17/H2O interface for a temperature range of 350-500 K.

temperature, consistent with earlier experimental studies of alkane-water interfaces.70 The temperature coefficient of interfacial tension (-0.08 mN/m · K) found in those studies is smaller in magnitude than the value of -0.186 mN/m · K found here through a linear regression of the data. Discrepancies may arise from the fact that the SPC/E water model underestimates the water surface tension over the entire temperature range of 300-500 K (γSPC/E:59,63 61.8-23.2 mN/m; expt.:71-73 71.7-29.5 mN/m). SPC/E water also has a smaller temperature coefficient of surface tension (-0.158 mN/m · K) than experiment (-0.21 mN/m · K).71-73 Finally, SPC/E water may not fully account for interfacial interactions due to inherent limitations of the model (lack of polarizability, single LJ diameter, etc.). These difficulties are not confined to SPC/E water but are common to most three-

∆2 ) ∆20 + ∆2cap ) ∆20 +

()

kBT L| ln 2πγ B0

(7)

where B0 is a small-wavelength, microscopic cutoff, often considered to be related to a characteristic molecular length (or width).49 In the case of contact between two simple liquids such as a protonated alkane and water, one can assume that the intrinsic width is not a strong function of temperature, and eq 7 can be used to determine ∆0 from the intercept of the plot of ∆2 versus T/γ. Figure 8 is such a plot for the C16H34/H2O system. Both substances show linear dependence for ∆2, resulting in ∆0 on the order of 1-2 Å. This is consistent with our previous findings20 for ∆0 at the liquid-vapor interface20 as well as earlier simulations of aqueous interfaces of short alkanes79-82 and recent X-ray reflectivity studies of perfluorohexane.40 In contrast, Mitrinovic et al.38 used X-ray reflectivity to measure interfacial widths of a series of alkanes of chain lengths from 6 to 22,

Liquid-Liquid Interfaces of SFA Diblock Copolymers

Figure 9. (a) (top) Histograms of cos θ for the angle between the H2O dipole (p) and the interface normal (N) for the C8F17C8H17/H2O interface as well as the H2O-vapor interface. (b) (bottom) Difference between histograms values at θ and π - θ from (a).

finding a relatively large intrinsic component, identified as the molecular radius of gyration (2-5.6 Å) for shorter alkanes and the correlation length for the longest alkanes. In the current study, we do not observe linearity in ∆2 versus T/γ for the C8F17C8H17/H2O interface, as seen in Figure 8. When the temperature of this system is varied, the enhancement of one block component in the interfacial region significantly impacts the properties of the interface. The intrinsic width and possibly B0 become functions of temperature. ∆0 cannot be determined from a linear fit of ∆2 versus T/γ. Despite this nonlinearity, it is clear from Figure 8 that any reasonable functional form relating ∆2 to T/γ will result in small values of ∆0 ) ∆((T/γ) ) 0). In this case, the best way to determine ∆0 would be to vary L| at fixed temperature and apply eq 7. Such a study would require the use of much larger interfaces due to the logarithmic dependence of ∆2 on L|; this would require a prohibitively large amount of additional computational resources and is beyond the scope of the present work. D. Molecular Orientation. Interfacial forces often orient molecules in these regions. In this section, we analyze the effect of SFA on the orientation of water at the interface between the two liquids. Several previous studies have determined the orientation of water near its liquid-vapor interface and near interfaces with other liquids.49,83-85 Liquid-vapor studies of water83,85 show that the dipole p lies parallel to the interface at the Gibbs surface, with a tendency to point into the bulk on the liquid side of the interface and a similar tendency to point into the vapor on the vapor side of the interface. A similar preference for p to align with the interface has been seen in H2O/1,2dichloroethane interfaces.84 Similarly, we determine the effect of the interface on water orientations through histograms of cos θ for p at, above, and slightly below the interface, where θ is measured with respect

J. Phys. Chem. B, Vol. 112, No. 50, 2008 16017

Figure 10. Density profiles for (a) (top) C16H34 in the C16H34/ C8F17C8H17 system at 375 K and (b) (bottom) C16H34 in the C16H34/ C15F31C1H3 system at 450 K plotted versus η ) (z - z0)t-1/2. Here, the z positions of each profile have been shifted by the calculated interfacial position z0 and the time scaled by t-1/2. Insets: Density profiles versus unscaled variable z.

to the outward normal from the water side. Figure 9a displays this data for the C8F17C8H17/H2O interface. Near the water-vapor interface, p preferentially lies parallel to the interface (at 90° to the normal), in good agreement with previous studies.83,85 Similar orientations are observed at the SFA-water interface. To demonstrate the difference between orientations above and below the Gibbs surface, we plot in Figure 9b the difference in histograms from Figure 9a at θ and π - θ. Positive values indicate preferential alignment along the outward normal, while negative values indicate alignment opposing the outward normal. A small normal component of p directed away from the Gibbs surface is observed both above and below the water liquid-vapor and water-SFA interfaces, as indicated in Figure 9b. This effect has been explained for interfaces of water and various chloromethanes as surface polarization leading to an electric field directed away from the Gibbs surface for water and into each adjacent region (H2O bulk, vapor, or contacting liquid).86 The orientation of p near the interface is remarkably similar for interfaces with vapor, SFA, and chloromethanes. IV. SFA-Alkane and SFA-Fluoroalkane Interfaces Despite the fact that SFAs have been the subject of a number of experimental and computational studies,4,7-20 the solubility of SFA has not been extensively examined. A small number of studies4,9,11,15 have investigated the solution behavior of a limited-range SFA in protonated alkanes and perfluorinated alkanes. Recent biomedical applications involving SFA necessitate a broader understanding of the solution and interfacial

16018 J. Phys. Chem. B, Vol. 112, No. 50, 2008

Pierce et al.

behavior of SFA with other liquids. To this end, this study has focused on simulations of SFAs in contact with analogous forms (i.e., protonated alkanes and perfluorinated alkanes) to understand the miscibility and immiscibility of SFAs and a range of protonated and fluorinated alkanes. The interface between C8F17C8H17(lower) and C16H34(upper) at 375 K has been illustrated in Figure 1b, with interdiffusion clearly shown. Such miscibility of SFAs in alkanes is characteristic of the systems that this study has addressed. As indicated by Meinert,4 the solubility of short SFAs in short alkanes and perfluorinated alkanes is quite good. The results of this study corroborate those results. A. Interdiffusion. Interdiffusion of two substances is often described by Fick’s one-dimensional diffusion equation87-89

[

∂Fs(z, t) ∂Fs(z, t) ∂ D(Fs(z, t)) ) ∂t ∂z ∂z

]

(8)

Figure 11. Diffusivity (D) of protonated and perfluorinated alkanes in C8F17C8H17 as a function of density, calculated using eq 9. Diffusivities are increasing functions of temperature, decrease with chain length, and are nearly concentration-independent.

where Fs(z, t) is the position and time-dependent mass density of the diffusing species and D(Fs(z, t)) is its diffusivity in the other species. When D is a function only of the concentration (mass density) at a particular position, eq 8 can be integrated using the Boltzmann similarity transformation (η ) zt -1/2) to yield

D(F) ) -

( | )

1 dF
2 dη

η(F)

-1

∫ F0ηdF′

(9)

The integral term in eq 9 can be recast in the following useful form

dF dη′ ∫ F0ηdF′) ∫ ηη η′ dη′ 0

(10)

where η0 refers to the scaled position at which the density becomes 0. Equation 10 is used to calculate the concentrationdependent diffusivity from the time-dependent density profiles written in terms of the scaling variable η. For Fickian diffusion, the profiles should all lie on a single master curve, as shown in Figure 10a and b for the diffusion of C16H34 into C8F17C8H17 at 375 K and into C15F31C1H3 at 450 K, respectively. The scaled profiles are described by a single master curve which is wellapproximated by an error function with a form given in eq 6. Unscaled density profiles at several times are shown in the insets. Diffusivities of a number of protonated alkanes and perfluorinated alkanes in contact with a number of liquids have been calculated using eq 9. Figure 11 displays several examples of diffusivity as a function of the concentration (normalized by the equilibrium liquid density F0) for protonated alkanes and perfluorinated alkanes in contact with C8F17C8H17. Diffusivities are approximately constant with D showing large variations only when F/F0 approaches 0 or 1, values at which the derivative of the density profiles approaches 0, leading to a divergence in eq 9. Each protonated or perfluorinated alkane-SFA system simulated here similarly exhibited a nearly concentration-independent diffusivity. Table 2 displays the average diffusivities of each substance in simulated systems of protonated and perfluorinated alkanes with SFA at several temperatures. This data is plotted in Figure 12. As expected, diffusivity is seen to be an increasing function of temperature and a decreasing function of chain length. Perfluorinated forms show a decreased diffusivity as a result of their increased viscosity.90

Figure 12. Average diffusivities of each substance in interfaces of protonated and perfluorinated alkanes with SFA.

TABLE 2: Average Diffusivity D for Each Substance in Systems of Protonated Alkanes and Perfluorinated Alkanes in SFAs

A

B

temperature (K)

C6H14 C6H14 C16H34 C16H34 C48H98 C48H98 C16F34 C16F34 C16H34 C16F34

C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C8F17C8H17 C15F31C1H3 C1F3C15H31

375 400 375 450 450 550 450 500 500 450

DA(B) (uncertainty) (10-6 cm2/s)

DB(A) (uncertainty) (10-6 cm2/s)

2.70(0.20) 3.85(0.15) 1.05(0.05) 3.75(0.15) 1.25(0.15) 1.75(0.05) 1.15(0.05) 1.45(0.05) 1.85(0.05) 1.30(0.10)

2.70(0.10) 2.65(0.15) 0.95(0.10) 3.40(0.10) 1.28(0.03) 1.60(0.10) 1.25(0.05) 1.95(0.05) 1.83(0.03) 1.55(0.05)

V. Conclusions The liquid-liquid interfacial behavior of semifluorinated alkane diblock copolymers with water, alkanes, and perfluorinated alkanes has been analyzed using atomistic molecular dynamic simulations. Aqueous interfaces of SFA as well as those of protonated and perfluorinated alkanes are found to be sharp (1-3 Å), with correspondingly high values of interfacial tension (30-60 mN/m). For SFA-water interfaces, hydrogen concentration enhancement is observed through increased density and residence time in the interfacial region, in agreement with results from studies of Langmuir monolayers of SFA at the water-air interface and in contrast to the observed fluorine enhancement seen at the SFA-vapor interface. Hydrogen enhancement is found to be an increasing function of temperature, owing to the increased flexibility of the protonated block

Liquid-Liquid Interfaces of SFA Diblock Copolymers in comparison to the fluorinated one. The response of the SFA surface to the presence of water leading to a change in surface structure and interfacial enhancement is indicative of the responsive nature of SFA diblock interfaces. In contrast to the sharp interfaces between SFA and water, for the chain lengths studied here, SFAs are found to be miscible with alkanes and perfluorinated alkanes. This miscibility is seen in the Fickian-type interdiffusion of SFAs with alkanes and perfluorinated alkanes, the calculated diffusivities being nearly independent of concentration. Miscibility is expected to decrease with increasing chain length due to the compounded effect of the energetic incompatibility of hydrogenated and fluorinated segments over a large number of units, an alluring topic for further study. Acknowledgment. We thank A. E. Ismail for a critical reading of the manuscript. D.P., G.S.G., and F.P. thank the DOE for partial support of this work under Contract No. ER46456. M.T. would like to thank the Donors of the American Chemical Society Petroleum Research Fund for partial support of this project. This work was performed, in part, at the Center for Integrated Nanotechnologies, a U.S. Department of Energy, Office of Basic Energy Sciences user facility. Sandia National Laboratories is a multiprogram laboratory operated by Sandia Corporation, a Lockheed-Martin Company, for the U.S. Department of Energy under Contract No. DE-AC04-94AL85000. References and Notes (1) Winter, N.; Benjamin, I. Israel J. Chem. 2007, 47, 115. (2) Winter, N.; Vieceli, J.; Benjamin, I. J. Phys. Chem. B 2008, 112, 227. (3) Lin, Y.; Skaff, H.; Emrick, T.; Dinsmore, A. D.; Russell, T. P. Science 2003, 299, 226. (4) Meinert, H.; Roy, T. Eur. J. Ophthamol. 2000, 10, 189. (5) Reiss, J. G. Fluorine Chemistry at the New Millenium - Fascinated by Fluorine; Elsevier Science: Amsterdam, The Netherlands, 2000. (6) Krafft, M. AdV. Drug DeliVery ReV. 2001, 47, 209. (7) Morgado, P.; Zhao, H.; Blas, F. J.; McCabe, C.; Rebelo, L. P. N.; Filipe, E. J. M. J. Phys. Chem. B 2007, 111, 2856. (8) Rabolt, J. F.; Russel, T. P.; Twieg, R. J. Macromolecules 1984, 17, 2786. (9) Twieg, J. R.; Russel, T. P.; Siemens, R.; Rabolt, J. F. Macromolecules 1985, 18, 1361. (10) Hopken, J.; Pugh, C.; Richtering, W.; Moller, M. Makromol. Chem. 1988, 189, 911. (11) Turberg, M. P.; Brady, J. E. J. Am. Chem. Soc. 1988, 110, 7797. (12) Gaines, G. L. Langmuir 1991, 7, 3054. (13) Hopken, J.; Moller, M. Macromolecules 1992, 25, 2482. (14) Huang, Z.; Acero, A. A.; Lei, N.; Rice, S. A.; Zhang, Z.; Schlossman, M. L. J. Chem. Soc., Faraday Trans. 1996, 92, 545. (15) Napoli, M. J. Fluorine Chem. 1996, 79, 59. (16) Binks, B. P.; Fletcher, P. D. I.; Kotsev, S. N.; Thompson, R. L. Langmuir 1997, 13, 6669. (17) Gang, O.; Ellman, J.; Moller, M.; Kraack, H.; Sirota, E. B.; Ocko, B.; Deutsch, M. Europhys. Lett. 2000, 49, 761. (18) Hariharan, A.; Harris, J. G. J. Chem. Phys. 1994, 101, 4156. (19) Escobedo, F. A.; Chen, Z. J. Chem. Phys. 2004, 121, 11463. (20) Pierce, F.; Tsige, M.; Borodin, O.; Perahia, D.; Grest, G. S. J. Chem. Phys. 2008, 128, 214903. (21) Abed, A. E.; Pouzet, E.; Faure, M.; Saniere, M.; Abillon, O. Phys. ReV. E 2000, 62, R5895. (22) Abed, A. E.; Faure, M.; Pouzet, E.; Abillon, O. Phys. ReV. E 2002, 65, 051603. (23) Broniatowski, M.; Macho, I.; Minones, J.; Dynarowicz-Latka, P. Appl. Surf. Sci. 2005, 246, 342. (24) Broniatowski, M.; Minones, J.; Macho, I.; Dynarowicz-Latka, P. Pol. J. Chem. 2005, 79, 1047. (25) Latka, P. D.; Perez-Morales, M.; Munoz, E.; Broniatowski, M.; Martin-Romero, M. T.; Camacho, L. J. Phys. Chem. B 2006, 110, 6095. (26) Kim, N.; Shin, S. J. Chem. Phys. 1999, 111, 6556. (27) Semenov, A. N.; Gonzalez-Perez, A.; Krafft, M. P.; Legrand, J.-F. Langmuir 2006, 22, 8703. (28) Nicolas, J. P.; Smit, B. Mol. Phys. 2002, 100, 2471. (29) Rivera, J. L.; McCabe, C.; Cummings, P. T. Phys. ReV. E 2003, 67, 011603.

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