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Interaction Forces between Nanoparticles in Diol-Water Mixtures: A Molecular Dynamics Study with Coarse-Grained Model Hiroyuki Shinto, Dai Iwahara, Minoru Miyahara, and Ko Higashitani* Department of Chemical Engineering, Kyoto University, Yoshida, Sakyo-ku, Kyoto 606-8501, Japan Received February 10, 2002 In the present study, we investigate the interaction force between hydrophilic nanospheres immersed in diol-water mixtures using a molecular dynamics simulation with a coarse-grained model. It is found that (i) the diol-water mixtures undergo a liquid-to-liquid phase separation between surfaces, which leads to the formation of a water lens between the surfaces and the accompanying attractive force, and (ii) the full-off force between the surfaces exhibits a peak in the diol-rich region. The simulation results obtained will be discussed in detail, by comparing with those in monohydric alcohol-water mixtures and with the experimental results by an atomic force microscope.
1. Introduction A confinement between surfaces often induces a phase transition of an intervening fluid, which leads to the formation of a lens of a second phase between the surfaces immersed in a bulk medium of another phase. This phenomenon is called a capillary-induced phase separation.1 Once a fluid confined between surfaces undergoes a phase separation, it gives rise to a strong attractive force between the surfaces; this force ranges up to several hundred nanometers and usually predominates over the other forces (e.g., electric double-layer and van der Waals forces). An understanding of the phase separation of fluids in confinement and the accompanying capillary force has been, therefore, a crucial subject in colloid and interface science. A surface force apparatus (SFA)2 and an atomic force microscope (AFM)3,4 are the powerful experimental devices to measure the interaction forces between two surfaces immersed in a medium of various fluids; however, our discussion here will be limited to the measurements of the force due to capillary-induced phase separation. This capillary force has been observed in several different cases (see Figure 5.20 of ref 1). The most common case is a vapor-to-liquid transition between surfaces in a gas phase (i.e., a capillary condensation).5-10 The force measurements * Corresponding author. Telephone: +81-75-753-5562. Fax: +81-75-753-5913. E-mail:
[email protected]. (1) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain: where Physics, Chemistry, and Biology Meet, 2nd ed.; Wiley-VCH: New York, 1999. (2) Israelachvili, J. N.; Adams, G. E. J. Chem. Soc., Faraday Trans. 1 1978, 74, 975. (3) Binning, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930. (4) (a) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Nature (London) 1991, 353. (b) Ducker, W. A.; Senden, T. J.; Pashley, R. M. Langmuir 1992, 8, 1831. (5) (a) Christenson, H. K. J. Colloid Interface Sci. 1988, 121, 170. (b) Christenson, H. K.; Yaminsky, V. V. Langmuir 1993, 9, 2448. (c) Wanless, E. J.; Christenson, H. K. J. Chem. Phys. 1994, 101, 4260. (6) (a) Crassous, J.; Charlaix, E.; Gayvallet, H.; Loubet, J.-L. Langmuir 1993, 9, 1995. (b) Crassous, J.; Charlaix, E.; Loubet, J.-L. Europhys. Lett. 1994, 28, 37. (7) Binggeli, M.; Mate, C. M. Appl. Phys. Lett. 1994, 65, 415. (8) Xu, L.; Lio, A.; Hu, J.; Ogletree, D. F.; Salmeron, M. J. Phys. Chem. B 1998, 102, 540. (9) He, M.; Blum, A. S.; Aston, D. E.; Buenviaje, C.; Overney, R. M.; Luginbuhl, R. J. Chem. Phys. 2001, 114, 1355.
also have exhibited a liquid-to-vapor transition (i.e., a capillary evaporation, which is the reverse of the aforesaid transition)11,12 and a liquid-to-liquid phase separation in binary liquid mixtures such as a hydrophobic liquid with water13,14 or alcohol contaminant,15 an alcohol-water mixture,16 and a dioxane-water mixture.17 Another cases of capillary phase separation have been found in the more complex systems such as a liquid crystal,18 a binary polymer mixture,19 and surfactant self-assembling systems of a isotropic sponge phase,20,21 a nematic phase,22 a bicontinuous microemulsion phase,23,24 and a micellar phase in the presence of a polymer.25 (10) Fuji, M.; Machida, K.; Takei, T.; Watanabe, T.; Chikazawa, M. J. Phys. Chem. B 1998, 102, 8782. (11) (a) Ishida, N.; Kinoshita, N.; Miyahara, M.; Higashitani, K. J. Colloid Interface Sci. 1999, 216, 387. (b) Ishida, N.; Sakamoto, M.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 5681. (c) Ishida, N.; Inoue, T.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 6377. (d) Ishida, N.; Sakamoto, M.; Miyahara, M.; Higashitani, K. J. Colloid Interface Sci. 2001, 235, 190. (12) Christenson, H. K.; Claesson, P. M. Adv. Colloid Interface Sci. 2001, 91, 391 and references therein. (13) (a) Christenson, H. K. J. Colloid Interface Sci. 1985, 104, 234. (b) Christenson, H. K.; Blom, C. E. J. Chem. Phys. 1987, 86, 419. (c) Christenson, H. K.; Fang, J.; Israelachvili, J. N. Phys. Rev. B 1989, 39, 11750. (14) Claesson, P. M.; Dedinaite, A.; Bergenståhl, B.; Campbell, B.; Christenson, H. K. Langmuir 1997, 13, 1682. (15) Mizukami, M.; Kurihara, K. Chem. Lett. 1999, 1999, 1005. (16) (a) Kanda, Y.; Nakamura, T.; Higashitani, K. Colloids Surf. A 1998, 139, 55. (b) Kanda, Y.; Iwasaki, S.; Higashitani, K. J. Colloid Interface Sci. 1999, 216, 394. (17) Kanda, Y.; Murata, T.; Higashitani, K. Colloids Surf. A 1999, 154, 157. (18) Kocˇevar, K.; Borsˇtnik, A.; Musˇevic, I.; Zˇ umer, S. Phys. Rev. Lett. 2001, 86, 5914. (19) Wennerstro¨m, H.; Thuresson, K.; Linse, P.; Freyssingeas, E. Langmuir 1998, 14, 5664. (20) (a) Petrov, P.; Olsson, U.; Christenson, H. K.; Miklavic, S.; Wennerstro¨m, H. Langmuir 1994, 10, 988. (b) Petrov, P.; Miklavic, S.; Olsson, U.; Wennerstro¨m, H. Langmuir 1995, 11, 3928. (21) (a) Antelmi, D. A.; Ke´kicheff, P.; Richetti, P. J. Phys. II 1995, 5, 103. (b) Antelmi, D. A.; Ke´kicheff, P.; Richetti, P. Langmuir 1999, 15, 7774. (22) (a) Moreau, L.; Richetti, P.; Barois, P. Phys. Rev. Lett. 1994, 73, 3556. (b) Richetti, P.; Moreau, L.; Barois, P.; Ke´kicheff, P. Phys. Rev. E 1996, 54, 1749. (23) Petrov, P.; Olsson, U.; Wennerstro¨m, H. Langmuir 1997, 13, 3331. (24) Moreau-Biensan, L.; Barois, P.; Richetti, P. In Supramolecular Structure in Confined Geometries; Manne, S.; Warr, G. G., Eds.; ACS Symposium Series 736; Oxford University Press: London, 1999; Chapter 4.
10.1021/la025618w CCC: $22.00 © 2002 American Chemical Society Published on Web 04/20/2002
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Several theoretical techniques have been employed for molecular-level investigation of the aforementioned capillary forces. A density functional theory (DFT),26 in which a molecular description of fluids is used, has been applied to a single-component fluid of Lennard-Jones (LJ) particles between surfaces.27-29 As a result, it elucidated several features of the attractive force due to condensation27,28 or evaporation in the capillary.29 The alternative is an integral equation theory (IET),30 which is based on the Ornstein-Zernike relation with a closure approximation and/or an interaction site model. The IET has been employed for analysis of the attractive force due to capillary evaporation in a pure liquid of LJ particles31 or water molecules.32 Furthermore, it has been successfully applied to binary fluids for analysis of the force due to capillary-induced liquid-to-liquid phase separation,33,34 in which a binary mixture of attractive and purely repulsive hard spheres was used to mimic a mixture of hydrophilic and hydrophobic molecules. Within the framework of DFT, however, the descriptions of a fluid employed are more or less approximate;27-29 also, the analyzed results by IET largely depend on the closure approximations used.35 For these reasons, it is necessary to compare carefully the results from DFT and IET with those from the computer simulation36 based on the molecular dynamics (MD) or the Monte Carlo (MC) method. It should be noted that the other theoretical techniques have been developed but applied only to analysis of the force due to capillary evaporation.37-39 Molecular simulation studies have elucidated several features of the forces due to capillary-induced phase separations. Most of these studies focused on the force due to capillary evaporation in a pure liquid of LJ particles37,40,41 or water molecules.42,43 Only a few simulation studies reported the force due to capillary condensation in a vapor of water44 or n-hexadecane.45 Very recently, the grand canonical MC (GCMC) method has been successfully applied to a vapor and a binary liquid mixture (25) Freyssingeas, E.; Antelmi, D. A.; Ke´kicheff, P.; Richetti, P.; Bellocq, A.-M. Eur. Phys. J. B 1999, 9, 123. (26) Davis, H. T. Statistical Mechanics of Phases, Interfaces, and Thin Films; Wiley-VCH: New York, 1996. (27) Frink, L. J. D.; van Swol, F. J. Chem. Phys. 1997, 106, 3782. (28) Bauer, C.; Bieker, T.; Dietrich, S. Phys. Rev. E 2000, 62, 5324. (29) Forsman, J.; Jo¨nsson, B.; Woodward, C. E.; Wennerstro¨m, H. J. Phys. Chem. B 1997, 101, 4253. (30) Hansen, J. P.; McDonald, I. R. Theory of Simple Liquids; 2nd ed.; Academic Press: London, 1986. (31) Kinoshita, M.; Iba, S.; Kuwamoto, K.; Harada, M. J. Chem. Phys. 1996, 105, 7177. (32) Kinoshita, M.; Hirata, F. J. Chem. Phys. 1996, 104, 8807. (33) (a) Kinoshita, M.; Iba, S.; Kuwamoto, K.; Harada, M. J. Chem. Phys. 1996, 105, 7184. (b) Kinoshita, M. Mol. Phys. 1998, 94, 485. (c) Kinoshita, M. Mol. Phys. 1999, 96, 71. (34) (a) Kinoshita, M. Chem. Phys. Lett. 2000, 325, 281. (b) Kinoshita, M. Chem. Phys. Lett. 2000, 326, 551. (c) Kinoshita, M. Chem. Phys. Lett. 2001, 333, 217. (35) Attard, P.; Patey, G. N. J. Chem. Phys. 1990, 92, 4970. (36) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Clarendon Press: Oxford, England, 1987. (37) Be´rard, D. R.; Attard, P.; Patey, G. N. J. Chem. Phys. 1993, 98, 7236. (38) Lum, K.; Chandler, D.; Weeks, J. D. J. Phys. Chem. B 1999, 103, 4570. (39) Truskett, T. M.; Debenedetti, P. G.; Torquato, S. J. Chem. Phys. 2001, 114, 2401. (40) Shinto, H.; Miyahara, M.; Higashitani, K. J. Colloid Interface Sci. 1999, 209, 79. (41) Bolhuis, P. G.; Chandler, D. J. Chem. Phys. 2000, 113, 8154. (42) Wallqvist, A.; Berne, B. J. J. Phys. Chem. 1995, 99, 2893. (43) Bratko, D.; Curtis, R. A.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 2001, 115, 3873. (44) Wensink, E. J. W.; Hoffmann, A. C.; Apol, M. E. F.; Berendsen, H. J. C. Langmuir 2000, 16, 7392. (45) (a) Luedtke, W. D.; Landman, U. Comput. Mater. Sci. 1992, 1, 1. (b) Landman, U.; Luedtke, W. D.; Ouyang, J.; Xia, T. K. Jpn. J. Appl. Phys. 1 1993, 32, 1444.
Shinto et al.
Figure 1. Illustration of the coarse-grained models of water and amphiphile molecules. Symbols w, h, and t denote waterlike, headlike, and taillike particles, respectively. Three amphiphiles are displayed: ht2h was employed in the present study; ht and ht3 were used in the previous study of ref 48.
of LJ particles confined between surfaces;46,47 consequently, the detailed features of the attractive force due to capillary condensation46 or liquid-to-liquid phase separation47 were elucidated. It has been found that the results of the abovementioned theories have been in good agreement with those of the molecular simulations. In a previous study,48 we computed the force between hydrophilic macrospheres immersed in alcohol-water mixtures using the MD simulation40 with a coarse-grained model.49 It was found that (i) the alcohol-water mixtures undergo a liquid-to-liquid phase separation between surfaces, which leads to the formation of a water lens between the surfaces and the accompanying strong attractive force; (ii) the full-off force between the surfaces exhibits a peak in the alcohol-rich region; and (iii) this peak appears at a higher concentration of alcohol to have a stronger pull-off force as an alcohol molecule has a longer hydrophobic chain.48 The simulation results agreed with the results of AFM measurements and verified the prediction therein.16 In this paper, we report a molecular simulation study of the force between hydrophilic macrospheres immersed in diol-water mixtures, where the results of the force between hydrophobic macrospheres in pure water are also given for comparison. We employed our MD technique40 and the coarse-grained model,49 which are almost the same as in our previous study for alcohol-water mixtures.48 The aim of the present study is to investigate the effects of the hydroxyl-terminal ends of alcohol and diol molecules on the capillary-induced phase separations and the accompanying forces. 2. Models Since the models used for diol-water mixtures and macrospheres are almost the same as in our previous study for alcohol-water mixtures,48 only a brief explanation is given here. Alcohol and diol are referred to as amphiphile in the present study. 2.1. Amphiphile-Water Mixtures. Water and amphiphile molecules were represented using three types of particles: waterlike, headlike, and taillike particles, which are referred to as w, h, and t particles, respectively.49 The w and h particles are hydrophilic, whereas the t particle is hydrophobic. A water molecule of w and an amphiphile molecule of ht2h are illustrated in Figure 1; also, two amphiphiles of ht and ht3, employed in our previous study,48 are shown. Amphiphiles ht and ht3 can be considered as a coarse-grained model of a linear alcohol (46) Shinto, H.; Uranishi, K.; Miyahara, M.; Higashitani, K. J. Chem. Phys., in press. (47) Greberg, H.; Patey, G. N. J. Chem. Phys. 2001, 114, 7182. (48) Shinto, H.; Miyahara, M.; Higashitani, K. Langmuir 2000, 16, 3361. (49) Shinto, H.; Tsuji, S.; Miyahara, M.; Higashitani, K. Langmuir 1999, 15, 578 and references therein.
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molecule with a single hydroxyl-terminal end, while ht2h can be regarded as that with double hydroxyl-terminal ends. The interaction between particles i and j in different molecules was given by a shifted Lennard-Jones (LJ) potential with energy parameter , core diameter σ, and cutoff radius rcut ij :
uinter (r) ) ij
{
cut φ(r) - φ(rcut ij ) r e rij (i,j ) w, h, t) r > rcut 0 ij
φ(r) ) 4
12
6
[( ) ( ) ] σ r
-
σ r
(1a) (1b)
where r is the distance between particles. Parameters for argon were used: /kB ) 119.8 K, σ ) 0.3405 nm, and m ) 39.948 g/mol, where m is the mass of a particle, and kB is the Boltzmann constant. To represent the hydrophilicity and hydrophobicity of the particles, the value of rcut ij ) 2.5σ or 21/6σ was used depending on the types of pairs: the intraspecies pairs of w-w, h-h, w-h, and t-t had attractive interactions using rcut ij ) 2.5σ; the interspecies pairs of w-t and h-t had no attractive interactions using 1/6 rcut ij ) 2 σ. Neighboring particles in an amphiphile were bonded together by
1 (r) ) k(r - l0)2 (i,j ) h, t) ubond ij 2
(2)
where the spring constant k ) 200/σ2 and the spring length l0 ) σ were used. Two-bond or more separated particles in an amphiphile interacted with each other via a shifted LJ potential with energy parameter , core diameter σintra ) (x3/21/6)σ and cutoff radius 21/6σintra ()x3σ):
uintra (r) ) ij
{
φ′(r) - φ′(21/6σintra) r e 21/6σintra (i,j ) h, t) (3a) r > 21/6σintra 0 φ′(r) ) 4
[( ) ( ) ] σintra r
12
-
σintra r
6
(3b)
Because of eq 3, the interaction between two-bond separated particles was repulsive when the angle between the two bonds with length σ each was less than 120°; otherwise, their interaction remained zero. Accordingly, ht2h chains were prevented from extremely bending by eq 3. Thus, the intermolecular potentials of w-w, w-ht2h, and ht2h-ht2h were given by the summation of eq 1, whereas the intramolecular potential of ht2h was given by the summation of eqs 2,3. It should be noted that in our previous study,48 eq 1 was employed for interactions between all pairs of particles regardless of whether they belonged to different molecules or not; in addition, eq 2 was used for interactions between bonded particles. The thermodynamic state of a fluid was the same as in our previous study:48 F* ) Fσ3 ) 0.7 and T* ) kBT/ ) 1.0, where F is the number density of fluid particles and T the temperature. The asterisk hereafter denotes the properties in units of the LJ fluid given by eq 1b. The average separation of the bonded particles was found to be 1.00σ in the present systems. 2.2. Macrospheres. The interaction between fluid particle j and macrosphere M of radius R ) 5σ was given
Figure 2. Potential energies for particle-particle and sphereparticle interactions represented by eqs 1b and 4b, respectively. The sphere has the radius of R ) 5σ.
by
uMj(r) ) ∞ reR ψ(r) - ψ(rcut ) R < r e R + rcut (j ) w, h, t) (4a) Mj Mj cut r > R + rMj 0
{
ψ(r) )
[ ( ) ( )] { [ ( ) ( )] [ ( ) ( ) ]}
2πFsurfσ2R 2 σ r 5r-R
10
-
σ r-R
4
+
πFvolσ3Rin 1 9 8 σ σ σ 8 3r 30 r - Rin Rin r - Rin 3 2 σ σ σ 2 (4b) r - Rin Rin r - Rin where r is the center-to-center distance between the sphere and particle, rcut Mj the cutoff distance of the particle center from the sphere surface, Fsurf ) 2-1/3/σ2, Fvol ) 1/σ3, and Rin ) R - 2-1/3σ.48 Figure 2 shows that the potential energy profile of eq 4b exhibit a minimum of -2.70 at r ) 5.99σ (i.e., r - R ) 0.99σ). Hydrophilic and hydrophobic spheres were represented in the same way as amphiphile-water mixtures: when a sphere and a particle are of the same kind, they had attractive interactions using rcut Mj ) 5.0σ; otherwise, they had no attractive interactions using rcut Mj ) 0.99σ. The sphere had the mass of mM ) m(2R/σ)3. The direct sphere-sphere interaction could be introduced as a function of the nearest surface separation D ()r - 2R).50 In the present study, however, it was assumed to be zero except for the excluded-volume effect:
Wdir(D) )
{
∞ D
