PRL 114, 108301 (2015)
PHYSICAL
REVIEW
week ending 13 MARCH 2015
LETTERS
sr Interactions and Stress Relaxation in Monolayers of Soft Nanoparticles at Fluid-Fluid Interfaces Valeria Garbin Department o f Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom Ian Jenkins, Talid Sinno, John C. Crocker, and K athleen J. Stebe Department o f Chemical and Biomolecular Engineering, University o f Pennsylvania, 220 South 33rd Street, Philadelphia, Pennsylvania 19104, USA (Received 5 October 2014; revised manuscript received 19 January 2015; published 9 March 2015) Nanoparticles with grafted layers of ligand molecules behave as soft colloids when they adsorb at fluidfluid interfaces. The ligand brush can deform and reconfigure, adopting a lens-shaped configuration at the interface. This behavior strongly affects the interactions between soft nanoparticles at fluid-fluid interfaces, which have proven challenging to probe experimentally. We measure the surface pressure for a stable 2D interfacial suspension of nanoparticles grafted with ligands, and extract the interaction potential from these data by comparison to Brownian dynamics simulations. A soft repulsive potential with an exponential form accurately reproduces the measured surface pressure data. A more realistic interaction potential model is also fitted to the data to provide insights into the ligand configuration at the interface. The stress of the 2D interfacial suspension upon step compression exhibits a single relaxation time scale, which is also attributable to ligand reconfiguration. DOI: 10.1103/PhysRevLett. 114.108301
PACS numbers: 82.70.Dd, 83.50.Lh
Soft colloids at fluid-fluid interfaces, for instance star copolym ers [1], m icrogels [2,3], and polym er- or ligandgrafted nanoparticles [4-9], stretch and deform, adopting shapes that are dictated by the interplay o f surface tension and deformability, m uch like in the wetting o f membranes, vesicles [10], and soft solids [11,12]. Ligand-grafted metal or sem iconductor nanocrystals at fluid-fluid interfaces are widely used in nanom aterials synthesis [13-15] and in catalytic processes [16]. Sim ulation studies predict the rearrangem ent o f the ligand brush into anisotropic lens shaped configurations when these nanoparticles adsorb at fluid-fluid interfaces [4-6,8]. This prediction is supported by x-ray reflectivity m easurem ents o f nanoparticle density at the interface [7]. These configurations are particularly im portant, as ligand rearrangem ents m odify the interpar ticle interactions, which ultim ately determ ine colloidal stability and phase behavior at the interface. Ligandm ediated interactions can be dom inant in the case of soft nanoparticles, w here the thickness o f the deformable grafted layer is com parable to the size o f the particle core. These interactions have been studied in sim ulations [9] but have never been characterized experimentally. D irect m ea surem ents o f the interparticle potential have been hampered by the challenge o f obtaining a stable nanoparticle sus pension at a fluid-fluid interface. Specifically, since adsorp tion at the interface exposes the nanoparticles to a second fluid with different polarity and solvent quality, colloidal stability is not always preserved [17], H ere w e report m easurem ents o f the steric repulsion betw een ligand-grafted nanoparticles, with a length o f the 0 0 3 1 -9 0 0 7 /1 5 /1 14(10)/108301(5)
ligand com parable to the radius o f the nanoparticle, within a fluid-fluid interface (see Fig. 1). We m easured the surface pressure o f a 2D nanoparticle suspension as a function of surface coverage, and related it to an effective pair potential using Brownian dynam ics simulations. A soft repulsive potential with exponential decay accurately captures the measured surface pressure. An em pirical interaction poten tial is also fitted to the data to provide insights into the ligand configuration. In a step-com pression experim ent w e find a slow relaxation time scale, which we conclude is due to slow rearrangem ents o f the ligands grafted on the surface o f the nanoparticles, resulting in a tim e-dependent interaction potential. The nanoparticles used for the experim ents are 4.5 nm gold nanocrystals grafted with an amphiphilic ligand, m ercapto-undecyl-tetra(ethylene glycol). The particle polydispersity, estim ated from a transm ission electron m icro graph provided by the supplier (Sigma-Aldrich), is at
FIG. 1. Schematic of nanoparticles at fluid-fluid interface with ligand rearrangements (drawing not to scale).
108301-1
© 2 0 1 5 American Physical Society
PRL 114, 108301 (2015)
PHYSICAL
REVIEW
least 10%. These particles exhibit spontaneous adsorption from an aqueous suspension onto the interface with fluorinated oil octafluoropentyl acrylate [18]. The oil was obtained from Sigma-Aldrich and used as received. The surface tension of the bare oil-water interface is Yo — 26 mN/m. Adsorption of the nanoparticles at the oil-water interface effectively reduces the surface tension [18]. We measured the effective surface tension by pendant drop tensiometry. Briefly, the shape of a pendant drop is determined by the balance of surface tension and gravita tional forces, described by the Bond number Bo = ApgR2/ y where Ap is the density difference and y the surface tension between the two fluids, g the acceleration due to gravity, and R the radius of the drop. A numerical solution to the Young-Laplace equation is fitted to the contour of the drop to extract the surface tension. In general, the effective surface tension is given by y = yo - n where n is the two-dimensional osmotic pres sure, referred to as surface pressure, due to the interfacial nanoparticles. If the interfacial phase is a stable suspension, and in the absence of extra stresses due to dynamic deformation, the measured pressure II0 is an equilibrium property of the suspension that only depends on the nano particle surface coverage
PHYSICAL
REVIEW
week ending 13 MARCH 2015
LETTERS
sr Interactions and Stress Relaxation in Monolayers of Soft Nanoparticles at Fluid-Fluid Interfaces Valeria Garbin Department o f Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom Ian Jenkins, Talid Sinno, John C. Crocker, and K athleen J. Stebe Department o f Chemical and Biomolecular Engineering, University o f Pennsylvania, 220 South 33rd Street, Philadelphia, Pennsylvania 19104, USA (Received 5 October 2014; revised manuscript received 19 January 2015; published 9 March 2015) Nanoparticles with grafted layers of ligand molecules behave as soft colloids when they adsorb at fluidfluid interfaces. The ligand brush can deform and reconfigure, adopting a lens-shaped configuration at the interface. This behavior strongly affects the interactions between soft nanoparticles at fluid-fluid interfaces, which have proven challenging to probe experimentally. We measure the surface pressure for a stable 2D interfacial suspension of nanoparticles grafted with ligands, and extract the interaction potential from these data by comparison to Brownian dynamics simulations. A soft repulsive potential with an exponential form accurately reproduces the measured surface pressure data. A more realistic interaction potential model is also fitted to the data to provide insights into the ligand configuration at the interface. The stress of the 2D interfacial suspension upon step compression exhibits a single relaxation time scale, which is also attributable to ligand reconfiguration. DOI: 10.1103/PhysRevLett. 114.108301
PACS numbers: 82.70.Dd, 83.50.Lh
Soft colloids at fluid-fluid interfaces, for instance star copolym ers [1], m icrogels [2,3], and polym er- or ligandgrafted nanoparticles [4-9], stretch and deform, adopting shapes that are dictated by the interplay o f surface tension and deformability, m uch like in the wetting o f membranes, vesicles [10], and soft solids [11,12]. Ligand-grafted metal or sem iconductor nanocrystals at fluid-fluid interfaces are widely used in nanom aterials synthesis [13-15] and in catalytic processes [16]. Sim ulation studies predict the rearrangem ent o f the ligand brush into anisotropic lens shaped configurations when these nanoparticles adsorb at fluid-fluid interfaces [4-6,8]. This prediction is supported by x-ray reflectivity m easurem ents o f nanoparticle density at the interface [7]. These configurations are particularly im portant, as ligand rearrangem ents m odify the interpar ticle interactions, which ultim ately determ ine colloidal stability and phase behavior at the interface. Ligandm ediated interactions can be dom inant in the case of soft nanoparticles, w here the thickness o f the deformable grafted layer is com parable to the size o f the particle core. These interactions have been studied in sim ulations [9] but have never been characterized experimentally. D irect m ea surem ents o f the interparticle potential have been hampered by the challenge o f obtaining a stable nanoparticle sus pension at a fluid-fluid interface. Specifically, since adsorp tion at the interface exposes the nanoparticles to a second fluid with different polarity and solvent quality, colloidal stability is not always preserved [17], H ere w e report m easurem ents o f the steric repulsion betw een ligand-grafted nanoparticles, with a length o f the 0 0 3 1 -9 0 0 7 /1 5 /1 14(10)/108301(5)
ligand com parable to the radius o f the nanoparticle, within a fluid-fluid interface (see Fig. 1). We m easured the surface pressure o f a 2D nanoparticle suspension as a function of surface coverage, and related it to an effective pair potential using Brownian dynam ics simulations. A soft repulsive potential with exponential decay accurately captures the measured surface pressure. An em pirical interaction poten tial is also fitted to the data to provide insights into the ligand configuration. In a step-com pression experim ent w e find a slow relaxation time scale, which we conclude is due to slow rearrangem ents o f the ligands grafted on the surface o f the nanoparticles, resulting in a tim e-dependent interaction potential. The nanoparticles used for the experim ents are 4.5 nm gold nanocrystals grafted with an amphiphilic ligand, m ercapto-undecyl-tetra(ethylene glycol). The particle polydispersity, estim ated from a transm ission electron m icro graph provided by the supplier (Sigma-Aldrich), is at
FIG. 1. Schematic of nanoparticles at fluid-fluid interface with ligand rearrangements (drawing not to scale).
108301-1
© 2 0 1 5 American Physical Society
PRL 114, 108301 (2015)
PHYSICAL
REVIEW
least 10%. These particles exhibit spontaneous adsorption from an aqueous suspension onto the interface with fluorinated oil octafluoropentyl acrylate [18]. The oil was obtained from Sigma-Aldrich and used as received. The surface tension of the bare oil-water interface is Yo — 26 mN/m. Adsorption of the nanoparticles at the oil-water interface effectively reduces the surface tension [18]. We measured the effective surface tension by pendant drop tensiometry. Briefly, the shape of a pendant drop is determined by the balance of surface tension and gravita tional forces, described by the Bond number Bo = ApgR2/ y where Ap is the density difference and y the surface tension between the two fluids, g the acceleration due to gravity, and R the radius of the drop. A numerical solution to the Young-Laplace equation is fitted to the contour of the drop to extract the surface tension. In general, the effective surface tension is given by y = yo - n where n is the two-dimensional osmotic pres sure, referred to as surface pressure, due to the interfacial nanoparticles. If the interfacial phase is a stable suspension, and in the absence of extra stresses due to dynamic deformation, the measured pressure II0 is an equilibrium property of the suspension that only depends on the nano particle surface coverage
