Improved in situ spring constant calibration for colloidal probe atomic force microscopy

Increasing AFM colloidal probe accuracy by optical tweezers

A precise determination of the cantilever spring constant is the critical point of all colloidal probe experiments. Existing methods are based on approximations considering only cantilever geometry and do not take into account properties of any object or substance attached to the cantilever. Neglecting the influence of the colloidal sphere on the cantilever characteristics introduces significant uncertainty in a spring constant determination and affects all further considerations. In this work we propose a new method of spring constant calibration for 'colloidal probe' type cantilevers based on the direct measurement of force constant. The Optical Tweezers based calibration method will help to increase the accuracy and repeatability of the AFM colloidal probe experiments.

Pickering Emulsion Transitions in 2,6-Lutidine Plus Water Critical Liquid Mixtures

Silica particle (S) stabilized oil-in-water Pickering emulsions are observed in the two-phase region of the critical liquid mixture 2,6-lutidine (L) plus water (W). De-emulsification is found at temperatures below a particle wetting transition temperature T_w(R) where T_w(R) decreases toward the lower critical temperature T_c for smaller particle radii R. The presence of a Pickering emulsion transition and its dependence upon particle radius can be explained by a competition between destabilizing gravitational forces and stabilizing forces originating from the critical interfacial tension. As a corollary to these observations, the line tension τ at the three-phase SLW contact line is determined as a function of temperature.

Large colloidal probes for atomic force microscopy: Fabrication and calibration issues

Atomic force microscopy (AFM) is a powerful tool to investigate interaction forces at the micro and nanoscale. Cantilever stiffness, dimensions and geometry of the tip can be chosen according to the requirements of the specific application, in terms of spatial resolution and force sensitivity. Colloidal probes (CPs), obtained by attaching a spherical particle to a tipless (TL) cantilever, offer several advantages for accurate force measurements: tunable and well-characterisable radius; higher averaging capabilities (at the expense of spatial resolution) and sensitivity to weak interactions; a well-defined interaction geometry (sphere on flat), which allows accurate and reliable data fitting by means of analytical models. The dynamics of standard AFM probes has been widely investigated, and protocols have been developed for the calibration of the cantilever spring constant. Nevertheless, the dynamics of CPs, and in particular of large CPs, with radius well above 10 μm and mass comparable, or larger, than the cantilever mass, is at present still poorly characterized. Here we describe the fabrication and calibration of (large) CPs. We describe and discuss the peculiar dynamical behaviour of CPs, and present an alternative protocol for the accurate calibration of the spring constant.

Influence of line tension on spherical colloidal particles at liquid-vapor interfaces

Atomic force microscopy (AFM) imaging of isolated submicron dodecyltrichlorosilane coated silica spheres, immobilized at the liquid polystyrene- (PS-) air interface at the PS glass transition temperature, T(g), allows for determination of the contact angle θ versus particle radius R. At T(g), all θ versus R measurements are well described by the modified Young's equation for a line tension τ = 0.93 nN. The AFM measurements are also consistent with a minimum contact angle θ(min) and minimum radius R(min), below which single isolated silica spheres cannot exist at the PS-air interface.

Interpreting atomic force microscopy measurements of hydrodynamic and surface forces with nonlinear parametric estimation

A nonlinear parameter estimation method has been developed to extract the separation-dependent surface force and cantilever spring constant from atomic force microscope data taken at different speeds for the interaction between a silica colloidal probe and plate in aqueous solution. The distinguishing feature of this approach is that it exploits information from the velocity dependence of the force-displacement data due to hydrodynamic interaction to provide an unbiased estimate of the functional form of the separation-dependent surface force. An assumed function for the surface force with unknown parameters is not required. In addition, the analysis also yields a consistent estimate of the in situ cantilever spring constant. In combination with data from static force measurements, this approach can further be used to quantify the extent of hydrodynamic slip.

Reliable measurements of interfacial slip by colloid probe atomic force microscopy. III. Shear-rate-dependent slip

We present experimental evidence and theoretical models that demonstrate that the slip length, which is the departure from the hydrodynamic no-slip boundary condition, cannot be constant as commonly assumed, but must decrease with increasing shear rate to avoid an unphysical divergence in the velocity of the fluid adjacent to the surface at small separations. The molecular origin of the shear rate dependence of the slip length is discussed. A new theoretical model for slip (the saturation model) is obtained, and it is shown to describe accurately colloid probe atomic force microscopy force measurements for all separations down to a few nanometers in two partially wetting situations (di-n-octyl phthalate on silanized silicon and bare silicon). Previous observations of slip length increasing with shear rate are explained as due to an imprecise calculation of the drag force on the cantilever. A new way of plotting experimental data is also presented, which provides a useful way to illustrate the slip length dependence on the shear rate.

Nanoparticle adsorption at liquid-vapor surfaces: influence of nanoparticle thermodynamics, wettability, and line tension

We developed a statistical mechanical theory that describes the adsorption of nanoparticles (NPs) at liquid-vapor surfaces. This theory accounts for the surface to bulk NP thermodynamic equilibrium, as well as the NP mechanical equilibrium, wettability, and line tension at liquid-vapor surfaces. The theory is tested by examining the adsorption of 5 nm diameter dodecanethiol-ligated gold NPs at the liquid-vapor surface of a homologous series of n-alkane solvents, from n-nonane to n-octadecane, where the NP wettability decreases with an increasing n-alkane chain length.

Reliable measurements of interfacial slip by colloid probe atomic force microscopy. I. Mathematical modeling

We developed a stable spread-sheet algorithm for the calculation of the hydrodynamic forces measured by colloid probe atomic force microscopy to be used in investigations of interfacial slip. The algorithm quantifies the effect on the slip hydrodynamic force for factors commonly encountered in experimental measurements such as nanoparticle contamination, nonconstant drag force due to cantilever bending that varies with different cantilevers, flattening of the microsphere, and calibration at large separations. We found that all of these experimental factors significantly affect the fitted slip length, approximately in the order listed. Our modeling is applied to fit new experimental data reproducibly. Using this new algorithm, it is shown that the fitting of hydrodynamic theories to experimental data is reliable and the fitted slip length is accurate. A "blind test" protocol was developed that produces a reliable estimate of the fitting error in the determination of both the slip length and spring constant. By this blind test, we estimate that our modeling determines the fitted slip length with an average systematic error of 2 nm and the fitted spring constant with a 3% error. Our exact calculation of the drag force may explain previous reports that the fitted slip length depends upon the shape and spring constant of the cantilever used to perform the measurements.