![Colloidal Probe Geometries](https://upload.wikimedia.org/wikipedia/commons/b/b7/Colloidal_Probe_Geometries.png)
The colloidal probe technique is commonly used to measure interaction forces acting between
colloidal particles
A colloid is a mixture in which one substance consisting of microscopically dispersed Solubility, insoluble particles is suspension (chemistry), suspended throughout another substance. Some definitions specify that the particles must be disperse ...
and/or planar surfaces in air or in solution. This technique relies on the use of an
atomic force microscope
Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very-high-resolution type of scanning probe microscopy (SPM), with demonstrated resolution on the order of fractions of a nanometer, more than 1000 times better than the diffr ...
(AFM). However, instead of a
cantilever
A cantilever is a rigid structural element that extends horizontally and is supported at only one end. Typically it extends from a flat vertical surface such as a wall, to which it must be firmly attached. Like other structural elements, a canti ...
with a sharp AFM tip, one uses the ''colloidal probe''. The colloidal probe consists of a colloidal particle of few micrometers in diameter that is attached to an AFM cantilever. The colloidal probe technique can be used in the ''sphere-plane'' or ''sphere-sphere'' geometries (''see figure''). One typically achieves a force resolution between 1 and 100 pN and a distance resolution between 0.5 and 2
nm.
The colloidal probe technique has been developed in 1991 independently by Ducker and Butt. Since its development this tool has gained wide popularity in numerous research laboratories, and numerous reviews are available in the scientific literature.
Alternative techniques to measure force between surfaces involve the
surface forces apparatus,
total internal reflection microscopy
Total internal reflection microscopy is a specialized optical imaging technique for object tracking and detection utilizing the light scattered from an evanescent field in the vicinity of a dielectric interface. Its advantages are a high signal-t ...
, and
optical tweezers
Optical tweezers (originally called single-beam gradient force trap) are scientific instruments that use a highly focused laser beam to hold and move microscopic and sub-microscopic objects like atoms, nanoparticles and droplets, in a manner simila ...
techniques to with video microscopy.
Purpose
The possibility to measure forces involving particles and surfaces directly is essential since such forces are relevant in a variety of processes involving colloidal and polymeric systems. Examples include
particle aggregation Particle agglomeration refers to formation of assemblages in a suspension and represents a mechanism leading to the functional destabilization of colloidal systems. During this process, particles dispersed in the liquid phase stick to each other, a ...
, suspension rheology,
particle deposition
Particle deposition is the spontaneous attachment of particles to surfaces. The particles in question are normally colloidal particles, while the surfaces involved may be planar, curved, or may represent particles much larger in size than the depos ...
, and adhesion processes. One can equally study similar biological phenomena, such as deposition of
bacteria
Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among ...
or the infection of
cells
Cell most often refers to:
* Cell (biology), the functional basic unit of life
Cell may also refer to:
Locations
* Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
by
virus
A virus is a submicroscopic infectious agent that replicates only inside the living cells of an organism. Viruses infect all life forms, from animals and plants to microorganisms, including bacteria and archaea.
Since Dmitri Ivanovsky's 1 ...
es. Forces are equally most informative to investigate the mechanical properties of
interfaces
Interface or interfacing may refer to:
Academic journals
* Interface (journal), ''Interface'' (journal), by the Electrochemical Society
* ''Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Lin ...
,
bubbles, capsules,
membrane
A membrane is a selective barrier; it allows some things to pass through but stops others. Such things may be molecules, ions, or other small particles. Membranes can be generally classified into synthetic membranes and biological membranes. B ...
s, or
cell wall
A cell wall is a structural layer surrounding some types of cells, just outside the cell membrane. It can be tough, flexible, and sometimes rigid. It provides the cell with both structural support and protection, and also acts as a filtering mech ...
s. Such measurements permit to make conclusions about the elastic or plastic deformation or eventual rupture in such systems.
The colloidal probe technique provides a versatile tool to measure such forces between a colloidal particle and a planar substrate or between two colloidal particles (see figure above). The particles used in such experiments have typically a diameter between 1–10 μm. Typical applications involve measurements of electrical
double layer forces Double layer forces occur between charged objects across liquids, typically water. This force acts over distances that are comparable to the Debye length, which is on the order of one to a few tenths of Nanometre, nanometers. The strength of these ...
and the corresponding surface potentials or
surface charge
Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge di ...
,
van der Waals force
In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic or covalent bonds, these attractions do not result from a chemical electronic bond; they are comparatively weak and th ...
s, or forces induced by adsorbed polymers.
[I. ; .]
Principle
The colloidal probe technique uses a standard
AFM for the force measurements. But instead the AFM cantilever with an attached sharp tip one uses the ''colloidal probe''. This colloidal probe is normally obtained by attaching a colloidal particle to a cantilever. By recording the deflection of the cantilever as a function of the vertical displacement of the AFM scanner one can extract the force acting between the probe and the surface as a function of the surface separation. This type of AFM operation is referred to as the ''force mode''. With this probe, one can study interactions between various surfaces and probe particles in the ''sphere-plane geometry''. It is also possible to study forces between colloidal particles by attaching another particle to the substrate and perform the measurement in the ''sphere-sphere geometry'', see figure above.
![Colloidal Probe Force Measurement](https://upload.wikimedia.org/wikipedia/commons/a/a0/Colloidal_Probe_Force_Measurement.png)
The force mode used in the colloidal probe technique is illustrated in the figure on the left. The scanner is fabricated from
piezoelectric crystals, which enable its positioning with a precision better than 0.1 nm. The scanner is lifted towards the probe and thereby one records the scanner displacement ''D''. At the same time, the deflection of the cantilever ''ξ'' is monitored as well, typically with a comparable precision. One measures the deflection by focusing a light beam originating from a non-coherent laser diode to the back of the cantilever and detecting the reflected beam with a split
photodiode
A photodiode is a light-sensitive semiconductor diode. It produces current when it absorbs photons.
The package of a photodiode allows light (or infrared or ultraviolet radiation, or X-rays) to reach the sensitive part of the device. The packag ...
. The lever signal ''S'' represents the difference in the photocurrents originating from the two halves of the diode. The lever signal is therefore proportional to the deflection ''ξ''.
During an approach-retraction cycle, one records the lever signal ''S'' as a function of the vertical displacement ''D'' of the scanner. Suppose for the moment that the probe and the substrate are hard and non-deformable objects and that no forces are acting between them when they are not in contact. In such a situation, one refers to a ''hard-core repulsion''. The cantilever will thus not deform as long not being in contact with the substrate. When the cantilever touches the substrate, its deflection will be the same as the displacement of the substrate. This response is referred to as the ''constant compliance'' or contact region. The lever signal ''S'' as a function of the scanner displacement ''D'' is shown in the figure below. This graph consists of two straight lines resembling a hockey-stick. When the surfaces are not in contact, the lever signal will be denoted as ''S''
0. This value corresponds to the non-deformed lever. In the constant compliance region, the lever signal is simply a linear function of the displacement, and can be represented as a straight line
: ''S'' = ''a'' ''D'' + ''b''
The parameters ''a'' and ''b'' can be obtained from a least-squares fit of the constant compliance region. The inverse slope ''a''
−1 is also referred to as the optical lever sensitivity. By inverting this relation for the lever signal ''S''
0, which corresponds to the non-deformed lever, one can accurately obtain the contact point from ''D''
0 = (''S''
0 − ''b'')/''a''. Depending on the substrate, the precision in determining this contact point is between 0.5–2 nm. In the constant compliance region, the lever deformation is given by
: ''ξ'' = (''S'' − ''S''
0)/''a''
In this fashion, one can detect deflections of the cantilever with typical resolution of better than 0.1 nm.
![Colloidal Probe Response Forces](https://upload.wikimedia.org/wikipedia/commons/e/e1/Colloidal_Probe_Response_Forces.png)
Let us now consider the relevant situation where the probe and the substrate interact. Let us denote by ''F''(''h'') the force between the probe and the substrate. This force depends on the surface separation ''h''.
In equilibrium, this force is compensated by the restoring force of the spring, which is given by the
Hooke's law
In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that ...
: ''F'' = ''k'' ''ξ''
where ''k'' is the spring constant of the cantilever. Typical spring constants of AFM cantilevers are in the range of 0.1−10 N/m. Since the deflection is monitored with a precision better 0.1 nm, one typically obtains a force resolution of 1−100 pN. The separation distance can be obtained from the displacement of the scanner and the cantilever deflection
: ''h'' = ''ξ'' + ''D'' − ''D''
0
Figure below illustrates how the cantilever responds to different force profiles. In the case of a soft repulsive force, the cantilever is repelled from the surface and only slowly approaches the constant compliance region. In such situations, it might be actually difficult to identify this region correctly. When the force is attractive, the cantilever is attracted to the surface and may become unstable. From stability considerations one finds that the cantilever will be unstable provided
: ''dF''/''dh'' > ''k''
This
instability
In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be mar ...
is illustrated in the right panel of the figure on the right. As the cantilever approaches, the slope of the force curve increases. When the slope becomes larger than the spring constant of the cantilever, the cantilever jumps into contact when the slope of the force curve exceeds the force constant of the cantilever. Upon retraction, the same phenomenon happens, but the point where the cantilever jumps out is reached at a smaller separation. Upon approach and retraction, the system will show a
hysteresis
Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of ...
. In such situations, a part of the force profile cannot be probed. However, this problem can be avoided by using a stiffer cantilever, albeit at the expense of an inferior force resolution.
Extensions
The colloidal probes are normally fabricated by gluing a colloidal particle to a tip-less cantilever with a
micromanipulator
A micromanipulator is a device which is used to physically interact with a sample under a microscope, where a level of precision of movement is necessary that cannot be achieved by the unaided human hand. It may typically consist of an input joysti ...
in air. The subsequent rewetting of the probe may lead to the formation of nanosized bubbles on the probe surface. This problem can be avoided by attaching the colloidal particles under wet conditions in AFM fluid cell to appropriately
functionalized cantilevers.
While the colloidal probe technique is mostly utilized in the sphere-plane geometry, it can be also used in the sphere-sphere geometry.
The latter geometry further requires a lateral centering of the two particles, which can be either achieved with an optical microscope or an AFM scan. The results obtained in these two different geometries can be related with the
Derjaguin approximation
The Derjaguin approximation (or sometimes also referred to as the proximity approximation), named after the Russian scientist Boris Derjaguin, expresses the force profile acting between finite size bodies in terms of the force profile between two ...
.
The force measurements rely on an accurate value of the spring constant of the cantilever. This spring constant can be measured by different techniques.
The ''thermal noise'' method is the simplest to use, as it is implemented on most AFMs. This approach relies on the determination of the mean square amplitude of the cantilever displacement due to spontaneous
thermal fluctuations
In statistical mechanics, thermal fluctuations are random deviations of a system from its average state, that occur in a system at equilibrium.In statistical mechanics they are often simply referred to as fluctuations. All thermal fluctuations b ...
. This quantity is related to the spring constant by means of the
equipartition theorem
In classical statistical mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of equipartition, equipartition of energy, or simply equipartition. T ...
. In the ''added mass method'' one attaches a series of metal beads to the cantilever and each case one determines the resonance frequency. By exploiting the relation for a
harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its Mechanical equilibrium, equilibrium position, experiences a restoring force ''F'' Proportionality (mathematics), proportional to the displacement ''x'':
\v ...
between the resonance frequency and the mass added one can evaluate the spring constant as well. The ''frictional force method'' relies on measurement of the approach and retract curves of the cantilever through a viscous fluid. Since the hydrodynamic
drag of a sphere close to a planar substrate is known theoretically, the spring constant of the cantilever can be deduced. The ''geometrical method'' exploits relations between the geometry of the cantilever and its elastic properties.
The separation is normally measured from the onset of the constant compliance region. While the relative surface separation can be determined with a resolution of 0.1 nm or better, the absolute surface separation is obtained from the onset of the constant compliance region. While this onset can be determined for solid samples with a precision between 0.5–2 nm, the location of this onset can be problematic for soft repulsive interactions and for deformable surfaces. For this reason, techniques have been developed to measure the surface separation independently (e.g.,
total internal reflection microscopy
Total internal reflection microscopy is a specialized optical imaging technique for object tracking and detection utilizing the light scattered from an evanescent field in the vicinity of a dielectric interface. Its advantages are a high signal-t ...
,
reflection interference contrast microscopy).
By scanning the sample with the colloidal probe laterally permits to exploit
friction
Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
*Dry friction is a force that opposes the relative lateral motion of t ...
forces between the probe and the substrate.
Since this technique exploits the
torsion
Torsion may refer to:
Science
* Torsion (mechanics), the twisting of an object due to an applied torque
* Torsion of spacetime, the field used in Einstein–Cartan theory and
** Alternatives to general relativity
* Torsion angle, in chemistry
Bi ...
of the cantilever, to obtain quantitative data the torsional spring constant of the cantilever must be determined.
A related technique involving similar type of force measurements with the AFM is the
single molecular force spectroscopy. However, this technique uses a regular AFM tip to which a single polymer molecule is attached. From the retraction part of the force curve, one can obtain information about stretching of the polymer or its peeling from the surface.
See also
*
Surface forces
Surface force denoted ''fs'' is the force that acts across an internal or external surface element in a material body. Surface force can be decomposed into two perpendicular components: normal forces and shear forces. A normal force acts norm ...
References
{{Reflist
Chemistry
Materials science
Colloidal chemistry