The value at a point (x,y,z) in thevolume is the deflection (force) on thecantilever at that position in space.
In this application note we discuss
the use of contact mode force curves(i.e., DC measurements of deflection).
However, volumes can also be
produced from any available imaging
mode such as TappingMode or phaseimaging. Force volumes can becollected in any environment in which
the microscope normally operates,including air and liquids.

Force volumes allow investigation of
the spatial distribution of almost any
force between tip and sample thatvaries with the distance between thetwo. Since force is the derivative ofenergy with respect to distance, thevolume data can be used to infer apotential energy map.
®

Digital Instruments NanoScope
software provides several methods toinvestigate the three-dimensional data
set generated by force volumeimaging. For example, simply clicking
on the pixel corresponding to the x-y
position of the curve(s) in the array(Figure 1) displays individual andmultiple force curves. Horizontal slices
through the volume of data can also
be displayed, showing the distributionof deflection values at particular zpiezo positions (Figure 2). The graphic
interface for force volume imaging isshown in Figure 3. After datacollection, the images and curves canbe processed with Digital Instruments
NanoScope off-line analysis software.

Z Position

When the tip comes into contact withthe surface during a force curve cycle,
the point of contact provides thetopography of the sample at that x-yposition. This can be used to produce
a low (lateral) resolution height imageof the surface, which is extremely
useful when attempting to uncouple theinteraction force data from topographic
information. Since the tip is not
dragged across the surface of thesample while obtaining the data,
lateral forces, which might otherwise
damage the sample, are very small.

Applications

Figure 2. Horizontal slices through a force
volume data set show the distribution ofdeflection values at each z position. In thefigure, darker regions correspond to larger
deflections. The top slice has a uniform
distribution of the lowest force because the tip
is not experiencing any force due to thesurface. The lowest slice has a uniform highforce because at each x-y position, the tip isin contact with the surface.

43A

B

21

CFigure 3. The force volume interface for Digital Instruments NanoScope software. The image is of aglass/platinum boundary. The large window on the left displays the height (or topography) image. Other
imaging modes (friction, phase, etc.) can be displayed here. The rectangular window in the lower rightdisplays the force curves as they are collected in real time. The small window in the upper right cornershows a slice through the volume of data. The force curves at particular x-y positions can be displayed bysimply clicking on either the height or force volume image. 2µm scan.

Currently most force volume imaging
is done with conventional AFM tips.
However, modifying tips to confer
specific chemical properties orattaching particles/molecules toact as specific probes allows a wide
range of nanoscale interactions to
be investigated.
Examples of the types of interactions
that can be examined follow.
Adhesion Maps
Adhesion between the tip and sample
can develop for numerous reasons.
Under ambient conditions the presenceof a capillary bridge between the tipand the fluid (“contamination”) layer onthe sample surface is the predominantorigin of adhesion. Adhesion maps
can be used to investigate thedistribution of hydrophilic andhydrophobic regions on a surface
which would differ in amount ofhydration (and, therefore, adhesion;
Figures 4 and 5). It is possible toperform the receptor-ligand typebinding experiments that have been
described in the literature in an attempt
to map the distribution of a receptor orligand in a cell membrane. A highly
sensitive, specialized model AFM,
the Digital Instruments MultiModePicoForce, has been developed by®

1.

Veeco Instruments for these experiments(see www.veeco.com for moreinformation).
Elasticity Maps
Force curves can also be used toinvestigate the elastic properties ofa material, by measuring the force
required to indent or deform thesurface. Force volumes can, therefore,
be used to produce micro-elasticity
maps of the sample that show local
variations in surface stiffness (Figure 6).
Different fabrication processes andtreatments of materials can result ininhomogeneities within the material,resulting in different values of theYoung’s modulus. Elasticity maps canidentify such defects. Similarly, elasticity
measurements of biological cells,
whose stiffness changes in response
to many factors, may identify
rearrangements of cytoskeletal elements
and other cellular components.
Electrostatic Maps
Electrostatic interactions between
two surfaces in liquids have been
described in great detail, and excellent
theoretical models exist. These models
predict the force experienced by acharged particle approaching acharged surface. AFM force curvesof a charged tip interacting with a2.

Figure 4. Horizontal slices taken from the force volume data set in Figure 3. Slices are 2µm square andare taken at the Z positions 1, 2, 3, 4 labeled in Figure 3. The distribution of adhesion forces is shown,i.e., slices from the retracting portion of the force curves. The labels (A,B,C) and numbering (1-4) are thesame as in Figure 3.

charged surface can be fit to suchmodels, providing information about
the electrostatic properties of asurface (Figure 7). Knowledge ofthe distribution of surface charge
density can, for example, offer
insight into the adsorption behavior
at heterogeneous liquid-solidinterferences, as well as help
characterize domains in membranes
and other biological structures.

Figure 5. Adhesion map of theplatinum/glass interface of Figure 3. Lighter
pixels represent greater adhesion. The map
was constructed by plotting the minimum
value of each retracting curve at its x-yposition. Note the variation of adhesion
across the interface.

3.

4.