Nanomechanical mapping

Using Equation 17.9, one can obtain the work of adhesion from the pull-off force 

Applying the appropriate contact mechanics toP-S relation, one can obtain the mechanical properties of elastic surface. The adhesion map indicates that even very stiff polymeric materials lie far away from the DMT zone, while most other types of polymeric materials, from rubber and gel to materials of intermediate stiffness, reside in the JKR zone. One of the reasons why sometimes the DMT model is still used regardless of this fact may be due to mathematical handiness, as expressed in Equation 2.4. The AFM cannot directly observe the contact area a hence, the form of the JKR model, which does not have an explicit solution for P(S), is evaded. 

To obtain the elasticity, this method requires the values at two points one is point D, where the force is equilibrated, and the other is point E, the point at the pull-off force. The JKR model gives 

As this formula uses the difference of indentation depth 8, one can obtain the reduced modulus E without ambiguous determination of Z.  

A single force-distance curve measurement gives the mechanical information at the contact area, typically of 

---

Huey, B. D. (2007). AFM and acoustics fast, quantitative nanomechanical mapping. 

Garcia R, Proksch R. Nanomechanical mapping of soft matter by bimodal force microscopy. Eur Polym J 2013 49(8) 1897-906. 

APPLICATION EXAMPLES OF NANOMECHANICAL MAPPING 3.3.1 Carbon Black-Reinforced Natural Rubber... 

Nanomechanical mapping has been applied to several material systems to date, as introduced in Section 3.3. However, in these applications we adopted Hertzian theory and argued only elastic modulus, and therefore the analyses were subject to many restrictions. More seriously, practical measurements must be performed under appropriate conditions to avoid other complex interactions, such as adhesion and viscoelasticity, and to obtain precise and correct results. Measurement in an aqueous environment to avoid adhesion effects is a possible example, where we can suppress the water capillary effect, which is unavoidable, and the major contribution to the adhesion force under ambient conditions. 

In this section we describe our recent progress in nanomechanical analysis to make it applicable to conditions where we cannot ignore the adhesive and viscoelastic effects, and where JKR contact plays an important role, as explained in Section 3.3. Then we discuss the realistic applicable limit of this theory based on several experimental results. Furthermore, the viscoelastic effect is treated experimentally and theoretically to some extent, with the future goal of making nanomechanical mapping a nanorheological mapping technique. 

Nishi, T., Nukaga, H., Fujinami, S., and Nakajima, K., Nanomechanical mapping of carbon black reinforced natural rubber by atomic force microscopy, Chinese J. Polym. Sci., 25,35 1 (2007). 

Based on the procedures described in the previous sections, one can obtain nanomechanical maps of a wide variety of polymeric and biological materials, including carbon black (CB)-reinforced natural rubber (NR) [40], carbon nanotube (CNT)-reinforced NR [41,42], reactive polymer blend [43], block copolymers [9,21,44,45], deformed plastics [46,47], human hair [48,49], honeycomb-patterned polymer films [50-52], CNT-reinforced hydrogel [53], and diffusion front of polymer [54,55]. The detailed descriptions are also found in other literatures [56-59]. Hereafter, several example studies are reviewed. 

Thermoplastic elastomers (TPEs), which combine the elastic response like rubber vulcanizates with the processability of thermoplastics, are becoming one of the industrially important polymeric materials [60-62]. The morphology control by processing conditions is a key issue to improve mechanical properties of TPEs. Therefore, the effects of processing conditions on morphology and microscopic mechanical properties ofpoly(styrene-fe-ethylene-co-butylene-fc-styrene) (SEES) triblock copolymer, one of the most widely used TPEs, is investigated by nanomechanical mapping [45]. 

Figure 17.5 Nanomechanical mapping results in FV-mode on SEES samples, (a) Original topographic, (b) sample deformation, (c) true topographic, and (d) JKR modulus (log-scale) images on cast sample, (e) Original topographic and (f) JKR modulus (log-scale) images on melt-compounded sample. The scan size of each image is 1.0 pm.

The results obtained here with AFM nanomechanical mapping indicate that this technique is very valuable in evaluating the mechanical properties of polymer materials at a micro or nanoscale and in visualizing the distribution of mechanical properties, which are not available by any other conventional characterizing methods. 

Wang D, Fujinami S, Nakajima K, Nishi T. True surface topography and nanomechanical mapping measurements on block copolymers with atomic force microscopy. Macromolecules 2010 43 3169-3172. 

---