1. Introduction
An Atomic Force Microscope (AFM) is a widely-used instrument to characterize the morphological, nanotribological, and nanomechanical properties of various surfaces [
1]. Applications of AFM in the nanoscale surface characterization of plant cells are expanding [
2]. Plant cells are naturally coated with an ultrathin extracellular membrane (less than hundreds of nanometers thick), collectively referred to as the cuticle layer. The main functions of the cuticle layer are to preserve the physiological integrity of the cell and strengthen its overall structural stability [
3,
4,
5]. The cuticle layer can be regarded as a multilayer, natural coating, primarily composed of biopolyester cutin, pectins, and lipid-derived compounds.
The surface nanomechanical properties of the cuticle layer are of significant biological and technological importance. For instance, in the field of plant cell morphogenesis, it has been shown that the nanomechanical properties of the cuticle layer influence the cell’s shape changes and the growth rate [
6,
7,
8]. In biomimicry, advances in the synthesis of artificial superhydrophobic surfaces—which mimic the hierarchical microstructure of plant leaves and petal surfaces—rely on an accurate characterization of the surface nanomechanical and nanotopographical features of plants’ cuticle layers [
9]. In the industrial-scale agriculture production, the nanoscale interfacial frictional properties of natural fibers restrain their mass flow and motion throughout different fiber processing stages [
10,
11].
Various AFM operation modes have been developed to investigate different physical and dimensional properties of thin films at the nanoscale. In conventional contact mode, the lateral deflection of a cantilever—pertaining to the plane of a sample surface—corresponds to the nanoscale friction between the tip and the surface. In the case of viscoelastic surfaces, the lateral deflection of a cantilever can be caused by (1) the shear friction between the tip and the surface (which may cause the plowing of the viscoelastic surface in front of the tip) and (2) the local tilt or slope of the surface. The nanoscale frictional properties of viscoelastic, compliant surfaces and their relations with the confined rheological properties have been investigated [
12]. For this class of materials, the nonperturbative surface friction is a factor of the internal molecular relaxations near the surface, manifesting themselves in terms of the viscoelastic energy dissipative characteristics of the surface.
In another AFM mode, known as the force–volume mode, multiple force–distance curves are obtained across a surface. A force–distance curve (FDC) is a plot of net forces acting on an AFM tip as a function of the z-position of the piezo when the tip is brought into contact with the surface, slightly indents it, and withdraws from it [
13,
14]. By extracting nanomechanical properties such as the adhesion, the modulus, and the surface deformation from multiple FDCs, it will be possible to generate an image of the mechanical property of interest across a surface area.
The force tapping mode is a modified version of force–volume mode. The main difference between two operation modes is that, in force tapping mode, the
z-piezo is driven by a sinusoidal wave, leading to the sinusoidal ramping (
Figure 1a), while in force–volume mode, the z-piezo follows a triangular motion, leading to the triangular ramping [
15]. In force tapping mode, during each period of probe modulation, a force–time plot is obtained by measuring the cantilever deflection as a function of time. A feedback loop system keeps the maximum applied force constant by adjusting the z-piezo extension (region C in
Figure 1a,b). (The upper plot in
Figure 1a shows one period of probe modulation in the force tapping mode.) In a real-time analysis, since the
z-piezo position as a function of time is known, a FDC is generated from the force–time curve by replacing the time variable with the z-position of the modulation (
Figure 1b).
The most prominent breakthrough of sinusoidal ramping is that the maximum indentation force can be applied and controlled more precisely, making it possible to study the nanomechanical properties of soft biomaterials [
16]. This is mainly because the tip velocity decreases in a nonlinear fashion and eventually reaches zero at the maximum extension of the
z-piezo. Therefore, more time will be given to the feedback loop system to adjust the
z-piezo extension and control the maximum applied force at a higher resolution. Nevertheless, quantifying certain nanomechanical properties of soft biological surfaces, such as the elastic modulus, can still be challenging. Due to their natural surface roughness (with respect to the radius of curvature of a tip apex) and viscoelasticity, an accurate mapping of the elastic modulus of biological surfaces requires an implementation of more elaborate contact mechanics models.
An individual cotton fiber is an extremely elongated epidermal cell on the cottonseed’s surface, inside a cotton boll. A completely mature cotton fiber cell is made up of five distinguishable layers. The layers, from the innermost to the outermost, are the cell lumen, the secondary cell wall, the winding layer, the primary cell wall, and the cuticle [
17]. The internal structure of a cotton fiber has been imaged with an AFM [
18,
19,
20]. These studies have collected AFM images of a cotton fiber’s cross-section and surface—often scanned in liquid with the tapping mode—to investigate the dimension and the orientation of cellulose microfibrils deposited within the fiber’s secondary cell wall. The fiber’s outermost layer, the cuticle, is a few tens of nanometers-thick and is mostly composed of lipids, fatty acids, alcohols, and pectins (generally, hydrophobic compounds, collectively termed as cotton wax) [
21,
22]. The self-assembly and the growth of wax crystals, extracted from plant cell surfaces, have been imaged with an AFM [
23]. These observations show that the morphology of wax crystals depends on the cell’s growth conditions, such as the temperature, the moisture content, the chemical composition of lipid compounds, and the structural template effects of the underlying substrate. The structure of individual macromolecules extracted from the cuticle layer of plant cells has been also studied with AFM nanotopography images. Round et al. used the AFM nanotopography images to investigate the branching, the molecular weight, and the molecular aggregation of individual pectin biopolymers extracted from the cuticle of a green tomato [
24].
In addition to its biological functionalities, the cotton fiber’s cuticle has significant technological importance. Throughout various industrial fiber-processing stages, the waxy compounds function as a natural lubricant and facilitate the smooth motion of the fiber flow by reducing the inter-fiber friction and the friction between fiber and machine parts [
11,
25,
26]. Studies have been conducted to investigate the nanoscale frictional and mechanical properties of the cuticular material of cotton fiber and other plant cells [
27,
28,
29]. Round et al. isolated cutin biofilm from the cuticle of a tomato fruit and investigated its rheology with an AFM as a function of moisture content [
28]. According to their results, the elastic modulus, obtained via the Hertz model, drastically decreased in a nonlinear fashion at the higher moisture content. Bhushan et al. examined the surface nanofriction of the plant leaves from four different species: lotus, colocasia, fagus, and magnolia [
30]. Their results show that the hydrophilic leaves (fagus and magnolia) exhibited higher friction coefficients compared to that of the hydrophobic surfaces (e.g., lotus and colocasia). They explained that, for the hydrophilic surfaces, the contact area is expected to be larger, mainly due to the higher probability of water meniscus formation between the tip and the leaf surface [
31].
Zhang et al. investigated the nanoscale frictional properties of cotton fibers [
32]. The nanoscale frictional properties of synthetic and natural fibers can be used to evaluate the yield and the performance of ultrathin surface coatings. The authors showed that the nanoscale friction coefficient increased after multiple washes in the absence of fabric conditioner. They concluded that excessive washing cycles damage fibers’ surface and increase their surface roughness, leading to higher friction forces between the spherical AFM probe and the fibers’ surface. They also showed that the nanoscale friction experiments on cotton fiber conform to Amontons’ phenomenological law of friction
, where,
Ff is the friction force,
L is the applied normal force, and
is the friction coefficient.
The main objective of this study was to quantify and compare the surface nanomechanical and nanoscale frictional properties of two different samples of cotton fiber which are known to have statistically distinct macroscale frictional properties. For this reason, the fiber samples were characterized with an AFM, both in contact and force tapping operation modes. Fundamental single-asperity nanoscale friction experiments on cotton fibers’ surface can be used to better understand the linkage between the nanoscale and macroscale frictional properties of fibers.
This study serves as a preliminary investigation into the surface characterization of cotton fibers with an AFM which opens new research avenues for further investigations on this field.
3. Results and Discussion
The AFM limits in producing height images of a cotton fiber’s surface at different length scales are presented in
Figure 2a. The absence of noise in the images shows that the described methodology successfully immobilized the fibers during scanning experiments. For more clarification, the main differences in the working principles of contact mode and force tapping mode (a.k.a., Bruker’s PeakForce QNM) are illustrated in
Figure 2b. In contact mode, the tip stays in contact with the surface throughout an entire raster scanning process, producing continuous scan lines. In the force tapping mode, however, each scan line is regenerated by connecting multiple points along the scanning direction of the probe. Each point in the three-dimensional space is the result of one tip–surface interaction during one sinusoidal modulation of the probe. The distance between the points determines the image resolution. The corresponding FDC at each interaction (
Figure 2c) can be recorded for further mechanical property analyses.
Figure 3a shows a scanning electron microscope image of two typical cotton fibers. Typical, false-color images of the nanomechanical properties of the fibers’ surface—produced in force tapping mode—are presented in
Figure 3b.
The 5 μm × 5 μm surface topography of the fibers’ surface obtained in force tapping mode are shown in
Figure 4 (four scans per each sample are presented). The scanned areas could have been acquired from different regions of the fibers’ surface. Since a mature cotton fiber is a convoluted structure with a bean-shape cross-section (
Figure 2a and
Figure 3a), the scanned areas can be concave, convex, or relatively flat. A sequence of furrows and ridges is evident on the fibers’ surface [
19].
Figure 5 shows the 2 μm × 2 μm surface topography images of the fibers’ surface obtained in contact mode (the corresponding friction images of the scanned areas, under different normal forces, are shown in
Figure 6 and
Figure 7). In addition to the furrows and ridges on the fibers’ surface, a series of irregular-shape, plaque-like surface aggregates is evident at this length scale [
19]. The granular surface aggregates are more abundant on sample B fibers (an average of 15 counts per scan area for sample B compared to an average of 1 count per scan area for sample A). While their exact nature is unknown, they can be due to the self-assembly and growth of wax crystals on the cuticle surface.
The friction images of the fibers obtained under 10 nN normal force (with respect to the 40-nm radius of curvature of the AFM tip apex) are shown in
Figure 6. Under this normal force, sample B shows higher nanoscale friction on average. The mean friction signal for sample B is 0.50 ± 0.01 V compared to the lower value of 0.33 ± 0.01 V for sample A.
Figure 7 shows the friction images of the fibers obtained under the higher normal force of 50 nN; as can be noted, the fibers’ surface from sample A exhibits significantly higher nanoscale friction compered to sample B.
The local variations in the nanoscale friction signal, which are more evident on sample B fibers, are due to topographical effects and can be explained by the ratchet mechanism [
37]. As the tip encounters an asperity with a given slope during raster scanning, it climbs against it and transmits a larger lateral deflection signal to the position-sensitive detector. However, the lateral deflection signal is in part due to the variations in the slope of the surface. The local variations are often referred to as the ratchet-mechanism component of friction. Even though the trace and retrace friction signals have been subtracted, the local variations are still evident in the produced images.
Figure 8 shows the histograms of the friction experiments under 50 nN normal force and their corresponding Gaussian fit. The distributions of the two samples are quite distinguishable. The average friction force is 1.48 ± 0.02 V for sample A, compared to the significantly lower value of 0.80 ± 0.02 V for sample B fiber.
The relationship between the nanoscale friction and normal force for tested fibers is depicted in
Figure 9. With an increase in normal force, the friction on sample B increases to a certain extent and then reaches a plateau. The sublinear relationship between the nanoscale friction and the normal force in a nonperturbative state is expected. In the absence of any surface wear, the friction is linearly proportional to the real contact area, which itself holds a sublinear relationship with the applied normal force [
38]. Therefore, a model of the form
(where,
b and
n are the hyperparameters and
is the inequality constraint) was fitted to the friction data using the method of least squares in MATLAB Optimization Toolbox™ (MathWorks, Natick, MA, USA).
The theoretical basis behind the fitted model is as follows. It is known that, according to the adhesion theory of friction,
where
is the effective shear strength of contacting bodies. Under nonperturbative friction, and if we assume that the contacting bodies deform in an elastic Hertzian regime, the real contact area can be obtained as
By substituting
into Equation (7), one can obtain
Equation (9) can then be generalized to the following form:
where
is a constant related to the shape, the mechanical properties, and the shear strength of the contact bodies.
By fitting Equation (10) to the friction data for sample B, and are obtained. The average of the coefficient of determination, , of the fitted models is 0.99, which is very close to the perfect r-squared value of 1. The extremely small average p-value (<0.0001) for the model hyperparameters indicates that both statistics are statistically significant at a 99% level of confidence (i.e., the model parameters are not equal to zero at a very high level of certainty).
The friction plot of sample A, however, does not reach a plateau within the range of applied normal force. Under the low normal forces, the friction increases in a nonlinear fashion but at a smaller rate compared to sample B (, , and values of 0.30, 0.45, and 1, respectively). With further increase in the normal force, the friction shifts to the higher values and exceeds the mean frictions for sample B. Under these normal forces (i.e., 30 nN and higher), the linear regression model is a perfect fit to the data with .
The shift, which can be interpreted as a transition phase in the friction profile of a surface, is due to the occurrence of surface damage and wear debris formation. It has been reported that, upon the occurrence of wear or surface debris, the friction force deviates from the nonlinearity regime and follows a simple linear regression model [
39]. With the development of plastic deformation during a sliding friction process, two situations are likely: either the wear debris remain between the contacting bodies and reduce the overall friction via rolling friction mechanism, or the displaced molecules pile up on the sides of the contacting bodies and cause higher friction by increasing the real contact area. Direct observation of either situation is not feasible with current commercial AFM technologies. To the authors’ knowledge, only Surface Apparatus can provide the real-time projection of nanoscale deformations between surfaces during friction experiments of thin films. In either situation,
, as presented in Equation (10), reaches unity, and Equation (7) takes the form of Amontons’ law of friction,
, stating that the friction force is linearly proportional to the normal force.
In AFM experiments, wear debris formed after friction experiments can be analyzed by rescanning the wider area of the previously tested region.
Figure 10a shows a typical molecular pile-up with the height of 140 nm on the sides of the previously scanned area from sample A. The pile-up formation, which is not evident on sample B surfaces (
Figure 10b), further confirms that the transition phase due to molecular displacement has occurred on sample A surfaces, evidently between 20 and 30 nN normal forces.
These results suggest that when the friction profile data conform to the Hertzian component of friction, those experiments might have been performed in a nonperturbative state, on the same material (i.e., lipid compounds on fiber’s surface as depicted in
Figure 10c). However, once the friction curve deviates from sublinearity, the remaining experiments might have been performed beyond elastic limits of the thin cuticle layer, probably on the layer underneath it (i.e., the primary cell wall as depicted in
Figure 10d). Based on these conclusions, we hypothesize that fibers from sample B with lower macroscale friction coefficients might have been coated with a thicker cuticle layer since we did not observe the transition phase in their friction profile, nor the trace of plastic deformation on their wear images.
Figure 11 shows the adhesion images of the fibers’ surface, obtained in PeakForce QNM
® mode. As can be noted, the average adhesion is significantly higher for sample B. The mean tip–surface adhesive force for the sample B fibers is 22.8 ± 12.0 nN compared to the lower value of 15.1 ± 7.0 nN for the sample A. The
p-value of zero indicates that the difference between the adhesion means is statistically significant at the 5% significance level.
The positive correlation between the adhesion (performed under the low normal force of 10 nN) and the friction under the same low normal force is in agreement with the adhesion theory of friction, which states that, during a nonperturbative single-asperity friction process, the friction force is adhesion-controlled ). In other words, the greater the single-asperity adhesion force, the larger the shear strength of the contacting asperities will be.
The magnitude of the adhesive force between an AFM tip and a surface depends chiefly on the likelihood of water meniscus formation (i.e., the capillary forces), the chemistry of surfaces, and the real contact area between contacting asperities. In the case of cotton fiber’s surface, the cuticle layer is essentially a hydrophobic compound. This makes the water meniscus formation hypothesis improbable. Therefore, we hypothesize that it is the chemistry of the cuticle layer (such as the hydrocarbon chain length of the lipids) which determines the overall attractive forces, the surface energies, and the mechanical properties of the fibers’ surface (i.e., its stiffness, Poisson ratio, and internal friction). It remains to be studied whether there is any direct correlation between the adhesion force and the thickness of the cuticle layer.
In addition to the average adhesive force for each scanned area, the local variation in the adhesive force can be noted from the adhesion images (
Figure 11a). The local variations tend to resemble the pattern of furrows and ridges on the fibers’ surface, mainly due to the folds on the primary cell wall (
Figure 3b). In general, if other factors are held constant, the adhesive force is larger for concave curvatures. This is because of their larger real contact area, which increases the probability of molecular adhesive bond formation (mostly in the form of van der Waals forces) between the tip and the surface.
Figure 12 shows the maps of the surface deformation of the fiber samples, obtained in PeakForce QNM
® mode, and distributions of surface deformation for all other tested fibers. The mean maximum penetration depth of the tip is considerably higher for sample A fibers. The mean maximum deformation for the sample A fibers is 20.9 ± 4.7 nm, compared to the lower value of 3.2 ± 1.4 nm for the sample B fibers. It has to be noted that the nanoscale deformation can be broken down into multiple physical components. According to JKR theory, under the elastic regime, the indentation depth
d is related to
R,
a, the Young’s modulus of the surface
, and
W:
Among these variables,
R was constant throughout the experiments. However,
a,
W, and
could vary in each experiment. The contact radius
a depends on
R,
,
L, and
W. Since the applied normal force was kept constant, the variation in the surface deformation
d could only be explained in terms of
W and
; that is, the increase in adhesion energy and/or reduction in the local stiffness increase the surface deformation. Thus, the higher surface deformation of sample A fibers is attributed to the combination of both its surface adhesion and stiffness. Both of these surface attributes are related to the chemistry and composition of the cuticle layer as functions of temperature and moisture content.
Since the real contact area between a tip and a surface cannot be measured in an AFM experiment, the best approach to estimate the real contact area is to employ different contact mechanics theories such as the Hertz, the JKR, and the DMT. The input average adhesion energy for sample A and B fibers (as computed from Equation (2)) were 0.08 and 0.12 N/m, respectively.
Figure 13 shows the estimated real contact area between a silicon nitride tip with a radius of curvature of 40 nm and a lipid surface as a function of the normal force and the adhesion energy. Each line in the plot shows the variation in the theoretical real contact area as a function of normal force for a given adhesion energy. The adhesion energy varies from 0 to 30 N/m. The variation in the real contact area between two samples was not noticeable at the selected length scale; therefore, a single line of
is emphasized to represents both samples.
For instance, under the normal force of 50 nN, based on the JKR theory, the estimated contact radius between a lipid layer and a silicon nitride tip with a radius of curvature of 40 nm is ~110 nm. Under the same conditions, the estimated contact radius based on the DMT theory is only ~6.5 nm. Among different contact theories, the JKR always overestimates the real contact area. This is because the JKR takes into account the short-range adhering force between the contacting surfaces once the contact is made, while the DMT only considers the long-range attractive forces before the contact is made. The Hertzian model underestimates the real contact area since it ignores attractive forces between the surfaces. It can be noted that all these models can be fitted to adhesion-controlled, nonperturbative, single-asperity friction data since their shape resembles friction curves very closely. In this study, we fitted the Hertz model to the fibers’ surface friction data mainly due to its simplicity. Among these theories, it is reported that the JKR model provided the most accurate estimate for the real contact area of biological and soft surfaces [
40].