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Abstract

Besides polyamide 11 (PA 11) outstanding properties, wear performance is considered a key factor for its continued widespread use. TiTanate NanoTubes (TTNT) have a huge potential as reinforcement in polymer matrix nanocomposites, and although nanotubes reinforcement capacity is well understood, its effect on tribological characteristics is still an open question. Thus, the present work has as objective to study the wear behavior of PA 11 and its nanocomposites, highlighting TTNT loading, functionalization and sodium content effects. Seeking the possibility to tailor properties, surface topography is investigated. Based on parameter classification, correlation and functional sense, an ideal roughness parameter set is defined. By taking measurements in X- and Y-axis, parameter variations and sensibility are also analyzed. From the results, maximum wear resistance can be reached in functionalized samples with low TTNT loading and high sodium content. Some roughness parameters demonstrate a moderate to strong correlation with wear performance. Parameter variations are mainly attributed to the non-stationarity of the surface.

Keywords

Polyamides nanocomposites polymer functionalization surface analysis roughness parameters mechanical properties

Introduction

Engineering polymers are being increasingly used in a wide variety of fields,^1,2 and several polymers can be considered as competitive materials for tribological applications.^3–5 To be suitable, polymeric materials, which usually exhibit mechanical strength, lightness, ease of processing and low cost, together with acceptable thermal and environmental resistances, have to show good abrasion and wear resistance.⁶ Among potential tribo-engineering polymers, polyamides (PA) can be highlighted.^7,8 Besides PA’s usual characteristics, such as high toughness, considerable tensile strength, low density, and good chemical resistance, wear performance is considered a key factor for its widespread applications.^6,9

Due to the feasibility of maximizing mechanical properties while preserving the inherent properties of polymers, nanoscale fillers have been extensively incorporated into polymers to produce polymer nanocomposites.^3,6,9–11 As for other thermoplastic matrices, several nanomaterials are suitable fillers for PA, improving their mechanical properties, including wear resistance.^11–16 The properties of the resulting nanocomposite depend on the intrinsic characteristics, dimensions, and shape of the inorganic fillers, including the interfacial bonding strength.^10,13,14 In recent years, special attention has been given to one-dimensional nanostructures as an outcome of its distinguished aspect ratio, which implies a high specific surface area, thus optimizing final properties.^17,18

The unique physicochemical properties of the titania nanostructure combined with its singular morphology make TiTania or TiTanate NanoTubes (TTNT) a promising useful material.^12,19 TTNT morphology and its residual sodium content are dependent on the synthesis conditions and washing step.^20–22 Therefore, different properties can be reached in the final product. To maximize the reinforcement effect, TTNT surface modification has been suggested.^21,23–25 The use of surfactants and coupling agents is appreciated, and silanes are recognized as efficient coupling agents that have found unrestricted use in nanocomposites.²⁶

Although the improvement of properties in polymers by incorporation of nanofillers has been studied, the mechanisms by which nanomaterials modify the tribological behavior in polymer nanocomposites are still not fully understood.^3,6,9,15 Tribological performance is intimately linked with surface texture, and understanding the characteristics of the surface, such as topography, is important in several applications such as wear, friction, and lubrication.^13,27 In fact, surface topography can have a significant impact on component longevity and reliability.²⁸ Alterations of surface topography, even if restricted to a small surface layer, may influence the properties of the component such as fatigue strength, resistance to corrosion and service life.^27,28

Surface topography can be described in terms of roughness parameters,²⁹ which can be considered a powerful tool for control, diagnostics, and prediction.^27,28 Despite many surface roughness parameters can be used to describe a surface, the effectiveness of several of them is always in discussion. On the one hand, a large number of parameters available could be seen as positive, leading to an increase in the power to describe texture completely. On the other hand, the myriad number of parameters can be misleading and related to systematic unsuccessful surface characterization attempts.^27,28,30 Therefore, there is a clear need for reducing the number of parameters or at least provide clear guidelines in parameter elaboration and selection.³¹

Although many investigations have been conducted to clarify surface features in different applications,^29,32,33 a lack of solid information still exists in the nanocomposite field. Then, the present work has the objective to study the tribological behavior of PA 11 and its nanocomposites. The effect of TTNT addition on the wear performance of PA 11 nanocomposite is analyzed and contributions of TTNT loading, functionalization and sodium content are highlighted. Surface roughness is discussed, and a set of roughness parameters is defined to characterize surface topography. Targeting the possibility of tailoring tribological properties, the correlation between wear behavior, surface roughness and TTNT addition are also investigated.

Experimental procedure

Nanocomposite processing

The TTNTs used in this work were obtained by hydrothermal alkaline synthesis, as described elsewhere.²⁰ TTNTs with high (TTNT/H) and low (TTNT/L) sodium contents were synthesized with, respectively, 8.45 wt% and 0.24 wt% of sodium content as measured by flame photometry, and specific surface areas of 224 and 283 m²/g, as measured by BET nitrogen adsorption at −196°C.²¹ Independent of the acidic washing step, X-Ray Powder Diffraction (XRPD) has confirmed the complete conversion of the starting anatase powder into layered titanates and Transmission Electron Microscopy (TEM) images have revealed the uniform nanotubular morphology of the as-synthesized TTNTs.²¹ A fraction of the TTNTs were functionalized (FTTNT/H and FTTNT/L) with 3-aminopropyltriethoxysilane (APTES), with over 98% of purity, following the functionalization procedures described in other works.^21,34 Considering the specific surface areas of high and low sodium TTNTs, APTES to TTNT mass ratios of 0.635 and 0.802 were used for TTNT/H and TTNT/L, respectively. The successful grafting of APTES on functionalized sample surfaces was confirmed by CNH elemental analysis, Fourier-transform infrared (FTIR) spectroscopy and thermogravimetric analysis (TGA). The grafting of APTES over TTNT surface occurs through Ti-O-Si primary chemical bonding.²¹

PA 11 produced from a renewable source (castor oil) and designed for extrusion (Rilsan® PA G BESNO TL, supplied by Ackerman) was used as matrix. Samples of neat PA 11 and nanocomposites reinforced with functionalized and non-functionalized TTNTs were manufactured using a twin-screw micro extruder (DSM Xplore, model 5-08-20) and a microinjector (DSM Xplore, model 4-11-10). Nanocomposites with TTNTs loading of 0.5 wt%, 1.0 wt%, and 2.0 wt% were produced.

Before processing, PA 11 was dried at 80°C for 8 h in an air circulation oven. The processing conditions used at the micro extruder were: temperatures of 275°C, 260°C, and 260°C at the heating zones; screw rotation speed of 100 rpm; and residence time of 4–6 min per batch. The microinjector processing conditions were: a mold temperature of 60°C and an injection pressure of 7 bar. Table 1 summarizes all nanocomposite combinations produced.

Table 1.

Summary of nanocomposite combinations produced.

Samples	TTNT content (wt%)	Sodium content	Functionalization
Neat PA 11	—	—	—
TTNT/L-1.0%	1.0	Low	No
TTNT/H-0.5%	0.5	High	No
TTNT/H-1.0%	1.0	High	No
TTNT/H-2.0%	2.0	High	No
FTTNT/L-0.5%	0.5	Low	Yes
FTTNT/L-1.0%	1.0	Low	Yes
FTTNT/L-2.0%	2.0	Low	Yes
FTTNT/H-0.5%	0.5	High	Yes
FTTNT/H-1.0%	1.0	High	Yes
FTTNT/H-2.0%	2.0	High	Yes

In order to detect possible interactions between TTNT and polyamide matrix, FTIR spectroscopy was performed.³⁵ Comparing the spectra of neat PA 11 and nanocomposites, only for the composites that contain functionalized TTNT two new bands were detected at 1742 and 1712 cm⁻¹. They could be associated to a free- and H-bonded C=O stretching vibrations that reflect bonding of terminal carboxyl group of PA to a silane amido group. More information about morphological and structural characteristics of PA 11 and its nanocomposites can be found elsewhere.^22,35

Wear test

The wear test was carried out following the recommendations of DIN 53516.³⁶ The equipment used in the test consisted of a rotating cylinder covered with a grinding paper (#180) and a sample holder, which rotates on its own axis. The combined movement action of spin and forward motion produces an average sliding path (L) of 40 m. The axial load (F_N) exerted on the sample holder, which ensured permanent contact of the sample with the rotating cylinder, was kept constant and equal to 9.81 N. Test specimens with a mean size of 20.0 mm length, 9.0 mm wide and 3.1 mm thickness were used.

Wear performance is commonly evaluated from loss of mass ( $Δ m$ ) results.³⁷ Thus, the samples were weighted within ± 0.0001 g before (m_o) and after (m_f) the wear test, making it possible to calculate the loss of mass, $Δ m = (m_{f} - m_{o})$ . Prior to weighting and after the wear test, the sample surfaces were lightly brushed in order to remove any residue left from sandpaper contact. In addition, specific wear rate (w_s) was also calculated, considering the applied normal load (F_N) and the sliding distance (L) (equation 1):

w_{s} = Δ m / (F_{N} . L)

Surface roughness measurement

Surface roughness was measured using a rugosimeter (Taylor Hobson). Surface roughness measurements had the objective to quantify the surface of specimens that were submitted previously to wear test. The probe was positioned in the same place for all samples ensuring that equipment always traveled the same distance for the X-axis—7.3 mm—and the Y-axis—2.8 mm, yielding two surface roughness measured per sample. For data analysis, the cut-off standard value of 0.8 mm was set.^27,37 Several roughness parameters available in Taylor Hobson rugosimeter were determined. Parameters symbols and definitions are present in Table 2.

Table 2.

Symbols and definitions of roughness parameters used.

Symbols	Definition
$R_{p m}$	Mean height of peaks
$R_{v m}$	Mean depth of valleys
R_t	Total height of the profile
R_z	Average peak to valley height
R_c	Mean height of profile elements
R_a	Arithmetic average roughness
R_q	Root mean square roughness
$R_{s k}$	Skewness
$R_{k u}$	Kurtosis
$R S$	Mean spacing of adjacent local peaks
$R S_{m}$	Mean spacing of profile elements
$R H S C$	High Spot Count
$R P_{c}$	Peak Count
$R l_{n}$	Evaluation length
$R Δ_{a}$	Average slope of the profile
$R Δ_{q}$	Root mean square slope of the profile
$R l_{o}$	Developed length of the profile

Results and discussion

Wear performance

The main results gathered from wear tests are summarized in Table 3 and are graphically presented in Figure 1. Although it was possible to precisely control the axial force during experiments, keeping it constant, it was impractical to guarantee a constant course distance, and small variations occurred. It is known that the relation between slipping distance and wear volume is tight.^37,38 Even with small deviations around the mean (± 3.0 m), slipping distance variation cannot be stated as insignificant. Looking at Figure 1 it becomes evident that even though the results of loss of mass and specific wear rate seem practically similar, the consideration of the slipping distance in specific wear rate prediction (Eq. 1) leads to major changes in the wear behavior Therefore, it is inaccurate not to consider the slipping distance in the wear study, making the use of specific wear rate preferable.

Table 3.

Wear tests results.

Samples	%Mass loss ( $Δ m$ )	Specific wear rate (w_s) (kg/mN)
Neat PA 11	27.0%	3.58E−07
TTNT/L-1.0%	22.0%	3.49E−07
TTNT/H-0.5%	21.5%	3.15E−07
TTNT/H-1.0%	19.7%	3.37E−07
TTNT/H-2.0%	27.5%	3.88E−07
FTTNT/L-0.5%	18.1%	2.61E−07
FTTNT/L-1.0%	28.4%	4.00E−07
FTTNT/L-2.0%	26.9%	3.89E−07
FTTNT/H-0.5%	10.9%	1.79E−07
FTTNT/H-1.0%	25.9%	3.60E−07
FTTNT/H-2.0%	19.6%	3.11E−07

Figure 1.

(a) Mass loss ( $Δ m$ ) and (b) specific wear rate (w_s) behavior of PA 11 and its nanocomposites.

Looking at the specific wear rate results (Table 3 and Figure 1(b)), the effects of the studied factors can be split into three major groups. Depending on functionalization and sodium content, TTNT addition promoted (i) an increase, (ii) a decrease, or even (iii) no significant change in wear resistance. It is important to note that the specific wear rate has an opposite nature compared to wear resistance.^38,39 Therefore, TTNT/H-2.0%, FTTNT/L-1.0% and FTTNT/L-2.0% composites that showed an increase in specific wear rate, demonstrated, accordingly to tribological properties, a decrease in wear resistance compared to neat polymer. In the same way, TTNT/H-0.5%, TTNT/H-1.0%, FTTNT/L-0.5%, FTTNT/H-0.5% and FTTNT/H-2.0% composites, which showed a decrease in specific wear rate, exhibited, consequently, an increase in wear resistance. Furthermore, the composites TTNT/L-1.0% and FTTNT/H-1.0% present almost the same behavior compared to neat PA 11. Among modified composites, it is meant to highlight FTTNT/L-0.5%, and FTTNT/H-0.5%, which showed a specific wear rate decrease over 27.0% and 50.0%, respectively, compared to neat polymer.

The different wear behavior obtained with the incorporation of TTNTs in the polymer matrix reflects the complexity of filler contribution in the tribological performance. Although the extent of the reinforcing effect depends greatly on the properties of the individual composite components, it can be expected that geometrical factors and the interaction of the components may play a significant role in tribological behavior.^6,38

According to classical concepts, an improvement in the friction and wear behavior of polymeric materials by the incorporation of filler is achieved by either mechanical or chemical reasons.¹³ The higher the wear rate is, the deeper the abrasive can penetrate the surface leading to additional material surface breakage and removal.³⁸ Thus, wear resistance can be maximized by enhancing material hardness, stiffness and toughness, or increasing material adhesion to the counterpart.^39,40 Moreover, especially in polymer composites, the addition of a harder, rigidity and inorganic phase, such as TTNT, should improve wear performance by enhancing polymer modulus and hardness, helping on the formation of a tenacious transfer film.^11,25,38,40

However, due to TTNT high specific surface area - an intrinsic result of its small size and high aspect ratio - particle agglomeration may occur, affecting the homogeneous dispersion of nanotubes, and hence resulting in severe abrasive wear. Also, as a result of its hydrophilic characteristic, the TTNT reinforcing effect may be inhibited by its poor adhesion to the polymer matrix, which may give rise to discontinuities and the initiation of cracks, increasing the specific wear rate.^6,14 Therefore, although wear resistance can be improved with the incorporation of TTNT, a further increase in TTNT content may be critical to the wear performance of the nanocomposite.^6,40

Taking a closer look at TTNT loading (Figure 2(a)), and although non-functionalized combinations showed a distinct trend in comparison to functionalized, it could be verified that lower specific wear rate was obtained for lower TTNT loading (0.5 wt%). If in one hand, the non-functionalized combinations presented a near monotonous increase in specific wear rate, i.e. wear resistance decay as TTNT loading increases, on the other hand, functionalized combinations showed a peak of wear in 1.0 wt% of TTNT with apparent drop up in 2.0 wt%. These results seem to indicate that due to its high specific surface area, even in a relatively low amount, 0.5 wt%, TTNT incorporation promoted an increase in wear resistance. However, a further increase of TTNT content led to a decrease in wear resistance, probably as a consequence of agglomeration and poor dispersion of the nanotubes. Indeed, SEM analysis conducted on previous studies^22,35 showed the presence of many agglomerates on fracture surfaces of PA 11 nanocomposites. Figure 3(a) shows an example of fracture surface of PA 11 nanocomposite containing 1.0 wt% of TTNT (Figure 3(a)). EDS analysis confirmed that agglomerates were Ti rich compounds (Figure 3(b)).

Figure 2.

Specific wear rate effect plots of PA 11 and its nanocomposites according to (a) TTNT loading, (b) functionalization and (c) sodium content.

Figure 3.

(a) SEM image of PA 11 nanocomposite containing 1.0 wt% of TTNT (TTNT/H-1.0%), showing the presence of agglomerates (→). (b) EDS analysis of an agglomerate.

In respect to functionalization, two different behaviors were verified (Figure 2(b)), demonstrating dependence with TTNT composition. For samples with 1.0 wt% of TTNT, the wear rate of non-functionalized (NF) combinations was lower than that of functionalized (F), showing a decrease in wear resistance with functionalization. Nonetheless, for 0.5 wt% and 2.0 wt% TTNT loadings, the effect of functionalization was the opposite, contributing to a decrease in specific wear rate and a consequent increase in wear resistance for functionalized nanocomposites. Physically, the increase of wear resistance due to functionalization may be explained by interfacial modifications. Functionalization through the use of a coupling agent can act at the interface creating a chemical bridge between reinforcement and matrix. It improves the interfacial adhesion when one end of the molecule is tethered to the reinforcement surface and the functionality at the other end reacts with the polymer phase.²³ Although filler/matrix interactions can be certainly maximized by the successful grafting of APTES on TTNT/H and TTNT/L surfaces, as demonstrated in previous works,^20,21 the reduction of TTNT dispersion problems cannot be guaranteed. The cause and effect relationship between functionalization, nanofiller content and dispersion are complex. Even though functionalization may decrease the average size of TTNT agglomerate, its influence on the final properties may be minimal or almost insignificant, as shown by composites with 1.0 wt% of TTNT.

Unlike TTNT loading and functionalization, a single behavior could be verified for sodium content in respect to wear properties (Figure 2(c)). Regardless of functionalization and TTNT loading, high sodium content (H) promotes a decrease in specific wear rate and consequent increase in wear resistance. Sodium content, in addition to being closely related to the amount of the interlayer water and of its influences on TTNT chemistry and thermal stability,^20,21 proved to be significant in respect to wear properties. Specific surface area modification, caused by sodium content variation after the washing step, may lead to alterations in adhesion and interface characteristics of TTNTs, which can influence directly the wear performance.^6,20 The lower the sodium in the composition is, the higher will be TTNT specific surface area.²⁰ A higher specific surface area may increase filler/matrix extension and thus enhance the reinforcing effect. On the other hand, it may promote agglomeration, inhibiting TTNT homogenously dispersion, and hence diminishing wear performance. Although it is complex to evaluate the specific surface area major contribution to wear performance, according to the increase of the specific wear rate when sodium content was decreased, it can be inferred that the capability of specific surface area to enhance the reinforcing effect of TTNT was surpassed by the negative effect induced by nanotube agglomeration.

Surface roughness analysis

Parameter set definition

Before starting a discussion about the results of the roughness parameters, a parameter set must be defined. This set must be robust enough to minimize parameters that show limited potential to adequately describe the surface and to avoid parameters that essentially describe the same surface features.⁴¹

Although roughness parameters are widely studied, there is a lack of information about their choice. Usually, parameters are selected according to their greater use, leaving aside their functional potential. De Chiffre et al.³¹ state that an ideal parameter set investigation has to follow an analytical approach. Firstly, roughness parameters have to be classified and parameter families specified. Secondly, independent of classification, correlation has to be analyzed, so equivalence and redundancy within each family can be revealed. At last, parameters must be chosen accordingly to their functional sense. An ideal parameter set must be restrictive, robust and fast. That is, a small number of parameters have to be capable of describing major surface features, parameter variation should be minimal over the same surface and between measuring method, and the parameters must be easy to implement.^42–44

Roughness parameters can be divided into three major groups: (i) amplitude or height sensitive parameters, (ii) wavelength or spacing sensitive parameters and (iii) hybrid parameters.⁴⁵ Amplitude parameters are directly related to the vertical characteristics of the surface deviations.²⁷ Due to the complexity of profile height, amplitude parameters are diverse. R_a and R_q give a general description of height variations; $R_{p m}$ , $R_{v m}$ , R_z, R_t and R_c characterize extreme features of the profile; and skewness ( $R_{s k}$ ) and kurtosis ( $R_{k u}$ ) provide more information about profile form.^28,46 It is difficult to describe the main surface features employing a single height parameter. Ordinarily, they complement each other and are used as a group. Amplitude family is commonly stated as the most important once height information seems to relate more promptly to functional importance.^27,43 Thus, the majority of roughness parameters belong to this class as well as the most used ones.

Unlike amplitude parameters, spacing parameters measure the horizontal characteristics of the surface deviations.^27,33 Although most surface features can be correlated with profile height, spatial properties also have to be described.³⁷ In this class, $R S$ and $R S_{m}$ , which describes peak spacing, $R l_{o}$ and $R l_{n}$ , which provide length information, and $R H S C$ and $R P_{c}$ , which give peaks count, can be highlighted.^28,46

When the use of amplitude and spacing parameters cannot describe successfully surface features, hybrid parameters adoption can be helpful. Hybrid parameters reflect amplitude and spacing information. Any changes, which occur in either profile height or spacing, may have an indirect effect on hybrid parameters.⁴³ Hybrid parameters generally characterize surface slope and curvature. $R Δ_{a}$ and $R Δ_{q}$ are classic examples of this class.^27,28

Besides roughness parameters, to complement surface characterization, parameter ratios can also be used. Among these relations, $R_{a} / R_{q}$ , $R_{p m} / R_{t}$ and $R S / R S_{m}$ can be highlighted. $R_{a} / R_{q}$ and $R_{p m} / R_{t}$ are amplitude parameter relations, which provide more information about profile form. Considering boundary theoretical cases, for a random profile $R_{a} / R_{q}$ can reach 0.80 and for a sinusoidal profile it can approach 0.90.²⁷ $R_{p m} / R_{t}$ gives general information about “emptiness” or “fullness” and can be related to skewness.²⁸ $R S / R S_{m}$ is a spacing parameter relation that reveals surface randomness. For a very random surface $R S / R S_{m}$ is low, yet for a determinist one it can approach unit.²⁷

Considering the previous parameter division and definitions, the roughness parameters measured were classified into families as shown in Figure 4. To check redundancy and equivalence between parameters within families, Pearson’s correlation coefficient ( $ρ$ ) was calculated using the experimental data from all tested nanocomposites (Table 4). Correlation increases as Pearson’s coefficient approach unit. Several parameters showed a strong correlation ( $|ρ| \geq 0.80$ ),⁴⁷ such as $R_{p m}$ , $R_{v m}$ and R_c with R_z ( $ρ \geq 0.91$ ), R_a with R_q ( $ρ = 0.97$ ), $R l_{n}$ with $R l_{o}$ ( $ρ = 0.91$ ), $R H S C$ with $R P_{c}$ ( $ρ = 0.85$ ), and $R Δ_{a}$ with $R Δ_{q}$ ( $ρ = 0.97$ ), demonstrating their potential to describe each other. It becomes evident that family proximity is directly related to correlation description. Parameters that describe similar profile features have a greater tendency to show the same behavior. Although most of the parameters showed a great correlation with their family neighbors, R_t, $R_{s k}$ , $R_{k u}$ , $R S$ and $R S_{m}$ did not follow this rule.

Figure 4.

Classification of surface roughness parameters. Highlighted parameters were selected to compose the parameter set.

Table 4.

Correlation between experimental surface roughness parameters. Green color illustrate a strong correlation ( $|ρ| \geq 0.8$ ), while yellow indicate a moderate correlation ( $0.5 \leq |ρ| < 0.8$ ) and red suggest a poor correlation ( $|ρ| < 0.5$ ) between parameters.⁴⁷

	Amplitude parameters									Hybrid parameters		Spacing parameters						Parameters ratios
	$R_{p m}$	$R_{v m}$	R_z	R_t	R_c	R_a	R_q	$R_{s k}$	$R_{k u}$	$R Δ_{a}$	$R Δ_{q}$	$R l_{o}$	$R l_{n}$	$R H S C$	$R P_{c}$	$R S$	$R S_{m}$	$R_{a} / R_{q}$	$R_{p m} / R_{t}$	$R S / R S_{m}$
$R_{p m}$	1.00	0.83	0.96	0.71	0.90	0.79	0.88	0.01	0.05	0.78	0.85	0.39	0.06	0.50	0.61	−0.02	−0.18	−0.09	0.13	0.26
$R_{v m}$	0.83	1.00	0.96	0.64	0.85	0.87	0.87	−0.37	−0.19	0.87	0.88	0.35	0.01	0.41	0.46	−0.40	−0.33	0.29	−0.44	0.09
R_z	0.96	0.96	1.00	0.70	0.91	0.87	0.91	−0.19	−0.08	0.86	0.90	0.39	0.03	0.48	0.56	−0.22	−0.26	0.11	−0.16	0.18
R_t	0.71	0.64	0.70	1.00	0.86	0.46	0.59	0.06	0.53	0.51	0.68	0.35	0.15	0.36	0.35	−0.07	0.26	−0.35	0.03	−0.21
R_c	0.90	0.85	0.91	0.86	1.00	0.77	0.87	−0.14	0.18	0.68	0.79	0.27	−0.02	0.34	0.42	−0.07	0.07	−0.13	−0.05	−0.02
R_a	0.79	0.87	0.87	0.46	0.77	1.00	0.97	−0.49	−0.43	0.82	0.81	0.19	−0.15	0.27	0.31	−0.24	−0.43	0.43	−0.31	0.33
R_q	0.88	0.87	0.91	0.59	0.87	0.97	1.00	−0.37	−0.24	0.78	0.81	0.19	−0.14	0.28	0.34	−0.10	−0.28	0.22	−0.16	0.31
$R_{s k}$	0.01	−0.37	−0.19	0.06	−0.14	−0.49	−0.37	1.00	0.66	−0.27	−0.20	0.11	0.20	0.06	0.18	0.46	0.17	−0.62	0.68	0.17
$R_{k u}$	0.05	−0.19	−0.08	0.53	0.18	−0.43	−0.24	0.66	1.00	−0.33	−0.16	0.05	0.17	−0.05	−0.05	0.47	0.67	−0.87	0.47	−0.26
$R Δ_{a}$	0.78	0.87	0.86	0.51	0.68	0.82	0.78	−0.27	−0.33	1.00	0.97	0.34	−0.07	0.52	0.65	−0.57	−0.63	0.40	−0.31	0.25
$R Δ_{q}$	0.85	0.88	0.90	0.68	0.79	0.81	0.81	−0.20	−0.16	0.97	1.00	0.40	0.01	0.56	0.65	−0.50	−0.46	0.26	−0.21	0.15
$R l_{o}$	0.39	0.35	0.39	0.35	0.27	0.19	0.19	0.11	0.05	0.34	0.40	1.00	0.91	0.90	0.60	−0.21	0.03	0.06	0.00	−0.20
$R l_{n}$	0.06	0.01	0.03	0.15	−0.02	−0.15	−0.14	0.20	0.17	−0.07	0.01	0.91	1.00	0.72	0.34	−0.01	0.29	−0.08	0.08	−0.34
$R H S C$	0.50	0.41	0.48	0.36	0.34	0.27	0.28	0.06	−0.05	0.52	0.56	0.90	0.72	1.00	0.85	−0.32	−0.11	0.02	0.10	−0.13
$R P_{c}$	0.61	0.46	0.56	0.35	0.42	0.31	0.34	0.18	−0.05	0.65	0.65	0.60	0.34	0.85	1.00	−0.36	−0.30	−0.06	0.17	0.00
$R S$	−0.02	−0.40	−0.22	−0.07	−0.07	−0.24	−0.10	0.46	0.47	−0.57	−0.50	−0.21	−0.01	−0.32	−0.36	1.00	0.53	−0.67	0.69	0.35
$R S_{m}$	−0.18	−0.33	−0.26	0.26	0.07	−0.43	−0.28	0.17	0.67	−0.63	−0.46	0.03	0.29	−0.11	−0.30	0.53	1.00	−0.71	0.34	−0.59
$R_{a} / R_{q}$	−0.09	0.29	0.11	−0.35	−0.13	0.43	0.22	−0.62	−0.87	0.40	0.26	0.06	−0.08	0.02	−0.06	−0.67	−0.71	1.00	−0.72	0.13
$R_{p m} / R_{t}$	0.13	−0.44	−0.16	0.03	−0.05	−0.31	−0.16	0.68	0.47	−0.31	−0.21	0.00	0.08	0.10	0.17	0.69	0.34	−0.72	1.00	0.24
$R S / R S_{m}$	0.26	0.09	0.18	−0.21	−0.02	0.33	0.31	0.17	−0.26	0.25	0.15	−0.20	−0.34	−0.13	0.00	0.35	−0.59	0.13	0.24	1.00

Parameter dissociation has to be carefully analyzed. On the one hand, the peculiar behavior of a parameter can make it special, being its choice indispensable to characterize a unique property of the profile. On the other hand, parameter disconnection may be just a consequence of a poor classification. It becomes evident, in the present study, that the latter alternative should be discarded. The highlighted parameters—R_t, $R_{s k}$ , $R_{k u}$ , $R S$ and $R S_{m}$ —have not only demonstrated a lack of relationship with their neighbors but also with the majority of parameters considered (Table 4). Thus, regardless of classification, their behaviors would always be detached from their families.

R_t can be considered unique among its group because it is measured over the evaluation length. Unlike R_z, $R_{p m}$ and $R_{v m}$ , that are average measurements, defined on the sampling length, reflecting the results of at least five peak-to-valley values, R_t represents a pure peak parameter defined on a single peak-to-valley value, actually the extreme one.^27,37 As so R_t is more sensitive to large deviations from the mean line.⁴⁶ For a random profile, typically from a surface resulting from a grinding process, R_t deviation against averaged values become prominent.

Skewness ( $R_{s k}$ ) and kurtosis ( $R_{k u}$ ) are commonly considered as supplementary, but important parameters, that provide additional roughness information to conventional amplitude parameters, such as R_a, R_q, R_z and R_t.^27,28 Although both $R_{s k}$ and $R_{k u}$ provide information about surface texture morphology, they describe distinct profile characteristics. $R_{s k}$ is used to measure the symmetry of the profile and $R_{k u}$ describes the sharpness of height distribution.^27,32

The definitions of $R S$ and $R S_{m}$ can clarify their singular behavior. Although both describe spacing peak information, $R S$ is defined at adjacencies of local peaks and $R S_{m}$ is calculated at the mean line. $R S$ and $R S_{m}$ are a direct portray of profile regularity.²⁸ As the surface becomes more random, the difference between $R S$ and $R S_{m}$ becomes more apparent. Therefore, $R S / R S_{m}$ ratio can be used as a good relation that summarizes $R S$ and $R S_{m}$ description characteristics.

Considering parameters importance and correlation previously discussed, a parameter set was established—R_z, R_t, R_q, $R_{s k}$ , $R_{k u}$ , $R S / R S_{m}$ , $R l_{o}$ , $R P_{c}$ and $R Δ_{q}$ . In order to characterize height sensitive information R_z, R_t, R_q, $R_{s k}$ and $R_{k u}$ were selected. R_z and R_t were chosen to describe extreme profile features; R_q was elected for describing general roughness rather than R_a because it is more sensitive to deviations³²; and $R_{s k}$ and $R_{k u}$ were defined to provide profile form properties. Contemplating spacing features, $R S / R S_{m}$ was chosen to represent $R S$ and $R S_{m}$ , being able to describe surface regularity; $R l_{o}$ was elected to describe sample length deviations rather than $R l_{n}$ because this parameter is sensitive to experimental cut-off; and $R P_{c}$ was preferable than $R H S C$ to describe peak count because its value is independent of evaluation length.⁴⁶ In addition to spacing and amplitude information, $R Δ_{q}$ was preferred to describe hybrid properties than $R Δ_{a}$ . Like R_q, $R Δ_{q}$ is more sensitive to slope deviations than $R Δ_{a}$ .²⁸

Function correlation

Once the parameter set has been defined, ensuring that the majority of surface features could be described, the functional correlation of surface roughness parameters must be tested. Surface topography can be a direct and reliable indicator of tribological performance.^13,27 Thus, for the control and design of tribological components, it is important to understand roughness parameters and function relation.³²

The term function describes the use of the surface.²⁷ Although function is open-ended, because polymer composites applications are tribological diverse, in most of the cases, it is of primary concern to develop polymeric composites that possess a consistent wear performance under dry sliding conditions.^39,40 Generally, the optimal tribological properties can be summarized by greater wear resistance.⁴⁸ Therefore, a good starting point to understand functional surface relations is to study wear and surface roughness parameter correlation.³²

Table 5 presents the Pearson’s correlation coefficient found between the parameter set and the specific wear rate, and Figure 5 shows the specific wear rate as a function of each surface roughness parameter. In general, no correlation between roughness parameters and wear behavior was observed, and $R S / R S_{m}$ was the only parameter that has shown a moderate correlation ( $0.5 \leq |ρ| < 0.8$ ) with wear rate.⁴⁷

Table 5.

Correlation between specific wear rate and roughness parameters defined on parameter set.

	R_z	R_t	R_q	$R_{s k}$	$R_{k u}$	$R Δ_{q}$	$R l_{o}$	$R P_{c}$	$R S / R S_{m}$
Specific wear rate (w_s)	−0.23	0.06	−0.18	−0.21	0.12	−0.23	−0.42	−0.23	−0.74

Figure 5.

Relationship between specific wear rate and the parameter set: (a) R_z, (b) R_t, (c) R_q, (d) $R_{s k}$ ,(e) $R_{k u}$ , (f) $R Δ_{q}$ , (g) $R l_{o}$ , (h) $R P_{c}$ and (i) $R S / R S_{m}$ .

It is important to remember that surface topography is not the only factor governing function, but one among the geometrical properties that exist simultaneously and interact with material properties and operating conditions.^31,38 Depending on the contributions of the material, the geometric properties and the operational conditions, wear performance may be completely different.³⁷ The potential of surface roughness parameters in describing wear rate is intimately linked to the amount of geometric properties contribution. When the effects of material properties or operational conditions greatly surpass the influence of surface topography on the wear performance, the ability of surface roughness parameters in describing the wear behavior may be minimal.

According to the literature, changes in material properties are sufficient to modify completely the dominant wear mechanism.^13,38,40,48 Particularly for composites subjected to an abrasive process, such as grinding, as filler content increases or/and as filler/matrix interaction extension is modified, the contribution of abrasive mechanisms to the wear of the material may be highly suppressed.^38,40 A transition from abrasive wear to adhesive wear may be experienced, and a great decrease in wear rate may occur.^13,49 It is important to note that a change in the dominant wear mechanism implies a consequent modification in the contact kinetics and tribological action.⁶ Hence, wear behavior may be entirely modified and so surface roughness and wear relation.

Therefore, surface roughness parameters and wear correlation may have been biased by the presence of FTTNT/L-0.5% and FTTNT/H-0.5% (Figure 5). As stated previously at the wear performance section, FTTNT/L-0.5% and FTTNT/H-0.5% showed an outstanding decrease in specific wear rate compared to neat PA 11 and the other nanocomposites. It seems that the particular combination of TTNT content and functionalization present in FTTNT/L-0.5% and FTTNT/H-0.5% led to a synergic improvement of material properties capable of modifying the dominant wear mechanism. This may have changed completely the wear behavior, explaining the peculiar surface roughness parameters and wear relation showed by those nanocomposites.

Considering FTTNT/L-0.5% and FTTNT/H-0.5% as outliers, Pearson’s correlation coefficient increases for most of the roughness parameters reaching levels of moderate to strong correlation with specific wear rate, such as R_z( $|ρ| > 0.78$ ), $R S / R S_{m}$ ( $|ρ| > 0.85$ ) and $R Δ_{q}$ ( $|ρ| > 0.89$ ), and a trend can be easily seen between roughness parameters and specific wear rate (Figure 5). Wear rate showed a positive effect when R_z, R_t, R_q, $R l_{o}$ and $R Δ_{q}$ increased, and a negative effect when $R S / R S_{m}$ increased. $R P_{c}$ , $R_{s k}$ and $R_{k u}$ demonstrated a low sensitivity to wear rate variations. To understand better the different effects of the surface roughness parameters on the wear rate, the relation between wear, roughness parameters, asperities and contact must be clarified.

Wear is closely related to the asperities and contacts between parts. For most surfaces in relative sliding or rolling contact, the area of effective contact is much smaller than the nominal contact area. The applied load is supported by several small local asperities, making up the real contact area, and the friction and wear behavior result from the interactions between these local asperities.³⁷ Wear rate is proportional to asperities contact pressure, but contact pressure is inversely proportional to the power of the real area of contact.^38,49 Hence, for a given applied load, a small change in the asperities may promote a corresponding modification in the effective contact area, which in turn may lead to a massive change in local contact pressure, influencing significantly the wear rate.

Asperities characteristics, such as sharpness, height, and distribution, are closely related to surface topographic properties, and so can be described by surface roughness parameters. These include the distribution of profile height (R_q, R_z, R_t), the profile shape ( $R_{s k}$ and $R_{k u}$ ), the density of profile peaks ( $R P_{c}$ ), the slope of asperities ( $R Δ_{q}$ ), the developed length of the profile ( $R l_{o}$ ) and the profile regularity ( $R S / R S_{m}$ ).²⁷ Nonetheless, the relation between profile properties and asperities characteristics is not fixed. Each profile property may influence asperities individually. Therefore, the effects of surface roughness parameters on wear rate may be diverse.

Wear rate increases as the distribution of profile height increases. Roughness (R_q) and extreme profile features (R_z and R_t) depend extensively on profile height. Thus, as roughness and extreme profile features increase, profile height may increase, which in turn leads to a decrease in the real contact area and an increase of wear rate (Figure 5(a) to (c)).⁴⁹

Wear rate may increase with profile shape modifications. Essentially, profile shape is described by the skewness ( $R_{s k}$ ) and kurtosis ( $R_{k u}$ ), which represents respectively profile symmetry and pointedness. A zero skewness and a kurtosis of three characterize a symmetrical Gaussian surface with an equal number of local maxima and minima above and below profile mean line.³⁷ Positively skewed surfaces are characterized by higher peaks or filled valleys, and higher kurtosis values correspond to sharper peaks, which result in a reduction in the real contact area and a very high contact pressure at asperities.^32,49 Thus, wear rate is maximized as kurtosis is increased and as the surface becomes more positively skewed.⁴⁹ Although tribological performance is significantly influenced by skewness and kurtosis, generally the effect of these roughness parameters on wear rate is considered secondary.^27,46 Commonly skewness and kurtosis show large scatter and for significant tribological change $R_{s k}$ and $R_{k u}$ difference should be higher than ±1 and ±2, respectively.³³ In the present study $R_{s k}$ and $R_{k u}$ difference did not reach significant levels, and therefore showed a small influence with wear rate (Figure 5(d) and (e)).

Wear rate increases as the slope of the asperities ( $R Δ_{q}$ ) increases. $R Δ_{q}$ shows a high correlation with diverse surface phenomena, including wear.⁴⁶ A high slope may lead to sharper peaks, which in turn may result in a minimal contact area and very high contact pressure at asperities, enhancing wear. In addition, asperities of high slopes also are more prone to plastically deform upon the application of a normal load, which may further increase the wear rate (Figure 5(f)).³⁷

Also, wear rate increases as the relative length of the profile ( $R l_{o}$ ) increases. For a surface with a high distribution of profile height, a high $R l_{o}$ may lead to high peaks or deep valleys. If high peaks are the majority, possibly a reduction in the real area of contact will result, which in turn will increase the wear rate (Figure 5(g)).

Wear rate may increase with the density of peaks ( $R P_{c}$ ). However, $R P_{c}$ alone is unable to describe the wear performance. As kurtosis and skewness, the number of local peaks ( $R P_{c}$ ) can be considered a roughness parameter of secondary effect. Although the number of contact points changes with $R P_{c}$ , wear rate is mainly influenced by the characteristics of local peaks, such as height, sharpness and slope, and not by their quantity (Figure 5(h)).

Wear rate increased as surface regularity ( $R S / R S_{m}$ ) decreased. When $R S / R S_{m}$ approaches unity, the surface shows a deterministic behavior, while when $R S / R S_{m}$ is low, the surface shows a random behavior.²⁷ Random surfaces are characterized by a random distribution of profile height. Usually, they are a result of a cumulative process, such as grinding, and of a large number of random discrete local events, i.e. singular contacts.⁴⁵ Due to the randomness of the profile, random surfaces may show a limited effective contact area, contributing to the wear rate increase (Figure 5(i)).

Parameters variation

A major factor in attempting to establish the relationship between the functional properties and surface topography is that parameters are subjected to variations.⁴⁴ Besides parameter set effectiveness in describing surface features, roughness parameters also have to be robust. Thus, understanding parameter variation may be a critical step towards a complete description of engineering surfaces both functionality and analytically.⁴⁴

However, the study of parameter variation may be complex. Surface roughness parameters, being necessarily imperfect statistical representation of a very complex geometrical structure, are more prone than many other physical measurements to scatter. The causes of parameter variation may be diverse and the degree of variability due to these causes may be different for different parameters.⁴² Although many efforts have been made to study parameter variation, the significance, sensitivity and main cause of parameter variation are still open questions.^27,42,44

Tables 6 and 7 show the values obtained for all roughness parameters for the neat PA11 and its nanocomposites according to the measured axis. Some surface parameter relations are also presented. Figure 6 summarizes the variations of the main surface roughness parameters, i.e. those which form the parameter set, obtained when comparing the measured axis. In Figure 6, the variation of the parameters is presented locally (Figure 6(a) to (e)), making it possible to analyze TTNT content, functionalization and sodium content contributions, and globally (Figure 6(f)), giving the possibility to examine also the overall sensitivity and robustness of the parameters.

Table 6.

Amplitude parameters and relations of neat PA11 and its nanocomposites.

Samples	Measurement axis	R_z (µm)	R_t (µm)	R_q (µm)	$R_{s k}$	$R_{k u}$	$\frac{R_{a}}{R_{q}}$	$\frac{R_{p m}}{R_{t}}$
Neat PA 11	X axis	76.97	118.63	19.76	0.19	2.67	0.82	0.51
Neat PA 11	Y axis	74.58	78.39	19.28	−0.49	2.31	0.84	0.37
TTNT/L-1%	X axis	83.45	114.68	21.75	−0.07	2.47	0.83	0.48
TTNT/L-1%	Y axis	81.48	95.88	20.43	−0.39	2.60	0.82	0.48
TTNT/H-0.5%	X axis	87.25	130.52	25.17	−0.16	2.92	0.79	0.50
TTNT/H-0.5%	Y axis	94.06	131.85	25.26	1.42	5.40	0.70	0.62
TTNT/H-1%	X axis	92.62	167.31	25.74	0.68	4.83	0.74	0.59
TTNT/H-1%	Y axis	139.69	148.56	37.45	0.25	2.00	0.84	0.55
TTNT/H-2%	X axis	110.71	169.52	26.64	0.31	3.28	0.78	0.53
TTNT/H-2%	Y axis	67.33	89.94	18.98	−0.73	2.87	0.81	0.44
FTTNT/L-0.5%	X axis	134.81	168.41	31.02	0.19	3.09	0.79	0.52
FTTNT/L-0.5%	Y axis	30.46	36.27	8.17	−0.36	2.70	0.82	0.42
FTTNT/L-1%	X axis	111.07	194.91	28.39	−0.67	3.51	0.78	0.50
FTTNT/L-1%	Y axis	118.68	156.69	26.59	0.37	3.32	0.82	0.57
FTTNT/L-2%	X axis	96.06	140.92	26.57	−0.09	3.03	0.79	0.51
FTTNT/L-2%	Y axis	96.64	106.27	25.45	−0.19	2.04	0.86	0.45
FTTNT/H-0.5%	X axis	109.84	166.64	27.77	0.16	2.94	0.81	0.52
FTTNT/H-0.5%	Y axis	78.05	96.75	19.45	0.66	3.37	0.80	0.60
FTTNT/H-1%	X axis	105.69	216.17	24.24	0.63	6.43	0.74	0.50
FTTNT/H-1%	Y axis	94.46	102.39	25.62	−0.16	1.99	0.85	0.46
FTTNT/H-2%	X axis	69.20	122.51	16.73	0.64	5.19	0.72	0.56
FTTNT/H-2%	Y axis	152.06	215.80	35.57	−0.32	4.11	0.74	0.48

Table 7.

Spacing and hybrid parameters and relations of neat PA11 and its nanocomposites.

Samples	Measurement axis	$R Δ_{a}$	$R Δ_{q}$	$R l_{o}$ (mm)	$R P_{c}$ (cm⁻¹)	$R S$ (µm)	$R S_{m}$ (µm)	$\frac{R S}{R S_{m}}$
Neat PA 11	X axis	25.35	31.01	6.43	39.30	115.93	369.00	0.31
Neat PA 11	Y axis	21.07	26.80	1.77	31.30	243.80	327.83	0.74
TTNT/L-1%	X axis	22.14	28.07	6.25	25.00	154.94	476.60	0.33
TTNT/L-1%	Y axis	24.18	30.36	1.82	37.50	112.04	539.55	0.21
TTNT/H-0.5%	X axis	21.92	27.12	6.23	30.40	197.93	494.83	0.40
TTNT/H-0.5%	Y axis	28.01	38.17	1.94	37.50	189.64	509.54	0.37
TTNT/H-1%	X axis	21.01	30.13	6.30	32.10	250.31	611.64	0.41
TTNT/H-1%	Y axis	35.61	40.79	2.06	31.30	134.44	401.73	0.33
TTNT/H-2%	X axis	32.20	38.31	6.94	57.10	134.42	445.04	0.30
TTNT/H-2%	Y axis	19.59	24.13	1.74	31.30	154.22	370.76	0.42
FTTNT/L-0.5%	X axis	34.49	40.02	7.11	48.20	176.45	390.41	0.45
FTTNT/L-0.5%	Y axis	8.15	11.75	1.63	37.50	174.00	641.69	0.27
FTTNT/L-1%	X axis	29.28	37.11	6.74	37.50	141.68	609.61	0.23
FTTNT/L-1%	Y axis	27.59	35.33	1.89	25.00	185.25	497.29	0.37
FTTNT/L-2%	X axis	27.87	32.90	3.76	28.10	171.97	376.33	0.46
FTTNT/L-2%	Y axis	22.07	26.47	1.80	25.00	190.14	430.43	0.44
FTTNT/H-0.5%	X axis	35.28	40.44	7.18	44.60	149.40	288.73	0.52
FTTNT/H-0.5%	Y axis	19.39	27.86	1.77	31.30	182.79	424.28	0.43
FTTNT/H-1%	X axis	26.94	35.26	6.58	35.70	164.02	571.00	0.29
FTTNT/H-1%	Y axis	27.87	34.74	1.90	43.80	177.16	274.21	0.65
FTTNT/H-2%	X axis	16.83	23.37	6.04	37.50	217.44	607.32	0.36
FTTNT/H-2%	Y axis	37.14	43.07	2.11	43.70	138.06	376.33	0.37

Figure 6.

Roughness parameters variation according to the measured axis in (a) neat PA11, (b) non-functionalized nanocomposites reinforced with TTNT low sodium content, (c) non-functionalized nanocomposites reinforced with TTNT high sodium content, (d) functionalized nanocomposites reinforced with TTNT low sodium content and (e) functionalized nanocomposites reinforced with TTNT high sodium content. (f) Overall mean and standard deviation of roughness parameters variations concerning PA11 and its nanocomposites.

Before starting to analyze in more detail the variation of the results, it is important to establish a systematic approach. After the calculation of parameter variations some questions must be drawn^27,42,44: (i) How parameters are varying? (ii) Does the surface really contain such a dramatic change that explains parameter relation? (iii) What are the possible causes of parameter variations? (iv) Does a systematic error of form exist? (v) What may be the predominant cause of parameter variation?

A clear change of surface roughness behavior according to the measured axis is perceptible in all combinations. Depending on the amount of TTNT, functionalization and sodium content, the variations of the parameters have changed (Figure 6). In general, $R_{s k}$ and $R l_{o}$ were more sensitive, and R_q and $R P_{c}$ were less sensitive to TTNT addition and measurement direction (Figure 6(f)). It is difficult to state if the variations measured really indicate surface roughness modification. It is inopportune to assert that nanocomposites may have led to oriented surface patterns and that those could be directly linked to the variation of the parameters with TTNT addition.

As stated previously, parameter variations causes are diverse. Dong et al.^42–44 relate parameter variations due to two main causes. Statistically, parameter variations can be linked to the non-stationarity of surfaces and limited independent samples, and physically, variations can be a consequence of inherent properties of the surface, data measurement and processing conditions. Besides, parameter variations are basically composed of two types of errors: (i) systematic and (ii) random.²⁷ Systematic errors are sometimes called bias and can be generally related to imperfect devices and measurement procedures, such as limited independent samples and data measuring and processing conditions. While random errors produce the scatter of readings and are caused mainly by a non-constant source of errors either in time or space, such as the non-stationarity of the surface.²⁷

Although systematic errors are difficult to analyze, the standard deviation may be a good starting point. Although a systematic error results from a persistent issue and leads to a stable variation in the measurement, deviations from the mean value, i.e. the standard deviation, should be minimal, once fluctuations of variation of the parameter are constant. Looking at Figure 6(f), $R l_{o}$ showed the lowest standard deviation among the parameter set, and its variation may be mainly associated with systematic errors. Indeed, $R l_{o}$ is closely related to the developed length of the profile, as so it is very sensitive to any change in the evaluation length. Due to the limited dimension of the samples, the distance traveled on the Y-axis was 62.0% lower than that performed on the X-axis in all samples. Although short-wavelength bandwidth and cut-off values were maintained constant, the evaluation length was considerably reduced in Y-axis. As a consequence, $R l_{o}$ showed a variation of about 69.0% confirming the main effect of evaluation length variation on it.

It is important to note that $R l_{o}$ was probably not the only factor affected by evaluation length modification. As a systematic error, evaluation length change influences all roughness parameters. However, the contribution of the axis length on parameter variation may be different for each roughness parameters, according to the sensibility of the parameter. It is impossible to state precisely the influence of evaluation length change on the other parameters, once in these parameters, random errors may also be presented.

The presence of a systematic variation may also indicate limited independent samples. However, its influence on the roughness parameters may have been minimal. Neither in $R l_{o}$ , governed by a systematic variation, the effect of an insufficient number of samples for the study of each nanocomposite combination may have shown significance. As stated previously, $R l_{o}$ variation (69%) was mainly influenced by evaluation length difference (62.0%) Therefore, the explanation for its variation may be linked to the modification in the axis distance traveled, thus leaving a small space for the possible effects caused by limited independent samples.

Besides systematic variation, it is also important to understand parameter variations induced by random errors. Ground surfaces generally exhibit non-stationarity.^42,44 During grinding the surface is subjected to many cutting points and the abrasive grains are randomly distributed producing a surface with random characteristics.^27,42 Surface randomness can be confirmed by $R_{a} / R_{q}$ and $R S / R S_{m}$ relations. On the average $R_{a} / R_{q}$ approaches 0.8 and $R S / R S_{m}$ 0.4 for neat PA11 and its nanocomposites (Tables 6 and 7), indicating a low surface regularity and a random profile.

The sensibility of each roughness parameter to the non-stationarity of the surface may be completely different. Commonly amplitude parameters are mainly affected by non-stationarity. As an accepted rule of thumb, higher-order relative moment parameters, such as $R_{s k}$ and $R_{k u}$ are subject to larger variation than lower-order parameters, such as R_q, R_z and R_t. However, this is not always true, and in some cases $R_{s k}$ or $R_{k u}$ may vary equally or lower than R_q, R_z and R_t, as shown in Figure 6(f). R_t is very sensitive to high peaks or deep scratches.⁴⁶ As so it usually exhibits a higher variation than R_q and R_z as a consequence of it strongly dependence on isolated events.³³ Due to its capability in describing surface regularity, $R S / R S_{m}$ is closely related to the randomness of the surface, and its variation may also be strictly linked to non-stationarity. As hybrid parameters can also describe amplitude information, $R Δ_{q}$ variation may also be explained by the non-stationarity of the surface.

Conclusions

The study shows promise results for the use of TTNT as reinforcing material on PA 11 in terms of wear performance. Depending on TTNT loading, functionalization and sodium content, different wear behaviors can be obtained. Wear resistance can be maximized in nanocomposites reinforced with a low amount of functionalized TTNT (0.5 wt%) of high sodium content. Although at first look the unceasing incorporation of a harder, rigid and inorganic phase, such as TTNT, shows potential to improve continuously PA wear performance, careful attention must be paid to TTNT dispersion and interaction with the polymeric matrix. Due to TTNT inherent characteristics, wear reinforcing effect may be suppressed by nanotube agglomeration and low adhesion to PA.

An efficient and robust roughness parameter set to characterize surface topography can be defined following an analytical approach based on parameter classification and correlation. Several roughness parameters demonstrate redundancy in describing some surface features, like $R_{p m}$ , $R_{v m}$ , R_c and R_z, R_a and R_q, $R l_{n}$ and $R l_{o}$ , $R H S C$ and $R P_{c}$ , and $R Δ_{a}$ and $R Δ_{q}$ . On the other hand, some roughness parameters demonstrate a single behavior, like R_t, $R_{s k}$ , $R_{k u}$ , $R S$ and $R S_{m}$ , being essential for the complete characterization of the surface topography.

Some roughness parameters reveal a moderate to strong correlation with wear performance. R_z, R_t, R_q, $R l_{o}$ and $R Δ_{q}$ increase as wear rate increases and $R S / R S_{m}$ decreases as wear rate decreases. Roughness parameters effect on wear performance may be linked with the distribution and features of asperities, which may lead to a large reduction in the real contact area, increasing consistently the wear rate.

Considering the roughness parameters studied, $R_{s k}$ and $R l_{o}$ demonstrate to be most sensitive to TTNT addition and measurement direction, while R_q and $R P_{c}$ show less sensitivity. The difference in the distance traveled between the X- and Y-axis produces a systematic error affecting all roughness parameters, however, non-stationarity of surface also contributes significantly to parameter variation. $R l_{o}$ variation can be mainly associated with systematic errors, such as the difference in evaluation length, while R_z, R_t, R_q, $R_{s k}$ , $R_{k u}$ , $R S / R S_{m}$ and $R Δ_{q}$ variations can be mainly attributed to the non-stationarity of the surface.

Footnotes

Acknowledgements

The authors acknowledge the grants from the Brazilian funding agencies CNPq and CAPES.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors received financial support from the Brazilian funding agencies CNPq (grant number 301299/2010-2) and CAPES (finance code 001).

ORCID iD

Ayrton Alef Castanheira Pereira

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Wear behavior of polyamide 11 reinforced with titanate nanotubes

Abstract

Keywords

Introduction

Experimental procedure

Nanocomposite processing

Wear test

Surface roughness measurement

Results and discussion

Wear performance

Surface roughness analysis

Parameter set definition

Function correlation

Parameters variation

Conclusions

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

ORCID iD

References