Estimating Nanoscale Surface Roughness of Polyethylene Terephthalate Fibers

Quantitation of surface roughness is difficult, if subtle, but significant differences cause an uncommon variance. We used atomic force microscopy to measure the surface roughness of polyethylene terephthalate (PET) fibers before and after a 30 s plasma treatment of 300 W. Samples were measured multiple times at different locations, in four scan sizes. The surface roughness was expressed in terms of nine roughness parameters. Despite the large number of data, simple statistics was not able to detect significant differences in roughness before and after plasma treatment. A factorial analysis of variance (ANOVA) of the normalized data and a sum of ranking differences analysis using four types of data preprocessing and their factorial ANOVA confirmed that (i) the plasma treatment had roughened the PET fiber surface; (ii) the roughness increases with the scanned area in the measured range; and (iii) what the best roughness parameters are in discriminating between surfaces before and after treatment. Although the compared roughness estimators were on different scales, a roughness estimation of the nanoscale surfaces was feasible, where other methods fail. The presented methodology can be applied widely and unambiguously for highly different method comparison tasks.


INTRODUCTION
Plasma treatments of textiles and fabrics have been extensively studied in the last decade as the textile industry is continuously trying to fulfill the increasing demand of society in terms of enhanced hydrophobic or hydrophilic properties, better printability, intelligent filtration properties, flame retardation, biocompatibility, self-cleaning finishes, and so forth. 1−3 For the preparation of textiles with functional coatings, surface modification is the most obvious and suitable technique. Several wet chemical methods are available to tailor surface properties but most of them bear several disadvantages like large chemicals and energy consumption, influence on the bulk properties of fibers, health and environmental hazard, and high cost. 4,5 Plasma technologies offer a much greener possibility for surface modification as they are dry technologies without cooling water utilization, need minimum amount of chemicals, are energy efficient, and have no pollution effect. 6−8 Furthermore, plasma treatments are restricted to the uppermost layer (10−20 nm) of the material without affecting the bulk properties. 9,10 Obviously, plasma treatment of surfaces is carried out in nonthermal or cold plasmas, where the thermodynamic equilibrium is not reached. 11,12 When a material is subjected to plasma treatment, chemical and morphological changes occur on the surface. 13 −15 Activation and cleaning are typical chemical processes during which the surface energy increases and the contaminations disappear, respectively. A typical morphological effect is etching, when the bulk material is damaged and gas-state byproducts, usually atoms or small molecules, are eliminated from the surface, resulting in the change of the surface roughness. 16−18 Usually all these processes take place simultaneously.
In our work, we studied the morphological changes of polyethylene terephthalate (PET) fibers induced by a plasma treatment [diffuse coplanar surface dielectric barrier discharge (DCSBD)]. The surface topography of untreated and treated samples has been characterized by atomic force microscopy (AFM), which can provide three-dimensional information about the surface morphology. According to a literature survey, 19−23 the roughness of the surface significantly changes, usually increases, during plasma treatment because of the etching effect of plasmas. However, an already large initial roughness may even decrease after plasma treatment as a result of erosion of the asperities. 24 Our earlier investigations of cellulose fibers by AFM 25 showed that a 30 s long plasma treatment caused a slight, but detectable roughness increase. However, the statistical significance could not be unequivocally ascertained. Interestingly, the roughness seemed to increase also with increasing scanned area. Therefore, in our current study we wanted to answer the following questions:  26−31 In this work, scanning electron microscopy (SEM) inspection found nanoscale damage of the PET fibers after being treated for 30 s in plasma (Figure 1). In particular, pits with elliptical openings, usually aligned to the fiber axis, and exfoliations were identified. However, this effect of the plasma treatment is hardly visible; therefore, the evaluation could be subjective and converting surface morphology changes into numbers is not easy.
In order to quantify the observed deteriorations, individual fibers were pulled out from samples of untreated and treated PET fabrics and scanned by AFM. The tip of the AFM cantilever is raster scanning downwards across the surface of the fiber from left to right. When the scanning parameters are set so that the feedback loop reacts quickly to the detected surface features, the deflection of the cantilever is minimal and the corresponding deflection image is poor in contrast, whereas the contrast of the height image is the best. On the contrary, when the scanning parameters are set to a slower feedback loop reaction, height image is poorer in contrast (as the tip is not closely tracking the surface), whereas the deflection image is sharper (as the cantilever is forced to deflect by the encountered surface irregularities). Both height and deflection images are recorded, but only height images are used in the analysis of the roughness data, as only these ones contain the needed point-by-point height information of the topography.
For illustration, typical height images are shown for both untreated and treated samples, in all four different scanning sizes, in the 3D color-coded, oblique view ( Figure 2).
By a simple visual inspection of these images, obvious differences in the roughness of the untreated and treated samples can be unequivocally stated only in the case of the smallest, 4 μm 2 scan areas. Figure 3 summarizes the results of roughness measurements before and after the plasma treatment by presenting boxplot charts of nine roughness parameters as a function of the scanned area. Two general trends can be observed: (1) the mean of the individual roughness parameters is generally increasing with increasing scan area, apparently tending to, but at the scan areas of the experiments, not reaching, a plateau level (cf. ref 32); (2) the means after plasma treatment are generally higher in absolute value than the ones before the treatment. However, a conclusion about the roughening effect of the 30 s plasma treatment can be drawn only if the whole set of corresponding data is compared. The outcome of univariate Mann−Whitney tests is that the roughness parameters are significantly different at the 0.05 error level at the lowest scan size (4 μm 2 ) only. At larger scan sizes, the roughening effect of the plasma treatment thus cannot be ascertained. However, the power of multivariate statistical analysis is evidenced in the following.
2.2. Effect of Roughness Parameters (Analysis of Variance of Normalized Raw Roughness Data, Table  S1). Normalization (NOR) was unavoidable as all roughness parameters were on different scales. Figure 4 shows that a classical box and whisker plot cannot discriminate between the roughness parameters. Therefore, we had to decompose the effect of factors by variance analysis. Table 1 summarizes the analysis of variance (ANOVA) results.
The plasma treatment (F 1 ) is highly significant: the roughness is considerably lower before treatment, irrespective of the chosen roughness parameter ( Figure S1). Almost all roughness parameters are equivalent, except for the peak count ( Figure S2). A post hoc least significant difference test  Representative 3D color-coded height maps of untreated, respectively, plasma-treated samples scanned at increasingly larger areas. Note that the height scale range is 160 nm for all images except for the two 4 μm 2 scans, where it is 80 nm.
differentiates peak count, but other post hoc tests (Bonferroni, Scheffe, etc.) do not. Levene's test for homogeneity of variances is not significant, showing that all roughness parameters originate from the same distribution. Vertical bars denote 0.95 confidence intervals.
The coupling of the first two factors (plasma treatment and scan area) can be seen in Figure 5.
The line plot reveals smaller roughness for untreated samples: the red dotted line runs always above the blue solid line.
The tendency is clear: as the scan area increases, the roughness also increases.
At F 2 = 25 μm 2 , the difference is not significant in F 1 , but the mean before treatment (b, blue full circle) is lower than after treatment (a, red empty box), even in this case.
The conclusions are obvious: plasma treatment causes coarsening of the surface, and it is worth to consider a larger scan size for better differentiation between samples before and after treatment at least in this measurement scale.
The rudeness of the modeling is revealed in the normal probability plot of residuals, eq 6 ( Figure S3).

Sum of Ranking Differences
Calculations. Sum of ranking differences (SRD) is able to compare and group the differently defined roughness parameters. The row average was selected as the benchmark. The scaling problem persists; hence, four types of data preprocessing has been carried out: NOR, rank transformation (RNK), range scaling (SCL), and standardization (STD).
As an example, the results for normalized SRD calculations can be seen in Figure 6.
Peak count is indistinguishable from random ranking. Therefore, it was eliminated from further analysis. Other roughness parameters group together, R z and R max being located closest to the reference. Similar SRD calculations have been completed for the other preprocessing methods (RNK, SCL, and STD; data not shown).
2.4. ANOVA of SRD Scores. Roughness parameters, except the peak count, were considered as factor 3, and four data preprocessing options as factor 4 with four levels: NOR, RNK, SCL, and STD (Table 2), see part 4.4. Sevenfold crossvalidation assigned uncertainty values to SRD values in a repeated random manner. In this way, 9 (roughness parameters) × 4 (preprocessing methods) × 14 (repetitions) = 448 SRD values were calculated and the effects of factors and their interactions were decomposed.
After decomposition of the role of various ways to determine roughness by AFM, and the preprocessing methods, the effect of the latter is only significant at the 1% level, that is, it is reassuring that we have not incorporated artificial information by using data preprocessing.
The various ways to determine roughness (F 3 ) and its interaction with preprocessing (F 3 × F 4 ) are highly significant, which can be seen in the next figure (Figure 7). Based on the model, the following roughness parameters are recommended: (i) the vertical distance of the highest point from the lowest point (maximal height, R max ); (ii) the mean vertical distance of the five highest points and five lowest

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http://pubs.acs.org/journal/acsodf Article points from the mean plane (10 points mean, R z ); and (iii) the mean vertical distance of the five highest points from the mean plane (average max. height, R pm ). The worst parameter for expressing roughness is the vertical distance of the highest point from the mean plane, that is, the R p .
It seems that the highest and deepest points are not symmetric; not the same roughness values are produced in case of positive and negative deviations from the mean plane.
The zigzag pattern in Figure 7 is arbitrary as it depends on the enumeration (ordering) of the roughness parameters. However, the significant differences in the means are real and the grouping is quite straightforward. A conservative Scheffet est amalgamates the three best roughness parameters into one group, the other parameters being significantly different from these three and from each other. The residuals of model (6) follow a normal distribution in a much better way than the (normalized) raw data do ( Figure  S4).
As for the future studies, we plan to include other roughness parameters in the comparison.

CONCLUSIONS
The plasma treatment causes a significant increase of the surface roughness, irrespective of the different ways of expressing the measured roughness. Plasma treatment caused an increase (ca. 20%) in the normalized roughness (independently of the way it was given).
The detection and quantification of slight roughness changes can be accomplished by AFM even if a relatively large variance is present in the measured data.
The most relevant and recommended roughness parameters are the vertical distance of the highest point from the lowest point (maximal height, R max ); the mean vertical distance of the five highest points and five lowest points from the mean plane (10 points mean, R z ); and the mean vertical distance of the five highest points from the mean plane (average max. height, R pm ).
An increase in the observing areas will enhance the detection of small roughness differences in the studied scale.
The sum of (absolute) ranking differences method is able to find subtle differences and hence it can group the relevant parameters even when the classical statistical tools fail. The best and worst parameters can also be determined.
Although the compared roughness estimators were on different scales, a roughness estimation of the nanoscale surfaces was feasible, where other methods fail. The presented SRD coupled with ANOVA can be applied widely and unambiguously also for highly different method comparison tasks.

EXPERIMENTAL SECTION
4.1. PET Fabric and Plasma System. A DCSBD plasma system was used for surface treatment of the PET fabric, (ROPLASS s.r.o., Brno, Czech Republic) in ambient air. The nonthermal plasma panel consisted of two systems of parallel strip-like electrodes embedded in alumina matrix. The plasma was ignited with sinusoidal high frequency, 10−20 kHz, high voltage with peak-to-peak values of up to 20 kV. To keep the system at low temperature, cold oil was circulated over the electrodes. The discharge was operated in air at 300 W, which provided a quasihomogeneous diffuse plasma surface. Both sides of the fabric samples were treated for 0.5 min. The treatments were performed on a commercial PET fabric ( 55 g/m 2 ). During the treatment, both sides of the samples were placed in the plasma. Before the treatment, the samples were thoroughly cleaned to remove any sizing agent.
4.2. Morphological Studies. Untreated and treated PET fabric samples were investigated by an EVO 40 scanning electron microscope (Carl Zeiss AG, Oberkochen, Germany) at 20 kV acceleration voltage. To avoid any electrostatic charging, the samples were coated with a 10 nm thin gold layer.
4.3. Surface Roughness Measurements. The surface roughness of individual PET fibers, which were removed from the untreated and treated fabric, was measured by a Dimension 3100 atomic force microscope equipped with a Nanoscope IIIa controller (Digital Instruments/Veeco, Santa Barbara, California, USA) on 4, 25, 45, and 64 μm 2 areas using silicon cantilevers in contact mode with a 512 × 512 pixel resolution. The main parts and the function of the AFM 33 are illustrated in Figure 8. The number of measurements for the above four scan sizes was 16, 11, 7, and 13 in the case of samples before plasma treatment, and 13, 15, 12, and 9 in the case of samples after plasma treatment. Known weaknesses and systematic errors of AFM scanning, such as tip convolution problems determined by tip radius and cone angle, no tracking of deep trenches and steep slopes, and so forth, were not taken into account in the data treatment.
Raw measurement files were processed using the Nanoscope software by first applying a third-order flattening. Nine widely used roughness parameters, see for example, ref 34, were determined, such as the 1. root mean square roughness (also R q )

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http://pubs.acs.org/journal/acsodf Article 3. max. height, R max , the vertical distance of the highest point from the lowest point; 4. 10 points mean, R z , the mean vertical distance of the five highest points and five lowest points from the mean plane; 5. peak count, the number of peaks higher than the threshold value (here: 0.1 R q ); 6. max. peak height (R p ), the vertical distance of the highest point from the mean plane; 7. average max. height (R pm ), the mean vertical distance of the five highest points from the mean plane; 8. max. depth (R v ), the vertical distance of the lowest valley from the mean plane; 9. average max. depth (R vm ), the mean vertical distance of the five lowest points from the mean plane. For the multivariate statistical analysis, the last two parameters (max. depth and average max. depth), being negative numbers, had to be reversed, their opposite values being denoted as R v_ and R vm_ . Several other roughness parameters derived from the AFM measurement data (see, e.g., ref 35) have not been included in the analysis. One of the excluded parameters was the (dimensionless) roughness factor (f r or r), defined as the ratio of the real (or rather, measured) surface area to the projected surface area. The roughness factor is relevant only in fields and applications where the real surface area is known, but this is rarely the case: for example, in electrochemistry and contact angle and wetting disciplines. 36 In our case, however, roughness parameters used in the field of tribology, more relevant for the application of such fibers, have been considered.
4.4. Data Preprocessing. The samples were arranged in the rows, whereas the roughness parameters were arranged in the columns of a table (called input matrix in the fields of chemometrics). Data reduction has not been carried out, as no constant or highly correlated variables were present. On the other hand, the above roughness parameters spanned over considerably different scales; therefore, proper scaling was unavoidable, using the most prevalent scaling options: NOR, RNK, SCL, and STD.
The NOR, often confused with STD, scales each variable to unit length, that is, it divides each matrix element by the column Euclidian norm (L2-norm) where i = 1, 2, ..., n is the number of rows (samples) in the input matrix. RNK substitutes the numerical values with rank numbers (also column wise), the smallest number receives rank number one, the second smallest two, and so on. STD is carried out in two steps: (i) centering (column mean is subtracted from each matrix element) and (ii) each centered matrix element is divided by the standard deviation of the respective column. It is denoted by STD.
4.5. Sum of Ranking Differences. This technique was recently developed for fair method comparison and readily received general usage from chromatographic column comparison 37 to multicriteria decision making. 38 It can easily be perceived that an actual method that is "closer" to a gold standard (reference) is better than any other alternative. Here, the nine roughness parameters defined in part 2.3 have been compared by SRD. It is interesting to know, which one is the best among them, which ones are equivalent, and whether there are any significant differences among them. The SRD technique coupled with ANOVA can answer these questions easily.
Row-averages were used as the gold standard (benchmark) as the biases of different measurement techniques also follow normal distribution, which is a widely and unambiguously accepted empirical finding in analytical chemistry (e.g., laboratories are compared using z-scores 39 with the assumption of normality in proficiency testing). After this data fusion operation, a column by column evaluation follows: the calculation of (absolute) differences between the standard and the individual vector rank-coordinates, and summation of the absolute differences for each sample. These values are the sum of the absolute ranking differences and are abbreviated as SRD. SRD values rank and group the individual roughness parameters.
The basic idea of SRD calculations is presented in ref 40 The SRD values are, in fact, Hamming or city block distances where r i is the rank number of object i for the actual roughness parameter and q i is the rank number of object i for the gold standard, here the row-average. Generally, only the normalized SRD values (scaled between 0 and 100) are plotted on the x and y axes, that is, not the line lengths carry information, but line grouping and closeness of lines to zero [i.e., a "good" roughness parameter is closer to the gold standard (reference) than a "worse" one], and their overlapping with the distribution of SRD values for randomized rank numbers. The latter is also plotted to the right y axis; overlapping means that the respective roughness parameter(s) is (are) indistinguishable from random ranking. This randomization test is called comparison of ranks with random numbers and denoted as CRRN. 41 Identical numbers in the input matrix may distort the ranking procedure; however, ranking with ties is also possible, using partial ranking: 40 our visual basic application program for MS Excel is downloadable from: http://aki.ttk.mta.hu/srd. All details, SRD distributions, and theoretical background are given in our earlier works. 40−42 The only limitation for SRD procedure is the too small number of rows: though the algorithm starts at the row number of three, the probability of accidental decision is heightened, then. Empirical evidences suggest that above the row number of six, the random ranking is negligible.
The entire SRD procedure contains not only the calculation of Hamming, or city block distances, but involves two validation steps: (i) a randomization test as shown above and (ii) n-fold cross-validation. The computer code allows calculating 5-to 10-fold cross-validation in a stratified and in a random manner (repeated resampling). In this work, we used where b 0 , b 1 , b 2 , ..., b 12 , and so forth, are constants. Altogether 885 roughness values were evaluated: 2 (treatment options) × 4 (scan areas) × 9 (roughness measures) × ∼12 (repetitions). The raw data can be found in Table S1.
(ii) A factorial ANOVA on SRD values: rescaling of the roughness parameters and ordering by SRD allows revealing more effects by factorial ANOVA. 43 The first ANOVA coupling with SRD has already been published in 2014. 44 Uncertainty values were assigned to SRD values by use of a sevenfold cross-validation as follows. Approximately 1/7th of the samples were removed with repetitions many times. SRD ranking of roughness parameters was completed on the remaining (approximately 6/7th) of the samples, that is, on the training sets, and the left-out part was simply ignored. As the number of samples during cross-validation is smaller, the variance is slightly overestimated (a conservative estimation). Roughness parameters were considered as factor 3 also here (F 3 ), except for the peak count that was excluded from further analysis. Four data preprocessing options were considered in SRD calculations (F 4 ): NOR, RNK, SCL, and STD, see part 2.4. Sevenfold cross-validation multiplied by the SRD values many (14) times: in such a way 9 (roughness parameters) × 4 (preprocessing methods) × 14 (repetitions) = 448 SRD values were calculated and the effects of factors and their interactions were decomposed. The following model was considered All statistical tests and ANOVA calculations were carried out by STATISTICA (data analysis software system), version 7.1. The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.9b04211.
Original data set; effect of plasma treatment at two levels, before and after treatment; effect of various ways to determine roughness by AFM; and normal probability plots of residuals showing improper and considerably better modeling (PDF)