# Hygroexpansion and Surface Roughness Cause Defects and Increase the Electrical Resistivity of Physical Vapor Deposited Aluminum Coatings on Paper

^{1}

^{2}

^{*}

## Abstract

**:**

_{EFF}of aluminum coatings. The sheet resistance of aluminum coated onto four different rough paper surfaces was measured via eddy currents at different relative humidity (0%–95%). The mass of aluminum per unit area was determined by inductively-coupled plasma mass spectrometry (ICP–MS). We calculated ρ

_{EFF}based on the measured resistance and aluminum mass per unit area, combined with a value for aluminum density from the literature. The substrate roughness was proportional to ρ

_{EFF}. Relative humidity correlated with the moisture content of the paper substrate according to the Guggenheim, Anderson, and De Boer (GAB) equation, whereas the moisture content showed a linear correlation with hygroexpansion. At relative humidity of up to 50%, hygroexpansion was linearly correlated with the increase in ρ

_{EFF}, which is related to the mechanical straining and deformation of aluminum. At higher humidity, aluminum started to crack first on rough substrates and later on smooth substrates. The increase in ρ

_{EFF}was larger on rough substrates. The findings highlight the need for information about substrate roughness, humidity, and hygroexpansion when eddy current measurement results are compared, and will help to ensure that aluminum coatings, applied by PVD, are defect-free.

## 1. Introduction

^{−6}mbar) so the water evaporates and the paper shrinks. After metallization, the paper is transferred to humid air and subsequently expands as water enters from the uncoated side. Consequently, the aluminum coating is strained and eventually cracks [3].

_{0}) of up to 2.2 were reported at a strain of 20% for copper coatings [14,15,16,17], with equivalent values of 3% at 20% strain for silver coatings [18] and 15,000 at 20% strain for aluminum coatings, depending on strain speed and aluminum thickness [19]. Moreover, this behavior was time dependent [19] and was influenced by the adhesion between the polymeric substrate and coating [14]. The fracture characteristics of such ductile materials must be carefully distinguished from those of brittle coatings such as silicon oxide or indium oxide [20]. To the best of our knowledge, the impact of hygroexpansion and roughness on the appearance of defects in aluminum coatings on paper substrates has not been investigated in detail, and it is unclear whether this can be monitored by measuring electrical resistance [21]. In this study, we therefore addressed the following questions:

- How does surface roughness correlate with the sheet resistance and effective resistivity of an aluminum coating?
- How does relative humidity (RH) affect the hygroexpansion of paper and how does it correlate with the sheet resistance and effective resistivity of the aluminum coating?
- Is there interdependency between substrate roughness and the sensitivity of aluminum coatings toward hygroexpansion?

_{Z}, the sorption isotherm and the hygroexpansion were determined. Then, the respective four different paper surfaces (coated and non-coated sides of the two different papers) were PVD-coated with aluminum. The amount of aluminum (d

_{NOMINAL}) was determined by inductively coupled plasma-mass spectrometry (ICP-MS) in combination with a value for aluminum density from the literature, and the resistance (R) of the coating was measured at different RH values. From d

_{NOMINAL}and R, the effective resistivity ρ

_{EFF}was derived. The increase of ρ

_{EFF}was determined according to the RH.

## 2. Materials and Methods

#### 2.1. Abbreviations

#### 2.2. PVD Coating of Aluminum on Paper

^{2}(Ahlstrom-Munksjö Oyj, Stockholm, Sweden) and Nikla Select with a grammage of 70 g/m

^{2}(Brigl & Bergmeister, Niklasdorf, Austria). Paper samples were cut to a size of 105 × 148 mm

^{2}. The samples were taped along all four edges onto a Metalkote paper carrier roll using thermally stable adhesive tape (Kapton, DuPont, Wilmington, DE, USA).

^{2}box coater (Leybold Vacuum, Cologne, Germany) at Fraunhofer IVV. This coater was adapted for the roll-to-roll coating of polymer webs by the introduction of deposition roll, un-winding and re-winding equipment (Lenze, Hameln, Germany). The equipment was controlled using VAC Cluster Tool Controller L560 (AIS Automation, Dresden, Germany). The box coater was equipped with a 160-m

^{3}/h, E2M175 rotary vacuum pump and a 505-m

^{3}/h EH500 roots pump (both from Edwards, UK), and a 850–1150-L/s TMP 1000 turbomolecular pump (Leybold Vacuum) to create a vacuum down to ~10

^{−6}mbar. Remaining moisture in the chamber was extracted using a Meissner cold trap (nitrogen-cooled copper pipe) and the deposition roll was water cooled. The pressure was determined using a PPT 100 Pirani gauge and a HPT100 hot-cathode Bayard–Alpert–Pirani wide-range gauge (both from Pfeiffer, Aßlar, Germany). The EV M-10 electron beam source with a 270° configuration was combined with a 10-kW Genius Carrera high voltage supply (both from Ferrotec, Unterensingen, Germany). The aluminum we used had a purity of 99.98%. The coating thickness was varied by changing the web speed from 0.5 to 3.5 m/min at steps of 0.5 m/min and an evaporation rate of 2–3.5 nm/s. During the evaporation process, the pressure in the chamber ranged from 10

^{−4}to 10

^{−5}mbar, resulting in an approximate mean free path of 0.9–9 m [12].

#### 2.3. Determination of Sheet Resistance via Eddy Currents at Different RH Values

^{2}and filled with 30 g silica gel. They were stored, together with the paper carrier roll, in the HDPE drum with silica gel.

_{■}) was measured using the eddy current method (EddyCus TF lab 4040, Suragus, Dresden, Germany). The skin depth with the applied set up was > 8 µm, which ensures the full penetration of the aluminum layer by the magnetic field. The area captured by the measurement was approximately 5 × 5 mm

^{2}. The sheet resistance R

_{■}of a resistor with thickness d and resistivity ρ is defined as

_{EFF}was then calculated from the thickness determined by ICP-MS (d

_{NOMINAL}) and the measured sheet resistance (R

_{■}):

#### 2.4. Inductively-Coupled Plasma—Mass Spectrometry (ICP-MS)

^{2}or 15 cm

^{2}, the aluminum was stripped off using 50, 30, 20, 10, or 5 mL 1.0 M of sodium hydroxide solution (Chemsolute 1.0 mol/L, Th. Geyer GmbH, Renningen, Germany). The volume of 1.0 M sodium hydroxide used was taken as the sample volume (V). After 1 h, the samples were mixed within the tubes and the liquid aluminous sample was diluted with double-distilled water. The dilution factor (f) was 1:10 or 2:10. The amount of aluminum in these diluted samples was determined using an Agilent 770x ICP-MS (Agilent Technologies, Santa Clara, CA, USA). We used an aluminum standard solution for calibration (ICP-multi-element standard solution IV 1.11355.0100; Merck, Darmstadt, Germany). The aluminum concentration of the standard solution was 1000 mg/L. For calibration, this standard solution was diluted with double-distilled water to concentrations of 0.10, 0.20, 0.25, 0.30, 0.50, 0.75, 1.00, 1.50, 2.00, 3.00, and 3.50 mg/L aluminum. The calibration delivered the correlation for the given concentration with signal intensity. This correlation allowed us to calculate the concentration (c) [mg/L] of aluminum in each sample from the signal intensity.

_{NOMINAL}was calculated using the determined concentration of aluminum c and a bulk value for density (δ

_{lit}) of 2.7 g/cm

^{3}taken from the literature [22], as shown in Equation (4). The coating weight (cw

_{NOMINAL}) [g/m

^{2}] was calculated according to Equation (5) [23].

#### 2.5. Sorption Isotherm

_{0}[g/100 g fiber] the monolayer moisture content, RH the relative humidity, and h and c are constants. c is a measure of the strength of binding of water to the primary binding sites, whereas h is a correction factor, which corrects the properties of the multilayer molecules relative to the bulk liquid [25,26]. The equation was fitted to the data using OriginPro 2016 (OriginLab Corporation, Wellesley Hills, MA, USA) and the Levenberg–Marquardt algorithm.

#### 2.6. Hygroexpansion

^{2}) from each paper. The samples were dried for 20 days in silica gel at 23 °C. Then, each was stored in the KBF720-230V climate chamber at 23 °C for 24 h, with sequentially increasing RH values of 35%, 50%, 70%, 85%, and 95%. The samples were taken one by one from the drum/climate chamber and scanned at a resolution of 1200 dpi (CanonScan LiDE 700F, Canon, Krefeld, Germany). Images were saved as a jpg file. Subsequently, the distance between certain measuring points (l

_{0,CD}, l

_{0,MD}) was measured using LAS v4.0 software (Leica Microsystems GmbH, Wetzlar, Germany). On each sample, we took three CD and three MD measurements. From these data, the percentage length increase ε at increasing RH values was calculated by setting l

_{0,CD}and l

_{0,MD}in relation to the increased lengths l

_{CD}and l

_{MD}, as shown in Equation (7).

#### 2.7. Surface Roughness

_{z}. In this method, the traversing length l

_{n}is divided into five equal-sized subsections l

_{r}, chosen according to DIN EN ISO 4288:1998 [27] and DIN EN ISO 3274:1998 [28] (in this case, 0.8 and 2.5 mm, respectively). In the single subsections, the single roughness Z

_{n}was determined. The single roughness is the difference between the highest and lowest points in one subsection l

_{r}[29]. From Z

_{n}, R

_{Z}is determined as the arithmethic average.

#### 2.8. Scanning Electron Microscopy (SEM)

#### 2.9. Statistical Methods

## 3. Results

#### 3.1. Surface Characterization via SEM and EDX

_{Z}are only used to describe certain features of a much more complex surface structure. To obtain a better visual impression, surface images were obtained by SEM (Figure 3).

#### 3.2. Effect of Substrate Roughness on Sheet Resistance and Resistivity

_{NOMINAL}on the sheet resistance is visible (for measurements at 50% RH). Apparently the sheet resistance (R

_{■}) inversely correlates with the aluminum thickness. This correlation is significantly different for different paper substrates, indicating that the resistivity is not the same on all paper substrates. Thus, the effective resistivity (ρ

_{EFF}) is calculated from the measured sheet resistance (R

_{■}) and the thickness (d

_{NOMINAL}) (Equation (2)).

_{EFF}was neither constant nor close to the value reported in the literature. In detail, four observations can be made from this figure.

_{OFFSET}[Ω∙nm] at high aluminum thickness, superimposed by a variable resistivity ρ

_{n}[Ω∙nm] at lower thickness (Equation (8)).

_{OFFSET}would not achieve literature values for bulk aluminum ρ

_{lit}. This can partially be explained as material properties are influenced by the PVD process conditions. Such process conditions include the residual oxygen and water vapor pressures, the kinetic energy of evaporated aluminum atoms, and the mean free path length. However, obviously a second factor affects the values, because the minimum resistivity ρ

_{OFFSET}increases with substrate roughness (Equation (9)). This can be explained; as a low roughness leads to small defects which can easily become overgrown with aluminum. In comparison, defects on very rough papers are too large to become overgrown, thus increasing the resistance R and minimum resistivity ρ

_{OFFSET}.

_{n}also depends on paper roughness R

_{Z}(Equation (10)).

_{n}(Equation (11)).

_{Z}) and ρ

_{OFFSET}(R

_{Z}) are functions of R

_{Z}. The individual numbers for these functions can be obtained for each experimental curve in Figure 5 by fitting Equation (12) to the data points (least square method). However it is not yet clear what f(R

_{Z}) and ρ

_{OFFSET}(R

_{Z}) actually are. To test this, the obtained numbers from the fit above are plotted versus R

_{Z}(Figure 6) so that the scaling of these functions becomes clear: f(R

_{Z}) correlates linearly with a slope c of 2964 Ω∙nm

^{2}/µm (Equation (13)). The scaling for ρ

_{OFFSET}(R

_{Z}) is obtained similarly to be linear with a slope of k = 0.5/µm. Additionally the linear plot intersects the y-axis and the respective y-value corresponds to ρ

_{lit}(Figure 7, Equation (14)). The correlation in ρ

_{OFFSET}(R

_{Z}) is less explicit. This may reflect the additional effects on ρ

_{OFFSET}, such as the effect of foreign atoms.

^{2}= 0.88). The results show that the resistivity is not constant, but rather increases with decreasing thickness. Additionally, roughness increases the resistivity, and this effect is much more pronounced.

#### 3.3. Effect of Substrate Hygroexpansion on Resistivity

#### 3.3.1. Sorption Isotherm

#### 3.3.2. Moisture Content and Hygroexpansion

#### 3.3.3. Relative Humidity and Hygroexpansion

#### 3.4. Effect of Hygroexpansion on Effective Resistivity

- Increasing humidity and thus hygroexpansion leads to an increase in resistance and effective resistivity (Figure 12). This implies that aluminum is stretched due to the hygroexpansion of the underlying paper, and hence cracks appear. The values shown are similar to those reported previously [3], where an increase in RH from 35% to 90% at 23 °C increased the resistance by about 40% for silver ink coatings.
- Initially, the increase in resistivity is almost linear with a strain with a small slope (Figure 12). The initial increase in resistivity follows the theoretical calculation according to Equation (20) [14]. This equation is based on the assumption that the volume of aluminum (cross section A × length l) is constant under tension ε, namely A ∙ l = A
_{0}∙ l_{0}. Under tension, the material thins out and thus A decreases and l increases due to plastic deformation. From that assumption Equations (18) to (20) are derived. Based on this correlation and Equation (17), γ can be calculated from the RH, as in Equation (21).$$\frac{R}{{R}_{0}}={\left(\frac{\mathrm{l}}{{l}_{0}}\right)}^{2}$$$$\frac{\mathsf{\rho}}{{\mathsf{\rho}}_{0}}={\left(\frac{l}{{l}_{0}}\right)}^{2}={\left(1+\mathsf{\epsilon}\right)}^{2}$$$$\mathsf{\gamma}=\frac{\mathsf{\rho}}{{\mathsf{\rho}}_{0}}-1={\left(1+\mathsf{\epsilon}\right)}^{2}-1$$$$\mathsf{\gamma}={\left(1+a\xb7\frac{{M}_{0\text{}}\xb7c\xb7h\xb7\mathrm{RH}}{\left(1-h\xb7\mathrm{RH}\right)\xb7\left(1-h\xb7\mathrm{RH}\text{}+c\xb7h\xb7\mathrm{RH}\right)}\right)}^{2}-1$$ - Higher substrate roughness leads to more imperfections and thus a lower crack onset strain (COS) (Figure 12). The COS is the strain where γ deviates from the linear region, according to Equations (21) and (20). The COS indicates the appearance of defects in the shapes of necks and cracks in the aluminum. These cracks strongly increase the resistance and thus the nominal resistivity [15]. The COS is reached at RH values of ~70% (ε
_{CD}≈ 0.6%) on paper surfaces without CC, but ~85% (ε_{CD}≈ 1.2%) on paper surfaces with CC. This indicates that the COS is lower for rougher surfaces (paper without CC), because higher roughness induces a heterogeneous thickness distribution and thus the appearance of defects. Defects can lead to local necks, which can cause further intense localized deformation, resulting in fast rupture [15]. - Higher substrate roughness leads to more cracks and a higher γ (Figure 14). γ on the rough side of the paper (without CC) is higher than that on the smooth side of the paper (with CC). As described in the previous observation, this leads to more defects, which consequently cause more voids and lead to a higher γ.
- The effect of aluminum thickness on γ cannot be defined (Figure 14). As the influence of roughness is much more pronounced than the effect of aluminum thickness, no clear correlation between aluminum thickness and γ can be observed. This is in line with the comparably low impact of thickness, as seen in Figure 8.

## 4. Conclusions

- Substrate roughness and hygroexpansion both increase the resistance and effective resistivity of aluminum coatings.
- Hygroexpansion increased the resistivity less than substrate roughness. When aluminum thickness is determined via eddy currents, these factors should either be taken into account or a standard material representing each process/substrate combination should initially be fully characterized, so that each new measurement can be related to the standard material.
- The effect of substrate roughness and aluminum thickness on resistance and effective resistivity can be mathematically modeled. The effect of substrate roughness becomes more pronounced for thinner coatings.
- When paper expands due to the uptake of water, the applied aluminum is stretched so that the effective resistivity increases. For low RH values, the relative effective resistivity increase γ correlates linearly with hygroexpansion and can thus easily be linked to RH via basic physical assumptions.
- γ is higher for rougher substrates. Moreover, aluminum has a lower crack onset strain on rough substrates.
- The effect of aluminum thickness on the relative effective resistivity increase is low and most probably superimposed by roughness and hygroexpansion.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Details of the experimental procedures and work flow used in this study. Following abbreviations are used: RH: relative humidity; mc: moisture content; ICP-MS: inductively coupled plasma-mass spectrometry, and R

_{■}: sheet resistance.

**Figure 3.**SEM images of the four paper surfaces that were PVD-coated with aluminum. Scale bars indicate 10 and 1 µm, respectively. The visible surface roughness induces defects in the aluminum coating and increases the electrical resistance.

**Figure 4.**Correlation between sheet resistance and aluminum thickness (lines are included for visual clarity).

**Figure 5.**Correlation between aluminum thickness and resistivity; fitted black lines according to Equation (12).

**Figure 8.**Correlation between substrate roughness R

_{Z}, aluminum thickness d

_{NOMINAL}, and effective resistivity ρ

_{EFF}, as described by Equation (15).

**Figure 12.**(

**a**) Metalkote with clay coating; (

**b**) Metalkote without clay coating; (

**c**) Nikla Select with clay coating; (

**d**) Nikla Select without clay coating. Correlation between the relative effective resistivity increase (γ) and CD hygroexpansion of Metalkote and Nikla Select on the sides of paper with and without clay coating (CC). γ sets the resistivity at a certain relative humidity (RH) in relation to the resistivity at 0% RH or 0% hygroexpansion, respectively. The linear slope represents the increase of resistivity due to the pure three-dimensional deformation, as described in Equations (20) and (21). Hygroexpansion, substrate roughness, and aluminum thickness affect γ and the crack onset strain (COS).

**Figure 13.**Relative effective resistivity increase (γ) at the crack onset strain (COS). This was at 85% relative humidity (RH) on Metalkote and Nikla Select with a clay coating (CC) and 70% RH on Metalkote and Nikla Select without a clay coating.

**Figure 14.**(

**a**) Relative effective resistivity increase (γ) at 85% relative humidity (RH); (

**b**) relative effective resistivity increase (γ) at 95% RH. Each for different aluminum thicknesses. No clear impact of thickness is visible. However, rougher surfaces led to greater γ (compare cases with and without clay coating [CC]).

Parameter | Metalkote | Nikla Select |
---|---|---|

M_{0} | 0.02693 | 0.02177 |

C | 20.2559 | 3382.55465 |

h | 0.87096 | 0.87546 |

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**MDPI and ACS Style**

Lindner, M.; Heider, J.; Reinelt, M.; Langowski, H.-C.
Hygroexpansion and Surface Roughness Cause Defects and Increase the Electrical Resistivity of Physical Vapor Deposited Aluminum Coatings on Paper. *Coatings* **2019**, *9*, 33.
https://doi.org/10.3390/coatings9010033

**AMA Style**

Lindner M, Heider J, Reinelt M, Langowski H-C.
Hygroexpansion and Surface Roughness Cause Defects and Increase the Electrical Resistivity of Physical Vapor Deposited Aluminum Coatings on Paper. *Coatings*. 2019; 9(1):33.
https://doi.org/10.3390/coatings9010033

**Chicago/Turabian Style**

Lindner, Martina, Julia Heider, Matthias Reinelt, and Horst-Christian Langowski.
2019. "Hygroexpansion and Surface Roughness Cause Defects and Increase the Electrical Resistivity of Physical Vapor Deposited Aluminum Coatings on Paper" *Coatings* 9, no. 1: 33.
https://doi.org/10.3390/coatings9010033