Calculation of the Contact Angle of Polymer Melts on Tool Surfaces from Viscosity Parameters

Article Calculation of the Contact Angle of Polymer Melts on Tool Surfaces from Viscosity Parameters

Gernot Zitzenbacher 1,* ID , Hannes Dirnberger 1, Manuel Längauer 1 and Clemens Holzer 2

1 Department of Materials Technology, School of Engineering, University of Applied Sciences Upper Austria, 4600 Wels, Austria; [email protected] (H.D.); [email protected] (M.L.) 2 Department Polymer Engineering and Science, Chair of Polymer Processing, Montanuniversitaet Leoben, 8700 Leoben, Austria; [email protected] * Correspondence: [email protected]; Tel.: +43-(0)50804-44520

Received: 18 October 2017; Accepted: 22 December 2017; Published: 30 December 2017

Abstract: It is of great importance for polymer processing whether and how viscosity inﬂuences the wettability of tool surfaces. We demonstrate the existence of a distinct relationship between the contact angle of molten polymers and zero shear viscosity in this paper. The contact angle of molten polypropylene and polymethylmethacrylate on polished steel was studied in a high temperature chamber using the sessile drop method. A high pressure capillary rheometer with a slit die was employed to determine the shear viscosity curves in a low shear rate range. A linear relation between the contact angle and zero shear viscosity was obtained. Furthermore, the contact angle and the zero shear viscosity values of the different polymers were combined to one function. It is revealed that, for the wetting of tool surfaces by molten polymers, a lower viscosity is advantageous. Furthermore, a model based on the temperature shift concept is proposed which allows the calculation of the contact angle of molten polymers on steel for different temperatures directly from shear viscosity data.

Keywords: polypropylene; polymethylmethacrylate; contact angle; viscosity; tool surface; wetting; injection molding; extrusion

1. Introduction Many phenomena in polymer processing are influenced by the wettability of solid surfaces by polymer melts. The wettability of solid surfaces in tools and molds affects the replication of surface structures and remolding forces in injection molding. As an example, in micro injection molding the wettability of the mold surface and the temperature dependence of viscosity near the glass transition temperature are important for the replication of surface structures [1]. Ejection forces decrease linearly with the contact angle of the polymer melt on the mold coating [2]. Rytka et al. [3] reported that the dewetting potential correlates well with the replicated height of different mold structures. A lower dewetting potential of a polymer leads to a better replication accuracy. Wettability also affects the polymer melt flow in flow channels and dies. Fluoropolymers on die surfaces influence wall slip and shark skin in polymer melt rheology. Hatzikiriakos et al. [4] investigated the effect of fluoropolymer coatings on high density polyethylene (HDPE). Seidel et al. [5] found that polyetheretherketone (PEEK) and polytetrafluoroethylene (PTFE) induce wall slip of the polymer melt and cause a smooth extrudate surface. Agassant et al. [6] reported that coatings such as PTFE, which enhance slip at the wall, reduce or even eliminate sharkskin. Hard coatings, which are often applied to screws and tools by physical vapor deposition (PVD) or plasma assisted chemical vapor deposition (PACVD), and metals can also influence the polymer melt flow and the extrudate appearance. Ramamurthy [7] studied the effect of different metals on wall slip and on the extrudate appearance of polyethylene. He observed that beryllium copper as

Polymers 2018, 10, 38; doi:10.3390/polym10010038 www.mdpi.com/journal/polymers Polymers 2018, 10, 38 2 of 12 a die material causes a lower critical wall shear stress for the onset of wall slip compared to steel. Rauwendaal [8] reported that the reduction of the pressure loss in a spiral mandrel extrusion die with a Lunac coating can be obtained. Zitzenbacher et al. [9,10] investigated the effect of diamond-like carbon (DLC), titanium nitride (TiN), titanium aluminum nitride (TiAlN), and steel on wall slip of a polypropylene copolymer and polymethylmethacrylate (PMMA). It was observed that a higher polarity as exhibited by TiN reduces wall slip of PP, especially at higher temperatures. PMMA slips only on polished steel, but no slip was found on DLC. Young’s equation [11] is needed to describe the wetting of a solid surface by a liquid

σSL = σS − σLcosθ (1)

It is obtained from a balance of the surface energy between the liquid and the solid σSL, the surface energy of the solid σS and the surface tension of the liquid σL including the contact angle θ at the three phase points of liquid, solid, and surrounding atmosphere. According to Kumar [12] a complete wetting (θ = 0◦), a partial wetting (0◦< θ < 90◦), a partial non-wetting (90◦ < θ < 180◦) and a total non-wetting (θ = 180◦) can be distinguished. Although the wettability of solid substrates is often determined at room temperature, the contact angle in the polymer melt state is needed for the explanation of phenomena which are related to the interface between polymers and tool or screw materials. Schonhorn et al. [13] investigated the wetting of aluminum, mica, and Teflon by an ethylene-vinyl acetate copolymer and polyethylene melts. Silberzan et al. [14] studied the spreading behavior of poly(dimethylsiloxane) (PDMS) liquids on silica surfaces at room temperature through optical microscopy and ellipsometry. Anastasiadis et al. [15] investigated the wetting of molten linear low density and high density polyethylene on steel and fluoropolymer coatings. Wulf et al. [16] studied the surface tension of a polystyrene melt dependent on temperature in a sessile drop experiment. Wouters et al. [17] determined the surface tension of epoxy resins, polyesters, and additives. Kopczynska [18] and Yang et al. [19] investigated the surface tension of molten polycarbonate (PC), polystyrene (PS), styrene acrylonitrile (SAN), polyethylene (PE), and polyamide 6 (PA 6). Zitzenbacher et al. [20] studied the contact angle of molten polypropylene (PP), HDPE, PMMA, and Polyamid 6.6 (PA 6.6) on steel and different coatings such as titanium aluminum nitride (TiAlN), titanium nitride (TiN), chromium nitride (CrN), silicone doped diamond-like carbon (DLC), and polytetrafluoroethylene (PTFE). They observed a decrease in the contact angle of the molten polymers with a rising surface energy of the coating. Vera et al. [21] investigated the contact angle of molten PP, acrylonitrile butadiene styrene (ABS), and PC on steel, different titanium nitride coatings (TiNOx, TiNOy, and TiNOz), CrN, and DLC. Furthermore, they measured the surface tension of the molten polymers and evaluated work of adhesion on the solid substrates. It is of great importance for polymer melt flow and surface structure replication whether and how viscosity influences the wettability of tool surfaces, especially in processes such as injection molding and extrusion technology. Furthermore, shear viscosity curves are often more easily available, but the contact angle of polymer melts on solid surfaces can only be determined in time consuming experiments. The goal of this paper was to study the influence of shear viscosity on the contact angle of molten polymers on tool steel. The contact angle was determined employing the sessile drop method in a high temperature chamber and the shear viscosity curves were measured in a low shear rate range using a high pressure capillary rheometer with a slit die. Furthermore, the contact angle and the shear viscosity curves were determined at elevated temperatures. It is demonstrated that the contact angle of the molten polymers is a function of zero shear viscosity. The data of the two different polymeric materials, PP and PMMA, are combined to one function. As a final result, a model is proposed to calculate the contact angle of polymer melts on steel for different temperatures directly from zero shear viscosity. Polymers 2018, 10, 38 3 of 12

2. Materials and Methods A polypropylene homopolymer (PP) HD 120 MO, produced by Borealis, Linz, Austria, and a polymethylmethacrylate (PMMA) PLEXIGLAS 7M from Evonik, Darmstadt, Germany, were investigated in this study in order to gain a better understanding about their processing behavior. PP HD 120 MO has a melt flow rate (MFR) of 8 g (10 min)−1 at 230 C/2.16 kg and is used for injection molding applications. PMMA PLEXIGLAS 7M has a MFR of 3.45 g (10 min)−1 at 230 ◦C/3.80 kg and is employed for extruded profiles and panels. The MFR values mentioned were taken from the material datasheets. The testing temperature range of the polymeric materials was chosen according to the material suppliers’ recommended melt temperature range. PP was studied at a temperature of 185, 200, 210, and 220 ◦C. The testing temperature of PMMA was 230, 240, 250, and 260 ◦C, respectively. PMMA was predried before the experiments. The viscosity curves of these polymeric materials were determined using a high pressure capillary rheometer Rheograph 6000, produced by Goettfert, Buchen, Germany, with a slit die. The slit die concept was employed because it allows the measurement of viscosity data in a low shear rate range, which was chosen between 0.1 and 350 s−1. Furthermore, directly measured pressure data is obtained which leads to true wall shear stresses, without having to use Bagley correction. First, the polymeric material was filled into the reservoir channel, melted, and heated up to the defined temperature. The slit die was heated to the same temperature. When extruding the melt, the piston velocity was increased stepwise in order to obtain rheological data at different apparent wall shear rate values. The wall shear stress τw was evaluated according to Walters [22]

HW ∆p τ = (2) w 2(H + W) ∆L where H is the height of the flow channel, W is the width of the flow channel, ∆L is the distance between the pressure transducers, and ∆p is the measured pressure loss. The apparent wall shear stress is . 6Q γ = (3) ap WH2 where Q is the volume flow rate. The Weissenberg–Rabinowitsch equation [23,24] was used to obtain the true shear rate at the wall

 .  . d γ . γap log ap γw = 3 +  (4) 4 d(logτw)

Shear viscosity η can then be evaluated by introducing Equations (2) and (4) in Equation (5)

τw η = . (5) γw

The measurement and evaluation of the viscosity dependent on shear rate was conducted at least four times at each temperature. A mean value was calculated from these data at each shear rate value to obtain the ﬁnal viscosity curve. The shear viscosity curve was approximated with the Bird-Carreau-Yasuda model [24] using the least squares method

n−1 . h . ai a η γ = η0 1 + λγ (6) where η0 is zero shear viscosity, λ is a time constant, n is the Power Law index, and a accounts for the width of the transition region between zero shear viscosity and the Power Law region. A Drop Shape Analyzer DSA 30S, produced by Kruess, Hamburg, Germany, with a high temperature chamber TC 21 was employed to measure the contact angle of the molten PP and PMMA Polymers 2018, 10, 38 4 of 12 on steel with the sessile drop method. The experiments were carried out under nitrogen atmosphere with a gas ﬂow rate of 20 NL·h−1 to avoid thermooxidative degradation of the polymeric materials. A schematic diagram of the test setup is shown in [20]. The X38CrMoV5 1 steel discs with a diameter of 40 mm and a thickness of 10 mm were heat treated and polished to an area-weighted surface roughness Sa of 15.1 ± 5.7 nm. The surface roughness of the steel samples was determined by means of a confocal microscope DCM3D, Leica Microsystems, Wetzlar, Germany at three positions on the sample, one in the center, and two 10 mm from the center, once in x- and once in y-direction. Before the contact angle measurements the steel discs were cleaned carefully with isopropanol using a tissue and dried with an air stream. Afterwards, thePolymers steel sample2017, 9, 38 was placed in the high temperature chamber and preheated 15 min to obtain a uniform4 of 12 temperature distribution. MicroInsystems, the next Wetzlar, step, the Germany polymer sampleat three waspositions placed on on the the sample, solid one surface in the with center a pair, and of two tweezers. 10 mm Thefrom positioning the center, ofonce the in polymer x- and once sample in y- wasdirection. conducted Before as the fast contact as possible angle measurements to avoid substantial the steel temperaturediscs were decreasecleaned andcarefully high nitrogenwith isopropanol loss in the using high temperaturea tissue and chamber. dried with After an melting air stream. the polymerAfterwards sample,, the thesteel drop sample shape was was placed recorded in the dependent high temperature on time withchamber a CCD and camera preheated with 15 a framemin to rateobtain of 1 a fps. uniform The contact temperature angle wasdistribution evaluated. using the recorded video data. The drop contour was approximatedIn the next with step a polynomial, the polymer function sample near was the placed base line. on the The solid slope surface of the approximationwith a pair of functiontweezers. inThe the positioning contact point of of the the polymer three phases sample was usedwas conducted to evaluate as the fast contact as possible angle. Each to avoid test was substantial carried outtemperature at least three decrease timesin and order high to verifynitrogen its loss reproducibility in the high and temperature a mean value chamber. was calculated. After melting the polymer sample, the drop shape was recorded dependent on time with a CCD camera with a frame 3.rate Results of 1 fps. The contact angle was evaluated using the recorded video data. The drop contour was approximated with a polynomial function near the base line. The slope of the approximation 3.1. Shear Viscosity Curves function in the contact point of the three phases was used to evaluate the contact angle. Each test was carriedThe out shear at least viscosity three oftimes PP in and order PMMA to verify dependent its reproducibility on shear rate and ata mean different value temperatures was calculated. is represented as the approximated curves in Figures1 and2. Table1 shows the Bird-Carreau-Yasuda parameters3. Results at different temperatures T, including the zero shear viscosity η0, the time constant λ, the Power Law index n, the width of the transition region a and the coefﬁcient of determination R2. The3.1. good Shear reproducibilityViscosity Curvesof the tests is indicated by the standard deviation of the measured shear viscosityThe values shear whichviscosity is dependent of PP and on PMMA shear rate dependent and temperature on shear betweenrate at different 0.5% and temperatures 4.8%. is representedBoth polymer as the melts approximated exhibit shear curves thinning in Figure behavior,s 1 and which 2. Table means 1 shows that shearthe Bird viscosity–Carreau decreases–Yasuda withparameters rising shear at different rate. Furthermore, temperatures shear T, inc viscosityluding the decreases zero shear with viscosity rising η temperature.0, the time constant The shear λ, the viscosityPower Law curve index of PP n, revealsthe width a negative of the transitio slope evenn region at low a and shear the rates.coefficientThe width of determination of the Newtonian R². The tableaugood reproducibility of PMMA decreases of the with tests rising is temperature.indicated by The the good standard approximation deviation of of the the measured measured viscosity shear 2 dataviscosity with thevalues Bird-Carreau-Yasuda which is dependent model on shear is indicated rate and by temperature the coefficient between of determination, 0.5% and 4.8R%..

10000 T = 185 °C T = 200 °C T = 210 °C T = 220 °C

1000 (Pa s) η

100 Shear viscosity

10 0.10 1 10 100 1000 . -1 Shear rate γ (s ) FigureFigure 1. Shear 1. Shear viscosity viscosity of ofpolypropylene polypropylene dependent dependent on on shear shear rate rate at atdifferent different temperatures. temperatures.

10000 T = 230 °C T = 240 °C T = 250 °C T = 260 °C

1000 (Pa s) η

100 Shear viscosity

10 0.10 1 10 100 1000 . -1 Shear rate γ (s ) Figure 2. Shear viscosity of polymethylmethacrylate dependent on shear rate at different temperatures.

Polymers 2017, 9, 38 4 of 12

Microsystems, Wetzlar, Germany at three positions on the sample, one in the center, and two 10 mm from the center, once in x- and once in y-direction. Before the contact angle measurements the steel discs were cleaned carefully with isopropanol using a tissue and dried with an air stream. Afterwards, the steel sample was placed in the high temperature chamber and preheated 15 min to obtain a uniform temperature distribution. In the next step, the polymer sample was placed on the solid surface with a pair of tweezers. The positioning of the polymer sample was conducted as fast as possible to avoid substantial temperature decrease and high nitrogen loss in the high temperature chamber. After melting the polymer sample, the drop shape was recorded dependent on time with a CCD camera with a frame rate of 1 fps. The contact angle was evaluated using the recorded video data. The drop contour was approximated with a polynomial function near the base line. The slope of the approximation function in the contact point of the three phases was used to evaluate the contact angle. Each test was carried out at least three times in order to verify its reproducibility and a mean value was calculated.

3. Results

3.1. Shear Viscosity Curves The shear viscosity of PP and PMMA dependent on shear rate at different temperatures is represented as the approximated curves in Figures 1 and 2. Table 1 shows the Bird–Carreau–Yasuda parameters at different temperatures T, including the zero shear viscosity η0, the time constant λ, the Power Law index n, the width of the transition region a and the coefficient of determination R². The good reproducibility of the tests is indicated by the standard deviation of the measured shear viscosity values which is dependent on shear rate and temperature between 0.5% and 4.8%.

10000 T = 185 °C T = 200 °C T = 210 °C T = 220 °C

1000 (Pa s) η

100 Shear viscosity

10 0.10 1 10 100 1000 . Shear rate γ (s-1) Polymers 2018, 10, 38 5 of 12 Figure 1. Shear viscosity of polypropylene dependent on shear rate at different temperatures.

10000 T = 230 °C T = 240 °C T = 250 °C T = 260 °C

1000 (Pa s) η

Polymers 2017, 9, 38 5 of 12 100 Both polymer melts exhibitShear viscosity shear thinning behavior, which means that shear viscosity decreases with rising shear rate. Furthermore, shear viscosity decreases with rising temperature. The shear viscosity curve of PP reveals 10a negative slope even at low shear rates. The width of the Newtonian 0.10 1 10 100 1000 . tableau of PMMA decreases with rising temperature.Shear rate γ (sThe-1) good approximation of the measured

viscosity data with the Bird–Carreau–Yasuda model is indicated by the coefficient Figureof determinationFigure 2. Shear 2. viscosityShear, R². viscosity of polymethylmethacrylate of polymethylmethacrylate dependent dependent on shear on rate shear at different rate at temperatures. different temperatures. TableTable 1. Bird-Carreau-Yasuda 1. Bird–Carreau–Yasuda parameters parameters of of the the polymerspolymers PP PP and and PMMA PMMA at different at different temperatures temperatures T includingT including the zerothe zero shear shear viscosity viscosityη 0η,0, the the timetime constantconstant λλ, ,the the Power Power Law Law index index n, then, thewidth width of the of the transitiontransition region regiona, and a, and the the coefﬁcient coefficient of of determination determination R²2. .

Polymer T (°C) ◦ η0 (Pa·s) λ (s) n (-) a (-) 2 R² Polymer T ( C) η0 (Pa·s) λ (s) n (-) a (-) R PP 185 3777.92 0.1059 0.27 0.68 1.00 PP 185 3777.92 0.1059 0.27 0.68 1.00 PP PP200 200 2628.462628.46 0.0368 0.0368 0.15 0.640.64 1.00 1.00 PP PP210 210 2210.412210.41 0.0472 0.0472 0.23 0.610.61 1.00 1.00 PP PP220 220 1719.041719.04 0.0358 0.0358 0.21 0.650.65 1.00 1.00 PMMA 230 5993.19 0.0574 0.35 1.62 1.00 PMMA PMMA230 240 5993.193585.80 0.0574 0.0141 0.35 0.08 0.851.62 1.00 1.00 PMMA PMMA240 250 3585.802213.47 0.0141 0.0054 0.08 0.00 0.630.85 1.00 1.00 PMMA 260 1553.75 0.0041 0.00 0.60 1.00 PMMA 250 2213.47 0.0054 0.00 0.63 1.00 PMMA 260 1553.75 0.0041 0.00 0.60 1.00 3.2. Contact Angle of the Molten Polymers The3.2. Contact contact Angle angle of the ofMolten the Polymers molten polymers on polished steel depends on temperature. Figures3 andThe 4contactshow angle the meanof the molten values polymer of the measureds on polished contact steel depends angle data on temperature. at different temperatures,Figures 3 includingand 4 theirshow positivethe mean andvalues negative of the measured deviations. contact The angle contact data angleat different values temperatures were taken, including at the end of the testtheir runs positive to ensure and negative stable deviations conditions.. The PP contact and PMMA angle values reveal were a decrease taken at the in theend contactof the test angle runs with risingto temperature. ensure stable Theconditions. contact PP angle and of PMMA molten reveal PP on a polisheddecrease steelin the is contact 85.0◦, 77.1angle◦, 72.6with◦ ,rising and 67.1◦ at temperaturestemperature.of The 185, contact 200, 210,angle and of 220molten◦C, PP respectively. on polished The steel low is 85.0°, positive 77.1°, and 72.6° negative, and 67.1° deviations at temperatures of 185, 200, 210, and 220 °C, respectively. The low positive and negative deviations indicate the high reproducibility of the tests. indicate the high reproducibility of the tests. ◦ TheThe contact contact angle angle of of molten molten PMMA PMMA onon polishedpolished steel steel is is 101.8, 101.8, 80.0, 80.0, 71.3 71.3,, and and68.0 68.0°C at Ca at a ◦ ◦ temperaturetemperature of 230,of 230, 240, 240, 250, 250,and and 260 °C,C, respectively. respectively. At the At temperature the temperaturess of 230 ofand 230 260 and°C, the 260 C, the positivepositive andand negative deviations deviations are are higher. higher.

120

100 )

° 80

Contact angle( 40

0 185 200 210 220 Temperature (°C)

FigureFigure 3. Contact 3. Contact angle angle of of molten moltenpolypropylene polypropylene on on steel steel at atdifferent different temperatures. temperatures.

PolymersPolymers2018 2017,,10 9,, 3 388 66 ofof 1212 Polymers 2017, 9, 38 6 of 12 120 120

100 100 )

° 80 )

° 80

60 60

Contact angle( 40

20 20

0 0 230 240 250 260 230 240Temperature (°C)250 260 Temperature (°C)

Figure 4. Contact angle of molten polymethylmethacrylate on steel at different temperatures. FigureFigure 4 4.. ContactContact angle angle of of molten molten polymethylmethacrylate polymethylmethacrylate on on steel steel at at different different temperatures. temperatures. 3.3. Relation Between the Contact Angle and Zero Shear Viscosity 3.3.3.3. Relation Relation B Betweenetween the the C Contactontact A Anglengle and and Z Zeroero S Shearhear V Viscosityiscosity Zero shear viscosity depends on material and process parameters. The consideration that the contactZZeroero angle shear shear of viscosity polymer dependsmelts on toolon material surfaces and could process be influenced parameters parameters. in a. similarT Thehe consideration consideration manner compared that that the the to contactcontactviscosity angle angle was of ofthe polymer polymer motivation melts melts to on onstudy tool tool thesurfaces surfaces relation could could between be be influenced influenced the contact in in a aangle similar similar and manner manner zero shear compared compared viscosity. to to viscosityviscosityThe mean was was values the the motivation motivation of the measured to to study study contactthe the relation relation angle between between data were the the contact contactplotted angle anglein dependence and and zero zero shear shear of zero viscosity. viscosity. shear TTheviscosityhe meanmean ( valuesseevalues Table of of the 1the). measuredThe measured dependence contact contact angleof the angle datacontact data were angle were plotted of plotted molten in dependence in PP dependence and ofPMMA zero shearof on zero zero viscosity shear shear viscosity(seeviscosity Table ( 1seeis). The presentedTable dependence 1). The in dependenceFigure of thes contact5 and of the6 angle. Thecontact of measured molten angle PPof data andmolten PMMAwere PP andapproximated on zeroPMMA shear on viscositywithzero shearlinear is viscositypresentedfunctions is inusing presented Figures the5 leastand in 6 Figure.squares The measureds 5method. and 6 data. TheThe were measuredapproximation approximated data functionwere with approximated linears and functions the coefficients with using linear the of 2 functionsleastdetermination squares using method. R the² are least g Theiven approximationsquares in Equation method.s ( functions7) andThe (8approximation) and the coefficients function of determinations and the coefficientsR are given of determinationin Equations (7) R² and are (8)given in Equations (7) and (8) PP: = 0.0086 + 53.34, 2 = 0.98 (7) PP : θ = 0.0086η0 + 53.34, R = 0.98 (7) PP: = 0.0086 + 53.34, 2= 0.98 (7) 0 PMMAPMMA: : 𝜃𝜃θ ==0.00770.0077𝜂𝜂η ++54.52,54.52𝑅𝑅2R, 2 ==0.990.99 (8)(8) 𝜃𝜃 𝜂𝜂0 0 𝑅𝑅 PMMA: = 0.0077 + 54.52, 2= 0.99 (8) 2 02 The Thevalues values of the of coefficient the coefficient of determination of determination𝜃𝜃 R are𝜂𝜂R slightlyare slightly below𝑅𝑅2 below 1, which 1, which indicates indicates a good a linear good 2 0 Thelinearcorrelatio values correlationn of between the betweencoefficient the contact the of contact determination angle angleand𝜃𝜃 zero and R shear zeroare𝜂𝜂 slightly shearviscosity viscosity. below𝑅𝑅. 1, which indicates a good linear correlatioTheThe n slopesslope betweens of Equation Equations the contacts ( (7)7 angle) and and (and (8)8) are arezero 0.0086 0.0086 shear and andviscosity 0.0077 0.0077. (Pa (Pa∙s)·−s)1,− respectively.1, respectively. Furthermore, Furthermore, the −1 thedifference differenceThe slope betweens between of Equation the the distancess distances (7) and on (8) onthe are the contact 0.0086 contact andangle angle 0.0077 coordinate coordinate (Pa∙s) ,axis respectively. axis of of Equation Equations Furthermore,s ( (7)7) and (8)( 8t)he isis differenceratherrather low.low b. TheseetweenThese valuesvalues the distances areare 53.3453.34 ◦on° forfor the PPPP contact andand 54.4254.42 angle◦° forfor coordinate PMMA.PMMA. axis of Equations (7) and (8) is rather low. These values are 53.34° for PP and 54.42° for PMMA. 120 120

100 100 )

° 80 ( ) θ

° 80 ( θ 60 60

40 Contact angle 40 Contact angle

20 20

0 0 0 1000 2000 3000 4000 5000 6000 7000 η 0 1000 2000Zero shear3000 viscosity4000 0 (Pa·s)5000 6000 7000 η Zero shear viscosity 0 (Pa·s) Figure 5. Contact angle of the molten polypropylene on steel dependent on zero shear viscosity and Figure 5. Contact angle of the molten polypropylene on steel dependent on zero shear viscosity and Figureapproximated 5. Contact with angle a linear of the function molten. polypropylene on steel dependent on zero shear viscosity and approximated with a linear function. approximated with a linear function.

Polymers 2018, 10, 38 7 of 12 Polymers 2017, 9, 38 7 of 12

Polymers 2017, 9, 38 120 7 of 12

120 100

) 100 °

( 80 θ ) °

( 80 60 θ

Contact angle 40

Contact angle 40 20

20 0 0 1000 2000 3000 4000 5000 6000 7000 Zero shear viscosity η (Pa·s) 0 0 0 1000 2000 3000 4000 5000 6000 7000 Figure 6. Contact angle of molten polymethylmethacrylateη on steel dependent on zero shear Figure 6. Contact angle of molten polymethylmethacrylateZero shear viscosity 0 on(Pa·s) steel dependent on zero shear viscosity viscosity and approximated with a linear function. andFigure approximated 6. Contact with angle a linear of molten function. polymethylmethacrylate on steel dependent on zero shear Ifviscosity the contact and appro angleximated can be with calculated a linear function. directly from zero shear viscosity for one polymer, this equationIf the could contact be the angle same can for be other calculated polymers. directly The contact from zero angle shear values viscosity of PP and for onePMMA polymer, were If the contact angle can be calculated directly from zero shear viscosity for one polymer, this thisplotted equation dependent could on be thezero same shear for viscosity other polymers. in one diagram The contact and angleapproximated values of with PP and one PMMA linear equation could be the same for other polymers. The contact angle values of PP and PMMA were werefunction plotted to pro dependentve this hypothesis on zero shear(see Figure viscosity 7) in one diagram and approximated with one linear functionplotted todependent prove this on hypothesis zero shear (see viscosity Figure7) in one diagram and approximated with one linear function to prove this hypothesis (see= Figure0.0077 7) + 54.92, = 0.98 (9) 2 θ = 0.0077η0 + 54.92, R =2 0.98 (9) Although PP and PMMA are completely𝜃𝜃 = 0 different.0077𝜂𝜂0 + polymeric54.92, 𝑅𝑅 materials= 0.98 , the relation between contact(9) angle and zero shear viscosity follows one function, which2 is supported by the coefficient of AlthoughAlthough PP and PP PMMA and PMMA are completely are completely different different0 polymeric polymeric materials materials,, the relation the relation between between contact determination R² of 0.98. Now, the contact𝜃𝜃 angle𝜂𝜂 of a polymer𝑅𝑅 melt on polished steel can directly be contactangle and angle zero and shear zero shearviscosity viscosity follows follows one onefunction, function, which which is issupported supported by by the the coefﬁcientcoefficient ofof calculated from zero shear viscosity of this material using Equation (9), but for a generalization of determinationdeterminationR R2² ofof 0.98.0.98. Now,Now, thethe contactcontact angleangle ofof aa polymerpolymer meltmelt onon polishedpolished steelsteel cancan directlydirectly bebe this finding, further experiments with other polymers are required. calculatedcalculated from from zero zero shear shear viscosity viscosity of of this this material material using using Equation Equation (9), ( but9), but for afor generalization a generalization of this of ﬁnding, further experiments with other polymers are required. this finding, further120 experiments with other polymers are required.

120 100 )

° 100 PP ( 80 θ PMMA )

° PP ( 80 θ 60 PMMA

60 40 Contact angle

40 Contact angle 20

20 0 0 1000 2000 3000 4000 5000 6000 7000 η 0 Zero shear viscosity 0(Pa·s) 0 1000 2000 3000 4000 5000 6000 7000 η Figure 7. Material invariant master curveZero of theshear contact viscosity angle 0(Pa·s) of molten polymers on steel dependent on zero shear viscosity and approximated with a linear function. FigureFigure 7. 7.Material Material invariantinvariant mastermastercurve curveof of thethe contactcontactangle angleof ofmolten molten polymerspolymerson on steelsteel dependentdependent 3.4. Implementationonon zero zero shear shear viscosity viscosity of a Temperature and and approximated approximated Shift Factor with with for a a linear thelinear Contact function. function. Angle

3.4. ImplementationZero shear viscosity of a Temperature η0 at different Shift temperatures Factor for the CT ontactcan be A calculatedngle from zero shear viscosity at a reference temperature T0 employing the temperature shift concept Zero shear viscosity η0 at different temperatures T can be calculated from zero shear viscosity at a reference temperature T0 employing the temperature( ) = ( ) shift, ( concept) (10)

0 0 0 𝑇𝑇 η where aT,η is the temperature shift factor for𝜂𝜂 ( 𝑇𝑇shear) =𝜂𝜂 viscosity.(𝑇𝑇 )𝑎𝑎 , (𝑇𝑇 ) (10)

The temperature shift factor of viscosity0 can 0be 0expressed𝑇𝑇 η at temperatures, T, well above the where aT,η is the temperature shift factor for𝜂𝜂 𝑇𝑇shear𝜂𝜂 viscosity.𝑇𝑇 𝑎𝑎 𝑇𝑇 glass transition temperature Tg (T > Tg + 100 °C) using Arrhenius’ law [25] The temperature shift factor of viscosity can be expressed at temperatures, T, well above the

glass transition temperature Tg (T > Tg + 100 °C) using Arrhenius’ law [25]

Polymers 2018, 10, 38 8 of 12

3.4. Implementation of a Temperature Shift Factor for the Contact Angle

Zero shear viscosity η0 at different temperatures T can be calculated from zero shear viscosity at a reference temperature T0 employing the temperature shift concept

η0(T) = η0(T0)aT,η(T) (10) where aT,η is the temperature shift factor for shear viscosity. The temperature shift factor of viscosity can be expressed at temperatures, T, well above the glass ◦ transition temperature Tg (T > Tg + 100 C) using Arrhenius’ law [25] E0 1 1 aT,η(T) = − (11) R T T0

◦ where E0 is the activation energy and R is the gas constant. The glass transition temperature is 108 C for PMMA and 0 ◦C for PP, respectively. It is assumed that the contact angle θ(T) at a certain temperature can be calculated from the contact angle at a reference temperature θ(T0) using a temperature shift factor aT,θ

θ(T) = θ(T0)aT,θ(T) (12)

Because of the linear relation between contact angle and zero shear viscosity and under consideration of Equation (9) the slope k can be expressed as

θ(T) − θ(T ) k = 0 = 0.0077 (13) η0(T) − η0(T0)

Introducing Equations (10) and (12) in Equation (13) yields

θ(T )[a θ(T) − 1] k = 0 T, (14) η0(T0)[aT,η(T) − 1]

Then, the temperature shift factor aT,θ for the contact angle can be expressed from Equation (14)

η0(T0) aT,θ(T) = k· ·[aT,η(T) − 1] + 1 (15) θ(T0)

After introducing Equation (15) in Equation (12), the contact angle θ can be calculated at different temperatures T from zero shear viscosity at reference temperature η0(T0) and from the temperature shift factor of viscosity aT,η

θ(T) = 0.0077η0(T0)[aT,η(T) − 1] + θ(T0) (16)

In the next step, this model was applied to the studied polymers. The temperature shift factor of viscosity aT,η of the polymer melts was calculated by employing Equations (10) and (11). The zero shear viscosity values η0, which were determined at different temperatures (see Table1), were shifted to the lowest temperature to obtain the activation energy, E0. A mean value for the activation energy was calculated from these data. The evaluated parameters for the calculation of the contact angle θ of PP and PMMA according to Equation (16) are given in Table2. A comparison of the calculated contact angle from viscosity parameters to the experimental determined values is presented in the Figures8 and9 . The negligible deviations between the calculated contact angle curve and the experimentally determined values conﬁrm the validity of the proposed model. It has to be considered that errors in the calculated values can occur below and above the studied temperature range. Polymers 2018, 10, 38 9 of 12

Table 2. Reference temperature T0, activation energy E0, zero shear viscosity at reference temperature η0(T0), and contact angle at reference temperature θ(T0) for the calculation of the temperature dependent contact angle from viscosity parameters of the polymers polypropylene (PP) and polymethylmethacrylate (PMMA) on steel.

◦ −1 ◦ Polymer T0 ( C) E0 (kJ·mol ) η(T0) (Pa·s) θ(T0)( ) PP 185 42.92 3777.92 85.0 PMMA 230 109.62 5993.19 101.8 Polymers 2017, 9, 38 9 of 12 Polymers 2017, 9, 38 9 of 12 120 120 Calculated 100 ExperimentalCalculated 100 Experimental ) °

( 80 ) θ °

( 80 θ 60 60

Contact angle 40

20 20

0 0170 180 190 200 210 220 230 240 170 180 190 Temperature200 210T (°C) 220 230 240 Temperature T (°C) FigureFigure 8.8. Comparison of the contact angleangle calculatedcalculated fromfrom viscosityviscosity parametersparameters toto experimentalexperimental Figure 8. Comparison of the contact angle calculated from viscosity parameters to experimental determineddetermined valuesvalues ofof moltenmolten polypropylenepolypropylene onon steelsteel dependentdependent onon temperature.temperature. determined values of molten polypropylene on steel dependent on temperature. 120 120 Calculated 100 ExperimentalCalculated 100 Experimental ) °

( 80 ) θ °

( 80 θ 60 60

Contact angle 40

20 20

0 0220 230 240 250 260 270 220 230 Temperature240 T (250°C) 260 270 Temperature T (°C) Figure 9. Comparison of the contact angle calculated from viscosity parameters to experimental FiguredeterminedFigure 9.9. Comparison values of molten of the polymethylmethacrylate contactcontact angleangle calculatedcalculated on fromfrom steel viscosity viscositydependent parametersparameters on temperature. toto experimentalexperimental determineddetermined valuesvalues ofof moltenmolten polymethylmethacrylatepolymethylmethacrylate onon steelsteel dependentdependent onon temperature.temperature. 4. Discussion 4. Discussion 4. DiscussionAccording to Young [11], the contact angle θ of a liquid on a solid is influenced by the surface According to Young [11], the contact angle θ of a liquid on a solid is influenced by the surface energyAccording of the solid, to Young the surface [11], thetension contact of the angle liquidθ of and a liquid the surface on a solid energy is influencedbetween the by solid the surfaceand the energy of the solid, the surface tension of the liquid and the surface energy between the solid and the energyliquid. ofWe the observed solid, the a decrease surface tension in the ofcontact the liquid angle and of polymer the surface melts energy on polished between thesteel. solid The and reason the liquid. We observed a decrease in the contact angle of polymer melts on polished steel. The reason liquid.for this We dependency observed a originate decreases in in the the contact decrease angle of ofthe polymer surface meltstension on of polished liquids steel.and polymer The reason melts for for this dependency originates in the decrease of the surface tension of liquids and polymer melts thiswith dependency rising temperature originates. S ineveral the decrease authors ofreported the surface the tensiondecrease of liquidsof surface and polymertension with melts rising with with rising temperature. Several authors reported the decrease of surface tension with rising risingtemperature temperature.. Eötvös Several [26] proposed authors reportedan equation the decreasewhich predicts of surface a linear tension dependence with rising of temperature. the surface temperature. Eötvös [26] proposed an equation which predicts a linear dependence of the surface Eötvöstension [of26 ]a proposedliquid on antemperature. equation whichOther predictsauthors [ a16 linear–19] observed dependence a decrease of the in surface surface tension tension of of a tension of a liquid on temperature. Other authors [16–19] observed a decrease in surface tension of liquidepoxy onresins, temperature. polyesters Other, PE, authorsPC, PS, [PMMA16–19], observed and PA melts a decrease with inrising surface temperature. tension of Furthermore, epoxy resins, epoxy resins, polyesters, PE, PC, PS, PMMA, and PA melts with rising temperature. Furthermore, polyesters,the decrease PE, in PC,the PS,contact PMMA, angle and of the PA molten melts with polymer risings temperature.on polished steel Furthermore, is influenced the by decrease a change in ofthe the decrease surface in energy the contact between angle steel of andthe moltenthe polymer polymer meltss on with polished rising steel temperature. is influenced by a change of theWe surface obtained energy a linear between relation steel between and the thepolymer contact melts angle with of therising molten temperature. polymer s and zero shear viscosity.We obtained This means a linear that relation the contact between angle the increases contact withangle rising of the zeromolten shear polymer viscosity.s and It zero has shearto be consideredviscosity. This that means zero shear that theviscosity contact can angle be influencedincreases with by temperature, rising zero shear pressure viscosity., and theIt has average to be molecularconsidered weight.that zero The shear used viscosity zero shearcan be viscosity influenced values by temperature, were obtained pressure from, andthe therheological average measurementmolecular weight. of shear The viscosity used zero curves shear at different viscosity temperatures values were and obtained fit the well from-known the rheologicalconcept of temperaturemeasurement shift of shear of viscosity viscosity. This curves temperature at different shift temperatures can be calculated and fitusing the thewell Arrhenius-known concept Equation of (seetemperature Equation shift (11)) of or viscosity the Will. iamsThis– temperatureLandel–Ferry shift Equation can be [calculated27] using the Arrhenius Equation (see Equation (11)) or the Williams–Landel–Ferry Equation [27] ( ) , ( ) = ( ) (17) ( ) = 1+ 0 (17) , −𝐶𝐶 𝑇𝑇 − 𝑇𝑇 𝑇𝑇 𝜂𝜂 1+ 0 𝑙𝑙𝑙𝑙𝑙𝑙𝑎𝑎 𝑇𝑇 −2𝐶𝐶 𝑇𝑇 − 𝑇𝑇0 𝑇𝑇 𝜂𝜂 𝐶𝐶 𝑇𝑇 − 𝑇𝑇 𝑙𝑙𝑙𝑙𝑙𝑙𝑎𝑎 𝑇𝑇 2 0 𝐶𝐶 𝑇𝑇 − 𝑇𝑇 Polymers 2018, 10, 38 10 of 12 the contact angle of the molten polymers on polished steel is influenced by a change of the surface energy between steel and the polymer melts with rising temperature. We obtained a linear relation between the contact angle of the molten polymers and zero shear viscosity. This means that the contact angle increases with rising zero shear viscosity. It has to be considered that zero shear viscosity can be influenced by temperature, pressure, and the average molecular weight. The used zero shear viscosity values were obtained from the rheological measurement of shear viscosity curves at different temperatures and fit the well-known concept of temperature shift of viscosity. This temperature shift can be calculated using the Arrhenius Equation (see Equation (11)) or the Williams-Landel-Ferry Equation [27]

−C1(T − T0) logaT,η(T) = (17) C2 + T − T0 which both depend exponentially on temperature. Herein, C1 and C2 are material specific parameters and T0 is the reference temperature. In this study, we found that based on the linear correlation between the contact angle of molten polymers and zero shear viscosity the temperature shift concept can also be applied to the contact angle of dependence of zero shear viscosity also determine temperature dependence of the contact angle polymer melts on steel surfaces. The Arrhenius Equation is based on the thermally activated overcoming of energy barriers in rotational potentials of molecule segments. When considering a melt drop on a steel surface, temperature change will lead to a rearrangement of the polymer chains so that the equilibrium of forces in the three-phase point between melt, atmosphere, and solid substrate remains fulfilled. We state that the same mechanisms which determine temperature of polymer melts on steel. It was also shown that the obtained relation between the contact angle and zero shear viscosity is a linear function, independent of the polymer used. This relation was verified for PP and PMMA. Other polymers have to be studied to enable a generalization of this relation between the contact angle and zero shear viscosity. Furthermore, zero shear viscosity depends on the average molecular weight. The average molecular weight and the width of the molecular weight distribution influence shear viscosity curves. When polymer grades with the same distribution width but different average molecular weight are compared, the viscosity curve with the higher average molecular weight is shifted to higher zero shear viscosity values. The reason can be found in zero shear viscosity η0, which exhibits a dependence on the average molecular weight Mw [28] a η0 ∼ Mw (18) where a is approximately 3.4. This means that zero shear viscosity of the same polymer increases with rising average molecular weight according to a power law. This study does not yet include grades with different average molecular weight, but there are plans to study in future work if molecular weight influences the contact angle in a similar way to temperature.

5. Conclusions Currently, the contact angle of molten polymers on solid substrates can only be determined in time consuming experiments at different high temperatures, but shear viscosity curves are often more easily available for polymeric materials. We demonstrate in this paper that viscosity inﬂuences the wetting of steel by molten polymers. The contact angle of molten polypropylene and polymethylmethacrylate on polished steel was directly calculated from zero shear viscosity. The obtained linear equation is valid for both polymers and allows the assignment of a certain zero shear viscosity to a contact angle value. Furthermore, for the wetting of solid surfaces by molten polymers as it takes place in injection molding, a lower viscosity is advantageous because the contact angle decreases with falling zero shear viscosity. The zero shear viscosity depends strongly on temperature and can be assigned with a shift factor to a Polymers 2018, 10, 38 11 of 12 certain temperature. Since temperature dependence of the wettability is of great interest, we proposed a model to calculate the contact angle at different temperatures directly from the temperature shift factor of viscosity, zero shear viscosity, and the contact angle at a reference temperature. The validity of our model is conﬁrmed by the good agreement with the experimentally determined contact angle values. As a prospect for future work, other polymers and tool materials have to be studied to enable a generalization of the relation between the contact angle and zero shear viscosity.

Acknowledgments: Financial support for vital parts of this project was provided by the State Government of Upper Austria and the European Union in the measure IWB 2020: ProFVK. Author Contributions: Gernot Zitzenbacher conceived and designed the experiments; Hannes Dirnberger and Manuel Längauer performed the experiments; Gernot Zitzenbacher, Hannes Dirnberger, Manuel Längauer, and Clemens Holzer analyzed the data; Gernot Zitzenbacher wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

References

1. Sorgato, M.; Masato, D.; Lucchetta, G. Effect of Vacuum Venting and Mold Wettability on the Replication of Micro-structured Surfaces. Microsyst. Technol. 2017, 23, 2543–2552. [CrossRef] 2. Pegoraro, A. Analysis of the Effect of Different Coatings on Ejection Forces in Micro Injection Moulding. Ph.D. Thesis, Università degli Studi di Padova, Padova, Italy, 13 April 2017. 3. Rytka, C.; Opara, N.; Andersen, N.K.; Kristiansen, P.M.; Neyer, A. On The Role of Wetting, Structure Width, and Flow Characteristics in Polymer Replication on Micro- and Nanoscale. Macromol. Mater. Eng. 2016, 301, 597–609. [CrossRef] 4. Hatzikiriakos, S.G.; Dealy, J.M. Effects of Interfacial Conditions on Wall Slip and Sharkskin Melt Fracture of HDPE. Int. Polym. Process. 1993, 8, 36–43. [CrossRef] 5. Seidel, C.; Merten, A.; Münstedt, H. The Die Material Influences the Melt Flow Behaviour: Plastic Extrusion Dies. Kunstst. Int. 2002, 10, 59–61. 6. Agassant, J.-F.; Arda, D.R.; Combeaud, C.; Merten, A.; Münstedt, H.; Mackley, M.R.; Robert, L.; Vergnes, B. Polymer Extrusion Instabilities and Methods for their Elimination or Minimisation. Int. Polym. Process. 2006, 21, 239–255. [CrossRef] 7. Ramamurthy, A.V. Wall Slip in Viscous Fluids and Influence of Materials of Construction. J. Rheol. 1986, 30, 337–357. [CrossRef] 8. Rauwendaal, C.J. Efficient Troubleshooting of Extrusion Problems. In Proceedings of the Polymer Processing Society Conference 2015, Graz, Austria, 21–25 September 2015. 9. Zitzenbacher, G.; Bayer, T.; Huang, Z. Influence of Tool Surface on Wall Sliding of Polymer Melts. Int. J. Mater. Prod. Technol. 2016, 52, 17–36. [CrossRef] 10. Zitzenbacher, G.; Huang, Z.; Holzer, C. Experimental Study and Modeling of Wall Slip of Polymethylmethacrylate Considering Different Die Surfaces. Polym. Eng. Sci. 2017, 1–8. [CrossRef] 11. Young, T. An Essay on the Cohesion of Fluids. Philos. Trans. R. Soc. Lond. 1805, 95, 65–87. [CrossRef] 12. Kumar, G.; Prabhu, K.N. Review of Non-reactive and Reactive Wetting of Liquids on Surfaces. Adv. Colloid Interface Sci. 2007, 133, 61–89. [CrossRef][PubMed] 13. Schonhorn, H.; Frisch, H.L.; Kwei, T.K. Kinetics of Wetting of Surfaces by Polymer Melts. J. Appl. Phys. 1966, 37, 4967–4973. [CrossRef] 14. Silberzan, P.; Léger, L. Spreading of High Molecular Weight Polymer Melts on High-Energy Surfaces. Macromolecules 1992, 25, 1267–1271. [CrossRef] 15. Anastasiadis, S.H.; Hatzikiriakos, S.G. The Work of Adhesion of Polymer/Wall Interfaces and its Association with the Onset of Wall Slip. J. Rheol. 1998, 42, 795–811. [CrossRef] 16. Wulf, M.; Michel, S.; Grundke, K.; del Rio, O.I.; Kwok, D.Y.; Neumann, A.W. Simultaneous Determination of Surface Tension and Density of Polymer Melts Using Axisymmetric Drop Shape Analysis. J. Colloid Interface Sci. 1999, 210, 172–181. [CrossRef][PubMed] 17. Wouters, M.; de Ruiter, B. Contact-angle Development of Polymer Melts. Prog. Org. Coat. 2003, 48, 207–213. [CrossRef] Polymers 2018, 10, 38 12 of 12

18. Kopczynska, A. Oberﬂächenspannungsphänomene bei Kunststoffen—Bestimmung und Anwendung. Ph.D. Thesis, University Erlangen-Nueremberg, Nueremberg, Germany, 2008. 19. Yang, D.; Xu, Z.; Liu, C.; Wang, L. Experimental Study on the Surface Characteristics of Polymer Melts. Colloids Surf. A 2010, 367, 174–180. [CrossRef] 20. Zitzenbacher, G.; Huang, Z.; Längauer, M.; Forsich, C.; Holzer, C. Wetting Behavior of Polymer Melts on Coated and Uncoated Tool Steel Surfaces. J. Appl. Polym. Sci. 2016, 133, 1–10. [CrossRef] 21. Vera, J.; Contraires, E.; Brulez, A.-C.; Larochette, M.; Valette, S.; Benayoun, S. Wetting of Polymer Melts on Coated and Uncoated Steel Surfaces. Appl. Surf. Sci. 2017, 410, 87–98. [CrossRef] 22. Walters, K. Rheometry; John Wiley & Sons: New York, NY, USA, 1975. 23. Rabinowitsch, B. Über die Viskosität und Elastizität von Solen. Z. Phys. Chem. 1929, 145, 1–26. [CrossRef] 24. Osswald, T.; Rudolph, N. Polymer Rheology: Fundamentals and Applications; Hanser Publishers: Munich, Germany, 2015. 25. Liu, C.Y.; He, J.; Keunings, R.; Bailly, C. New Linearized Relation for the Universal Viscosity−Temperature Behavior of Polymer Melts. Macromolecules 2006, 39, 8867–8869. [CrossRef] 26. Eötvös, R. Ueber den Zusammenhang der Oberﬂächenspannung der Flüssigkeiten mit ihrem Molecularvolumen. Ann. Phys. 1886, 263, 448–459. [CrossRef] 27. Williams, M.L.; Landel, R.F.; Ferry, J.D. The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-forming Liquids. J. Am. Chem. Soc. 1955, 77, 3701–3707. [CrossRef] 28. Staudinger, H.; Heuer, W. Über hochpolymere Verbindungen, 33. Mitteilung: Beziehungen zwischen Viscosität und Molekulargewicht bei Poly-styrolen. Ber. Dtsch. Chem. Ges. 1930, 63, 222–234. [CrossRef]

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