The authors would like to thank to Heraeus Precious Metals GmbH &amp; Co. KG for their support and supply of commercial silver pastes, especially M. K&#246;nig for fruitful discussions. Special thanks go to M. Schmalz for experimental support. C. Y&#252;ce gratefully acknowledges financial support by the 100 prozent erneuerbar stiftung. Finally, we acknowledge financial support from the Federal Ministry for Economic Affairs and Energy (Grant no. 0325775G).

<ol>
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The authors have nothing to disclose.

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the manifold requirements during processing and application of such complex fluids. This investigation includes the determination of yield stress, viscosity, wall slip velocity, structural recovery after large deformation and elongation at break as well as tensile force during filament stretching. A summary of all applied methods, obtained information, and paste characteristics are summarized in Table 1.
The importance of video recordings for reliable determination of rheological quantities of highly filled suspensions showing wall slip, shear banding and sample spillover in parallel-plate rotational rheometry is demonstrated. Video recordings enable the determination of the true deformation profile and the flow field at the sample rim using appropriate markers. It is necessary to study this deformation behavior before analyzing the results of rheological experiments. Thus measurement parameter settings and plate roughness values can be identified for which viscosity measurements are possible. The paste yield stress can be determined either using a vane geometry or plate-plate geometry with appropriate roughness.
Viscosity determination is possible using plate-plate geometry only with a carefully selected plate roughness depending on sample composition. Higher roughness does not necessarily result in lower wall slip. The shear rate or shear stress range in which viscosity determination can be done is limited by the yield stress and the onset of sample spill.
Furthermore, the slip velocity can be measured directly and measuring conditions at which plug flow, shear banding or sample spillover occur can be identified clearly. For wall slip measurements smooth surfaces were used as the upper shearing plate and a rough bottom plate to allow slip only at the upper plate. This slip velocity can be calculated directly from the angular velocity of the upper plate. For both pastes slip occurs at stress levels well below the apparent yield stress. Similar observations have been reported for suspensions of glass beads25, clay suspensions27, soft microgel pastes as well as for emulsions28,29,30. Here a linear increase of vslip with &#964;app is found. This is in line with the observations of Aral et al.25 who also determined vslip using visualization of the flow field at the rim of the investigated glass bead suspensions.
Seth et al. have shown that the scaling of slip velocity with applied stress is controlled by the interaction between the soft particles they used in their study and the wall. For the case where there is no specific adherence of particles to the wall, they also find a linear relationship between vslip and stress but a quadratic scaling is found for the particles weakly adhering to the wall28,29,30. The studies on soft particle pastes also reveal a characteristic slip velocity V* at the yield stress and a elastohydrodynamic model is presented29 allowing to calculate V* from physical fluid and particle parameters which can be determined independently: V*&#160;~&#160;&#947;y2&#160;(G0&#160;R&#160;/&#160;&#951;s)&#160;(GP&#160;/&#160;G0)1/3. This characteristic slip velocity depends on the pastes yield strain &#947;y and elastic modulus G0, solvent viscosity &#951;s, as well as particle radius R and modulus GP. The values resulting from this simple estimate (VA* = 375 &#181;m s-1 and VB* = 118 &#181;m s-1) agree very well with the experimental results (Figure 9) not only with respect to the order of magnitude but also regarding the difference between paste A and B.
Sample spillage is observed here at a critical rotational speed characteristic for each paste. Spillage does not occur in the pure vehicles. This phenomenon limits rheological characterization of the pastes and may also be relevant for certain processing or coating operations but its physical origin still remains unsolved.
Video recordings further indicate that wall slip, plug flow and sample spill can be excluded during oscillatory shear tests. Therefore, the decrease and increase in shear moduli observed during three stage oscillatory shear tests with small oscillation amplitude in stage I and III as well as large deformation amplitude <img alt="Equation" src="/files/ftp_upload/55377/55377eq2.jpg" /> &#62;<img alt="Equation" src="/files/ftp_upload/55377/55377eq2.jpg" />c can be directly attributed to structural break down and recovery. It could be shown that the degree of irreversible structural change during oscillatory shear increases with increasing deformation amplitude in stage II until a saturation is reached at deformations corresponding to the crossover of G&#39; and G&#39;&#39; in the amplitude sweep test, but the irreversible damage is independent of the duration of high amplitude shear in stage II. The change in modulus and hence sample structure due to large shear deformation in stage II is termed irreversible here since after waiting times of more than 104 s, the storage modulus is far lower than its initial value (data not shown). The data shown in Figure 15 are restricted to waiting times of 1,500 s for the sake of clearness. However, it should be noted that the time scale of the printing process is on the order of seconds or even below. This is not accessible with the conventional rotational rheometer setup used in this study.
The gap heights used in this study are also much larger than typical mesh openings in screen-printing of modern printed electronics. Rheological measurements using plate-plate geometry cannot be done at such small gap openings due to limitations of mechanical adjustment for large plates typically used in rheological measurements. Furthermore, large gap separations have been chosen here to ease visualization of the sample deformation at the rim.
Filament stretching tests using a capillary breakup elongational rheometer and a tensile tester can be used to characterize the deformation and breakup behavior of highly filled pastes in elongational flows. The elongation at the break and the maximum force during elongation are parameters obtained from these tests and may be related to the squeegee snap-off during screen-printing.
Finally, significant differences were observed in all the experiments described above for the two commercial silver pastes investigated in this study. An extended discussion of the relevance of the rheological paste properties for their performance will be addressed in a subsequent paper based on data for a broad variety of different pastes and vehicles.

Front side metallization of silicon solar cells is commonly realized using traditional screen-printing. Besides stencil printing, inkjet printing and flexographic printing1, screen-printing has been used since the 1970s for numerous printing applications2. It is a versatile technique and in solar cell production, it ensures simple and fast metallization at a low printing cost. However, the flow properties of screen-printing pastes have to be carefully adjusted to guarantee undisturbed, defect free processing. This is particularly challenging in solar cell metallization since narrow uniform line patterns have to be achieved. Furthermore, paste recipes have to be carefully adjusted to avoid sedimentation of the high density silver particles, phase separation and particle aggregation.
The highly concentrated conductive screen-printing pastes for front-side metallization of solar cells mainly consist of three components3,4,5,6: the conductive material, generally micron-sized silver particles providing good electrical conductivity7,8; the continuous phase, the so-called vehicle, a mixture of organic binders, solvents and additives promoting particle wetting, film formation and adhesion to the substrate that also includes additives to adjust the flow behavior, especially allowing the paste to pass the narrow screen meshes easily; and the inorganic binder (glass powder) acts as an adhesion promoter and activates the sintering process at lower temperatures.
Printing fine lines with a high aspect ratio requires silver pastes that exhibit a high yield stress and a pronounced shear-thinning behavior9. The high yield stress guarantees good shape accuracy and a high aspect ratio whereas strong shear-thinning and a correspondingly low viscosity at high shear rates are necessary when the paste flows through narrow mesh openings, where the paste is exposed to high shear rates estimated to be beyond 103 s-1 10.
During the printing process, pastes are exposed to very different deformation rates and stresses. First, the paste rests on the screen; then the squeegee acts and the paste penetrates through screen openings onto the substrate. After application of the paste on the silicon wafer, structure and viscosity must recover quickly to prohibit paste spreading on the substrate. This would reduce solar cell performances due to higher shading losses10,11,12,13,14,15. Interruptions, the so-called meshmarks, in printed finger lines can occur at cross points of mesh wires depending on paste rheology. The time for leveling out the meshmarks should be as long as necessary but also short enough to keep the finger line spreading as low as possible16.
The squeegee pressure required for the paste to flow through the meshes onto the substrate has to be adjusted carefully to the high yield stress necessary to provide good shape accuracy3,6,9,17,18. Particles are closely packed, interact strongly and form complex structures. Accordingly, besides yield stress, shear thinning and thixotropy, various other complex flow phenomena like shear banding or avalanching may occur in such suspensions19,20,21. Wall slip is also crucial to concentrated suspensions22,23,24,25. A thin layer of liquid of lower viscosity, i.e. a layer depleted or free of particles is formed next to the wall25,26,27,28,29,30,31 and may control flow through narrow gaps or channels.
So a comprehensive rheological characterization of screen-printing pastes is essential in order to improve processing properties and product features. In this study, two commercial silver pastes are characterized. These pastes exhibit substantially different printing performances. The rheological characterization of such materials is very demanding. Even the simple determination of the steady shear viscosity using a rotational rheometer is a major challenge due to wall slip, plug flow, shear banding and paste spill. Accordingly, previous studies focused on oscillatory shear measurements10,17,21 or on the characterization of low concentrated silver pastes, so-called inks3,6,15, for which the above-mentioned phenomena are unlikely to occur.
Protocols for a robust and meaningful characterization of the flow behavior of concentrated silver pastes can be defined with the help of video recordings. A rotational shear rheometer with a parallel-plate sample fixture is used in this study, clearly demonstrating that plug flow, wall slip, and shear banding depend on the plate roughness in a non-trivial manner.
In previous work, time-dependent development of wall slip in steady torsional flow of concentrated suspensions was examined for different plate roughness. The flow of highly concentrated suspensions of solid glass spheres in polymer binder solution was visualized and an increased plate or inner cylinder roughness prevented wall slip. However, increasing plate roughness resulted in fracture of the samples22,25. Fracture occurred at smaller apparent shear rates when the wall roughness was increased. The tips of the asperities of the roughened surfaces might act as stress concentration points at the plate surface, initiating fracture at shear stresses &#964; smaller than the yield stress &#964;y25.
Wall slip is considered to be important for the screen-printing performance of highly concentrated pastes. The paste glides through the mesh easier at higher wall slip and its deposit on the substrate is increased significantly32. With the help of video recordings, wall slip can be directly observed for different experimental protocols. The slip velocity can be determined directly from the angular velocity of the rotating plate using smooth plates with low roughness. But flow behavior determination on silver pastes is an inherent limitation. The suspensions are non-transparent, so optical flow field observations can only be done at the sample rim. Previous studies have tried to determine wall slip and deformation within the samples simultaneously. They observed slip below the yield stress and found a quadratic dependence of slip velocity on the shear stress. The flow behavior of transparent clay suspensions was investigated by Pignon27 following the deformation of a dye pigment line injected into the bulk material. Persello et al.26 have investigated concentrated aqueous silica suspensions. They found that increasing plate roughness to suppress wall slip does not result in a homogenous sample deformation but provoked bulk fracture. Slip and sample deformation in pastes of soft microgel particles and concentrated emulsions has been intensively discussed in a series of papers28,29,30,31. Fluorescent tracer particles were used to determine the flow field within these transparent samples in a cone-plate geometry. They found a characteristic slip velocity V* at the yield stress of the respective material and a power law for the increase of slip velocity with shear stress &#964; below &#964;y. An exponent of one was found for non-adhering particles and two in the case of weak attraction between particles and wall.
In the study presented here the development of deformation and flow under controlled stress and controlled shear rate conditions is monitored. In contrast to the findings reported in Reference 25, increasing plate roughness does not result in fracture for both investigated pastes. Also, wall slip and plug flow cannot be suppressed just by increasing plate roughness. These phenomena seem to be controlled by the ratio of particle size and plate roughness. Sample spill sets in at a characteristic rotational speed presumably determined by the balance between centrifugal forces acting on and friction at the rheometer plate. However, the shear rate range in which the viscosity determination is possible can be determined, and simultaneously wall slip can be quantified. Furthermore, a capillary rheometer is used to determine the viscosity at higher shear rates relevant for the printing process.
Despite the difficulties with steady shear rheometry, well-defined oscillatory shear deformation can be implemented easily. A three-stage oscillation test (constant frequency, different oscillation amplitudes) simulates the screen-printing process10 and allows for studying structural recovery of the paste:
In the first &#34;pre-print&#34; step, a small deformation is applied to determine the elastic and viscous properties at rest. The second &#34;print&#34; step simulates the blade coating and the paste passing the screen mesh by applying a sufficiently high deformation amplitude breaking the paste structure. In the final &#34;post-print&#34; step, a small deformation is applied to detect the structural recovery of the paste. The initial modulus value should be reached quickly to avoid paste spreading but not too fast to avoid meshmarks. The investigations presented here confirm that the structural recovery is incomplete as previously reported by Zhou21. Zhou could show that the structural change is caused by the breaking of filler clusters of filler-matrix decoupling using silver particles suspended in ethyl cellulose solution. Video recordings in this study reveal that the observed irreversible structural change is not an artefact related to the occurrence of wall slip, shear banding, plug flow or sample spill. Additionally, it is found that the degree of structural breakdown strongly depends on the deformation amplitude applied in stage two, but hardly depends on the time interval of the applied strain. This aspect was not perceived in the experiments of Zhou. The influence of the paste composition on structural breakdown and recovery will be discussed in a subsequent paper.
Finally, a method to simulate the paste behavior during screen snap-off is presented. A capillary breakup elongational rheometer and a commercial tensile tester are used to determine the stretch ratio at which the pastes break and the maximum axial force during stretching as a function of elongation velocity.
Video recordings have turned out to be indispensable for finding the appropriate measurement protocols necessary for a meaningful rheological characterization of silver pastes using parallel-plate rotational rheometry. Video data enabled the determination of shear rate and shear stress regimes in which physically well-defined yield stress and viscosity values could be determined. The appropriate choice of plate roughness and plate separation parameters was also based on these video recordings. Experimental settings for which wall slip, pure plug flow, shear banding or sample spillage occur could be unequivocally identified. The pastes investigated here are used for front side metallization of solar cells. However, a careful video supported rheological characterization is also important for various other kinds of concentrated suspensions including high density, micron-sized particles.

<table border="1" fo:keep-together.within-page="1" fo:keep-with-next.within-page="always">
	<tbody>
		<tr>
			<td>endoscopy</td>
			<td>Visitool</td>
			<td>TVS80.280.BF6.AD10.2</td>
			<td>full name: TV-Endoskop, C-Mount, Variookular 2X, &#216; 8mm x ca. 280mm, 0&#176;, BF:6mm, AD 10mm</td>
		</tr>
		<tr>
			<td>commercial silver paste&#160;</td>
			<td>Heraeus Deutschland GmbH &#38; Co. KG 
			Global Business Unit Heraeus Photovoltaics</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>rheometer A</td>
			<td>Anton Paar</td>
			<td>Physica MCR 501</td>
			<td>Rq = 2 - 4 &#181;m</td>
		</tr>
		<tr>
			<td>rheometer B</td>
			<td>Thermo Scientific</td>
			<td>Haake Mars II</td>
			<td>Rq = 1.15 &#181;m 
			Rq = 9 &#181;m</td>
		</tr>
		<tr>
			<td>rheometer C</td>
			<td>Thermo Scientific (formerly Haake GmbH)</td>
			<td>Rheostress 150</td>
			<td>vane geometry</td>
		</tr>
		<tr>
			<td>sandpaper</td>
			<td>Jean Wirtz D&#252;sseldorf Metallographie</td>
			<td>P320 C</td>
			<td>Rq = 9 &#181;m 
			grain size = 46.2 &#177; 1.5</td>
		</tr>
		<tr>
			<td>recording software</td>
			<td>Debut Video Capture</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>LED Spotlight</td>
			<td>Kaleep&#160;</td>
			<td>48W Led Work Lights 
			Offroads Lights 
			Lamp Spotlight Floodlight&#160;</td>
			<td></td>
		</tr>
		<tr>
			<td>capillary breakup elongational rheometer</td>
			<td>Thermo Scientific (Haake)</td>
			<td>HAAKE CaBER1</td>
			<td></td>
		</tr>
		<tr>
			<td>tensile tester</td>
			<td>Stable Micro Systems, Godalming, UK</td>
			<td>TA.XT plus 
			Texture Analyzer&#160;</td>
			<td></td>
		</tr>
		<tr>
			<td>50 N load cell</td>
			<td>Stable Micro Systems, Godalming, UK</td>
			<td>Serialnumber: 10256249</td>
			<td></td>
		</tr>
		<tr>
			<td>a modified capillary rheometer</td>
			<td>G&#246;ttfert Rheograph 2000 (G&#246;ttfert Werkstoff-Pr&#252;fmaschinen GmbH, Buchen Germany)</td>
			<td></td>
			<td></td>
		</tr>
		<tr>
			<td>500 bar pressure transducer</td>
			<td>Gefran, Selingenstadt, Germany</td>
			<td></td>
			<td></td>
		</tr>
	</tbody>
</table>

challenges in rheological characterization of highly concentrated suspensions &#8212; a case study for screen-printing silver pastes

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the manifold requirements during processing and application of such complex fluids. In this investigation, measuring protocols for a conclusive assessment of different process relevant rheological parameters have been evaluated. This includes the determination of yield stress, viscosity, wall slip velocity, structural recovery after large deformation and elongation at break as well as tensile force during filament stretching.
The importance of concomitant video recordings during parallel-plate rotational rheometry for a significant determination of rheological quantities is demonstrated. The deformation profile and flow field at the sample edge can be determined using appropriate markers. Thus, measurement parameter settings and plate roughness values can be identified for which yield stress and viscosity measurements are possible. Slip velocity can be measured directly and measuring conditions at which plug flow, shear banding or sample spillover occur can be identified clearly. 
Video recordings further confirm that the change in shear moduli observed during three stage oscillatory shear tests with small deformation amplitude in stage I and III but large oscillation amplitude in stage II can be directly attributed to structural break down and recovery. For the pastes investigated here, the degree of irreversible, shear-induced structural change increases with increasing deformation amplitude in stage II until a saturation is reached at deformations corresponding to the crossover of G' and G'', but the irreversible damage is independent of the duration of large amplitude shear. 
A capillary breakup elongational rheometer and a tensile tester have been used to characterize deformation and breakup behavior of highly filled pastes in uniaxial elongation. Significant differences were observed in all experiments described above for two commercial screen-printing silver pastes used for front side metallization of Si-solar cells.

Watch this Scientific Journal Video about Challenges in Rheological Characterization of Highly Concentrated Suspensions Ã¢â‚¬â€ A Case Study for Screen-printing Silver Pastes at JoVE.com

Challenges in Rheological Characterization of Highly Concentrated Suspensions ÃƒÆ’Ã‚Â¢ÃƒÂ¢Ã¢â‚¬Å¡Ã‚Â¬ÃƒÂ¢Ã¢â€šÂ¬Ã‚Â A Case Study for Screen-printing Silver Pastes

A protocol for a robust and application relevant rheological characterization of highly concentrated suspensions is presented. Silver pastes used for screen-printing application in solar cell production are employed as model systems.

Challenges in Rheological Characterization of Highly Concentrated Suspensions &#8212; A Case Study for Screen-printing Silver Pastes

A comprehensive rheological characterization of highly concentrated suspensions or pastes is mandatory for a targeted product development meeting the ...

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