RESEARCH PAPER
Rheological behavior of silver nanowire conductive inks during screen printing
Shohreh Hemmati .Dale P.Barkey .Nivedita Gupta
Received:10May 2016/Accepted:9August 2016ÓSpringer Science+Business Media Dordrecht 2016
Abstract The rheological behavior of silver nano-wire (AgNW)suspensions adapted for screen printing inks was investigated.Aqueous silver nanowire inks consisting of AgNW (length of 30l m,and diameter of 40and 90nm),dispersant and binder were formu-lated.The effect of AgNW content on the rheological behavior of the ink and the build-up of ink structure after screen printing were examined as they depend on applied shear and temperature.Rheological measure-ments under conditions that mimic the screen printing process were done to asss viscoelastic properties induced by flow alignment of the wires and the subquent recovery of the low shear structure.The Stretched Exponential model (SEmo)was ud to model the recovery process after screen printing to obtain the characteristic time of the recovery or build-up process.The characteristic time was determined at veral temperatures to obtain the activation energy of recovery.The domination of Brownian motion or non-Brownian motion behavior can be characterized by a Peclet number,which is the ratio of shear rate to the rotational diffusion coefficient.The Peclet number and the dimensionless concentration of wires were ud to
asss the recovery mechanism.The steady viscosity at low and high shear rates was also treated by an activation energy analysis.
Keywords Silver nanowire ÁScreen printing ÁRheology ÁConductive ink ÁBuild-up mechanism ÁNanomaterials
Introduction
Printed circuits are ud in many devices including solar panels,touch screens,and flexible circuits.Conductive inks or pastes can be defined as materials that can be ud to print conductive circuits on various substrates.Three esntial com-ponents in conductive inks are conductive filler,solvent,and binder (Faddoul et al.2012a ,b ).Metal nanowires (NWs)are among the most promising materials for conductive fillers due to their unique electrical and structural properties.Among metal nanowires,AgNWs are excellent candidates for this function becau of the high electrical and thermal conductivity of bulk silver.
A number of printing methods such as gravure printing,inkjet printing,and screen printing have been ud to fabricate printed patterns and circuits with conductive inks (Aleeva and Pignataro 2014).Among the,screen printing is inexpensive and rapid (Yin et al.2008).The even patterns and sharp line definition required of the printed patterns depend on the
Electronic supplementary material The online version of this article (doi:10.1007/s11051-016-3561-4)
contains supple-mentary material,which is available to authorized urs.S.Hemmati ÁD.P.Barkey (&)ÁN.Gupta
Department of Chemical Engineering,University of New Hampshire,Durham,NH 03824,USA e-mail:dpb@unh.edu
J Nanopart Res (2016) 18:249 DOI 10.1007/s11051-016-3561-4
rheological behavior of the inks.Strong shear thinning behavior permits charging of the ink at low shear onto the screen,followed by printing through the screen at high shear(Hemmati et al.2015).Rapid recovery of the low shear viscosity after printing is necessary to obtain sharp line definition.Hence,suitable inks exhibit thixotropic rheological behavior with both time dependence and shear thinning.While rapid viscosity recovery promotes sharp line definition,too rapid recovery inhibits voidfilling andfilm leveling (Faddoul et al.2012a,b;Hemmati et al.2015).Hence, the time-scale for viscosity recovery,a function of structure build-up is critical to line definition andfilm leveling.The Stretched Exponential model(SEmo) has been suggested to predict and model the structural build-up in suspensions such as conductive inks (Barnes1997;Sabuj Mallik2009).
The rheological properties of water-bad silver nanowire conductive inks are complex and scale-de
pendent.The appropriate rheometer configuration, measurement protocol,and data analysis must be lected carefully(Hemmati et al.2015;Mewis and Wagner2012).In the systems,particle diffusion and interactions play a crucial role in producing the obrved rheological behavior.Depending on the strength of interactions,the AgNWs can form different structures,which in turn determine the rheological characteristics of the ink during the steps of the printing process(Mewis and Wagner2012). Theflow characteristics and rheological behavior of the silver nanostructure dispersion depend strongly on the content,size,and shape of the silver nanos-tructures.This behavior is controlled by the balance among different interactions including Brownian motion,as well as thermodynamic and hydrody-namic interactions.The rheological behavior of the AgNWs ink is controlled by the alignment and orientation of silver nanowire with respect to the flow.Brownian motion tends to randomize orienta-tion.On the other hand,hydrodynamic interactions at high shear tend to align the wires in the direction of flow.At low shear rate,the random orientation of the wires promotes momentum transport and increas the viscosity.At high shear,the nanowires orient in the direction of theflow decreasing the viscosity. When the shear rate is suddenly decread,recovery of high viscosity is a rate process that depends on the speed with which the wires become randomized (Zhou et al.2011).
Suspension viscosity increas with increasing AgNW content.Brownian motion at low shear rate andflow orientation at high shear rate also increa in strength(Mewis and Wagner2012;Willenbacher and Georgieva2013).The rheological behavior of the suspension depends on the AgNW interactions, which are coupled to particle concentration and network structure.The dominance of different inter-actions strongly depends on the AgNWs content of the suspension,which can be classified as dilute, mi-dilute,or concentrated.The transition between dilute,mi-dilute,and concentrated dispersions can be predicted bad on the number density of particles and their diameter and length(Cassagnau2013).The rotational Peclet number,which is the ratio of applied shear rate to the rotational diffusion coeffi-cient,can be ud to investigate the dominance of Brownian motion compared to non-Brownian motion (Litchfield and Baird2006;Quemada1998).In addition to Brownian motion,there are other mech-anisms,especially in the concentrated regime,and the contribution and quantity of each mechanism are not precily known.In this situation,the behavior can be quantified in terms of activation energy (Chandler2014).
Governing equations
A step change in shear rate is followed by a time-dependent transition from one steady shear stress to another becau the change in suspension structure is a rate process.In moving from a high shea
r to a low shear state,the more oriented arrangement of wires changes to a more random arrangement.This tran-sition is referred to as build-up.In the peak hold(PH) test,a low shear rate is applied initially,the shear is then stepped to a high rate andfinally stepped back to the low rate,mimicking the quence of ink charging, through-screen printing,andfilm leveling in screen printing.
The time dependence of the transition from high to low shear can be correlated with the Stretched Exponential model(SEmo)(Barnes1997;Sabuj Mallik2009),expresd in the Eq.(1).
g¼g0þg1Àg0
ðÞ1ÀexpðÀðt=sÞrÞ
ðÞ;ð1Þwhere g0is the steady viscosity at high shear rate,g? is the steady viscosity at low shear rate,s is the characteristic time for the transition,and r is a
249 Page2of11J Nanopart Res(2016) 18:249
dimensionless constant that can be assumed to be unity in the simplest ca.The values of g0and g?are obtained from the PH test.The time constant s is found byfitting to the SEmo equation(Barnes
1997;Sabuj Mallik2009).
The dependence of characteristic time on temper-ature can be expresd in the form of Arrhenius equation(Eq.2).
1 s TðÞ¼
1
s0
expÀE a=RT
ðÞ;ð2Þ
where1
s0
is the frequency factor,E a the activation energy,R the universal gas constant,and T the absolute temperature.A mi-log plot of the rate constant versus the reciprocal temperature provides the para
meters(Eq.3).
ln
1
s
¼ln
1
s0老年人脑梗
À
E a
R
1
T
:ð3Þ
The slope of the natural log of the1
s
versus1
T
plot
givesÀE a
R .In dilute suspensions of AgNWs,the wires
can rotate easily without any interference from the other wires,and the wire diffusivity is controlled by Brownian motion.In mi-dilute suspensions,there are particle interactions between neighboring wires that inhibit free rotation.In concentrated suspensions of AgNWs,the wire dimensions are large
compared to the spacing between wires,and the volume of interaction should be considered(Cassagnau2013). The transition from dilute to mi-dilute suspensions can be evaluated through a dimensionless constant
t L3¼b;ð4Þwhere t is the number density(the numbers of wires per unit volume),L the wire length,and b a dimensionless constant.A b value less than30 corresponds to the dilute regime(Cassagnau2013).一年级诗歌
The value of1
d L2can b
e ud to correlate the transition
to the concentrated regime.In concentrated suspen-
sions,t[1
d L2:.At higher concentration(t[4:2
d L2
)the
wires orient into a nematic regime(Cassagnau2013).
The viscosity recovery after screen printing can be due either to particle–particle interactions or Brown-ian motion.The transition from Brownian to non-Brownian recovery can be evaluated with a rotational Peclet number(or Weisnberg number)(Litchfield and Baird2006;Zhou et al.2011)Pe¼
_c
D r
;ð5Þ
where D r is the rotational diffusion coefficient and_c the shear rate.For wire structures,the rotational diffusion coefficient can be estimated by Eq.(6) (Litchfield and Baird2006).
D r¼
d K b T ln a r
ðÞ
3pg L3t L3
ðÞ
;ð6Þ太极熊
where d is a constant equal to unity in this ca,K b the Boltzmann constant,a r the particle aspect ratio,t the number density of particles,and L their length (Litchfield and Baird2006).Very large Peclet num-bers Pe)1indicate a non-Brownian mechanism during the viscosity recovery,and low Peclet numbers (Pe(1)indicate a Brownian mechanism(Cassagnau 2013;Litchfield and Baird2006).
The dependence of viscosity on temperature can be expresd by Eq.(7).
g¼K0_c nÀ1exp E a=RT
ðÞ;ð7Þwhere K0is a pre-exponential constant,_c the shear rate, n the power law exponent,and E a the activation for momentum transfer,which can be expresd in terms of the activation enthalpy(H)and activation entropy (S)(H.D.Chandler2014).
E a¼HÀTS:ð8ÞThe temperature dependence of the low viscosity at high shear(g I)corresponds to the viscosity at the end of the cond interval in the PH test,and the viscosity at the end of recovery process(g R)corresponds to the viscosity at the end of third interval in the PH test which can be written as
g I¼K0_c nÀ1e H IÀTS I
ðÞ;ð9Þg R¼K0_c nÀ1e H RÀTS R
RT
ðÞ:ð10Þ
Plots of the natural log of g I and g R versus1
两地汤组成
T
provide the activation enthalpies,
ln g I¼
H I
R
1
T
þln K0_c nÀ1
À
S I
R
;ð11Þln g R¼
H R
R
1
T
þln K0_c nÀ1学生成长手册
精彩美文
À
S R
R
;ð12Þ
the slopes of give H I
R
and H R
R
;
respectively.
J Nanopart Res(2016) 18:249 Page3of11249
通经活络的中药Materials and methods
Water-bad ink was formulated with commercial AgNWs[AgNWs-90-Blue Nano(diameter of90nm and length of30l m)]as conductive or metalfiller,de-ionized(DI)water and Isopropyl Alcohol[(IPA), PHARMCO-AAPER,231HPLC99]as solvent or carrier,Carboxymethyl Cellulo(CMC,Sigma-Aldrich,419237)as a binder or thickener,and Dispex Ultra FA4416[(Old Hydropalat216),BASF]as a dispersive agent.Inks with AgNWs-90contents of4, 5,6,and7%by weight were prepared.To investigate the effect of the AgNW dimensions on the rheological behavior of the inks,different AgNWs[AgNWs-40-Blue Nano(diameter of40nm and length of30l m)] ink contents of4,5,and6%by weight were prepared.
The Peak Hold(PH)test to simulate screen printing was carried out in a titanium plate–plate rheometer AR 550(Hemmati et al.2015).The plate radius was 40mm and the gap was500l m,giving a sample volume of0.628cm3.A constant shear rate was applied in three intervals.A shear rate of0.1/s was applied for30s to simulate the charging of the ink onto the mesh before printing.A shear rate of2
00/s was then applied for30s to simulate through-screen printing.Finally,a shear rate of0.1/s was applied for 2min to simulate viscosity recovering after printing (Hemmati et al.2015).In order to investigate the effect of temperature on the build-up of the ink structure after printing,the PH test was repeated at temperatures of288,298,308,and318K.In addition, the PH test was repeated at a lower recovery shear rate (0.04/s)to investigate the effect of shear rate on the build-up and viscosity recovery mechanisms.
Results and discussion
Simulation of screen printing(PH test)
Figure1shows the measured viscosity versus time in the PH test for5wt%AgNWs(AgNWs-90)ink at veral temperatures.Figure2shows the measured viscosity versus time in the PH test at two values of shear rate during the recovery process for5wt% AgNWs(AgNWs-90)ink.Figure3shows the mea-sured viscosity versus time in the PH test for5wt% AgNWs(AgNWs-40)ink at veral temperatures.The viscosity depends strongly on AgNWs content.This effect is stronger at higher concentration of AgNWs. At any concentration of AgNWs,the viscosity is higher at lower temperature presumably becau of the higher solvent viscosity at lower temperature.More-over,the viscosity is l
arger at lower shear rate,which corresponds to the shear thinning thixotropic behavior of the ink.Comparison of the results for40and90nm AgNWs shows that ink prepared with smaller-diam-eter wires has higher viscosity at the same weight fraction of metal.The results for the PH tests are summarized in Table1.This table illustrates quanti-tatively the viscosity decrea during printing at high
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shear rate due to the shear thinning behavior of the ink. Moreover,this table shows how viscosity increas with increasing AgNWs content.Finally,this table shows that higher aspect ratio wires(AgNWs-40compared to AgNWs-90)at the same mass fraction produce a larger viscosity.The difference between the 5and6wt%viscosities for AgNW-90is within experimental error.The large increa at7%corre-sponds to the transition to a nematic regime.Addi-tional results for lower AgNWs-
40content can be found in the supplementary information(Fig.S1; Table S1).
Correlation of build-up structure(SEmo)
The viscosity recovery process was correlated by fitting a time constant from the SEmo.The results are shown in Figs.4and5for5wt%AgNWs(AgNWs-90)ink.Figure4shows the dependence on tempera-ture,and Fig.5shows the dependence on shear rate during recovery.Figure6shows the temperature dependence for5wt%AgNWs(AgNWs-40)ink. Similar results for lower AgNW-40content can be found in the supplementary information(Figure S2).
The results show that the rate of viscosity recovery depends on the silver nanowire content, temperature,and applied shear rate.Correlation with the SEmo provides a characteristic time for the recovery process(Barnes1997;Sabuj Mallik2009). The model is bad on the assumption that viscosity recovery proceeds by a transition from a more oriented structure at high shear to a more random structure at low shear rate.If the structure can be characterized by one parameter that varies smoothly from the high shear value to the low shear value,and the rate of the transition is proportional to the difference between the structural parameter and its equilibrium value at low shear,one obtains the exponential time dependence of the SEmo.The characteristic time,as a model
parameter,is correlated with the shear thinning thixotropic behavior of the AgNWs inks.The charac-teristic time reprents the required time for viscosity recovery and silver nanowire rearrangements after the printing process without ink spreading in order to have sharp line definition of the printed pattern.
The reciprocal of the time constant is a rate constant.The rate constant is a function of the mechanisms by which the structure becomes random-ized and of the thermal energy available to drive the mechanism.Hence,we can treat the rate constant with a conventional Arrhenius plot.
清水煮虾
A plot of the natural log of the recovery process rate constant versus the reciprocal of temperature is shown in Fig.7for AgNWs-90.A linearfit to the data is also shown.Similar results for AgNWs-40are shown in Fig.8.
In every ca,the slope of each linearfit,equal to ÀE a
R
is negative,which gives a positive activation energy.A higher activation energy reprents a higher barrier to nanowire movement.The activation ener-gies for experiment are summarized in Table2,and the values are consistently near20kJ.
Dilute/mi-dilute/concentrated regime transition The mechanism of viscosity recovery or build-up depends on the suspension concentration becau the concentration determines the frequency and charac-ter of interaction between wires.The suspension concentrations can be categorized as dilute,mi-dilute,or concentrated.The criteria for transition from dilute to mi-dilute regimes are determined by a dimensionless constant b which is defined as t L3. The number density of particles and the value of b for lected silver nanowire contents are shown in Table3.
The results of the four different silver nanowire contents from4to7wt%illustrate that in all
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