Heat Manipulation
Thermal Response of Transparent Silver Nanowire/ PEDOT:PSS Film Heaters Shulin Ji, Weiwei He, Ke Wang, Yunxia Ran, and Changhui Ye*
Thermal response behavior of transparent silver nanowire/PEDOT:PSS film heaters are intensively studied for manipulating heating temperature, response time, and power consumption. Influences of substrate heat capacity, heat transfer coefficient between air and heater, sheet resistance and dimension of Ag nanowire film, on the thermal response are investigated from thermodynamic analysis. Suggestion is given for practical applications that if other parameters are fixed, Ag nanowire coverage can be utilized as an effective parameter to adjust the thermal response. The heat transfer coefficient plays opposite roles on thermal response speed and achievable steady temperature. A value of ≈32 W m−2 K−1 is obtained from transient process analysis after correcting it by considering heater resistance variation during heating tests. Guidance of designing heaters with a given response time is provided by forming Ag nanowire film with a suitable sheet resistance on substrate of appropriate material and a certain thickness. Thermal response tests of designed Ag heaters are performed to show higher heating temperature, shorter response time, and lower power consumption (179 °C cm2 W−1) than ITO/FTO heaters, as well as homogeneous temperature distribution and stability for repeated use. Potential applications of the Ag heaters in window defogging, sensing and thermochromism are manifested.
1. Introduction Transparent heaters have received much attention in recent years, due to their wide applications as defogging windows,[1–9] the heating substrate of displays,[10–12] the heating source of sensors, reaction cells, and microchips.[13–18] Transparent heaters refer to resistance devices that work as surface heating source when subjecting to an electric current by coating a transparent and conductive layer. The accurate and fast control of temperature through adjusting input voltage or current makes transparent heater better choice of heating source than traditional heating elements. It is clear that thermal response time, steady heating temperature and
Dr. S. L. Ji, W. W. He, K. Wang, Y. X. Ran, Prof. C. H. Ye Key Laboratory of Materials Physics and Anhui Key Laboratory of Nanomaterials and Technology Institute of Solid State Physics Chinese Academy of Sciences Hefei 230031, P. R. China E-mail: [email protected] DOI: 10.1002/smll.201401690 small 2014, DOI: 10.1002/smll.201401690
temperature uniformity, and cycling stability are important performance indexes of transparent heaters. These indexes could influence application functions dramatically. For example, the response time of defogging vehicle windows affects the safety of driver considering fast movement of vehicles. The display color could be changed by the response time and temperature uniformity of the heating substrate.[10–12,19] The sensitivity and the reproducibility of sensors, reaction cells, and microchips are limited by the response time and cycling stability of the heating substrate.[13,14,16,18] Therefore, it is essential to gain knowledge of the thermal response behavior of transparent heaters to manipulate these indexes for different application purposes. There have been many reports about transparent heaters, however, only limited reports deal with transient thermal characteristics of transparent heaters.[6,11,20–22] Influencing factors including material coverage on the substrate, the size of the conducting film, and the heat transfer coefficient have been analyzed. Nevertheless, a key factor of substrate thickness, which affects the response time, has not been systematically studied in a wide range.[11] Moreover, in the reported investigations, heater resistance was supposed to be constant,
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which is not necessarily true.[4,14,21,23–25] Variation of heater resistance during thermal response test could influence the thermodynamic analysis results, especially for heaters with a high temperature.[26] For example, heat transfer coefficient, a parameter extracted from the analysis, could be altered by temperature coefficient of resistance. Finally, the importance of heat transfer coefficient to thermal response behavior of transparent heaters is well known, and its relationship with material coverage on substrate was systematically studied.[22] However, the physical meaning of its effect on thermal response behavior of transparent heaters, especially the opposite effect on steady temperature and transient response speed, has not been fully depicted. Understanding of its effect will guide the design of transparent heaters for different application demands such as energy saving or fast response. Transparent heaters could be made from designed array of wound metal wire with certain wire diameter and spacing for uniform heat distribution and transparency.[10,27,28] Considering the complexity of designing the wound metal wire array, new type of transparent heaters based on transparent and conductive films (TCFs) have attracted much attention. TCF heaters include traditional metal oxide heaters,[1,13–15,29–31] carbon nanotube (CNT) and graphene heaters,[2–6,11,16,17,20,21,23,24,27,32,33] and newly developed metal network heaters.[7–9,12,18,22,26] The drawbacks of complicated fabrication process, loss of conductivity after repeated bending, slow thermal response, non-neutral color,[29] and consumption of scarce indium prevent metal oxide heaters from high-end applications. The deficiency of large sheet resistance and slow thermal response has to be overcome for CNT/graphene heaters. Ag nanowire film heaters have advantages of high transmittance, low resistivity, neutral color, and ease of fabrication.[34,35] Ag nanowires (AgNWs) could be synthesized by a facile solution method,[36] and could be easily dispersed to coat on flexible substrates with a curved surface.[34,35] In addition, the percolation-like conductivity of these nanostructured films makes it possible to tune the sheet resistance substantially with the maintenance of a relatively high transmittance.[37] Generally, nanowires with small diameters and a large length to diameter ratio benefit the performance.[38] The tunability of the sheet resistance by changing the thickness of the films facilitates the construction of transparent heaters with optimal thermal response time and electrical power consumption. A few reports on Ag TCF heaters have been published to improve the temperature uniformity,[7] haze,[18] oxidation resistance,[8] and flexibility of the heaters.[9,12] However, so far, only one study has paid attention to the thermal response of Ag TCF heaters.[22] In the present work, transparent AgNW film heaters on substrates of different materials with varied thickness were prepared. Substrate thickness related thermal response was analyzed from heat capacity point of view. Other factors, such as heat transfer coefficient, sheet resistance, heating dimension that influenced the thermal response behavior were also studied. The results were utilized to design heaters with tunable response time. Finally, fast heating and cooling tests were examined on designed heaters to test their usability in practical application fields.
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Figure 1. SEM images of uniformly connected AgNW/PEDOT:PSS film heaters: a) before heating test, and b) after repeated heating tests at ≈120 °C for 50 times.
2. Results and Discussion 2.1. Morphologies of AgNWs and AgNW/PEDOT:PSS Film Heaters As shown in Figure 1 and Figure S1 (Supporting Information), high quality AgNWs were synthesized. The length of AgNWs could be extended to the range of 50–100 µm with an average diameter of ≈100 nm. Aspect ratio of AgNWs is as high as 500–1000 which is beneficial for better performance.[38] AgNWs with face centered cubic structure grew preferentially in direction. No obvious impurities such as surface oxides were detected for fresh AgNWs according to energy dispersive spectrometer (EDS) spectrum. Uniformly interconnected AgNWs were formed on substrates, and inter-wire connection by poly(3,4-ethylenedioxy thiophene):poly(styrenesulfonate) (PEDOT:PSS) ensuring conductive path could be observed in Figure 1. Actually, sheet resistance of the film on glass substrate reduced by orders of magnitude to an excellent value of ≈4 Ω sq−1 after PEDOT:PSS coating. Sheet resistance of the film on PET substrate was further reduced through cold isostatic pressing to a value of ≈3 Ω sq−1. Most importantly, no observable morphology change such as transformation of nanowires to nanoparticles appeared after test at a temperature as high as ≈120 °C for 50 times, which manifests the thermal stability of these heaters for repeated use.
2.2. Optical Properties of AgNW/PEDOT:PSS Film Heaters Compared with optical properties of heaters before heating test, total transmittance of those after repeated heating tests at ≈120 °C for 50 times almost kept unchanged (Figure S2a, Supporting Information). It manifests the excellent transparence stability for repeated use. Diffusive transmittance, reflectance, and haze of heaters reduced simultaneously after the heating tests (Figure S2, Supporting Information). This phenomenon could be ascribed to reduced scattering
© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
small 2014, DOI: 10.1002/smll.201401690
Thermal Response of Transparent Silver Nanowire/PEDOT:PSS Film Heaters
by inter-connected AgNWs. The nanowires connected more closely through smoothing effect under repeated heating tests. SEM images of AgNW films before and after repeated heating tests shown in Figure 1 support this idea. The reduced scattering at the AgNW film/substrate interface led to decreased diffusive transmittance and that at the AgNW film/ air interface led to decreased reflectance, which is conducive to the good optical performance of transparent heaters. For different purpose of practical applications, heaters of varying sheet resistances were prepared on PET substrate. Optical properties of AgNW/PEDOT:PSS film/PET heater with sheet resistance of 500 Ω sq−1 were exhibited in Figure S3 (Supporting Information). Taking into account the total transmittance of PET substrate (88.5% at 550 nm) and AgNW/PEDOT:PSS film/PET heater (82.8% at 550 nm), a value of 93.6% was approximately calculated for the total transmittance of AgNW/PEDOT:PSS film.[39]
2.3. Thermal Response Behavior of AgNW/PEDOT:PSS Film Heaters We tested the thermal power output performance of heaters by inputting a constant voltage at 0 s and turning it off at 300 s. Temperature profiles of heater with substrate thickness of 1.1 mm were recorded and exhibited in Figure 2a. The target temperature could be manipulated by changing the input voltage. Repeated heating tests were performed by inputting and turning off the voltage (6 V) for 50 times (Figure S4, Supporting Information). The temperature-time curves kept unchanged and the maximum temperature slightly increased (Figure 2b), and stability test under electrical stress at an applied bias for 2 h showed no significant degradation of achievable temperature (Figure S5b, Supporting Information), both of which manifest the stability for repeated and long term use. The slight increase of the maximum temperature in Figure 2b indicating slight decrease of heater resistance could be ascribed to more closely connected nanowires as shown in Figure 1 after heating. This smoothing effect under repeated heating tests was mentioned before. Moreover, homogeneous temperature was achieved as shown in Figure 3. Charge balance by the PEDOT:PSS layer[40] helped to achieve this goal as clay platelets did in previous report.[7] Without this PEDOT:PSS layer, unsuccessful even dispersing of AgNWs during film coating could lead to temperature fluctuation across the film (Figure S6, Supporting Information). Their homogeneous temperature makes AgNW/PEDOT:PSS heaters good candidates of heating substrates for low power consumption and transparent sensors that require uniform heating temperature to enhance the sensitivity of the device.[41] Checking the temperature-time curves of AgNW/ PEDOT:PSS film heaters on 1.1 mm-thick glass, we noticed that the temperature plateau was not horizontal for 300 s heating time. This effect was aggravated in heaters on thicker glass substrates (2 mm and 4.5 mm in thickness), and even when the heating time was extended to 600 s, no complete temperature plateaus were observed (Figure S7, Supporting Information). The thicker the substrate, the longer time small 2014, DOI: 10.1002/smll.201401690
Figure 2. a) Temperature–time curves under different input voltages, and b) cycling performance of AgNW/PEDOT:PSS film heater on 1.1 mm-thick glass substrate with sheet resistance of ≈4 Ω sq−1 and total transmittance of ≈70% at 550 nm.
was needed to achieve the temperature plateau. The slow increase of temperature was ascribed to a large heat capacity of thick substrates. When ultrathin glass (0.15 mm in thickness) was used as the heater substrate, this effect disappeared and target temperature plateau was achieved within 25 s (Figure 4). For heaters with thick substrates, heat from AgNW film conducted into the substrate beneath and was largely stored, which affected the rapid increase of the temperature. When input voltage was turned off, heat supply from the film stopped and stored heat in the substrate began
Figure 3. Visual (left panel) and IR (right panel) images showing temperature uniformity of transparent AgNW/PEDOT:PSS film heaters.
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CdT =
U2 dt − hA(T −T0 )dt R
CdT = − hA(T −T0 )dt
T = T0 + = T0 +
Figure 4. Temperature–time curves of AgNW/PEDOT:PSS film heater on ultrathin glass substrate (0.15 mm in thickness) with sheet resistance of ≈4 Ω sq−1 and total transmittance of ≈70% at 550 nm.
to conduct back into the film, which affected the rapid decrease of the temperature. We will quantitatively analyze the effect of substrate heat capacity on temperature-time curve in the following section. Temperature of the heater is determined by two processes: inflow and storage of the electrical energy, and outflow and releasing of the energy through heat transfer to air. The heat loss includes heat transfer by convection and radiation. Regarding heat radiation, studies gave different estimations of its contribution to the total heat loss of heaters. Some researchers neglected it by considering the low temperature of heaters ( t off )
(3)
hA ⎞ t − U2 ⎛ 1− e C ⎟ RhA ⎜⎝ ⎠ t − ⎞ U2 ⎛ 1− e τ ⎟ ⎜ RhA ⎝ ⎠
T = T0 + (Toff −T0 )e = T0 + (Toff −T0 )e
τ=
( t < t off )
−
−
(4) ( t < t off )
hA ( t − t off ) C
t − t off τ
C mc ρ Adc ρdc = = = hA hA hA h
(5) (t > t off )
(6)
In above equations, Toff refers to temperature at the time of turning off the electricity, toff the time of turning off the electricity, C, c, ρ, and d the heat capacity, the specific heat capacity, the density, and the thickness of the substrate, respectively. R is the resistance of the heater, and U a constant voltage applied on the heater. τ depicts the time constant of the transient thermal response and equals to C/hA. Due to the small thickness ratio (
Thermal Response of Transparent Silver Nanowire/ PEDOT:PSS Film Heaters Shulin Ji, Weiwei He, Ke Wang, Yunxia Ran, and Changhui Ye*
Thermal response behavior of transparent silver nanowire/PEDOT:PSS film heaters are intensively studied for manipulating heating temperature, response time, and power consumption. Influences of substrate heat capacity, heat transfer coefficient between air and heater, sheet resistance and dimension of Ag nanowire film, on the thermal response are investigated from thermodynamic analysis. Suggestion is given for practical applications that if other parameters are fixed, Ag nanowire coverage can be utilized as an effective parameter to adjust the thermal response. The heat transfer coefficient plays opposite roles on thermal response speed and achievable steady temperature. A value of ≈32 W m−2 K−1 is obtained from transient process analysis after correcting it by considering heater resistance variation during heating tests. Guidance of designing heaters with a given response time is provided by forming Ag nanowire film with a suitable sheet resistance on substrate of appropriate material and a certain thickness. Thermal response tests of designed Ag heaters are performed to show higher heating temperature, shorter response time, and lower power consumption (179 °C cm2 W−1) than ITO/FTO heaters, as well as homogeneous temperature distribution and stability for repeated use. Potential applications of the Ag heaters in window defogging, sensing and thermochromism are manifested.
1. Introduction Transparent heaters have received much attention in recent years, due to their wide applications as defogging windows,[1–9] the heating substrate of displays,[10–12] the heating source of sensors, reaction cells, and microchips.[13–18] Transparent heaters refer to resistance devices that work as surface heating source when subjecting to an electric current by coating a transparent and conductive layer. The accurate and fast control of temperature through adjusting input voltage or current makes transparent heater better choice of heating source than traditional heating elements. It is clear that thermal response time, steady heating temperature and
Dr. S. L. Ji, W. W. He, K. Wang, Y. X. Ran, Prof. C. H. Ye Key Laboratory of Materials Physics and Anhui Key Laboratory of Nanomaterials and Technology Institute of Solid State Physics Chinese Academy of Sciences Hefei 230031, P. R. China E-mail: [email protected] DOI: 10.1002/smll.201401690 small 2014, DOI: 10.1002/smll.201401690
temperature uniformity, and cycling stability are important performance indexes of transparent heaters. These indexes could influence application functions dramatically. For example, the response time of defogging vehicle windows affects the safety of driver considering fast movement of vehicles. The display color could be changed by the response time and temperature uniformity of the heating substrate.[10–12,19] The sensitivity and the reproducibility of sensors, reaction cells, and microchips are limited by the response time and cycling stability of the heating substrate.[13,14,16,18] Therefore, it is essential to gain knowledge of the thermal response behavior of transparent heaters to manipulate these indexes for different application purposes. There have been many reports about transparent heaters, however, only limited reports deal with transient thermal characteristics of transparent heaters.[6,11,20–22] Influencing factors including material coverage on the substrate, the size of the conducting film, and the heat transfer coefficient have been analyzed. Nevertheless, a key factor of substrate thickness, which affects the response time, has not been systematically studied in a wide range.[11] Moreover, in the reported investigations, heater resistance was supposed to be constant,
© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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1
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S. L. Ji et al.
which is not necessarily true.[4,14,21,23–25] Variation of heater resistance during thermal response test could influence the thermodynamic analysis results, especially for heaters with a high temperature.[26] For example, heat transfer coefficient, a parameter extracted from the analysis, could be altered by temperature coefficient of resistance. Finally, the importance of heat transfer coefficient to thermal response behavior of transparent heaters is well known, and its relationship with material coverage on substrate was systematically studied.[22] However, the physical meaning of its effect on thermal response behavior of transparent heaters, especially the opposite effect on steady temperature and transient response speed, has not been fully depicted. Understanding of its effect will guide the design of transparent heaters for different application demands such as energy saving or fast response. Transparent heaters could be made from designed array of wound metal wire with certain wire diameter and spacing for uniform heat distribution and transparency.[10,27,28] Considering the complexity of designing the wound metal wire array, new type of transparent heaters based on transparent and conductive films (TCFs) have attracted much attention. TCF heaters include traditional metal oxide heaters,[1,13–15,29–31] carbon nanotube (CNT) and graphene heaters,[2–6,11,16,17,20,21,23,24,27,32,33] and newly developed metal network heaters.[7–9,12,18,22,26] The drawbacks of complicated fabrication process, loss of conductivity after repeated bending, slow thermal response, non-neutral color,[29] and consumption of scarce indium prevent metal oxide heaters from high-end applications. The deficiency of large sheet resistance and slow thermal response has to be overcome for CNT/graphene heaters. Ag nanowire film heaters have advantages of high transmittance, low resistivity, neutral color, and ease of fabrication.[34,35] Ag nanowires (AgNWs) could be synthesized by a facile solution method,[36] and could be easily dispersed to coat on flexible substrates with a curved surface.[34,35] In addition, the percolation-like conductivity of these nanostructured films makes it possible to tune the sheet resistance substantially with the maintenance of a relatively high transmittance.[37] Generally, nanowires with small diameters and a large length to diameter ratio benefit the performance.[38] The tunability of the sheet resistance by changing the thickness of the films facilitates the construction of transparent heaters with optimal thermal response time and electrical power consumption. A few reports on Ag TCF heaters have been published to improve the temperature uniformity,[7] haze,[18] oxidation resistance,[8] and flexibility of the heaters.[9,12] However, so far, only one study has paid attention to the thermal response of Ag TCF heaters.[22] In the present work, transparent AgNW film heaters on substrates of different materials with varied thickness were prepared. Substrate thickness related thermal response was analyzed from heat capacity point of view. Other factors, such as heat transfer coefficient, sheet resistance, heating dimension that influenced the thermal response behavior were also studied. The results were utilized to design heaters with tunable response time. Finally, fast heating and cooling tests were examined on designed heaters to test their usability in practical application fields.
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Figure 1. SEM images of uniformly connected AgNW/PEDOT:PSS film heaters: a) before heating test, and b) after repeated heating tests at ≈120 °C for 50 times.
2. Results and Discussion 2.1. Morphologies of AgNWs and AgNW/PEDOT:PSS Film Heaters As shown in Figure 1 and Figure S1 (Supporting Information), high quality AgNWs were synthesized. The length of AgNWs could be extended to the range of 50–100 µm with an average diameter of ≈100 nm. Aspect ratio of AgNWs is as high as 500–1000 which is beneficial for better performance.[38] AgNWs with face centered cubic structure grew preferentially in direction. No obvious impurities such as surface oxides were detected for fresh AgNWs according to energy dispersive spectrometer (EDS) spectrum. Uniformly interconnected AgNWs were formed on substrates, and inter-wire connection by poly(3,4-ethylenedioxy thiophene):poly(styrenesulfonate) (PEDOT:PSS) ensuring conductive path could be observed in Figure 1. Actually, sheet resistance of the film on glass substrate reduced by orders of magnitude to an excellent value of ≈4 Ω sq−1 after PEDOT:PSS coating. Sheet resistance of the film on PET substrate was further reduced through cold isostatic pressing to a value of ≈3 Ω sq−1. Most importantly, no observable morphology change such as transformation of nanowires to nanoparticles appeared after test at a temperature as high as ≈120 °C for 50 times, which manifests the thermal stability of these heaters for repeated use.
2.2. Optical Properties of AgNW/PEDOT:PSS Film Heaters Compared with optical properties of heaters before heating test, total transmittance of those after repeated heating tests at ≈120 °C for 50 times almost kept unchanged (Figure S2a, Supporting Information). It manifests the excellent transparence stability for repeated use. Diffusive transmittance, reflectance, and haze of heaters reduced simultaneously after the heating tests (Figure S2, Supporting Information). This phenomenon could be ascribed to reduced scattering
© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
small 2014, DOI: 10.1002/smll.201401690
Thermal Response of Transparent Silver Nanowire/PEDOT:PSS Film Heaters
by inter-connected AgNWs. The nanowires connected more closely through smoothing effect under repeated heating tests. SEM images of AgNW films before and after repeated heating tests shown in Figure 1 support this idea. The reduced scattering at the AgNW film/substrate interface led to decreased diffusive transmittance and that at the AgNW film/ air interface led to decreased reflectance, which is conducive to the good optical performance of transparent heaters. For different purpose of practical applications, heaters of varying sheet resistances were prepared on PET substrate. Optical properties of AgNW/PEDOT:PSS film/PET heater with sheet resistance of 500 Ω sq−1 were exhibited in Figure S3 (Supporting Information). Taking into account the total transmittance of PET substrate (88.5% at 550 nm) and AgNW/PEDOT:PSS film/PET heater (82.8% at 550 nm), a value of 93.6% was approximately calculated for the total transmittance of AgNW/PEDOT:PSS film.[39]
2.3. Thermal Response Behavior of AgNW/PEDOT:PSS Film Heaters We tested the thermal power output performance of heaters by inputting a constant voltage at 0 s and turning it off at 300 s. Temperature profiles of heater with substrate thickness of 1.1 mm were recorded and exhibited in Figure 2a. The target temperature could be manipulated by changing the input voltage. Repeated heating tests were performed by inputting and turning off the voltage (6 V) for 50 times (Figure S4, Supporting Information). The temperature-time curves kept unchanged and the maximum temperature slightly increased (Figure 2b), and stability test under electrical stress at an applied bias for 2 h showed no significant degradation of achievable temperature (Figure S5b, Supporting Information), both of which manifest the stability for repeated and long term use. The slight increase of the maximum temperature in Figure 2b indicating slight decrease of heater resistance could be ascribed to more closely connected nanowires as shown in Figure 1 after heating. This smoothing effect under repeated heating tests was mentioned before. Moreover, homogeneous temperature was achieved as shown in Figure 3. Charge balance by the PEDOT:PSS layer[40] helped to achieve this goal as clay platelets did in previous report.[7] Without this PEDOT:PSS layer, unsuccessful even dispersing of AgNWs during film coating could lead to temperature fluctuation across the film (Figure S6, Supporting Information). Their homogeneous temperature makes AgNW/PEDOT:PSS heaters good candidates of heating substrates for low power consumption and transparent sensors that require uniform heating temperature to enhance the sensitivity of the device.[41] Checking the temperature-time curves of AgNW/ PEDOT:PSS film heaters on 1.1 mm-thick glass, we noticed that the temperature plateau was not horizontal for 300 s heating time. This effect was aggravated in heaters on thicker glass substrates (2 mm and 4.5 mm in thickness), and even when the heating time was extended to 600 s, no complete temperature plateaus were observed (Figure S7, Supporting Information). The thicker the substrate, the longer time small 2014, DOI: 10.1002/smll.201401690
Figure 2. a) Temperature–time curves under different input voltages, and b) cycling performance of AgNW/PEDOT:PSS film heater on 1.1 mm-thick glass substrate with sheet resistance of ≈4 Ω sq−1 and total transmittance of ≈70% at 550 nm.
was needed to achieve the temperature plateau. The slow increase of temperature was ascribed to a large heat capacity of thick substrates. When ultrathin glass (0.15 mm in thickness) was used as the heater substrate, this effect disappeared and target temperature plateau was achieved within 25 s (Figure 4). For heaters with thick substrates, heat from AgNW film conducted into the substrate beneath and was largely stored, which affected the rapid increase of the temperature. When input voltage was turned off, heat supply from the film stopped and stored heat in the substrate began
Figure 3. Visual (left panel) and IR (right panel) images showing temperature uniformity of transparent AgNW/PEDOT:PSS film heaters.
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CdT =
U2 dt − hA(T −T0 )dt R
CdT = − hA(T −T0 )dt
T = T0 + = T0 +
Figure 4. Temperature–time curves of AgNW/PEDOT:PSS film heater on ultrathin glass substrate (0.15 mm in thickness) with sheet resistance of ≈4 Ω sq−1 and total transmittance of ≈70% at 550 nm.
to conduct back into the film, which affected the rapid decrease of the temperature. We will quantitatively analyze the effect of substrate heat capacity on temperature-time curve in the following section. Temperature of the heater is determined by two processes: inflow and storage of the electrical energy, and outflow and releasing of the energy through heat transfer to air. The heat loss includes heat transfer by convection and radiation. Regarding heat radiation, studies gave different estimations of its contribution to the total heat loss of heaters. Some researchers neglected it by considering the low temperature of heaters ( t off )
(3)
hA ⎞ t − U2 ⎛ 1− e C ⎟ RhA ⎜⎝ ⎠ t − ⎞ U2 ⎛ 1− e τ ⎟ ⎜ RhA ⎝ ⎠
T = T0 + (Toff −T0 )e = T0 + (Toff −T0 )e
τ=
( t < t off )
−
−
(4) ( t < t off )
hA ( t − t off ) C
t − t off τ
C mc ρ Adc ρdc = = = hA hA hA h
(5) (t > t off )
(6)
In above equations, Toff refers to temperature at the time of turning off the electricity, toff the time of turning off the electricity, C, c, ρ, and d the heat capacity, the specific heat capacity, the density, and the thickness of the substrate, respectively. R is the resistance of the heater, and U a constant voltage applied on the heater. τ depicts the time constant of the transient thermal response and equals to C/hA. Due to the small thickness ratio (
