Electrical Double Percolation of Polybutadiene/Polyethylene Glycol Blends Loaded with Conducting Polymer Nanofibers

The critical phenomena of double percolation on polybutadiene (PB)/polyethylene glycol (PEG) blends loaded with poly-3-hexylthiophene (P3HT) nanofibers is investigated. P3HT nanofibers are selectively localized in the PB phase of the PB/PEG blend, as observed by scanning force microscopy (SFM). Moreover, double percolation is observed, i.e., the percolation of the PB phase in PB/PEG blends and that of the P3HT nanofibers in the PB phase. The percolation threshold (φcI) and critical exponent (tI) of the percolation of the PB phase in PB/PEG blends are estimated to be 0.57 and 1.3, respectively, indicating that the percolation exhibits two-dimensional properties. For the percolation of P3HT nanofibers in the PB phase, the percolation threshold (φcII) and critical exponent (tII) are estimated to be 0.02 and 1.7, respectively. In this case, the percolation exhibits properties in between two and three dimensions. In addition, we investigated the dimensionality with respect to the carrier transport in the P3HT nanofiber network. From the temperature dependence of the field-effect mobility estimated by field-effect transistor (FET) measurements, the carrier transport was explained by a three-dimensional variable range hopping (VRH) model.


Introduction
Conductive polymer composites (CPC) that comprise immiscible polymer blends and conductive fillers are novel composite materials, featuring advantages of both polymer blends and conductive fillers. Generally, by loading conductive fillers such as carbon black (CB) [1][2][3][4][5][6][7][8], carbon nanotubes (CNTs) [9][10][11][12][13][14], and graphene [5], it was reported that the resultant mechanical strength and electrical properties can be drastically modified. In particular, the conductivity can be changed from that of an insulator to that of a conductor by increasing the amount of fillers. Furthermore, fillers have been reported to be located selectively in a specific phase [1][2][3]5,7,10,11,13,14] or at the interface of the macro-phase separations [1,4,6,8,9,12]. This selective localization of conductive fillers contributes to reducing the amount of fillers required for obtaining conductive properties. Sumita et al. reported that CPCs with blended matrices have two different hierarchies of percolation at different scales, known as double percolation [1]. When loaded in high-density polyethylene (HDPE)/poly(methyl methacrylate) (PMMA) blends, CB was selectively located in the HDPE phase of macro-phase separation, and the HDPE phase was estimated to be the conductive phase. In this case, the electrical conduction was determined by the percolation of CB in the HDPE phase and the percolation of the conductive HDPE phase in HDPE/PMMA blends. In this system, the conductivity increased significantly at a low volume fraction of CB less than 0.05-0.1, which corresponds to the conductive percolation threshold ϕ c . In the double percolation system using CNTs as a filler, a ϕ c Polymers 2020, 12, 2658 3 of 11 The affinity between the P3HT nanofiber and PB or PEG was determined by scanning force microscopy (SFM) of the P3HT/PB or P3HT/PEG composites, as shown in Figure S1 in Supporting Information A. In P3HT/PB, P3HT nanofibers were dispersed uniformly in the PB matrix, whereas in P3HT/PEG, nanofibers were aggregated and distributed unevenly in the PEG matrix. PB/PEG blends loaded with P3HT nanofibers were prepared in accordance with the procedure reported in the cases of polymethyl methacrylate (PMMA) or polystyrene (PS) as the matrix [25,26,29]. P3HT, PB, and PEG powders were added to a solvent mixture composed of chloroform, as a good solvent of P3HT, and anisole, as a poor solvent of P3HT, stirred at 60-70 • C for 60 min. The weight ratio of P3HT was fixed at 0.05 wt% in all samples, with 70:30 (v/v) solvent mixture of chloroform/anisole. For varying the blended matrix composition, we prepared solutions with a volume fraction of ϕ PB = V PB /(V PB + V PEG ) of approximately 0.22-0.93 with a fixed ratio of P3HT to the matrix of 10 wt%. V PB , V PEG , and V P3HT are the volume of PB, PEG, and P3HT components, respectively, estimated from the weight and density of each component. On the other hand, for varying the density of P3HT nanofibers in the blended matrix, we prepared solutions with a volume fraction of ϕ P3HT = V P3HT /(V PB + V P3HT ) of 0.02-0.30 with a fixed matrix composition (ϕ PB = 0.72-0.73). As P3HT had a good affinity with the PB component to be localized in the PB phase, we used the volume fraction ϕ P3HT instead of V P3HT /(V PB + V PEG + V P3HT ). Each solution was cooled gradually to 20 • C at a rate of 25 • C/h without stirring. Over one week of incubation, the transparent yellow solution turned into a turbid reddish-brown suspension, indicating fiber formation. Films of PB/PEG blends loaded with P3HT nanofibers were prepared by spin casting the suspensions at 2000 rpm for 90 s on a substrate, followed by removal of the residual solvent by vacuum drying.

Characterization of PB/PEG Blends Loaded with P3HT Nanofibers
Pt electrodes with a length of 0.6 mm and a gap of 40 µm were fabricated with a bottom-contact configuration by sputter deposition (EIS-200ER, Elionix Inc., Tokyo, Japan), using a shadow mask on a piece of doped Si wafer with a 255 nm SiO 2 layer that was thermally grown on top (SiO 2 /Si), purchased from SEIREN KST Corp. (Fukui, Japan), as shown in Figure S2 in Supporting Information B.
The microscopic structure of the composites was observed in air with a scanning probe microscope (SPM; Nanocute/NanoNavi IIe, Hitachi High-Tech Science Corp., Tokyo, Japan) under the SFM mode. The instrument was equipped with a commercial silicon cantilever (OMCL-AC160TS-C3, Olympus Corp., Tokyo, Japan) with a spring constant and a resonant frequency of approximately 26 N/m and 300 KHz, respectively. The thickness was measured by a stylus profilometer (Dektak XT-S, Bruker Japan Inc., Yokohama, Japan).
Field-effect transistor (FET) measurements were conducted by a two-probe method in vacuum below 10 −5 Torr, using a system combining a cryogenic probing station (LIPS, Nagase Techno-Engineering Co. Ltd., Tokyo, Japan) and the Keithley model 236 source measure unit (SMU) (Keithley Instruments, Inc., Cleveland, OH, USA) to measure the source-drain characteristics, and a Keithley 2400 digital source meter (Keithley Instruments, Inc., Cleveland, OH, USA) for applying the gate voltage.

Selective Localization of P3HT Nanofibers in PB/PEG Blends
To confirm the distribution of P3HT nanofibers in the PB/PEG blended matrix, SFM observation of the thin-film of the composites was performed by changing the blend ratio of PB/PEG. Figure 1 shows SFM phase images with changing ϕ PB from 0.22 to 0.72. Through all images, the sea-island structure originating from the macro-phase separation was observed. In all images, the bright phase corresponded to the PB component. For low values of ϕ PB (Figure 1a (major) phase of the PB component was at ϕ c of between 0.40 and 0.57, and a continuous structure of the PB phase could be observed at ϕ PB greater than ϕ c . Furthermore, it was found that P3HT nanofibers were positioned mostly in the PB component of the sea-island structure. P3HT nanofibers were mostly localized in the island phase at ϕ PB < ϕ c , while nanofibers were mostly localized in the continuous sea phase at ϕ PB > ϕ c , indicating that P3HT nanofibers were selectively partitioned into the PB phase. In particular, the percolation behavior of the PB phase in PB/PEG blends selectively embedded with P3HT nanofibers could be observed with increasing ϕ PB .
Polymers 2020, 12, x 4 of 11 partitioned into the PB phase. In particular, the percolation behavior of the PB phase in PB/PEG blends selectively embedded with P3HT nanofibers could be observed with increasing φPB.

Electrical Conductivity of PB/PEG Blends Loaded with P3HT Nanofiber
The electrical conductivity of PB/PEG blends loaded with P3HT nanofibers was investigated. With increasing φPB at a fixed P3HT ratio, the percolation of the PB phase in the PB/PEG blends were observed as an electrical percolation of the conductivity σ because the PB phase selectively embedded with P3HT nanofibers can be regarded as a conductive phase. Figure 2 shows the φPB dependence of σ of the PB/PEG blends loaded with P3HT. The PB/PEG blends had almost constant σ values in the low φPB region, while σ increased drastically with φPB in the region above the crossover point at φBR =

Electrical Conductivity of PB/PEG Blends Loaded with P3HT Nanofiber
The electrical conductivity of PB/PEG blends loaded with P3HT nanofibers was investigated. With increasing ϕ PB at a fixed P3HT ratio, the percolation of the PB phase in the PB/PEG blends were observed as an electrical percolation of the conductivity σ because the PB phase selectively embedded with P3HT nanofibers can be regarded as a conductive phase. Figure 2 shows the ϕ PB dependence of σ of the PB/PEG blends loaded with P3HT. The PB/PEG blends had almost constant σ values in the low ϕ PB region, while σ increased drastically with ϕ PB in the region above the crossover point at ϕ BR = 0.57. When ϕ PB < 0.57, PB phase as a minor component formed isolated island, and the electrical conduction suggested to be dependent on the sea phase of PEG component, which embedded with P3HT, only to a small extent, connecting the conductive PB islands. As the PB phase has a continuous structure at ϕ PB over 0.57, σ increases due to the percolation of the PB phase in the PB/PEG blends. P3HT, only to a small extent, connecting the conductive PB islands. As the PB phase has a continuous structure at φPB over 0.57, σ increases due to the percolation of the PB phase in the PB/PEG blends. Here, φPB = 0.57 can be regarded as the percolation threshold φc I . In the percolation model, σ follows the relation ~( − ) ; thus, a critical exponent t I could be estimated to be 1.3 from the slope of the inserted chart in Figure 2. In the percolation model, it is known that two-dimensional percolation theoretically has a critical exponent of 1.3 [34]; hence, this composite film evidently exhibits two-dimensional percolation of the PB phase. Here, the average diameter of the islands of the PB component in Figure 1b was estimated to be 4.4 µm, which corresponded to a characteristic length of the sea-island structure around the critical point. The characteristic length was much larger than the film thickness of approximately 60-100 nm, and the degree of freedom was suppressed in the direction of the thickness; therefore, it was evident that the percolation behaved as a twodimensional system with t I of 1.3. Furthermore, the percolation threshold φc I of 0.57 also indicated the two-dimensional percolation because φc of two-and three-dimensional percolation was theoretically estimated to be 0.45 and 0.16, respectively [35].
On the other hand, increasing P3HT ratio in the matrix at a fixed PB/PEG ratio, drastically increased σ. Figure 3 shows the φP3HT dependence of the conductivity σ of the PB/PEG blends loaded with P3HT. σ was less than 10 -8 S cm -1 in the region of φP3HT < 0.02. Therefore, the percolation threshold φc II was estimated to be 0.02, which was considerably smaller than φc I . Generally, anisotropic fillers with small diameters and high aspect ratios, such as CNTs, are reported to exhibit a low percolation threshold from 0.08 to 3 wt% in CPC with a blended matrix [8][9][10][11][12][13][14]. Furthermore, in our previous studies on composite films of P3HT nanofibers in polymethacrylate (PMMA), a significant amount of conductivity was measured for the ratio of P3HT/PMMA at approximately 5 wt% [28]. The SFM observations at different ratios of P3HT/PMMA was reported previously [31]. The nanofiber network formation was observed above 1 wt% and nanofiber aggregation occurred above 10 wt%. The results of the present study show that the P3HT nanofiber with a diameter of approximately 15 nm [24] and an aspect ratio of more than 100 resulted in φc II = 0.02, which is consistent with the results of previous studies.
Conductivity σ is assumed to follow the relation ~( − ) , and the critical exponent t II Here, ϕ PB = 0.57 can be regarded as the percolation threshold ϕ c I . In the percolation model, ; thus, a critical exponent t I could be estimated to be 1.3 from the slope of the inserted chart in Figure 2. In the percolation model, it is known that two-dimensional percolation theoretically has a critical exponent of 1.3 [34]; hence, this composite film evidently exhibits two-dimensional percolation of the PB phase. Here, the average diameter of the islands of the PB component in Figure 1b was estimated to be 4.4 µm, which corresponded to a characteristic length of the sea-island structure around the critical point. The characteristic length was much larger than the film thickness of approximately 60-100 nm, and the degree of freedom was suppressed in the direction of the thickness; therefore, it was evident that the percolation behaved as a two-dimensional system with t I of 1.3. Furthermore, the percolation threshold ϕ c I of 0.57 also indicated the two-dimensional percolation because ϕ c of two-and three-dimensional percolation was theoretically estimated to be 0.45 and 0.16, respectively [35].
On the other hand, increasing P3HT ratio in the matrix at a fixed PB/PEG ratio, drastically increased σ. Figure 3 shows the ϕ P3HT dependence of the conductivity σ of the PB/PEG blends loaded with P3HT. σ was less than 10 −8 S cm −1 in the region of ϕ P3HT < 0.02. Therefore, the percolation threshold ϕ c II was estimated to be 0.02, which was considerably smaller than ϕ c I . Generally, anisotropic fillers with small diameters and high aspect ratios, such as CNTs, are reported to exhibit a low percolation threshold from 0.08 to 3 wt% in CPC with a blended matrix [8][9][10][11][12][13][14]. Furthermore, in our previous studies on composite films of P3HT nanofibers in polymethacrylate (PMMA), a significant amount of conductivity was measured for the ratio of P3HT/PMMA at approximately 5 wt% [28]. The SFM observations at different ratios of P3HT/PMMA was reported previously [31]. The nanofiber network formation was observed above 1 wt% and nanofiber aggregation occurred above 10 wt%. The results of the present  [24] and an aspect ratio of more than 100 resulted in ϕ c II = 0.02, which is consistent with the results of previous studies.
Conductivity σ is assumed to follow the relation σ ∼ φ P3HT − φ II c t II , and the critical exponent t II could be estimated to be 1.7 from the slope of the inserted chart in Figure 3. This value is between the theoretical critical exponent of two-dimensional percolation of 1.3 and three-dimensional percolation of 2.0 [36]; thus, these composites likely have percolation dimensionality that is between that of two and three dimensions. The length of the P3HT nanofiber was almost a few µm [24]. This length was comparable to the width of the continuous channel comprising the PB component approximately 2 µm, but was an order of magnitude larger than the film thickness. Thus, t II of 1.7, which was larger than t I and an intermediate value of two-and three-dimensional percolation, was agreeable. In previous studies of CPCs using CB or CNT as fillers, t was reported to be in the range of 1.3 to 6.4 [6,9,10,36]. Please note that a value of t much larger than 2.0 was frequently reported, which was far from the ideal value estimated by percolation theory, and was ascribed to the effect of aggregation on CB or CNT. In sharp contrast, our system presented in this work shows that the P3HT nanofibers were well-dispersed in the PB phase without apparent aggregation, resulting in a critical exponent within the ideal range. previous studies of CPCs using CB or CNT as fillers, t was reported to be in the range of 1.3 to 6.4 [6,9,10,36]. Please note that a value of t much larger than 2.0 was frequently reported, which was far from the ideal value estimated by percolation theory, and was ascribed to the effect of aggregation on CB or CNT. In sharp contrast, our system presented in this work shows that the P3HT nanofibers were well-dispersed in the PB phase without apparent aggregation, resulting in a critical exponent within the ideal range. Figure 3. The volume fraction of P3HT nanofiber φP3HT dependence of the conductivity σ. The percolation threshold φc II was estimated to be 0.02. The inserted chart shows log σ v/s. log (φP3HTφc II ). From a slope, the critical exponent t II can be estimated to be 1.7.
The double percolation, percolation thresholds, and critical exponents of both percolations observed in our present system are summarized in Figure 4. The percolation of the PB phase loaded with the P3HT nanofiber in the PB/PEG blend was observed at a larger scale. φc I and t I of this percolation were estimated to be 0.57 and 1.3, respectively, which corresponded to two-dimensional percolation. By contrast, the percolation of the P3HT nanofiber network in the PB phase was observed at a smaller scale. φc I and t I of this percolation were estimated to be 0.02 and 1.7, respectively, which was regarded as the percolation with intermediate dimensionality between two and three. The values characterizing the critical phenomena of our system were in the theoretical estimation, unlike inorganic fillers such as CB and CNT. This ideal behavior was ascribed to the characteristics of our system being the composition of all polymer materials, including fillers well-dispersed in a selective phase. The percolation threshold ϕ c II was estimated to be 0.02. The inserted chart shows log σ v/s. log (ϕ P3HT -ϕ c II ). From a slope, the critical exponent t II can be estimated to be 1.7.
The double percolation, percolation thresholds, and critical exponents of both percolations observed in our present system are summarized in Figure 4. The percolation of the PB phase loaded with the P3HT nanofiber in the PB/PEG blend was observed at a larger scale. ϕ c I and t I of this percolation were estimated to be 0.57 and 1.3, respectively, which corresponded to two-dimensional percolation. By contrast, the percolation of the P3HT nanofiber network in the PB phase was observed at a smaller scale. ϕ c I and t I of this percolation were estimated to be 0.02 and 1.7, respectively, which was regarded as the percolation with intermediate dimensionality between two and three. The values characterizing the critical phenomena of our system were in the theoretical estimation, unlike inorganic fillers such as CB and CNT. This ideal behavior was ascribed to the characteristics of our system being the composition of all polymer materials, including fillers well-dispersed in a selective phase.
percolation. By contrast, the percolation of the P3HT nanofiber network in the PB phase was observed at a smaller scale. φc I and t I of this percolation were estimated to be 0.02 and 1.7, respectively, which was regarded as the percolation with intermediate dimensionality between two and three. The values characterizing the critical phenomena of our system were in the theoretical estimation, unlike inorganic fillers such as CB and CNT. This ideal behavior was ascribed to the characteristics of our system being the composition of all polymer materials, including fillers well-dispersed in a selective phase.

Field-Effect Mobility of PB/PEG Blends Loaded with P3HT Nanofiber
To investigate the carrier transport around the critical threshold, FET measurements of the PB/PEG blend films loaded with P3HT nanofibers were performed. Figure 5 shows the transfer characteristics of the sample with a fixed P3HT ratio to the matrix (approximately 10 wt%) but a different φPB = 0.40 and 0.72, which are below and above the critical threshold φc I , respectively. In

Field-Effect Mobility of PB/PEG Blends Loaded with P3HT Nanofiber
To investigate the carrier transport around the critical threshold, FET measurements of the PB/PEG blend films loaded with P3HT nanofibers were performed. Figure 5 shows the transfer characteristics of the sample with a fixed P3HT ratio to the matrix (approximately 10 wt%) but a different ϕ PB = 0.40 and 0.72, which are below and above the critical threshold ϕ c I , respectively. In both cases, a typical p-type property was observed, where the marked amplification of I DS with respect to the negative gate voltage V G , but the on-off ratio of 30 and 13 was very small. Here, the field-effect mobility (µ) was determined using the following relation: where L is the spacing between the electrodes, W is the width of the electrodes, and C ox is the capacitance of the insulation layer of SiO 2 (255 nm thick), shown in Table S1 in Supporting Information B. From the transport characteristics, µ was estimated to be 1.85 × 10 −4 cm 2 V −1 s −1 (ϕ PB = 0.40) and 2.86 × 10 −3 cm 2 V −1 s −1 (ϕ PB = 0.72), indicating that µ increased by an order of magnitude at ϕ c I .
In the region of ϕ PB < ϕ c I , the conducting PB component formed a separated island phase and slightly embedded P3HT in the PEG sea phase connected with the PB islands. Carrier transport in the sea phase is ascribed to the rate-limiting step of conduction and decreases the carrier mobility. On the other hand, in the region of ϕ PB > ϕ c I , µ was comparable to that of P3HT nanofibers composited in PMMA single matrix reported previously [25][26][27][28]; hence, the carrier conduction was scarcely affected by the PEG island phase.
Polymers 2020, 12, x 7 of 11 both cases, a typical p-type property was observed, where the marked amplification of IDS with respect to the negative gate voltage VG, but the on-off ratio of 30 and 13 was very small. Here, the field-effect mobility (μ) was determined using the following relation: where L is the spacing between the electrodes, W is the width of the electrodes, and Cox is the capacitance of the insulation layer of SiO2 (255 nm thick), shown in Table S1 in Supporting Information B. From the transport characteristics, μ was estimated to be 1.85 × 10 -4 cm 2 V -1 s -1 (φPB = 0.40) and 2.86 × 10 -3 cm 2 V -1 s -1 (φPB = 0.72), indicating that μ increased by an order of magnitude at φc I . In the region of φPB < φc I , the conducting PB component formed a separated island phase and slightly embedded P3HT in the PEG sea phase connected with the PB islands. Carrier transport in the sea phase is ascribed to the ratelimiting step of conduction and decreases the carrier mobility. On the other hand, in the region of φPB > φc I , μ was comparable to that of P3HT nanofibers composited in PMMA single matrix reported previously [25][26][27][28]; hence, the carrier conduction was scarcely affected by the PEG island phase. The field-effect mobility of the PB/PEG blend film with φPB = 0.72 (> φc I ) loaded with P3HT nanofiber at a fixed P3HT to matrix ratio (approximately 10 wt%) was measured from 60 K to 300 K, and the results are shown in Figure 6. With increasing temperature, μ increased as thermo-activated The field-effect mobility of the PB/PEG blend film with ϕ PB = 0.72 (>ϕ c I ) loaded with P3HT nanofiber at a fixed P3HT to matrix ratio (approximately 10 wt%) was measured from 60 K to 300 K, and the results are shown in Figure 6. With increasing temperature, µ increased as thermo-activated behavior. The relationship of log µ with T −1/4 was almost linear; hence, the carrier transport was suggested to be a three-dimensional variable range hopping (VRH) type. This VRH relationship is consistent with that of various types of conducting polymers reported previously [37], and the effect of the matrix on the carrier conduction thus could not be observed. As the carrier transport can be regarded as a percolation of carriers in the nanofiber network, we could see three types of percolation with different scales in PB/PEG blends loaded with P3HT nanofibers, and the dimension decreased from three to two with an increase in the observation scale.

Conclusions
We investigated the critical phenomena of double percolation on polybutadiene (PB)/polyethylene glycol (PEG) blends loaded with poly-3-hexylthiophene (P3HT) nanofibers. P3HT nanofibers were selectively located in the PB phase of the PB/PEG blends, and hence the PB phase could be regarded as a conductive phase. In this system, double percolation phenomena could be observed. The percolation threshold of the PB phase in the PB/PEG blends was φc I = 0.57, and the critical exponent t I was estimated to be 1.3. These critical values indicated two-dimensional percolation. The film thickness of approximately 60-100 nm, which was considerably smaller than the characteristic length of the PB islands, also indicated that the percolation behaved as a twodimensional system. On the other hand, the percolation threshold of the P3HT nanofiber in the PB phase was φc II = 0.02, and the critical exponent t II was estimated to be 1.7. As the length of the P3HT nanofiber was comparable to the width of the continuous channel comprising the PB component, it was an order of magnitude larger than the film thickness. This was in agreement with that t II of 1.7 was an intermediate value between two-and three-dimensional percolation. As a result, the critical phenomena of double percolation on polymer blends loaded with P3HT nanofibers can be clearly explained by the percolation theory. In addition, the temperature dependence of the field-effect mobility estimated by FET measurement was also explained by the three-dimensional VRH model. As the carrier transport can be regarded as a percolation of carriers in the nanofiber network, we could see multi-percolation with different scales in PB/PEG blends loaded with P3HT nanofibers.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1: The SFM phase images of P3HT nanofiber composited in a) PB and b) PEG matrix (20 µm × 20 µm). From the images, P3HT nanofibers were uniformly dispersed in PB matrix while nanofibers aggregated each other in PEG matrix., Figure S2: Optical microscope images of a substrate with electrodes for measuring conductivity and estimating the field-effect mobility, Figure S3: Temperature dependence of the transfer characteristics of the PB/PEG blend film loaded with P3HT nanofiber with φPB = 0.72 (> φc I ) from 60 K to 300 K, Table S3: The spacing between the electrodes L, the width of the electrodes W, and the capacitance of the insulation layer of SiO2 (255-nm thick) Cox.

Conclusions
We investigated the critical phenomena of double percolation on polybutadiene (PB)/polyethylene glycol (PEG) blends loaded with poly-3-hexylthiophene (P3HT) nanofibers. P3HT nanofibers were selectively located in the PB phase of the PB/PEG blends, and hence the PB phase could be regarded as a conductive phase. In this system, double percolation phenomena could be observed. The percolation threshold of the PB phase in the PB/PEG blends was ϕ c I = 0.57, and the critical exponent t I was estimated to be 1.3. These critical values indicated two-dimensional percolation. The film thickness of approximately 60-100 nm, which was considerably smaller than the characteristic length of the PB islands, also indicated that the percolation behaved as a two-dimensional system. On the other hand, the percolation threshold of the P3HT nanofiber in the PB phase was ϕ c II = 0.02, and the critical exponent t II was estimated to be 1.7. As the length of the P3HT nanofiber was comparable to the width of the continuous channel comprising the PB component, it was an order of magnitude larger than the film thickness. This was in agreement with that t II of 1.7 was an intermediate value between two-and three-dimensional percolation. As a result, the critical phenomena of double percolation on polymer blends loaded with P3HT nanofibers can be clearly explained by the percolation theory. In addition, the temperature dependence of the field-effect mobility estimated by FET measurement was also explained by the three-dimensional VRH model. As the carrier transport can be regarded as a percolation of carriers in the nanofiber network, we could see multi-percolation with different scales in PB/PEG blends loaded with P3HT nanofibers.
Supplementary Materials: The following are available online at http://www.mdpi.com/2073-4360/12/11/2658/s1, Figure S1: The SFM phase images of P3HT nanofiber composited in (a) PB and (b) PEG matrix (20 µm × 20 µm). From the images, P3HT nanofibers were uniformly dispersed in PB matrix while nanofibers aggregated each other in PEG matrix., Figure S2: Optical microscope images of a substrate with electrodes for measuring conductivity and estimating the field-effect mobility, Figure S3: Temperature dependence of the transfer characteristics of the PB/PEG blend film loaded with P3HT nanofiber with ϕPB = 0.72 (>ϕcI) from 60 K to 300 K, Table S3: The spacing between the electrodes L, the width of the electrodes W, and the capacitance of the insulation layer of SiO 2 (255-nm thick) Cox.