Figure 1 reveals the chemical buildings of the mannequin methods, PTB7-Th and ITIC. Specifically, PTB7-Th (also referred to as PCE10 or PBDTTT-EFT) is a excessive efficiency polymer based mostly on two-dimensional (2D) benzodithiophene (BDT) and thieno[3,4-b]thiophene (TT) models^{19}. In this examine, we investigated the part behavior of the ternary CB/PTB7-Th/ITIC resolution based mostly on the Flory–Huggins lattice mannequin. According to Yilmaz et al.^{43}, the Flory–Huggins mannequin for a ternary polymer resolution may very well be expressed as follows^{44,45},

$$frac{{Delta G_{combine} }}{RT} = n_{1} ln phi_{1} + n_{2} ln phi_{2} + n_{3} ln phi_{3} + chi_{12} n_{1} phi_{2} + chi_{13} n_{1} phi_{3} + chi_{23} n_{2} phi_{3}$$

(1)

the place (Delta G_{combine}) is the molar Gibbs power of mixing,* R* is the Gas fixed, *T* is temperature, (phi_{i}) is quantity fraction of element *i*, and (n_{i}) is the quantity of moles of element (i). Furthermore,(chi_{ij} {{ = hat{V}_{1} } mathord{left/ {vphantom {{ = hat{V}_{1} } {RT}}} proper. kern-nulldelimiterspace} {RT}}left( {delta_{i} – delta_{j} } proper)^{2} + 0.34) is the intermolecular interplay parameter^{46}, during which (hat{V}_{1}) is a molar quantity of solvent and (delta_{i}) or (delta_{j}) is a solubility parameter of element (i) or (j) (= 1, 2, and 3). Note that on this work, the parts 1, 2, and 3 correspond to solvent, polymer, and nonsolvent, respectively. Then, via the equilibrium of the chemical potential, (Delta mu_{i}^{alpha } = Delta mu_{i}^{beta } quad left( {i = 1,;2,;3} proper)), the binodal curve may very well be calculated for ternary methods^{30}. Here, (Delta mu_{i}) is outlined as ({{partial Delta G_{combine} } mathord{left/ {vphantom {{partial Delta G_{combine} } {partial n_{i} }}} proper. kern-nulldelimiterspace} {partial n_{i} }}), and the spinodal curve and vital level may very well be obtained from the second and third derivatives of (Delta G_{combine}), respectively, in line with our earlier works^{30,31,32} (see supplementary data for particulars). Here, the parameters used for this theoretical work had been summarized in Table 1. Note that the molar quantity ((v_{i} = {{MW_{i} } mathord{left/ {vphantom {{MW_{i} } {rho_{i} }}} proper. kern-nulldelimiterspace} {rho_{i} }})) may very well be calculated from the ratio of molecular weight and density. For instance, PTB7-Th has (v_{2}) = {(300,000 g/mol)/(1.15 g/cm^{3})} = 260,870 cm^{3}/mol and ITIC has (v_{3}) = {(1428 g/mol) /(1.24 g/cm^{3})} = 1152 cm^{3}/mol, respectively.

Figure 2 reveals the ternary isothermal part diagrams of the CB/PTB7-Th/ITIC system as a operate of the quantity common molecular weight (M_{n}) (bodily, equal to chain size) at *T* = 298 Ok. Table 2 reveals the parameters used for calculating these part diagrams. As proven in Fig. 2, the vital level could shift up from the axis (PTB7-Th and ITIC) with rising (M_{n}), indicating the liquid–liquid (L–L) demixing is extra favorable in excessive (M_{n}) polymer. Notably, the vital factors (left( {phi_{1c} ,;phi_{2c} ,;phi_{3c} } proper)) are (0.6774, 0.0659, 0.2566) at 50 kg/mol, (0.7249, 0.0443, 0.2307) at 100 kg/mol, (0.7543, 0.0311, 0.2145) at 200 kg/mol, and (0.7676, 0.0251, 0.2071) at 300 kg/mol, respectively. Hence, as rising (M_{n}), one part resolution will be simply phase-separated at diluted focus. Here, the demixing hole is outlined by binodal curve, indicating L-L part transition. Furthermore, the hole space between binodal and spinodal curve is a metastable area whereas the world beneath the spinodal is an unstable area. When an answer passes via a spinodal curve into an unstable area, we name it spinodal decomposition^{50,51}. Kahn and Hilliard advised a kinetic mannequin for explaining the spinodal decomposition course of as follows^{50,51},

$$frac{partial c}{{partial t}} = Mleft( {frac{{partial^{2} f}}{{partial c^{2} }}} proper)nabla^{2} c – 2Mkappa nabla^{4} c$$

(2)

the place (c) is focus, *t* is time, *M* is a mobility, *f* is a free power density of homogeneous materials of composition *c* and (kappa) is a constructive parameter, respectively. In polymer solutions, *f* corresponds to (Delta G_{combine})^{52,53,54}. Basically, it’s Fick’s regulation of diffusion with diffusivity (D = Mleft( {{{partial^{2} f} mathord{left/ {vphantom {{partial^{2} f} {partial c^{2} }}} proper. kern-nulldelimiterspace} {partial c^{2} }}} proper)). In unstable area, ‘({{partial^{2} f} mathord{left/ {vphantom {{partial^{2} f} {partial c^{2} }}} right. kern-nulldelimiterspace} {partial c^{2} }} < 0) → (;;D < 0)’ signifies an uphill diffusion, leading to (1) a spontaneous part separation with out nucleation, and (2) connectivity of the D:A phases becoming for interpenetrating BHJ construction for polymer PV gadgets. On the opposite hand, in a metastable area, ‘ ({{partial^{2} f} mathord{left/ {vphantom {{partial^{2} f} {partial c^{2} }}} right. kern-nulldelimiterspace} {partial c^{2} }} > 0) → (;;D > 0)’ denotes a down-hill diffusion, the place nucleation course of wants a piece (*W*) as follows^{55},

$$W = 4pi r^{2} gamma – frac{4}{3}pi r^{3} Delta P$$

(3)

the place (gamma) is the floor rigidity on the interface, *r* is the radius of nucleus, and (Delta P) is the hydrostatic stress requiring to keep up nucleus in equilibrium with the outside part. Through the primary spinoff of Eq. (3), we could acquire a vital radius, (r_{crit} = {{2gamma } mathord{left/ {vphantom {{2gamma } {Delta P}}} proper. kern-nulldelimiterspace} {Delta P}}). Hence, the minimal work ((W_{min })) is ({4 mathord{left/ {vphantom {4 3}} proper. kern-nulldelimiterspace} 3} cdot pi r_{crit}^{2} gamma), indicating {that a} nucleus can develop when (r > r_{crit}) in any other case it collapses. At this second, it’s noteworthy that above two part separation mechanism (i.e., spinodal decomposition and nucleation-and-growth) are amorphous-amorphous (or L-L) part separation. However, as shared with insulating polymers (*i.e*., saturated hydrocarbons with sp^{3} hybridization), not solely amorphous part separation, but additionally crystallization might proceed concurrently in polymer solutions. Specifically, within the PTB7-Th:ITIC system, ITIC is very crystallizable, indicating that the crystallization of ITIC may very well be one other route for part separation.

Figure 3 reveals the ternary part diagrams of the CB/PTB7-Th/ITIC system as a operate of temperature. Here, by rising temperature, the vital factors had been shifted down towards the PTB7-Th‒ITIC axis, indicating the higher vital resolution temperature (UCST) part behavior. Importantly, the temperature-induced part separation (TIPS) is a typical course of for a membrane formation based mostly on the UCST part behavior. At this second, it’s noteworthy that though π-bonded semiconducting polymer and saturated insulating polymer have totally different hybridization akin to sp^{2}p_{z} vs. sp^{3}, the origin of part separation akin to TIPS, immersion precipitation, and others may very well be shared one another, indicating that the wealthy data amassed within the area of insulating polymers^{56,57} may very well be utilized for π-bonded semiconducting and metallic polymers.

Figure 4 reveals the ternary part diagrams of (a) CB/PTB7-Th/PC_{61}BM and (b) CB/PTB7-Th/PC_{71}BM methods for analyzing the impact of electron acceptors on the part behavior of polymer solutions. These part diagrams in Fig. 4 may very well be in contrast with that of CB/PTB7-Th/ITIC (at *T* = 298 Ok and *M*_{n} = 300 kg/mol) in Fig. 2nd. As proven in Fig. 4, the fullerene derivatives (PC_{61}BM and PC_{71}BM) have a greater miscibility with PTB7-Th than the non-fullerene ITIC by displaying a smaller demixing hole beneath every spinodal curve. Furthermore, PC_{71}BM is extra miscible with PTB7-Th than PC_{61}BM within the PTB7-Th/CB solutions. Table 2 summarizes the parameters used for this comparability.

Until now, we investigated part behavior of ternary polymer solutions based mostly on Flory–Huggins concept. Now, allow us to look at it utilizing experimental instruments akin to AFM, water contact-angle and XRD. Figure 5 reveals the tapping mode AFM top picture of a pure PTB7-Th movie, exhibiting a extremely disordered morphology with common floor roughness (~ 0.65 nm) and root-mean-square roughness (~ 0.914 nm). On the opposite hand, its corresponding part picture reveals uniformity inside the instrumental decision of this AFM (see Figure S1 in Supplementary Information). In addition, we investigated the topographies of every mix movie as a operate of composition (Figure S2). However, in our examine, by the AFM picture alone, it was onerous to interpret the part behavior of PTB7-Th:ITIC movie samples. Hence, we depend on different experimental methodologies akin to XRD and water contact-angle measurement.

Figure 6a reveals the water contact-angle knowledge as a operate of composition, which was carried out to look at the floor power relying on the microstructures of a movie as our earlier research^{30,32}. Note that the info is a median worth by measuring eight totally different spots of a movie. As proven in Fig. 6a, the general commentary is that the contact angle change at ~ 60 ± 10 wt.% ITIC, during which just a little fluctuation in knowledge could comprise an experimental uncertainty on this water contact-angle experiment. Second, when the composition is bigger than or equal to ~ 70 wt.% ITIC, the water contact angle decreases linear, indicating the enhancement of hydrophilicity of skinny movies. This is as a result of ITIC with *δ* = 11.8 (cal/cm^{3})^{1/2} is extra polar than PTB7-Th with *δ* = 9.3 (cal/cm^{3})^{1/2} (see Table 1). Importantly, to the very best of authors’ data, that is the primary detailed report demonstrating that the contact-angle measurement may very well be a great tool for figuring out the part separation of π-bonded polymer blends. Figure 6b reveals a schematic expression concerning a part separation course of within the PTB7-Th:ITIC movies. When there may be small quantity of ITIC within the binary mix movie, ITIC could dissolve into the free quantity of PTB7-Th, forming a strong resolution. However, when the composition of PTB7-Th:ITIC is ~ 60 ± 10 wt. % ITIC, the ITIC molecules could also be phase-separated out. Note that if the water contact-angle knowledge weren’t associated with the phase-separation morphology however with a easy composition solely (PTB7-Th:ITIC wt. ratio), it might lower linearly from 70.51 ± 4.84° (PTB7-Th) to 38.80 ± 3.99° (ITIC). However, as proven in Fig. 6a, the info pattern just isn’t linear, however shows a drastic change at ~ 60 ± 10 wt. % ITIC, suggesting a part separation as schematically defined in Fig. 6b.

Figure 7 reveals the XRD sample as a operate of composition. When the composition of the PTB7-Th:ITIC blends is within the vary of 10 to 60 wt.% ITIC, the XRD patterns are overlapped with a pure PTB7-Th polymer (i.e., 0 wt.% ITIC) as proven in Fig. 7a. Here, it’s notable that the extremely disordered PTB7-Th is thought to be on the boundary of amorphous and semicrystalline^{39}. However, on this examine, in line with the XRD knowledge in Fig. 7a, PTB7-Th is solely amorphous, displaying a typical amorphous halo. In normal, amorphous polymers haven’t any lengthy vary order aside from a brief one though there have been some reviews claiming domestically ordered areas in an amorphous polymer^{58,59}. Interestingly, when the composition is within the vary of 70 to 100 wt.% ITIC (Fig. 7b and c), the sharp crystallite peaks had been noticed, indicating that ITIC was phase-separated out via crystallization. Notably, the crystallite dimension (*t*) was estimated via the Scherrer equation (t = {{Ok cdot lambda } mathord{left/ {vphantom {{Ok cdot lambda } {left( {beta cdot cos theta } proper)}}} proper. kern-nulldelimiterspace} {left( {beta cdot cos theta } proper)}}), during which *Ok* is 0.98, (lambda) is 0.154 nm, and (beta) is a full width at half most (FWHM) at angle, (2theta approx 21.3^circ). Resultantly, when the compositions of PTB7-Th:ITIC blends had been 30:70, 20:80, 10:90, and 0:100 (weight ratio), the estimated *t* was 65.5 nm, 68.8 nm, 77.2 nm, and 68.7 nm, respectively (see Table 3). Hence, the typical crystallite dimension is ~ 70.05 ± 5.01 nm. However, if we calculate the amorphous halo based mostly on the identical Scherrer equation, the *t* worth could be 1.3 nm when (beta) = 0.118682 and (2theta approx 23.5^circ), indicating the height is an amorphous halo as anticipated. Note that ITIC single crystal was reported to have lattice parameters of **a** = 14.88 Å, **b** = 15.47 Å, **c** = 18.08 Å, *α* = 99.27°, *β* = 101.50°, and *γ* = 108.37°^{60}. Thus the estimated *t* worth is lower than any lattice parameter of ITIC, suggesting that the PTB7-Th:ITIC blends (ITIC (le) 60 wt.%) are in amorphous state as proven in Fig. 7a. Finally, contemplating that, via the XRD patterns, we will look at solely crystallization as an proof of part separation (i.e., liquid–strong part transition), the ternary part diagrams in Figs. 2, 3, and 4 displaying liquid–liquid part transition (akin to spinodal decomposition in an unstable area and nucleation-and-growth in a metastable area) ought to be vital for understanding the part behavior of PTB7-Th based mostly blends and solutions, at the least qualitatively. Remind that two totally different part separation (i.e., amorphous L-L and crystallization) could proceed concurrently^{56,57} in polymer solutions with a crystallizable element, suggesting that it is very important perceive ternary part diagrams in Figs. 2, 3, and 4 based mostly on Flory–Huggins concept.

### Phase behavior of π-conjugated polymer and non-fullerene acceptor (PTB7-Th:ITIC) solutions and blends

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### Phase behavior of π-conjugated polymer and non-fullerene acceptor (PTB7-Th:ITIC) solutions and blends

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### Phase behavior of π-conjugated polymer and non-fullerene acceptor (PTB7-Th:ITIC) solutions and blends

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