## 1 Introduction  
Windows are an essential component in almost every building. Switchable glass, also known as a smart window, provides tunable shading that can improve the indoor occupant comfort and reduce the energy consumption caused by heating and cooling of a building [1, 2]. For smart windows, electrochromic materials are of high interest [3, 4]. Along with an electrolyte containing small ions, electrochromic thin films can offer a reversible coloration under an applied voltage [1, 5]. Tungsten oxide (WO\({}_{3}\)) is a widely used electrochromic material [6, 7] that can change color from colorless transparent to dark blue with good switching characteristics upon reduction and intercalation of small charge-balancing countercations such as H\({}^{+}\), Li\({}^{+}\), Na\({}^{+}\), or K\({}^{+}\) ions [7]. Thin films of WO\({}_{3}\) can be fabricated by various deposition techniques [8] such as sputtering [9, 10], thermal vapor deposition [11, 12], or sol-gel processing [13, 14] from precursor solutions by spin-coating [14], dip-coating [15] or electrodeposition [16] which provide good options of device production at low cost and low environmental footprint [8]. Precursor solutions based on tungsten hexachloride [17; 18], peroxotungstic acid [14; 19], sodium tungstate [16; 20] or ammonium metatanugstate [21] have been used successfully for the preparation of tungsten oxide thin films. Further, the internal structure of WO\({}_{3}\) can be tuned in a wide range using such solution-based approach [22; 23]. The electrochromic properties of tungsten oxide and, in particular, the charge transport in the films are highly influenced by the structure (amorphous vs. crystalline) and the porosity of the films [2; 15]. Compact WO\({}_{3}\) thin films with improved electrochromic characteristics could be obtained from a precursor solution containing peroxotungstic acid upon annealing of the samples at 250 \({}^{\circ}\)C, and it was observed that amorphous WO\({}_{3}\) thin films showed a larger change in coloration between the colored and bleached state, a faster diffusion of ions and a higher coloration efficiency compared to crystalline films [14]. The addition of polymers or surfactants as structure-directing agents into the precursor solution allows a facile modification of the porosity and atomic arrangement (amorphous vs. crystalline) of the WO\({}_{3}\) films [22; 23]. Polyethylene glycol (PEG) of different molecular weight has been largely used in sol-gel processes to inhibit crystallization of WO\({}_{3}\)[22; 24]. [PERSON] et al. [25] and [PERSON] et al. [26] added PEG 600 to a tungsten hexachloride-based precursor solution and prepared WO\({}_{3}\) thin films by dip-coating followed by heat treatment at different temperatures. The films prepared in the presence of PEG 600 and annealed at 300 \({}^{\circ}\)C showed a higher coloration efficiency compared to the films prepared without PEG 600 [25; 26]. [PERSON] et al. [27] used PEG 400 as additive in a peroxotungstic acid-based precursor solution in a volume ratio of 1:10. Thin films were obtained by dip-coating and annealing at 300 \({}^{\circ}\)C. These films exhibited better electrochromic characteristics than the films prepared without polymers [27]. Hence, the addition of PEG 400 or PEG 600 consistently provided WO\({}_{3}\) films with a high active surface area leading to good electrochromic properties [25; 26; 27]. The proper amount of polymer in the precursor solution is crucial for adjusting the structure and porosity of the films [22]. WO\({}_{3}\) thin films which were electrodeposited by [PERSON] et al. [28] showed that the amount of PEG 400 in the peroxotungstic acid deposition solution significantly influenced the morphology of the films and, thus, their electrochromic characteristics. WO\({}_{3}\) thin films with improved electrochromic properties could also be obtained by addition of polyethylene glycol of a higher molecular weight such as PEG 2000 [29] or PEG 20,000 [30] with different precursor solutions.