# Wetting and Evaporation of Solvents on Thin Soluble Substrates

^{*}

## Abstract

**:**

## 1. Introduction

_{0}being the ratio of gravitational forces to capillary [5,6]. The crossover between the two regimes with $\alpha =0.5$ and $\alpha =0.1$ corresponds to the characteristic time [3]:

## 2. Materials and Methods

#### 2.1. Materials

^{−1}are spin-coated onto commercial glass slides. Polymers of ${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}and of ${\overline{M}}_{\mathrm{W}}=524\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}have been bought from PSS Polymer Standards Service and have a narrow molar mass distribution ($PDI={\overline{M}}_{\mathrm{W}}/{\overline{M}}_{\mathrm{N}}=1.04$). The remaining polymers having wider molar mass distribution $PDI\approx 2$ have been bought from Sigma-Aldrich and Carl Roth. Prior to the coating process for substrate preparation, glass slides are cleaned in an ultra sonic bath of acetone and then in ethanol for 30 $\mathrm{min}$ each and dry blown in a nitrogen stream. We use solutions of 6 $\mathrm{wt}\%$ polystyrene in toluene (analytical grade, Carl Roth) for the coating process. By varying the rotation speeds in the range of 1401 to 4615 RPM, we achieve a coating thickness of $(600\pm 50)$ $\mathrm{n}$$\mathrm{m}$. Substrates with coatings of ${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}represent outliers with a typical thickness of $=700$ nm. The thicknesses are measured by pealing of a small area of coating and comparing the surface level of the glass substrate to the coating. The coatings show smooth surfaces with arithmetical mean roughness of ${S}_{\mathrm{A}}\approx 15\mathrm{n}\mathrm{m}$. The properties of the coatings are reported in Table 1. Surface roughness and coating thickness are obtained using a µsoft expert confocal microscope profilometer from NanoFocus AG. For the experiments, toluene (analytical grade, Carl Roth) is used as the wetting solvent.

#### 2.2. Experimental Set-Up and Measurement Procedure

^{−1}. This is performed a single time in lack of a sufficient amount of substrates. The temperature inside the test cell was measured to be (20–23) ${}^{\circ}$C during the experiments. The wetting process is recorded using a Photron SA-X2 high speed camera at a temporal resolution of 3 $\mathsf{\mu}$$\mathrm{s}$, 1 $\mathrm{m}$$\mathrm{s}$ or 20 $\mathrm{m}$$\mathrm{s}$, depending on the wetting stage. For visualising the droplet shape during spreading, we use a shadowgraphy set-up in which collimated light reaches the camera sensor through telecentric lenses. Only those rays of the originally collimated light that pass through the droplet are refracted and do not reach the camera sensor. The spatial resolution during experiments is $10.6$ $\mathsf{\mu}$$\mathrm{m}$/$\mathrm{px}$

^{−1}. The same set-up is used for the observation of droplet evaporation. Image processing of the wetting (contact angle, contact radius and droplet volume) is performed using in house MATLAB codes.

^{−1}and $1.6$ $\mathrm{n}$$\mathrm{m}$, respectively. Structure recognition and measurement within the acquired surface maps is performed using in house MATLAB codes together with the ridge detection algorithm of Steger [24] implemented in the ImageJ software by Wagner et al. [25].

## 3. Results and Discussion

#### 3.1. Wetting

^{−1}. As the molar mass determines the solubility of the polymer, this result also indicates that the dissolution process does not significantly affect the initial stage spreading and that the time scale for dissolution processes of our coatings is larger than ${\tau}_{\mathrm{init}}$. Wetting exponents $\alpha >0.5$ exceed the prediction of Biance et al. [3] for liquids on inert surfaces. As already pointed out by Muralidhar et al. [10], a possible release of Gibbs free energy during spreading on non-inert surfaces generates an additional driving force for wetting [27]. The difference in free Gibbs energy for solution processes of polymers in solvents can be expressed by Flory–Huggins theory [28,29]. Accordingly, free Gibbs energy varies with the degree of polymerisation. If the additional release of Gibbs free energy were a dominant mechanism for initial stage wetting, we would have observed a strong dependency of $\alpha $ on ${\overline{M}}_{\mathrm{W}}$. This is not the case: the variation of $\alpha $ with ${\overline{M}}_{\mathrm{W}}$ is comparable with the error bars in Figure 4. The weak dependence of $\alpha $ on ${\overline{M}}_{\mathrm{W}}$ supports our hypothesis that solution processes do not affect initial stage wetting. Muralidhar et al. [10] reported $\alpha =0.5$ for the same solvent–substrate combination on thick polymer substrates, which is close to our findings. The trend reported here, however is inverse to the findings of Muralidhar et al. who found a slight increase in $\alpha $ with increasing of polymer molar mass.

^{−1}is observed, with a prominent difference between the substrates having close values of ${\overline{M}}_{\mathrm{W}}$ (${\overline{M}}_{\mathrm{W}}=320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}and ${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}). The substrate coatings with ${\overline{M}}_{\mathrm{W}}=320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}and ${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}differ from each other in two respects (see Table 1): the molar mass distribution of the polymer (or polydispersity) and thickness. Both of these parameters can affect the total lateral dissolution rates of the substrate coating and therefore the wetting dynamics. The substrate coatings with ${\overline{M}}_{\mathrm{W}}\ge 335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}have a narrower distribution of molar mass than the substrates with ${\overline{M}}_{\mathrm{W}}\le 320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}. As reported by Körner et al. [30], the molar mass distribution affects the dissolution rate of polymers. A broader molar mass distribution is accompanied by the presence of long polymer chains which reportedly dominate the dissolution process and limit the polymer dissolution rate [31]. This effect would lead to a higher dissolution rate of the substrate coating with ${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}in comparison to the substrate coating with ${\overline{M}}_{\mathrm{W}}=320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}and promote a faster spreading for the polymer with ${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}, as the polymer with ${\overline{M}}_{\mathrm{W}}=320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}is expected to contain a higher fraction of long polymer chains. However, the substrate with a narrower molar mass distribution (${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}) is characterised by a much slower initial wetting speed, which indicates that the presence of long polymer chains does not dominate the dissolution and spreading process in this case. Yet, a broader molar mass distribution is also accompanied by the presence of short polymer chains. Although they do not dominate the overall dissolution process, single chains are prone to enter the bulk solvent early. Those chains affect the viscosity near their original position in the substrate. It has been established that for semi-dilute polystyrene solutions in benzene, which is a non-polar solvent, the viscosity of solutions scales as ${\eta}_{\mathrm{r}}=\eta /{\eta}_{\mathrm{s}}\sim {\overline{M}}_{\mathrm{W}}^{3.1}{c}^{4.6}$ with c being the volume concentration of the polymer and ${\eta}_{\mathrm{s}}$ the dynamic viscosity of the pure solvent [32]. It can be expected that a similar trend is followed by the viscosity of polystyrene solutions in toluene. Therefore, we suggest that the presence of short polymer chains in the liquid does not lead to the change of the wetting behaviour. As seen from Figure 1, the substrate coating with (${\overline{M}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}) used in these experiments is thicker than all other coatings (700 $\mathrm{n}$$\mathrm{m}$ thick in comparison to approximately 600 $\mathrm{n}$$\mathrm{m}$). We suggest that this difference could be responsible for longer absolute dissolution times of the coating and lower late stage wetting speeds. We note that the qualitative behaviour of lower late stage wetting speed for high molar mass substrates holds for both groups (narrow and broad molar mass distribution) of polymers presented within this work.

#### 3.2. Evaporation

^{−1}is an example for the sensitivity of droplet evaporation experiments on droplet spreading. The drop spreading over this substrate resulted in an unusually high spreading radius within this particular experiment, leading to a higher surface area of the droplet and therefore higher total mass loss per time.

^{3}. with the evaporation rate determined from Equation (4). We use the material properties of pure toluene at $21{}^{\circ}\mathrm{C}$: $D=7.69\times {10}^{-6}$ m

^{2}s

^{−1}and ${c}_{\mathrm{v}}=0.1239\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$ as derived from the work in [37]. As the test cell is flushed with nitrogen before and during experiments, we set $H=0$. Equation (4) predicts a linear decrease of droplet mass (and thereby volume) with time. This prediction agrees well with our experimental findings. Within Figure 7, it can be seen that evaporation kinetics predicted from Equation (4) is close to our experimental findings. This confirms that the presence of polymer inside our droplets does not influence the evaporation strongly. Additionally, this serves as evidence that the weak nitrogen flow through the test cell does not enact a strong convective evaporation. However, the most of our evaporating drops show a slightly larger rate of the volume loss than predicted by Equation (4). This could be due to the chosen coefficient D, which according to [37] fluctuates within 4 $\mathrm{K}$ by up to 10%.

#### 3.3. Surface Structure

^{−1}) show smooth ridge lines with only low amplitude long wave perturbations. Polymers with a medium molar mass ($\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}=320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}and $\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}) tend to show low numbers of perturbations along the ridge line (or perturbations with a long average wave length) with high amplitude. Polymers with a low molar mass ($\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}=192\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}and $\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}=280\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}) tend to produce many perturbations along the ridge line (or perturbations with a short wave length) with lower amplitudes. These characteristics are not related to the initial surface roughness of the coatings. The roughness of the surface coatings is just slightly higher ($\Delta {R}_{\mathrm{a}}\approx 2\mathrm{n}\mathrm{m}$) for lower polymer molar masses on our overall smooth surfaces (see Table 1). A possible explanation for the formation of ridge perturbations was delivered by Poulard and Damman [46]. They conducted drying experiments with droplets of polydimethyolsiloxane (PDMS) solutions on inert surfaces and measured the surface left behind after complete solvent evaporation. Some of their structures resemble the ones we present within this work and also show perturbations. For their system, Poulard and Damman [46] have attributed the appearance of perturbations to the Rayleigh–Plateau instability and related the number of observed fingers to the critical wavelength of the Rayleigh–Plateau theory: $\lambda \approx 2$ W, with the perturbations wavelength $\lambda $ and the ridge cross-sectional width W. However, this principle cannot be observed for the full range of our experiments. A possible explanation for this discrepancy lies in viscosity. Near the contact line a PS solution in a semi-diluted state is created. For this case, the relative viscosity of PS solutions in similar solvents scales with $\eta \sim {\overline{M}}_{\mathrm{W}}^{3.1}$ and ${c}^{4.6}$ [32] as already mentioned earlier. Solutions of polymers with a high degree of polymerisation are therefore highly viscous compared to solutions with low molar mass polymers at the same volumetric concentration. A high viscosity near the contact line represents a damping mechanism which could suppress the development of ridge deformation.

**Figure 10.**Illustration of the term ridge line used within this work. The figure shows a portion of a pertubed ridge as depicted in Figure 8. Image obtained with a PS of 335 $\mathrm{k}\mathrm{g}$/$\mathrm{mol}$

^{−1}.

**Figure 11.**Ridge line diameters after wetting and evaporation of solvent droplets on different substrates. For comparability, ridge line diameters are divided by the initial solvent droplets radius R. The error bars represent the standard deviation of the mean values.

**Figure 12.**Ridge heights over angular coordinate show pertubations along ridge line. Graphs show heights above original coating level. Coating molar mass shows influence on pertubation frequency and amplitude. For a better visualisation, only half cycles are depicted.

## 4. Conclusions

- (a)
- The spreading of a solvent droplet on thin non-polar coatings can be divided into two qualitatively different stages. During a first rapid stage, the droplet spreads in accordance with the power law found in literature for inert surfaces. For this stage, which ends after ≈10 ms, the spreading kinetics is independent from the molar mass, or solubility, of the coating. After this initial stage, the contact line speed slows down dramatically and continues spreading for ≈10 ms. The spreading does not scale with a simple power law, as the spreading mechanism and the liquid material properties change during the process. For this late stage wetting, which makes up 30% of the wetted area within our experiments, spreading kinetics strongly depends on coating solubility. Higher solubility results in higher wetting speeds and larger final wetted area.
- (b)
- During evaporation, solvent droplet contact lines stay pinned at the final wetting radius. This results in a linear decrease in volume over time. The molecular weight of the dissolved polymer has no dominant impact on the observed evaporation rates.
- (c)
- Solvent evaporation leads to the formation of coffee ring-like structures. The shape of these circular structures depends on the solubility of the coating polymer. Low solubility leads to smooth structures. Highly soluble polymers create highly perturbed structures.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Kawase, T.; Sirringhaus, H.; Friend, R.H.; Shimoda, T. Inkjet printed via—Hole interconnections and resistors for all—polymer transistor circuits. Adv. Mater.
**2001**, 13, 1601–1605. [Google Scholar] [CrossRef] - Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Wetting and spreading. Rev. Mod. Phys.
**2009**, 81, 739–805. [Google Scholar] [CrossRef] - Biance, A.L.; Clanet, C.; Quéré, D. First steps in the spreading of a liquid droplet. Phys. Rev. E
**2004**, 69, 016301. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Bird, J.C.; Mandre, S.; Stone, H.A. Short-time dynamics of partial wetting. Phys. Rev. Lett.
**2008**, 100, 234501. [Google Scholar] [CrossRef] [Green Version] - Cazabat, A.M.; Cohen Stuart, M.A. Dynamics of wetting: Effects of surface roughness. J. Phys. Chem.
**1986**, 90, 5845–5849. [Google Scholar] - Tanner, L.H. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D Appl. Phys.
**1979**, 12, 1473. [Google Scholar] [CrossRef] - Voinov, O.V. Hydrodynamics of wetting. Fluid Dyn.
**1976**, 11, 714–721. [Google Scholar] [CrossRef] - Kistler, S.F. Hydrodynamics of wetting. Wettability
**1993**, 6, 311–430. [Google Scholar] - Seaver, A.E.; Berg, J.C. Spreading of a droplet on a solid surface. J. Appl. Polym. Sci.
**1994**, 52, 431–435. [Google Scholar] [CrossRef] - Muralidhar, P.; Bonaccurso, E.; Auernhammer, G.K.; Butt, H.J. Fast dynamic wetting of polymer surfaces by miscible and immiscible liquids. Colloid Polym. Sci.
**2011**, 289, 1609–1615. [Google Scholar] [CrossRef] - Dupas, J.; Verneuil, E.; Ramaioli, M.; Forny, L.; Talini, L.; Lequeux, F. Dynamic wetting on a thin film of soluble polymer: Effects of nonlinearities in the sorption isotherm. Langmuir
**2013**, 29, 12572–12578. [Google Scholar] [CrossRef] [PubMed] - Dupas, J. Wetting of Soluble Polymers. Ph.D. Thesis, Université Pierre et Marie Curie, Paris, France, 2012. [Google Scholar]
- Morris, S.J.S. On the contact region of a diffusion-limited evaporating drop: A local analysis. J. Fluid Mech.
**2014**, 739, 308–337. [Google Scholar] [CrossRef] [Green Version] - Jambon-Puillet, E.; Carrier, O.; Shahidzadeh, N.; Brutin, D.; Eggers, J.; Bonn, D. Spreading dynamics and contact angle of completely wetting volatile drops. J. Fluid Mech.
**2018**, 844, 817–830. [Google Scholar] [CrossRef] [Green Version] - Bonaccurso, E.; Butt, H.J.; Hankeln, B.; Niesenhaus, B.; Graf, K. Fabrication of microvessels and microlenses from polymers by solvent droplets. Appl. Phys. Lett.
**2005**, 86, 124101. [Google Scholar] [CrossRef] - Li, G.; Butt, H.J.; Graf, K. Microstructures by solvent drop evaporation on polymer surfaces: Dependence on molar mass. Langmuir
**2006**, 22, 11395–11399. [Google Scholar] [CrossRef] - Gonuguntla, M.; Sharma, A. Polymer patterns in evaporating droplets on dissolving substrates. Langmuir
**2004**, 20, 3456–3463. [Google Scholar] [CrossRef] - Kawase, T.; Shimoda, T.; Newsome, C.; Sirringhaus, H.; Friend, R.H. Inkjet printing of polymer thin film transistors. Thin Solid Film.
**2003**, 438, 279–287. [Google Scholar] [CrossRef] - Sirringhaus, H.; Kawase, T.; Friend, R.H.; Shimoda, T.; Inbasekaran, M.; Wu, W.; Woo, E.P. High-resolution inkjet printing of all-polymer transistor circuits. Science
**2000**, 290, 2123–2126. [Google Scholar] [CrossRef] [Green Version] - Gans, B.J.D.; Hoeppener, S.; Schubert, U.S. Polymer—Relief microstructures by inkjet etching. Adv. Mater.
**2006**, 18, 910–914. [Google Scholar] [CrossRef] - Lee, W.H.; Park, Y.D. Inkjet etching of polymers and its applications in organic electronic devices. Polymers
**2017**, 9, 441. [Google Scholar] [CrossRef] [Green Version] - Grimaldi, I.A.; De Girolamo Del Mauro, A.; Nenna, G.; Loffredo, F.; Minarini, C.; Villani, F. Microstructuring of polymer films by inkjet etching. J. Appl. Polym. Sci.
**2011**, 122, 3637–3643. [Google Scholar] [CrossRef] - Asmussen, F.; Ueberreiter, K. Velocity of dissolution of polymers. Part II. J. Polym. Sci.
**1962**, 57, 199–208. [Google Scholar] [CrossRef] - Steger, C. An unbiased detector of curvilinear structures. IEEE Trans. Pattern Anal. Mach. Intell.
**1998**, 20, 113–125. [Google Scholar] [CrossRef] [Green Version] - Wagner, T.; Hiner, M.; Raynaud, X. Ij-Ridgedetection: Ridge Detection [Image Processing]. 2017. Available online: https://zenodo.org/record/845874 (accessed on 26 October 2020).
- Eddi, A.; Winkels, K.G.; Snoeijer, J.H. Short time dynamics of viscous drop spreading. Phys. Fluids
**2013**, 25, 013102. [Google Scholar] [CrossRef] - Warren, J.A.; Boettinger, W.J.; Roosen, A.R. Modeling reactive wetting. Acta Mater.
**1998**, 46, 3247–3264. [Google Scholar] [CrossRef] - Flory, P.J. Fifteenth spiers memorial lecture. Thermodynamics of polymer solutions. Discuss. Faraday Soc.
**1970**, 49, 7–29. [Google Scholar] [CrossRef] - Rauch, J. Diffusion und Thermodiffusion in Polymerlösungen. Ph.D. Thesis, Universität Bayreuth, Bayreuth, Germany, 2006. [Google Scholar]
- Körner, A.; Larsson, A.; Andersson, Å.; Piculell, L. Swelling and polymer erosion for poly (ethylene oxide) tablets of different molecular weights polydispersities. J. Pharm. Sci.
**2010**, 99, 1225–1238. [Google Scholar] [CrossRef] - Körner, A.; Larsson, A.; Piculell, L.; Wittgren, B. Molecular information on the dissolution of polydisperse polymers: Mixtures of long and short poly (ethylene oxide). J. Phys. Chem. B
**2005**, 109, 11530–11537. [Google Scholar] [CrossRef] - Adam, M.; Delsanti, M. Viscosity of semi-dilute polymer solutions. J. Phys. Fr.
**1982**, 43, 549–557. [Google Scholar] [CrossRef] - Dupas, J.; Verneuil, E.; van Landeghem, M.; Bresson, B.; Forny, L.; Ramaioli, M.; Lequeux, F.; Talini, L. Glass Transition Accelerates the Spreading of Polar Solvents on a Soluble Polymer. Phys. Rev. Lett.
**2014**, 112, 188302. [Google Scholar] [CrossRef] - Tay, A.; Lequeux, F.; Bendejacq, D.; Monteux, C. Wetting properties of charged and uncharged polymeric coatings—effect of the osmotic pressure at the contact line. Soft Matter
**2011**, 7, 4715–4722. [Google Scholar] [CrossRef] - Tay, A.; Bendejacq, D.; Monteux, C.; Lequeux, F. How does water wet a hydrosoluble substrate? Soft Matter
**2011**, 7, 6953–6957. [Google Scholar] [CrossRef] - Monteux, C.; Tay, A.; Narita, T.; Wilde, Y.D.; Lequeux, F. The role of hydration in the wetting of a soluble polymer. Soft Matter
**2009**, 5, 3713–3717. [Google Scholar] [CrossRef] - Erbil, H.Y.; Avci, Y. Simultaneous determination of toluene diffusion coefficient in air from thin tube evaporation and sessile drop evaporation on a solid surface. Langmuir
**2002**, 18, 5113–5119. [Google Scholar] [CrossRef] - Saritha, S.; Neogi, P.; Wang, J.C. Wetting by polymer solutions. Polymer
**2006**, 47, 6263–6266. [Google Scholar] [CrossRef] - Hu, H.; Larson, R.G. Evaporation of a sessile droplet on a substrate. J. Phys. Chem. B
**2002**, 106, 1334–1344. [Google Scholar] [CrossRef] - Deegan, R.D.; Bakajin, O.; Dupont, T.F.; Huber, G.; Nagel, S.R.; Witten, T.A. Capillary flow as the cause of ring stains from dried liquid drops. Nature
**1997**, 389, 827. [Google Scholar] [CrossRef] - Jarusuwannapoom, T.; Hongrojjanawiwat, W.; Jitjaicham, S.; Wannatong, L.; Nithitanakul, M.; Pattamaprom, C.; Koombhongse, P.; Rangkupan, R.; Supaphol, P. Effect of solvents on electro-spinnability of polystyrene solutions and morphological appearance of resulting electrospun polystyrene fibers. Eur. Polym. J.
**2005**, 41, 409–421. [Google Scholar] [CrossRef] - Corneliussen, R.; Rice, S.A.; Yamakawa, H. On the thermodynamic properties of solutions of polar polymers. A comparison of experiment and theory. J. Chem. Phys.
**1963**, 38, 1768–1778. [Google Scholar] [CrossRef] - De Gennes, P.G.; Gennes, P.G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, USA, 1979. [Google Scholar]
- Powers, P.O. Solubility of polystyrene. Ind. Eng. Chem.
**1949**, 41, 2213–2217. [Google Scholar] [CrossRef] - Powers, P.O. Solubility of Polystyrene in Hydrocarbons. Ind. Eng. Chem.
**1949**, 41, 126–130. [Google Scholar] [CrossRef] - Poulard, C.; Damman, P. Control of spreading and drying of a polymer solution from Marangoni flows. Europhys. Lett.
**2007**, 80, 64001. [Google Scholar] [CrossRef]

**Figure 1.**Sketch of the experimental set-up. Contact between solvent and substrate is initiated by increasing the volume of a solvent droplet until it touches the substrate. The distance between cannula and substrate (and thereby the initial drop diameter) can be varied by adjusting the vertical position of the substrate holder. Collimated light reaches the CMOS sensor of a high-speed camera through telecentric optics. Dry nitrogen is used to ensure a controlled atmosphere within the test cell.

**Figure 2.**Two images of wetting experiments at the initial stage. The reflection of the actual droplet shadow can be observed at the bottom region of the pictures due to the camera alignment. Toluene on PS (${\overline{M}}_{\mathrm{W}}=320\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}).

**Figure 3.**Wetting radius over time for a whole droplet life course. Two separate recordings ($1\mathrm{m}\mathrm{s}$ resolution, solid line and $20\mathrm{m}\mathrm{s}$ resolution, dashed line) are shown within the same plot. The sudden change in wetting speed at $\tau \approx 10\mathrm{m}\mathrm{s}$ marks the end of the initial wetting phase. The insert magnifies the wetting process for $\tau >{\tau}_{\mathrm{init}}$ in linear representation. The parameter $\Delta {r}_{\infty}$ (see Equation (3)) and the initial wetting speed $\beta \Delta {r}_{\infty}$ are given as dashed lines for toluene drops on PS (${\overline{M}}_{\mathrm{W}}=$ 320 $\mathrm{k}\mathrm{g}$/$\mathrm{mol}$

^{−1}).

**Figure 4.**Wetting characteristics for initial and late stage wetting of toluene on polystyrene coatings with different molar masses. Initial wetting dynamics are characterised by $\alpha $ from Equation (3). Late stage dynamics are characterised by the first temporal derivation of Equation (1) at $\Delta \tau =0$, or the inaugural wetting speed of late stage wetting, respectively. The error bars represent the standard deviation of the mean values. The experimental point corresponding to $\beta \Delta {r}_{\infty}$ for ${\overline{M}}_{\mathrm{W}}=192\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}contains no bars. This experiment has been performed only once.

**Figure 5.**Dynamic contact angle over capillary number during late stage spreading. C

_{a}is calculated with the initial material properties of pure toluene.

**Figure 6.**Contact angle (dashed line) and contact radius over time during late stage spreading and a large part of evaporation. Because of the low temporal resolution, the initial wetting stage as presented in Figure 3 cannot be observed. After approximately 10 $\mathrm{s}$, late stage wetting stops and the contact radius stays constant. The contact angle decreases linearly after the contact line is pinned. The last seconds of evaporation are excluded due to faulty image processing as the ridge formation interferes with contact angle determination. Toluene on PS ($\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}=335\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}).

**Figure 7.**Solvent droplet volume over time during spreading and evaporation as obtained by image evaluation. The black line represents the results of computations according to the model presented in Hu and Larson [39]. Plot markers are placed for easier distinction between curves.

**Figure 8.**Surface appearance after evaporation of solvent droplets on different substrates. The top half of each image displays microscope photographs. The bottom half displays height maps. Both representations are recorded simultaneously using a confocal microscope.

**Figure 9.**Coatings height profile along diameter after solvent evaporation for different coating molar masses. The non-symmetry for ${\overline{M}}_{\mathrm{W}}=192\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}stems from perturbations along the ridge line as presented in Figure 8 and Figure 12. Profiles are magnified in height.

Substrate Properties | |||
---|---|---|---|

mass average molar mass | dispersity of chain lengths | thickness | roughness |

$\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}$ | $\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{W}}/\phantom{\rule{0.83328pt}{0ex}}\overline{\phantom{\rule{-0.83328pt}{0ex}}M\phantom{\rule{-0.83328pt}{0ex}}}{\phantom{\rule{0.83328pt}{0ex}}}_{\mathrm{N}}$ | e | ${R}_{\mathrm{a}}$ |

/ | / | / | |

$\mathrm{k}\mathrm{g}$/$\mathrm{mol}$^{−1} | - | $\mathrm{n}$$\mathrm{m}$ | $\mathrm{n}$$\mathrm{m}$ |

192 | $\approx 2$ | $600\pm 50$ | $3.6$ |

280 | $\approx 2$ | $600\pm 50$ | $4.3$ |

320 | $\approx 2$ | $600\pm 50$ | $1.1$ |

335 | 1.04 | $700\pm 50$ | $1.3$ |

524 | 1.04 | $600\pm 50$ | $1.6$ |

**Table 2.**Influence of polymer concentration on material properties of PS-toluene solutions (${\overline{M}}_{\mathrm{W},\mathrm{PS}}=299\mathrm{k}\mathrm{g}/\mathrm{mol}$

^{−1}) [41].

Mass Fraction of PS in Toluene / % | ||||
---|---|---|---|---|

0 | 10.3 | 18.7 | 25.7 | |

$\eta /\mathrm{m}\mathrm{Pa}\mathrm{s}$ | 0.52 | 33 | 236 | 1098 |

$\sigma /\mathrm{m}\mathrm{N}\mathrm{m}$^{−1} | 27.4 | 30.2 | 30.0 | 29.9 |

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Wolf, C.; Gambaryan-Roisman, T.
Wetting and Evaporation of Solvents on Thin Soluble Substrates. *Colloids Interfaces* **2020**, *4*, 48.
https://doi.org/10.3390/colloids4040048

**AMA Style**

Wolf C, Gambaryan-Roisman T.
Wetting and Evaporation of Solvents on Thin Soluble Substrates. *Colloids and Interfaces*. 2020; 4(4):48.
https://doi.org/10.3390/colloids4040048

**Chicago/Turabian Style**

Wolf, Christian, and Tatiana Gambaryan-Roisman.
2020. "Wetting and Evaporation of Solvents on Thin Soluble Substrates" *Colloids and Interfaces* 4, no. 4: 48.
https://doi.org/10.3390/colloids4040048