Pore-Fiber Transport Dynamics of Aqueous Cosolvent Solutions in Paper

After inkjet printing onto uncoated and unsized paper, the ink is first imbibed into the interfiber pores and subsequently absorbed by the cellulose fibers. The achievable print quality depends on the rate of this pore-fiber transport. The latter is accompanied by mechanical expansion of the fibers and the paper sheet. Therefore, we systematically monitored the swelling dynamics of several paper types as a function of ink composition by means of four different measurement techniques. Using aqueous cosolvent solutions as model inks, we found an approximately exponential relation of the time scales of pore-fiber transport with the cosolvent concentration and an approximately linear relation with its molecular weight. Addition of surfactants can substantially speed-up pore-fiber transport.

Table S1 lists the material properties of the pure cosolvents used in this study.Figure S1(a) shows surface tension γ cs values measured with a Wilhelmy plate (red circles) of aqueous poly(ethylene glycol) solutions for different molecular weights M W and a constant initial cosolvent concentration of c 0 = 60 wt%. Figure S1(b) reports data of the viscosity 1,3,4 µ cs (red circles) of aqueous poly(ethylene glycol) solutions as a function of molecular weight M W for a constant initial co-solvent concentration of c 0 = 60 wt%.The solid line in Fig. S1(a with fit parameters D 11 = 0.158 and β = 0.81.

II. EXPERIMENTAL METHODS
Figure S2 shows the suction plate used for white-light interferometry, laser triangulation and confocal displacement metrology experiments.It consists of a polished Al plate with a 4 × 4 mm 2 hole array (hole diameter approximately 90 µm).A step of height 100 µm (close to the the thickness values d sub of the papers A and B) was machined into the plate to serve as a reference surface for the WLI experiments.The throttle valve was adjusted such that the underpressure in the vacuum chamber was kept at the minimum necessary to keep the paper flat.

A. Laser triangulation metrology
Laser triangulation is a technique for measuring surface displacements.Figure S3 illustrates its operating principle.A laser beam is projected onto the target surface to form a laser spot, which is imaged onto a line detector.From the image location, the vertical position of the target surface can be reconstructed.

B. Confocal displacement metrology
Confocal displacement metrology is another measurement method for vertical positions and displacements of a reflective surface.Figure S4 illustrates its operating principle.Due to chromatic aberration, the different spectral components of a white-light beam are focused at different focal planes below the objective.In fact, this information is encoded into spectral characteristics of the light reflected from the sample.The spectrum of the light on the basis of the wavelength dependence of longitudinal chromatic aberration will provide enough information over the depth scanning.It is worth mentioning that the small measurement spot size enables detecting small objects and most importantly can be useful for even diffuse and reflecting objects.

A. Laser triangulation metrology
Figure S5 shows example data of the thickness swelling amplitude for aqueous solutions of TEG on paper A obtained with laser triangulation using a Micro Epsilon  optoNCDT ILD2300-10BL system operating at a wavelength of 405 nm.Frequent issues are baseline drift and erratic signals.The swelling amplitude for pure water in Fig. S5 is about a factor of 3 lower than observed with microscopy-based thickness monitoring.

B. Confocal displacement metrology
During the experiment, a droplet of co-solvent solution (volume 2 µl) is deposited onto the paper sample using a Hamilton digital syringe close to the optical axis of the sensor.In this fashion, fast spreading and imbibition towards the measurement spot is ensured, while the droplet itself does not obstruct the measurement.We used a Micro Epsilon IFS2405-10 system.
As the paper sample expands in thickness, the surface displacement is recorded and the thickness change is calculated.Fig. S6 shows an example of the swelling dynamics for an aqueous EG solution with initial concentration c 0 = 20 wt%.The red solid line is a fit according with fit parameters D 12 = 32 µm and The noise amplitude is on order of ±5 µm.Unfortunately, the method did not work for higher values of c 0 .Our hypothesis is that since glycols are very nearly refractiveindex-matched to cellulose, the surface reflectivity of the wet paper dropped and its transmission increased too much for the sensor to accurately detect the location of the top surface.

C. Microscopy-based thickness monitoring
Figure S7(a-d) shows the thickness expansion strain ϵ TD as a function of time for different droplet volumes V drop of pure water.Figure S7(e,f) illustrates the maximum strain and drying time as a function of V drop .We conclude that the chosen value of V drop = 1 µl is in a range where the expansion strain and thus the porefiber transport do not depend on V drop .As long as any timescale of interest is shorter than the drying time (t dry ≈ 150 s for V drop = 1 µl), the solvent evaporation and the corresponding change in solution concentration and viscosity do not affect the pore-fiber transport significantly.
Figure S8 shows the short swelling time t s and long swelling time t l as a function of the initial co-solvent concentration c 0 for aqueous DEG solutions.The behavior is qualitatively analogous to that of EG and TEG (see Fig. 4 in the manuscript).
Figure S9 shows the short swelling time t s and persistent strain ϵ ps of paper A as a function of the initial surfactant concentration c s for aqueous solutions of glycerol (c 0 = 40 wt%) containing either SDS or Triton X-100.
FIG. S1.(a) Surface tension and (b) viscosity of aqueous poly(ethylene glycol) solutions as a function of molecular weight.The co-solvent concentration was kept constant at c0 = 60 wt%.The filled red circles in (a) represent experimental data and those of (b) are from Refs.[1-4].The solid lines are fit curves according to Eqs. (1,2).
FIG. S2.(a) Schematic representation of the suction plate setup.(b) Vertical cross-section through suction plate.
FIG. S5.Thickness swelling amplitude of paper A as a function of time after deposition of aqueous solutions of TEG measured by laser triangulation.
FIG. S6.Thickness expansion as a function of time for an aqueous solution of EG (c0 = 20 wt%) in paper A monitored by confocal displacement metrology.
FIG. S7.Effect of droplet volume on thickness expansion strain and drying time for pure water.(a-d) Thickness expansion strain ϵTD as a function of time for different droplet volumes V drop = 0.4, 0.8, 1 and 1.6 µl, respectively.(e) Maximum strain and (f) drying time as a function of V drop .
FIG. S8.(a) Short swelling time ts of paper A as a function of initial concentration c0 of DEG (green diamonds).The dashed and solid lines represent fit functions according to Eqs. (6) and (7) of the main manuscript, respectively.(b) Long swelling time t l of paper A as a function of c0 for DEG.The solid line represents the fit function according to Eq. (4) of the main manuscript.
FIG. S9.(a) Short swelling time ts and (b) persistent strain ϵps of paper A as a function of the initial surfactant concentration cs for aqueous 40 wt% solutions of glycerol with added SDS (red circles) and Triton X-100 (blue squares).

TABLE S1 .
Material properties of pure co-solvents.The values of viscosity µcs and surface tension γcs are given for temperatures of 20 o C and 25 o C, respectively.