
==== Front
Langmuir
Langmuir
la
langd5
Langmuir
0743-7463
1520-5827
American Chemical Society

39224037
10.1021/acs.langmuir.4c01965
Article
Pore-Fiber Transport Dynamics of Aqueous Cosolvent Solutions in Paper
Karimnejad Sajjad †
Gonnet Elian †
Wang Shuo †
Mansouri Hamid ‡
Tomozeiu Nicolae ‡
https://orcid.org/0000-0001-8846-5555
Darhuber Anton A. *†
† Fluids & Flows Group, Department of Applied Physics, Eindhoven University of Technology, 5600MB Eindhoven, The Netherlands
‡ Canon Production Printing, 5914HH Venlo, The Netherlands
* Email: a.a.darhuber@tue.nl.
03 09 2024
17 09 2024
40 37 1952819537
24 05 2024
22 08 2024
22 08 2024
© 2024 The Authors. Published by American Chemical Society
2024
The Authors
https://creativecommons.org/licenses/by/4.0/ Permits the broadest form of re-use including for commercial purposes, provided that author attribution and integrity are maintained (https://creativecommons.org/licenses/by/4.0/).

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.

Stichting voor Fundamenteel Onderzoek der Materie 10.13039/501100001712 i43-FIP Canon Production Printing Netherlands NA NA Ministerie van Economische Zaken 10.13039/501100003195 NA Technische Universiteit Eindhoven 10.13039/501100003005 NA University of Twente 10.13039/501100001834 NA document-id-old-9la4c01965
document-id-new-14la4c01965
ccc-price
==== Body
pmcIntroduction

Inkjet printing technology has numerous applications ranging from flexible electronics1 to the graphical printing industry.2 For printing on paper, water-based inks are an environmentally friendly option. In terms of weight fraction, the two main constituents of aqueous inkjet printing inks are typically water as the primary solvent and polar liquids of low volatility such as glycerol or poly(ethylene glycols). The latter are called cosolvents and make up 5–50% of the ink volume.3 They serve several purposes, most importantly as humectants to prevent inkjet nozzle clogging.4

Pore-fiber transport5−8 of the liquid-phase ink components is an important factor in inkjet printing. It influences how close to the surface of a paper sheet the colorant pigments will be immobilized, thereby affecting color depth. Moreover, it influences the lateral spreading of an ink dot and thus the achievable resolution. An important aspect is how the rate of fiber absorption compares to the drying time in an inkjet printer, which typically ranges from 1 to 10 s.

Paper consists mainly of fibers, which are composed of cellulose fibrils.9 These fibrils contain amorphous and crystalline domains in a proportion that critically depends on the chemical and mechanical processes applied during paper making.10,11 There is consensus that it is primarily the amorphous domains that can accommodate solvent molecules and swell in the process.12−19

Water-induced swelling of thin cellulose-based porous media and single fibers has been studied extensively.13,20−23 Letková et al.24 measured a swelling time of roughly 1 s for never-recycled paper sheets made of bleached hardwood kraft pulp with a short-time swelling amplitude (i.e., a relative increase in thickness) of about 60%.24 After seven recycling steps, the swelling time increased to 1.75 s and the short-time swelling amplitude decreased to 40%. They observed a fast (order 1 s) as well as a slow swelling process (order 1 h). Schuchardt and Berg performed swelling measurements of a single carboxymethyl cellulose fiber and reported a short swelling time of 15–60 s and a long one of the order of 10 min.25 Geffert et al.26 and Jablonskỳ et al.27 found analogous results using hand sheets of bleached sulfate pulp composed of a blend of hardwood species and commercial newsprint paper, respectively.

In this manuscript, we determined pore-fiber transport rates of aqeuous cosolvent solutions in commercial paper substrates by monitoring the transient swelling of the paper sheets after droplet deposition. Due to the low stiffness of wet paper, we employed four optical noncontact techniques: white light interferometry (WLI), microscopy-based thickness monitoring, laser triangulation, and confocal microscopy. We measured the expansion strain in the thickness direction (TD) as a function of time and systematically varied the cosolvent composition and concentration. Moreover, we studied the influence of various anionic and nonionic surfactants.

Experimental Section

Materials and Material Properties

As substrates, we used the following uncoated, uncalendered and unsized papers from three different manufacturers:paper ‘A’ (grammage g = 80g/m2, thickness dsub = 104 μm).

paper ‘B’ (g = 90g/m2, dsub = 116 μm, ash content 12%).

paper ‘C’ (g = 80g/m2, dsub = 180 μm, made from cotton linters, ashless).

Papers A and B are commercial printing papers, whereas paper C is a commercial filter paper. Judging by the much larger value of dsub for the same value of g, paper C is subject to less compression during manufacture than paper A. Our selection of uncoated, uncalendered and unsized paper types is further motivated in the Discussion section. To protect the papers from changes in ambient conditions, they are stored in a sealed container until each experiment.

The cosolvents listed in Table 1 were purchased from Sigma-Aldrich and used as received. We selected them because they are nontoxic, environmentally friendly and industrially relevant. Moreover, PEG offers the key benefit that oligomers of different molecular weight (MW) are commercially available in high purity grades. This allows to tune the ratio of the molecular size and the intrafiber poresize of the cellulose fibers. Aqueous cosolvent solutions were prepared by mixing deionized water (Millipore Direct-Q3 R) and a pure cosolvent at a certain mass ratio in a glass bottle. Masses were measured with a precision scale (Kern, ALT 220-5DAM). For some experiments, we added the anionic surfactants sodium dodecyl sulfate (SDS) and sodium lauroyl sarcosinate (SLS) to the cosolvent solutions or the nonionic surfactants Triton X-100 (TX-100) and Brij30, see Table 1. Their chemical structures are presented as insets in Figure 6. For one experiment, we used hexadecane (Sigma-Aldrich product number H6073, MW = 226 g/mol).

Table 1 List of Cosolvents and Surfactants Including Sigma-Aldrich Product Numbers and Molecular Weights (MWs)

cosolvent/surfactant	product#	MW	
glycerol	449770	92.1	
ethylene glycol (EG)	324558	62.1	
diethylene glycol (DEG)	32160	106.1	
triethylene glycol (TrEG)	90390	150.2	
tetrathylene glycol (TEG)	110175	194.2	
polyethylene glycol 300 (PEG6)	49770	300 ± 15	
Brij30	235989	362	
Triton X-100 (TX-100)	T9284	647	
sodium dodecyl sulfate (SDS)	436143	288.4	
sodium lauroyl sarcosinate (SLS)	61744	293.4	

We used a concentric-cylinder viscometer (Brookfield II+Pro) to measure viscosities and a Wilhelmy plate (NIMA, PTP-10) together with a precision scale (Kern, ALT 220-5DAM) for measuring surface tensions of cosolvent solutions.

Experimental Setups and Procedures

In this section, the methods utilized for monitoring pore-fiber transport will be discussed in detail. All experiments were conducted at room temperature (298 ± 2) K and an ambient relative humidity of (40 ± 10)%. Paper ‘A’ is typically used for all the experiments, unless otherwise stated. Information pertaining to laser triangulation and confocal microscopy can be found in the Supporting Information (Section II and Figures S2–S4).

White-Light Interferometry (WLI)

We used a Bruker NPFLEX white light interferometer with a 5× objective lens and a 0.55× demagnification lens, resulting in a field of view of approximately 2 mm. The built-in camera has 640 × 480 pixels. The paper samples are placed horizontally, i.e., parallel to the xy-plane. The objective lens is scanned along the vertical z-direction over a range of approximately 90 μm with a scan rate of approximately 25 μm/s. This results in a time resolution of approximately 3.6 s. For every camera pixel, corresponding to a specific (x,y)-position on the sample, the z-position corresponding to zero optical path difference relative to a reference beam is obtained.28,29

To prevent the paper from curling and bulging and to keep it flat and in contact with its support surface during an experiment, samples were placed on a suction plate. The plate comprises a hole array (hole diameter 100 μm, array period 200 μm, array dimensions 4 × 4 mm2) that is connected to a vacuum cavity and an oil-free membrane pump. The underpressure was set to the minimum required to keep the paper flat using a needle valve between the pump and the cavity. In this fashion, the change in the average z-coordinates of the top surface of the sample Δz reflects its thickness expansion.

Microscopy-Based Thickness Monitoring

We used the same method employed in the past e.g., by Lee et al.,23 Chang and Kim,30 and Kvick et al.31Figure 1a illustrates the setup for microscopy-based paper thickness monitoring. A sheet of paper is supported in a vertical orientation by two anodized metal holders under an upright microscope (Olympus BX50) with a 10× objective. The microscope is equipped with a CCD camera (Basler piA1000-60gm, 1004 × 1004 pixels, field of view 710 × 710 μm) and records a cross-section view of a paper sheet to monitor its thickness change. At the top of the metal holders, there is a recess (dimensions 5 × 5 mm2), through which model ink can be deposited onto the paper substrate. We used a Hamilton digital syringe to deposit droplets of volume V = 1 μL. The volume should be as small as possible to minimize the droplet imbibition time (≈ 1 s for V = 1 μL of pure water), but large enough to keep the reproducibility of V sufficiently high and the diameter of the wet zone (typically6 4–5 mm) larger than the cellulose fiber length (typically32 1–2 mm) (see Supporting Information, Figure S7). The metal holders keep the paper sample as flat as possible and minimize movements of the paper sheet during droplet deposition and swelling. The paper sheets are oriented with their machine direction parallel to the optical axis of the microscope to minimize buckling-induced displacements.7

Figure 1 (a) Experimental setup for microscopy-based paper thickness monitoring. (b,c) Top-view of a paper sheet (b) before and (c) after liquid deposition. The scale bar in (b) corresponds to 100 μm.

Results and Discussion

The thickness increase of the paper sheets after droplet deposition is quantified in terms of the expansion strain in the thickness direction1

where dsub(t) denotes the time-dependent thickness of the paper sheet after cosolvent deposition and dsub,dry that of dry paper, i.e., prior to liquid deposition. The parameter Δz ≡ dsub(t) – dsub,dry corresponds to the thickness expansion.

White-Light Interferometry

The raw WLI data consist of 640 × 480-sized matrices with z(x,y)-coordinates that represent the topography of the paper surface. An example is shown in Figure 2a. Figure 2b shows corresponding histograms of z-coordinates obtained with a sample of paper A before and after deposition of an EG solution droplet (c0 = 80 wt %). These histograms reflect the surface roughness of a paper sheet and represent a sample area of approximately 1.5 × 2 mm2. The bin sizes for the dry and wet sample were chosen to be 0.3 and 0.5 μm, respectively. The vertical dashed lines represent the mean values of the distributions. Their difference Δz equals the average thickness expansion of the sample. Figure 2c depicts the time evolution of thickness expansion strain ϵTD for the same experiment. A rapid increase in Δz is observed in the first 25 s, after which expansion continues at a much slower rate. The black solid line is a fit according to a single exponential fit function2

which represents the first 25 s of the data very well. The numerical values of the fit parameters are D1 = 0.22 and ts = 8 s. The parameter ts quantifies the short swelling time, i.e., when the swelling amplitude reaches 63% of its asymptotic value.

Figure 2 (a) Pseudocolor plot of the WLI raw data z(x,y) of dry paper A. The color range from dark blue to yellow represents a height variation of 34 μm. The scale bar corresponds to 0.75 mm. (b) Histograms of z-coordinates for paper A before (blue) and 87 s after (magenta) deposition of an EG solution droplet (c0 = 80 wt %). The vertical dashed lines indicate the mean values of the distributions. (c) Thickness expansion strain ϵTD as a function of time for an aqueous EG solution (c0 = 80 wt %, circles). The solid (black) and dashed (red) lines are fits according to eqs 2 and 3, respectively.

Since the data for t > 30 s do not conform to a single exponential, we also performed a fit according to a double exponential fit function3

which is represented by the red dashed line in Figure 2c. Here, D2,3, ts and tl are fit parameters with numerical values 0.191, 0.06, 7.4, and 37 s, respectively. The double exponential function results in an excellent fit over the entire data range, but yields essentially the same value of ts as the single-exponential fit.

Microscopy-Based Thickness Monitoring

Figure 3a,b shows the thickness expansion strain ϵTD after droplet deposition as a function of time for EG and TEG solutions, respectively, and different values of c0. For pure water, the swelling occurs within the first few seconds, whereas it takes about 22 s for pure EG and considerably longer for pure TEG. For the data shown in Figure 3 and all subsequent figures, we define the short swelling time ts as the instant when the expansion strain reaches 63% of an asymptotic value ϵ∞. As an example, the chosen value of ϵ∞ for pure EG is indicated by a red arrow. For most curves, ϵ∞ corresponds to the maximum value of ϵTD. However, the curve corresponding to an 80 wt % TEG solution in Figure 3b clearly exhibits more than one time scale, which requires a different choice for ϵ∞, as indicated by the blue horizontal arrow.

Figure 3 Thickness expansion strain ϵTD as a function of time for (a) EG and (b) TEG solutions and different values of c0. The dotted lines are fits according to the Berens and Hopfenberg (BH) model.

A notable feature in Figure 3a,b is the presence of persistent strain ϵps , i.e., the fact that the paper thickness does not return to its original dry value.7 This is due to the fact that cosolvents are essentially nonvolatile on the time scale of our experiments. Consequently, the fraction of the deposited cosolvents that are transported into the fiber interior, induces a certain remanent level of fiber swelling even after the water has evaporated. For both EG and TEG, the persistent strain ϵps increases with c0 up to a maximum value c0,crit beyond which it decreases. For EG and TEG the values of c0,crit are approximately 60 and 40 wt %, respectively.

Figure 4a shows the short swelling time ts as a function of the initial concentration c0 for EG and TEG solutions. Open symbols correspond to microscopy-based thickness expansion data and the filled square to the WLI experiment from Figure 2, demonstrating the excellent agreement between the two experimental methods. Analogous data for DEG are presented in Figure S8 of the Supporting Information.

Figure 4 (a) Short swelling time ts of paper A as a function of initial concentration c0 of EG (black squares) and TEG (red circles) solutions. The dashed and solid lines represent fitfunctions according to eqs 6 and 7, respectively. (b) Long swelling time tl of paper A as a function of c0 for EG (black squares) and TEG (red circles) solutions. The black solid line represents an exponential fit-function according to eq 4. The dashed solid line is a guide to the eye. Open symbols in (a,b) correspond to microscopy-based thickness expansion data, the solid blue squares to the WLI experiment in Figure 2.

Figure 4b shows the long swelling time tl as a function of c0 for EG and TEG solutions. The black line in Figure 4b corresponds to the fit function4

with fit-parameters D4 = 0.42 s and cc = 17 wt %, which represents the experimental data very well. For TEG, a drastic increase in tl by more than 2 orders of magnitude is observed at a concentration c0 = (70 ± 10) wt %, see Table 2.

Table 2 Long Swelling Time tl of Aqueous TEG Solutions as a Function of c0

c0 (wt %)	tl (s)	
60	37 ± 10	
80	>6000	
100	>10,000	

Figure 5a shows the thickness expansion strain ϵTD as a function of time for different cosolvents and paper types and a constant initial concentration c0 = 60 wt %. We also performed one experiment using pure hexadecane (green curve in Figure 5a), which is a nonpolar liquid. It does not induce any swelling of cellulose-based paper, although it readily imbibes into the interfiber pore space.

Figure 5 (a) Thickness expansion strain ϵTD(t) for different cosolvents and paper types and a constant initial concentration c0 = 60 wt %. Solid lines correspond to paper A, the long-dashed line to paper B. The gray curve corresponds to a 60 wt % TEG solution containing 2.34 wt % SDS. The short-dashed lines are fits according to the Berens and Hopfenberg model. (b) Short swelling time ts for water and aqueous cosolvent solutions as a function of molecular weight MW for a constant value of c0 = 60 wt %. Open circles correspond to paper A, solid red squares to paper B, the open orange diamond to paper C. The dashed and solid lines represent fitfunctions according to eqs 6 and 7 respectively. (c) Persistent strain ϵps versus MW for water and aqueous cosolvent solutions with initial concentrations c0 = 60 wt % (red squares) and 40 wt % (green circles).

The corresponding short swelling times ts are plotted in Figure 5b. They increase approximately linearly with cosolvent molecular weight. Within experimental reproducibility, the three paper types exhibit identical values of ts. The persistent strain ϵps monotonically decreases with increasing MW as shown in Figure 5c. For comparison and as a reference value we have added the maximum strain for pure water. The solid line represents the fit function5

with fit-parameters D5 = 0.61 and MWc = 250 g/mol.

Figure 6a shows the dependence of the short swelling time ts of paper A on the initial concentration cs of the surfactants SDS, SLS, Triton X-100, and Brij30 in 60 wt % TEG solutions. Interestingly, ts falls below the value of a surfactant-free 60 wt % TEG solution for SDS and Triton X-100 at small values of cs. According to Figure 6b, the persistent strain ϵps monotonically decreases with cs for c0 = 60 wt %, but remains constant for c0 = 40 wt %. Analogous data for aqueous surfactant solutions containing 40 wt % glycerol are available in Figure S9 of the Supporting Information.

Figure 6 (a) Short swelling time ts and (b) persistent strain ϵps of paper A as a function of the initial surfactant concentration cs for TEG solutions with SDS (red circles), TX-100 (blue squares), SLS (green diamonds), and Brij30 (black star). Solid and open symbols correspond to c0 = 40 and 60 wt %, respectively. Orange triangles denote surfactant-free solutions (cs = 0). The gray lines are guides to the eye.

Validity – Imbibition Dynamics vs Pore-Fiber Transport

Measuring pore-fiber transport rates via the dynamics of swelling requires the imbibition time timb to be smaller than the swelling time ts. Nicasy et al. used a nuclear magnetic resonance (NMR) technique to investigate water transport in sheets of printing paper.33 They found an imbibition time scale of 0.07 s and a much larger swelling time scale of 0.7 s. For comparison, we found a very similar value of ts = (0.6 ± 0.15) s for paper A. The requirement of imbibition outpacing swelling motivates our choice for uncoated, unsized and uncalendered paper types, as coatings, hydrophobization and calendering all tend to slow down imbibition.34

Aqueous cosolvent solutions have a markedly higher viscosity μ than pure water.6 Based on Darcy’s law, we expect the imbibition time to scale proportional to μ. Based on the model of Wang et al.,8 we expect ts to scale proportional with μ as well, up to c0 ≈ 50 wt %. Beyond this concentration, an additional retardation effect is provided by the amount of water being insufficient to plasticize the cellulose fiber walls. Consequently, for the papers studied, the criterion of timb ≪ ts is fulfilled for all cosolvents and all concentrations.

Validity – Sheet Swelling vs Fiber Swelling

Inferring pore-fiber transport rates from measurements of the swelling dynamics of a papersheet also requires the latter to be primarily a consequence of the concerted swelling of the individual cellulose fibers. A conceivable alternative origin of swelling could be the loss of fiber–fiber bonds, the fibers becoming loose, leading to a loss of the cohesion of the paper structure. This scenario is reminiscent of hair being immersed in water. The key question in this context is thus whether fiber–fiber bonds are stable upon liquid deposition. The drastic reduction of mechanical stiffness and tear strength of paper upon water addition35 seems indeed to point toward a loss of stability. However, mechanical properties are typically assessed via stress–strain curves and therefore via application of external forces. In the case of ink deposition, no external forces are present that could lead to macroscopic relative displacements of individual fibers. Furthermore, Hirn and Schennach argue that the softening of the fibers might be an equally important contribution to the moisture-induced strength decrease of papersheets as the weakening of the fiber bonds.36

Two important mechanisms contributing to the fiber–fiber bond strength are interdiffusion and mechanical interlocking,36−41 which are not expected to disappear completely upon water addition. Moreover, Nanko and Ohsawa42 and Hobisch et al.43 showed that pulp fines predominantly aggregate at and near the fiber–fiber bond areas as do binders,44 adding another nonvanishing rheological component to the bond strength upon water addition.

Because the droplet imbibition time is shorter than the short swelling time in our experiments, the effective dry solids content does not fall below 60%. At this level, wet paper still maintains a non-negligible fraction (typically 3–10%) of its dry strength,45−47 again indicating that the interfiber bonds are weakened, but remain intact. Therefore, we believe that the scenario of a total loss of fiber cohesion is not relevant to our experiments.

A second reason why there could exist a sheet-swelling time scale that is unrelated to pore-fiber transport, is the relaxation of built-in drying stresses. It is conceivable that its primary origin is a weakening of the interfiber bonds (rather than the fibers becoming softer), which might not adhere to the same time scale as pore-fiber transport. We believe that the impact of drying-stress relaxation is similar in scale to the persistent strain ϵps observed upon deposition and subsequent evaporation of pure water, which is generally on order of 2–3% in the thickness direction for papers A, B and C (see Supporting Information, Figure S7a–d). This is small compared to the maximum swelling amplitude, which is on order of 50%. The value of ϵps(100 wt % H2O) = 2–3% is consistent with literature values of the in-plane strain relaxation observed for restrained-dried paper upon cycling of the ambient relative humidity,48−50 assuming the expansion coefficient in the thickness direction is 20 times higher than in the cross-machine direction (CD).7,51 Moreover, we conducted additional experiments, where we first hydrated the paper sample twice with pure water and waited 2 h for unrestrained drying before depositing 1 μL of a TEG solution (c0 = 60 wt %). The purpose of the prehydration treatment was to remove any drying stresses present in the as-manufactured paper sample. The resulting values of ts and ϵps were identical to the ones in Figures 4 and 5 within error bars. Therefore, we believe that sheet-level drying stress relaxation does not invalidate the interpretation of our results toward pore-fiber transport, either.

Effect of Cosolvent Concentration on Swelling Dynamics

Glycerol, poly(ethylene glycols) and cellulose have similar molecular structures containing polar alcohol and ether groups. This chemical compatibility allows cosolvents to penetrate the amorphous parts of cellulose fibers and thus induce swelling. Water plays a pivotal role in the pore-fiber transport dynamics of cosolvent solutions, as it acts as a plasticizer of the cellulose fiber walls and as it reduces the solution viscosity. Its presence in sufficient amounts therefore promotes the transport of cosolvents from pores to the fibers.6,52 Consequently, the swelling rate and the swelling amplitude induced by cosolvent solutions are expected to decrease with c0.

Both EG and TEG exhibit similar behavior in Figure 3, however the swelling time scales for TEG are longer. Moreover, max(ϵTD) and the persistent strain ϵps for TEG are lower than for EG. As we will show below and in the next subsection, these differences can be attributed to the difference in molecular weight (MW) of the two cosolvents.

For both cosolvents, increasing c0 results in more swelling and thus more cosolvent residing in the fibers up to a critical value c0,crit ≈ 50 wt %.6−8 In equilibrium, this trend of ϵTD monotonically increasing with c0 continues up to c0 = 100 wt %.7 However, above c0,crit the reduced water content in the solution restricts cosolvent transport and an equilibrium distribution is not attained before the water has evaporated. To illustrate that, we added a droplet of pure water (volume 1 μL) to the wet zone resulting from deposition of a 60 wt % TEG solution droplet (volume 1 μL) at t = 1000 s in Figure 3b. This rehydration step6 increased max(ϵTD) and the persistent strain by about 75%.

The dashed lines in Figure 4a correspond to the fit functions6

and the solid ones to7

Here, γcs and μcs are the (concentration dependent) surface tension and the viscosity of the cosolvent solutions8 and D6,7 are fit parameters. They reproduce the experimental data increasingly well, which indicates that viscosity is the dominant factor, but the effect of surface tension is non-negligible. The scaling of eq 7 with the liquid material parameters is the same as in Washburn’s or Darcy’s law, which indicates that capillary wicking is the dominant transport mechanism governing the short swelling time scale. A remaining difference to the experimental data – indicated by the shaded areas in Figure 4 – becomes apparent for c0 ≳ 50 wt %. This difference, which increases with c0, is ascribed to the incomplete or retarded plasticization of the cellulose fibers for low water contents.8

Influence of Molecular Weight

In the previous subsection, we concluded that viscosity and surface tension are the key material parameters that determine the pore-fiber transport rates. The dashed and solid lines in Figure 5b correspond to eqs 6 and 7, respectively. They represent the experimental data well up to DEG. Because surface tension is a strong function of c0, but a weak function of MW for aqueous PEG solutions (see Figure S1a in the Supporting Information), the relative difference between the dashed and solid lines in Figure 5b is smaller than in Figure 4. The viscosity of aqueous PEG solutions is well represented by a power law μcs ∼ (MW)β. For c0 = 60 wt %, the exponent β ≈ 0.81 is close to 1 (see Figure S1b in the Supporting Information). The ratio of μcs/γcs thus scales almost perfectly linearly with MW.

The shaded region in Figure 5b highlights the deviation of the data points from the Darcy-scaling represented by eq 7, which starts to be noticeable above MW ≈ 130. We expect that the dependence of ts on MW eventually diverges as MW approaches the cutoff value, beyond which solute molecules are excluded from the intrafiber pores.53,54 Reported cutoff MW values are in the range of 250–5000.55−57

Influence of Surfactants

Addition of surfactants to aqueous cosolvent solutions affects the solution viscosity only weakly,58,59 with the exception of Brij30, see Table 3, which contains values of the surface tension γ and viscosity μ corresponding to some of the data points in Figure 6. In contrast, the surface tension is reduced substantially by approximately 25–55% for surfactant concentrations close to or above the critical micelle concentration (cmc), see Table 3. According to eq 7, one would expect that the swelling time ts should increase by a corresponding factor above the cmc.60 However, the experimental data in Figure 6a show a marked decrease of ts below the value of a surfactant-free 60 wt % TEG solution for small values of cs for SDS and TX-100. We ascribe this phenomenon to the reduction of the wetting delay by surfactant solutions, which is likely related to the expedited displacement of air that fills the pore space prior to ink imbibition.61 According to Fowkes62 and Cohen and Rosen,63 the wetting delay time of aqueous surfactant solutions on cotton to good approximation scales as twd ∼ cs–β for concentrations below the cmc. Therefore, we expect the biggest reduction of ts at or above the cmc.

Table 3 Surface Tension γcs and Viscosity μcs of Aqueous 60 wt % TEG Solutions as a Function of Surfactant Concentration cs for a Temperature of (22.8 ± 0.3) °C

surfactant	cs (wt %)	γcs (mN/m)	μcs (mPa s)	
 	0	51.3 ± 0.2	10.6	
SDS	0.5	44.9 ± 0.2	10.7	
SDS	1.9	39.9 ± 0.2	11.3	
SDS	2.34	39.3 ± 0.2	11.2	
SLS	1.2	35.9 ± 0.2	11.8	
SLS	2	32.8 ± 0.2	11.6	
TX-100	0.2	32.4 ± 0.3	8.7	
TX-100	0.4	31.2 ± 0.3	9.5	
TX-100	2	32.7 ± 0.2	12.0	
Brij30	2	28.4 ± 0.2	22.3	

In pure water, the cmc of SDS is 0.234 wt %, that of SLS is 0.4 wt %, and that of Triton X-100 is 0.026 wt %.64−67 For both anionic surfactants such as SDS and nonionic surfactants such as Tween and Triton X-100, the cmc increases with increasing cosolvent concentration.68−75 Based on the results of Ye et al.,69 we estimate the cmc of TX-100 in a 60 wt % TEG solution to be approximately 10 times higher than in pure water, i.e., around 0.26 wt %. According to Dey et al.,75 the cmc of SDS in a 60 wt % EG solution is approximately 4 times higher than in pure water, i.e., around 1.0 wt %.

Figure 6b shows that addition of surfactants does not affect ϵ∞ for c0 = 40 wt %. In contrast, surfactants decrease the persistent strain ϵps compared to a surfactant-free, 60 wt % TEG solution. This indicates that a smaller fraction of the cosolvent reaches the interior of the cellulose fibers for c0 = 60 wt %.

Origin of Two Swelling Time Scales

Solvent transport due to capillary imbibition into a porous medium or due to diffusion with a constant diffusion coefficient is characterized by Washburn or Fickian dynamics, which would give rise to a single swelling time scale. In our experiments in Figures 2, 3 and 5a, we frequently observe the presence of a shorter and a longer time scale. This is not uncommon and has also been observed e.g., in the swelling of starch granules by water,76−78 hydrogels,79,80 cellulose-based materials,81−85 and polymers.86−94

The occurrence of more than one time scale indicates that there is more than one mechanism at play. Berens and Hopfenberg (BH) devised an empirical model that accounts for solvent transport in polymers based on a combination of Fickian diffusion and polymer relaxation processes.95 The latter are ascribed to relatively large scale segmental motions of the polymer chains that are facilitated by the progressive swelling of the polymer matrix due to the increase in solvent content. Although for pore-fiber transport in cellulose fibers, Darcy flow might be dominant over diffusive transport, they both give rise to similar dynamics. The black dotted lines in Figure 3 and the dashed lines in Figure 5a are fits according to the BH model, which generally match the data very well.

In our experiments, we consider aqueous cosolvent solutions, i.e., mixtures of solvents with disparate molecular weights. The BH model takes only a single solvent into account. The time dependence of ϵTD for 80 and 100 wt % TEG solutions in Figure 5b is rather linear. This is reminiscent of case II sorption, where typically the effective transport coefficient strongly increases with solvent content, the solvent substantially swells the polymer and sharp penetration fronts are observed.96 Hermans and Vermaas97 observed the occurrence of a propagating sharp sorption front after immersion of a dry cellulose filament into water. For an aqueous 38 wt % glycerol solution, two separate fronts were observed. They interpreted the second as a glycerol front penetrating the region that has previously been plasticized by the passing of the first water front. It is unclear whether such sharp fronts also occur in chemically and mechanically processed (beaten) cellulose fibers as present in commercial printing paper. In the context of the BH model, the observed linear time dependence of ϵTD for 80 and 100 wt % TEG solutions can be reproduced by a substantially longer time scale tl ≈ (1000–10000) s.

Interpretation of WLI-Based Swelling Measurements

While the swelling times determined with the two methods agree well in Figure 4, the swelling amplitude observed with WLI in Figure 2 is about 50% smaller compared to that observed with microscopy-based thickness monitoring in Figure 3a. By design, WLI is a surface-metrology method. When applied to paper, usually a sparse data set results due to the considerable surface roughness. The full-width-at-half-maximum (FWHM) of the histogram corresponding to dry paper is 10.8 μm. Interestingly the FWHM of wet paper (16.5 μm) is larger than (1 + ϵTD)(FWHM)dry. This might be an indication that the increase in transparency and reduction in scattering due to the presence of liquid6 allows subsurface locations to contribute to the WLI signal. This would result in an artificial reduction in swelling amplitude. Such an effect could explain the difference between the WLI and microscopy-based swelling amplitude measurements. The same observation holds for other optical methods based on light reflection such as confocal displacement metrology and laser triangulation, as reported in the Supporting Information (Section III, Figures S5 and S6).

Conclusions

We have studied pore-fiber transport and the associated swelling dynamics of paper substrates after deposition of aqueous solutions of glycerol and poly(ethylene glycols). The latter are commonly added as cosolvents to water-based inks for inkjet printing. Typically we observe a short [ts ≈ (1–20) s] and a long [tl ≈ (20–10000) s] time scale. The short time scale depends approximately exponentially on the concentration and approximately linearly on the molecular weight of the cosolvents.

For cosolvent concentrations up to about 50 wt %, the short time scale is governed by capillary imbibition into the cellulose fibers, whereas at higher concentrations, it slows down due to the retarded or lacking plasticization of the fiber walls by water. The experimental data can be well-represented by the Berens and Hopfenberg model, according to which the long time scale represents the influence of polymer relaxation as a consequence of the increasing solvent content.

Glycerol has a similarly low vapor pressure as TEG at room temperature,98−100 but a significantly smaller short swelling time scale compared to TEG, which is likely related to the smaller molecular weight, higher surface tension and lower viscosity for concentrations below 50 wt %. As such it might lead to faster ink fixation compared to TEG.

Addition of surfactants can significantly reduce the short time scale. However, at high cosolvent concentrations, they tend to reduce the persistent swelling strain and thus the total quantity of cosolvent transported into the fiber interior.

We used optical noncontact methods that are compatible with the low mechanical stiffness and strength of wet paper. Methods based on light reflection from the top surface of paper were found to yield swelling amplitudes that are consistently smaller than optical monitoring of the cross-section of a papersheet. The reason is likely related to the finite penetration depth of light along the thickness direction of the paper sheet.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.langmuir.4c01965.Material properties of the pure cosolvents and aqueous mixtures; experimental setups and results based on laser triangulation and confocal displacement metrology; additional results concerning the short swelling time: dependence on drop volume, DEG concentration and surfactant concentration for 40 wt % glycerol solutions (PDF)

Supplementary Material

la4c01965_si_001.pdf

The authors declare no competing financial interest.

Acknowledgments

This work is part of an Industrial Partnership Program (i43-FIP) of the Foundation for Fundamental Research on Matter (FOM), which is part of The Netherlands Organisation for Scientific Research (NWO). This research programme is cofinanced by Canon Production Printing, University of Twente, Eindhoven University of Technology, and the “Topconsortia voor Kennis en lnnovatie (TKI)” allowance from the Ministry of Economic Affairs.
==== Refs
References

Yan K. ; Li J. ; Pan L. ; Shi Y. Inkjet printing for flexible and wearable electronics. APL Mater. 2020, 8 , 120705 10.1063/5.0031669.
Zapka W. Handbook of Industrial Inkjet Printing; John Wiley & Sons: 2017.
Cordwell J. ; Double P. ; Edwards M. ; Morris D. ; Hopper A. Inks & printing process. 2018; European patent EP2655522B1.
Schmid C. In Formulation and Properties of Waterborne Inkjet Inks; Magdassi S. , Ed.; World Scientific: Singapore, 2010; Chapter 7.
Venditti G. ; Murali V. ; Darhuber A. A. Inkjet deposition of surfactant solutions onto thin moving porous media. Coll. Surf. A Physicochem. Eng. Asp. 2022, 634 , 127832 10.1016/j.colsurfa.2021.127832.
Wijburg M. G. ; Wang S. ; Darhuber A. A. Transport and evaporation of aqueous co-solvent solutions in thin porous media. Coll. Surf. A: Physicochem. Eng. Aspects 2023, 656 , 130268 10.1016/j.colsurfa.2022.130268.
Wong C.-L. ; Wang S. ; Karimnejad S. ; Wijburg M. G. ; Mansouri H. ; Darhuber A. A. Transient deformation and swelling of paper by aqueous co-solvent solutions. Soft Matter 2023, 19 , 1202–1211. 10.1039/D2SM01388F.36656620
Wang S. ; Darhuber A. A. A numerical model for the transport and drying of solutions in thin porous media — Coffee-stain effect and solute ring formation. Coll. Surf. A: Physicochem. Eng. Aspects 2024, 682 , 132839 10.1016/j.colsurfa.2023.132839.
Salmén L. In Paper Products Physics and Technology; Ek M. ; Gellerstedt G. ; Henriksson G. , Eds.; de Gruyter: Berlin, 2009; Vol. 3 , Chapter 2.
Glas D. ; Paesen R. ; Depuydt D. ; Binnemans K. ; Ameloot M. ; De Vos D. E. ; Ameloot R. Cellulose Amorphization by Swelling in Ionic Liquid/Water Mixtures: A Combined Macroscopic and Second-Harmonic Microscopy Study. ChemSusChem 2015, 8 , 82–86. 10.1002/cssc.201402776.25363520
Burger D. ; Winter A. ; Subbiahdoss G. ; Oberlerchner J. T. ; Beaumont M. ; Tamada Y. ; Rosenau T. Partial Amorphization of Cellulose through Zinc Chloride Treatment: A Facile and Sustainable Pathway to Functional Cellulose Nanofibers with Flame-Retardant and Catalytic Properties. ACS Sust. Chem. & Eng. 2020, 8 , 13576–13582. 10.1021/acssuschemeng.0c03492.
Isogai A. ; Onabe F. ; Usuda M. Swelling Behaviour of Cellulose by Chemical and Mechanical Treatments. Sen’i Gakkaishi 1992, 48 , 487–492. 10.2115/fiber.48.9_487.
Mantanis G. I. ; Young R. A. ; Rowell R. M. Swelling of compressed cellulose fiber webs in organic liquids. Cellulose 1995, 2 , 1–22. 10.1007/BF00812768.
Kocherbitov V. ; Ulvenlund S. ; Kober M. ; Jarring K. ; Arnebrant T. Hydration of Microcrystalline Cellulose and Milled Cellulose Studied by Sorption Calorimetry. J. Phys. Chem. B 2008, 112 , 3728–3734. 10.1021/jp711554c.18307340
Ioelovich M. Accessibility and crystallinity of cellulose. BioResources 2009, 4 , 1168 10.15376/biores.4.3.1168-1177.
Hubbe M. ; Ayoub A. ; Daystar J. ; Venditti R. ; Pawlak J. Enhanced Absorbent Products Incorporating Cellulose and Its Derivatives: A Review. BioResources 2013, 8 , 6556–6629. 10.15376/biores.8.4.6556-6629.
Zhang C. ; Li P. ; Zhang Y. ; Lu F. ; Li W. ; Kang H. ; Xiang J.-f. ; Huang Y. ; Liu R. Hierarchical porous structures in cellulose: NMR relaxometry approach. Polymer 2016, 98 , 237–243. 10.1016/j.polymer.2016.06.036.
Ottesen V. ; Syverud K. Swelling of individual cellulose nanofibrils in water, role of crystallinity: an AFM study. Cellulose 2021, 28 , 19–29. 10.1007/s10570-020-03517-8.
Wertz J.-L. ; Bédué O. ; Mercier J. P. Cellulose Science and Technology; EPFL Press: Lausanne, 2010.
Stamm A. J. ; Tarkow H. The Penetration of Cellulose Fibers. J. Phys. Chem. 1950, 54 , 745–753. 10.1021/j150480a001.
Philipp B. ; Schleicher H. ; Wagenknecht W. The influence of cellulose structure on the swelling of cellulose in organic liquids. J. Polym. Sci. Polym. Symp. 1973, 42 , 1531–1543. 10.1002/polc.5070420356.
Qing Y. ; Wu Y. ; Cai Z. ; Li X. Water-triggered dimensional swelling of cellulose nanofibril films: Instant observation using optical microscope. J. Nanomat. 2013, 2013 , 594734 10.1155/2013/594734.
Lee M. ; Kim S. ; Kim H.-Y. ; Mahadevan L. Bending and buckling of wet paper. Phys. Fluids 2016, 28 , 042101 10.1063/1.4944659.
Letková E. ; Letko M. ; Vrška M. Influence of recycling and temperature on the swelling ability of paper. Chem. Pap. 2011, 65 , 822–828. 10.2478/s11696-011-0089-z.
Schuchard D. R. ; Berg J. C. Liquid transport in composite cellulose—superabsorbent fiber networks. Wood Fiber Sci. 1991, 342–357.
Geffert A. ; Vacek O. ; Jankech A. ; Geffertová J. ; Milichovský M. Swelling of cellulosic porous materials - mathematical description and verification. BioResources 2017, 12 , 5017–5030. 10.15376/biores.12.3.5017-5030.
Jablonskỳ M. ; Botkova M. ; Šutỳ Š. ; Šmatko L. ; Šima J. Accelerated ageing of newsprint paper: changes in swelling ability, WRV and electrokinetic properties of fibres. Fibres Text. East. Eur. 2014, 104 , 108.
Bauer W. ; Weber M. ; Chanbai S. In Encyclopedia of Tribology; Wang Q. J. ; Chung Y.-W. , Eds.; Springer US: Boston, MA, 2013; pp 4115–4127.
Schmit J. ; Pakuła A. In Handbook of Advanced Nondestructive Evaluation; Ida N. ; Meyendorf N. , Eds.; Springer International Publishing: Cham, 2019; pp 421–467.
Chang S. ; Kim W. Dynamics of water imbibition through paper with swelling. J. Fluid Mech. 2020, 892 , A39 10.1017/jfm.2020.219.
Kvick M. ; Martinez D. M. ; Hewitt D. R. ; Balmforth N. J. Imbibition with swelling: Capillary rise in thin deformable porous media. Phys. Rev. Fluids 2017, 2 , 074001 10.1103/PhysRevFluids.2.074001.
Salminen L. ; Liukkonen S. ; Alava M. Ground Wood Fiber Length Distributions. BioResources 2014, 9 , 1168–1178. 10.15376/biores.9.1.1168-1178.
Nicasy R. J. K. ; Waldner C. ; Erich S. J. F. ; Adan O. C. G. ; Hirn U. ; Huinink H. P. Liquid uptake in porous cellulose sheets studied with UFI-NMR: Penetration, swelling and air displacement. Carbohydr. Polym. 2024, 326 , 121615 10.1016/j.carbpol.2023.121615.38142096
Nicasy R. J. K. ; Waldner C. ; Erich S. J. F. ; Adan O. C. G. ; Hirn U. ; Huinink H. P. Liquid penetration in hydrophobised cellulose based sheets. Cellulose 2024, 31 , 5527–5544. 10.1007/s10570-024-05934-5.
Vitale T. Effects of Water on the Mechanical Properties of Paper and their Relationship to the Treatment of Paper. In MRS Proc.; 1992; Vol. 267 , pp 397–427.
Hirn U. ; Schennach R. Comprehensive analysis of individual pulp fiber bonds quantifies the mechanisms of fiber bonding in paper. Sci. Rep. 2015, 5 , 10503 10.1038/srep10503.26000898
Wellons J. D. Adhesion in cellulosic and wood-based composites; Plenum Press: New York, 1981; pp 127–146.
Hubbe M. A. Bonding Between Cellulosic Fibers in the Absence and Presence of Dry-Strength Agents – A Review. BioRes. 2006, 1 , 281–318. 10.15376/biores.1.2.281-318.
Gardner D. J. ; Oporto G. S. ; Mills R. ; Azizi Samir M. A. S. Adhesion and Surface Issues in Cellulose and Nanocellulose. J. Adhesion Sci. Technol. 2008, 22 , 545–567. 10.1163/156856108X295509.
Thomson C. I. ; Lowe R. M. ; Ragauskas A. J. First characterization of the development of bleached kraft softwood pulp fiber interfaces during drying and rewetting using FRET microscopy. Holzforschung 2008, 62 , 383–388. 10.1515/HF.2008.069.
Hirn U. ; Schennach R. Fiber-fiber bond formation and failure: Mechanisms and analytical techniques. In Trans. XVIth Fund. Res. Symp. (Oxford); 2017; pp 839–863.
Nanko H. ; Ohsawa J. Mechanisms of fibre bond formation. In Trans. IXth Fund. Res. Symp. (Oxford); 1989; pp 783–830.
Hobisch M. A. ; Zabler S. ; Bardet S. M. ; Zankel A. ; Nypelö T. ; Eckhart R. ; Bauer W. ; Spirk S. How cellulose nanofibrils and cellulose microparticles impact paper strength—A visualization approach. Carbohydr. Polym. 2021, 254 , 117406 10.1016/j.carbpol.2020.117406.33357893
Sauret A. ; Boulogne F. ; Soh B. ; Dressaire E. ; Stone H. A. Wetting morphologies on randomly oriented fibers. Eur. Phys. J. E 2015, 38 , 62 10.1140/epje/i2015-15062-y.26123768
Dunlop-Jones N. In Paper Chemistry; Roberts J. C. , Ed.; Blackie: London, 1991; Chapter 6, p 76.
Myllytie P. ; Holappa S. ; Paltakari J. ; Laine J. Effect of polymers on aggregation of cellulose fibrils and its implication on strength development in wet paper web. Nordic Pulp & Paper Res. J. 2009, 24 , 125–134. 10.3183/npprj-2009-24-02-p125-134.
Myllytie P. ; Yin J. ; Holappa S. ; Laine J. The effect of different polysaccharides on the development of paper strength during drying. Nordic Pulp & Paper Res. J. 2009, 24 , 469–477. 10.3183/npprj-2009-24-04-p469-477.
Larsson P. ; Gimaker M. ; Wagberg L. The influence of periodate oxidation on the moisture sorptivity and dimensional stability of paper. Cellulose 2008, 15 , 837–847. 10.1007/s10570-008-9243-3.
Larsson P. A. ; Wagberg L. Influence of fibre-fibre joint properties on the dimensional stability of paper. Cellulose 2008, 15 , 515–525. 10.1007/s10570-008-9203-y.
Vonk N. ; Peerlings R. ; Geers M. ; Hoefnagels J. Re-understanding the In-plane Hygro-expansion of Freely and Restrained Dried Paper Handsheets. In Trans. of the XVIIth Fundam. Res. Symp. (Cambridge); 2022; pp 421–440.
Dave N. ; Fijen M. J. ; Claassen F. ; Schoenmakers N. P. T. ; Massart T. J. ; Geers M. G. D. ; Peerlings R. H. J. Accuracy of hygro-expansive curl predictions for paper sheets based on homogenised 2D and 3D network representations. Eur. J. Mech. A 2024, 106 , 105339 10.1016/j.euromechsol.2024.105339.
Yasuda H. ; Ikenberry L. D. ; Lamaze C. E. Permeability of solutes through hydrated polymer membranes. Part II. Permeability of water soluble organic solutes. Makromol. Chem. 1969, 125 , 108–118. 10.1002/macp.1969.021250111.
Stone J. E. ; Scallan A. M. A structural model for the cell wall of water-swollen wood pulp fibres based on their accessibility to macromolecules. Cell. Chem. Technol. 1968, 2 , 343–358.
Stone J. E. ; Scallan A. M. ; Donefer E. ; Ahlgren E. Cellulases and Their Applications; ACS: 1969; Chapter 13, pp 219–241.
Lin J. K. ; Ladisch M. R. ; Patterson J. A. ; Noller C. H. Determining Pore Size Distribution in Wet Cellulose by Measuring Solute Exclusion Using a Differential Refractometer. Biotechnol. Bioeng. 1987, 29 , 976–981. 10.1002/bit.260290809.18576547
Neuman R. P. ; Walker L. P. Solute exclusion from cellulose in packed columns: Experimental investigation and pore volume measurements. Biotechnol. Bioeng. 1992, 40 , 218–225. 10.1002/bit.260400205.18601107
Ibbett R. N. ; Kaenthong S. ; Phillips D. A. S. ; Wilding M. A. Solute adsorption and exclusion studies of the structure of never-dried and re-wetted cellulosic fibres. J. Mater. Sci. 2007, 42 , 6809–6818. 10.1007/s10853-006-1426-4.
Pal R. Rheological behaviour of concentrated surfactant solutions and emulsions. Colloids Surf. 1992, 64 , 207–215. 10.1016/0166-6622(92)80101-7.
Kodama M. ; Miura M. The Second CMC of the Aqueous Solution of Sodium Dodecyl Sulfate. II. Viscosity and Density. Bull. Chem. Soc. Jpn. 1972, 45 , 2265–2269. 10.1246/bcsj.45.2265.
We checked that the contact angle of sessile droplets in contact with the paper sheet is roughly the same (12 ± 5 deg.) for 60 wt % TEG solutions with and without 1.2 wt % SDS.
Berg J. C. In Absorbent Technology; Chatterjee P. ; Gupta B. , Eds.; Textile Science and Technology; Elsevier: 2002; Vol. 13 ; pp 149–198.
Fowkes F. M. Role of Surface Active Agents in Wetting. J. Phys. Chem. 1953, 57 , 98–103. 10.1021/j150502a021.
Cohen A. W. ; Rosen M. J. Wetting properties of nonionic surfactants of homogeneous structure C12H25(OC2H4)xOH. J. Am. Oil Chem. Soc. 1981, 58 , 1062–1066. 10.1007/BF02679327.
Venditti G. ; Murali V. ; Darhuber A. A. Inkjet printing of surfactant solutions onto thin moving porous media. Coll. Surf. A: Physicochem. Eng. Aspects 2022, 634 , 127832 10.1016/j.colsurfa.2021.127832.
Sayem Alam Md. ; Mohammed Siddiq A. ; Mandal A. B. The Micellization and Clouding of Nonionic Surfactant, Poly(Ethylene Glycol) t-Octylphenyl Ether (Triton X-100): Effect of Halide Ions of (Sodium Salt) Electrolytes. J. Dispers. Sci. Technol. 2016, 37 , 1385–1394. 10.1080/01932691.2015.1105751.
Gad E. A. M. ; El-Sukkary M. M. A. ; Ismail D. A. Surface and thermodynamic parameters of sodium N-acyl sarcosinate surfactant solutions. J. Am. Oil Chem. Soc. 1997, 74 , 43–47. 10.1007/s11746-997-0117-x.
Hac-Wydro K. ; Palasińska I. ; Miśkowiec P. The comparative studies on the ability of anionic surfactants to bind lead(II) ions. J. Mol. Liq. 2016, 219 , 1071–1077. 10.1016/j.molliq.2016.02.067.
Hanyak M. ; Sinz D. K. N. ; Darhuber A. A. Soluble surfactant spreading on spatially confined thin liquid films. Soft Matter 2012, 8 , 7660–7671. 10.1039/c2sm25484k.
Ye X.-L. ; Li Y.-S. ; Hu X.-J. The Aggregation of Triton X-100 in Ethylene Glycol. Acta Phys.-Chim. Sin. 1994, 10 , 456 10.3866/PKU.WHXB19940517.
Gracie K. ; Turner D. ; Palepu R. Thermodynamic properties of micellization of sodium dodecyl sulfate in binary mixtures of ethylene glycol with water. Can. J. Chem. 1996, 74 , 1616–1625. 10.1139/v96-179.
Khan H. ; Seddon J. M. ; Law R. V. ; Brooks N. J. ; Robles E. ; Cabral J. T. ; Ces O. Effect of glycerol with sodium chloride on the Krafft point of sodium dodecyl sulfate using surface tension. J. Colloid Interface Sci. 2019, 538 , 75–82. 10.1016/j.jcis.2018.11.021.30500469
Panda A. K. ; Sarkar G. ; Manna K. Physicochemical Studies on Surfactant Aggregation 1. Effect of Polyethylene Glycols on the Micellization of SDS. J. Disper. Sci. Technol. 2009, 30 , 1152–1160. 10.1080/01932690802701630.
Glenn K. M. ; Moroze S. ; Bhattacharya S. C. ; Palepu R. M. Effect of Ethylene Glycol on the Thermodynamic and Micellar Properties of Tween 40, 60, and 80. J. Disper. Sci. Technol. 2005, 26 , 79–86. 10.1081/DIS-200040137.
Das S. ; Thapa U. ; Ismail K. Aggregation and Adsorption Behaviors of Sodium Deoxycholate in Water–Ethylene Glycol Medium. Bull. Chem. Soc. Jpn. 2010, 83 , 1352–1358. 10.1246/bcsj.20100152.
Dey J. ; Sultana N. ; Ismail K. Counter ion binding in solutions of sodium dodecylsulfate in water–ethylene glycol mixtures and the Corrin–Harkins equation. J. Mol. Liq. 2015, 207 , 107–111. 10.1016/j.molliq.2015.03.030.
Desam G. P. ; Li J. ; Chen G. ; Campanella O. ; Narsimhan G. A mechanistic model for swelling kinetics of waxy maize starch suspension. J. Food Eng. 2018, 222 , 237–249. 10.1016/j.jfoodeng.2017.11.017.
Desam G. P. ; Li J. ; Chen G. ; Campanella O. ; Narsimhan G. Swelling kinetics of rice and potato starch suspensions. J. Food Process Eng. 2020, 43 , e13353 10.1111/jfpe.13353.
Palanisamy A. ; Deslandes F. ; Ramaioli M. ; Menut P. ; Plana-Fattori A. ; Flick D. Kinetic modelling of individual starch granules swelling. Food Structure 2020, 26 , 100150 10.1016/j.foostr.2020.100150.
Tanasić J. ; Erceg T. ; Tanasić L. ; Baloš S. ; Klisurić O. ; Ristic I. The influence of reaction conditions on structural properties and swelling kinetics of polyurethane hydrogels intended for agricultural purposes. React. Funct. Polym. 2021, 169 , 105085 10.1016/j.reactfunctpolym.2021.105085.
Yavari N. ; Azizian S. Mixed diffusion and relaxation kinetics model for hydrogels swelling. J. Mol. Liq. 2022, 363 , 119861 10.1016/j.molliq.2022.119861.
Sanopoulou M. ; Roussis P. P. ; Petropoulos J. H. A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics. J. Polymer Sci. B: Polymer Phys. 1995, 33 , 993–1005. 10.1002/polb.1995.090330702.
Perrin L. ; Nguyen Q. T. ; Sacco D. ; Lochon P. Experimental Studies and Modelling of Sorption and Diffusion of Water and Alcohols in Cellulose Acetate. Polym. Int. 1997, 42 , 9–16. 10.1002/(SICI)1097-0126(199701)42:1<9::AID-PI637>3.0.CO;2-A.
Sanopoulou M. ; Petropoulos J. Sorption and longitudinal swelling kinetic behaviour in the system cellulose acetate-methanol. Polymer 1997, 38 , 5761–5768. 10.1016/S0032-3861(97)00127-4.
Mericer C. ; Minelli M. ; Giacinti Baschetti M. ; Lindström T. Water sorption in microfibrillated cellulose (MFC): The effect of temperature and pretreatment. Carbohydr. Polym. 2017, 174 , 1201–1212. 10.1016/j.carbpol.2017.07.023.28821046
Espino-Pérez E. ; Bras J. ; Almeida G. ; Plessis C. ; Belgacem N. ; Perré P. ; Domenek S. Designed cellulose nanocrystal surface properties for improving barrier properties in polylactide nanocomposites. Carbohydr. Polym. 2018, 183 , 267–277. 10.1016/j.carbpol.2017.12.005.29352884
Long F. A. ; Richman D. Concentration Gradients for Diffusion of Vapors in Glassy Polymers and their Relation to Time Dependent Diffusion Phenomena. J. Am. Chem. Soc. 1960, 82 , 513–519. 10.1021/ja01488a002.
Tang Y. ; Lu J. R. ; Lewis A. L. ; Vick T. A. ; Stratford P. W. Structural Effects on Swelling of Thin Phosphorylcholine Polymer Films. Macromolecules 2002, 35 , 3955–3964. 10.1021/ma0117918.
Chandra P. ; Koros W. J. Sorption and transport of methanol in poly(ethylene terephthalate). Polymer 2009, 50 , 236–244. 10.1016/j.polymer.2008.10.031.
Sabard M. ; Gouanvé F. ; Espuche E. ; Fulchiron R. ; Seytre G. ; Fillot L.-A. ; Trouillet-Fonti L. Influence of film processing conditions on the morphology of polyamide 6: Consequences on water and ethanol sorption properties. J. Membr. Sci. 2012, 415–416 , 670–680. 10.1016/j.memsci.2012.05.048.
Burgess S. K. ; Mikkilineni D. S. ; Yu D. B. ; Kim D. J. ; Mubarak C. R. ; Kriegel R. M. ; Koros W. J. Water sorption in poly(ethylene furanoate) compared to poly(ethylene terephthalate). Part 2: Kinetic sorption. Polymer 2014, 55 , 6870–6882. 10.1016/j.polymer.2014.10.065.
Almeida G. ; Domenek S. ; Perré P. TransPoly: A theoretical model to quantify the dynamics of water transfer through nanostructured polymer films. Polymer 2020, 191 , 122256 10.1016/j.polymer.2020.122256.
Mallarino S. ; Renaud A. ; Trinh D. ; Touzain S. The role of internal stresses, temperature, and water on the swelling of pigmented epoxy systems during hygrothermal aging. J. Appl. Polym. Sci. 2022, 139 , e53162 10.1002/app.53162.
Hassanpour B. ; Karbhari V. M. Moisture and Glass Transition Temperature Kinetics of Ambient-Cured Carbon/Epoxy Composites. J. Compos. Sci. 2023, 7 , 447 10.3390/jcs7110447.
Nezili Y. ; Mdarhri A. ; El Aboudi I. ; Brosseau C. ; Zaghrioui M. ; Ghorbal A. ; He D. ; Bai J. Solvent polarity impacts the sorption kinetics and tensile properties of carbon black filled elastomers. Polymer 2023, 264 , 125563 10.1016/j.polymer.2022.125563.
Berens A. ; Hopfenberg H. Diffusion and relaxation in glassy polymer powders: 2. Separation of diffusion and relaxation parameters. Polymer 1978, 19 , 489–496. 10.1016/0032-3861(78)90269-0.
Thomas N. ; Windle A. A theory of case II diffusion. Polymer 1982, 23 , 529–542. 10.1016/0032-3861(82)90093-3.
Hermans P. H. ; Vermaas D. Density of cellulose fibers. I. Introduction and experiments on the penetration of liquids into dry cellulose. J. Polym. Sci. 1946, 1 , 149–155. 10.1002/pol.1946.120010301.
Krieger U. K. ; et al. A reference data set for validating vapor pressure measurement techniques: homologous series of polyethylene glycols. Atmos. Meas. Technol. 2018, 11 , 49–63. 10.5194/amt-11-49-2018.
Ross G. R. ; Heideger W. J. Vapor Pressure of Glycerol. J. Chem. Eng. Data 1962, 7 , 505–507. 10.1021/je60015a019.
Cammenga H. K. ; Schulze F. W. ; Theuerl W. Vapor pressure and evaporation coefficient of glycerol. J. Chem. Eng. Data 1977, 22 , 131–134. 10.1021/je60073a004.
