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Spectroscopic Methods to Investigate Liquid–Porous Material Interactions: An Overview of Optical and Electrical Impedance Techniques

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Abstract

An overview of spectroscopic methods to investigate physical processes specific to the water-based ink/substrate interaction is made in this work. Optical techniques (as VIS reflectometry, IR-ATR and spectroellipsometry) and electrical impedance spectroscopy have been employed to study physical phenomena that describe the interaction between water-based mixtures and the substrate for printing; the latter can be absorbent (porous) or non-absorbent of liquid. Therefore, evaporation of aqueous mixtures and/or liquid penetration in porous paper are the main subjects of these studies. After brief introduction in each method, examples of various particular cases are presented and analyzed: evaporation of pure liquids and mixtures, water penetration into paper of various thicknesses, the penetration of different liquids into plain paper. The method of spectroellipsometry was used to characterize the coating of the coated paper for printing industry.

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Notes

  1. With the courtesy of Tiny Ritzen who performed the SEM measurements.

  2. The constant apparatus \(\chi \) is defined by the geometry of the ATR system and the settings of the spectrometer. Our setup uses a Bruker spectrometer with a Ge ATR crystal. In data analysis, according to the model proposed in Tomozeiu (2014), we use the ratio of the measured signal as a function of time: \((\mathfrak {I}(0)-\mathfrak {I}({t}))/\mathfrak {I}(0)={f}({t}^{{\alpha }})\); therefore this constant \(\chi \) will not influence the outputs of the model and its use for data analyzing.

  3. Although porous media generally have a complex structure, theoretically they can be modeled as a single, vertical capillary or as an assembly of such capillaries. Based on this, most of the publications in this field use in the first approximation the Washburn equation (Washburn 1921) to discuss the rate of advancing front of the liquid into material; if s is the length of liquid in capillary, r is the radius of capillary, \({\sigma }\) is the liquid surface tension, \(\eta \) is the viscosity of the liquid and \(\theta \)—the contact angle, according to this model the length of the liquid in capillary varies in time as:

    $$\begin{aligned} s=\sqrt{\frac{{\sigma }\cdot \hbox {cos}\theta }{{2}\cdot \eta }\cdot {r}}\cdot {{t}^{1/2}} \end{aligned}$$

    Defining the penetration rate as the derivative of liquid length in capillary versus time, we get:

    $$\begin{aligned} \frac{\hbox {d}s}{\hbox {d}t}=\sqrt{\frac{{\sigma }\cdot \hbox {cos}\theta }{8\cdot \eta }\cdot {r}}\cdot {{t}^{-1/2}}, \end{aligned}$$

    expression which shows the dependence of the liquid penetration rate on both the liquid properties (\({\sigma }\), \(\eta \), \(\theta )\) and the paper characteristics (r, \(\theta )\). According to this, the penetration rate is larger for liquids with high surface tension and low viscosity.

  4. Here “quasi-constant” means that the value is not “frozen” but has small variations (see the argZ in Fig. 18 for \(t< 10\) s) that in the first approximation can be neglected.

  5. See the relation (15), where \(\alpha \) describes the variation in time of the normalized capacity. We mention that a similar study can be made considering the electrical resistance of the sample.

Abbreviations

E :

Intensity of the electrical field assigned to the infrared radiation (V/m)

\({E}_{0}\) :

Intensity of the electrical field at the ATR crystal–sample interface (V/m)

\({\lambda }\) :

Optical radiation wavelength (\(\upmu \)m)

\({\varpi }\) :

Optical radiation wavenumber \((\hbox {cm}^{-1})\)

\({n}_{1}\) :

Refractive index of the ATR crystal (dimensionless)

\({n}_{2}\) :

Refractive index of the measured sample (dimensionless)

\({\theta }\) :

Angle of the ATR crystal (\(^{\circ }\))

\(\varDelta \) :

Thickness of the ATR crystal (mm)

\({{\delta }}_{\mathrm{p}}\) :

Depth of penetration of the evanescent electrical field (\(\upmu \)m)

L :

Thickness of the probed sample by ATR measurement (\(\upmu \)m)

d(t):

Thickness of the liquid layer (\(\upmu \)m)

N :

Number of reflections at the ATR crystal/sample interface (dimensionless)

\(\mathfrak {I}\) :

Intensity of the ATR signal assigned to water (%)

\({\chi }\) :

Constant of the measurement setup (dimensionless)

c :

Molecular concentration of the investigated specie \((\hbox {cm}^{-3})\)

\(\gamma \) :

Absorption coefficient \((\hbox {cm}^{-1})\)

\(\varepsilon \) :

Paper porosity (%)

s :

Distance travelled of the advancing front of the liquid into porous paper (\(\upmu \)m)

\({\xi }\) :

Parameter that describes liquid penetration into porous paper

\({\alpha }\) :

Parameter that reveals the time dependence of liquid penetration (dimensionless)

\({\rho }\) :

Complex reflectance ratio in ellipsometry (dimensionless)

\({R}^{{s},{p}}\) :

Amplitude of s and p polarized light after reflection and normalized to their initial values (dimensionless)

\(\varPsi \) :

Ellipsometry parameter that describes the amplitude ratio (dimensionless)

\(\varDelta \) :

Ellipsometry parameter that describes the phase difference (\(^{\circ }\))

\({\delta }_{{q}0}\) :

Phase of the incident light with polarization q: \(q=s,p\) (\(^{\circ }\))

\({\delta }_{{qr}}\) :

Phase of the reflected light with polarization q: \(q=s,p\) (\(^{\circ }\))

\(\in \) :

Complex dielectric constant (dimensionless)

\(\in _{1}\) :

Real part of dielectric constant (dimensionless)

\(\in _{2}\) :

Imaginary part of dielectric constant (dimensionless)

Z :

Complex electric impedance (\(\Omega \))

\({\omega }\) :

Angular frequency (radians per second)

\({\varphi }\) :

Phase shift by which the current lags the voltage, impedance argument (\(^{\circ }\))

C :

Electrical capacity of the sample (F)

\({C}_{0}\) :

Electrical capacity of the measurement cell (F)

R :

Electrical resistance (\(\Omega \))

\(\in _{0 }\) :

Vacuum dielectric constant (F/m)

\(\in _{\mathrm{dp}}\) :

Relative dielectric constant of dry paper (dimensionless)

\(\in _{\mathrm{wp}}\) :

Relative dielectric constant of wet paper (dimensionless)

p:

Symbol refers to paper

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Acknowledgments

The author acknowledges the full support received from the A&PS department of Océ Technologies during this research.

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Tomozeiu, N. Spectroscopic Methods to Investigate Liquid–Porous Material Interactions: An Overview of Optical and Electrical Impedance Techniques. Transp Porous Med 115, 603–629 (2016). https://doi.org/10.1007/s11242-016-0683-1

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