Cited by 30Terahertz technology and applicationsMicrowave and Dielectric Measurement TechniquesThermography and Photoacoustic Techniques

Measuring Open Porosity of Porous Materials Using THz-TDS and an Index-Matching Medium

Open access
Naftaly, Mira, Tikhomirov, Iliya, Hou, Peter, Markl, Daniel·2020·Sensors

Abstract

The porosity of porous materials is a critical quality attribute of many products ranging from catalysis and separation technologies to porous paper and pharmaceutical tablets. The open porosity in particular, which reflects the pore space accessible from the surface, is crucial for applications where a fluid needs to access the pores in order to fulfil the functionality of the product. This study presents a methodology that uses terahertz time-domain spectroscopy (THz-TDS) coupled with an index-matching medium to measure the open porosity and analyze scattering losses of powder compacts. The open porosity can be evaluated without the knowledge of the refractive index of the fully dense material. This method is demonstrated for pellets compressed of pharmaceutical-grade lactose powder. Powder was compressed at four different pressures and measured by THz-TDS before and after they were soaked in an index-matching medium, i.e., paraffin. Determining the change in refractive index of the dry and soaked samples enabled the calculation of the open porosity. The results reveal that the open porosity is consistently lower than the total porosity and it decreases with increasing compression pressure. The scattering losses reduce significantly for the soaked samples and the scattering centers (particle and/or pore sizes) are of the order of or somewhat smaller than the terahertz wavelength. This new method facilitates the development of a better understanding of the links between material properties (particles size), pellet properties (open porosity) and performance-related properties, e.g., disintegration and dissolution performance of pharmaceutical tablets.

AI snapshot

Written from the paper’s full text.

TL;DR

The paper presents a THz-TDS method with an index-matching medium (paraffin) to measure open porosity of porous compacts without knowing the fully dense refractive index. Applied to lactose pellets, open porosity is lower than total porosity and decreases with compression pressure, while scattering losses drop after soaking and disintegration time rises with pressure.

Key findings

  • Open porosity was calculated from the refractive-index difference between dry and paraffin-soaked pellets: for a B01 pellet made at 3 × 10⁷ N/m², \(p_{\text{open}} = \Delta n_{\text{eff}}/(n_{\text{paraffin}} - 1) \approx 0.085/(1.475 - 1) \approx 0.18\). Open porosity was consistently lower than total porosity, except at the highest pressure where the difference lay within experimental error.
  • Scattering loss in compressed pellets followed a power law; for the B01 example, scattering loss behaved as \(1.8 f^{2.65}\), indicating scattering centers (particle and/or pore sizes) of the order of or somewhat smaller than the terahertz wavelength.
  • Paraffin reduced interface reflection from 0.027 for lactose–air to 0.006 for lactose–paraffin. Away from absorption at 2.2 THz, the loss difference between dry and soaked pellets decreased with pressure as porosity and scattering decreased; at the absorption peak at 1.38 THz there was no measurable difference.
  • Disintegration time rose steeply with compression pressure and correlated with decreasing porosity; the loss difference continued to decrease throughout the pressure range and may offer a better indirect estimate of disintegration time than the refractive-index difference.

Methods

  • α-Lactose monohydrate powder was compressed into pellets using 0.200 ± 0.02 g powder, 13 mm diameter, and ~1 mm thickness, at four pressure levels (batches B01–B04) with four pellets per pressure. Particle size was d10 = 16.74 ± 0.30 µm, d50 = 45.97 ± 0.16 µm, and d90 = 105.74 ± 1.47 µm; true density was 1.543 ± 0.004 g/cm³.
  • THz-TDS measured dry pellets and pellets soaked in paraffin oil for at least 6 h, then drained. Each pellet was measured 10 times with repositioning; refractive index and loss coefficient were calculated using standard formulae. Open porosity was obtained from \(\Delta n_{\text{eff}}/(n_{\text{paraffin}} - 1)\) with \(n_{\text{paraffin}} = 1.475\).
  • Disintegration testing used a Copley DTG 2000 in 800 mL distilled water at 37 °C, measuring five to seven tablets per pressure level.

Limitations

  • Stated: the proposed method is destructive compared with previously published non-destructive THz-TDS procedures. THz-TDS does not provide information about individual pores or pore size distribution, and the measured optical parameters are averaged over the sample volume traversed by the beam (4 mm beam diameter, F# = 2).
  • Evident from the text: the demonstration is limited to pharmaceutical-grade lactose pellets and paraffin as the index-matching medium, with only four pressure levels and a small number of pellets/tablets per level; no independent open-porosity reference method is reported for validation.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.3390/s20113120

Cites

Statistics

Nothing to recompute.

Claims the paper makes

0 of 21 cited sources checked · 0 supported · 0 flagged

  • Findingown data

    Open porosity decreases with increasing compression pressure.

    “The results reveal that the open porosity is consistently lower than the total porosity and it decreases with increasing compression pressure.”
    • Also stated in: § 4. Discussion · hedged
      “The results indicate that the open porosity decreases with increasing compression pressure.”
    Quote in the paperSubstantial claim
  • Findingown data

    Scattering losses reduce significantly for the soaked samples.

    “The scattering losses reduce significantly for the soaked samples and the scattering centers (particle and/or pore sizes) are of the order of or somewhat smaller than the terahertz wavelength.”
    • Also stated in: § 3. Results · plain
      “The loss in soaked pellets becomes constant within measurement uncertainty, except for a small excess at the lowest pressure.”
    Quote in the paperSubstantial claim
  • Findingreasoning

    At the absorption peak, the loss remains constant because the relative contribution of scattering is negligible.

    “At the absorption peak, in contrast, shown in the inset, the loss remains constant because the relative contribution of scattering is negligible.”
    Quote in the paperNot a substantial claim
  • Findingreasoning

    The loss difference rises with frequency due to stronger scattering.

    “The loss difference rises with frequency due to stronger scattering.”
    Quote in the paperNot a substantial claim
  • Findingown data

    The refractive index increases in soaked pellets as paraffin replaces air in the open pores.

    “The effect of paraffin is also observed in the refractive index (Figure 3b), which increases in the soaked pellets as paraffin replaces air in the open pores.”
    Quote in the paperSubstantial claim
  • May combine two claims. 15
  • Classified as probably not a substantial claim. 7
  • The quote only partly states this claim. 1
  • May combine two claims.

    Findingown data

    Open porosity is consistently lower than total porosity, except at the highest pressure where the difference lies within experimental error.

    “The results reveal that the open porosity is consistently lower than the total porosity and it decreases with increasing compression pressure.”
    • Also stated in: § 3. Results · plain
      “It is seen that, as expected, the total porosity consistently exceeds open porosity, except at the highest pressure where the difference lies within the experimental error.”
    • Also stated in: § 5. Conclusions · plain
      “Our results reveal that the open porosity is consistently lower than the total porosity.”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Findingown data

    Paraffin oil has high THz transparency and a refractive index similar to that of lactose.

    “Paraffin oil was chosen as an index-matching medium because of its high THz transparency and its similar refractive index to that of lactose, as seen in Figure 2.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data

    The increase in refractive index and the difference between refractive indices of dry and soaked pellets both deviate from linear, consistent with porosity.

    “The increase in refractive index in Figure 5a and the difference between refractive indices of dry and soaked pellets in Figure 5b both deviate from linear, as consistent with porosity in Figure 5c, which compares the values of total porosity and the values of open porosity calculated from the data in Figure 5b using Equation (3).”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data

    At the absorption peak @ 1.38 THz there is no measurable difference between dry and soaked pellets; away from absorption @ 2.2 THz the difference decreases with pressure as porosity and scattering decrease.

    “As expected, at the absorption peak @ 1.38 THz there is no measurable difference; whereas away from absorption @ 2.2 THz the difference decreases with pressure as porosity, and therefore scattering, decreases.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data

    The refractive index difference and loss difference as functions of DT both drop steeply at first and then flatten out.

    “It is seen that both drop steeply at first and then flatten out.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    THz-TDS has been demonstrated to measure porosity of rocks and pharmaceutical tablets and to analyze anisotropy of pore structures.

    “This method has been demonstrated to measure the porosity of rocks [20] and pharmaceutical tablets [21,22,23] as well as to analyze the anisotropy of pore structures [18,24].”
    Quote in the paperSubstantial claim0 of 6 sources checked
    • cites [20] Heshmat, 2017, Terahertz scattering and water absorption for porosimetry, Opt. Express source

      Not checked in the free run.

    • cites [21] Bawuah, 2014, Detection of porosity of pharmaceutical compacts by terahertz radiation transmission and light reflection measurement techniques, Int. J. Pharm. source

      Not checked in the free run.

    • cites [22] Bawuah, 2016, Noninvasive porosity measurement of biconvex tablets using terahertz pulses, Int. J. Pharm. source

      Not checked in the free run.

    • cites [23] Markl, 2017, Characterization of the pore structure of functionalized calcium carbonate tablets by terahertz time-domain spectroscopy and X-ray computed microtomography, J. Pharm. Sci. source

      Not checked in the free run.

    • cites [18] Markl, 2018, Fast and non-destructive pore structure analysis using terahertz time-domain spectroscopy, Int. J. Pharm. source

      Not checked in the free run.

    • cites [24] Bawuah, 2016, A structure parameter for porous pharmaceutical tablets obtained with the aid of Wiener bounds for effective permittivity and terahertz time-delay measurement, Int. J. Pharm. source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductcitation

    The THz-TDS system was frequency-calibrated and its amplitude linearity was verified.

    “The THz-TDS was frequency-calibrated and had its amplitude linearity verified, as described in [26].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [26] Naftaly, 2009, Linearity calibration of amplitude and power measurements in terahertz systems and detectors, Opt. Lett. source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductreasoning

    Each pellet was measured 10 times with removal and replacement to average over positioning errors.

    “Each pellet was measured 10 times; each time it was removed from the sample holder, then replaced to average over positioning errors.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationown data

    THz-TDS coupled with an index-matching medium can measure open porosity and analyze scattering losses of powder compacts.

    “This study presents a methodology that uses terahertz time-domain spectroscopy (THz-TDS) coupled with an index-matching medium to measure the open porosity and analyze scattering losses of powder compacts.”
    • Also stated in: § 5. Conclusions · boosted
      “This study demonstrated a methodology that uses THz-TDS coupled with an index-matching medium to measure the open porosity and to analyze scattering losses of powder compacts.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationcitation

    The rise in disintegration time is primarily attributed to decreasing porosity and changes in pore structure.

    “This is primarily attributed to the decreasing porosity (Figure 7b) and also to changes in the pore structure [29].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [29] Markl, 2017, Non-destructive determination of disintegration time and dissolution in immediate release tablets by terahertz transmission measurements, Pharm. Res. source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Disintegration time is known to largely depend on tablet porosity and is in many cases the rate-determining process.

    “DT is known to largely dependent on the tablet porosity and it is in many cases the rate-determining process [6,7].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [6] Markl, 2017, A review of disintegration mechanisms and measurement techniques, Pharm. Res. source

      Not checked in the free run.

    • cites [7] Markl, 2018, Characterisation of pore structures of pharmaceutical tablets: A review, Int. J. Pharm. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    Light scattering due to porosity can be separated from absorption losses, making it possible to gain insight into pore size.

    “We have also shown that light scattering due to porosity can be separated from absorption losses, making it possible to gain insight into pore size.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S2 (checkable).

    Premisenone given

    Open porosity is relevant for many functional materials and products where a fluid needs to enter the porous medium.

    “The open porosity is relevant for many functional materials and products, where a fluid needs to enter the porous medium in order to fulfil its functionality, such as heterogenous catalysts, separation technologies, pharmaceutical tablets and filtering media; or conversely where closed pores are required, as in insulation and barrier media.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Open porosity is crucial for enabling fluid access and initiating tablet dissolution.

    “The open porosity, i.e., the pore space accessible from the surface, is crucial for enabling fluid access and initiating tablet dissolution, which is an essential process in an effective treatment using an orally delivered drug product.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [6] Markl, 2017, A review of disintegration mechanisms and measurement techniques, Pharm. Res. source

      Not checked in the free run.

    • cites [7] Markl, 2018, Characterisation of pore structures of pharmaceutical tablets: A review, Int. J. Pharm. source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning

    The presented methodology enables direct measurement of open porosity and facilitates better understanding of the relationship between material properties, tablet properties and performance attributes.

    “The presented methodology enables a direct measurement of the open porosity and thus facilitates the development of a better understanding of the relationship between material properties (e.g., particle size), tablet properties (porosity) and performance attributes (disintegration and dissolution).”
    Quote in the paperSubstantial claim
  • The quote only partly states this claim.

    Interpretationreasoning

    The proposed method does not require a calibration data set of pellets compacted at various pressures paired with known total porosity values.

    “This procedure is not required for the proposed method where we use an index-matching medium to determine the open porosity.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Premisereasoning

    The pores in a tablet drive the liquid uptake process, which is necessary to initiate swelling/dissolution of particles.

    “The pores in a tablet drive the liquid uptake process, which is necessary to initiate the swelling/dissolution of particles.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Interpretationown data

    The loss difference continues to decrease throughout the range of pressures examined and may offer a better insight and a tool for indirect estimates of DT.

    “However, the loss difference continues to decrease throughout the range of pressures examined, and therefore may offer a better insight and a tool for indirect estimates of DT.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning

    The new method facilitates development of a better understanding of the links between material properties, pellet properties and performance-related properties.

    “This new method facilitates the development of a better understanding of the links between material properties (particles size), pellet properties (open porosity) and performance-related properties, e.g., disintegration and dissolution performance of pharmaceutical tablets.”
    • Also stated in: § 5. Conclusions · plain
      “This new method facilitates the development of a better understanding of the links between material properties (particles size), pellet properties (open porosity) and performance-related properties, e.g., disintegration and dissolution performance of pharmaceutical tablets.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Interpretationnone given

    The proposed method is destructive compared to the non-destructive procedure previously published.

    “However, it is important to note that the proposed method is destructive compared to the non-destructive procedure previously published.”
    Quote in the paperNot a substantial claim
20 of 20
  • The paper relies on this without support.

    Open pores are completely filled with paraffin after soaking, while closed pores remain air-filled.

    “The measured refractive index combines contributions from lactose, air in pores, and paraffin in the case of soaked pellets.”
    “neff,soaked=pclosednair+popennparaffin+(1−pclosed−popen)nlactose”
  • The paper relies on this without support.

    The measured refractive index combines contributions from lactose, air in pores, and paraffin in soaked pellets.

    “The measured refractive index combines contributions from lactose, air in pores, and paraffin in the case of soaked pellets.”
  • The paper relies on this without support.

    The measured loss coefficient combines contributions from lactose absorption and scattering by pores, and absorption by paraffin in soaked pellets is negligible.

    “The measured loss coefficient combines contributions from lactose absorption and from scattering by pores, whereas absorption by paraffin in soaked pellets is negligible.”
  • The paper relies on this without support.

    Index-matching fluid has not previously been used to study porosity in pharmaceutical tablets.

    “To the best of our knowledge this is the first time that index-matching fluid has been used to study porosity in pharmaceutical tablets.”
4 of 4

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Sample porosity must be minimised because it affects the accuracy of the refractive index obtained from terahertz measurements.

    “Sample porosity must be minimised as it affects the accuracy of the RI obtained from terahertz measurements [1,9,10,14,20,21].”

    From Polymer Pellet Fabrication for Accurate THz-TDS Measurements (2022) · cites this paper as [14]

  • PTFE pellets have minimal open (surface connected) pores.

    “This investigation suggested minimal open (surface connected) pores (Figure A3) [14].”

    From Polymer Pellet Fabrication for Accurate THz-TDS Measurements (2022) · cites this paper as [14]

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Figure 4b is identified as both scattering loss and refractive-index difference

    Minor

    The text assigns the loss difference to Figure 4a and the refractive-index difference to Figure 4b, but says the scattering-loss power law was fitted to Figure 4b. The figure reference for that fit is inconsistent with the paper's own description of the panels.

1 of 1

The citation lists haven’t been fetched yet

References 29 · Cited by 30

Authors
Naftaly, M., Tikhomirov, I., Hou, P., & Markl, D.
Affiliations
  • National Physical Laboratory (GB)
  • Engineering and Physical Sciences Research Council (GB)
Corresponding author
Markl, Daniel
Venue
Sensors
Publisher
MDPI AG
Published
2020-05-31
Volume
20
Issue
11
Pages
3120
ISSN
1424-8220 (ISSN-L)
OpenAlex
W3029669078
Cited by
30
References
29
Citations by year
2026: 4 · 2025: 2 · 2024: 4 · 2023: 10 · 2022: 9 · 2021: 1
FWCI
1.72
Type
journal article
Language
en
Open access
Locations
  • Sensors (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • Strathprints: The University of Strathclyde institutional repository (University of Strathclyde) (acceptedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
H2020 Marie Skłodowska-Curie Actions (765426)
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Terahertz technology and applications
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Microwave and Dielectric Measurement Techniques
  • Physical Sciences › Engineering › Mechanics of Materials › Thermography and Photoacoustic Techniques
Keywords
effective porosity, porous media, terahertz time-domain spectroscopy, alkanes, powder compacts, compression pressure, refractive index, scattering loss, tablets

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