Method Development for Contactless Resonant Cavity Dielectric Spectroscopic Studies of Cellulosic Paper

Summary

A protocol for the non-destructive analysis of the fiber content and relative age of paper.

Abstract

The current analytical techniques for characterizing printing and graphic arts substrates are largely ex situ and destructive. This limits the amount of data that can be obtained from an individual sample and renders it difficult to produce statistically relevant data for unique and rare materials. Resonant cavity dielectric spectroscopy is a non-destructive, contactless technique which can simultaneously interrogate both sides of a sheeted material and provide measurements which are suitable for statistical interpretations. This offers analysts the ability to quickly discriminate between sheeted materials based on composition and storage history. In this methodology article, we demonstrate how contactless resonant cavity dielectric spectroscopy may be used to differentiate between paper analytes of varying fiber species compositions, to determine the relative age of the paper, and to detect and quantify the amount of post-consumer waste (PCW) recycled fiber content in manufactured office paper.

Introduction

Paper is a sheeted, heterogenous, manufactured product comprised of cellulosic fibers, sizing agents, inorganic fillers, colorants, and water. The cellulose fibers may originate from a variety of plant sources; the raw material is then broken down through a combination of physical and/or chemical treatments to produce a workable pulp consisting primarily of cellulose fibers. The cellulose in the paper product may also be recovered secondary, or recycled fiber¹. The TAPPI Method T 401, "Fiber analysis of paper and paperboard," is currently the state of the art method for identifying fiber types and their ratios present within a paper sample and is utilized by many communities². It is a manual, colorimetric technique reliant on the visual acuity of a specially trained human analyst to discern the constituent fiber types of a paper sample. Furthermore, sample preparation for the TAPPI 401 method is laborious and time consuming, requiring physical destruction and chemical degradation of the paper sample. Staining with specially prescribed reagents renders fiber samples subject to the effects of oxidation, making it difficult to archive samples for preservation or specimen banking. Thus, the results from TAPPI Method T 401 are subject to human interpretation and are directly dependent upon the visual discernment of an individual analyst, which varies based upon that individual’s level of experience and training, leading to inherent errors when comparing results between and within sample sets. Multiple sources of imprecision and inaccuracy are present as well³. Additionally, the TAPPI method is incapable of determining the quantity of secondary fiber or the relative age of paper samples^4,5.

In contrast, the resonant cavity dielectric spectroscopy (RCDS) technique we describe in this article offers analytical capabilities that are well-suited for paper examinations. Dielectric spectroscopy probes the relaxation dynamics of dipoles and mobile charge carriers within a matrix in response to rapidly changing electromagnetic fields, such as microwaves. This involves molecular rotational reorientation, making RCDS particularly well-suited to examine the dynamics of molecules in confined spaces, such as the water adsorbed on the cellulose fibers imbedded within a sheet of paper. By using water as a probe molecule, RCDS simultaneously can extract information on the chemical environment and physical conformation of the cellulose polymer.

The chemical environment of the cellulose fibers influences the extent of hydrogen bonding with water molecules, hence the ease of motion in response to the fluctuating electromagnetic fields. The cellulosic environment is determined, in part, by the concentrations of hemicellulose and lignin in the paper analyte. Hemicellulose is a hydrophilic branched polymer of pentoses, while lignin is a hydrophobic, cross-linked, phenolic polymer. The amounts of hemicellulose and lignin in a paper fiber are a consequence of the paper-making process. Adsorbed water in paper partitions between the hydrophilic sites, and the hydrogen bonding within the cellulose polymer, especially with the adsorbed water molecules, influences the level of cross-linking within the cellulose structure, the level of polarizability, and the architecture of pores within the cellulose polymer⁵. The total dielectric response of a material is a vector sum of all the dipole moments within the system and can be distinguished via dielectric spectroscopy through the use of effective medium theories^6,7. Similarly, the capacitance of a dielectric material is inversely proportional to its thickness; hence, resonant cavity dielectric spectroscopy is ideal to study sample-to-sample thickness reproducibility of ultra-thin films materials such as paper^8,9,10. While there is a significant body of work pertaining to the use of dielectric spectroscopy techniques to study wood and cellulose products, the scope of those studies has been limited to paper manufacturability issues^11,12,13. We have taken advantage of the anisotropic nature of paper to demonstrate the application of RCDS to testing paper beyond moisture and mechanical properties^14,15,16 and to show that it yields numerical data that can be used in quality assurance techniques such as gauge capability studies and real-time statistical process control (SPC). The method also has inherent forensic capabilities and can be used to quantitatively confront environmental sustainability concerns, support economic interests, and detect altered and counterfeit documents.

Resonant cavity dielectric spectroscopy (RCDS) theory and technique
RCDS is one of several dielectric spectroscopy techniques available¹⁷; it was chosen specifically because it is non-contact, non-destructive, and experimentally simple in comparison to other methods of dielectric spectroscopy. In contrast to other analytical techniques used to study the properties of paper, RCDS eliminates the need for duplicate sets of measurements to account for the two sides of a sample sheet¹⁸. The resonant microwave cavity technique has the advantage of being sensitive to both the surface and bulk conductivity. For example, the surface conductance of a sample material is determined by tracking a change in the quality factor (Q-Factor) of the cavity as a specimen is progressively inserted into the cavity in quantitative correlation with the specimen’s volume^18,19,20. Conductivity can be obtained by simply dividing surface conductance by the specimen thickness. The surface conductance of a thin, sheeted material like paper functions as a proxy for the dielectric profile of a material under test (MUT), as it is directly proportional to the dielectric loss, ε", of the MUT^18,19,20. Dielectric loss is an indication of how much heat is dissipated by a dielectric material when an electric field is applied across it; materials with greater conductance will have a higher dielectric loss value than less conductive materials.

Experimentally, the dielectric loss, ε", associated with the specimen's surface is extracted from the rate of decrease of cavity resonance quality factor (Q) (i.e., energy loss), with increasing volume of specimen¹⁹. The Q is determined at the resonant frequency f from the 3 dB width, Δf, of the resonant peak at the resonant frequency f, Q = Δf /f. This relation is quantitatively correlated with the slope of the line given by Equation 1 below, where  represents the difference of the reciprocal of the Q-factor of the specimen from the Q-factor of the empty cavity, is the ratio of the volume of the inserted specimen to the volume of the empty cavity, and the line intercept, b", accounts for the non-uniform field in the specimen, as shown in Figure 1¹⁹.

    (Equation 1)

In this article, we illustrate the broad utility of this technique by determining the ratios of fiber species (speciation), determining the relative age of naturally and artificially aged papers, and quantifying the recycled fiber content of white office copier paper analytes. Whereas the RCDS technique may be suitable for studying other topics, such as aging issues in paper insulation in electric power apparatus, such studies are outside the scope of the current work but would be interesting to pursue in the future.

Protocol

1. Setup of materials

1. Record all manufacturing information provided with the ream of paper (e.g., basis weight, manufacturer's advertised PCW content, and manufacturer’s advertised brightness).
2. Take an average of ten thickness measurements along a sheet from the ream, using a caliper.
3. Identify the machine and cross directions of the sheet (i.e., the machine direction is the long dimension).
4. Using a protractor identify and cut the paper along the desired strip angle between the machine and cross directions.
5. Using a rotary cutter, slice test strips 0.5 cm wide by 8 cm long in the target orientation for the sample.
6. Label samples from one end and store between glass microscopy slides. Store until testing under nitrogen atmosphere.
   NOTE: It is advisable to wear gloves and perform handling with tweezers to avoid creasing and / or contaminating the paper samples.

2. Accelerated paper fade testing

NOTE: Paper samples are aged under UV-light at elevated temperature at laboratory ambient humidity. The aging is performed using an accelerated weathering chamber equipped with 340 nm UVA bulbs, at an irradiance of 0.72 W/m² at 50 °C for 169 h, by following the following protocol.

1. Calibrate the UV-sensors, by running the calibration radiometer routine pre-preprogrammed in the UV-based accelerated weathering chamber.
2. Calibrate the temperature sensors by running the P4 calibrate panel temperature program pre-preprogrammed in the weathering chamber.
3. Measure the pre-post-aging color of the paper samples using a portable spectrophotometer operating in the visible wave range from 400 nm to 800 nm.
4. Select appropriate standard test cycles pre-preprogrammed in the weathering chamber.
5. Mount whole sheets of test papers on the flat panel (optionally, mount one sheet of either side of the flat panel).
6. Fasten the flat panels to the sample holders with snap rings, pushing the rings snugly against the panel.
7. Install the panel holders with the stop pin down.
8. Attach aluminum blanks to mount in the panel holders for condensation.
9. For uniform exposure, reposition the test samples (at least five times) during the test cycle.
10. Measure the post-aging color of the paper samples using a portable spectrophotometer.
11. Cut sample strips out of the aged paper samples to fit the resonant cavity. The typical specimen area is 0.5 cm (width) x 8 cm (length).
    NOTE: For these tests, we use commercially produced colored 90 g/m² (gsm) (24 lb) office paper of two different compositions: virgin and 30% recycled fibers (i.e., 0% and 30% post-consumer waste [PCW] recycled fiber content, respectively).

3. Setup of equipment and taking resonant cavity measurements

NOTE: The resonant cavity testing fixture consists of an air-filled standard WR-90 rectangular waveguide. The cavity has a 10 mm x 1 mm slot machined in the center for specimen insertion. The waveguide is terminated on both ends by the WR-90 to coax adapters that connect the cavity with a microwave network analyzer via semi-rigid coaxial cables. The coupling adapters are nearly cross polarized with respect to the waveguide polarization angle, which creates sharp impedance discontinuities at both waveguide ends and consequently the cavity walls. The polarization angle is about 87°, which is sufficient to achieve optimal power loading into cavity while maximizing the quality factor. The quality factor, Q₀, and the resonant frequency, f₀, of the empty cavity at the third odd resonant mode TE₁₀₃ at which we make the measurements are 3.200 and 7.435 GHz respectively. The measurements are performed in ambient laboratory conditions by following the protocol listed below.

1. Record the temperature and relative humidity and take the initial reading of the quality factor Q₀, and the resonant frequency f₀ of the empty cavity.
2. Position the specimen secured in the sample holder above the slot at the center of the cavity. During the measurements, the specimen is inserted into cavity through this slot in steps of increasing volume V_x= h_x·w·t, where h_x is the specimen length inserted into cavity, and w and t are the specimen width and thickness respectively.
3. Using the Vernier caliper on the sample mount, insert the sample into the cavity by Δh_x = 50 µm increments and take readings of the quality factor and resonant frequency at each step until the sample has been lowered 10 mm (1 cm) into the cavity.
4. Retract the sample from the interior at the same increments of 50 µm and take readings of the quality factor and resonant frequency until the sample has been fully retracted.
5. Store the sample between glass slides and return them to nitrogen atmosphere.
6. The dielectric loss, ε", of the paper samples is obtained from the slop of the perturbation (Equation 1). Optionally, the dielectric constant, ε' can be obtained from the measured V_x, and the resonant frequency f_x by solving the perturbation equations for (ε' – 1) as described in elsewhere^18,19,20.

Results

Rationale for choosing the 60° strip angle
The cut orientation of the test sample influences the magnitude of the dielectric response, as shown in the graph in Figure 2. In initial experiments, test strips were cut from the orthogonal angles of the sheet, as is standard practice for measuring physical properties in paper science; however, strips cut from non-orthogonal angles along the paper sheet have provided the greatest resolution between paper types, particularly at...

Discussion

We have shown elsewhere that the presence of lignin content of fibers does significantly alter the dielectric behavior of manufactured papers¹⁵. Speciation is not only important in the QA/QC testing of modern papers but of great interest in the study of historical papers which were predominantly manufactured from non-wood plant sources, such as bamboo, hemp, flax, and papyrus. As shown in Figure 7, our technique can distinguish between non-wood plant sources (100% cot...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
commercially produced colored office paper	Neenah Paper		Purchased from Staples
Q-Lab QUV accelerated weathering chamber	Q-Lab Corporation, Westlake, OH
X-Rite eXact	X-Rite, Inc., Grand Rapids, MI
Agilent N5225A network analyzer	Agilent Technologies, Santa Rosa, CA
WR90 rectangular waveguide	Agilent Technologies, Santa Rosa, CA		R 100 (a = 10.16 mm, b = 22.86 mm, lz =127.0mm)
JMP data analysis software	SAS, Cary, NC