www.advancedsciencenews.com
www.pss-b.com
simulated, [15,16] sintered steel fi ber mats that exhibited an out-of- plane Poisson ’ s ratio of 1.7 0.4 throughout the 7% applied strain. These mats were 10 mm thick and consisted of continu- ous fi bers (12 μ m in diameter) that occupied about 20% of the mat ’ s total volume and randomly oriented lying mostly in the plane of the mat. [14 – 16] Baughman et al. produced paper made of carbon nanotubes, called buckypapers, using a process similar to traditional papermaking, and found them to be in-plane aux- etic. [17,18] The buckypapers contained single-walled carbon nano- tubes (SWNTs), multiwalled carbon nanotubes (MWNTs), or SWNT/MWNT mixtures. The buckypapers were only 50 μ m thick; their in-plane Poisson ’ s ratio varied as the composition of the buckypaper changed. It decreased from þ 0.06 to a mini- mum of 0.20 when the ratio of MWNTs ( 12 nm diameter, 200 μ m long) to SWNTs ( 1 nm diameter, less than 1 μ mlong) was increased from 0 to 100 wt% with the sign-change occurring at around 73 wt%. This result, however, was in contrast to the positive in-plane Poisson ’ s ratios regularly observed in traditional paper. [2,7,8] Berhan et al. modeled and explained out-of-plane aux- etic response in 3D fused fi ber networks through the use of fi nite element analysis, [19] highlighting the role of compression (or net- work porosity) and out-of-plane fi ber orientation angle. In their simulations, auxetic response was found to be larger for higher compression ratios and lower out-of-plane angles. [19] In a subse- quent study, [20] they found large out-of-plane auxetic responses in commercially obtained sintered steel fi ber mats; Poisson ’ s ratios of 18.6, 8.1, and 5.4 were obtained for mats of porosity 60, 70, and 80%, respectively. Composites of these mats produced using polydimethylsiloxane were all found to be auxetic; Poisson ’ s ratios of 9.0, 9.0, and 3.7, respectively, were obtained. [20] In a combined theoretical and experimental study, Rawal et al. identi fi ed critical needling parameters in nonwoven fabrics necessary to produce anisotropic fi ber networks having large out-of-plane auxetic response. [21] Electrospun PLLA fi ber networks as described by Domaschke et al. have been predicted and experimentally found to show auxetic behavior in which fi ber buckling is thought to produce signi fi cant auxetic response. [22] Negi and Picu have described an interesting connection between auxetic behavior and tensegrity in a modeling examination of non-crosslinked fi ber networks. [23] In each of these examples, the nature and magnitude of the observed Poisson ’ s ratio were found to be closely related to some, if not all, network character- istics such as density/porosity, fi ber connectivity, fi ber dimen- sions, fi ber bending, and mechanical properties of fi bers themselves — further inspiring us to assess the effect of such parameters on the auxetic response in paper. Recently, we examined a particular (albeit ubiquitous) subset of nonwovens, called needle-punched nonwovens, that normally are not auxetic as-produced, but can be made so through a heat- compression treatment. [9,24 – 29] Due to the needling operation employed during their manufacture, they possess bundles of through-thickness fi bers embedded in an entangled network of fi bers lying primarily in the plane of the fabric. [30] We found that heat and pressure caused these fi ber bundles to buckle, in addition to causing a considerable compression (and hence den- si fi cation) of the fabric, resulting in a subsequent out-of-plane auxetic response for them. [9,24 – 29] Interested readers are referred to our previous work for a series of fi gures that illustrate this mechanism for auxeticity. [25] Although the presence of
through-thickness fi ber bundles is unique to needle-punched nonwovens, we believe that the auxetic response stems also partly from the increased network density (synonymous to increased fi ber- fi ber contacts) and perhaps increased fi ber-bending and entanglements — which is partly a motivation for this study. Commodity nonwovens that are not needle-punched, like wool felt studied recently, have structural similarities to paper and were found to exhibit out-of-plane auxetic behavior in both as-received and treated states. [26,27] Additionally, in-plane Poisson ’ s ratio of a variety of nonwovens has, as expected, been reported to be positive (with the exception of Baughman ’ sbucky- papers) by several researchers. [31 – 35] In order to better understand the effect of network parameters on auxetic response in paper more closely, we decided to produce our own paper in laboratory (called handsheets). Our previous work investigated commercially produced papers, where the composition of the paper and processing were not within our control. Producing handsheets for this work allows us to produce papers containing only cellulose fi bers of our choosing, reduce the number of processing variables and material factors that could be in fl uencing the auxetic response, and ultimately exam- ine the relationships between network structure to the auxetic response. Additionally, there are certain process differences between industrial and laboratory papermaking, which render key structural differences between commercial papers and hand- sheets. Unlike most commercial papers, lab handsheets do not have a preferential fi ber alignment along machine direction because industrial papermaking utilizes a continuously moving fi ber web. [13,36 – 38] While processes such as re fi ning, pressing, drying, etc., for handsheet preparation are quite different from an industrial setting, they offer generous process control to sci- entists. [36,39] The process of re fi ning (referred to as “ beating ” when referring to handsheets), [39] for example, results in gener- ating small fi brils over the surface of fi bers that enhance their hydrogen bonding potential with other fi bers, and consequently affect paper ’ s deformation characteristics. [39,40] To provide a clear set of variables for study, we varied a number of relevant procedural and structural parameters while preparing handsheets. Bleached kraft pulps obtained from both hardwood (HW) and softwood (SW) were used, knowing that the lengths of hardwood fi bers ( 1 mm) are shorter than those of softwood fi bers ( 3mm). [40,41] Secondly, two-thirds of the handsheets of each type were made from re fi ned pulp where two different levels of re fi ning were used. Lastly, by using different amounts of fi bers, handsheets of different weights (and hence different densities) could be prepared. Handsheets were made without using fi llers, additives, or coatings, ruling out any interferences with the intrinsic deformation of the network.
2. Experimental Section 2.1. Preparation of Handsheets
Paper handsheets were produced at the Pulping and Papermaking laboratory in the Renewable Bioproducts Institute (RBI), Georgia Tech (Atlanta, USA). Bleached kraft soft- wood and kraft hardwood pulp were obtained from International
2400589 (2 of 10)
Phys. Status Solidi B 2025 , 2400589
© 2025 The Author(s). physica status solidi (b) basic solid state physics published by Wiley-VCH GmbH
Made with FlippingBook. PDF to flipbook with ease