Filtration Efficiencies of Nanoscale Aerosol by Cloth Mask Materials Used to Slow the Spread of SARS-CoV-2.

Filtration efficiency (FE), differential pressure (ΔP), quality factor (QF), and construction parameters were measured for 32 cloth materials (14 cotton, 1 wool, 9 synthetic, 4 synthetic blends, and 4 synthetic/cotton blends) used in cloth masks intended for protection from the SARS-CoV-2 virus (diameter 100 ± 10 nm). Seven polypropylene-based fiber filter materials were also measured including surgical masks and N95 respirators. Additional measurements were performed on both multilayered and mixed-material samples of natural, synthetic, or natural-synthetic blends to mimic cloth mask construction methods. Materials were microimaged and tested against size selected NaCl aerosol with particle mobility diameters between 50 and 825 nm. Three of the top five best performing samples were woven 100% cotton with high to moderate yarn counts, and the other two were woven synthetics of moderate yarn counts. In contrast to recently published studies, samples utilizing mixed materials did not exhibit a significant difference in the measured FE when compared to the product of the individual FE for the components. The FE and ΔP increased monotonically with the number of cloth layers for a lightweight flannel, suggesting that multilayered cloth masks may offer increased protection from nanometer-sized aerosol with a maximum FE dictated by breathability (i.e., ΔP).

It has been recognized that the global spread of the Severe Acute Respiratory Syndrome Coronavirus 2 (pan class="Species">SARS-CoV-2) has limited the supply of medical masks and particulate filtering facepiece respirators (e.g., N95), so it has been recommended that their use be restricted to healthcare settings.[1] As of this writing, the World Health Organization (WHO) and the United States Centers for Disease Control and Prevention (US CDC) suggest that cloth masks be used in nonmedical settings to reduce the transmission of n>n class="Species">SARS-CoV-2.[2,3] The majority of states in the United States and more than 130 nations, corresponding to over 75% of the global population, have issued official guidelines requiring or recommending the wearing of masks in public locations to mitigate the spread of COVID-19, the disease caused by SARS-CoV-2. Thus, nonmedical use of facial coverings will likely consist of masks made from a variety of fibrous cloth materials utilizing a range of designs and construction techniques. The WHO has stated the need for rapid dissemination of research investigating the performance of relevant mask parameters, for example, material, design, and construction, for reducing exposure to micrometer-sized droplets and nanometer-sized aerosol particles at size ranges relevant to the virus (90 nm diameter core with ≈20 nm spike proteins).[1,3,4] Particle measurements from hosptials in Wuhan, China demonstrated that viable COVID-19 virus likely exists in particles with diameters between 250 nm and 500 nm.[5]

Facemasks can provide two modes of protection:[6] (1) by protecting the localized population from an pan class="Disease">infected mask wearer by trapping expelled virus-laden atomized material (droplets or aerosol) and (2) by protecting the mask wearer from ambient virus-laden atomized material by filtering inhaled air.[7] This reduces the risk of both direct and indirect viral exposure, respectively, thereby decreasing the probability of n>n class="Disease">infection.[6]

Prior research into cloth masks follows the history of pan class="Disease">infectious diseases spread by droplets or aerosol and dates back to the 1918–1919 n>n class="Species">influenza pandemic.[8,9] After that time, the publication record on the utility of cloth masks is sparse, and most research has focused on the effectiveness of single use masks available in many developed countries for healthcare or other occupational settings.[10−16] The prior research shows that cloth materials offer limited protection from particles in the size regime of SARS-COV2.[10−12]

When particles interact with a filter fiber, it is generally accepted that they are “collected” by a fiber and retained through van Der Waals forces.[17] For small particles, Brownian motion increases the probability a particle will interact with a filter fiber. At larger sizes, particles can be intercepted by a fiber when they are within one particle radius. When particle inertia becomes sufficiently high, the particle may no longer follow a flowing gas streamline resulting in a higher probability of inertially impacting a fiber. Electrostatic deposition, occurring due to a charge difference between a fiber and a particle, can also be important in some materials. Collectively, the sum of these efficiencies, diffusion (E), interception (E), impaction (E), and electrostatic deposition (E), yield the single fiber efficiency (E = E + E + E + E). The reader is directed to the span class="Gene">eminal works by Brown,[18] n>n class="Gene">Emi,[19] Fuchs,[20,21] and Liu[22] for detailed descriptions of filtration theory.

The filtration efficiency (FE) is a common metric for reporting particle capture efficiency of material and is related to E through[18−23]where α, L, and D are the material porosity (i.e., packing density), filter thickness, and fiber or yarn diameter, respectively. The FE can be quantified by measuring the upstream and downstream (N and N, respectively) number density of particles per volume of air (particles cm–3) where particles N passed through the filter and particles N were incident on the filter (see Figure S1 of the Supporting Information), and the difference between N and N represents the particles captured by the filter. FE is reported as a percentage (by multiplying eq by 100) and is a function of the particle diameter (D), the flow rate through the filter, and the filter medium.[10−16,24,25]

The variability of test methods (mask materials vs fitted mask on pan class="Species">human-scale forms vs standard mask testbed measurements) and the broad range of materials tested make direct quantitative compan>rability between published studies highly challenging.[10−16] In studies before 2020, the published FE of cotton-based fabrics was 5% to 60% when tested against an n>n class="Chemical">NaCl aerosol with 20 nm ≤ D ≤ 1000 nm, 10% for spherical 100 nm latex particles, and <10% for 100 nm diesel soot.[10−12] Generally, the published FE of cloth filter media is much lower when compared to facepiece respirators that are regulated for use in healthcare and other professional settings; for example, the FFP2 (EU standard, EN 149–2001) or the N95 (USA, NIOSH-42C FR84), which are rigorously tested to ensure FE ≥ 94% and FE ≥ 95%, respectively, for 300 nm D NaCl.[26,27] Notably, a recently published study suggests that masks from cloth filter media can be constructed that may afford better protection for the wearer than an N95 respirator for particles between 10 nm and 200 nm in size due to an enhancement in E by specific types of cloth arranged in a multilayered configuration.[15]

The study reported here aims to pan class="Gene">aid in the call for research testing the performance of cloth-based media that are relevant for mask use.[3] The FE and differential pressure (ΔP, Pa), which is related to breathability, were measured for 32 relevant cloth materials (14 cotton, 1 wool, 9 synthetic, 4 synthetic blends, and 4 synthetic/cotton blends) that may be used in facemasks. The FE and ΔP were measured under controlled laboratory conditions utilizing size selected n>n class="Chemical">NaCl aerosol with particle mobility diameters (D) between 50 and 825 nm, a size regime relevant for the removal of SARS-CoV-2 particles,[6,28] and in accordance to standard established filter testing protocols, Parts 3 and 5 of EN 1822 and ISO 29463, using size selected charged and neutralized aerosol, respectively. For comparison, the FE and ΔP of 7 polypropylene containing materials (2 surgical facemasks, an N95 filter, N95 fabric, a high- and low-density medical wrap, and a purported HEPA vacuum bag), 2 papers (coffee filter and paper towels), and 4-layered samples of different materials were also measured. The samples in this study were systematically chosen and characterized by their composition, yarn count, weave type (which has been relatively understudied),[29] and mass with the goal of establishing a relationship between these parameters and measured FE and ΔP when tested against nanometer-sized aerosol under well controlled laboratory conditions using established filter testing protocols.

Results and Discussion

Both nanometer-sized aerosol particles and micrometer-sized droplets can be captured by a filter.[17] The FE is a function of D, D, fiber packing density, and flow rate.[25] Freshly generated particles may be highly charged but immediately start to neutralize after pan class="Gene">emission.[30] Ambient aerosols are expected to have a net neutral average charge that follows a Boltzmann distribution after <100 min aloft[25] (note, lifetimes of nanopan>rticles span>n hours to days over this size range).[31] Differences in the charge state or distribution of charges of the aerosol may impan>ct the measured FE with E typically enhancing FE.[32]

The distribution of particle sizes filtered by a material can be broadened by using random arrays or layered structures containing a distribution of fiber diameters.[23,33] This has allowed for the development of filtration media with excellent FE across a broad range of D at reasonable ΔP (e.g., the N95 mask and HEPA filters, see Figure B1,2) and may also give insight into the design and use of cloth materials for facemasks for the capture of virus-laden aerosols. Therefore, an understanding of the filter structure (including weave structure, yarn count, and yarn mass) and material composition (natural, synthetic, or blended materials) may be important for the FE of cloth materials and may provide a deeper understanding in the complex parameter space that influences the FE of cloth mask materials.

Figure 1

Transmitted light imagery of nonwoven and woven face mask materials. (A1–3) Outer, intermediate, and inner layers of a N95 mask showing randomly oriented spun-bond (A1) and melt-blown (A2 and A3) synthetic fibers.[34] (B1,2) Outer and inner surfaces of poplin weave cotton fibers in lightweight flannel (sample Cotton 10). Note: Transmitted light grayscale intensities have been inverted so fibers appear lighter relative to voids; all scale bars represent 1 mm with subsections of 200 μm in length.

There have been several suggestions that FE may be related to textile parameters. Recently, Konda et al. (2020)[15] indicated an increase in FE as a function of higher yarn count (described as pan class="Gene">TPI in the cited article and summarized in their Figure , and which herein will be discussed as yarns inch–2 unless otherwise noted; 2.54 cm = 1 in). Other studies have suggested that the cover factor, defined as the sum of the number of yarns per unit length to the square root of the yarn count for the warp and weft directions (see Supporting Information for definitions), is also related to a fabric’s filtration level (but not FE directly).[35] The cover factor indicates the extent to which the area of a fabric is covered by one set of yarns, and a fabric with a high cover factor would have a low density of open span>ce relative to fabric material for a given area. Cover factor is differentiated from packing density, as cover factor assumes the yarns are solid and nonporous, thus underestimating a materials porosity. Other parameters that may play a role are yarn mass, fabric texture, and fabric composition. Past studies at the National Bureau of Standards (n>n class="Disease">NBS, currently the National Institute of Standards and Technology, NIST) indicated relationships between yarn count, fabric mass, and weave type with permeability to air, which is related to the ΔP and the level of breathability through the material.[29]

Figure 3

Filtration efficiency (FE) as a function of number of fabric layers for a cotton fiber poplin weave in a lightweight flannel (Cotton 10). (A) Particle number densities per volume of air for the upstream (N, black) and downstream (N) particle counters as a function of number of layers (colored lines). Shown N was measured for a one-layer sample but was representative of the N measured for all samples. (B) Calculated FE as a function of D and number of layers (colored lines). (C) Measured differential pressure (ΔP, Pa) across the material as a function of number of fabric layers. Gray line and plot maximum correspond to NIOSH recommended maximum differential pressure across filter mask for exhaling (245.2 Pa, 25 mm H2O) and inhaling (343.25 Pa, 35 mm H2O), respectively.[27,45] (D) Minimum measured FE as a function of number of layers. (E) Quality factor (QF) as a function of number of fabric layers. Horizontal line shows QF = 3 (WHO recommendation).[3] (F) Maximum penetrating particle size (MPPS, nm) as a function of number of fabric layers. Lines in B correspond to bi-Gaussian fits of the data, while lines in C and D are shown to guide the eye.

Electrostatics, as discussed by Konda et al. (2020)[15] and Zhao et al. (2020),[36] may be another important parameter and are addressed in this investigation by studying the impact of particle and cloth charge (see further). A theoretical model of fabric electrostatics was proposed by Alekseeva et al. (2007)[37] and suggested that fabrics can behave like a capacitor, collecting electric charge in the gaps (pores) in fibers of the fabric. The specific properties are potentially dependent on fiber composition, weave type and pan class="Disease">tightness (related to cover factor), production and processing methods, and can be influenced by atmospheric conditions (humidity, pressure, and temperature).[38] The electrostatics of cloth materials are more commonly (although not always) discussed for synthetic as opposed to natural fibers.[39]

The FE values of 41 samples, 32 cloth materials (14 cotton, 1 wool, 9 synthetic, 4 synthetic blends, 4 synthetic/cotton blends), 2 paper materials, and 7 pan class="Chemical">polypropylene-based fiber filter materials, were measured at 15 equally log-span>ced mobility diameters (D) resulting in D span>nning 50 nm ≤ D ≤ 825 nm. Particles were charge neutralized (as recommended by Parts 3 and 5 of the EN 1822 mask filtration protocol) using a soft X-ray source and size selected by a differential mobility analyzer.[27] For compan>rison, seven of the samples were reneutralized after size selection in accordance with the ISO 29643 filter testing standard. Particle number densities upstream (N) and downstream (N) of the sample were recorded by condensation particle counters (n>n class="Chemical">CPC) for 30 s at 1 Hz at each D. These data were averaged, and 1σ standard deviations were calculated at each D bin. Measured 1σ standard deviations in N were ≈2.5% with a CPC accuracy of ≈3% for N < 2 × 104 cm–3 (independently calibrated by optical methods),[40] and ≈2% day-to-day variability in FE for the same sample and ∼1% sample-to-sample variability in FE, resulting in an assumed 5% combined uncertainty for FE; see Figures S13 and S28 for day-to-day and sample-to-sample variabilities, respectively. The N was scaled based upon the CPC counting mode (single particle versus photometric; see Figure S2 and corresponding discussion in the Supporting Information), and the FE was calculated from eq .

Representative FE values as a function of D are shown in Figure for four of the tested samples (an N95 respirator, the base fabric that is used to make an N95 respirator, a surgical mask, and a 65%/35% cotton/polyester twill polyester/cotton blend 3, twill weave, 229 yarns inch–2). Importantly, the measured data capture the FE under conditions where leaks are absent. The aerosol after size selection had moderate net charge (q, where +1 ≤ q ≤ ∼ + 4 due to charge neutralization prior to the measurement).[41] The impact of particle charge on FE was tested by also measuring the FE of 7 samples that were reneutralized after size selection (dashed light lines and squares in Figure and blue traces in Figures n class="Gene">S21, S36, S39, S49, S50, S51, and S52). The measured data indicate that particle charge does not impact FE of the measured cloth materials. In addition, the FE of polyester/cotton blend 3 was quantified by passing the size selected aerosol through an aerosol particle mass analyzer (APM) and subsequently reneutralizing (olive triangles in Figures and S39). The tandem DMA-APM effectively removes the presence of particles with q > + 1 that may exit the DMA.[42,43] With the exception of the surgical mask that uses polypropylene layers for filtration, aerosol reneutralization (and mass selection) did not affect FE (all values were within 1σ uncertainty), see Figure , suggesting that E is not significant for these cloth materials under current conditions and is in agreement with previous observations.[10]

Figure 2

Measured filtration efficiency (FE) as a function of particle mobility diameter (D) for an N95 respirator (black), the N95 base fabric (orange), a surgical mask (pink), and a twill (blue). The solid bold lines and circles represent the base sample, while the dashed light lines and squares correspond to the reneutralized samples. Olive triangles correspond to the twill FE measured with an aerosol particle mass analyzer and reneutralization. Uncertainties in FE are ±5%. See discussion in text. Corresponding distributions of N and N can be found in Section S3 of the Supporting Information.

Measured filtration efficiency (FE) as a function of particle mobility diameter (D) for an N95 respirator (black), the N95 base fabric (orange), a surgical mask (pink), and a twill (blue). The solid bold lines and circles represent the base sample, while the dashed light lines and squares correspond to the reneutralized samples. pan class="Species">Olive triangles correspond to the twill FE measured with an aerosol particle mass analyzer and reneutralization. Uncertainties in FE are ±5%. See discussion in text. Corresponding distributions of N and N can be found in Section S3 of the Supporting Information.

The FE values presented here are likely higher than typically measured on a mask testing device as required for regulatory compliance (e.g., US 42 CFR 84 or EN143) and should be interpreted as the maxipan class="Gene">mum expected FE of the material for mechanical processes (E, E, and E). Unless otherwise noted, the reported values are shown for aerosols that were not reneutralized after size selection (see additional sample FE curves of reneutralized aerosol in Section S3 of the Supporting Information).

Previous studies have reported values of FE and the most penetrating particle size (MPPS, i.e., D at FE) for mask comparability.[10−16] In this study, FE and MPPS were determined by converting FE to penetration efficiency (PE = 100% – FE) and fit to a logarithmic bi-Gaussian distribution (see eq ).[44] A bi-Gaussian distribution was chosen as it describes the shape of the data over the measured range and is loosely related to the functional form of FE vs D (see eq ). The interpolated bi-Gaussian pan class="Disease">fits are shown for all measured samples in Section S3 of the Supporting Information with representative data in Figure .

An N95 mask is constructed of a multilayered assemblage of polymer fibers with a distribution of D to efficiently bind particles of all D resulting in FE values that are nearly invariant with D with an average FE of (99.9 ± 0.1)% (1σ standard deviation across the 15 measured D; see Figures and S50). Except for the sample cut from a N95 mask, the FE of each tested material had a consistent and typical U-shaped curve (increased inertial impaction and interception with larger Dvs increased diffusion at smaller D),[25] see Figure , that was exclusive for each material tested (see Section S3 of the Supporting Information for all N and FE vs D plots). Some materials, for example, sueded polyester (Polyester 3, poplin weave, 152 yarns inch–2), had a high FE (75%) at D < 200 nm and low FE (<25%) at D > 500 nm. In comparison, a heavy chiffon (Polyester 4, plain weave, 152 yarns inch–2), exhibited a FE that was only weakly dependent on D, but averaged ∼30% across the entire D range. A third poplin weave, light chiffon polyester (Polyester 6) of the same yarn count and base-fiber of the previous two fabrics mentioned had an FE < 25% across the range of D sizes measured. All three have different areal masses (85 mg inch–2, 107 mg inch–2, and 38 mg inch–2, respectively). These data suggest that FE has a complex interplay between fiber type, sample mass, and construction methods (weave or bond structures). A detailed correlation analysis of these parameters for several of the woven samples is discussed further.

Initial investigations of the efficacy of cloth masks during the 1918 pan class="Species">influenza pandemic showed that increasing the number of cloth layers in a facemask (1 layer to 8 layers) was important in the reduction of microbial growth on plates placed downstream of fabrics and exposed to aqueous aerosol droplets containing bacteria.[8,9] Another study showed an analogous benefit by increasing the number of mask layers up to 4 layers of cotton gauze.[9] A similar trend was observed in this study for a lightweight flannel (Cotton 10) using 1 to 5 layers of cloth (see Figure ). Figure A and B show N (particle concentration, particles cm–3) and FE as a function of the number of layers, respectively. The ΔP (see Section S1, Figure S1) across the fabric and FE increase monotonically with the number of layers present (see Figure C,D). More than 4 layers of this sample exceeded the NIOSH recommended ΔP during exhalation through a fitted mask (245.2 Pa, 25 mm H2O).[46] The quality factor (QF) was also calculated as a function of the number of layers, see Figure E. The QF is a commonly used factor to evaluate filter performance under common experimental conditions:[23]QF increases as FE increases or ΔP decreases. QFs reported in the literature utilize both ln and log10.[23,36,47] The ln form was used in this study in accordance with the WHO recommendation.[3] The QF was nearly invariant with the number of fabric layers, consistent with multiplicative FE and additive changes in ΔP with the number of fabric layers. Lastly, the maximum penetrating particle size (MPPS), defined as the D of FE, shown in Figure F, is 300 nm for a single layer and slightly increases with the number of fabric layers to 350 nm for 4 layers of fabric.

Filtration efficiency (FE) as a function of number of fabric layers for a cotton fiber poplin weave in a lightweight flannel (Cotton 10). (A) Particle number densities per volume of air for the upstream (N, black) and downstream (N) particle counters as a function of number of layers (colored lines). Shown N was measured for a one-layer sample but was representative of the N measured for all samples. (B) Calculated FE as a function of D and number of layers (colored lines). (C) Measured differential pressure (ΔP, Pa) across the material as a function of number of fabric layers. Gray line and plot maxin class="Gene">mum correspond to NIOSH recommended maximum differential pressure across filter mask for exhaling (245.2 Pa, 25 mm H2O) and inhaling (343.25 Pa, 35 mm H2O), respectively.[27,45] (D) Minimum measured FE as a function of number of layers. (E) Quality factor (QF) as a function of number of fabric layers. Horizontal line shows QF = 3 (WHO recommendation).[3] (F) Maximum penetrating particle size (MPPS, nm) as a function of number of fabric layers. Lines in B correspond to bi-Gaussian fits of the data, while lines in C and D are shown to guide the eye.

The ΔP and FE curves were measured for 38 cloth materials spanning 50 nm ≤ D ≤ 825 nm. The FE and MPPS were calculated by fitting the distribution to a bi-Gaussian from which QF was determined (see Figure for FE and QF and Figure S3 for MPPS; average MPPS across all samples was (252 ± 45) nm). The samples, listed above and in Tables S1 and S2 in Section S2 of the Supporting Information, were classified by fiber content as natural, synthetic, synthetic blend, synthetic/cotton blend, paper, and n class="Chemical">polypropylene-based. The ΔP and FE of the cloth and paper samples were measured utilizing two layers of the respective materials and as envisioned when constructing a multilayer mask. Synthetic blend 3 (waffle weave, towel) and medical-grade materials (high-density and low-density wraps, HD and LD, respectively) were measured as a single layer due to sample thickness (Synthetic blend 3) or per the manufacturer’s use instructions (wraps). The N95, N95 fabric, and HEPA vacuum bag were constructed of multiple, separable thin layers of synthetic fibers and used as received. As of this writing, the medical-grade wraps are regulated for specific use in healthcare settings and are not currently approved for use in masks in the United States.[48] However, they have been utilized in emergency situations by frontline healthcare workers in the United States and are included only to aid in comparability to cloth and other tested materials. Additionally, while the HEPA vacuum bag tested here contains polypropylene, some HEPA filters may be made from inorganic glasses.

Figure 4

Measured samples categorized by type from left to right: cotton (orange), synthetic (pink), synthetic blend (blue), synthetic/cotton blend (olive), paper (green), and polypropylene-based (light orange). (A) Yarn mass (mg yarn–1), (B) differential pressure across sample (ΔP, Pa), (C) minimum filtration efficiency (FE, %), (D) quality factor, QF (kPa–1). The average most penetrating particle size (D) across all samples was 252 ± 45 nm with individual values plotted in Figure S5. Uncertainties in B and C are ±4.9 Pa (2× manometer read uncertainty) and ±5% (expanded uncertainty), while uncertainties in D were propagated from B and C. Abbreviations: Polyester (poly) and Cotton (Cott).

Measured samples categorized by type from left to right: cotton (orange), synthetic (pink), synthetic blend (blue), synthetic/cotton blend (pan class="Species">olive), paper (green), and n>n class="Chemical">polypropylene-based (light orange). (A) Yarn mass (mg yarn–1), (B) differential pressure across sample (ΔP, Pa), (C) minimum filtration efficiency (FE, %), (D) quality factor, QF (kPa–1). The average most penetrating particle size (D) across all samples was 252 ± 45 nm with individual values plotted in Figure S5. Uncertainties in B and C are ±4.9 Pa (2× manometer read uncertainty) and ±5% (expanded uncertainty), while uncertainties in D were propagated from B and C. Abbreviations: Polyester (poly) and Cotton (Cott).

The areal mass yarn–1 (see Figure A), a normalized mass value and not an absolute value for each yarn set, spanned almost an order of magnitude across the range of cotton and synthetic samples. The measured ΔP (shown in Figure B) also spanned a broad range and was nearly zero for open weaves, for example, Cotton 11 (muslin cotton) and Rayon, and near 334 Pa (34 mm pan class="Chemical">H2O) for the most tightly woven samples (e.g., Cotton 4, down proof ticking), which also was one of the highest yarn count samples measured. The FE of the measured samples ranged from ≈100% for a cut-out section from an N95 mask to 0% (within measurement uncertainty) for Polyester 6 (light chiffon) and Cotton 11 (muslin). Porosity, which was reported for the fabrics measured by Konda et al. (2020),[15] was not calculated for these samples as the length scale of smaller fabric pores (>150 nm) was below the resolution of the imaging instrument (≈ 20 μm, see Figure S4, Figures S54, and S55).

Of the fabrics tested, the top three fabrics with the highest FE were 100% cotton: Cotton 4 (down proof ticking), Cotton 8 (woven hand towel), and Cotton 10 (lightweight flannel). The FE of pan class="Species">Cottons 4 and 8 did not exhibit a statistically significant difference (p > 0.05), assuming 5% uncertainty. Cotton 4 (229 yarns inch–2) exceeded the NIOSH exhalation ΔP limit (245 Pa, 25 mm n>n class="Chemical">H2O).[46] Notably, it approached the maximum 343 Pa (35 mm H2O) inhalation ΔP limit recommended for mask use by NIOSH.[27] For comparability of cloth to other tested materials, the measured FE of 2 layers of a high performing cloth (Cotton 8, FE = 32%) was lower than those measured for the low- (FE = 70%) and high-density (FE = 86%) medical-grade wraps, the N95 mask (FE > 99.9%), and the HEPA vacuum bag (FE = 94%). Cotton 8 also had a similar FE to the two tested surgical masks (30.5%) and coffee filter (34.4%). The other top cotton fabrics were of average (≈ 150 yarns inch–2) to low (≤100 yarns inch–2) yarn counts, with the lowest being Cotton 8 (≈ 100 yarns inch–2). These materials had 24% ≤ FE ≤ 32%, and 57 Pa (5.8 mm H2O) ≤ ΔP ≤ 106 Pa (10.8 mm H2O).

The other two fabrics in the top five were Synthetic blend 2 (twill weave, synthetic, ≈ 200 yarns inch–2) and Polyester 5 (100% polyester, poplin weave, ≈ 230 yarns inch–2). The FE performances of these two fabrics do not exhibit a statistically significant difference (see Table S2 in Section S1 in the Supporting Information) assuming an uncertainty of 5%. The synthetic blend had a moderately high yarn count and the second highest ΔP (300 Pa, 30.6 mm pan class="Chemical">H2O) of the all samples. While it met the NIOSH inhalation ΔP limit,[45] it exceeded the exhalation limit.[46] Polyester 5 had a higher yarn count, and the ΔP (104 Pa, 10.6 mm pan class="Chemical">H2O) was well below NIOSH limits. No trends were observed between the type of fabric weave and the measured FE. The top five fabrics had weaves ranging from plain (Cotton 4), to block (Cotton 8), to poplin (Cotton 10, Polyester 5) and twill (Synthetic blend 2). Descriptions of weaves can be found in Table S38.

Visual inspection of all top performing, highest FE, cotton samples showed some amount of fiber raised from the weave structure. For Cotton 9, which fell within the top half of FE performance, and Cotton 10, the raised fibers were nap formed during manufacturing. Nap is an intentional textural feature made from directionally oriented raised fibers that protrude from the 2-dimensional plane of the fabric. Directionality can be lost without intervention (i.e., brushing) as the result of use, and the fibers can form aperiodic patterns similar to those seen in fiber-web fabrics (e.g., Figure ). Imaging of the two flannels showed they were more heavily napped on their outer side as opposed to their inner side and were the most heavily napped/raised fiber textured of almost all the materials measured (see Figures pan class="Gene">S15 and pan class="Gene">S17 in Section S3 of the Supporting Information for imaging of each measured sample and Figure B1,2). These two flannel, Cotton 10 and Cotton 9, had similar yarn counts (≈ 150 yarns inch–2) and yarn widths: Cotton 10 (weft) 0.26 mm ± 0.04 mm, (warp) 0.18 mm ± 0.03 mm; Cotton 9 (warp) 0.19 mm ± 0.02 mm, (weft) 0.30 mm ± 0.03 mm). The other top performing cotton fabrics exhibited a similar, raised fiber texture, although not to the same extent. This raised fiber texture was not observed for Polyester 5 or Synthetic blend 2. Additional textural features were observed as raised fibers for Cotton 8 (woven hand towel) and are likely related to fabric construction.

The fabric with the lowest FE was Polyester 6 (lightweight chiffon), followed by, in ascending FE, Cotton 11 (muslin), Polyester 1 (knit), Rayon, and (Polyester/cotton blend 1, 65% polyester/35% cotton). Four out of the five fabrics with the lowest FE were synthetic. Two fabrics, Polyester 6 and Cotton 11, had visually open weave structures compared to all other fabrics analyzed (see Figures S19 and pan class="Gene">S29 in Section S3 of the Supporting Information). All had yarn counts <250 yarns inch–2. Rayon, Polyester 1, and Polyester 6 had no appan>rent raised fibers, while Polyester/cotton blend 1 and Cotton 11 had very few observable raised fibers. All were highly breathable, with ΔP < 88.2 Pa (9 mm n>n class="Chemical">H2O).

The QF is a relative metric for assessing the overall performance of a filter through the combination of FE and ΔP (see eq and Figure D). For measurements at similar flow rates, higher QF typically implies improved performance; the WHO recommends utilizing cloth masks with QF > 3.[3]QF ranged from >50 kPa–1 for the N95 mask and HEPA filter to <0.3 kPa–1 for Nylon, Cotton 11 (muslin), and Polyester 6 (lightweight chiffon). Paradoxically, two of the highest QFs were for materials with low FE and ΔP: Rayon, QF = (10.8 ± 2.5) kPa–1, FE = 2.1%, and ΔP = 1.9 Pa, and Synthetic blend 1, cotton/Spandex, (13.5 ± 2.5) kPa–1, 15.3%, 13 Pa. These QF values are similar to those of the medical grade wraps (QF ≈ 13), surgical masks (average QF ≈ 9), and the N95 fabric (QF ≈ 8), which all had significantly higher FE. For these low ΔP materials, FE can be improved by constructing masks with many layers (compared to the 2 layers used presently) while maintaining QF (e.g., Figure E); however, the number of layers required to obtain the desired FE will likely limit functionality in other ways (e.g., FE> 30% would require ∼34 layers of Rayon), whereas Cotton 8, woven hand towel, (6.2 kPa ± 0.3) kPa–1, 32%, 62 Pa, had a moderate QF, FE, and ΔP, respectively.

The FE and ΔP data were statistically evaluated using correlation calculations to determine if relationships existed between measured values and textile parameters for both 100% cotton and 100% polyester fabrics. No statistically significant relationships were found for parameter sets with a sufficient number of samples (n = 5 for 100% polyester and n = 11 for 100% cotton). Details of analyses and results can be found in Tables S34–S37 in Section S5 of the Supporting Information. Sample sizes, after they were controlled for outliers and samples with easily discernible weave patterns and yarn counts, were relatively small (2 < n > 9) and may have attributed to the nonsignificant results. A larger data set from additional samples collected from similarly controlled populations may provide more insight into the effect of these variables on FE and ΔP.

In their recent paper, Zhao et al. (2020)[36] related the measured electrostatic properties of common household fabrics (many similar to those studied here) to the fiber chpan class="Gene">emistry. A similar discussion can be had relating the mechanical filtering ability of a textile to the fiber sources, yarn widths, and textile construction. Mechanical filtration of aerosols by fiber filters is partially dependent on the fiber diameter[49] and the range of diameters of the fibers.[50] Fiber shape may also be an important factor.[51] For synthetic-based appan>rel textiles, the fibers used to construct yarns tend to be set and have a relatively small variability in width and shape.[39] Generally, natural fibers have more variability, which can be influenced by many factors. For plant-sourced materials (e.g., cotton), these factors can include plant type, growing conditions, and postharvesting processing methods.[52] Cotton has been reported to have fiber diameters from ≈1 μm to ≈22 μm with a similar range of fiber width variability (≈ 20 μm) found within singular crops. For animal-sourced materials (e.g., wool), factors may be animal type/breed[53] and seasonal nutrition levels of the animals.[54] n>n class="Species">Sheep wools have been reported to have fiber diameters spanning <17 μm to ∼40 μm,[55] with intrabreed variability of ≈20 μm. Although this in range fiber diameter is not as broad as those reported for high filtering synthetic nanofibers (spanning nm to μm),[56] they do provide a broad fiber diameter range and can be used to form fiber-webs for particle filtration. These two features are those often found in filter media that have been shown to have good FE values.[57]

In this study, many woven fabrics were found to form fiber-webs, with the highest concentration being apparent for the 100% cotton flannel samples. These webs, the result of fibers being raised away from the woven structure of the textile, can result in an increase of pan class="Disease">material disorder, thereby disrupting flowing gas streamlines and providing more surfaces with which the aerosols can interact. This may provide a mechanism to explain why the medium range yarn count (≈ 150 yarns inch–2) Cotton 10 out-performed other fabrics with higher yarn counts (e.g., Cotton 6 and Cotton 13) or synthetics with visually tighter weaves (e.g., Polyester 5). Additionally, this suggests that cover factor, discussed above, may not be a good individual indicator of FE for fabrics displaying these textures. Interestingly, the cotton batting sample (Cotton 14) showed a relatively low FE despite consisting of fiber-webs. More research is needed to understand these observations.

In addition to measuring materials from a single type of cloth, two-layered (multimaterial) structures were also investigated in accordance with recent findings by Konda et al. (2020)[15] who measured FE > 95% for masks comprised of combinations of two layers of a synthetic and natural fabric using n class="Chemical">NaCl aerosol that was not size selected. Combinations of cotton and synthetic fabrics identical, or nearly identical, to those outlined in Konda et al. were tested here, and the present results were not consistent with the prior findings (Figure A). Because of the low-pressure differentials measured, QF values in Konda et al. were over 1000 kPa–1, 250–500-times higher than measured in this study; see values in Figure A.[15] Additional combinations that were exclusive to this investigation (see Figure B) were also tested. Konda et al. hypothesized that the measured FE resulted from dissimilar layered fabrics increasing electrostatic charge (and hence E) at the interface between the two layers. In this study, an attempt was also made to increase the charge between the layered structures by rubbing the materials against one another wearing latex gloves for 30 s, as described recently by Zhao et al. (2020)[36] and by Perumalraj (2015)[58] for woven fabrics. This did not significantly impact the measured FE (see Figure A). Subsequently, the multilayered samples also did not exhibit a significant difference in the measured FE when compared to the product of the individual FE for the components (sum of individual efficiencies in eq ), see Figure A. Zhao et al. (2020)[36] showed that intense rubbing of materials using latex for 30 s increased the FE for some synthetics but did not increase FE for cotton samples. The high FE reported by Konda et al. (2020)[15] is an intriguing observation that is inconsistent with the results presented here and may be an artifact of sampling a freshly generated NaCl aerosol (e.g., Forsyth et al. (1998))[59] that has not reached charge equilibrium (either through the passage of time or utilizing a charge neutralizer prior to exposing the aerosol to the sample). Thus, while their FE may be applicable to freshly emitted virus-laden particles (e.g., from a cough etc.), they are likely less representative of neutral or weakly charged particles or those that persist in the ambient environment.

Figure 5

Comparison of ΔP, FE, and QF for single component layers and mixed layered materials. Samples and mixed samples are coordinated by color. (A) Top 3 samples are single layers and bottom 4 are mixtures using fabric samples either similar, or identical to those reported in Konda et al. (2020).[15] Samples marked with ∗ were rubbed together for 30 s while wearing latex gloves to aid in sample charging as in Zhao et al. (2020).[36] Pink diamonds show data from Konda et al. (2020).[15] (B) Top 3 samples are single layers and bottom 2 are mixtures using fabric samples exclusive to this investigation.

Comparison of ΔP, FE, and QF for single component layers and mixed layered materials. Samples and mixed samples are coordinated by color. (A) Top 3 samples are single layers and bottom 4 are mixtures using fabric samples either similar, or identical to those reported in Konda et al. (2020).[15] Samples marked with ∗ were rubbed together for 30 s while wearing pan class="Chemical">latex gloves to n>n class="Gene">aid in sample charging as in Zhao et al. (2020).[36] Pink diamonds show data from Konda et al. (2020).[15] (B) Top 3 samples are single layers and bottom 2 are mixtures using fabric samples exclusive to this investigation.

The presented measured data may be utilized to highlight cloth materials that have a reasonable (based on NIOSH guidelines) ΔP and a high FE. These data are discussed further for the best performing cloth samples; microscopic images of each are shown in Figure , and data are tabulated in Table . The top performing samples show a broad array of structure. This information plus that presented earlier reinforces the fact that visual appearance is not necessarily indicative of a fabric’s filtration and pressure differential properties as previously suggested.[15] For example, the top performing cloth was Cotton 8, which had a visually loose weave, a high FE (32.0% ± 1.6%) and low ΔP (61.8 Pa ± 4.9 Pa), and a resulting QF of (6.25 ± 0.27) kPa–1. In comparison, Cotton 6, which had a visually tighter weave and high yarn count (812 yarns inch–2), had a lower FE (20.3 ± 1.02) % and a higher ΔP (128.5 ± 4.9) Pa, with a resulting low QF of (1.77 ± 0.04) kPa–1. Another high yarn count fabric (Cotton 13, ≈ 600 yarns inch–2, and the same weave type as Cotton 8) did not make this top five list and had statistically the same FE (Cotton 13 FE = 19.7% ± 1.0%) as Cotton 8 despite having ∼200 less yarns inch–2.

Figure 6

Transmitted light images of top performing fabrics based on FE and ΔP that fall within NIOSH guidelines and are listed in Table : (A) Cotton 8 (hand towel, 100% cotton, block weave), (B1, B2) outer and inner surfaces of Cotton 10 (light flannel, poplin weave, 100% cotton), respectively, (C) Polyester 5 (apparel fabric, poplin weave, 100% polyester), (D) Cotton 6 (inner surface, pillowcase, 100% cotton, satin weave, see SI for image of other side), and (E) Polyester 2 (soft spun, 100% polyester, plain weave). Note: Transmitted light grayscale intensities have been inverted so fibers appear lighter relative to voids; all scale bars represent 1 mm with subsections of 200 μm in length.

Table 1

Top Fabrics Based on FE that Fall within NIOSH ΔP Guidelinesa

sample and weave	source/descriptor	TPI (yarn inch–2)	FEmin (%)	ΔP (Pa)	QFc (kPa–1)
Cotton 8, block	hand towel	102b	32.0 ± 1.6	61.8 ± 4.9	6.25 ± 0.27
Cotton 10, poplin	lightweight flannel	152	24.3 ± 1.07	106.0 ± 4.9	2.62 ± 0.07
Polyester 5, poplin	poplin apparel fabric	229	21.4 ± 1.08	104.0 ± 4.9	2.32 ± 0.06
Cotton 6, satin	pillowcase	812	20.3 ± 1.02	128.5 ± 4.9	1.77 ± 0.04
Polyester 2, plain	soft spun apparel fabric	152	20.2 ± 1.02	177.6 ± 4.9	1.27 ± 0.03

Samples and sources, yarns inch–2 (reported as threads inch–2 (TPI) in the table), FE, ΔP, and QF for 2 layers of select samples. Uncertainties are 1σ.

Sample is constructed of a complex design that results in a variable TPI across the fabric area. Reported value is an estimated average TPI.

The WHO recommends utilizing cloth masks with QF > 3.[3]

Transmitted light images of top performing fabrics based on FE and ΔP that fall within NIOSH guidelines and are listed in Table : (A) Cotton 8 (hand towel, 100% cotton, block weave), pan class="Gene">(B1, B2) outer and inner surfaces of Cotton 10 (light flannel, poplin weave, 100% cotton), respectively, (C) Polyester 5 (appan>rel fabric, poplin weave, 100% polyester), (D) Cotton 6 (inner surface, pillowcase, 100% cotton, satin weave, see SI for image of other side), and (E) Polyester 2 (soft spun, 100% polyester, plain weave). Note: Transmitted light grayscale intensities have been inverted so fibers appear lighter relative to voids; all scale bars represent 1 mm with subsections of 200 μm in length.

Samples and sources, yarns inch–2 (reported as threads inch–2 (pan class="Gene">TPI) in the table), FE, ΔP, and QF for 2 layers of select samples. Uncertainties are 1σ.

Sample is constructed of a complex design that results in a variable pan class="Gene">TPI across the fabric area. Reported value is an estimated average n>n class="Gene">TPI.

Other 2-layered cloth materials that offer a similar combination of FE and ΔP are shown in Table . Using the reasonable assumption that the monotonic change in ΔP with the number of layers (e.g., Cotton 10, lightweight cotton flannel shown in Figure C) is similar for other cotton materials, it can be hypothesized that the following material combinations and structures may provide the best breathability and FE: a 6-layered mask (by extrapolation from the change in ΔP observed in Figure C) of Cotton 8 or a 4-layered assembly of lightweight flannel (sample Cotton 10, FE = 48% and ΔP = 216 Pa). Note that these hypothesized constructions are based upon measured FE and ΔP data and do not consider the other potential guidelines that may affect mask performance such as the current WHO recommendation of utilization of mixtures of hydrophobic and hydrophilic layers[3] and the effects of mask fitment.[13]

Nonwoven, synthetic fabrics utilized in masks, such as the N95, are often constructed using a melt-bond process. Part of the goal of this process is to stabilize and compress (e.g., calendaring) the manufactured fiber-webs to enhance filtration. Similar steps to engineer the processing of natural fabrics may be necessary to improve, and help maintain, the performance of the above suggested natural fiber materials. Cloth materials with similar microscale structure could be pursued in future investigations. Comparisons between studies measuring cloth FE are challenging due to experimental parameters that may influence mask performance (e.g., sample flow rate, aerosol generation scheme, charge neutralization, and variability in protocols). Future work in this area should use established techniques and officially recognized methods such as EN 1822 or ISO standard methods. On the basis of the findings presented here, other important future research areas of cloth masks may include (1) investigating the relationship between fiber diameters, diameter ranges, and sources with FE and ΔP of select best performing fabrics, (2) an examination of the extent of napping or raised fibers on FE and ΔP and (3) the effect of washing/decontamination on FE, (4) the impact of seams, (5) the influence of relative humidity, or (6) high face velocities such as encountered during pan class="Disease">coughing or sneezing on FE.

Conclusion

Cloth materials considered in the construction of facemasks to reduce the transmission of pan class="Species">SARS-CoV-2 were evaluated for key factors in mask performance: the filtration efficiency (FE), differential pressure (ΔP), and fabric construction parameters. The results indicate that there is a complex interplay between fabric type, weave, and yarn count and the filtration of nanometer-sized aerosol particles. The best performing cloth materials had moderate yarn counts with visible raised fibers. No measured cloth masks performed as well as an N95. The measured data of mixed cloth assemblies were in contrast to recent measurements by Konda et al., where mixed assemblies of multiple materials did not synergistically impan>ct the measured FE beyond the product of individual FE values.[15] The measured data indicate that particle charge does not impan>ct FE for both natural and synthetic fabrics.

Importantly, the presented data were measured under idealized conditions that eliminate or minimize leaks, which are important determinants in mask performance.[13] Other factors that may influence mask performance include fiber width, relative humidity, fabric moisture content, seams across the fabric, fabric nap/texture, and washing or degradation of the fabric.[60] Extending the measured particle size to mimic larger droplets will also pan class="Gene">aid in understanding fabric filtration.

The method of measuring FE using a combination of aerosol size selection and particle counting is widely available and may enable other research laboratories to perform similar measurements under controlled conditions enabling quantitative comparability of materials. The combination of microscopy and FE applied to other mask materials may allow rapid screening of a broad array of relevant materials or combinations to construct a detailed database for the optimization of FE to reduce exposure to virus-sized particles.

Materials and Methods

Samples

Samples were acquired from multiple sources by the authors and those acknowledged. Samples were cut into a circular shape of 2.5 cm diameter using a cleaned stainless-steel form and scissors. Samples were used as received and were equilibrated at ∼22 °C and at ambient relative humidity, 30% to 50%, prior to measurement. Most samples were measured in two layers, see text, and were loaded into the sample assembly as individual layers to avoid the potential of perfect registration between the two layers, which may reduce the measured FE.

The measured samples did not shed particles under the flow conditions described in this study. However, materials that meet the HEPA filtration standard may be constructed from multiple types of materials including layered polymers or glass (pan class="Chemical">SiO2) fibers. Using mask materials that meet the HEPA filter standard under conditions they were not designed for, such as cutting or the physical deformation of the filter membrane, may cause the shedding of nano- or microscale fibers from the filter increasing the likelihood of inhalation or ingestion by the mask wearer.

The fabric characterization experiments presented can be split into two sets: (1) material microscopy image analysis for fabric structure to assess material yarn count, weave, and mass measurements, and (2) the filtration efficiency of aerosolized material.

Material Imaging

Imaging was completed with an USB digital microscope (Innovation Beyond Imagination) equipped with 8 brightfield LED lights, a color CMOS sensor, and a high speed 24-bit DSP. Images were collected in diffuse reflected light (LED, ring illuminated) and transmitted light (LED lightbox, Tiktec Laboratories, using size A4 or A5). All images were calibrated to a millimeter length scale, and resolution was calculated to be ∼20 μm (see Supporting Information S4 for details). Calibration was completed for each fabric type imaged. This was necessary as the differing thicknesses of the fabrics resulted in utilization of slightly different fields of view for each sample set. Preliminary processing, yarn counts, and yarn width measurements were completed in ImageJ (v. 1.8.0_112 with Fiji).[61,62] All images were length-scale calibrated and converted to an eight-bit gray scale before analyses. Additional image processing was completed in Digital Surf (Mountain Laboratories, v. 8) and was utilized to create the inverted grayscale images shown in Figure . Reflected and transmitted light images, yarn widths, and yarn count data can be found in SI S3.

Weave Types and Yarn Count, Width, and Mass Measurements

Reported weave types were either determined by visual inspection following the descriptions outlined in Table S38 in Section S7 of the Supporting Information or listed as described by the manufacturer. Two or more different sample sites were analyzed for each fabric for determination of yarn widths, and, unless otherwise stated, n = 20 yarns were measured. Measurements were completed manually and recorded using the measure subroutine in ImageJ. Widths were measured between yarn crossing junctions (i.e., not at the overlap of the yarns). Yarn counts were completed by measuring 1 mm across either axis of an image (starting in a void space) and then counting the number of yarns that fell under that line. Both front interior and exterior faced yarns were counted. Mean, standard deviation (reported to 1σ), minin class="Gene">mum, and maximum values are reported for the warp and weft yarn widths (see Section S3 of the Supporting Information). Warp and weft yarn directions were utilized in this study following textile industry practices. Warp yarns are those placed on a loom before being interwoven with weft yarns (see Figure S4). Identification of these yarns was completed by either visual inspection of the selvedge or by analyzing the weave and looking for reed marks (marks left by a tool used to separate and space yams) in the samples.

Yarn counts were also conducted separately in the warp and weft directions. Reported yarn counts are the average results of n = 5 measurements across 2 or more different sample sites. In cases where there was no clear warp:weft yarn structure (e.g., knits, block, and waffle weave samples), a single value is reported for the number of yarns counted in along 1 mm of the horizontal direction of the image. Mass yarn–1 measurements are relative to a 1 cm2 area and were calculated by dividing measured masses by the total number of yarns (sum of warp and weft yarns) counted for the same size area.

Filtration Efficiency

FE measurements mimicked Parts 3 and 5 of the EN 1822 mask filtration protocol (aerosol remains un-neutralized after size selection) or the ISO 29463 testing standard (aerosol is reneutralized after size selection); see Figure S1. Aerosol was generated from a 10 mg mL–1 aqueous solution of pan class="Chemical">NaCl using a constant output atomizer supplied with dry (dew point < −75 °C), HEPA-filtered air (25 psig). Of the 2.2 L min–1 flow that was generated, 0.3 L min–1 was sampled and conditioned using two n>n class="Chemical">silica gel diffusion dryers (desiccant was replaced daily prior to data collection). The aerosol was then passed through a soft X-ray charge neutralizer and size selected, at a mobility diameter (D), using a differential mobility analyzer (DMA) and a 10:1 sheath:aerosol flow. Under these experimental conditions, the range of aerosols selected was 50 nm ≤ D ≤ 825 nm. The ∼0.3 L min–1 of aerosol exiting the DMA was then mixed with ∼2.7 L min–1 HEPA-filtered dilution air (ambient laboratory air with ∼30% relative humidity) and either passed to a condensation particle counter (CPC) or through a 25 mm plastic filter holder (with stainless steel filter backing) to a CPC to measure the upstream (N) and downstream (N) particle number densities, respectively. Both CPCs sampled at 1.5 L min–1 and the face velocity at the filter holder was ≈ 6.3 cm s–1 and in line with NIOSH guidelines. Conductive (carbon black impregnated) silicone tubing was used throughout the experiment to prevent aerosol scavenging. The material under test was held in a plastic filter holder with a polymer gasket that electrically isolated the material. No attempts were made to electrically ground the tested material.

The downstream pan class="Chemical">CPC had been previously calibrated by a spectroscopic method using n>n class="Chemical">ammonium sulfate aerosol, see Radney and Zangmeister (2018).[40] Using this method, the CPC calibration is better than 3% for number densities (N) < 2 × 104 cm–3; see additional details in the Supporting Information. At larger values of N, N and N deviated from each other, so they were compared multiple times daily using the described arrangement without fabric in the filter assembly. Both CPCs (TSI 3775) also switched between a single particle counting mode and a photometric counting mode at ∼5 × 104 cm–3. The transition between modes was set by the manufacturer and automated based on the rate of change of N as a function of time. The transition regime of two instruments behaved similarly, but their set points may have been slightly offset under some measurement conditions. Two methods were used to account for this variation: (1) measurements with 4.5 × 104 cm–3 ≤ N ≤ 5.5 × 104 cm–3 were excluded from the determination of the minimum FE, and (2) separate comparison curves between N and ND were used for N ≥ 4.5 × 104 cm–3 and N ≤ 5.5 × 104 cm–3 (see Figure S2).

Experimental and data acquisition were controlled by custom software written in our laboratory. D (15 samples equally log spaced spanning 50 nm ≤ D ≤ 825 nm) was set by a computer and the particle counts were allowed to stabilize for 30 s. The N and N were then recorded for 30 s at 1 Hz, after which the next D was sequentially selected. The 30 s data (representing one technical replicate) were then averaged and a 1σ standard deviation calculated. The FE was then calculated from eq with the relative uncertainty in FE including the propagated 1σ uncertainties in N and N. The total time required to collect an FE curve for a single fabric sample was ∼15 min.

For all presented FE values, we assume an uncertainty of 5% that derives from (1) measured 1σ standard deviations of N ≈ 2.5%, (2) pan class="Chemical">CPC accuracy ≈ 3% (we assume this is constant for all N and not just N < 2 × 104 cm–3), (3) an ∼2% day-to-day variability in FE for the same sample, and (D) ∼1% sample-to-sample variability in FE for the same material.

The calculated FE curves were then converted to penetration efficiency (PE = 100% – FE) and fit as a function of D to a logarithmic bi-Gaussian distribution (i.e., a logarithmically transformed bi-Gaussian distribution):where PE is the maxipan class="Gene">mum penetration efficiency of the material. To be consistent with other reports, we report all data as the filtration efficiency (FE) as shown in eq .

The differential pressure (ΔP, Pa) across the filter sample was measured using one of two manometers with ranges of 0 to 245.17 Pa and 0 to 490.3 Pa; to convert from Pa to mm pan class="Chemical">H2O to Pa, divide by 9.80665 Pa.[63] The reported ΔP across the filter represents the difference between the filter assembly with and without a filter present. Uncertainty in ΔP was calculated as twice the manometer read error (±4.9 Pa, 1σ).

Outlier and Correlation Calculations

The 100% cotton (n = 11) and 100% polyester (n = 5) sample sets were selected for correlation calculations by controlling for fiber type (cotton or polyester) and utilizing data sets on fabrics only with definite yarn counts. The data sets consisted of the following parameters: FE (%), ΔP (mm pan class="Chemical">H2O), weft and warp yarn widths (mm), weft and warp yarn counts (yarn inch–1), yarn count (yarns inch–2), and areal yarn mass (mg yarn–1). Parameter outliers were determined by calculating the first (25%) and third (75%) quartiles, determining the interquartile range from these values, calculating the upper and lower bounds of the range, and then rejecting any data value that fell outside of these bounds. Results from these calculations along with other descriptive statistical values for each parameter analyzed are presented in Tables S34 and S35 in Section S5 of the Supporting Information.

The remaining data were tested for normal distribution using the Shapiro-Wilk Test for Normality.[64] Normality test results were employed to determine whether to use a parametric (Pearson Product Moment Correlation, normally distributed data sets, eq ) or a nonparametric (Spearman Rank-Order Correlation, non-normally distributed data sets, eq ) correlation equation on pairs of data sets:where x and y are raw values for the ith set, n is the number of observations, and rg(x) and rg(y) are converted ranks for defined values.

These tests were selected under the assumptions that (1) variables are independent, (2) the values in the nonparametric sets are interval variables, and (3) there is a monotopic relationship between variables. Paired sets where both data sets failed the Shapiro-Wilk test and paired sets where only one failed the Shapiro-Wilk test were treated with the Spearman test, and the Pearson test was only utilized with pairs that both tested positive for normality. Pearson coefficients (r), and Spearman coefficients (r), and their corresponding p-values (ρp and ρs, respectively) were calculated in SigmaPlot (version 14).[65] Results are reported in Tables S36 and S37 in Section S5 of the Supporting Information. Calculated coefficients were evaluated for significance based on the following criteria: variables with p-values below 0.050 and positive (+) coefficients tend to increase together; pairs with p-values below 0.050 and negative coefficients (−) have one variable that tends to decrease while the other increases. There is no significant relationship between two variables for pairs where the p-values are greater than 0.050.[65] Presented correlation results should be interpreted cautiously given the small number of observations in this study per the controlled population sizes.