QUANTITATIVE DISORDER ANALYSIS AND PARTICLE REMOVAL EFFICIENCY OF FIBER-BASED FILTER MEDIA

Abstract

A process for predicting and adjusting particle removal efficiency of fiber-based filter media based on quantification of disorder. An order parameter may be extracted through Raman spectroscopy or scanning electron microscopy. Production processes may be adjusted to change (e.g., increase) the particle removal efficiency of fiber-based filter media utilizing a predefined correlation between order parameter and particle removal efficiency. The filter media may be utilized in masks, filters, and other applications.

Claims

1. A method of estimating particle filtering efficiency of polymer fiber filter media, the method comprising: extracting an order parameter squared (S.sup.2) value of a polymer fiber filter media from an image of the polymer fiber filter media; and utilizing a predefined relationship between particle filtering efficiency and S.sup.2 to determine an estimated particle filtering efficiency for the polymer fiber filter media.

2. The method of claim 1, wherein: the predefined relationship between particle filtering efficiency and S.sup.2 comprises a substantially linear function.

3. The method of claim 2, wherein: the particle filtering efficiency declines as S.sup.2 increases.

4. The method of claim 1, wherein: the particle filtering efficiency comprises an organic particle filtering efficiency.

5. The method of claim 1, wherein: the polymer fiber filter media comprises polypropylene fibers.

6. The method of claim 1, including: utilizing the estimated particle filtering efficiency for the polymer fiber filter media to adjust a parameter of a polymer fiber filter media fabrication process to increase the particle filtering efficiency of the polymer fiber filter media.

7. The method of claim 1, wherein: the polymer fiber filter media comprises a non-woven mat.

8. The method of claim 1, wherein: the polymer fiber filter media comprises at least one polymer selected from the group consisting of polypropylene, polybenzimidazone (PBI), polyester and polypropylene/polyethylene bicomponent spunbond fibers (PP/PE-BCS).

9. The method of claim 1, wherein: the image of the polymer fiber filter media comprises a scanning electron microscope (SEM) image or a Raman spectroscopy image; extracting the S.sup.2 value from the image includes: 1) selecting a region of interest from the image; 2) fitting two curves to a pixel intensity histogram of the region of interest, the curves corresponding to bright and dark areas of the image; and 3) determining S.sup.2 by calculating a ratio of the area of the bright area to a total area, wherein the total area is the sum of the bright and dark areas.

10. The method of claim 1, including: fabricating a filter using the polymer fiber filter media; wherein: the filter comprises a mask or a filter configured to be used in a HVAC system.

11. A method of fabricating polymer fiber filter media, comprising: determining a predefined relationship between an order parameter squared (S.sup.2) of the polymer fiber filter media and a process parameter of a fabrication process used to fabricate the polymer fiber filter media; determining S.sup.2 for a polymer fiber filter media made using the fabrication process; and utilizing a predefined relationship between S.sup.2 and a property of the polymer fiber filter media to adjust the process parameter to control the property of the polymer fiber filter media.

12. The method of claim 11, wherein: the property of the polymer fiber filter media comprises particle removal efficiency.

13. The method of claim 12, wherein: the process parameter is adjusted to increase the particle removal efficiency.

14. The method of claim 11, wherein: the polymer fiber filter media comprises at least one polymer selected from the group consisting of polypropylene, polybenzimidazone (PBI), polyester and polypropylene/polyethylene bicomponent spunbond fibers (PP/PE-BCS).

15. The method of claim 11, wherein: the polymer fiber filter media comprises a non-woven mat.

16. The method of claim 11, including: extracting an order parameter squared (S.sup.2) value of a polymer fiber filter media from an image of the polymer fiber filter media; and utilizing a predefined relationship between particle filtering efficiency and S.sup.2 to determine an estimated particle filtering efficiency for the polymer fiber filter media.

17. The method of claim 11, including: forming a protective mask by positioning the polymer fiber filter media between protective layers of porous material.

18. The method of claim 11, including: forming a filter configured for use in at least one of a HVAC system and a powered air filtration unit.

19. A method of controlling a material property, the method comprising: determining an order parameter for a material that has been produced by a production process; utilizing the order parameter and a predefined relationship between the order parameter (S) the material property to be controlled to adjust at least one variable of the production process such that the material property satisfies predefined criteria.

20. The method of claim 19, wherein: the material property comprises Young's Modulus; the predefined relationship between the order parameter (S) the material property comprises a substantially linear relationship between order parameter square (S.sup.2) and Young's Modulus.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In the drawings:

[0017] FIG. 1A is a graph showing an intensity versus Raman shift analysis of a first polypropylene sample, resulting in an S.sup.2 value of 0.3937;

[0018] FIG. 1B is a graph showing an S.sup.2 analysis of a pixel intensity histogram of an SEM image of a second polypropylene sample, resulting in an S.sup.2 value of 0.5152;

[0019] FIG. 1C is a flowchart showing a process for extracting an order parameter squared (S.sup.2) value from an image;

[0020] FIG. 1D is a partially schematic enlarged view of a fiber-based filter media;

[0021] FIG. 2A is a graph showing Raman spectra for polypropylene with curve fits to the peaks near 970 cm.sup.−1 and 985 cm.sup.−1 for selected temperatures;

[0022] FIG. 2B is a graph showing S.sup.2 as a function of temperature for polypropylene, wherein S.sup.2 is extracted from Raman spectra;

[0023] FIG. 3 is a graph showing calculated S.sup.2 value of a polypropylene material versus voltage used during a melt-electrospinning process employed to make the polypropylene material;

[0024] FIG. 4A is a graph showing the percentage of each structural motif for a polypropylene material as a function of S.sup.2 at a balanced composition of x=0.5, wherein the inset shows a possible reference motif A.sub.2B(0);

[0025] FIG. 4B is a graph showing the percentage of each structural motif for polypropylene as a function of x at S=0, wherein the inset shows an A.sub.3 (1) motif;

[0026] FIG. 5A is a graph showing organic removal efficiencies as a function of S.sup.2 for three different polypropylene-based mask filters, wherein the inset is the pressure drop across each filter as a function of S.sup.2, and wherein the error bars for S.sup.2 values are within (less than) the size of the symbols;

[0027] FIG. 5B is a graph showing organic removal efficiencies of polybenzimidazole (PBI) filters as a function of S.sup.2, wherein the inset at the bottom left is the pressure drop across each filter as a function of S.sup.2, and the inset at the top right is the average fiber diameter as a function of S.sup.2, and wherein the error bars for S.sup.2 values are within (less than) the size of the symbols;

[0028] FIG. 5C is a graph showing filtering efficiencies as a function of S.sup.2 for polypropylene/polyethylene bicomponent spunbond (PP/PE-BCS) fibers, wherein the inset is the filtering efficiency as a function of S.sup.2 for filters made of polyester, and wherein the error bars for S.sup.2 values are within (less than) the size of the symbols;

[0029] FIG. 6 is an isometric view of a protective mask;

[0030] FIG. 7 is a partially schematic cross sectional view of the mask of FIG. 6 taken along the line VII-VII;

[0031] FIG. 8 is a graph showing Young's Modulus as a function of S.sup.2for various materials;

[0032] FIG. 9 is a graph showing Young's Modulus as a function of S.sup.2for various materials;

[0033] FIG. 10 is a graph showing Young's Modulus as a function of S.sup.2 for ultra high molecular weight polyethylene (UHMWPE); and

[0034] FIG. 11 is a graph showing Young's Modulus as a function of S.sup.2 for carbon fiber.

DETAILED DESCRIPTION

[0035] For purposes of description herein the terms “upper,” “lower,” “right,” “left,” “rear,” “front,” “vertical,” “horizontal,” and derivatives thereof shall relate to a polymer chain as oriented in FIGS. 4A and 4B. However, it is to be understood that the device may assume various alternative orientations and step sequences, except where expressly specified to the contrary. It is also to be understood that the specific devices and processes illustrated in the attached drawings, and described in the following specification are simply exemplary embodiments of the inventive concepts defined in the appended claims. Hence, specific dimensions and other physical characteristics relating to the embodiments disclosed herein are not to be considered as limiting, unless the claims expressly state otherwise.

[0036] Additionally, unless otherwise specified, it is to be understood that discussion of a particular feature or component extending in or along a given direction or the like does not mean that the feature or component follows a straight line or axis in such a direction or that it only extends in such direction or on such a plane without other directional components or deviations, unless otherwise specified.

[0037] There are many applications where the introduction of controlled disorder into a material can enhance a property of interest. The study of quantifying the degree of disorder in materials emerged in the middle 20.sup.th century from x-ray diffraction studies of binary metal alloys, such as AuCu and ZnCu. In order to describe the observed changes in x-ray diffraction peak intensity as samples of metal binary alloys were heated, Bragg and Williams defined an order parameter, S, commonly referred to now as the Bragg-Williams order parameter. For an alloy with constituent elements A and B, it may be expressed as:

S=r.sub.A+r.sub.B−1   (1)

[0038] where r.sub.A, is the fraction of “A” atoms on A-atom lattice sites, and r.sub.B is the fraction of “B” atoms on B-atom lattice sites. In this context, we reference the perfectly ordered structure where all atoms are on their respective (ideal) site. For such a sample S is equal to unity, which means that the sample must have: equal numbers of A and B atoms, A-atom lattice sites only occupied by A atoms, and B-atom lattice sites only occupied by B atoms (i.e., r.sub.A=r.sub.B=1). At the other extreme for such a sample, in which the A and B atoms are randomly distributed over both A-atom and B-atom lattice sites (i.e., r.sub.A=r.sub.B=0.5), S is equal to 0.

[0039] In some cases, the order parameter may be determined through x-ray diffraction. However, as discussed in more detail below, S may be measured utilizing other techniques, including Raman spectroscopy, reflection high-energy electron diffraction, transmission electron microscopy and scanning electron microscopy (SEM). Each of these techniques directly measure S.sup.2 instead of S, and S.sup.2 values are therefore discussed herein. It will be understood that, as used herein, “order parameter” broadly refers to a measure of disorder, and “order parameter” is not limited to S or S.sup.2 as disclosed herein.

[0040] In general, it may be possible to correlate disorder to system-level properties in some situations through the application of an (sing model in conjunction with cluster expansion theory, where a linear relationship between the system-level property and S.sup.2 emerges. The present disclosure discusses the disorder in fibrous networks (e.g., polypropylene-based fibers) of fiber-based filter media of the type that may be utilized in personal protective equipment such as masks and in filters (e.g., powered air filters, filters for HVAC systems, etc.). System level properties of the network of fibers (e.g., filtering efficiency) may vary linearly with the square of the order parameter (S.sup.2). Thus, the system level properties for these materials can be controlled and tuned by systematically varying the degree of disorder present in the fiber or polymer of the filter media. This can be advantageous at both the design and manufacturing stages. This may apply to particulate masks such as those used by healthcare and construction workers, water filtration, air conditioning filters, and protective safety vests such as those made of Kevlar®. This is also believed to apply to properties of individual polymers, where the property of interest may be, for example, strength, UV tolerance, or (in the case of OLEDs such as those used in displays) the color of emitted light and the material resistivity through analysis of published temperature-dependent measurements.

Methods

[0041] In an example according to an aspect of the present disclosure, the S.sup.2 value of published Raman spectra of polypropylene samples was measured in accordance with the approach of Loveluck and Sokoloff, “Theory of the optical properties of phonon systems with disordered force constants, with application to NH.sub.4Cl,” J. Phys. Chem. Solids 34, 869 (1973), as well as from intensity analysis of SEM images. Peaks in a Raman spectrum associated with the S=1 ordered structure have integrated intensities proportional to S.sup.2, while peaks associated with the completely disordered structure have an integrated intensity proportional to (1−S.sup.2). The corresponding equations can then be rearranged to extract the order parameter from the Raman spectrum of a single sample. Specifically,

J.sub.s=1/J.sub.s=0=S.sup.2/(1−S.sup.2)   (2)

[0042] where J.sub.S=1 is the integrated intensity of a peak associated with the ordered structure, and J.sub.S=0 is the integrated intensity of the disordered structure feature.

[0043] FIG. 1A shows the results of an S.sup.2 analysis according to the present disclosure (implemented utilizing a computer) on a published Raman spectrum of a polypropylene sample. The peak near 970 cm.sup.−1 is the peak associated with disordered polypropylene, and the peak near 995 cm.sup.−1 is the peak associated with completely ordered polypropylene.

[0044] In the case of SEM image analysis, the S.sup.2 value of a sample is equal to the percentage of sample image area corresponding to bright regions. However, bright and dark areas corresponding to the ordered and disordered regions, respectively, can be identified by first thresholding the image near the average pixel intensity of the bright regions.

[0045] With reference to FIG. 1B, the analysis process (extraction of S.sup.2) involves utilizing a computer to fit two curves to the pixel intensity histogram, one representing the disordered regions and one representing the ordered regions. The threshold for the image may be chosen at the peak of the ordered curve, or it may be selected at an integer multiple of the standard deviation, σ, away from the peak of the ordered curve, depending on the relative location of the intersection between the ordered and disordered curves.

[0046] FIG. 1C shows a process 10 for calculating the threshold value of an image 5 (FIG. 1D) of a sample 4 of fiber-based filter media. It will be understood that one or more steps of process 10 may be implemented utilizing a computer that is configured (e.g. programmed) to execute the steps. Process 10 starts as shown at 12, and proceeds to step 14 which includes converting the image 5 to grayscale. A region of interest 8 (FIG. 1D) may be selected as shown in step 16. In general, the region of interest 8 may be selected before or after converting an image to grayscale. The region of interest 8 may be selected by an individual inspecting one or more images 5, or the region of interest 8 may be selected by a computer algorithm. In general, the region of interest may have virtually any shape, and may be selected to leave out (exclude) regions having defects or artifacts that are not representative of the sample 4.

[0047] The process 10 further includes calculating a pixel intensity histogram of the selected region 8 (see, e.g., FIG. 1B). At step 20, an algorithm (e.g., a stochastic funnel algorithm) is used to calculate initial curve fitting parameters for two skewed Gaussian curves to the pixel intensity histogram data. In the example of FIG. 1B, the skewed Gaussian curves are shown as the disordered and ordered curves, and the over-all fit is also shown in FIG. 1B. Referring again to FIG. 1C, at step 22, the least squares method is used to calculate the Gaussian curve parameters using the initial curve fitting parameters from step 20.

[0048] At step 24, a root-finding algorithm (e.g., Newton's method) is used to find the intersection between the two Gaussian curves resulting from the fit. At step 26, a number of standard deviations at the intersection is away from the curve where the highest center point is calculated. The threshold value is set to the value of the highest center point value minus the floor of that number of standard deviations.

[0049] At step 28, a binary threshold is performed on the region of interest 8 in the grayscale image 5 (FIG. 1D) using the threshold calculated in step 26. This results in a black and white image (not shown) with black (dark) and white (bright) regions corresponding to disordered and ordered regions, respectively. At step 30, the squared order parameter (S.sup.2) value of the region of interest 8 is calculated by counting the bright (white) pixels in the binary image and dividing this number by the total number of pixels (white and black) contained with the region of interest. Because the areas of each pixel is the same, the ratio of bright pixels to total pixels is equal to a ratio of the white area to the total area. The method 10 then ends as shown at 32.

Results and Discussion

[0050] One method for experimentally verifying that a material or system can have states of varying degrees of ordering is by measuring S.sup.2 of a sample as a function of temperature. Landau theory describes order-disorder transitions as second-order transitions, and as a result, the order parameter of a system as a function of temperature is:

S(T)=√{square root over (α.sub.0(T.sub.C−T)/β)}  (3)

[0051] where α.sub.0 and β are material-dependent constants, and T.sub.C is the critical temperature below which S=0. Squaring both sides of Eq. 3 yields:

S.sup.2(T)=(α.sub.0/β)T.sub.C−(α.sub.0/β)T   (4)

[0052] Therefore, if S.sup.2 exhibits a linear trend with temperature for a system, it can be taken as evidence that the system is undergoing an order-disorder transition.

[0053] FIGS. 2A and 2B show the results of such an analysis applied to the reported Raman spectra of a polypropylene sample systematically heated in 5° C. increments from 30° C. to 225° C. (see Hiejima, Y. et al., “Investigation of the Molecular Mechanisms of Melting and Crystallization of Isotactic Polypropylene by in Situ Raman Spectroscopy,” Macromolecules, Vol. 50, 2017, pp. 5867-5876). In order to apply Eq. 2 to extract S.sup.2, two peaks are first identified in the Raman spectrum of polypropylene, one arising from disorder and one arising from order. According to the Landau theory, S should decrease with increasing temperature, and thus disorder-related peaks (which have a (1−S.sup.2) dependence) should increase in intensity with increasing temperature, whereas peaks associated with the ordered structure (which have an S.sup.2 dependence) should decrease in intensity with increasing temperature.

[0054] From FIG. 2A, it can be seen that with increasing temperature, the peak at 995 cm.sup.−1 is decreasing in intensity while the peak at 970 cm.sup.−1 is increasing in intensity; thus, the peak at 995 cm.sup.−1 is associated with the ordered structure and the peak at 970 cm.sup.−1 is associated with the disordered structure. Using these two peaks and Eq. 2, S.sup.2 was estimated for the Raman spectra reported by Hiejima et al. for temperatures up to the melting point (see Hiejima, Y. et al., “Investigation of the Molecular Mechanisms of Melting and Crystallization of Isotactic Polypropylene by in Situ Raman Spectroscopy,” Macromolecules, Vol. 50, 2017, pp. 5867-5876). The results, plotted as a function of temperature in FIG. 2B, show a clear linear trend between S.sup.2 and temperature—as predicted by the Landau theory for a system undergoing an order-disorder transition. This provides additional evidence that polymers (e.g., polypropylene polymers) may have some degree of disorder somewhere within their structure, as has been previously established using x-ray diffraction (see Hikosaka, M. et al., “The order of the molecular chains in isotactic polypropylene crystals,” Polymer Journal, Vol. 5, 1973, pp. 111-127; Auriemma, F. et al., “Structural Disorder in the a Form of Isotactic Polypropylene,” Macromolecules 33, Oct. 1, 2000; and De Rosa, C. et al., “A polymorphism in polymers: A tool to tailor material's properties,” Polymer Crystallization, 2020, 3:e10101).

[0055] Another property of polymers such as polypropylene that can be obtained from the data in FIG. 2A is the critical temperature, T.sub.C. From Eq. 3, T.sub.C is equal to the dependent-axis intercept of the line defined by the S.sup.2 versus Tc relationship. Applying linear regression to the data in FIG. 2B, Tc for the order-disorder transition in a polypropylene sample was found to be 834° C. This transition temperature is well above the melting point of polypropylene, which may, at least initially, seem to rule out the possibility of achieving a zero value of S.sup.2, or even an S.sup.2 value below 0.30. However, it may be possible to achieve such S.sup.2 values through non-equilibrium growth conditions. For example, an S.sup.2 close to 0 for ZnSnN.sub.2 has been achieved through plasma-assisted molecular beam epitaxy at a temperature of 420° C. (Appendix A), a non-equilibrium crystal growth technique, despite the fact that the critical temperature for ZnSnN.sub.2 is predicted to be over 3000 K (see Lany, S. et al., “Monte Carlo simulations of disorder in ZnSnN.sub.2 and the effects on the electronic structure,” Phys. Rev. Materials, Vol. 1, 035401 August 2017). Melt-electrospinning is an example of a technique for polypropylene that can reach S.sup.2 values corresponding to temperatures above its melting point. Melt-electrospinning processes may be used in mask production. FIG. 3 shows the influence of the applied voltage on the S.sup.2 value of the resulting polypropylene during a melt-electrospinning process, confirming that such an approach can be used to access low values of the Bragg-Williams order parameter for this material.

[0056] Disorder in polypropylene is related to variations in orientation of the methyl groups relative to the polymer chain. This is commonly referred to as tacticity; the methyl groups are on the same side of the chain for isotactic polypropylene, on alternating sides for syndiotactic polypropylene, and randomly aligned for atactic polypropylene. This tacticity can be represented using an (sing model wherein a spin “up” is assigned to a methyl group on one side of the polymer chain and a spin “down” is assigned to a methyl group located on the opposite side of the polymer chain. (sing models have previously been developed and applied to polymers such as isotactic vinyl polymer. However, the approach described herein is fundamentally different. Whereas previous models considered the entire set of possible sequences that can occur in a given chain, disorder may be described herein in terms of the percentages of the structural motifs present in the polymer. Although the set of complete structural motifs described herein is contained within previous models, previous models may obscure the fundamental importance of the variety of structural motifs in determining system-level properties.

[0057] A methodology for modelling disorder is described in U.S. patent application Ser. No. 17/011,648 filed Sep. 3, 2020, entitled “Band Gap Engineered Materials,” and U.S. patent application Ser. No. 17/313,947 filed May 6, 2021, entitled “Method of Developing Vaccines,” the entire contents of which are incorporated herein by reference. This methodology may be utilized to identify the reference structural motif associated with the ordered structure as three polypropylene blocks with methyl groups on alternating sides with respect to each other, as shown in the inset of FIG. 4A. This defines the syndiotactic structure as the S=1 structure (since an S=1 structure must have equal numbers of spins, which in this case corresponds to equal numbers of methyl groups on opposite sides of the polymer chain). There are six other possible structural motifs, one of which—the A.sub.3 (1) motif—is shown inset in FIG. 4B. In this notation scheme, “A” denotes a methyl group oriented in the “upward” direction (for the orientation of the polymer chain shown in the insets of FIGS. 4A and 4B) and “B” denotes a methyl group oriented in the opposite direction, which in this case is out of the page as shown by the red and black highlighted methyl groups in the inset of FIG. 4A for the AB.sub.2 (0) motif. The number in parenthesis represents the number of methyl groups in the opposite orientation of the corresponding methyl group characterizing the reference (S=1) motif. Thus, A.sub.3 (1) denotes the motif with all upward-oriented methyl groups, with one methyl group misoriented relative to the reference motif.

[0058] The six other possible structural motifs only occur within the polymer when some degree of disorder is present in the structure, with the percent occurrence depending on both S and x, where x is the fraction of methyl groups oriented along a specific side of the polymer. Thus, isostatic polypropylene with methyl groups oriented along one side would have x=1, while isostatic polypropylene with methyl groups oriented along the opposite side would have x=0. FIG. 4A shows the percentage of each motif present in polypropylene with x=0.5 as a function of S.sup.2, and FIG. 4B plots the percentage of each motif at S=0 as a function of x.

[0059] A system-level property dominated by pair interactions can be expressed as:

P(x, S)=[P(x=0.5, S=1)−P(x, S=0)]S.sup.2−P(x, S=0)   (5)

[0060] where P(x, S) is the system property at the given composition x and degree of ordering S. To investigate whether the particle removal efficiencies of polymer fiber filter media (polypropylene masks and filters) is such a system-level property of this material, S.sup.2 values of fiber-based polypropylene masks and filters were extracted from SEM images (see Lee, S. et al., “Reusable Polybenzimidazole Nanofiber Membrane Filter for Highly Breathable PM2.5 Dust Proof Mask”, ACS Applied Materials & Interfaces 11, Jan. 7, 2019, pp. 2750-2757).

[0061] It was determined that the reported filtering efficiency (measured using organic particulate matters generated from dioctyl phthalate) follows a linear trend with S.sup.2 predicted by Eq. 5, as shown in FIG. 5A. In general, the particle removal efficiency of filters and masks increases with increasing disorder in the polypropylene. A possible explanation for this trend may be found by considering the structural motifs that occur with increasing disorder. Specifically, the motifs dominated by methyl groups on the same side of the polymer chains occur in increasing percentages as S decreases, as can be seen in FIG. 4A for the case of x=0.5, while the percentage of the reference motif with a sequence of methyl groups on alternating sides decreases with decreasing S.sup.2. Not wishing to be bound by a specific theory, this nevertheless suggests that same-side methyl-group-dominated motifs may provide a more significant barrier to particles passing through than the alternating-side reference motif, leading to better particle filtering (removal) efficiencies for more disordered polypropylene structures.

[0062] An S.sup.2 analysis according to an aspect of the present disclosure was applied to masks made of other fibrous filter media materials, such as polybenzimidazole (PBI), polyester and polypropylene/polyethylene bicomponent spunbond fibers (PP/PE-BCS). FIGS. 5A-5C show the results of these analysis for these materials.

[0063] The results for three different commercial polypropylene-based mask filters are shown in FIG. 5A. The inset of FIG. 5A is the pressure drop across each filter as a function of S.sup.2, and wherein the error bars for S.sup.2 values are within the size of the symbols, and error bars for measured quantities from the literature, such as removal efficiencies, are included when reported.

[0064] For the PBI samples (FIG. 5B), the filtering efficiency was measured using organic particulate matters generated from dioctyl phthalate (see Lee, S. et al., “Reusable Polybenzimidazole Nanofiber Membrane Filter for Highly Breathable PM2.5 Dust Proof Mask”, ACS Applied Materials & Interfaces 11, Jan. 7, 2019, pp. 2750-2757). In FIG. 5B, the inset at the bottom left is the pressure drop across each filter as a function of S.sup.2, and the inset at the top right is the average fiber diameter as a function of S.sup.2, and wherein the error bars for S.sup.2 values are within the size of the symbols, and error bars for measured quantities from the literature, such as removal efficiencies, are included when reported.

[0065] For the PP/PE-BCS (FIG. 5C), the removal efficiencies were measured using charge neutral sodium chloride (see Liu, J. et al., “Low resistance bicomponent spunbond materials for fresh air filtration with ultra-high dust holding capacity,” RSC Advances 7, 2017, pp. 43879-43887), and for the polyester samples the removal efficiencies were measured for particles with a diameter of 0.5 microns (see Agranovski, I. E. et al., “Enhancement of the performance of low-efficiency HVAC filters due to continuous unipolar ion emission,” Aerosol Science and Technology 40, 2006, pp. 963-968). In FIG. 5C, the inset is the filtering efficiency as a function of S.sup.2 for filters made of polyester, and wherein the error bars for S.sup.2 values are within the size of the symbols, and error bars for measured quantities from the literature, such as removal efficiencies, are included when reported.

[0066] As shown in FIGS. 5B and 5C and the inset of FIG. 5C, as in the case of polypropylene, each of these materials demonstrates a linear relationship between their filtering efficiency and S.sup.2.

[0067] While the particle removal efficiency of a filter media is typically associated with features such as fiber diameter (with smaller diameter fibers yielding higher removal efficiencies), the trend seen in the removal efficiencies above may actually be due to the ordering of the material. Evidence for this can be seen in the graph inset in the top right of FIG. 5B, which shows the average fiber diameter as a function of S.sup.2 for three PBI films. The plot shows that there is no linear trend between the average fiber diameter and S.sup.2, while for the same three filters there is a linear trend between the S.sup.2 of the polymers and the filter removal efficiency. Thus, the results shown in FIGS. 5A-5C demonstrate that a model of disorder described herein for polypropylene has applications to a broad range of polymer-based fibers.

[0068] Additionally, the insets to FIGS. 5A and 5B plot the pressure drop across the polypropylene and PBI based filters as a function of S.sup.2. While all of the samples of each material lie on the same S.sup.2 line for the removal efficiency, the pressure drops of the same filters do not fall along a single line for each material. Thus, there does not appear to be a linear relationship between S.sup.2 of the material and the pressure drop of the type predicted by a spin-based model according to the present disclosure. This result suggests that pressure drop, unlike the filter efficiency, is not dominated by the ordering of the polymers, and instead is driven by the larger structural features of the filter, such as number and density of layers in the filter. Raman spectroscopy and SEM are straightforward and powerful techniques for characterizing and understanding these fiber structures. A model according to an aspect of the present disclosure provides a way to achieve masks with improved filtering efficiencies and lower pressure drops. Specifically, the S.sup.2 values of the polymers in the filter media and the overall structure of the filter and filter media can be tuned (adjusted) during fabrication to improve the filter efficiency and/or reduce pressure drops.

[0069] With reference to FIGS. 6 and 7, a mask 40 may comprise an N95 mask having an outer protective layer 41, a central layer 42, and an inner protective layer 43. Protective layers 41 and 43 may comprise cloth or other suitable known materials. The central layer 42 may comprise a non-woven fiber-based filter media or mat having a plurality of polymer fibers 45. The polymer fibers 45 may comprise polypropylene or other polymer as discussed in more detail above. The central layer 42 may be manufactured utilizing known processes. Various production parameters (variables) may be adjusted during production to change or control the properties of the polymer fibers 45 and central layer 42 of mask 40. For example, correlations between various production parameters and resulting S.sup.2 values can be determined empirically. Because the correlation between S.sup.2 and filtration efficiency can be determined, the S.sup.2 value for samples of fibrous filter media such as central layer 42 can be determined, and the production parameters may be adjusted to provide a desired S.sup.2 value corresponding to a desired filtration efficiency. In general, the S.sup.2 value of a filtration media (e.g., central layer 42) may correspond to various properties of the filtration media, and the S.sup.2 value may therefore be determined for filtration media samples, and the production processes may be adjusted as required to provide the desired properties in the filtration media.

[0070] The S.sup.2 value for various filtration media may also be utilized to select a filtration media for a specific application. For example, various samples of filtration media (e.g., central layer 42 of mask 40) may be ranked according to the S.sup.2 value for a sample to determine the predicted filtration efficiency of the various samples. Optionally, additional further testing may be conducted on samples having the highest predicted filtration efficiency to confirm the predicted filtration efficiencies.

[0071] The disclosed order-disorder transition in polypropylene is based on temperature-dependent measurements of the Bragg-Williams order parameter S. A model is proposed for the corresponding structural disorder based on the alignment of methyl groups along the polymer chain. Additionally, a system level property of polypropylene—its particle filtering efficiency—follows the predicted spin (Ising) based model equation relating material properties and S2. Although the discussion herein generally focusses on polypropylene fibers, the concepts and processes disclosed herein are not limited to a specific polymer or material, but rather apply broadly to other polymers and fiber systems, including carbon fibers. The concepts and processes disclosed herein may be utilized to quantify and understand the impact of structural disorder at the material level in a broad range of fiber systems, which can be used to evaluate filter designs, mask cleaning strategies, Young's Modulus, and may also form a basis for quality control in manufacturing.

[0072] With further reference to FIGS. 8-11, control of order parameter (S) or order parameter squared (S.sup.2) may also be used to control Young's Modulus in various materials. In general, various parameters (variables) can be varied/controlled during production of a material to thereby control S.sup.2 of the material. The correlation between S.sup.2 and Young's Modulus may be used to control (adjust) production variables to provide a material having a specific S.sup.2 value, which will provide the desired Young's Modulus.

[0073] It will be understood by one having ordinary skill in the art that construction of the described device and other components is not limited to any specific material. Other exemplary embodiments of the device disclosed herein may be formed from a wide variety of materials, unless described otherwise herein.

[0074] It is also important to note that the construction and arrangement of the elements of the filtration media and related components as shown in the exemplary embodiments is illustrative only. Although only a few embodiments of the present innovations have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters, mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter recited. For example, elements shown as integrally formed may be constructed of multiple parts or elements shown as multiple parts may be integrally formed, the operation of the interfaces may be reversed or otherwise varied, the length or width of the structures and/or members or connector or other elements of the system may be varied, the nature or number of adjustment positions provided between the elements may be varied. It should be noted that the elements and/or assemblies of the system may be constructed from any of a wide variety of materials that provide sufficient strength or durability, in any of a wide variety of colors, textures, and combinations. Accordingly, all such modifications are intended to be included within the scope of the present innovations. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions, and arrangement of the desired and other exemplary embodiments without departing from the spirit of the present disclosure.

[0075] It will be understood that any described processes or steps within described processes may be combined with other disclosed processes or steps to form structures (filtration media and the like) within the scope of the present disclosure. The exemplary structures and processes disclosed herein are for illustrative purposes and are not to be construed as limiting.

[0076] It is also to be understood that variations and modifications can be made on the aforementioned structures and methods without departing from the concepts of the present disclosure, and further it is to be understood that such concepts are intended to be covered by the following claims unless these claims by their language expressly state otherwise.

[0077] The above description is considered that of the illustrated embodiments only. Modifications of the processes, materials, and structures will occur to those skilled in the art and to those who make or use filters and other such items. Therefore, it is understood that the embodiments shown in the drawings and described above are merely for illustrative purposes and not intended to limit the scope of the method and filtration media, which is defined by the following claims as interpreted according to the principles of patent law, including the Doctrine of Equivalents.