Patent Publication Number: US-2020283957-A1

Title: Apparatus, systems and methods for making re-pulpable insulated paper products

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is a continuation-in-part of U.S. Utility patent application Ser. No. 16/590,224 entitled “RE-PULPABLE INSULATED PAPER PRODUCTS AND METHODS OF MAKING AND USING THE SAME,” and filed on Oct. 1, 2019, which claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 62/739,735 filed on Oct. 1, 2018 entitled “RE-PULPABLE INSULATED PAPER PRODUCTS AND METHODS OF MAKING AND USING THE SAME,” the subject matter of both of which is hereby incorporated by reference in their entirety. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates generally to apparatus and systems for making insulated paper products. The present invention further relates to methods of making insulated paper products. 
     BACKGROUND OF THE INVENTION 
     With the advent of on-line shopping, many goods are now delivered directly to the consumer&#39;s front door from distributors such as Amazon and others. Food and other temperature sensitive materials are typically shipped inside an insulated box. The insulation is typically some kind of polymeric closed-cell foam or a poly(ethylene) bubble-wrap type material and perhaps a metalized reflective film, which is inserted into the cardboard box prior to shipping. 
     While cheap to produce, manufacture, and highly insulating, expanded polystyrene has many disadvantages. Expanded polystyrene (1) is persistent in the environment, contributing to ocean pollution and long term landfills, (2) is frequently litter that is unsightly and may cause obstruction in the guts of smaller animals when ingested, (3) is not recyclable in most municipalities, (4) has to be separated from the box prior to recycling, (5) has to be inserted inside the box, and (6) does not nest, meaning that it is expensive to ship, and bulky to store. 
     The economic impact of using incompatible materials in a production environment is often underappreciated.  FIG. 25  shows how a stack of freshly made corrugated cardboard sheets are cut into an unfolded box by a rotary die/roller, ready to be inspected by quality control and shipped off to the customer. Card cuttings and trimmings from this process, along with any reject box, are shredded and then fed directly back into the repulping process ( FIG. 7 ) as pre-consumer scrap card. This is made back into furnish. Introducing treatments, coatings, liners, and other materials into the cardboard box that cannot be fed directly back into the re-pulping process complicates the production process and risks increasing paper machine ( FIG. 8 ) down-time if mistakes are made. Using an incompatible material means that the scrap, and any trimmings from that cardboard material must be segregated, and handled separately from the usual cardboard. 
     Presently, frozen or chilled food is shipped in cardboard containers with thermally insulating inserts. Such inserts are either expanded poly(styrene) foam (sold under the tradename Styrofoam), and or poly(olefin) bubble wrap which may or may not be metalized to decrease radiative heat transfer. Occasionally, expanded polyurethane foam is used in combination with a plastic film liner. None of these materials can be used in a cardboard box manufacturing line because any scrap containing these synthetic polymers would have to be segregated from the regular pulp. For this reason, cardboard boxes are made separately from the insulating material. Furthermore, the insulating material has to be removed prior to recycling the box as many municipalities do not recycle plastic films or expanded polystyrene. 
     For similar reasons, some paper beverage cups are also difficult to recycle. They are coated with a low molecular weight polyethylene, which causes problems when introduced into the pulp. 
     What is needed is a highly thermally insulating paper structure that provides one or more of the following benefits: (1) is non-toxic and safe for use with food, (2) maintains frozen or chilled food temperatures for the time needed to ship foods, (3) is curb-side ready—that is recyclable by municipal recycling services without separation or segregation from other papers in the waste stream, (4) trimmings generated during the paper product (e.g., cardboard box) manufacture are able to be repulped and directly sent back into the paper product (e.g., cardboard box) production stream without having to be segregated, (5) is able to withstand crushing by stacking, (6) is able to maintain integrity with condensation formation after being placed in a freezer then exposed to humid air, and (7) is biodegradable or biodestructable. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to machine configurations that can be used to make insulated paper products that (1) insulate food positioned therein and/or surrounded thereby, (2) are biodegradable or biodestructable, recycleable, repulpable, and (3) do not require additional inserts to keep food cold or hot. The disclosed insulated paper products utilize multiple ways to introduce insulating materials into and/or onto a variety of paper products. For example, thermally insulating materials may be introduced into the paper furnish prior to casting the furnish onto a paper-forming wire mesh. Alternatively, or in addition, the insulating material may be introduced between layers of paper as they are formed. Alternatively, or in addition, insulating materials may be incorporated into adhesives used to bond paper layers to one another. Alternatively, or in addition, insulating materials along with adhesives may be incorporated into a layer used to bond paper layers to one another. 
     The present invention is directed to machine configurations that can be used to produce insulated paper products. In one exemplary embodiment, the insulated paper product of the present invention comprises an insulated paper product comprising two or more paper layers and insulating material, wherein (1) when two or more paper layers are present, the two or more paper layers form an integral paper product, and (2) at least one of (a) one layer in combination with the two or more paper layers comprises the insulating material, and (2)(b) the integral paper product itself has a non-uniform distribution of insulating material therethrough. 
     In another exemplary embodiment, the insulated paper product produced by the present invention comprises a corrugated integral paper product comprising: a first linerboard layer comprising one or more first paper layers, a second linerboard layer comprising one or more second paper layers, and a fluted paper layer comprising one or more fluted paper layers or a honeycomb layer positioned between the first linerboard layer and the second linerboard layer, wherein (i) the first linerboard layer, (ii) the second linerboard layer, and (iii) the fluted paper layer or the honeycomb layer may each independently comprise insulating material that has a low thermal conductivity and/or low emissivity. 
     In another exemplary embodiment, the insulated paper product produced by the present invention comprises a corrugated integral paper product comprising: a first linerboard layer comprising one or more first paper layers, a second linerboard layer comprising one or more second paper layers, and a fluted paper layer comprising one or more fluted paper layers or a honeycomb layer positioned between the first linerboard layer and the second linerboard layer, wherein (i) the first linerboard layer, (ii) the second linerboard layer, and (iii) the fluted paper layer or the honeycomb layer may each independently comprise insulating material therein or thereon. 
     In one desired embodiment, the insulated paper product comprises a fully recyclable, re-pulpable, biodegradeable, biodestructable, and thermally insulated cardboard box. 
     The present invention is further directed to methods of making insulated paper products. In one exemplary embodiment, the method of making an insulated paper product comprises: forming an insulated paper product comprising: one or more paper layers and insulating material, wherein (1) when two or more paper layers are present, the two or more paper layers form an integral paper product, and (2)(a) at least one of: (i) one layer in combination with the one or more paper layers comprises the insulating material and (ii) one paper layer within the one or more paper layers has a non-uniform distribution of insulating material therein, or (2)(b) the integral paper product itself has a non-uniform distribution of insulating material therethrough. 
     These and other features and advantages of the present invention will become apparent after a review of the following detailed description of the disclosed embodiments and the appended claims. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The present invention is further described with reference to the appended figure, wherein: 
         FIG. 1  depicts a perspective view of an exemplary paper product of the present invention; 
         FIGS. 2A-2C  depict exemplary cross-sectional views of the exemplary paper product shown in  FIG. 1  as viewed along line  2 - 2  shown in  FIG. 1 ; 
         FIG. 3  depicts a perspective view of another exemplary paper product of the present invention; 
         FIGS. 4A-4F  depict exemplary cross-sectional views of the exemplary paper product shown in  FIG. 3  as viewed along line  4 - 4  shown in  FIG. 3 ; 
         FIGS. 5A-5B  depict perspective views of other exemplary paper products of the present invention (also referred to herein as “an integral paper product”); 
         FIGS. 6A-6D  depict exemplary cross-sectional views of the exemplary paper product shown in  FIG. 5B  as viewed along line  6 - 6  shown in  FIG. 5B ; 
         FIG. 7  depicts a schematic view of process steps and process components used to form the exemplary paper products of the present invention; 
         FIGS. 8A-8C  depict an exemplary process flow in an exemplary papermaking process suitable for use in forming the exemplary paper products of the present invention; 
         FIG. 9  depicts a side view of a paper layer forming process step suitable for forming a single paper layer within any of the exemplary paper products of the present invention; 
         FIG. 10  depicts a side view of another paper product forming process step suitable for forming an exemplary three-layered paper product of the present invention; 
         FIG. 11  depicts a side view of another paper product forming process step suitable for forming an exemplary paper product of the present invention; 
         FIG. 12  depicts a side view of another paper product forming process step suitable for forming an exemplary paper product of the present invention comprising a layer of insulating material; 
         FIGS. 13A-13I  depict side views of seven paper layer forming processes, each of which is suitable for forming a paper within any of the exemplary paper products of the present invention; 
         FIGS. 14A-14C  depict exemplary storage containers comprising any one of the exemplary insulated paper products of the present invention; 
         FIG. 14D  depicts an exemplary cross-sectional view of the wall structure of the exemplary hot beverage cup shown in  FIG. 14C ; 
         FIGS. 15-18A  depict additional exemplary storage containers comprising any one of the exemplary insulated paper products of the present invention; 
         FIG. 18B  depicts a close-up cross-sectional view of the wall structure of the exemplary shipping container shown in  FIG. 18A ; 
         FIG. 19  depicts an exemplary cross-sectional view of a wall structure of an exemplary shipping container; 
         FIGS. 20A-20B  depict a paper layer having a uniform distribution of insulating particles and a paper layer having a non-uniform distribution of insulating particles; 
         FIGS. 21A-21B  depict possible heat pathways through (i) the paper layer having a uniform distribution of insulating particles shown in  FIG. 20A  and (ii) and the paper layer having a non-uniform distribution of insulating particles shown in  FIG. 20B ; 
         FIGS. 22-23  depict views of an apparatus that may be used to determine the rate of heat transfer of paper samples and/or insulating materials with  FIG. 22  depicting a cross sectional view of the apparatus and  FIG. 23  depicting an exploded cross-sectional view of the apparatus; 
         FIG. 24  graphically shows the heat transfer rates of various materials; 
         FIG. 25  depicts a schematic view of known processes for forming boxes from a rectangular corrugated sheet with waste (e.g., trimmings and defective boxes) generated from the process; 
         FIG. 26  depicts a corrugated structure of the present invention with one side coated and 
         FIG. 27  depicts single faced corrugate paper hot beverage cup sleeves including the net and cross section. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is directed to machines for making insulated paper products comprising fibers  11  (e.g., wood pulp fibers  11 ) and insulating material  12 . Although shown in all figures, each paper layer  10  comprises fibers  11  (e.g., wood pulp fibers  11 ) with or without other paper layer additives including, but not limited to, the insulating material  12 . Some definitions of fibers, paper, and packaging, as well as product specification and fiber sources, are provided below. 
     As used herein, the term “paper” is used to identify a type of non-woven material in which fibers are randomly oriented in all directions. Fibers principally made from cellulose are poured as a slurry on a mesh screen. As the paper is formed, the fibers come into contact with each other, and physically bond with neighboring fibers via a variety of interactions, including hydrogen bonding. The fibers originally come from plants including trees, although synthetic and mineral fibers, or other types of fibers, may optionally be included. Often, the paper also contains recycled fiber. Wood may be sourced from direct harvesting of trees from forest land, or from lumber industry byproducts (such as sawdust). 
     Paper fibers may include the fibrous portions from many parts, including softwoods (such as those plants with needles instead of leaves, for example, loblolly pine) and hardwoods. Other plants that yield useful paper fibers include but are not limited to bamboo, sugar cane, wheat straw, reed grass, mischanthus grass, coconut fiber, hemp fiber, cotton fiber, jute, palm, reeds, and papyrus. Cellulose fibers in many plants are bound together with lignin. 
     In the case of virgin (non-recycled) fiber, much of the lignin is removed during the pulping process. Recycled paper may include fibers from corrugated, fiber board, writing paper, pressboard, card, newspaper, tissue paper, specialty papers, linerboard, containerboard, boxboard, PE-lined paperboard, carton material, cup stock, or foodboard. 
     When made from trees, the pulping process involves methods to separate the individual cellulosic fibers into a slurry, as well as remove some or all of the lignin. Pulping methods may include a) thermomechanical pulping, which involves the use of steam and sheer forces generated between a spinning and a stationary plate, b) chemical pulping, which uses strong chemicals to break down the pulp by dissolving the lignin, and/or c) the semi-chem process, which uses a combination of mechanical and chemical methods. Most often, fluted medium board (e.g., fluted medium board  23 ) is made using semi-chem process pulp and/or recycled paper fiber. Other types of pulp include solid bleached sulfate pulp, chipboard, and kraft. 
     Paper (and paper layer  10  (and paper ply  10 ), as used herein, may broadly include any material that includes 5% or more cellulose fibers (discussed further below). Other additives, including insulating material  12 , other particles/additives/components that impart grease resistant and/or water resistant, as well as other particles/additives/components to impart strength. Non-paper (and non-paper layer  30 ) is anything containing less than 5% of cellulose fibers (discussed further below). 
     As used herein, the term insulating material, such as insulating material  12 , is used to described inorganic or organic materials that provide some degree of insulation. The term insulating material, as in insulating material  12 , does not include air alone or any other gas alone, although air and/or another gas could be trapped within one or more inorganic or organic insulating material  12 . 
     Paper products  10 / 100 ′/ 60 , comprising fibers  11  (e.g., wood pulp fibers  11 ) and insulating material  12 , can either be made flat (e.g., insulated paper products  100 / 100 ′) using a screen to make flat materials, or alternatively be molded, vacuum formed, or thermoformed from a pulp suspension to form essentially three-dimensional (non-flat) objects (e.g., molded or otherwise formed containers  60  shown in  FIGS. 14A-18B ). Such three-dimensional paper products include certain packaging, for instance, egg crates and egg cartons, packaging that protects the corners of products shipped in the mail, biodegradable compost containers, biodegradable plant pots, disposable urinals and bed pans used in hospitals, disposable cat litter boxes, and the like. Additives, including insulating material  12 , may be included within the paper products  10 / 100 ′/ 60  to impart thermal insulation properties, strength under moist or wet conditions, impart water repellency or water proofing, impart grease absorption resistance, increase strength, improve the color, improve printability, or other aesthetic aspects. 
     When forming a given paper layer  10 , pre-consumer scrap corrugate may be added to a disintegrator and agitated to form a thick recycled pulp. This pulp may be further refined using a Holland Beater, subjecting the paper fibers to high sheer, and reducing the pulp freeness. The refined pulp may be diluted and further refined by being screened for large and small particles prior to use. The thick pulp is diluted with water, and placed into an agitated stock tank. Retention aids and other additives may be added to the stock tank prior to use. 
     Pulp is pumped from the stock tank and mixed in-line with water to further reduce the consistency of the pulp, on the way to the headbox. The headbox is set up with a series of weirs that allow diluted pulp to uniformly flow onto a moving wire. As the pulp flows onto the wire, water drains from the pulp, leaving the fibers on the wire. As the water drains, the fibers stop moving, and begin to interlock forming a sheet. As the water level begins to fall, the structure of the pulp layer becomes apparent. Foils and rollers beneath the wire assist in the water drainage. Vacuum slots are then used to actively remove free water trapped in the pulp layer by capillary action. The pulp may also be heated to reduce the viscosity of water, allowing for faster drainage. 
     The paper machine may have more than one headbox, and more than one forming wire. 
     Following vacuum slot treatment, the two sheets may be combined by bringing them into contact. The combined sheet is then trimmed and transferred onto the felt press for further water extraction. From the felt press, the sheet is fed into a series of steam-heated rollers which dry the remaining moisture from the sheet using heat. The paper may be calendared, coated or subjected to other treatments prior to rolling the sheet at the end of the machine. 
     Additives, including insulating material  12 , may be added to the paper pulp prior to casting on the paper wire or otherwise molding the pulp into a product  10 / 100 ′/ 60 . Alternatively, additives, including insulating material  12 , may be added at the size press, or after the steam can dryers. Additives, including insulating material  12 , can also be added to a clay coating (e.g., coating  30 ) often applied to liner board (e.g., liner board  21 / 22 ) to make clay coated kraftback, or clay coated newsback. 
     Additives may also be added to layers of paper using other means such as spray nozzles, slot-die coaters, curtain coating, or other means. Additives may be added to the paper as a slurry, that includes other materials besides water, such as starches, modified starches, paper fibers, dewatering additives, flocculants, pH buffers, and other additives. 
     There are many different configurations of the spray nozzles and spray booms. Nozzles  229  may be arranged on spray booms  262  in a variety of ways to spray mixtures of paper pulp fibers and insulating materials onto the wet or dry paper. Typically, the spray nozzle plume is flattened to give a fan shaped spray pattern, verses a conical spray emission. The nozzles may be arranged in series, so that one spray boom sprays on top of the deposit made by a spray-boom further up line, there by depositing multiple layers of pulp and or insulating material layers on top of one another. In one embodiment the spray nozzles are arranged in such a way that the spray plumes intersect, so that most points of the web receive deposition from more than one spray nozzle. The fan of the spray nozzles is angled with respect to the web direction. This allows multiple nozzles to direct to the web without the fans interfering with the momentum of neighboring spray fans. The spray nozzles may be used in combination with a slot-die or similar deposition technology. 
     Atomization or spray systems are numerous with many known in the art. Pressurized spray systems force liquids at high pressure through a narrow opening under moderate pressure, such as around 40 psi. If the pressure drops before and after the nozzle is sufficient, the liquid will form small droplets in a plume instead of a stream of liquid. The shape of the spray plume may be changed by the shape of the exit nozzle, thereby making a fan shaped plume or a conical shaped plume. The shape of the plume can also be altered using compressed air, forcing the plume into a fan. 
     Alternately, air assisted atomization may be used. Air-assisted atomization uses an air venturi to suck a stream of liquid into a fast-moving airstream. The liquid breaks up into small droplets as it leaves the nozzle. Additional air may be used to shape the plume into a fan shape. Alternatively, a bell coater could be used to generate a cloud of atomized coating. A bell coater works by allowing coating to run onto a either a disk or bell-shaped device spinning at high speed. Coating is flung off the disc in very small drops. Alternatively, atomization nozzles that include an acoustic horn or an acoustic transducer can be used to atomize a mixture of insulating elements and fiber. The acoustic horn can be housed directly behind an atomization orifice, or the nozzle itself may be energized with acoustic energy supplied by a transducer. The acoustic energy may be audible—around 1000 Hz to 15,000 Hz, or it may be ultrasonic from 15,000 Hz to 40,000 Hz. 
     Paper packaging (e.g., containers  60  shown in  FIGS. 14A-18B ), formed from the insulated paper products  100 / 100 ′/ 100 ″ made using the present invention, may include a wide variety of formats, including: regular slotted container (RSC), overlap slotted container, full overlap slotted container, special center slotted container, Bag-in-Box, center special overlap slotted container, center special full-overlap slotted container, snap- or 1-2-3-bottom box with tuck top, snap- or 1-2-3-bottom box with RSC top, Full Bottom File Box, Hamper Style, Ft. Wayne Bottom or Anderson Lock Bottom, Bellows Style top and Bottom Container, Integral Divider Container, RSC with Internal Divider or Self Divider Box, Full-telescope Design-style Box, Full-telescope Half-slotted Box, Partial-Telescope Design-style Box, Partial-telescope half-slotted box, Design-Style Box with cover, Half-slotted Box with cover, Octagonal Double Cover Container, Double cover box, Interlocking Double-Cover box, double-thickness score-line box, one-piece folder, two-piece folder, three-piece folder, fiver panel folder, one piece folder with air cell/end buffers (used to protect e.g. books), wrap-around blank, tuck folder, one piece telescope, double-slide box, number 2 or 3 bliss box, recessed end box, self-erecting box, pre-glued auto bottom with RSC top flaps, four corner tray, self-erecting six-corner tray, flange box, Arthur lock bottom, valentine lock container, reverse valentine lock container. 
     Medium board used in the insulated paper products  100 / 100 ′/ 100 ″ made using the present invention may be fluted with flutes of different dimensions. See, for example, exemplary fluted medium board  23  shown in  FIGS. 6A-6D ). The Fiber Box Handbook defines flutes and flute dimensions as: A, B, C, E, F, G, K, N, as well as R/S/T/D. The liner and medium papers may also be tested and rated by different burst grade: 125-350 SW, 23-55 ECT, 200-600 DW, 42-82 ECT DW, 700-1300 TW, 67-112 ECT TW. The carton or box (e.g., box  61 ) may then be folded into the following industry known styles: reverse tuck, snap lock, automatic bottom, straight tuck, tuck top snaplock bottom, tuck top automatic bottom, seal end, beers, mailing envelopes, folder, and simplex. 
     As discussed herein, the insulated paper products of the present invention may comprise a single paper layer with insulating material dispersed therein or thereon, or may comprise two or more paper layers in combination with insulating material, wherein the insulating material is within one or more of the paper layers of the insulated paper product and/or is present as a component within the insulated paper product (e.g., as a separate layer from the paper layers and/or as a filler within a layer or component of the insulated paper product). See, for example, exemplary insulated paper products  100 / 100 ′/ 100 ″ in  FIGS. 1-6D . 
     The insulated paper products made using the present invention may further comprise one or additional layers other than the one or more paper layers and possible layers of insulating material. Suitable additional layers may include, but are not limited to, a coating that provides enhanced emissivity of the insulated paper product, a coating that provides a desired color and/or surface texture for the insulated paper product, and a coating that provide enhanced water-repellency (e.g., waterproofing properties) to the insulated paper product. See, for example, exemplary insulated paper products  100 / 100 ′/ 100 ″ in  FIGS. 6A-6D . 
     In exemplary insulated paper product  100 / 100 ′/ 100 ″ shown in  FIG. 6A , a corrugated cardboard structure  100 / 100 ′/ 100 ″ comprises two liner boards  21 / 22  bonded to a fluted medium board  23 . One (or both) of the liner boards  21 / 22  may be coated (e.g., clay coated) with coating layer  30  for aesthetics. The fluted medium  23  may have a range of flute dimensions, which are classified by the industry as A-flute through F-Flute. Each liner board  21 / 22  may be made from one ply of paper  10 / 100 ′, or it may comprise two or more plies  10 / 100 ′. Other types of board that could be used in combination with the above-described insulated paper products  100 / 100 ′/ 100 ″ discussed above: pressboard—pressed fiber board; honeycomb board—e.g., two liner boards  21 / 22  with a honeycomb spacer in between. 
     In addition, any of the insulated paper products made using the present invention described herein may be configured into a variety of shapes. For example, in some embodiments, the insulated paper product is in the form of an insulated cup or mug that may be used to house a hot beverage such as coffee. Such insulated paper products may be used instead of STYROFOAM® cups, eliminating the disposal and environmental problems associated with STYROFOAM® cups. In other embodiments, the insulated paper product is in the form of insulated packaging for temporary storage and transport of items such as food, medicines, etc. Such insulated paper products may be in the form of an insulated box, corrugated or not corrugated, as well as many other packaging items discussed herein. See, for example, exemplary insulated paper products  100 / 100 ′/ 100 ″ in  FIGS. 14A-18B . 
     Regardless of configuration and/or shape, the insulated paper products  100 / 100 ′/ 100 ″ made using the present invention provide a degree of insulation due to the construction of one or more paper layers  10  within a given insulated paper products  100 / 100 ′/ 100 ″. For example,  FIGS. 20A-20B  depict cross-sectional representations of exemplary paper composite layers  10  containing insulating material particles  12 , represented as circles, and fibers  11 . Both paper composite layers  10  contain the same number of circles, representing the insulating material particles  12 . The paper composite layer  10  shown in  FIG. 20A  has a substantially uniform distribution of insulating material particles  12 , whereas the paper composite layer  10  shown in  FIG. 20B  has a non-uniform distribution of insulating material particles  12 . 
     In addition,  FIGS. 21A-21B  provide a representation of possible conductive pathways that heat could take through exemplary paper composite layers  10  shown in  FIGS. 20A-20B . While materials made using the present invention should not be limited by theory, in the case of the paper composite layer  10  shown in  FIG. 20A , it is believed that the insulating particles  12 , evenly distributed, lengthen the pathway of the conducted heat, thereby slowing heat transfer down. While the paper composite layer  10  shown in  FIG. 20B  has the same number of particles  12  (represented by the same number of circles), the particles  12  are concentrated in a narrow layer of the paper composite layer  10 . Heat is partially blocked by the high concentration of insulating particles  12 , reducing heat flow considerably in the paper composite layer  10  shown in  FIG. 20B  compared to the paper composite layer  10  shown in  FIG. 20A . 
     The present invention is further directed to methods of making and using the herein disclosed and described insulated paper products. The insulated paper products may be made using papermaking equipment and techniques so as to produce one or more paper layers. As discussed herein, the methods of making the insulated paper products of the present invention involve the strategic placement of one or more insulating materials within a given insulated paper product and/or the strategic placement of one or more optional coatings on the insulated paper product so as to provide superior insulating properties, as well as other properties to the insulated paper product. Exemplary method steps and procedures for forming insulated paper products of the present invention are shown/described in  FIGS. 7-13I . 
       FIG. 7  describes an exemplary method  200  for forming paper from wood pulp and pre-consumer trimmings/scrap cardboard. After removal of bark and leaves etc., a wood composition of tree-wood is approximately ⅓ cellulose, ⅓ lignin, and ⅓ water. Wood is fed into a disintegrator  201 , which grinds the wood and feeds it into a beater  202 . Pulp is made in the beater  202 . After prolonged beating, the fibers undergo morphological changes. Fibers tend to collapse from round fibers into more of a kidney shaped cross-section, and the fibers become slightly more hydrophobic as beating continues. 
     As the layers of paper are formed and further processed, trimmings and rejected card (e.g., damaged, warped, etc.) is shredded and fed back into the pulping process. The card is washed in a wash clean device  203  to the extent possible to remove inks etc., then fed back into the beater  202 . 
       FIGS. 8A-8C  depict an exemplary process of forming paper sheets  10 . As shown in  FIG. 8A , pulp (furnish) is pumped into a header box  204 . The fiber content of the furnish is approximately 1-2 wt % at this stage. A gate  205  allows furnish to flow out onto the moving forming wire (a fine mesh conveyor.)  206 . The forming wire  206  may be 75-100 feet long. Initially, water drains via gravity, however, further down, vacuum boxes  207  beneath the wire  206  assist water removal, increasing the fiber content to around 20-30 wt %. 
     As shown in  FIG. 8B , the material (˜20-30 wt % fiber) is then fed through one or more felt presses  208 , which “blot” the precursor paper (i.e., precursor to paper layer  10 ), removing more water, and increasing the fiber content to around 45-50 wt %. If starch or another additive is to be applied, then that may be done at the size press  209  prior to drying. 
     As shown in  FIG. 8C , drying may be affected in a number of ways, including running over steam cans  210 , or entering a long hot air-drying tunnel (not shown). After passing through calendar rolls  211  and prior to winding, the paper  10  may be between 6 to 10% moisture content. 
       FIG. 9  depicts an exemplary furnish flowing out of a header box gate  205  onto the moving forming wire (a fine mesh conveyor.)  206 , showing water draining through the moving forming wire  206 , and fibers coalescing and concentrating as the wire  206  moves along. 
       FIG. 10  depicts an exemplary process step for forming a multiple ply linerboard  100 . The linerboard  100  may be made from more than one paper ply  10  during the manufacturing process. More than one header box  204  and wire line  206  may be running simultaneously, so that two or more wet paper sheets  10  are combined at laminator nip rolls  212  prior to entering the felt press  208 .  FIG. 10  shows three plies  10  being combined to make a thicker linerboard  100  prior to entering a felt press  208 . 
       FIG. 11  depicts details of an exemplary linerboard  100  suitable for use in forming an insulated paper product  100 / 100 ′/ 100 ″ of the present invention or a component (e.g., a layer or outer linerboard) of an insulated paper product  100 / 100 ′/ 100 ″ of the present invention. As shown in  FIG. 11 , exemplary linerboard  100  comprises two sheets of paper  10  laminated to one another. Exemplary linerboard  100  further comprises a first clay coating  30  directly on an outer surface  13  of one of the paper layers  10 , and an outermost second white clay coating  30  so as to provide a printable surface/layer  38  for exemplary linerboard  100 . First clay coating  30  evens out the valleys and troughs of the rough paper  10 , leaving a smooth surface for high-quality printing. 
       FIG. 12  depicts details of another exemplary linerboard  100  suitable for use in forming an insulated paper product  100 / 100 ′ of the present invention or a component (e.g., a layer or outer linerboard) of an insulated paper product  100 / 100 ′ of the present invention. As shown in  FIG. 12 , a thermally insulating additive layer  20  comprising insulating material  12  may be incorporated into an exemplary linerboard  100  via an additive applicator  213 . In this case, layer  20  of insulating material  12  is positioned between two layers of paper  10  within exemplary linerboard  100  comprising three layers of paper  10 . As shown in  FIG. 12 , a second additive applicator  213  could be used to provide another layer of additives (e.g., insulating material  12  or some other material) between the other two layers of paper  10  within exemplary linerboard  100  comprising three layers of paper  10 . 
       FIGS. 13A-13I  depict various ways of incorporating insulating material  12  within or on a given paper layer  10  or an insulated paper product  100 / 100 ′. As shown in  FIG. 13A , thermally insulating material  12  is added to the pulp, wherein the thermally insulating material  12  has a density that that is close to that of water. In this case, as the furnish drains, the insulating materials  12  are incorporated evenly, substantially uniformly throughout the paper  10  thickness. 
     In  FIG. 13B , a non-uniform distribution of insulating material  12  results from the use of insulating material  12  having a density lower (or much lower) than that of water. In this case, gravitational forces cause water to drain downward, but insulating material  12  tends to move upward as the furnish proceeds along moving wire  206 . This leads to a higher concentration of insulating particles  12  on an upper side/surface of the paper  10 . In some embodiments of the present invention, it has been surprisingly discovered that the insulating properties of a paper layer  10  are enhanced when the insulating additives  12  are concentrated on one face of the paper  10  versus distributed substantially uniformly throughout the thickness. 
     In  FIG. 13C , another procedure is shown so as to result in a non-uniform distribution of insulating particles  12  within an insulated paper product  100 / 100 ′. As shown in  FIG. 13C , a second head box  204  may be used to deposit a layer of insulating mater  12  and optional fibers on top of a lower layer of fibers (e.g., furnish) as the combined furnish proceeds along moving wire  206 . 
     In  FIG. 13D , another procedure is shown so as to result in a non-uniform distribution of insulating particles  12  within an insulated paper product  100 / 100 ′. As shown in  FIG. 13D , a third head box  204  may be used to deposit a layer of insulating mater  12  and optional fibers on top of a lower layer of fibers (e.g., furnish) as the combined furnish proceeds along moving wire  206 . 
     In  FIG. 13E , another procedure is shown so as to result in a non-uniform distribution of insulating particles  12  within an insulated paper product  100 ′. As shown in  FIG. 13E , a first and a second head box  204  may be used to form two plies of fiber. A middle layer containing insulating material  12  is deposited as a liquid via a slot-die coater  261 , or via a spray boom  262 , or as a solid via a shilling roller  263 . In  13 E, the top layer of pulp is first cast onto a separate wire  206 , and then transferred onto the middle layer of the non-uniform composite  100 ′. The slot-die coaters  261  are well known, being similar to curtain coaters. Slot-die coaters  261  may include an agitation means (not shown) within the head  265  to ensure that feed is consistent and settling is avoided. More advanced slot-die coaters  261  include such inventions as the Hydra-Sizer technology supplied by GL&amp;V Pulp &amp; Paper Group, Lawrenceville Ga. 
     In  FIG. 13F , another procedure is shown so as to result in a non-uniform distribution of insulating particles  12  within an insulated paper product  100 ′. As shown in  FIG. 13F , a nozzle  229  is used to feed pulp  11  into the gap  268  between a vacuum roll  267  and a forming felt  206 . A middle layer containing insulating material  12  is deposited as a slurry in layer  20 . In  13 F, the top layer of pulp  11  is applied by a second head box nozzle  229 . Such nozzle pulp applicators  229  are described in U.S. Pat. No. 5,645,689 entitled “Multilayer Headbox” to Voith Sulzer Papiermaschinen GmbH. Furthermore, Inventia disclose ‘Aq-Vane’ technology for preventing mixing of layers as they are delivered by a multi-layered head. Aq-Vane incorporates an interstitial layer of water between layers of pulp as they are laid down. “ Multi - layer technology in papermaking ” by Daniel Soderberg, of Innventia, and the  KTH Royal Institute of Technology, Stockholm: Presentation at the Marcis Wallenberg Prize Symposium , Stockholm, Sweden, Oct. 2, 2012. 
       FIG. 13G  depicts another method of making an insulated paper product  100 ′ with non-uniform cross section containing an uneven distribution of insulating material  12 . A multi-layer headbox  204  is used to put down the first two layers (e.g., each of which independently comprises pulp  11  and/or insulating material  12 ) on a forming wire  206 , which are then pressed with felt. Consecutive layers (e.g., layers  3  and  4 , each of which independently comprises pulp  11  and/or insulating material  12 ) are added followed by felt presses after each additional layer. 
       FIG. 13H  depicts details of another procedure to result in a non-uniform distribution of insulating particles  12  within an insulated paper product  100 ′. As shown in  FIG. 13H , a first and a second head box  204  may be used to form two plies  10  of fiber  11 . Zones A through G represent various observable stages of water removal from the pulp  11 . The first header box  204  lays down a low-solids pulp slurry  10  onto a first moving wire  206 , on top of a forming plate  241 . The forming plate  241  gives the pulp  11  time to spread out before fast draining begins in Zone B. Foils  243  touching beneath the wire  206  assist in pulling water from the pulp  11  in Zones B through E. The pulp  11  on the wire  206  in Zone A-B is very fluid, as the pulp  11  is still moving within the water. In Zone B-C the pulp  11  has ‘settled’ on the wire  206 , and the surface tension of the pulp  11  on wire  206  is flat. Beginning at C, the surface tension of the pulp  11  on the wire  206  is no longer flat, however, the pulp layer  10  is still wet enough to be visually ‘shiny.’ Zone C-E the wet pulp  11  on the wire  206  appears to become less and less smooth as the water drains and fiber  11  is left behind. As the pulp  11  travels over the first vacuum box  244  in Zone E, the pulp  11  becomes lighter, and non-reflective as much more of the moisture is removed than by gravity. By the time that the pulp  11  reaches Zone G, or Zone G2, the pulp  11  is at around 22 wt % of the sheet (i.e. 78 wt % water) and the two layers of paper  10  are able to bond together. If the pulp is significantly dryer than 22 wt % fiber/78 wt % water, then bonding between the two plies becomes weaker because the fibers are less free to interact as the sheet further dries. If the pulp is significantly wetter than 22 wt % fiber, then the two plies may bond less and the combined sheet may not be dry enough for transfer from the couch roll to the felt. Zones E2, F2, and G2 on the second forming wire  206  correspond to Zones E, F, G on first forming wire  206 . 
     Additional mechanisms beneath and above the wire (not shown) continue to assist in the removal of water at the wet end, before it is passes into the felt press. A steam shower may be used to heat up the wet paper. The elevated temperature reduces the viscosity of water, allowing it to be drained from the paper faster. Alternatively, the wet paper may be formed using hot water in the headbox. Another alternative could be that the moving web is heated using gas-fired or electrically powered infra-red heaters suspended above the wet paper web, to heat the web and reduce the viscosity of water. 
     Additional vacuum boxes may also be used to help extract additional water by sucking it through the back side of the wire. Finally, the wire carrying the wet sheet passes over a couch roll. The couch roll is a perforated cylinder connected to a vacuum line which sucks additional water from the paper as it is peels off the wire and onto the felt press. The felt press is the first part of the drying section, effectively pressing the wet sheet between two felts in a continuous manner. 
     One or more spray nozzle boom  262  with one or more nozzles  229  and/or slot-die coaters  261  were placed at various zones A-G and E2-G2 to apply a layer of insulating material  12  between the two paper layers  10 , and assessed for various properties. 
       FIG. 13I  depicts various different exemplary configurations of the spray nozzles  229  and spray booms  262 . Nozzles  229  may be arranged on spray booms  262  in a variety of ways to spray mixtures of paper pulp fibers  11  and insulating materials  12  onto the wet or dry paper  10 . Typically, the spray nozzle plume is flattened to give a fan shaped spray pattern, verses a conical spray emission. The nozzles  229  may be arranged in series, so that one spray boom  262  sprays on top of the deposit made by a spray-boom  262  further up line, there by depositing multiple layers of pulp  11  and/or insulating material  12  layers on top of one another. In one embodiment the spray nozzles  229  are arranged in such a way that the spray plumes intersect, so that most points of the web  10  receive deposition from more than one spray nozzle  229 . The fans of the spray nozzles  229  are angled with respect to the web direction. This allows multiple nozzles  229  to direct to the web  10  without the fans interfering with the momentum of neighboring spray fans. The spray nozzles  229  may be used in combination with a slot-die  261  or similar deposition technology. 
     Atomization or spray systems are numerous with many known in the art. Pressurized spray systems force liquids at high pressure through a narrow opening under moderate pressure, such as around 40 psi. If the pressure drops before and after the nozzle is sufficient, the liquid will form small droplets in a plume instead of a stream of liquid. The shape of the spray plume may be changed by the shape of the exit nozzle, thereby making a fan shaped plume or a conical shaped plume. The shape of the plume can also be altered using compressed air, forcing the plume into a fan. 
     Alternately, air assisted atomization may be used. Air-assisted atomization uses an air venturi to suck a stream of liquid into a fast-moving airstream. The liquid breaks up into small droplets as it leaves the nozzle. Additional air may be used to shape the plume into a fan shape. Alternatively, a bell coater could be used to generate a cloud of atomized coating. A bell coater works by allowing coating to run onto a either a disk or bell-shaped device spinning at high speed. Coating is flung off the disc in very small drops. Alternatively, atomization nozzles that include an acoustic horn or an acoustic transducer can be used to atomize a mixture of insulating elements and fiber. The acoustic horn can be housed directly behind an atomization orifice, or the nozzle itself may be energized with acoustic energy supplied by a transducer. The acoustic energy may be audible—around 1000 Hz to 15,000 Hz, or it may be ultrasonic from 15,000 Hz to 40,000 Hz. 
     The insulated paper products made using the apparatus, systems and methods of the present invention may further comprise one or more of the following features: 
     (1) Fiber Blend, Recycling, and Strength: 
     Short length fibers tend to come from refined hardwood, while longer fibers come from softwood. A good ratio of 75% softwood 25% hardwood balances the properties of the two types of fiber, optimizing tensile strength. Recently, hemp fibers have come under increasing attention as a paper additive. Hemp fibers are far longer than other pulp fibers, help increase strength due to increasing contact points and bonding, and so may be subjected to multiple recycling steps—far more than regular wood fibers. Hemp fibers, being much longer than softwood may be recycled around 40 times vs. 6 for other types of fiber. One or more of these materials/features could be incorporated into any of the here-in described insulated paper layer  10  and/or insulated paper product  100 / 100 ′ and/or corrugated paper product  100 ″ and/or storage container  60 . 
     In order to increase the ability of wood fibers to bond more through surface interactions, additional processes may be used to further fibrillate the fibers. For instance, the fibers may be subjected to an extreme high-shear environment, such as a colloid mill. The high sheer environment of two plate spinning in contact fibrillates cellulose fiber aggregates, increasing bonding, as well as the propensity to retain filler solids. Other ways to fibrillate the fiber can include prolonged beating in a mechanical Hollander pulp beater such as disclosed in the U.S. Pat. No. 1,883,051 or by high-sheer mixing, high-speed mixing, or media milling. Fibrillated cellulose may increase porosity of the paper and paper strength due to enhanced bonding area between fibers. Other ways to increase strength is by including nanocellulose into the paper formulation. One or more of these materials/features could be incorporated into any of the here-in described paper layer  10  and/or insulated paper product  100 / 100 ′ and/or corrugated paper product  100 ″ and/or storage container  60 . 
     The inventors have also found that when paper fibers are forced through a pressurized spray system, they may appear to fibrillate as if they had been further refined in a pulp beater or a colloid mill. Without wishing to be limited by theory, the inventors speculate that the sheer forces created by the pressure drop experienced by the fibers as they leave the nozzle may fibrillate and further refine the pulp. The fibrillation is believed to contribute to higher bond strength between the plies. 
     (2) Water Resistance Repulpability: 
     Rosin is often used as part of a two-part system to impart moisture resistance in paper (e.g., paper layer  10  and/or insulated paper product  100 / 100 ′ and/or corrugated paper product  100 ″ and/or storage container  60 ). The second part is post addition of aluminum salt solutions—e.g. aluminum chloride or aluminum sulfate. The aluminum reacts with the rosin soap to make a hydrophobic coating, which may impact repulpability yield. However, including a chelating agent somewhere in another component of the paper product may remove the aluminum from the rosin, thereby increasing the repulpability yield. Other areas of the paper that could carry the chelating agent may include the starch adhesive, and internal layer—for instance, the fluted medium, or an inner layer of the composite. Vapor-Guard R5341B or Barrier Grip 9471A (The International Group Inc., Titusville Pa.) are also useful as barrier coatings that provide the paper with a degree of grease and water resistance, and are described along with other suitable materials in Georgia Pacific Patent Application Publication No. US2019/0077537. 
     The present invention is further described by the following additional embodiments, examples, and claims. It should be understood that any feature and/or component described herein may be present alone or in combination with any other feature and/or component or combination of features and/or components described herein to form the here-in described paper layer  10  and/or insulated paper product  100 / 100 ′ and/or corrugated paper product  100 ″ and/or storage container  60  of the present invention. It should be further understood that the numbered embodiments provided below describe many embodiments of the present invention, some claimed and some unclaimed. Even though some of the features in the numbered embodiments provided below may not be claimed, the unclaimed feature(s) in the numbered embodiments provided below do form part of the present invention, and may optionally be incorporated into any claimed product. 
     (3) Thermally Insulating Fillers: 
     Thermally insulating fillers for addition at the wet end tend to be of very low density. These may include perlite, perlite coated with copper ions, expanded perlite, perlite hollow microspheres (such as available from Richard Baker Harrison Ltd., UK, or CenoStar Corporation (US), or Sil-Cel® microcellular aluminum silicate filler particles made by creating a structure of multicellular spherical bubbles comprising perlite, available from Silbrico (US), Sil-Cel® microspheres are available in a range of particle sizes, and may be coated or uncoated, or Dicaperl HP-2000 perlite microspheres, as sold by Dicalite (US), or flaked or milled perlite (such as Dicapearl LD1006 also sold by Dicalite), porous volcanic materials (such as pumice), vermiculite (including MicroLite® vermiculite dispersions, available from Dicalite), hollow expanded vermiculite, glass foams (such as Owens Corning), recycled glass foams (such as manufactured by GrowStone Inc.), cellular glass insulation materials, cenospheres (such as available from CenoStar Corp.), glass bubbles (such as available from 3M under the trade designations iM30K, iM16k, and K20, as well as Q-Cel glass), ceramic microspheres, plastic microspheres, and synthetic hollow microspheres (such as available from Kish Company Inc.), silica aerogels (such as those available from Aspen Aerogels, and those that may be incorporated into paints and coatings under the Enova® and Lumira® brand from Cabot), microporous polyolefin-based aerogels (such as disclosed in US Patent Application Publication No. 2016/0272777 to Aspen Aerogels Inc.), organic aerogels such as those disclosed in PCT WO 2019121242 to Henkel AG &amp; Co. KGAA which comprise thiol-epoxy based aerogels, xerogels (i.e., collapsed aerogels), seagels (i.e., microfoams made from agar and alginates), foamed starch, foamed paper pulp, agar, foamed agar, alginates, foamed alginates, bismuth oxychloride, metalized ceramics, metalized fibers, cadmium yellow pigment (cadmium disulfide), or any combination thereof. Examples of commercially available insulating materials  12  include, but are not limited to, FOAMGLAS® products commercially available from Owens Corning (Pittsburgh Pa.); and Growstone products commercially available from Growstone, LLC, a subsidiary of Earthstone International Inc. (Santa Fe, N. Mex.). Recycled glass suitable for use as insulating materials  12  is typically crushed to a finely divided powder and mixed with a blowing agent, e.g., carbon or limestone. It is then passed into a furnace hot enough to begin to melt the glass. As the glass powder particles begin to fuse, the blowing agent gives off a gas or vapor, forming bubbles inside the glass. This generates a porous, mostly closed cell glass foam, with high thermal and sound insulation properties. Vermiculite may also be used as a suitable insulating material  12 . Vermiculite is a hydrous phyllosilicate mineral that undergoes significant expansion when heated. Exfoliation occurs when the mineral is heated sufficiently, and the effect is routinely produced in commercial furnaces. Vermiculite is formed by weathering or hydrothermal alteration of biotite or phlogopite. 
     As taught in co-pending U.S. patent application Ser. No. 16/590,224 “Repulpable Insulated Paper Products and Methods of Making and Using the Same” filed on Oct. 1, 2019, the inventors found that adding a given amount of insulating additive and substantially evenly distributing it throughout the cross section of the web was less effective than taking the same amount of insulating material and concentrating it into a thinner layer within the paper cross sectional structure. In other words, forming a non-uniform distribution of insulating material through the cross section. This patent application is directed at machinery and adaptations of existing paper making assets to enable the production of such paper products. 
     ADDITIONAL EMBODIMENTS 
     Apparatus for Making Insulated Paper Products 
     1. An apparatus for making insulated paper products  10 / 100 / 100 ′ with an uneven cross-sectional distribution of insulating material  12  therethrough, said apparatus comprising:
         a first paper forming wire  206  moving along a first papermaking path;   a first headbox  204  positioned to deposit a first pulp slurry onto the first paper forming wire  206 ;   a first formation plate  241  positioned below the first paper forming wire  206  proximate the first headbox  204 ;   at least one first nozzle  229  positioned to deposit first insulating material  12  onto the first paper slurry  10  on the first paper forming wire  206 ;   one or more vessels  242 , each vessel  242  being (i) sized to house the first insulating material  12 , and (ii) in fluid communication with the at least one first nozzle  229 ;   a second paper forming wire  206  moving along a second papermaking path;   a second headbox  204  positioned to deposit a second pulp slurry  10  onto the second paper forming wire  206 ; and   a second formation plate (not shown) positioned below the second paper forming wire  206  proximate the second headbox  204 ;   wherein the second paper forming wire  206  is positioned to deposit a second paper ply  10  onto a first paper ply  10  with first insulating material  12  deposited thereon positioned along the first paper forming wire  206  so as to form the insulated paper product  10 / 100 / 100 ′ with the first paper ply  10  forming a first outer surface of the insulated paper product  10 / 100 / 100 ′ and the second paper ply  10  forming a second outer surface of the insulated paper product  10 / 100 / 100 ′ opposite the first outer surface.
 
2. The apparatus of embodiment 1, further comprising:
   at least one second nozzle  229  positioned to deposit second insulating material  12  onto the second paper slurry on the second paper forming wire  206 .
 
3. The apparatus of embodiment 2, wherein the one or more vessels (i) are sized to house the first insulating material  12  and the second insulating material  12 , and (ii) are in fluid communication with the at least one first nozzle  229  and the at least one second nozzle  229 .
 
4. The apparatus of embodiment 2 or 3, wherein the one or more vessels comprises (a) a first set of one or more first vessels (i) sized to house the first insulating material  12 , and (ii) in fluid communication with the at least one first nozzle  229 , and (b) a second set of one or more second vessels (i) sized to house the second insulating material  12 , and (ii) in fluid communication with the at least one second nozzle  229 .
 
5. The apparatus of any one of embodiments 2 to 4, wherein the one or more vessels contain the first insulating material  12  and the second insulating material  12 .
 
6. The apparatus of any one of embodiments 1 to 5, wherein the one or more vessels contains (i) a mixture of the first insulating material  12  and pulp fiber  11 , (ii) a mixture of the second insulating material  12  and pulp fiber  11 , or (iii) both (i) and (ii).
 
7. The apparatus of any one of embodiments 1 to 6, wherein the one or more vessels contains (i) a mixture of from about 50.0 weight percent (wt %) to about 98.0 wt % of the first insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, (ii) a mixture of from about 50.0 wt % to about 98.0 wt % of the second insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, or (iii) both (i) and (ii).
 
8. The apparatus of any one of embodiments 1 to 7, wherein the one or more vessels contains (i) a mixture of from about 90.0 wt % to about 98.0 wt % of the first insulating material  12  and from about 10.0 weight percent (wt %) to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, (ii) a mixture of from about 90.0 wt % to about 98.0 wt % of the second insulating material  12  and from about 10.0 weight percent (wt %) to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, or (iii) both (i) and (ii).
 
9. The apparatus of any one of embodiments 1 to 8, wherein the at least one first nozzle  229  is capable of depositing a high solids mixture (i.e. from about 2.0 wt % to about 30.0 wt % solids; or any value or range therebetween, in increments of 0.1 wt %) comprising water and from about 50.0 wt % to about 98.0 wt % of the first insulating material  12  and from about 50.0 weight percent (wt %) to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, onto the first paper slurry at a rate of between about 0.5 and about 5.0 US gallons per minute (or any value or range between about 0.5 and about 5.0 gallons per minute, in increments of 0.1 gallons per minute), and generating a dry basis weight of up to about 500 gsm grams per square meter (gsm) (or any value or range between about 50.0 gsm to about 500 gsm, in increments of 0.1 gsm) of the mixture.
 
10. The apparatus of any one of embodiments 2 to 9, wherein the at least one second nozzle  229  is capable of depositing a high solids mixture (i.e. from about 2.0 wt % to about 30.0 wt % solids; or any value or range therebetween, in increments of 0.1 wt %) comprising water and from about 50.0 wt % to about 98.0 wt % of the second insulating material  12  and from about 50.0 weight percent (wt %) to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, onto the second paper slurry at a rate of between about 0.5 and about 5.0 US gallons per minute, and generating a dry basis weight of up to about 500 gsm of the mixture.
 
11. The apparatus of any one of embodiments 1 to 10, wherein the at least one first nozzle  229  comprises two or more first nozzles  229 .
 
12. The apparatus of embodiment 11, wherein the two or more first nozzles  229  are positioned in series with one another along the first paper forming wire  206 .
 
13. The apparatus of any one of embodiments 2 to 12, wherein the at least one second nozzle  229  comprises two or more second nozzles  229 .
 
14. The apparatus of embodiment 13, wherein the two or more second nozzles  229  are positioned in series with one another along the second paper forming wire  206 .
 
15. The apparatus of any one of embodiments 1 to 14, further comprising: one or more spray booms  262 , each spray boom  262  ( a ) being positioned so as to extend over (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii) (e.g., in a width direction; perpendicular to the travel path of the paper slurry  10 ), and (b) being capable of supporting one or more nozzles  229 .
 
16. The apparatus of any one of embodiments 1 to 15, further comprising: one or more vacuum slots  244 , each vacuum slot  244  ( a ) being positioned below (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii) (e.g., in a width direction; perpendicular to the travel path of the paper slurry  10 ) and (b) being capable of removing water from a paper slurry  10  (e.g., first and/or second paper slurry  10 ) positioned on (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii).
 
17. The apparatus of any one of embodiments 1 to 16, further comprising: one or more foils  243 , each foil  243  ( a ) being positioned below (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii) (e.g., in a width direction; perpendicular to the travel path of the paper slurry  10 ) and (b) being capable of removing water from a paper slurry  10  (e.g., first and/or second paper slurry  10 ) positioned on (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii).
 
18. The apparatus of any one of embodiments 1 to 17, further comprising: one or more slot coaters  261 , each slot coater  261  ( a ) being positioned above (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii) (e.g., in a width direction; perpendicular to the travel path of the paper slurry  10 ) and (b) being capable of depositing material (e.g., pulp, additives, insulating material  12 , water, etc.) onto (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii).
 
19. The apparatus of embodiment 18, wherein at least one nozzle  229  is positioned downstream along the first paper forming wire  206  from the one or more slot coaters  261 .
 
20. The apparatus of any one of embodiments 1 to 19, further comprising: a process controller  245  capable of bringing the first paper ply  10  and the second paper ply  10  into contact with one another when the first paper ply  10  and the second paper ply  10  are still wet and able to bond to one another. Process controller  245  may control one or more process variables including, but not limited to, independent forming wire  206  speeds, independent header box  204  material deposition rates, independent nozzle  229  material deposition rates, independent slot coater  261  material deposition rates, etc.
 
21. The apparatus of any one of embodiments 1 to 20, further comprising: a process controller  245  capable of bringing the first paper ply  10  and the second paper ply  10  into contact with one another when the first paper ply  10  and the second paper ply  10  each independently comprise from about 70.0 wt % to about 90.0 wt % water (or any value or range between about 70.0 wt % and about 90.0 wt % water, in increments of 0.1 wt %), more preferably, from about 78.0 wt % to about 85.0 wt % water, and even more preferably, about 80.0 wt % to about 84.0 wt % water.
 
22. The apparatus of any one of embodiments 1 to 21, further comprising: one or more drying sections (not shown), wherein forced air in applied onto the insulated paper product  10 / 100 / 100 ′ to further remove water within the insulated paper product  10 / 100 / 100 ′.
 
23. The apparatus of any one of embodiments 1 to 22, further comprising: one or more edge trimmers  246  operatively adapted to trim an edge onto the insulated paper product  10 / 100 / 100 ′.
 
24. The apparatus of embodiment 23, wherein the one or more edge trimmers  246  comprise one or more water jet edge trimmers  246 . As discussed above, other apparatus/machine components that could be used in the present invention include, but are not limited to, one or more vacuum boxes, one or more couch rolls, one or more steam showers, one or more InfraRed heaters, or any combination thereof.
 
25. The apparatus of any one of embodiments 1 to 24, wherein the insulated paper product  10 / 100 / 100 ′ formed by the apparatus comprises at least one layer of insulating material  12 , wherein the layer of insulating material  12  comprises first insulating material  12  deposited by the at least one first nozzle  229  and second insulating material  12  deposited by the at least one second nozzle  229 .
 
26. The apparatus of any one of embodiments 1 to 25, wherein the insulated paper product  10 / 100 / 100 ′ formed by the apparatus comprises at least one layer comprising a mixture of insulating material  12  and pulp fiber  11 , wherein the mixture comprises first insulating material  12  and pulp fiber  11  deposited by the at least one first nozzle  229  and second insulating material  12  and pulp fiber  11  deposited by the at least one second nozzle  229 .
 
27. The apparatus of any one of embodiments 1 to 26, wherein the insulated paper product  10 / 100 / 100 ′ formed by the apparatus comprises five layers, the five layers being: (a) the first paper ply  10 , and (b) a layer of first insulating material  12  from the first paper forming wire  206 , (c) a central layer of pulp fibers  11  deposited onto (i) the first paper forming wire  206 , (ii) the second paper forming wire  206 , or (iii) both (i) and (ii), and (d) a layer of second insulating material  12 , and (e) the second paper ply  10  from the second paper forming wire  206 . See, for example,  FIG. 5A .
       

     Systems for Making Insulated Paper Products 
     28. A system for making insulated paper products  10 / 100 / 100 ′ with an uneven cross-sectional distribution of insulating material  12  therethrough, said system comprising: 
     the apparatus of any one of embodiments 1 to 27; 
     pulp fibers  11 ; and 
     first insulating material  12 . 
     29. The system of embodiment 28, further comprising: second insulating material  12 .
 
30. The system of embodiment 28 or 29, further comprising: (i) a mixture of from about 50.0 wt % to about 98.0 wt % of first insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, (ii) a mixture of from about 50.0 wt % to about 98.0 wt % of second insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, or (iii) both (i) and (ii).
 
31. The system of any one of embodiments 28 to 30, further comprising: (i) a mixture of from about 90.0 wt % to about 98.0 wt % of first insulating material  12  and from about 10.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, (ii) a mixture of from about 90.0 wt % to about 98.0 wt % of second insulating material  12  and from about 10.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, or (iii) both (i) and (ii).
 
32. The system of any one of embodiments 28 to 31, wherein each of the first insulating material  12  and the second insulating material  12  independently comprises particles (i) having an average particle size of less than about 1000 microns (μm), and (ii) comprising perlite, expanded perlite, perlite hollow microspheres, perlite microspheres, milled expanded perlite, perlite flakes, cenospheres, glass bubbles, glass microbubbles, vermiculite, hollow expanded vermiculite, or any combination thereof.
 
33. The system of embodiment 32, wherein the particles having an average particle size of less than about 500 microns (μm).
 
34. The system of embodiment 32 or 33, wherein the particles having a multi-modal particle size distribution.
 
35. The system of any one of embodiments 32 to 34, wherein said particles consist of perlite, expanded perlite, perlite hollow microspheres, perlite microspheres, milled expanded perlite, perlite flakes, or any combination thereof.
 
36. A system for making insulated paper products  10 / 100 / 100 ′ with an uneven cross-sectional distribution of insulating material  12  therethrough, said system comprising:
         (I) an apparatus comprising:
           a first paper forming wire  206  moving along a first papermaking path;   a first headbox  204  positioned to deposit a first pulp slurry onto the first paper forming wire  206 ;   a first formation plate  241  positioned below the first paper forming wire  206  proximate the first headbox  204 ;   at least one first nozzle  229  positioned to deposit first insulating material  12  onto the first paper slurry  10  on the first paper forming wire  206 ;   one or more vessels  242 , each vessel  242  being (i) sized to house the first insulating material  12 , and (ii) in fluid communication with the at least one first nozzle  229 ;   a second paper forming wire  206  moving along a second papermaking path;   a second headbox  204  positioned to deposit a second pulp slurry  10  onto the second paper forming wire  206 ;   a second formation plate (not shown) positioned below the second paper forming wire  206  proximate the second headbox  204 ; and   at least one second nozzle  229  positioned to deposit second insulating material  12  onto the second paper slurry on the second paper forming wire  206 ,   
           wherein the second paper forming wire  206  is positioned to deposit a second paper ply  10  onto a first paper ply  10  with first insulating material  12  deposited thereon positioned along the first paper forming wire  206  so as to form the insulated paper product  10 / 100 / 100 ′ with the first paper ply  10  forming a first outer surface of the insulated paper product  10 / 100 / 100 ′ and the second paper ply  10  forming a second outer surface of the insulated paper product  10 / 100 / 100 ′ opposite the first outer surface; and   (II) pulp fiber  11 , first insulating material  12 , and second insulating material  12 .
 
37. The system of embodiment 36, wherein the apparatus comprises the apparatus of any one of embodiments 2 to 27; and the first insulating material  12 , and the second insulating material  12  are each independently one or more particles recited in any one of embodiments 32 to 35.
       

     Methods of Making Insulated Paper Products 
     38. A method of making an insulated paper product  10 / 100 / 100 ′ with an uneven cross-sectional distribution of insulating material  12  therethrough, said method comprising: forming one or more first paper layers  10  with first insulating material  12  thereon and/or therein on the first paper wire  206 ; forming one or more second paper layers  10  with optional second insulating material  12  thereon and/or therein on the second paper wire  206 ; and combining the one or more first paper layers  10  with first insulating material  12  with the one or more second paper layers  10  with optional second insulating material  12  so as to form the insulated paper product  10 / 100 / 100 ′ with the one or more first paper layers  10  forming a first outer surface of the insulated paper product  10 / 100 / 100 ′ and the one or more second paper layers  10  forming a second outer surface of the insulated paper product  10 / 100 / 100 ′ opposite the first outer surface.
 
39. The method of embodiment 38, further comprising: depositing the second insulating material  12  onto the one or more second paper layers  10  on the second paper forming wire  206 .
 
40. The method of embodiment 38 or 39, further comprising: depositing (i) a mixture of the first insulating material  12  and pulp fiber  11 , (ii) a mixture of the second insulating material  12  and pulp fiber  11 , or (iii) both (i) and (ii) onto the first paper forming wire  206  and/or the second paper forming wire  206 .
 
41. The method of any one of embodiments 38 to 40, further comprising: depositing (i) a mixture of from about 50.0 wt % to about 98.0 wt % of the first insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, (ii) a mixture of from about 50.0 wt % to about 98.0 wt % of the second insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, or (iii) both (i) and (ii) onto the first paper forming wire  206  and/or the second paper forming wire  206 .
 
42. The method of any one of embodiments 38 to 41, further comprising: depositing (i) a mixture of from about 90.0 wt % to about 98.0 wt % of the first insulating material  12  and from about 10.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, (ii) a mixture of from about 90.0 wt % to about 98.0 wt % of the second insulating material  12  and from about 10.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, or (iii) both (i) and (ii) onto the first paper forming wire  206  and/or the second paper forming wire  206 .
 
43. The method of any one of embodiments 38 to 42, wherein the at least one first nozzle  229  deposits a high solids mixture (i.e. from about 2.0 wt % to about 30.0 wt % solids; or any value or range therebetween, in increments of 0.1 wt %) comprising water and from about 50.0 wt % to about 98.0 wt % of the first insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, onto the first paper slurry at a rate of between about 0.5 and about 5.0 US gallons per minute, and generating a dry basis weight of up to about 500 grams per square meter (gsm) of the mixture onto the first paper forming wire  206 .
 
44. The method of any one of embodiments 38 to 43, wherein the at least one second nozzle  229  deposits a high solids mixture (i.e. from about 2.0 wt % to about 30.0 wt % solids; or any value or range therebetween, in increments of 0.1 wt %) comprising water and from about 50.0 wt % to about 98.0 wt % of the second insulating material  12  and from about 50.0 wt % to about 2.0 wt % of pulp fiber  11 , based on total solids in the mixture, onto the second paper slurry at a rate of between about 0.5 and about 5.0 US gallons per minute, and generating a dry basis weight of up to about 500 gsm of the mixture onto the second paper forming wire  206 .
 
45. The method of any one of embodiments 38 to 44, wherein the at least one first nozzle  229  comprises two or more first nozzles  229 .
 
46. The method of embodiment 45, wherein the two or more first nozzles  229  are positioned in series with one another along the first paper forming wire  206 .
 
47. The method of any one of embodiments 38 to 46, wherein the at least one second nozzle  229  comprises two or more second nozzles  229 .
 
48. The method of embodiment 47, wherein the two or more second nozzles  229  are positioned in series with one another along the second paper forming wire  206 .
 
49. The method of any one of embodiments 38 to 48, further comprising: incorporating insulating material  12  within the one or more first paper layers  10  and/or the one or more second paper layers  10 .
 
50. The method of embodiment 49, wherein said incorporating step comprises forming a non-uniform distribution of the insulating material  12  within at least one paper layer  10  of the one or more first paper layers  10  and/or the one or more second paper layers  10 .
 
51. The method of any one of embodiments 38 to 50, further comprising: incorporating one or more additives, other than the insulating material  12 , into at least one paper layer  10  within the one or more first paper layers  10  and/or the one or more second paper layers  10 . Suitable additives include, but are not limited to, copper ions, waxes, synthetic (e.g., polymeric or glass) fibers, silica, surface modified silica, transition metal surface modified silica, cyclodextrin, sodium bicarbonate, silicones to impart grease and water resistance, metalized ceramic particles, metalized fibers, cationic starches, cationic polymers, such as cationic guar gum, poly(ethylene imine) (e.g., poly(ethylene imine marketed as Polymin P and available from Aldrich Chemical), fillers, sizes, binders, clays including bentonite clay, kaolin clay, and other minerals, calcium carbonate, calcium sulfate, and other materials that may be added to paper products for different reasons, and any combinations thereof. The filler may make the paper more receptive to printing, for instance, or make the paper glossy. Many fillers have a density greater than 1.0 g/cm 3 . Flocculants and retention aids, may also be included such as high molecular weight poly(acrylamide), poly(ethylene imine), cationic quar gum, and other cationic polymers. Sizes and binders may also be added to help provide strength to papers, and can include starches, hydrocolloids, artificial and natural polymer latexes, such as RHOPLEX® acrylic resins from Dow Chemical and ROVENE® binders from Mallard Creek Polymers (Charlotte N.C.). Water soluble polymers, such as poly(vinyl alcohol), and poly(acrylic acid) may also be added to the paper. Sometimes, water resistance on the final box is required. Vapor-Guard R5341B or Barrier Grip 9471A (The International Group Inc., Titusville Pa.) are useful as barrier coatings that provide a given paper layer  10  with a degree of grease and/or water resistance.
 
52. The method of any one of embodiments 38 to 51, further comprising: coating an outer surface  13 / 15  of the insulated paper product  10 / 100 / 100 ′ with an insulating coating, the insulating coating comprising (i) one or more insulating materials comprising bismuth oxychloride, mica, bismuth oxychloride-coated mica, zinc oxide, aluminum-doped zinc oxide, zinc sulfide, cadmium sulfide, bismuth vanadate, gypsum, sericite, powdered silicon, silver-coated glass bubbles, aluminum oxide, hollow polymeric microsphere pigments, or any mixture or combination thereof, and (ii) a binder.
 
53. The method of embodiment 52, wherein the insulating coating comprises one or more insulating materials comprising bismuth oxychloride, mica, zinc oxide, aluminum-doped zinc oxide, zinc sulfide, cadmium sulfide, bismuth vanadate, sericite, or any mixture or combination thereof.
 
54. The method of embodiment 52 or 53, wherein the insulating coating comprises one or more insulating materials comprising bismuth oxychloride, mica, zinc oxide, aluminum-doped zinc oxide, or any mixture or combination thereof.
 
55. The method of any one of embodiments 52 to 54, wherein the insulating coating comprises from about 50.0 weight percent (wt %) to about 99.9 wt % of the one or more insulating materials and from about 50.0 wt % to about 0.1 wt % of the binder.
 
56. The method of any one of embodiments 52 to 55, wherein the insulating coating comprises from about 90.0 wt % to about 99.9 wt % of the one or more insulating materials and from about 10.0 wt % to about 0.1 wt % of the binder.
 
57. The method of embodiment 56, wherein the binder comprises a latex binder.
 
58. The method of any one of embodiments 52 to 57, wherein each insulating coating independently comprises one or more coating layers with each coating layer comprising the insulating material and the binder.
 
59. The method of any one of embodiments 52 to 58, wherein at least one insulating coating comprises two or more coating layers with each coating layer comprising the insulating material and the binder.
 
60. The method of any one of embodiment 59, wherein the two or more coating layers comprise (i) a first coating comprising zinc oxide, aluminum-doped zinc oxide, or any mixture or combination thereof, and (ii) a second coating applied onto the first coating and comprising bismuth oxychloride, bismuth oxychloride-coated mica, or any mixture or combination thereof.
 
61. The method of any one of embodiments 38 to 06, wherein the insulating material  12  has a material density of less than 1.0 g/cm 3  (or any value between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., 0.48 g/cm 3 , or any range of values between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., from 0.10 g/cm 3  to 0.50 g/cm 3 ).
 
62. The method of any one of embodiments 38 to 61, wherein at least one layer  10  of the insulated paper product  10 / 100 / 100 ′ has a layer density of less than 1.0 g/cm 3  (or any value between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., 0.78 g/cm 3 , or any range of values between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., from 0.20 g/cm 3  to 0.75 g/cm 3 ). It should be further understood that any number of layers  10  of the one or more paper layers  10  may have an independent layer density, each of which is less than 1.0 g/cm 3  (or any value between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., 0.44 g/cm 3 , or any range of values between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., from 0.18 g/cm 3  to 0.85 g/cm 3 ).
 
63. The method of any one of embodiments 38 to 62, wherein the insulated paper product  10 / 100 / 100 ′ has an integral paper product density of less than 1.0 g/cm 3  (or any value between 0.01 g/cm 3  and 0.99, g/cm 3  in multiples of 0.01 g/cm 3 , e.g., 0.77 g/cm 3 , or any range of values between 0.01 g/cm 3  and 0.99 g/cm 3 , in multiples of 0.01 g/cm 3 , e.g., from 0.18 g/cm 3  to 0.53 g/cm 3 ).
 
     In addition, it should be understood that although the above-described apparatus, systems and methods for making insulated paper products are described as “comprising” one or more components or steps, the above-described apparatus, systems and methods may “comprise,” “consists of,” or “consist essentially of” the above-described components or steps of the apparatus, systems and methods. Consequently, where the present invention, or a portion thereof, has been described with an open-ended term such as “comprising,” it should be readily understood that (unless otherwise stated) the description of the present invention, or the portion thereof, should also be interpreted to describe the present invention, or a portion thereof, using the terms “consisting essentially of” or “consisting of” or variations thereof as discussed below. 
     As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having,” “contains”, “containing,” “characterized by” or any other variation thereof, are intended to encompass a non-exclusive inclusion, subject to any limitation explicitly indicated otherwise, of the recited components. For example, an apparatus, system and/or method that “comprises” a list of elements (e.g., components, layers or steps) is not necessarily limited to only those elements (or components or steps), but may include other elements (or components or steps) not expressly listed or inherent to the apparatus, system and/or method. 
     As used herein, the transitional phrases “consists of” and “consisting of” exclude any element, step, or component not specified. For example, “consists of” or “consisting of” used in a claim would limit the claim to the components, materials or steps specifically recited in the claim except for impurities ordinarily associated therewith (i.e., impurities within a given component). When the phrase “consists of” or “consisting of” appears in a clause of the body of a claim, rather than immediately following the preamble, the phrase “consists of” or “consisting of” limits only the elements (or components or steps) set forth in that clause; other elements (or components) are not excluded from the claim as a whole. 
     As used herein, the transitional phrases “consists essentially of” and “consisting essentially of” are used to define apparatus, systems and methods that includes materials, steps, features, components, or elements, in addition to those literally disclosed, provided that these additional materials, steps, features, components, or elements do not materially affect the basic and novel characteristic(s) of the claimed invention. The term “consisting essentially of” occupies a middle ground between “comprising” and “consisting of”′. 
     Further, it should be understood that the herein-described apparatus, systems and methods may comprise, consist essentially of, or consist of any of the herein-described components, layers and features, as shown in the figures with or without any feature(s) not shown in the figures. In other words, in some embodiments, the apparatus, systems and methods of the present invention do not have any additional features other than those shown in the figures, and such additional features, not shown in the figures, are specifically excluded from the apparatus, systems and methods. In other embodiments, the apparatus, systems and methods of the present invention do have one or more additional features that are not shown in the figures. 
     The present invention is described above and further illustrated below by way of examples, which are not to be construed in any way as imposing limitations upon the scope of the invention. On the contrary, it is to be clearly understood that resort may be had to various other embodiments, modifications, and equivalents thereof which, after reading the description herein, may suggest themselves to those skilled in the art without departing from the spirit of the present invention and/or the scope of the appended claims. 
     EXAMPLES 
     Insulated paper products similar to exemplary insulated paper products  100 / 100 ′/ 100 ″/ 60  shown and described in  FIGS. 1-6D, 14A-21B and 26-27  were prepared on a Fourdrinier machine (see, for example,  FIG. 8A ) using a 24″ wide wire with various machine configurations to lay down insulating material in layers on top of newly formed wet paper. This pilot paper machine was also equipped with a second head box and a second Fourdrinier with the capability to add a second wet paper ply and lay it down on top of the first layer ( FIG. 13H ). 
     Example 1. Paper Containing Insulating Materials 
     Test Methods: 
     % Solids Analysis: 
     A polystyrene disposable weigh boat was accurately weighed to 4 decimal places (tare mass). Approximately 1-2 gram of liquid was placed in the weigh boat, and promptly weighed to four decimal places (gross-wet mass.) Subtracting the tare from the gross-wet mass gives the net-wet mass. The weigh boat was carefully tilted and rocked from side to side, allowing the liquid to coat the bottom of the weigh boat evenly, then it was placed in a cupboard for 24-48 hours to evaporate at room temperature. The dry weigh boat was re-weighed to four decimal places (gross-dry mass). Subtracting the tare from the gross-dry mass gives the net-dry mass. 
       % solids=100*net-dry/net-wet 
     Modified Lee&#39;s Disk Heat Transfer Rate Test Method 
     Lee&#39;s disk method is a known way to measure thermal conductivity in thin sheets with low conductivity. A modified version of the Lee&#39;s disk was used to measure the heat transfer rate of samples generated, assembled using available laboratory equipment, to enable a large number of tests to be conducted in a short period of time. Instead of allowing the materials to reach thermal equilibrium, a digital hotplate was used to maintain a set temperature for one side of the sample. The apparatus is depicted in  FIG. 34  (cross section) and  FIG. 35  (exploded cross section). 
     Materials/Equipment Used: 
     
         
         
           
             Paperboard sample(s) 
             Circular cutting device set to cut 113 mm diameter circles (100 cm 2 ) 
             Calipers 
             Scientific Balance, accurate to 0.001 g 
             Digital hot plate  70  that heats to at least 37° C. (98.6° F.) and with a heating surface  71  at least 113 mm in diameter 
             10×Aluminum disks  72 , 113 mm in diameter (100 cm 2 ) and painted matte black on one surface (McMaster 1610T37) 
             Insulating hot plate guard  73 , capable of withstanding temperatures greater than 37° C. (98.6° F.) and constructed to fit the hot plate  70  and the sample stack being used (McMaster 93475K65) 
             IR Camera  74  &amp; Image Analysis Software (the Flir E-40 Thermal Camera, available from Flir Systems Inc. Goleta Calif.) 
             Timer 
           
         
       
    
     Assumptions: 
     This test method assumes constant heat flow, and no edge losses or other effects from convection or radiation-based heat transfer (all the heat flows through the disks and sample). 
     Method: 
     1. Cut 102 mm diameter circular paper samples and label appropriately. Ideally at least three samples can be cut from a single sheet. Five samples are recommended for each datapoint. Measure and record the thickness and weight of each sample using Vernier calipers. 
     2. Turn on the hot plate  70  and set the temperature to 37° C. Place the Insulating Guard  73  around the hot plate  70 . Set one Aluminum disk  72  on the hot plate  70 , black side facing up. Once this disk  72  has reached 37° C., sample testing can begin. The temperature can be checked by using the IR camera  74 . 
     3. While the hot plate  70  heats up, allow the other Aluminum disks  72  to sit out and come to room temperature. Measure the room temperature using the IR camera  74 , and also use the IR camera  74  to confirm all the Aluminum disks  72  have reached room temperature. 
     4. When ready to test, in quick succession:
         Place the paper sample  10  on top of the hot plate aluminum disk  72     Place a room temperature aluminum disk  72  on top of the paper sample  10 , black side up   Start a timer for 1 and 2 minutes       

     5. At the end of one minute, record the temperature of the top black disc  72  registering in the Flir thermal camera  74 . After two minutes, once again record the temperature and take an IR image of the top surface  75  of the aluminum disk  72 . Remove the top aluminum disk  72  and paper sample  10 . Set aside to cool. 
     6. Repeat steps  4  &amp;  5  until all samples  10  have been tested. If running more than 9 tests, it must be ensured that the aluminum disks  72  cool all the way to room temperature before being reused. 
     Representative warming curves are shown in  FIG. 36 . The best technical way to approximate the thermal conductivity would be to monitor the temperature rise of the aluminum disk  72  measured over time until the system reached a steady state. The ambient room temperature would have to be taken into consideration too. To allow the inventors to undertake rapid screening, while compensating with variations in room temperature, a snapshot approach was chosen to record the temperature of the aluminum plate  72  via the Flir Thermal imaging camera  74 . A first measurement was made immediately after placing the sample  10  and aluminum disk  72  onto the pre-warmed hotplate (T 0 )  70  and then every 30 seconds for the next 3 mins 30 seconds. The temperature rise after 3 mins and 30 seconds was recorded in ° C. (T 3.5 ). The measurement was repeated, ideally 5 times and an average taken. 
       Delta  T=T   3.5  min− T   0  
 
     As the thickness of the sample also impacts the rate of heat transfer, the average thickness of the samples (d) was used to adjust the average temperature rise measurements over 3.5 mins. A “standard” thickness was chosen based upon a target material thickness (d std ). The average temperature rise was adjusted using the formula: 
       Thickness Adjusted Delta  T  TADT= T   3.5min   −T   0   *d/d   std . 
     The TADT is the heat transfer rate and is related to thermal conductivity in that the lower the TADT, then the lower the thermal conductivity of the sample. 
     % Ash Content: 
     These tests were carried out by Western Michigan State University, Kalamazoo Mich., according to TAPPI T 211 om-16 Ash in wood, pulp, paper and paperboard: combustion at 525° C. Approximately 10.0 g of paper was accurately weighed, and then ashed in a muffle furnace at 525° C. The remaining ash was then re-weighed to determine ash content. 
     % Moisture: 
     These tests were carried out by Western Michigan State University, Kalamazoo Mich., according to TAPPI T 550 om-13 Determination of equilibrium moisture in pulp, paper and paperboard. 
     Repulpability: 
     Repulpability was tested by SGS Integrated Paper Services Inc., Appleton Wis. according to the “Voluntary Standard for Repulping and Recycling Corrugated Fiberboard treated to Improve its Performance in the Presence of Water and Water Vapor Protocol of 2013”, generated by the Fiber Box Association, headquartered in Elk Grove Village, Ill., 60007. Repulpable means the test material that can undergo the operation of re-wetting and fiberizing for subsequent sheet formation, using the process defined in this standard. In the repulpability test, materials are weighed, pulped in a specific manner using laboratory equipment, run through a laboratory disintegrator, and then run through a screen. The amount of rejected material is compared to the material that could be reused as pulp to make board as a % by mass. Two figures are derived: The first is the acceptable recovery of the fiber based upon the mass of material first entered into the test, and the second is the percentage of the recovered fiber that is accepted, not rejected. These figures constitute the “% re-pulpability”, and the fiber box association has determined that a pass for both measures of repulpability is &gt;85%. Other parameters recorded are: a) material fouling the equipment during pulping or forming b) material that does not disintegrate and has to be removed (becomes part of the rejects) 
     Canadian Standard Method Pulp Freeness Test: 
     This test is used to measure the rate of drainage of water through pulp. The drainage rate has been shown to be related to the surface conditions and the swelling of the fibers. The pulp freeness was assessed at Western Michigan University according to TAPPI (Technical Association of Pulp and Paper Industries) test method T 227 om-09 as revised 2009, using a freeness tester apparatus, as described in the TAPPI test method. 
     Adhesive Bonding/Pin Adhesion and Ply Separation Test: 
     This is an important test to ensure the strength of the bonds between the flutes and the liner board, which in turn relates to the integrity and strength of the box structure. A jig is used, with pins that fit between the corrugated flutes. The stress force needed to separate the layers of the corrugated card is measured. The Fiber Box Association has several tests for this bond strength. 
     Estimated Ply Bonding Assessment Method: 
     Multi-ply paper sheets were assessed for ply bonding, and ranked from 1 to 6. This assessment was subjective, and based upon the difficulty or ease of separating the plies of the paper sheet. An assessment of 1 denotes that the two-ply separated with very little effort, whereas 6 denotes great difficulty in delamination. The assessment was based upon manually tearing, picking, and pulling the plies apart, observing and comparing the force needed to separate the plies. While subjective, we did find good general agreement between this assessment and the Scott Ply Bond test and Ring Crush data where it those were measured. 
     Scott Ply Bond Test Method 
     The Scott Plybond test measures the internal bonding strength of paper in the z-direction, using a lifting motion that is similar to peeling, however, performed in a repeatable manner. A pendulum strikes an aluminum angle bar that has been taped to the paper using double-sided sticky tape. If the paper has high internal bond strength, the energy in the pendulum is absorbed to a greater degree. This test can be used for both single-ply products and multi-ply products. Scott Ply Bond was tested by Western Michigan University, Kalamazoo Mich., according to TAPPI test method: TAPPI/ANSI T 569 om-14. 
     Ring Crush Test Method: 
     Ring crush testing was performed by SGS Integrated Paper Services Inc., Appleton Wis., according to TAPPI test method T 818 cm-18 Ring crush of paperboard flexible beam method. Ring crush basically gives a measure of paper strength in the machine and cross web directions. 
     Pulp Preparation Method—from Pre-Consumer OCC: 
     Commercial bailed re-consumer OCC (“Old Corrugated Cartons”—a mixture of clippings, as well as reject packaging) was fed into a disintegrator and disintegrated in hot water. The pulp was then let down with water to give a freeness of around 500 CSF (Canadian Standard Freeness) at a consistency of approximately 1.75%. Freeness of pulp is a measure of precisely how rapidly water can drain from a diluted fiber furnishes suspension. Drainage rate is related to the surface conditions and swelling of the fibers. Freeness of pulp tends to be decreased by refining and beating. The higher the freeness number, the more easily water will drain through the web. To further assist drainage on the wire, a retention aid was also added to the pulp stock tank. 
     Insulation Element Density: 
     The insulating elements used to mitigate conductive heat transfer are very low in density. 1 g of Innova aerogel powder occupies around 7 cm 3  of volume. The perlite microspheres and milled and classified expanded perlite flake are of similarly low density, in the range of 100-200 kg·m −3 . If we assume that the density of paper fiber is approximately 1 g·cm −3 , then the following is approximately true regarding the % by volume: 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                   
                 Approximate  
               
               
                   
                 % Perlite 
                 % Perlite 
               
               
                   
                 by mass: 
                 by volume: 
               
               
                   
                   
               
             
            
               
                   
                 66.7% 
                 93% 
               
               
                   
                   50% 
                 88% 
               
               
                   
                   30% 
                 75% 
               
               
                   
                   25% 
                 70% 
               
               
                   
                   20% 
                 64% 
               
               
                   
                   15% 
                 55% 
               
               
                   
                   10% 
                 44% 
               
               
                   
                   5% 
                 27% 
               
               
                   
                   
               
            
           
         
       
     
     Paper Machine Modifications: Slot-Die Coater and Spray Nozzle: 
     The inventors explored placement positions of various combinations of spray nozzle(s) and slot-die along the Fourdrinier, in positions A-G and E2-G2 ( FIG. 13H ) to form a multi-ply sheet of paper. 
     First header box Fourdrinier: laydown: Target basis wt: 135 gsm dry 
     Second head box Fourdrinier laydown: Target basis wt: 67 gsm dry 
     Spray nozzle: 1 US gallon per minute at 40 psi, 12″ nozzle height, 11″ wide spray fan: Positions A through C disrupted the pulp so much to cause web breaks. At positions D through G, the nozzle was able to deposit layers of various fillers and/or fiber pulp, which were then covered by a layer of fiber from the second headbox and Fourdrinier. 
     Top Ply: 67 gsm 
     Middle Ply: Formulation ID: JL3-039-07 
     1 gal per min spray nozzle, with 11″ spray fan, 40 psi. of the following:
         Water: 9.5 kg   Dry pulp: 0.0845 kg   iM30k glass bubbles 0.55 kg       

     Base ply: 135 gsm 
     Linespeed: 30 ft. per min 
     Pulp freeness: 400 SCF 
     The sheet ply bonding was assessed visually, and manually and ranked 1 to 6—with 6 being the best bonded and 1 being very easy to delaminate. 
     For Sample ID LO, 20 g of a solution of 0.5% cationic guar gum was added to the spray formulation as a retention aid. 
     For Sample ID LL, flaked expanded perlite (Dicapearl LD1006, Dicalite Corp.) was substituted for glass microbubbles in formulation JL3-039-07. No retention aid was used in the spray formulation in this case. 
                                                         Sheet           Estimated               Ash   Measured   TADT/° C.   Ply       Sample   Spray    Content    dry Basis    (average of 5   Bonding       ID   Position   %   wt./gsm   measurements)   (1-6)                                                        LC   D     15%   164   15.1   6       LE   E     21%   198   12.0   4       LN   F     18%   192   13.3   3       LO   F   19.8%   186   11.1   5       LL   F   29.4%   256   9.6   4                    
The lower the TADT, the better the insulation properties of the material. Ash content of the sheet was assumed to be substantially all due to the insulating additive introduced. Note that the sprayed insulating layer within sample ID LL contained 87% by mass of insulating additive (calculated).
 
     These data demonstrate that as the amount of applied additive increases, thermal insulation also increases. These data also show that interplay bonding is less satisfactory when the amount of additive is increased. 
     The slot-die system was also tested for web destruction and additive laydown. Water was run through the slot-die, which laid down a 9″ wide curtain on the base ply at 2.2 gallon per minute at positions A through D along the first wire. The slot-die was found to be gentle enough that it did not appear to disrupt the web, nor did it cause web breakage. Additives, such as 18 micron diameter glass microbubbles (sold as iM30k, supplied by 3M) were suspended in water, and were added to the pulp at positions B, C, and D. The additive was included into the paper web between two pulp sheets, one from the first headbox, and the other from the second headbox. However, the top and bottom ply did not bond at all in the areas in which the slot die laid down additive. This led to delamination of the plies in the final sheet. 
     While the slot-die could be modified to allow laying down mixtures of pulp and additive, the configuration of the slot-die and supporting equipment was not amenable to laying down mixtures of pulp and additive during this trial, due to clog formation. In order to achieve some mixing of the additive with the pulp fiber, a turbulizer was made by fastening commonly available multiple plastic self-locking nylon cable ties (such as UV resistant heavy duty cable ties, product model number TR88302 sold by TR Industrial, or sold as “Zip Ties” available for sale on www.ziptie.com) to a 1″ OD schedule 40 PVC pipe, leaving the excess cable tie ends aligned and pointing away from the pipe. The tips of the zip-ties were held just touching the top of the moving web at the point of introduction of the additive by the slot-die. The makeshift turbulizer was tested just upstream from the slot-die introduction point and just downstream (in the machine direction) from the introduction point. The turbulizers made a slight positive to bonding improvement, when the turbulizer was positioned approximately 3-5 mm downstream from the addition point, however the improvement was not sufficient to provide satisfactory inter-ply bonding (bonding ranking 2 vs. 1). 
     However, when the slot-die was used to first lay down additives in positions B, C, or D, then followed by spray application of fiber at positions E and/or F, ply bonding was improved and significant amounts of additive were introduced into the middle layer of the paper. Furthermore, the inventors also found that additional additives may be added to the spray along with the fiber to further increase additive levels, and hence thermal insulation. 
     Top Ply: 67 gsm 
     Middle Ply: Combination of Slot-die and Sprayed materials: 
     Slot Die Formulations at position C. 9″ laydown width. 
     
       
         
           
               
               
               
               
             
               
                   
                   
               
               
                   
                 Sample  
                   
                   
               
               
                   
                 ID 
                 Water 
                 iM30k 
               
               
                   
                   
               
             
            
               
                   
                 PA 
                 15.95 kg 
                  1.08 kg 
               
               
                   
                 PB 
                 16.49 kg 
                 0.540 kg 
               
               
                   
                 PC 
                 15.95 kg 
                  1.08 kg 
               
               
                   
                 PD 
                 15.95 kg 
                  1.08 kg 
               
               
                   
                 PE 
                 15.95 kg 
                  1.08 kg 
               
               
                   
                 PF 
                 14.87 kg 
                  2.16 kg 
               
               
                   
                   
               
            
           
         
       
     
     Formulations sprayed onto base ply, on top of the slot-die layed down area, at position E on the Fourdrinier. 11″ laydown width. 40 psi pressure. 
     
       
         
           
               
               
               
               
               
             
               
                   
               
               
                 Sample  
                   
                   
                   
                   
               
               
                 ID 
                 Water 
                 Dry pulp 
                 iM30k 
                 LD1006 
               
               
                   
               
             
            
               
                 PA 
                 9.5 kg 
                 0.08455 kg 
                 0 
                 0 
               
               
                 PB 
                 9.5 kg 
                 0.08455 kg 
                 0.1375 kg 
                 0 
               
               
                 PC 
                 9.5 kg 
                 0.08455 kg 
                 0.1375 kg 
                 0 
               
               
                 PD 
                 9.5 kg 
                 0.08455 kg 
                  0.55 kg 
                 0 
               
               
                 PE 
                 9.5 kg 
                 0.08455 kg 
                 0 
                 0.275 kg 
               
               
                 PF 
                 9.5 kg 
                 0.08455 kg 
                 0 
                 0.275 kg 
               
               
                   
               
            
           
         
       
     
     Base ply: 135 gsm 
     Linespeed: 30 ft. per min 
     Pulp freeness: 400 SCF 
                                                                             Combined                                       Additive       Ring   Ring   Estimated           Sheet    Measured   TADT/   laydown in   Scott   Crush   Crush   Ply       Sample   Ash   dry Basis   ° C.   middle layer    Bond/   MD/   CD/   Bonding       ID   Content   wt./gsm   (average)   (% by mass)   psi   f.lb/6 in   f.lb/6 in   (1-6)                  PA   33.2%   317   5.6   94%   27   82   70   4       PB   26.1%   317   6.2   91%   42   89   71   5       PC   36.2%   367   4.6   95%   29   69   57   3       PD   49.7%   424   2.8   96%   (NT)   37   37   2       PE   45.2%   384   4.4   95%   14   46   43   2       PF   53.8%   441   2.9   97%   (NT)   34   37   1                    
The lower the TADT, the better the insulation properties of the material. Ash content of the sheet was assumed to be substantially all due to the insulating additive introduced. Combined additive laydown in middle layer is theoretical based upon solids added to the web by the spray nozzle and/the slot die to form the middle layer (calculated: 100*Mass Additive/Mass Additive+Fiber). NT=Not tested.
 
Paper Machine Modifications with Multiple Nozzles:
 
     Three nozzles were suspended above the two Fourdriniers in various positions to explore formation of paper sheets exhibiting a non-uniform cross-sectional distribution of thermally insulating materials. Fittings allowed for larger or smaller nozzles to be installed above the web, giving nominally 1 US gallon per minute flow, 2 US gallon per minute, 3 US gallon per minute, 4 US gallon per minute, etc. The height from the web of each nozzle could also be adjusted to control the spread of the spray fan onto the web. Two spray heights were chosen, giving 11″ wide spray width, or 23″ wide spray width. 
     The pulp freeness was measured at 504 Standard Canadian Freeness, and thick pulp consistency was 1.75%. 150 g of cationic guar gum was dispersed into 4 gallon of hot water over 40 minutes, after which the pH was adjusted with citric acid solution to pH 5.00-6.00. The mixture was stirred for a further 20 minutes before adding to approximately 4,500 lbs of pulp feedstock at 1.75% consistency. The basis weight of both the bottom and top ply was set to 135 gsm, giving a total of 270 gsm basis weight, at 30 ft./min. 
     The following spray formulation was used for all spray nozzles: 
     Dicapearl LD 1006 (Dicalite Management Group, PA): 0.538 kg 
     Pulp at 1.75% consistency and 504 CSF: 2.956 kg 
     Water: 13.548 kg 
     Stirred 5-10 minutes 
     cationic guar gum (Lotioncrafter, Eastsound Wash.) 0.5% solution 0.050 kg 
     Stirred for at least 5 additional minutes prior to use. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
               
               
                 Sample  
                 Nozzle  
                 Position 
                 Nozzle 
                 Position 
                 Ply  
               
               
                 ID 
                 1 
                 1 
                 2 
                 2 
                 Bonding 
               
               
                   
               
             
            
               
                 RA 
                 1 gpm, 11″ wide 
                 E 
                 — 
                 — 
                 Good 
               
               
                 RB 
                 1 gpm, 23″ wide 
                 E 
                 — 
                 — 
                 Good 
               
               
                 RC 
                 1 gpm, 23″ wide 
                 E 
                 1 gpm,  
                 E 2   
                 Best 
               
               
                   
                   
                   
                 23″ wide 
                   
                   
               
               
                 RD 
                 1 gpm, 23″ wide 
                 E 
                 1 gpm,  
                 F 
                 Good 
               
               
                   
                   
                   
                 23″ wide 
                   
                   
               
               
                 RE 
                 2 gpm, 23″ wide 
                 E 
                 — 
                 — 
                 Good 
               
               
                   
               
            
           
         
       
     
     The runability of these codes informed the next set of conditions: 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Sample 
                 Nozzle 
                 Posn. 
                 Nozzle 
                 Posn. 
                 Nozzle  
                 Posn. 
                   
               
               
                 ID 
                 1 
                 1 
                 2 
                 2 
                 3 
                 3 
                 Note 
               
               
                   
               
             
            
               
                 RF 
                 2 gpm,  
                 E 
                 2 gpm,  
                 E 2   
                 — 
                 — 
                 a) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
                   
                   
                   
                   
               
               
                 RG 
                 2 gpm,  
                 E 
                 2 gpm,  
                 E 2   
                 2 gpm,  
                 F 
                 b) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
                   
                 23″ wide 
                   
                   
               
               
                 RH 
                 2 gpm,  
                 E 
                 2 gpm,  
                 G 
                 — 
                 — 
                 c) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
                   
                   
                   
                   
               
               
                 RI 
                 2 gpm,  
                 E 
                 2 gpm,  
                 F 
                   
                   
                 d) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
               
               
                   
               
               
                 Notes: 
               
               
                 a) Reasonably good bonding between plies. 
               
               
                 b) Water addition to the pulp was reduced at the header boxes to reduce moisture and improve bonding of the two plies 
               
               
                 c) &amp; d)-these two codes were tested to explore the impact of spray positioning with regard to add-on of the additive. In general, we found that if the multi-ply paper could be transitioned from the wire to the felt press, then ply bonding would be acceptable after drying. 
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                   
               
               
                 Sample 
                 Nozzle 
                 Posn. 
                 Nozzle 
                 Posn. 
                 Nozzle  
                 Posn. 
                   
               
               
                 ID 
                 1 
                 1 
                 2 
                 2 
                 3 
                 3 
                 Note 
               
               
                   
               
             
            
               
                 RL 
                 2 gpm,  
                 E 
                 2 gpm,  
                 E 2   
                 2 gpm,  
                 F 
                 e) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
                   
                 23″ wide 
                   
                   
               
               
                 RM 
                 2 gpm,  
                 E 
                 2 gpm,  
                 E 2   
                 — 
                 — 
                 f) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
                   
                   
                   
                   
               
               
                 RN 
                 2 gpm,  
                 E 
                 2 gpm,  
                 E 2   
                 2 gpm,  
                 F 
                 g) 
               
               
                   
                 23″ wide 
                   
                 23″ wide 
                   
                 23″ wide 
               
               
                   
               
               
                 Notes: 
               
               
                 e) 3 gallon per minute was removed from the each of the two headboxes 
               
               
                 f) For RM, both spray nozzle formulations substituted 75-micron uncoated perlite microspheres, sold as Sil-32, as part of the Sil-Cell range of lightweight fillers for concrete, available from Silbrico Corp. Hodgkins IL, instead of Dicapearl LD 1006. 
               
               
                 g) For RN, all three spray nozzle formulations substituted 75-micron uncoated perlite microspheres, sold as Sil-32, as part of the Sil-Cell range of lightweight fillers for concrete, available from Silbrico Corp. Hodgkins IL, instead of Dicapearl LD 1006. 
               
            
           
         
       
     
     The present invention is described above and further illustrated below by way of claims, which are not to be construed in any way as imposing limitations upon the scope of the invention. On the contrary, it is to be clearly understood that resort may be had to various other embodiments, modifications, and equivalents thereof which, after reading the description herein, may suggest themselves to those skilled in the art without departing from the spirit of the present invention and/or the scope of the appended claims.