METHOD FOR MANUFACTURING COEXTRUDED CROSSLINKED POLYOLEFIN FOAM WITH POLYAMIDE COATING LAYERS

Abstract

This paper describes continuous, physically crosslinked, closed-cell, multi-layer foam structures comprising a foam layer made of polypropylene, polyethylene, or a combination of polypropylene and polyethylene, and a polyamide coating layer. The multi-layer foam structure can be obtained by co-extruding a multi-layer structure comprising at least one foam layer composition and at least one coating layer composition, irradiating the co-extruded structure with ionizing radiation, and continuously foaming the irradiated structure.

Description

METHOD FOR MANUFACTURING COEXTRUDED CROSSLINKED POLYOLEFIN FOAM WITH POLYAMIDE COATING LAYERS Cross-reference to related applications This application claims priority and benefit from U.S. Application No. 16 / 836,229, filed on March 31, 2020, and U.S. Application No. 16 / 836,389, filed on March 31, 2020, all of the contents of which are incorporated herein by reference. Field of dissemination The present invention relates to multilayer polyamide / polyolefin foam coating structures and a method for producing these structures. More particularly, it relates to a method for producing multilayer polyamide / polyolefin foam coating structures of crosslinked and coextruded polyolefin. Background of the invention Cross-linked polyolefin foam can be used in various commercial applications, including, but not limited to, interior trim components in vehicles, such as door panels. To prepare polyolefin foam for use in a vehicle door panel, the foam layer is typically laminated first to a film, fabric, or sheet to create a bilaminate. This flexible bilaminate then needs to be combined with a rigid substrate to form the panel. Several production methods are used within the automotive industry to combine flexible bilaminate with the panel. These methods include thermoforming techniques such as negative vacuum forming (NVF) and positive vacuum forming (PVF), compression molding, and low-pressure molding (LPM), among others. In low-pressure molding, the bilaminate is placed in a mold with the film, fabric, or sheet facing surface A of the mold. The mold is closed, and polypropylene is injected into side B of the cavity, filling the mold to form the panel. In commercial production processes, it is common for the polypropylene to be a random copolymer or impact-modified homopolymer with a very high melt flow rate (50 to 125 grams per 10 minutes at 230 °C) injected at approximately 200 °C. Problems arise with the design and implementation of LPM. The hot polypropylene in and around the injection point can cut or degrade the foam because the injection temperature can be well above the foam's melting point. In one scenario, an orange-peel-like visual defect may be observed from surface A in and around the injection point. In another scenario, the foam around the injection point may be completely cut, leaving a visible depression of the film, fabric, or sheet at the injection site. Manufacturers have implemented several techniques to help reduce these problems. One technique is to inject the polypropylene into the stub portion of the bilaminate. While this is generally effective in resolving issues of cutting and foam degradation within the mold cavity, it increases the cost of making the panel. Injection into the stubs requires the stubs to be longer along at least one side of the mold. The stubs along the injection side will also contain the injected polypropylene. The cost of disposing of the additional stubs, which include both the bilaminate and the injected polypropylene, can be substantial. Furthermore, the stubs are not easily recyclable, which adds to the cost of this additional waste. Another technique for reducing foam shear and degradation defects in LPM is the use of a flexible trilaminate. A trilaminate can be the same as an LPM bilaminate with a flexible homopolymer-based TPO or TPE layer laminated to the “B” side of the bilaminate. The TPO or TPE layer acts as a protective skin layer and / or a sacrificial skin layer between the foam and the injected polypropylene. However, problems also arise with the use of trilaminate in LPM. The TPO or TPE layer thickness can be substantial relative to the overall thickness of the bilaminate, increasing material costs. A second lamination step is required to produce the trilaminate, further increasing its cost. Finally, the protective TPO or TPE layer is also prone to cutting and degradation at the injection site. Vehicle door panel manufacturers using LPM technology commonly continue to inject the polypropylene into the waste portion of the trilaminate. While the amount of waste required for this configuration is less than with a bilaminate, it still requires more waste than would be needed if injected directly into the mold cavity. The cost of discarding the additional waste, which includes both the trilaminate and the injected polypropylene, is substantial.Difficulty with recycling the scraps adds additional cost to this manufacturing technique. Brief description of the disclosure It has been discovered that it is possible to produce a physically cross-linked, closed-cell polyolefin foam with at least one polyamide coating layer in a continuous process. The multi-layered structure can be laminated to a film, fabric, or sheet to create a bilaminate. The bilaminate can then be used in LPM applications and overcome the problems associated with traditional LPM bilaminates and trilaminates used to produce interior vehicle trim components. In some applications, the polyamide layer can act as a more effective protective layer (compared to a TPO or TPE layer) for the polypropylene being injected. Common commercial polyamides vary widely in their melting temperature, but most exhibit a melting temperature higher than that of homopolymer polypropylene. Therefore, a polyamide can be selected that is not only higher than the melting temperature of the injected polypropylene but also higher than the injection temperature. The high melting temperature of the polyamide can ensure that it remains intact, providing a barrier that will not melt or shear when in contact with the injected polypropylene, even at the injection point. Furthermore, injection in the scrap region may become unnecessary, further reducing scrap waste costs.The polyamide coating layer can be substantially thinner than a TPO or TPE layer when properly chosen for the LPM process as a non-sacrificial layer, thereby further reducing material costs. Maleic anhydride-grafted polypropylene can be a suitable compatibilizer between polyolefin and polyamide. Maleic anhydride-grafted impact-modified polypropylene homopolymers and maleic anhydride-grafted random copolymers are commercially abundant. This may allow for a direct replacement of the injected impact-modified homopolymer or random copolymer with minimal adjustments in a traditional LPM manufacturing process. In some embodiments, a method is provided for forming a multi-layer foam structure, the method comprising: coextruding a first layer comprising polypropylene, polyethylene, or a combination of polypropylene and polyethylene and a chemical foaming agent, and a second layer on one side of the first layer, the second layer comprising a combination of polyamide and polypropylene, polyethylene, or a combination of polypropylene and polyethylene; irradiating the coextruded layers with ionizing radiation; and foaming the irradiated, coextruded layers. In some embodiments, the first layer may comprise at least 70% by weight of polypropylene, polyethylene, or a combination of polypropylene and polyethylene. In some embodiments, the second layer may comprise at least 40% by weight of polyamide.In some embodiments, the second layer may comprise at most 50% by weight of polypropylene, polyethylene, or a combination of polypropylene and polyethylene; and at least 40% by weight of polyamide. In some embodiments, the second layer may be less than 1 mm thick. In some embodiments, the first layer may comprise a crosslinking promoter in an amount of 0.5% to 5% by weight. In some embodiments, the first layer may comprise additives in an amount of 1% to 20% by weight. In some embodiments, the second layer may comprise additives in an amount of 1% to 10% by weight. In some embodiments, the polypropylene may have a melt flow rate of 0.1 grams to 25 grams per 10 minutes at 230 °C. In some embodiments, the polyethylene may have a melt flow rate of 0.1 grams to 25 grams per 10 minutes at 190 °C.In some embodiments, the amount of chemical foaming agent in the first layer is 3 to 15% by weight. In some embodiments, the chemical foaming agent may comprise azodicarbonamide. In some embodiments, the ionizing radiation may be selected from the group consisting of alpha, beta (electrons), X-rays, gamma rays, and neutrons. In some embodiments, the coextruded structure may be irradiated up to four times separately. In some embodiments, the ionizing radiation may be an electron beam with an accelerating voltage of 200 kV to 1500 kV. In some embodiments, the absorbed electron beam dosage may be 10 kGy to 500 kGy. In some embodiments, the ionizing radiation may crosslink the extruded structure to a degree of crosslinking of 2075%. In some embodiments, foaming may comprise heating the irradiated structure with molten salt and radiant heaters or a hot air oven.In some versions, the density of the multi-layer foam structure can range from 20 kg / m³ to 250 kg / m³. In some versions, the multi-layer foam structure can have an average closed-cell size of 0.05 mm to 1.0 mm. In some versions, the multi-layer foam structure can have a thickness of 0.2 mm to 50 mm. As used here, the singular forms of “a,” “an,” “the,” and “a” are intended to include the plural forms, unless the context indicates otherwise. It should be understood that the term “and / or,” as used here, refers to and encompasses any and all possible combinations of one or more of the listed associated items. It should also be understood that the terms “includes,” “comprises,” and / or “comprises,” when used, specify the presence of features, integrators, stages, operations, elements, components, and / or units, but do not preclude the presence or addition of one or more of the features, integrators, stages, operations, elements, components, units, and / or groups thereof. It is understood that the aspects and modalities described herein include those that are "consisting of" and / or "essentially consisting of" aspects and modalities. For all methods, systems, compositions, and devices described herein, the methods, systems, compositions, and devices may either comprise the listed components or steps, or may "consist of" or "essentially consist of" the listed components or steps.When a system, composition, or device is described as “consisting essentially of” the listed components, the system, composition, or device contains the listed components and may contain other components that do not substantially affect the performance of the system, composition, or device, but also does not contain any other components that substantially affect the performance of the system, composition, or device other than those components expressly listed; or does not contain a sufficient concentration or quantity of the additional components to substantially affect the performance of the system, composition, or device.When a method is described as “consisting essentially of” the listed steps, the method contains the listed steps, and may contain other steps that do not substantially affect the result of the method, but the method does not contain any other steps that substantially affect the result of the method other than the steps expressly listed. In disclosure, “substantially free from” a specific component, specific composition, specific compound, or specific ingredient in various forms means that less than approximately 5%, less than approximately 2%, less than approximately 1%, less than approximately 0.5%, less than approximately 0.1%, less than approximately 0.05%, less than approximately 0.025%, or less than approximately 0.01% of the specific component, specific composition, specific compound, or specific ingredient is present by weight. Preferably, “substantially free from” a specific component, specific composition, specific compound, or specific ingredient indicates that less than approximately 1% of the specific component, specific composition, specific compound, or specific ingredient is present by weight. The additional advantages will be readily apparent to those skilled in the art from the following detailed description. The examples and descriptions herein are intended to be illustrative and not restrictive. Brief description of the figures Several modalities are described, by way of example only, with reference to the attached figures, in which: FIG. 1 is a cross-sectional image of an unfoamed microtome slice from example 1B at a magnification of 100x; FIG. 2 is an image of example 1 B foamed at a magnification of 20x and 45° of the coating surface; FIG. 3 is a cross-sectional image of a microtome section of example 2A not foamed at a magnification of 100x; FIG. 4 is an image of example 2A foamed at a magnification of 20x and 45° of the coating surface; FIG. 5 is a cross-sectional image of a microtome slice of the unfoamed 2D example at a magnification of 10Ox; FIG. 6 is an image of the foamed 2D example at a magnification of 20x and 45° of the coating surface; FIG. 7 is a cross-sectional image of an unfoamed microtome slice from example 2G at a magnification of 10Ox; and FIG. 8 is an image of example 2G foamed at a magnification of 20x and 45° of the coating surface. Detailed description of the exemplary modalities Methods are described for producing coextruded, closed-cell, cross-linked, multi-layer foam structures comprising at least one foam layer including polypropylene, polyethylene, or combinations thereof, and at least one coating layer including polyamide. The methods for producing a coextruded, closed-cell, cross-linked, multi-layer foam structure may include the steps of (a) coextrusion, (b) irradiation, and (c) foaming. Coextrusion is the extrusion of multiple layers of material simultaneously. This type of extrusion uses two or more extruders to distribute a constant volumetric flow of material to an extrusion head (die) that can extrude the materials into the desired shape. In the coextrusion step, foam compositions can be fed into multiple extruders to form a multi-layered, non-foamed structure. For example, foam composition A can be fed into one extruder, and foam composition B can be fed into a second extruder. The method of feeding ingredients into the extruders can be based on the extruder design and the available material handling equipment. Premixing the foam composition ingredients can be done, if necessary, to facilitate dispersion. A Henshel mixer can be used for this premixing. All ingredients can be premixed and fed through a single orifice in the extruder. Alternatively, ingredients can be fed individually through separate designated orifices for each ingredient.For example, if the crosslinking promoter or any other additive is a liquid, the promoter and / or additives can be added through a feed gate (or gates) in the extruder or through a vent opening in the extruder (if equipped with venting) instead of being premixed with solid ingredients. Combinations of premixing and orifice feeding of individual ingredients can also be used. Each extruder can distribute a constant amount of each composition into one or more manifolds followed by a laminating die to create a coextruded, non-foamed, multi-layer sheet. There are two common methods for coextruding materials: (1) feed block manifolds; and (2) multiple manifolds within the die. The elements of a feed block manifold may include: (a) inlet holes for top, middle, and bottom layers; (b) an optimized melt lamination area that channels separate flow streams into a laminated melt stream within the feed block; (c) an adapter plate between the feed block and the sheet die; and / or (d) a sheet die (similar to a monolayer die), where the laminated melt stream enters the center of the die and disperses along the manifold, flowing out of the die outlet as a distinct, multi-layer extruded product.The elements of a multi-collector die may be: (a) similar to a single-layer die, except that there is more than one feed channel; (b) that each melt channel has its own choke bar for flow control; and / or (c) that the melt streams converge within the die near the outlet and emerge as a distinct multi-layer extruded product. Layer thicknesses can be determined by the design of the manifolds and die. For example, an 80 / 20 feed block manifold can distribute compositions in approximately a 4:1 ratio when the speed and size of each extruder are matched accordingly. This ratio can be altered by changing, for example: (a) the relative extrusion speed between extruders; (b) the relative size of each extruder; and / or (c) the composition (i.e., viscosity) of the individual layers. The overall thickness of the multi-layer sheet can be controlled by the overall die clearance. However, the overall thickness of the multi-layer sheet can also be adjusted, for example, by stretching (i.e., pulling) the molten multi-layer extruded product and / or by flattening the molten multi-layer extruded product through a clamping point. Multi-layer structures may include at least two layers made of different compositions. In some embodiments, multi-layer structures include at least one layer made of a foam composition and at least one layer made of a non-foam coating composition. In some embodiments, the structure may be a B / A layered structure, a B / A / B layered structure, a B / A / C layered structure, or it may have multiple other layers. In some embodiments, multi-layer structures may include additional layers such as bonding layers, film layers, and / or additional foam layers, among others. A coating composition fed into the extruder may include at least one polyamide and one polypropylene, polyethylene, or a combination thereof. A foam composition fed into the extruder may include one polypropylene, polyethylene, or a combination thereof. Polyamides are polymers that contain an amide group (-CONH-) as a recurring part of the chain. Polyamide includes, but is not limited to, aliphatic polyamide produced by a condensation reaction of two bifunctional monomers or by ring-opening addition polymerization of cyclic chemical compounds. Polyamide can be a homopolymer, copolymer, terpolymer, or a mixture. Importantly, a polyamide mixture or semicrystalline polyamide is preferred over a polyamide mixture or amorphous polyamide. Commercially available aliphatic polyamide homopolymers include, but are not limited to, types 6, 11, 12, 46, 410, 56, 510, 511, 512, 513, 514, 66, 69, 610, 612, 613, 1010, 1012, and 1212. Commercially available aliphatic polyamide copolymers include, but are not limited to, types 6 / 66, 6 / 69, 610 / 66, and 56 / 12. Commercially available aliphatic polyamide terpolymers include, but are not limited to, type 6 / 66 / 12. Polypropylene includes, but is not limited to, polypropylene, impact-modified polypropylene, polypropylene-ethylene copolymer, impact-modified polypropylene-ethylene copolymer, metallocene polypropylene, metallocene-ethylene polypropylene copolymer, metallocene polypropylene olefin block copolymer (with a controlled block sequence), polypropylene-based polyolefin plastomer, polypropylene-based polyolefin elasto-plastomer, polypropylene-based polyolefin elastomer, polypropylene-based thermoplastic polyolefin blend, and polypropylene-based thermoplastic elastomeric blend. Polypropylene can be of a high melt strength type. Furthermore, polypropylenes can be grafted with maleic anhydride. Polyethylene includes, but is not limited to, low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE) (homopolymer, copolymer with butene or hexene or octene, terpolymer with butene and / or hexene and / or octene), very low-density polyethylene (VLDPE) (homopolymer, copolymer with butene or hexene or octene, terpolymer with butene and / or hexene and / or octene), linear very low-density polyethylene (VLLDPE) (homopolymer, copolymer with butene or hexene or octene, terpolymer with butene and / or hexene and / or octene), high-density polyethylene (HDPE), polyethylene-propylene copolymer, metallocene polyethylene, metallocene-propylene ethylene copolymer, and metallocene polyethylene olefin block copolymer (with a sequence (controlled block)Any of which may contain compatibilizers or grafted copolymers containing acetate and / or ester groups. These polyethylenes may be grafted with maleic anhydride. These polyethylenes may also be copolymers and terpolymers containing acetate and / or ester groups and may be ionomers of terpolymers and copolymers containing acetate and / or ester groups. A non-foam coating composition fed into the extruder may include at least approximately 40% by weight of polyamide, preferably at least approximately 50% by weight of polyamide, more preferably at least approximately 60% by weight of polyamide, and even more preferably at least approximately 70% by weight of polyamide. In some embodiments, the polyamide in the non-foam coating composition fed into the extruder may be greater than or equal to approximately 40% by weight of polyamide, 50% by weight of polyamide, 60% by weight of polyamide, or 70% by weight of polyamide. In some embodiments, the polyamide in the non-foam coating composition fed into the extruder may be less than or equal to approximately 95% by weight of polyamide, 90% by weight of polyamide, 85% by weight of polyamide, or 80% by weight of polyamide. In some embodiments, the polyamide in the non-foam coating composition fed into the extruder may be approximately 40% by weight to 95% by weight of polyamide, 50% by weight to 90% by weight of polyamide, 60% by weight to 85% by weight of polyamide, or 70% by weight to 80% by weight of polyamide. In some embodiments, the amount of polyethylene, polypropylene, or a combination thereof in the non-foam coating composition fed into the extruder may be greater than or equal to approximately 5% by weight, 10% by weight, or 20% by weight of polyethylene, polypropylene, or a combination thereof. In some embodiments, the amount of polyethylene, polypropylene, or a combination thereof in the non-foam coating composition fed into the extruder may be less than or equal to approximately 50% by weight, 40% by weight, 35% by weight, or 30% by weight of polyethylene, polypropylene, or a combination thereof. In some embodiments, the amount of polyethylene, polypropylene, or a combination thereof in the non-foam coating composition fed into the extruder may be 5% by weight to 50% by weight, 10% by weight to 40% by weight, or 20% by weight to 30% by weight of polyethylene, polypropylene, or a combination thereof. A foam composition fed into the extruder may include at least approximately 75% by weight of polypropylene, polyethylene, or a combination thereof, preferably at least approximately 80% by weight, more preferably at least approximately 85% by weight, and even more preferably at least approximately 90% by weight. In some embodiments, the foam composition fed into the extruder may be at least approximately 70% by weight, 80% by weight, or 85% by weight polypropylene, polyethylene, or a combination thereof. In some embodiments, the foam composition fed into the extruder may be at most approximately 98% by weight, 95% by weight, or 90% by weight of polypropylene, polyethylene, or a combination thereof. In some embodiments, the foam composition fed into the extruder may be approximately 70% by weight to 98% by weight, 80% by weight to 95% by weight, or 85% by weight to 90% by weight of polypropylene, polyethylene, or a combination thereof. Since a wide range of multi-layer structures and foam articles can be created with the described compositions, a wide range of polyamides, polypropylenes, and polyethylenes can be employed in the compositions to meet various in-process manufacturing requirements and commercial end-use requirements. A non-limiting example of polypropylene is an isotactic homopolypropylene. Commercially available examples include, but are not limited to, Braskem's FF018F, Total Petrochemicals' 3271, and Phillips 66's COPYLENEMRCH020. A non-limiting example of an impact-modified polypropylene is a homopolypropylene with ethylene-propylene (EP) copolymer rubber. The rubber may be amorphous or semicrystalline but is not present in sufficient quantity to impart any plastomeric or elastomeric properties to the material. Some non-limiting examples of commercially available impact-modified polypropylene are Braskem's TI4003F and TI4015F, and Lyondel IBasell's PRO-FAXMR8623 and PRO-FAXMRSB786. “Polypropylene-ethylene copolymer” is polypropylene with random ethylene units. A few non-limiting examples of commercially available polypropylene-ethylene copolymers are 6232, 7250FL, and Z9421 from Total Petrochemicals, 6D20 and DS6D81 from Braskem, and PRO-FAXMRRP311H and ADSYLMR7415 XCP from LyondeIBasell. “Impact-modified polypropylene-ethylene copolymer” is polypropylene with random ethylene units and ethylene-propylene (EP) copolymer rubber. The rubber may be amorphous or semicrystalline but is not present in sufficient quantity to impart any plastomeric or elastoplastomeric properties to the material. A non-limiting example of a commercially available impact-modified polypropylene-ethylene copolymer is Braskem's PRISMAMR6910. “Metalocene polypropylene” refers to metallocene syndiotactic homopolypropylene, metallocene atactic homopolypropylene, and metallocene isotactic homopolypropylene. Non-limiting examples of metallocene polypropylene include those commercially available under the trade names METOCENE® from LyondeIBasell and ACHIEVE® from ExxonMobil. Metallocene polypropylenes are also commercially available from Total Petrochemicals and include, but are not limited to, grades M3551, M3282MZ, M7672, 1251, 1471, 1571, and 1751. “Metallocyanin-ethylene polypropylene copolymer is syndiotactic metallocene, atactic metallocene, and isotactic metallocene polypropylene with random ethylene units. Commercially available examples include, but are not limited to, LumiceneMRMR10MX0 and LumiceneMRMR60MC2 from Total Petrochemicals, PurellMRSM170G from Lyondell IBasell, and the WINTECMR product line from Japan Polypropylene Corporation. “Metalocene polypropylene olefin block copolymer is a polypropylene with alternating crystallizable hard blocks and amorphous soft blocks that are not randomly distributed, i.e., with a controlled block sequence. An example of a “metallocene polypropylene olefin block copolymer” includes, but is not limited to, the INTUNEMR product line from Dow Chemical Company. “Polypropylene-based polyolefin plastomer” (POP) and “polypropylene-based polyolefin elastoplastomer” are metallocene- and non-metallocene-propylene-based copolymers with plastomeric and elastoplastomeric properties. Non-limiting examples include those commercially available under the trade names VERSIFYMR (metallocene) from Dow Chemical Company, VISTAMAXXMR (metallocene) from ExxonMobil, and KOATTROMR (non-metallocene) from LyondellBasell (a line of plastomeric polymers based on 1-butene; some grades are 1-butene-based homopolymers, and others are 1-butene-polypropylene-based copolymers). “Polypropylene-based polyolefin elastomer” (POE) is both a metallocene and a non-metallocene propylene-based copolymer with elastomeric properties. Non-limiting examples of propylene-based polyolefin elastomers are those commercially available polymers under the trade names VERSIFYMR (metallocene) from Dow Chemical Company and VISTAMAXXMR (metallocene) from ExxonMobil. Polypropylene-based thermoplastic polyolefin blends (TROs) are polypropylene, polypropylene-ethylene copolymer, metallocene homopolypropylene, and metallocene-ethylene polypropylene copolymer, containing ethylene-propylene copolymer rubber in sufficiently large quantities to impart plastomeric, elastoplastomeric, or elastomeric properties to the thermoplastic polyolefin blend (TPO). Non-limiting examples of TPO polymers include those commercially available under the trade names THERMORIJNMR and ZELASMR from Mitsubishi Chemical Corporation, ADFLEXMR and SOFTELLMR from LyondeIBasell, TELCARMR from Teknor Apex Company, and WELNEXMR from Japan Polypropylene Company. TPO can be produced by multi-stage polymerization (e.g., ZELASMR, ADFLEXMR, SOFTELLMR, and WELNEXMR) or by blending (e.g., THERMORUNMR and TELCARMR). “Polypropylene-based thermoplastic elastomer blend” (TPE) is polypropylene, polypropylene-ethylene copolymer, metallocene homopolypropylene, and metallocene-ethylene polypropylene copolymer, having diblock or multiblock thermoplastic rubber modifiers (SEBS, SEPS, SEEPS, SEP, SERC, CEBC, HSB, and the like) in sufficiently large quantities to impart plastomeric, elastoplastomeric, or elastomeric properties to the thermoplastic elastomer blend (TPE). Non-limiting examples of polypropylene-based thermoplastic elastomer blend polymers are those commercially available polymer blends under the trade names GLSMRDYNAFLEXMR and GLSMVERSAFLEXMR from PolyOne Corporation, MONPRENEMR from Teknor Apex Company, and DURAGRIPMR from Lyondel IBasell. Any of the polypropylenes described above can also be of the high-melt strength (HMS) type. Polypropylene manufacturers employ various methods to strengthen the polymer at the melt stage. For example, polypropylene exhibiting long-chain branching (LCB) can be identified as a high-melt strength polypropylene. Non-limiting examples of high-melt strength polypropylene include polymers commercially available under the trade names DAPLOY® from Borealis, AMPPLEO® from Braskem, and WAYMAX® from Japan Polypropylene Corporation. Any polypropylene blend, but most commonly TPO and TPE, can be optionally extended with oil, e.g. mineral oil, Chevron's PARALUXMR process oils, etc., to further soften the blend, enhance the haptic property of the blend, or improve the processability of the blend. “LDPE” and “LLDPE” are low-density polyethylene and linear low-density polyethylene, respectively. Non-limiting examples of LDPE include at least those provided by Dow (e.g., 6401) and Nova (e.g., NovapolMRLF-0219-A). Non-limiting examples of LLDPE include at least those provided by ExxonMobilMR (e.g., LLP8501.67) and Dow (e.g., DFDA-7059 NT 7). Commercial LLDPE polymers are typically copolymers or terpolymers containing α-olefins of butene and / or hexene and / or octene. “VLDPE and VLLDPE are very low-density polyethylene and linear very low-density polyethylene and usually copolymers or terpolymers containing α-olefins of butene and / or hexene and / or octene. Non-limiting examples of VLDPE and VLLDPE are commercially available under the trade name FLEXOMER® from Dow Chemical Company and particular grades of STAMYLEX® from Borealis. “Metalocene polyethylene” is metallocene-based polyethylene with properties ranging from non-elastic to elastomeric. Non-limiting examples of metallocene polyethylene are commercially available under the trade names ENGAGE® from Dow Chemical Company, ENABLE® and EXCEED® from ExxonMobil®, and QUEO® from Borealis. Metallocene polyethylene olefin block copolymer is a polyethylene with alternating crystallizable hard blocks and amorphous soft blocks that are not randomly distributed, i.e., with a controlled block sequence. An example of a metallocene polyethylene olefin block copolymer includes, but is not limited to, the INFUSE® product line from Dow Chemical Company. All of the above polyethylenes can be grafted with maleic anhydride. Non-limiting commercially available examples include ADMERMRNF539A from Mitsui Chemicals, DuPontMRBYNELMR4104 from Dow, and OREVACMR18360 from Arkema. It should be noted that many commercially available polyethylenes grafted with maleic anhydride also contain rubber. These polyethylenes can also be copolymers and terpolymers containing acetate and / or ester groups. Comonomeric groups include, but are not limited to, vinyl acetate, methyl acrylate, ethyl acrylate, butyl acrylate, glycidyl methacrylate, and acrylic acid. Non-limiting examples are commercially available under the trade names DuPontMRBYNELMR, DuPontMRELVAXMR, and DuPontMRELVALOYMR from Dow; EVATANEMR, LOTADERMR, and LOTRYLMR from Arkema; ​​and ESCORENEMR, ESCORMR, and OPTEMAMR from ExxonMobil. The polypropylenes and polyethylenes listed above can be functionalized. Functionalized polypropylenes and polyethylenes include a grafted monomer. Typically, the monomer is grafted onto the polypropylene or polyethylene by a free-radical reaction. Suitable monomers for the preparation of functionalized polypropylenes and polyethylenes include, for example, olefinic unsaturated monocarboxylic acids, such as acrylic acid or methacrylic acid, and the corresponding tert-butyl esters, such as tert-butyl (meth)acrylate; olefinic unsaturated dicarboxylic acids, such as fumaric acid, maleic acid, and itaconic acid, and the corresponding mono- and / or di-tert-butyl esters, such as mono- or di-tert-butyl fumarate and mono- or di-tert-butyl maleate; olefinic unsaturated dicarboxylic anhydrides, such as maleic anhydride; and olefinic unsaturated monomers containing sulfo or sulfonyl, such as...p-Styrenesulfonic acid, 2(meth)acrylamido-2-methylpropenesulfonic acid or 2-sulfonyl-(meth)acrylate, olefinic unsaturated monomers containing oxazolinyl, for example, vinylxylazines and vinylxoline derivatives, and olefinic unsaturated monomers containing epoxy, for example, glycidyl (meth)acrylate or allyl-glycidyl ether. The most commonly available commercially functionalized polypropylenes are those functionalized with maleic anhydride. Non-limiting examples include the ADMERMRQF and QB series from Mitsui Chemicals, the PLEXARMR6000 series from Lyondell / IBasell, the DuPont BYNELMR5000 series from Dow Chemical Company, and the OREVACMRPP series from Arkema. The most commonly available commercially functionalized polyethylenes are also those functionalized with maleic anhydride. Non-limiting examples include the ADMERMRNF and SE series from Mitsui Chemicals, the PLEXARMR1000, 2000, and 3000 series from LyondelIBasell, the DuPont MRseries BYNELMR2100, 3000, 3800, 3900, and 4000 from Dow, and the OREVAC MR PE and T series and some of the LOTADERMR series from Arkema. The most popular method for making polyamide compatible with polypropylene and polyethylene in various industries is through the use of polypropylene or polyethylene grafted with maleic anhydride. For example, in flexible food packaging, a polyamide film can be bonded to a polypropylene film by applying a bonding layer of polypropylene grafted with maleic anhydride between the two films. It should be noted that polyethylenes functionalized with other grafted monomers are also commercially available. Non-limiting examples include the DuPontMRseries BYNELMR1100, 2200, and 3100 from Dow Chemical Company and the LOTADERMRAX series from Arkema. It should also be noted that polymers other than polypropylene and polyethylene functionalized with maleic anhydride are also commercially available. For example, Addivant's ROYALTUFMR series are a series of ethylene propylene diene monomer (EPDM) rubbers functionalized with maleic anhydride. As another example, Kraton's KRATONMRFG series are a series of SEBS polymers functionalized with maleic anhydride. The coating layer may contain at least one grade of extrusion or general-purpose polyamide. Extrusion and general-purpose polyamides can be characterized as having approximately high to medium viscosity. A high- to medium-viscosity polyamide is more likely to match the melt flow characteristics of the foamable layer, resulting in greater thickness uniformity in each coextruded layer from the center to the edges of the die. Most types of polyamide are hygroscopic, and the moisture content in a polyamide can affect its melt flow and flow resistance at a given shear rate. Because moisture content affects flow characteristics, alternative standards for melt flow rate and melt volume rate are commonly applied to polyamides.ISO 307 and ASTM D789 are two such standards used to quantify the viscosity of polyamides. In ISO 307, polyamides can be dissolved in dilute solutions using certain specified solvents to determine a viscosity number. In ASTM D789, polyamides can be dissolved in concentrated solutions using a certain specified solvent to determine a relative viscosity. The corresponding standards ISO 16396-1 and ASTM D6779 provide guidance to manufacturers of commercial polyamide for identifying products under a standardized system. These nomenclature systems can help polyamide manufacturers identify grades, as appropriate, for extrusion (molded film, sheet, etc.), injection molding, blow molding, and so on. It is important to note that viscosity numbers and relative viscosity numbers are not published by most polyamide manufacturers.Instead, polyamide resins are usually marketed under general viscosity categories (very low, low, medium (or standard), medium high, high, etc.) and recommended processing applications (general extrusion, injection, composition, monofilament, melt spinning, industrial yarn, etc.). The composition of any foamable layer and any coating layer provided herein may contain at least one polypropylene having a melt flow rate of approximately 0.1 grams to approximately 25 grams per 10 minutes at 230°C. The composition of any foamable layer and / or any coating layer provided herein may also contain at least one polyethylene having a melt flow rate of approximately 0.1 grams to approximately 25 grams per 10 minutes at 190°C. In some embodiments, the melt flow rate of the polypropylene and / or polyethylene is preferably approximately 0.3 grams to approximately 20 grams per 10 minutes at 230°C and 190°C, respectively, and more preferably approximately 0.5 grams to approximately 15 grams per 10 minutes at 230°C and 190°C, respectively.The melt flow index (MFI) value for a polymer is defined and measured according to ASTM D1238 at 230 °C for polypropylenes and polypropylene-based materials and at 190 °C for polyethylenes and polyethylene-based materials using a 2.16 kg plunger for 10 minutes. The test time may be reduced for resins with relatively high melt flow. The MFI can provide a measure of a polymer's flow characteristics and is an indication of the molecular weight and processability of a polymer material. High MFI values ​​correspond to low viscosities. If the MFI values ​​are too high, extrusion according to this disclosure cannot be carried out satisfactorily. Problems associated with excessively high MFI values ​​include low pressures during extrusion, difficulties setting the thickness profile, uneven cooling profile due to low melt viscosity, poor melt strength, and / or machine problems. Conversely, low MFI values ​​correspond to high viscosities.MFI values ​​that are too low can cause high pressures during melt processing, sheet quality and profile problems, and higher extrusion temperatures that lead to a risk of decomposition and activation of the foaming agent. The aforementioned MFI ranges are also important for foaming processes because they can reflect the material's viscosity, which affects foam formation. While not limited by any single theory, it is believed that there are several reasons why particular MFI values ​​are more effective. A material with a lower MFI can improve certain physical properties as the molecular chain length increases, creating more energy required for the chains to flow under applied stress. Furthermore, the longer the molecular chain (MW), the more crystal entities the chain can crystallize, thus providing greater strength through intermolecular bonding. However, at excessively low MFI values, the viscosity becomes too high. Conversely, polymers with higher MFI values ​​have shorter chains.Therefore, in a given volume of a material with higher MFI values, there are more chain ends at a microscopic level compared to polymers with lower MFI values. These chain ends can be rotated, creating free volume due to the space required for this rotation (e.g., rotation occurring above the polymer's glass transition temperature, Tg). This can increase the free volume and allow for easy flow under tensile forces. In addition to polymers, the compositions fed into extruders may also contain additives compatible with the production of the disclosed multilayer structures. Common additives include, but are not limited to, organic peroxides, antioxidants, lubricants, processing aids, heat stabilizers, colorants, flame retardants, anti-static agents, nucleating agents, plasticizers, antimicrobials, fungicides, light stabilizers, UV absorbers, antiblocking agents, fillers, deodorants, odor adsorbents, antifogging agents, volatile organic compound (VOC) adsorbents, semi-volatile organic compound (SVOC) adsorbents, thickening agents, cell size stabilizers, metal deactivators, and combinations thereof. In some embodiments, the amount of additives other than chemical foaming agents and crosslinking promoters in a foam layer composition may be less than or equal to approximately 20% PPR, approximately 15% PPR, approximately 10% PPR, or approximately 8% PPR of the composition. In some embodiments, the amount of additives other than chemical foaming agents and crosslinking promoters in a foam layer composition may be greater than or equal to approximately 1% PPR, approximately 2% PPR, approximately 4% PPR, or approximately 6% PPR of the composition. In some embodiments, the amount of additives other than chemical foaming agents and crosslinking promoters in a foam layer composition may be from approximately 1% PPR to 20% PPR, approximately 2% PPR to 15% PPR, approximately 4% PPR to 10% PPR, or approximately 6% PPR to 8% PPR of the composition.In some forms, the amount of additives other than chemical foaming agents and crosslinking promoters in a foam layer composition may be approximately 1.7% to 20.7% by weight, approximately 2.7% to 15.7% by weight, approximately 3.7% to 10.7% by weight, approximately 4.7% to 8.7% by weight, or approximately 5.7% to 7.7% by weight of the foam layer composition. In some embodiments, the amount of additives in a coating layer composition may be less than or equal to approximately 20% PPR, approximately 15% PPR, approximately 10% PPR, approximately 7% PPR, approximately 5% PPR, or approximately 3% PPR of the composition. In some embodiments, the amount of additives in a coating layer composition may be greater than or equal to approximately 0.5% PPR, approximately 1% PPR, approximately 2% PPR, or approximately 3% PPR of the composition. In some embodiments, the amount of additives in a coating layer composition may be from approximately 0.5% PPR to 20% PPR, approximately 1% PPR to 10% PPR, or approximately 2% PPR to 7% PPR of the composition. In some forms, the amount of additives in a coating layer composition can be approximately 0.5% by weight to 20% by weight, approximately 1% by weight to 10% by weight, or approximately 2% by weight to 6% by weight of the coating layer composition. Regardless of how the ingredients are fed into the extruders, the shear force and mixing within an extruder can be sufficient to produce a homogeneous layer. Co-rotating and counter-rotating twin-screw extruders can provide sufficient shear force and mixing through the extruder barrel to extrude a layer with uniform properties. Specific energy is an indicator of how much work is being applied during the extrusion of ingredients for a layer and how intense the extrusion process is. Specific energy is defined as the energy applied to a material being processed by the extruder, normalized to a per-kilogram basis. Specific energy is quantified in kilowatts of energy applied per kilogram of total material fed per hour. Specific energy is calculated according to the formula: KW (applied) feedrate (^) ,where KW (applied} KW(motor rating) * (% torque from maximum allowable in decimal form) * RPM(actual running RPM) * 0.97 (gearbox efficiency) Max RPM (capability of extruder) Specific energy can be used to quantify the amount of cutting and mixing of the ingredients within the extruder. Extruders used to form the multi-layer structures described herein may be capable of producing a specific energy of at least approximately 0.100 kWh / kg, preferably at least approximately 0.125 kWh / kg, and more preferably at least approximately 0.150 kWh / kg. Any foamable layer may contain a chemical foaming agent (CFA). The extrusion temperature for any foamable layer may be from 0°C to 10°C below, and preferably more than 10°C below, the thermal decomposition onset temperature of the chemical foaming agent. If the extrusion temperature exceeds the thermal decomposition temperature of the foaming agent, the foaming agent will decompose, resulting in undesirable foam preforming. The extrusion temperature for any coating layer may be from 0°C to 10°C below, and preferably more than 10°C below, the thermal decomposition onset temperature of the chemical foaming agent in any foamable layer adjacent to the coating layer.If the extrusion temperature of the coating layer exceeds the thermal decomposition temperature of the foaming agent in the adjacent layer, then the foaming agent in the adjacent layer may decompose, which also results in unwanted foam pre-formation. The foam layer composition can include a variety of different chemical foaming agents. Examples of chemical foaming agents include, but are not limited to, azo compounds, hydrazine compounds, carbazides, tetrazoles, nitrous compounds, and carbonates. Furthermore, a chemical foaming agent can be used alone or in any combination. In some embodiments, azodicarbonamide (ADCA) is a chemical foaming agent that can be used. An example of an ADCA foaming agent is UNIFOAMMRTC-18I, manufactured by PT Lauten Otsuka Chemical. Thermal decomposition of ADCA typically occurs at temperatures between approximately 200°C and 240°C. To prevent ADCA from thermally decomposing in the extruder, the extrusion temperature can be maintained at or below 200°C. The amount of chemical foaming agent in a foam layer composition may be less than or equal to approximately 30% PPR, approximately 20% PPR, approximately 15% PPR, approximately 10% PPR, or approximately 8% PPR of the composition. In some embodiments, the amount of chemical foaming agent in a foam layer composition may be greater than or equal to approximately 1% PPR, approximately 2% PPR, approximately 3% PPR, approximately 4% PPR, or approximately 5% PPR of the composition. In some embodiments, the amount of chemical foaming agent in a foam layer composition may be approximately 1% PPR to 30% PPR, approximately 2% PPR to 20% PPR, approximately 3% PPR to 15% PPR, approximately 4% PPR to 10% PPR, or approximately 5% PPR to 8% PPR of the composition.In some applications, the amount of chemical foaming agent in a foam layer composition can range from approximately 1% to 30% by weight, approximately 2% to 20% by weight, 3% to 15% by weight, approximately 4% to 10% by weight, or approximately 5% to 7% by weight of the foam layer composition. The amount of chemical foaming agent may depend on the thickness of the unfoamed sheet, the desired foam thickness, the desired foam density, the materials being extruded, the crosslinking percentage, the type of chemical foaming agent (different foaming agents can generate significantly different amounts of gas), and other factors. It should be noted that the quantities of foaming agent listed above may be specific to ADCA only. Other foaming agents may produce varying amounts of volumetric gas per mass of CFA and should be considered accordingly. For example, when comparing ADCA to the foaming agent p-toluenesulfonyl semicarbazide (TSS), if a foamable layer contains 40 PPR of ADCA, approximately 63 PPR of TSS would be required to generate roughly the same amount of gas during the foaming step. If the difference between the decomposition temperature of the thermally decomposing foaming agent and the melting point of the polymer with the highest melting point is significant, a catalyst can be used to decompose the foaming agent. Examples of catalysts include, but are not limited to, zinc oxide, magnesium oxide, calcium stearate, glycerin, and urea. The lower temperature limit for extrusion can be that of the polymer with the highest melting point. If the extrusion temperature falls below the melting temperature of the polymer with the highest melting point, unwanted unmelted masses will appear. After foaming, the extruded layer produced below this lower temperature limit may exhibit uneven thickness, a non-uniform cell structure, cell collapse pockets, and other undesirable characteristics. Regardless of whether the foaming agents are physical, chemical, or a combination, conventional extrusion foaming produces polymer sheets where both primary surfaces are significantly rougher than equivalent structures produced by the described method. The surface profile of a multi-layer (as well as single-layer) foam sheet can be critical in many applications, and therefore, extrusion foam sheets cannot be used for these applications. These applications may require a smooth foam surface to achieve desired properties, such as ease of lamination to a film, fabric, fiber layer, or leather; percentage of contact area in lamination; visual aesthetics; and so on.The PCT publication WO 2016109544, which is hereby incorporated in full by reference, includes examples illustrating the difference in surface roughness between extruded foamed polymer sheets and equivalent foamed polymer sheets produced by the described method. The rougher surfaces of extruded foam articles in general can be caused by larger cell sizes (when compared to foams produced in accordance with this disclosure). Although cell size and cell size distribution may not be as critical in most commercial applications, because surface roughness is a function of cell size, foams with larger cells may be less desirable than foams with smaller cells for applications requiring a smooth foam surface. The thickness of the non-foamed, coextruded, multi-layer structure can range from approximately 0.1 mm to approximately 30 mm, from approximately 0.2 mm to approximately 25 mm, from approximately 0.3 mm to approximately 20 mm, or from approximately 0.4 mm to approximately 15 mm. In some embodiments, any individual coating layer can have a thickness of at least approximately 0.02 mm, at least approximately 0.05 mm, at least approximately 0.1 mm, at least approximately 0.15 mm, or at least approximately 0.2 mm. In some embodiments, any individual coating layer can have a thickness of less than or equal to approximately 1.0 mm, approximately 0.7 mm, or approximately 0.4 mm. In some embodiments, any individual coating layer can have a thickness of approximately 0.01 mm to 1.0 mm or 0.02 mm to 0.7 mm.In some embodiments, the thickness of the non-foamed coating is not limited in how thin it can be relative to the general non-foamed coextruded multi-layer sheet, and can be as thin as approximately 0.1 pm, or the usual thickness of a very thin bonding layer used in barrier films and multi-layer flexible packaging. In some embodiments, a foam layer of the unfoamed coextruded multilayer structure may have a thickness of approximately 0.1 mm to 5 mm, approximately 0.5 mm to 4 mm, approximately 1 mm to 3 mm, or approximately 1 mm to 2 mm. In some embodiments, a foam layer of the unfoamed coextruded multilayer structure may have a thickness less than or equal to approximately 5 mm, approximately 3 mm, approximately 2 mm, approximately 1.5 mm, approximately 1 mm, or approximately 0.5 mm. In some embodiments, a foam layer of the unfoamed coextruded multilayer structure may have a thickness greater than or equal to approximately 0.1 mm, approximately 0.5 mm, approximately 1 mm, approximately 1.5 mm, approximately 2 mm, or approximately 3 mm. In some configurations, the overall thickness of the non-foamed, coextruded, multi-layer structure can be measured using a stem-style thickness gauge attached above a flat base. The gauge tip can be fitted with a hemispherical contact point with a radius of 1.6 mm. The stem is raised, and the non-foamed structure is placed on the base. A force of 100 gf to 150 gf can be applied to the structure at the contact point during measurement. In some applications, the coating thickness of the non-foamed, coextruded, multi-layer structure can be measured using a microscope. To measure the coating thickness, a small sample can be cut from the continuous sheet structure, and the cross-section of the sample can be sliced ​​into thin sections using a microtome. A section can then be placed under the viewing microscope. A measurement can be taken with either a digital or traditional microscope. A typical commercial digital microscope may have various software features to facilitate thickness measurement. A traditional commercial microscope may have a lens with measurement scales to facilitate thickness measurement. The coating can be thin and easily foldable when melted to significantly hinder the expansion of the foamable layers during the foaming step. The coating's thickness, flexibility, melt strength, and crosslinking percentage are among the many physical properties that can impede the foaming expansion of the other layers. The thickness, flexibility, melt strength, and crosslinking percentage of the foamable layers, as well as the final thickness and density of the foamed layers, are also factors in whether the coating inhibits the expansion of the foamable layers. A general guideline for maximum coating thickness is that it should not exceed approximately 20%, approximately 15%, approximately 10%, or approximately 5% of the overall coextruded non-foamed sheet.If the coating thickness is greater than approximately 20% of the general coextruded non-foamed sheet, problems may arise with curling, buckling, and folding of the multi-layer sheet upon itself as the multi-layer sheet heats up and foams. It is important to distinguish between physical crosslinking and chemical crosslinking. In chemical crosslinking, crosslinks are generated using crosslinking promoters, but without the use of ionizing radiation. Chemical crosslinking typically involves the use of peroxides, silanes, or vinylsilane. In peroxide crosslinking processes, crosslinking usually occurs in the extrusion die. For silane and vinylsilane crosslinking processes, crosslinking usually occurs after extrusion in a secondary operation where the crosslinking of the extruded material can be accelerated with heat and moisture. Regardless of the chemical crosslinking method, chemically crosslinked foam sheets typically exhibit primary surfaces that are significantly rougher than equivalent structures produced by the physical method.The surface profile of a multi-layer (as well as single-layer) foam sheet can be critical in many applications, and therefore chemically crosslinked foam sheets cannot be used for these applications. These applications may require a smooth foam surface to achieve desired properties, such as ease of lamination to a film, fabric, fiber layer, or leather; percentage of contact area in lamination; visual aesthetics; etc. PCT publication WO 2016109544 includes examples illustrating the difference in surface roughness between chemically crosslinked foamed polymer sheets and equivalent foamed polymer sheets produced by the described method. The rougher surfaces of chemically crosslinked foamed articles in general can be caused by larger cell sizes (when compared to foams produced according to this description). Although cell size and size distribution are not critical in most commercial applications because surface roughness is a function of cell size, foams with larger cells may be less desirable than foams with smaller cells for applications requiring a smooth foam surface. Examples of ionizing radiation include, but are not limited to, alpha, beta (electrons), x-rays, gamma rays, and neutrons. Among these, an electron beam with uniform energy can be used to prepare the crosslinked polyolefin foam / crosslinked polyolefin coating structure. The exposure time, irradiation frequency, and accelerating voltage after electron beam irradiation can vary widely depending on the degree of crosslinking and the thickness of the multilayer structure. However, ionizing radiation generally ranges from approximately 10 kGy to approximately 500 kGy, approximately 20 kGy to approximately 300 kGy, or approximately 20 kGy to approximately 200 kGy. If the exposure is too low, cell stability may not be maintained after foaming.If the exposure is too high, the moldability of the resulting multilayer foam structure may be poor. Moldability is a desirable property when the multilayer foam sheet is used in thermoforming applications. Furthermore, the unfoamed sheet can soften due to exothermic heat release after exposure to electron beam radiation, such that the structure may deform when the exposure is too high. Additionally, the polymeric components may also degrade due to excessive polymer chain cleavage. The coextruded, non-foamed, multi-layer sheet can be irradiated up to four separate times, preferably no more than twice, and preferably only once. If the irradiation frequency exceeds approximately four times, the polymer components may suffer degradation such that, after foaming, for example, uniform cells are not created in the resulting foaming layers. When the thickness of the extruded structure is greater than approximately 4 mm, it may be preferable to irradiate each primary surface of the multi-layer profile with ionized radiation to make the degree of crosslinking between the primary surfaces and the inner layer more uniform. Electron beam irradiation offers the advantage that coextruded sheets of varying thicknesses can be effectively crosslinked by controlling the electron acceleration voltage. The acceleration voltage can generally range from approximately 200 kV to approximately 1500 kV, approximately 400 kV to approximately 1200 kV, or approximately 600 kV to approximately 1000 kV. If the acceleration voltage is lower than approximately 200 kV, the radiation may not reach the inner portion of the coextruded sheets. As a result, the cells in the inner portion may be coarse and uneven during foaming. Furthermore, an acceleration voltage that is too low for a given thickness profile can cause arcing, resulting in perforations or tunneling in the foamed structure.On the other hand, if the accelerating voltage is greater than approximately 1500 kV, then the polymers may degrade. In some configurations, the radiation source may be directed towards layer B of the unfoamed coextruded multilayer sheet during irradiation. In some configurations, the radiation source may be directed towards layer A of the unfoamed coextruded multilayer sheet during irradiation. Regardless of the type of ionizing radiation selected, crosslinking can be achieved such that the composition of the extruded structure is crosslinked from approximately 20 to approximately 75% or from approximately 30 to approximately 60%, as measured by the "Toray Gel Fraction Percentage Method." According to the "Toray Gel Fraction Percentage Method," tetralin solvent is used to dissolve non-crosslinked polyolefin components in a composition. Essentially, the non-crosslinked polyolefin material is dissolved in tetralin, and the degree of crosslinking is expressed as the weight percentage of crosslinked material in the entire composition. The apparatus used to determine the polymer crosslinking percentage includes: 100 mesh (0.11 mm (0.0.045 inch diameter wire); type 304 stainless steel bags; numbered wires and clamps; a Miyamoto thermostatic oil bath apparatus; an analytical balance; a fume hood; a gas burner; a high-temperature oven; an antistatic gun; and three 3.5-liter wide stainless steel containers with lids. The reagents and materials used include high molecular weight tetralin solvent, acetone, and silicone oil. Specifically, an empty wire mesh bag is weighed and the weight recorded. For each sample, 100 milligrams ± 5 milligrams of sample are weighed and transferred to the wire mesh bag. The weight of the wire mesh bag and the sample, usually in the form of thinly sliced ​​foam scraps, is recorded. Each bag is attached to the corresponding number of wires and clamps. When the solvent temperature reaches 130 °C, the envelope (bag and sample) is immersed in the solvent.The samples are swirled up and down approximately 5 or 6 times to loosen any air bubbles and thoroughly wet them. The samples are then attached to a shaker and shaken for three (3) hours to allow the solvent to dissolve any foam. The samples are then cooled in a fume hood. They are washed by swirling up and down approximately 7 or 8 times in a container of primary acetone. The samples are washed a second time in a second acetone wash. The washed samples are then washed once more in a third container of fresh acetone, as before. The samples are then hung in a fume hood to evaporate the acetone for approximately 1 to 5 minutes. The samples are then dried in a drying oven for approximately 1 hour at 120°C. The samples are cooled for a minimum of approximately 15 minutes.The wire mesh bag is weighed on an analytical balance and the weight is recorded. The crosslinking is then calculated using the formula 100*(CA) / (BA), where A = weight of empty wire mesh bag; B = weight of wire bag + foam sample before immersion in tetralin; and C = weight of wire bag + dissolved sample after immersion in tetralin. It is important to note that polyamide does not dissolve in tetralin. Therefore, the gel percentage calculated in the previous method includes both the crosslinked polyolefin components and the polyamide components. Suitable crosslinking promoters include, but are not limited to, commercially available difunctional, trifunctional, tetrafunctional, pentafunctional, and higher-functionality monomers. These crosslinking monomers are available in liquid, solid, granular, and powder forms.Examples include, but are not limited to, acrylates or methacrylates such as 1,6-hexanediol diacrylate, 1,6-hexanediol triacrylate, ethylene glycol diacrylate, ethylene glycol dimethacrylate, trimethylolpropane trimethacrylate, tetramethylolmethane triacrylate, 1,9-nonanediol dimethacrylate, and 1,10-decanediol dimethacrylate; allyl esters of carboxylic acids (such as trimellitic acid trialyl ester, pyromellitic acid trialyl ester, and oxalic acid diallyl ester); allyl esters of cyanulic acid or isocyanulic acid such as trialyl cyanurate and trialyl isocyanurate; Maleimide compounds such as N-phenylmaleimide and N,N'-m-phenylenylenebismaleimide; compounds having at least two triple bonds such as italic acid dipropagyl of maleic acid; and divinylbenzene. Additionally, these crosslinking promoters can be used alone or in any combination.Divinylbenzene (DVB), a difunctional liquid crosslinking monomer, may be used as a crosslinking promoter in this disclosure. For example, a suitable commercially available DVB may include DVB HP by Dow Chemical Company. The amount of crosslinking promoter in a foam layer composition may be less than or equal to approximately 5% PPR, approximately 4% PPR, approximately 3% PPR, approximately 2.5% PPR, approximately 2% PPR, approximately 1.5% PPR, or approximately 1% PPR of the composition. In some embodiments, the amount of crosslinking promoter in a foam layer composition may be greater than or equal to approximately 0.5% PPR, approximately 1% PPR, approximately 1.5% PPR, approximately 2% PPR, approximately 2.5% PPR, approximately 3% PPR, or approximately 4% PPR of the composition. In some embodiments, the amount of crosslinking promoter in a foam layer composition may be approximately 0.5% PPR to 5% PPR, approximately 0.5% PPR to 3% PPR, approximately 1% PPR to 3% PPR, or approximately 2% PPR to 3% PPR of the composition.In some forms, the amount of crosslinking promoter in a foam layer composition can be approximately 0.5% by weight to 5% by weight or approximately 1% by weight to 3% by weight of the foam layer composition. It should be noted that the quantities of crosslinking promoter listed above may be specific to DVB only. Other crosslinking promoters may be more or less efficient at crosslinking than DVB. Therefore, the quantity required for another crosslinking promoter should be considered accordingly. Crosslinking promoters can vary in crosslinking efficiency based on the ionizing radiation dose, the polymers being crosslinked, the chemical structure of the monomer, the number of functional groups in the monomer, and whether the monomer is a liquid or a powder. Appropriate crosslinks can be generated using a variety of techniques and can form intermolecularly, between different polymer molecules, and intramolecularly between portions of a single polymer molecule. These techniques include, but are not limited to, providing crosslinking promoters that are cleaved from a polymer chain and providing polymer chains that incorporate a crosslinking promoter containing a functional group that can form a crosslink or be activated to form a crosslink. After irradiating the coextruded sheet, foaming can be achieved by heating the crosslinked multilayer sheet to a temperature higher than the decomposition temperature of the thermally decomposing blowing agent. Foaming can be carried out at approximately 200°C to 260°C or approximately 220°C to 240°C in a continuous process. A continuous foaming process may be preferable to a batch process for the production of continuous foam sheet. Foaming can typically be achieved by heating the cross-linked multi-layer sheet with molten salt, radiant heaters, a vertical or horizontal hot air oven, microwave energy, or a combination of these methods. Foaming can also be carried out in an impregnation process using, for example, nitrogen in an autoclave, followed by free foaming using molten salt, radiant heaters, a vertical or horizontal hot air oven, microwave energy, or a combination of these methods. Optionally, the cross-linked multi-layer sheet can be softened by preheating before foaming. This can help stabilize the expansion of the structure after foaming, particularly with thick, rigid sheets. The overall thickness of the multi-layer foam sheet can be measured according to JIS K6767. The thickness of the coating layer of a multi-layer foam sheet can be measured using a microscope. To measure the coating layer, a small sample can be taken from the foam structure of the continuous foam sheet. The sample can be cut with an extra-sharp blade, and the cross-section can be viewed along the cut with a microscope. A measurement can be taken with either a digital or traditional microscope. A typical commercial digital microscope may have various software features to facilitate thickness measurement. A traditional commercial microscope may have a lens with measuring scales to facilitate thickness measurement. The density of multi-layer foam sheets can be defined and measured using sectional or overall density, rather than core density, as measured by JIS K6767. Multi-layer foam sheets produced using the method described above can produce foams with sectional or overall densities of approximately 20 kg / m³ to 250 kg / m³, approximately 30 kg / m³ to 200 kg / m³, or approximately 50 kg / m³ to 150 kg / m³. The sectional density can be controlled by the amount of blowing agent and the thickness of the extruded structure. If the density of the multi-layer foam sheet is less than approximately 20 kg / m³, the sheet may not foam efficiently due to the large amount of chemical blowing agent required to achieve the desired density.Furthermore, if the sheet density is less than approximately 20 kg / m³, then the sheet expansion during the foaming step can become increasingly difficult to control. Additionally, if the density of the multi-layer foam sheet is less than approximately 20 kg / m³, then the foam can become increasingly prone to cell collapse. Consequently, it can be difficult to produce a multi-layer foam sheet with uniform cross-sectional density and thickness at a density lower than approximately 20 kg / m³. In some forms, the multi-layer foam sheet is not limited to a section density of approximately 250 kg / m³. Foam with a section density of approximately 350 kg / m³, approximately 450 kg / m³, or approximately 550 kg / m³ can also be produced. However, a foam sheet with a density of less than approximately 250 kg / m³ may be preferable, as higher densities can generally be prohibitively expensive compared to other materials that can be used in a given application. Foam layers produced using the method described above may have closed cells. Preferably, at least 90% of the cells have undamaged cell walls, preferably at least 95%, and more preferably 98%. The average cell size may be from approximately 0.05 mm to approximately 1.0 mm, and preferably from approximately 0.1 mm to approximately 0.7 mm. If the average cell size is less than approximately 0.05 mm, then the density of the foam structure may typically be greater than 250 kg / m³. If the average cell size is larger than 1 mm, the foam may have an uneven surface. There is also a possibility that the foam structure may tear undesirably if the cell population in the foam does not have the preferred average cell size. This can occur when the foam structure is stretched or portions of it undergo secondary processing.The cell size in foam layers can have a bimodal distribution representing a population of cells in the core of the foam structure that are relatively round and a population of cells in the lining near the surfaces of the foam structure that are relatively flat, thin and / or oblong. The overall thickness of the multi-layer polyolefin foam / polyamide coating sheet can range from approximately 0.2 mm to approximately 50 mm, from approximately 0.4 mm to approximately 40 mm, from approximately 0.6 mm to approximately 30 mm, or from approximately 0.8 mm to approximately 20 mm. If the thickness is less than approximately 0.2 mm, foaming may not be efficient due to significant gas loss from the primary surfaces. If the thickness is greater than approximately 50 mm, expansion during the foaming step can become increasingly difficult to control. Consequently, it can become increasingly difficult to produce a multi-layer polyolefin foam / polyolefin coating sheet with uniform cross-sectional density and thickness. In some embodiments, a coating layer of the coextruded foamed multi-layer structure can have a thickness of approximately 0.0001 mm to 0.2 mm, approximately 0.001 mm to 0.15 mm, or approximately 0.05 mm to 0.1 mm. In some embodiments, a foam layer of the coextruded foamed multi-layer structure may have a thickness of approximately 0.5 mm to 6 mm, approximately 1 mm to 5 mm, or approximately 2 mm to 4 mm. In some forms, the desired thickness can be achieved by a secondary process such as slicing, trimming, or joining. Slicing, trimming, or joining can produce a thickness range from approximately 0.1 mm to approximately 100 mm. The thickness of the coating layer can be reduced when foam forms on the multi-layer sheet. This is because the foamable layers expand, stretching the coating layers. Therefore, for example, if the multi-layer sheet expands to twice its original area, the coating thickness can be expected to be reduced by approximately half. If the multi-layer sheet expands to four times its original area, the coating thickness can be expected to be reduced to approximately one-quarter of its original thickness. The disclosed multi-layer foam structures can be used in a variety of applications. One such application is as a product manufactured through LPM (Linear Polymer Manufacturing). The brief description provided a description of the multi-layer foam structure as a trim component in a vehicle interior (specifically, a door panel). However, the multi-layer foam structure is not limited to vehicle door panels and can also be used in other interior vehicle parts, such as door roll bars, door inserts, door fillers, trunk fillers, armrests, center consoles, seat cushions, seat backs, headrests, seat back panels, knee pads, or headliners. Another application is in thermoformed articles. To thermoform the multilayer foam structure, the structure can be heated to the melting point of both the polyolefin foam layer and the polyamide coating layer. Since most commercially available polyamides have a higher melting point than the polyolefin components described in the disclosure, the multilayer foam structure can be heated to the polyamide's melting point. An example of a thermoformed item is an automotive air duct. A closed-cell foam structure can be particularly suitable for this application due to its lower weight (compared to solid plastic), its insulating properties that help maintain the temperature of the air flowing through the duct, and its vibration resistance (compared to solid plastic). A polyamide coating on the exterior of the multi-layered air duct can protect it from contact with under-hood fluids and greases inside the vehicle, which could negatively affect the functionality of the polyolefin foam. The coating can also protect the foam layer from punctures and cuts during installation and throughout the vehicle's lifespan. Therefore, a firm polyolefin foam with a polyamide coating can be suitable for an automotive air duct. In some embodiments, multi-layer foam structures may be laminates containing the multi-layer foam and a laminate layer. Preferably, the laminate layer may be applied to one side (i.e., surface) of a foam layer opposite the coating layer. In these laminates, the multi-layer foam structure may be combined, for example, with a film and / or sheet. Examples of suitable materials for these layers include, but are not limited to, polyvinyl chloride (PVC); thermoplastic polyolefin (TPO); thermoplastic urethane (TPU); fabrics such as polyester, polypropylene, rag, and other textiles; leather; and / or fiber layers such as nonwovens. These layers may be manufactured using standard techniques that are well known to those skilled in the art. Importantly, the multi-layer foam of the disclosure may include multiple other layers. In these laminates, one layer can be bonded to an adjacent layer by chemical bonds, mechanical means, or combinations thereof. Adjacent laminate layers can also be bonded together by any other means, including the use of attractive forces between materials with opposite electromagnetic charges or attractive forces between materials that are either predominantly hydrophobic or predominantly hydrophilic. To meet the requirements of any of the above applications, the structures described in this disclosure may be subjected to various secondary processes, including, but not limited to, embossing, corona or plasma treatment, surface roughening, surface smoothing, drilling or micro-drilling, splicing, cutting, trimming, layering, bonding, and hole punching. Examples Raw materials for the examples Table 1 below provides a list of components and descriptions of those components used in the following examples. Table 1 Materials used to produce crosslinked and coextruded polyolefin foam with polyamide coating layers Component Type Manufacturer MFI Description / Notes PA 1212BR- III PA1212 Shandong Dongchen New Technology — commercially produced GrilamidMR L20 PA12 EMS-CHEMIE (EMSGRIVORY) — commercially produced Plexar® PX6006 Random copolymer of MAH-gPP-PE Lyondel IBasell 4.0 (2.16 kg, 230 °C) random copolymer of polypropylene grafted with maleic anhydride commercially produced 6232 Random copolymer of PP / PE Total Petrochemicals 1.3- 1.6 (2.16 kg, 230 °C) commercially produced Infuse™ OBC 9107 OBC (PE / octane-based copolymer) Dow 0.75–1.25 (2.16 kg, 190 °C) commercially produced olefin block copolymer Adflex™ Q100F rTPO (PP / PE random copolymer-based) Lyondell IBasell 0.5–0.7 (2.6 kg, 230 °C) commercially produced reactor thermoplastic polyolefin Unifoam® TC-181 foaming chemical agent (ADCA) PT Lauten Otsuka Chemical — commercially produced azodicarbonamide DVB HP crosslinking promoter Dow — 80% content commercially produced DVB PR086 antioxidant pack Amfine Chemical — a Toray Plastics (America) standard antioxidant pack consisting of 100% antioxidant powder PR023 antioxidant pack (LDPE vehicle) Techmer PM a Toray standard antioxidant pack Plastics (America) for polyolefin foam, composed of Techmer PM, consisting of 14% antioxidants, 0.35% calcium stearate and 85.65% low-density polyethylene (LDPE) vehicle resin TPM11166 processing aid (LLDPE / butene copolymer vehicle) Techmer PM commercially produced processing aid blend 9040 black concentrate (PE / methyl acrylate copolymer carrier) Modern Dispersions commercially produced color concentrate, 40% carbon black filler, typical carbon black particle size 19 Nm. Conversion process for examples Table 2 below provides formulation and coextrusion information for examples 1 and 2. All the samples foamed when the multi-layered sheet was heated with molten salt. TABLE 2. Crosslinked and coextruded polyolefin foam with polyamide coating layers - Examples Formulaciones resinas (% PPR y % general) aditivos (% PPR y % general) PA1 PA12 Copolí Copolí OBC rTPO agent promo paquet envase auxiliar concen 212 mero mero (copolí (basa e torde e de antioxi de trado aleator aleator mero do en químic reticul antioxi dante procesa negro io de io de basad copolí o ación dante (vehíc miento (portad ΜΑΗ- PP / o en mero espu ulo de (vehícul orde g-PP- PE PE / oct aleato mante LDPE) o de copolí PE ano) rio de (ADC copolím mero PP / A) ero de de PE PE) LLDPE / / acriiat buteno) o de metilo) Axis ID mpl o layer ID PA Plexar Infuse Adflex Unifoa 1212 Grila ® ™ ™ m® BR- midMR PX600 OBC Q100 TC- DVB PR08 PR02 TPM111 III L20 6 6232 9107 F 181 HP 6 3 66 9040 Axis mpl o 1 Coating layer B 75 % 25 % 72.8 24.27 2 % % 1.0% 2% 0.97 % 1.9 % Layer A (foam) 25% 25% 40% 10% 21.46 21.46 34.33 8.58 % % % % 6.50 2.50 % % 5.5 % 2% 5.58 2.15 4.72% 1.72% % % Example mpl o2 Coating layer B 75% 25% 72.82 24.27 % % 1.0 % 2% 0.97 % 1.9 % Layer A (foamed) 25% 25% 40% 10% 21.46 21.46 34.33 8.58 % % % % 6.50 2.50 % % 5.5 % 2% 5.58 2.15 4.72% 1.72% % % TABLE 2 (CONTINUED) COEXTRUSION Example ID Layer ID Coating Energy Thickness General Temperature Sheet No No Extrusion Melt Foamed Foamed Extruder Type (kW-h / kg) (SC) (mm) (mm) Example 1 Coating Layer B 80 / 20 Feed Block Collector Twin Screw Co-extrusion 0.25 199 1.57 - 1.70 0.23-0.30 Layer A (foamed) Twin Screw Co-extrusion 0.17 Not Recorded* ___ Example 2 Coating Layer B 80 / 20 Feed Block Collector Twin Screw Co-extrusion 0.30 185 1.41 - 1.49 0.21 - 0.24 Layer A (foamed) Twin Screw Co-extrusion 0.19 Not Recorded* ___ * The fusion probe thermocouple is not working Table 3 below provides irradiation and multilayer structure properties for Examples 1 and 2. The unfoamed sheet sections of Example 1 were irradiated in three separate doses and were further identified as Examples 1A to 1C. The unfoamed sheet sections of Example 2 were irradiated in seven separate doses and were further identified as Examples 2A to 2G. Table 3 Crosslinked and coextruded polyolefin foam with polyamide coating layers - Examples IRRADIATION FOAM FORMATION IMAGE S ID of the example ID of the layer Which layer is facing the radiation source? Dosed voltage (kGy) e (kV) Formation temperature Thickness Density of (coating= gel foam pm, general (°C) foam=mm) (kg / m3) (%) Are photos of non-foamed and foamed included? Example 1A Coating layer B 45 750 236 0.07 101 45 Layer A (foamed towards radiation 2.8) Example 1B Coating layer B 60 750 236 0.08 97 54 yes Layer A (foamed towards radiation 2.7) Example 1C Coating layer B 75 750 236 0.06 91 58 Layer A (foamed towards radiation 3.1) Example 2A Coating layer B 30 750 234 0.05 83 22 yes Layer A (foamed towards radiation 2.6) Example 2B Coating layer B 45 750 234 0.04 74 32 Layer A (foamed towards radiation 2.7 Example 2C Coating layer B 60 750 234 0.04 66 42 Layer A (foamed towards radiation 3.0 Example Layer of 75 750 234 0.04 62 48 yes or 2D coating B Layer A (foamed towards radiation 3.2 Example 2E Coating layer B 90 750 234 0.03 66 55 Layer A (foamed towards radiation 3.1 Example 2F Coating layer B 105 750 234 0.03 64 58 Layer A (foamed towards radiation 3.3 Example 2G Coating layer B 120 750 234 0.03 71 61 yes Layer A (foamed towards radiation 3.2 Cross-sectional images of microtome slices of the non-foamed multilayered structures of examples 1B, 2A, 2D, and 2G at 100X magnification can be found in Figures 1, 3, 5, and 7. Images of the corresponding foamed examples 1B, 2A, 2D, and 2G at 20X magnification can be found in Figures 2, 4, 6, and 8. This application discloses several numerical ranges in the text and figures. The disclosed numerical ranges inherently support any interval or value within the disclosed numerical ranges, including endpoints, even if a precise range limitation is not explicitly stated in the specification, because this disclosure can be practiced across the entire disclosed numerical range. The foregoing description is presented to enable a person skilled in the art to make and use the disclosure, and is provided in the context of a particular application and its requirements. Several modifications to the preferred embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the disclosure. Accordingly, it is not proposed that this disclosure be limited to the embodiments shown, but rather that the broadest scope consistent with the principles and features disclosed herein be agreed upon. Finally, all disclosures in the patents and publications referenced in this application are hereby incorporated by reference.

Claims

1. A method for forming a multilayer foam structure comprising: coextrusion; a first layer comprising: polypropylene, polyethylene, or a combination of polypropylene and polyethylene; and a chemical foaming agent; and a second layer on one side of the first layer, the second layer comprising: polyamide; and polypropylene, polyethylene, or a combination of polypropylene and polyethylene; irradiating the coextruded layers with ionizing radiation; and foaming the irradiated coextruded layers.

2. The method according to claim 1, wherein the first layer comprises at least 70% by weight of polypropylene, polyethylene, or a combination of polypropylene and polyethylene.

3. The method according to any of claims 1 to 2, wherein the second layer comprises at least 40% by weight of polyamide.

4. The method according to any of claims 1 to 3, wherein the second layer comprises at most 50% by weight of polypropylene, polyethylene, or a combination of polypropylene and polyethylene; and at least 40% by weight of polyamide.

5. The method according to any of claims 1 to 4, wherein the thickness of the second layer is less than 1 mm.

6. The method according to any of claims 1 to 5, wherein the first layer comprises a crosslinking promoter in an amount of 0.5% by weight to 5.0% by weight.

7. The method according to any of claims 1 to 6, wherein the first layer comprises additives in an amount of 1% by weight to 20% by weight.

8. The method according to any of claims 1 to 7, wherein the second layer comprises additives in an amount of 1% by weight to 10% by weight.

9. The method according to any of claims 1 to 8, wherein the polypropylene has a melt flow index of 0.1 grams to 25 grams per 10 minutes at 230 °C.

10. The method according to any of claims 1 to 9, wherein the polyethylene has a melt flow index of 0.1 grams to 25 grams per 10 minutes at 190 °C.

11. The method according to any of claims 1 to 10, wherein the amount of chemical foaming agent in the first layer is 3 to 15% by weight.

12. The method according to any of claims 1 to 11, wherein the foaming chemical agent comprises azodicarbonamide.

13. The method according to any one of claims 1 to 12, wherein the ionizing radiation is selected from the group consisting of alpha, beta (electrons), X-rays, gamma, and neutrons.

14. The method according to any of claims 1 to 13, wherein the coextruded structure is irradiated up to four times separately.

15. The method according to any of claims 1 to 14, wherein the ionizing radiation is an electron beam with an accelerating voltage of 200 kV to 1500 kV.

16. The method according to claim 15, wherein an absorbed electron beam dosage is 10-500 kGy.

17. The method according to any of claims 1 to 16, wherein the ionizing radiation cross-links the extruded structure to a degree of cross-linking of 20% to 75%.

18. The method according to any of claims 1 to 17, wherein the foaming comprises heating the irradiated structure with molten salt and radiant heaters or a hot air oven.

19. The method according to any of claims 1 to 18, wherein the density of the multi-layer foam structure is 20 kg / m3 to 250 kg / m3.

20. The method according to any of claims 1 to 19, wherein the multi-layer foam structure has an average closed cell size of 0.05 mm to 1.0 mm.

21. The method according to any of claims 1 to 20, wherein the multi-layer foam structure has a thickness of 0.2 mm to 50 mm.