Anisotropy and Mechanical Properties of Nanoclay Filled, Medium-Density Rigid Polyurethane Foams Produced in a Sealed Mold, from Renewable Resources

Medium-density rigid polyurethane (PU) foams are often produced in sealed molds; therefore, the processes inside the mold and structure of the produced foam blocks need to be understood. The structural and mechanical anisotropy is shown to be the third variable along with (1) concentration of the nanoclay filler and (2) density, to determine the mechanical properties of the filled PU foam composites produced in a sealed mold. The varying anisotropy of the specimens hinders the accurate evaluation of the filling effect. The methodology for the estimation of the anisotropy characteristics of specimens from different locations within the nanoclay filled PU foam blocks is elaborated. A criterion, based on analysis of Poisson’s ratios, is formulated for the selection of specimens with similar anisotropy characteristics. The shear and bulk moduli are estimated theoretically, dependent on the filler’s concentration, using the experimentally determined constants.


Introduction
Rigid polyurethane (PU) foams of medium apparent density~200-250 kg/m 3 are widely applied as a structural material in various engineering solutions, especially in the automotive industry for test milling, design studies and modelling; as substructures for model pastes; making of simple negative molds and laminating molds; for impact absorption, etc. [1][2][3][4]; as encapsulants for electronic components to mitigate harsh thermal and mechanical environments and to provide electrical isolation [5,6], etc.
In PU foam production, one sustainable solution is the use of recycled materials instead of petrochemical raw materials. The poly(ethylene terephthalate) (PET) manufacturing by-product provides an appropriate resource for aromatic polyester polyols. PU foams obtained from these polyols have better mechanical and thermal properties because of the introduction of the aromatic structure into the PU polymer matrix [7][8][9][10].
Nanoclay, such as montmorillonite (MMT), has become a popular nanofiller in many polymeric systems as it imparts characteristics such as light weight, improved thermal stability, flame retardancy, and high compressive strength [9,[11][12][13][14]. However, the hydrophilic nature of MMT causes a weak interfacial adhesion with the polymer matrix which is hydrophobic [14]. Modification of the MMT is needed in order to enhance the compatibility and dispersibility of the MMT in the polymer matrix, thus improving the load transfer efficiency of the system [14,15]. The interface between the filler and the polymer matrix in the nanocomposites constitutes a larger area than in ordinary composites based on micrometer-sized fillers; therefore, the interface impacts the properties of the nanocomposites to a higher degree [12,15].

Raw Materials
The aromatic polyester polyol (APP) NEOpolyol-380 used in the given investigation was produced by Neo Group, Rimkai, Lithuania. The company produces mainly PET granules and PET bottles. The by-product of those commodities comprises PET dust and other industrial waste, which is directly transferred into a glycolysis reactor where it is converted into APP. A higher functional polyether polyol based on sorbitol Lupranol 3422 (contains only secondary hydroxyl groups, OH value 490 mg KOH/g) from BASF, Ludwigshafen, Germany, was added to increase the cross-linkage density of the polymer matrix. An additive surfactant NIAX Silicone L6915 was used to obtain closed-cell PU foams. The reactive delayed action time amine-based catalyst NP-10, available from Momentive Performance Materials Inc., Niskayuna, NY, USA, was used. Tris(chloropropyl)phosphate (TCPP) from LANXESS Deutschland GmbH, El Dorado, AR, USA, was used as a flame retardant. Water acts as a chemical blowing agent and releases carbon dioxide CO 2 in reaction with isocyanate. Polymeric diphenylmethane diisocyanate-IsoPMDI 92140 (pMDI) from BASF, Ludwigshafen, Germany, -was used as an isocyanate component (NCO = 31.5 wt.%).

Production of NEOpolyol-380 PU Foams in a Sealed Mold
Rigid polyurethane (PU) foams blocks shaped as a truncated pyramid, top 15 × 15 cm, bottom 14 × 14 cm, height 5 cm and inner volume 0.00105 m 3 , were produced in a sealed steel mold, Figure 1. The polyol component was made by weighing the components (he recycled polyol NEOpolyol-380, cross-linking agent Lupranol 3422, flame retardant, blowing agent, catalyst and surfactant) and stirring them for 1 min with a mechanical stirrer at 2000 rpm. similar anisotropy characteristics reduced the influence of anisotropy variations, especially for the reference material-the neat PU foams-and thus, the accuracy of estimation of the filling effect on the mechanical properties was increased.

Raw Materials
The aromatic polyester polyol (APP) NEOpolyol-380 used in the given investigation was produced by Neo Group, Rimkai, Lithuania. The company produces mainly PET granules and PET bottles. The by-product of those commodities comprises PET dust and other industrial waste, which is directly transferred into a glycolysis reactor where it is converted into APP. A higher functional polyether polyol based on sorbitol Lupranol 3422 (contains only secondary hydroxyl groups, OH value 490 mg KOH/g) from BASF, Ludwigshafen, Germany, was added to increase the cross-linkage density of the polymer matrix. An additive surfactant NIAX Silicone L6915 was used to obtain closed-cell PU foams. The reactive delayed action time amine-based catalyst NP-10, available from Momentive Performance Materials Inc., Niskayuna, NY, USA, was used. Tris(chloropropyl)phosphate (TCPP) from LANXESS Deutschland GmbH, El Dorado, AR, USA, was used as a flame retardant. Water acts as a chemical blowing agent and releases carbon dioxide CO2 in reaction with isocyanate. Polymeric diphenylmethane diisocyanate-IsoPMDI 92140 (pMDI) from BASF, Ludwigshafen, Germany, -was used as an isocyanate component (NCO = 31.5 wt %).

Production of NEOpolyol-380 PU Foams in a Sealed Mold
Rigid polyurethane (PU) foams blocks shaped as a truncated pyramid, top 15 × 15 cm, bottom 14 × 14 cm, height 5 cm and inner volume 0.00105 m 3 , were produced in a sealed steel mold, Figure 1. The polyol component was made by weighing the components (he recycled polyol NEOpolyol-380, cross-linking agent Lupranol 3422, flame retardant, blowing agent, catalyst and surfactant) and stirring them for 1 min with a mechanical stirrer at 2000 rpm. The pMDI and polyol components were weighed and mixed with a mechanical stirrer at 2000 rpm for 15 s. The mold was preheated to 50 °C and an appropriate amount of the reacting mixture was poured into it; then, the mold was sealed. The mass of the reacting mixture was calculated in order to obtain PU foams with an approximate apparent overall density of 250 kg/m 3 . The pMDI and polyol components were weighed and mixed with a mechanical stirrer at 2000 rpm for 15 s. The mold was preheated to 50 • C and an appropriate amount of the reacting mixture was poured into it; then, the mold was sealed. The mass of the reacting mixture was calculated in order to obtain PU foams with an approximate apparent overall density of 250 kg/m 3 .
The mixed-in air and gases of the chemical reactions escaped from the mold through 4 peripheral and 1 central gas-release holes (PGRH-s and CGRH). The CGRH was closed after all air/gases had escaped and the foaming mixture started to come out. The PGRH-s were left open and the foams sealed them by coming out and hardening. Then the PU foams were cured at 50 • C for 2 h. The mold was cooled to room temperature; PU foam block was removed and conditioned for at least 24 h. In a sealed mold, where overpressure occurs, the PU foams' gaseous cells are more spherical than ellipsoidal, so that an isotropic structure is obtained. In a study on sandwich panel manufacturing, a sealed mold and overpressure was used to obtain an isotropic PU foam core [24]. The closeness of the PU foams' structure to isotropic one depends on how high the overpressure is. In sandwich panels manufactured at a lower overpressure, an anisotropic structure can be observed [25].
The PU foams' formulation is given in Table 1. The formulation comprised~15% of recycled materials. The recycled APP NEOpolyol-380 can be considered a sustainable raw material, because it is produced from industrial PET waste. Nanoclay Cloisite-30B was added as a filler in concentrations η = 0.00, 0.25, 0.50, 1.00, 2.00, 3.00 and 5.00% of the mass of the filled reacting mixture by mixing the filler into the NEOpolyol-380 with a high shear mixer Silverson, East Longmeadow, MA, USA, for 20 min at 8000 rpm.
The mass of the liquid reacting mixture, poured into the mold, was calculated so as to make PU foam blocks of apparent overall density ≈250 kg/m 3 (skins included; ISO 845:2006). The technological target was to keep the mass of the filled reacting mixture constant for all 7 concentrations: m 0 = 250 g = const. Foaming in a sealed mold, with counter-pressure, is supposed to provide PU foams of nearly isotropic structure.
The content of closed cells in neat PU foams was measured (ISO 4590:2016). Density of neat, free-rise PU foams of the given formulation, see Table 1, was determined, producing foams in an open mold of the same transversal dimensions as those of the sealable mold. The value of overpressure in the sealed mold was calculated as p ov = ρ sm /ρ 0 , where ρ sm is the apparent overall density of a block produced in a sealed mold and ρ 0 is the same for a block produced in an open mold.

XRD Analysis
When nanoclay is filled into a monolithic polymer or plastic foam, the mechanical properties of the composite are determined by the degree of dispersion, intercalation, and/or exfoliation of the filler. Intercalation and exfoliation of Cloisite-30B monolayers were evaluated via the basal spacing by X-ray diffraction (XRD), at a 5 wt.% concentration of nanoclay (from the mass of NEOpolyol-380) in "Cloisite-30B-NEOpolyol-380" dispersions. The dispersions were made by (a) high shear mixing with a mixer Silverson, East Longmeadow, MA, USA, the effective mixing time 20 min at 8000 rpm and (b) sonication, the effective sonication time 20 min. An Ultrasonic Cell Crusher, MRC, Holon, Israel, was applied over short periods, frequency 20-25 Hz, 5 s of active period and 5 s of passive period to reduce heating of the mixture. Temperature limit was set to 40 • C and was controlled by a water bath. At both dispersion modes, milky, homogenous, and stable dispersions were produced.
The "Bruker D8 Discover" diffractometer, Bruker AXS GmbH Karlsruhe, Germany, was applied to obtain XRD patterns of the "Cloisite-30B-NEOpolyol-380" dispersions. The diffractometer comprised a "LynxEye" detector, operated in 0D-mode and a copper radiation source (CuKα), operated at a wavelength λ = 0.15418 nm. The tube voltage of the diffractometer was set to 40 kV and the current to 40 mA. The width of the divergence slit was 0.2 mm and that of the anti-scattering slit 8.0 mm. An appropriate amount of dispersion was spilled into holders, which were rotated during measurement. Registration of the XRD patterns was made at a speed of scan 10 s/0.01 • from 1.5 to 7 degrees (in the 2θ scale).

NEOpolyol-380 PU Foams' Blocks and Specimens
The mass of the 7 NEOpolyol-380 PU foam blocks was determined. Each block was divided into four sections: C-a and C-b for compression specimens; T-a and T-b for tension specimens, see Figure 2, where the foams' rise direction was parallel to the axis OX 3 and X 1 OX 2 was the plane of isotropy. Molding skins, thickness~8 . . . 10 mm, were cut off prior to making the specimens.
Five compression specimens shaped as cubes of dimensions 22 × 22 × 22 mm were made from each section C-a and C-b and their apparent core density (ISO 845:2006, further density) was determined. Three parallelepipeds, size ≈ 10 × 33 × 140 mm, precursors of tension specimens, were made from each section T-a and T-b and their density was determined. A dumbbell shaped tension specimen with a straight work zone of dimensions l t0 ≈ 10 × 24 × 50 mm was made from each precursor. Prior to the test, the work zone was marked on the tension specimens and its dimensions were measured. After testing, the work zone elements were cut from the ruptured specimen, weighed and initial density in the work zone was calculated.
The compression specimens were made as cubes in order to measure the lateral and transversal displacements simultaneously, on one and the same side of a specimen. The values of the displacements allowed us to calculate the Young's moduli and Poisson's ratios in compression (1) parallel and (2) perpendicular to the foams' rise direction. The size of specimens was chosen so as to have them located in the zone of uniform density of the PU foam blocks, because the compressive response of PU foams is more sensitive to nonhomogeneous density than the tensile response. The tension specimens were made with their longitudinal axis parallel to the axis OX 1 , Figure 2; thus, the elasticity modulus E 1 , Poisson's ratio ν 12 and strength σ 11 were determined both in compression and tension and a comparison could be made.

Gradient of Density
To estimate gradient of density ρ' = δρ/δx 2 along axis OX 2 in the sections C-a and C-b, their density was determined prior to making compression specimens. The relative difference in densities was calculated as R = ∆ρ/ρ C-a = (ρ C-a − ρ C-b )/ρ C-a , where ρ C-a and ρ C-b are density of the sections. Additional estimation of NEOpolyol-380 foams' structure at the sides of the blocks was made with a light microscope Diamond MCXMP500, MICROS Produktions-& Handels GmbH, Sankt Veit an der Glan, Austria, on thin layers of foams, in transmitted lighting, magnification 10×.

Density of Compression and Tension Specimens
The locations of the compression specimens in the NEOpolyol-380 PU foams' blocks were denoted as "Side" (1, 1 and 5, 5 ), "Intermediate" (2, 2 and 4, 4 ) and "Central" (3, 3 ), Figure 2. The average density, standard deviation and coefficient of variations were estimated for specimens from the sections C-a and C-b. The densities of specimens from similar locations 1, 1 ; 2, 2 ; 3, 3 ; 4, 4 and 5, 5 in the sections C-a and C-b were compared to estimate the density distribution along the axis OX 2 . Density distribution along axis OX 1 was estimated, comparing densities of specimens 1 . . . 5 and 1 . . . 5 .
The locations of the tension specimens in the blocks were denoted as "Bottom" (1, 1 ), "Middle" (2, 2 ) and "Top" (3, 3 ), Figure 2. The average density, standard deviation and coefficient of variations were estimated for (1) the precursors and (2) the straight part of the tension specimens. Densities of (1) the precursors and (2) the straight part of the tension specimens from similar locations 1, 1 ; 2, 2 and 3, 3 in the sections T-a and T-b were compared to estimate the density distribution along the axis OX 2 . Density distribution along axis OX 3 was estimated, comparing densities of specimens 1-3 and 1 -3 . Density distribution along axis OX 1 was estimated, comparing densities of the precursors and of the straight part.
Densities of compression specimens from locations 3 and 3 were compared with the densities of tension specimens from locations 2 and 2 , located side by side in a block, symmetrically to the plane X 1 OX 3 , at a similar coordinate OX 3 ( Figure 2).

Mechanical Testing
The mechanical response of NEOpolyol-380 PU foams was tested in compression and tension according to the main principles of ISO 844:2021 and ISO 1926:2009. Stress-strain curves were registered on a testing machine Z-100 TEW, Zwick GmbH & Co. KG, Ulm, Germany, with a video extensometer videoXtens 2-120 HP and a camera uEye 01-3483CP-M-GL. The five compression specimens of the section C-a were loaded parallel to the rise direction OX 3 and those of the section C-b, perpendicular to the RD (parallel to axis OX 1 ), Figure 2. The 3 + 3 = 6 tension specimens of both sections T-a and T-b were loaded perpendicular to the RD (parallel to axis OX 1 ). Displacement was measured parallel to the loading direction: (a) in compression on a base l c = 10 mm and (b) in tension on a base l t = 30 mm, as well as in the transversal direction on bases l c ' = l t ' = 15 mm in compression and in tension, Figure 2. The crosshead speed was 10%/min (2.2 mm/min in compression and 5 mm/min in tension); ambient temperature ≈ 23 • C. Because of the limited height of the mold, the compressive specimens had similar dimensions in the transversal and lateral directions and a homogeneous compressive stress field [1] could not be ensured in the measurement zone. Therefore, the calculated compression modulus E 1 (E 3 ) was considered as stiffness of the specimen in compression parallel to axis OX 1 (OX 3 ).

Poisson's Ratios and Density
Poisson's ratios of cellular plastics depend on structural anisotropy and do not depend directly on density [4,22,23]. To examine it closely, light-weight, highly homogeneous, monotropic, neat PU foams of a standard petrochemical formulation, produced in a free-rise, of different densities <90 kg/m 3 , were ordered from an industrial-scale production enterprise.
Five blocks of core foams, size 50 × 50 × 20 cm, were supplied. The foams were tested in compression and tension according to the main principles of ISO 844:2021 and ISO 1926:2009. To ensure a homogeneous stress field in the measurement zone, the compression specimens were made as rectangular prisms of dimensions 100 × 50 × 50 mm, strain rate 10%/min. The tension specimens were made dumbbell shaped, dimensions of the straight part 20 × 25 × 55 mm, strain rate 10%/min. Displacement was measured parallel to the loading direction, base 30 mm, both in compression and tension as well as in the transversal direction, bases 50 mm in compression and bases 25 mm and 20 mm in tension. Electromechanical testing machine Z-100 TEW, Zwick GmbH & Co. KG, Ulm, Germany, was used for mechanical testing. Four specimens were tested for each data point; the ambient temperature was T = +23 • C. Density of specimens was determined prior to testing.
Moduli E 1 and E 3 , Poisson's ratios ν 12 , ν 13 , ν 31 and ν 32 were determined from the initial, linear region of the stress-strain curves, which were registered for loading in compression parallel and perpendicular to the foams' rise direction and in tension parallel to the rise direction. Strength σ 11max , σ 33max and the corresponding strain ε 11max , ε 33max in compression as well as strength σ 33max and elongation at break ε 33max in tension were determined from the stress-strain curves.

The Criterion of Similar Anisotropy Characteristics
The structure and elastic properties of PU foams often exhibit anisotropy of a certain mode as orthotropy or monotropy [1,2,4,22,23]. Foams produced in an open mold of equal transversal dimensions are monotropic [26][27][28][29]: The degree of monotropy, DM, can be characterized by the ratio of (1) moduli E 3 /E 1 or E 3 /E 2 ; (2) Poisson's ratios ν 31 /ν 13 or ν 32 /ν 23 ; (3), average projections of cells' diameters d 3 /d 1 or d 3 /d 2 ; (4) the average projections of polymeric struts' length l 3 /l 1 or l 3 /l 2 , etc. [1,23,30]. The bigger the height to width ratio of the open mold, the higher the degree of monotropy in the produced foams. Upon reaching the lid, the liquid reacting mixture foaming proceeds similar to a free-rise and the foams are expected to be monotropic/isotropic in a mold with a square cross-section.
The properties of the NEOpolyol-380 PU foams in a block are determined by (1) symmetry of the mold in the horizontal plane X 1 OX 2 , (2) the limiting dimensions of the lab-scale mold, especially height, (3) cooling at the sides, top and bottom of the mold due to nonadiabatic processes, (4) the different rise speeds of the foams in the centre and at the sides of the mold, etc. The specimens occupy different locations in the block relative to the factors mentioned that influence their anisotropy characteristics. Thus, anisotropy is the third variable along with (1) the concentration of the filler and (2) density, determining the mechanical properties of PU foams. Simultaneous variation of several of the foams' characteristics does not permit correct estimation of the dependence of the mechanical properties on the concentration of filler.
It was proposed to reduce the influence of anisotropy variations by selecting specimens with similar characteristics of anisotropy. Since Poisson's ratios of cellular plastics depend on structural anisotropy and do not depend directly on density [4,22,23], a criterion, based on the analysis of the Poisson's ratios, was formulated for the selection of specimens of similar anisotropy characteristics: mode and degree. For NEOpolyol-380 PU foams, produced in a mold of equal transversal dimensions (Figures 1 and 2), the anisotropy mode is monotropy/isotropy and the degree of monotropy DM is estimated by the ratios of Poisson's ratios: DM = ν 31 /ν 13 or DM = ν 32 /ν 23 .
A criterion of similar anisotropy characteristics was formulated: the absolute value of the relative difference between the Poisson's ratio of a specimen and the average value of the corresponding experimental data set must not exceed a predefined limit: |R1 n | ≤ δ 1 ; n = 1, 2, . . . , N1, |R2 n | ≤ δ 2 ; n = 1, 2, . . . , N2 and |R3 n | ≤ δ 3 ; n = 1, 2, . . . , N3, where δ 1 , δ 2 , δ 3 -parameters (5) The values of the parameters were set to δ 1 = δ 2 = δ 3 = 0.1 (10%). To test the selected data, the average values and relative differences were calculated for the selected data sets and their elements were checked again for fulfilling the criterion, now with the recalculated average values and relative differences. The experimental data of the specimens, whose Poisson's ratios fulfil the criterion, were selected for further processing (normalizing, averaging, etc.); the others were excluded. If such data was detected, which do not fulfill the criterion, the selection procedure.

Normalizing of the Mechanical Properties to a Common Density
For each concentration of filler, there were three groups of NEOpolyol-380 PU foam specimens: (1) five specimens for compression parallel to axis OX 1 , (2) five specimens for compression parallel to OX 3 and (3) six specimens for tension parallel to OX 1 . When, in each group, the mechanical properties and density were averaged over the selected specimens, different average densities were acquired, which made comparison of the mechanical properties inaccurate. Therefore the mechanical properties had to be recalculated to a certain common density (normalized).
An empirical relationship exists between a modulus (or strength) and the density of rigid, isotropic, neat PU foams [1,4].
The parameters A and b depend on several factors: (1) the formulation of the polyurethane matrix, (2) the type and concentration of filler, (3) the foaming mode: free-rising (anisotropic foams) or in a sealed mold (isotropic foams), (4) the loading mode: compression or tension, since PU foams often exhibit different mechanical properties in compression and in tension, even in the elastic region, (5) direction of the external load relative to the symmetry elements of the foams; e.g., parallel or perpendicular to the rise direction, (6) shape and aspect ratio of the specimens (height to width), (7) length and location of the measurement base, (8) strain rate, etc. At each combination of the mentioned factors, it would be necessary to produce PU foams in a sufficiently large density range to determine A and b accurately. With A and b known, the value of a modulus or strength can be determined at any density, for which the Equation (6) is valid.
Analysis of the experimental data of Poisson's ratios and moduli showed that the filled NEOpolyol-380 PU foams produced were nearly isotropic. Then at each concentration η of the filler where B(η) and c(η) are parameters. At each concentration of filler, the number of compression specimens in a group was ≤5 and the number of tension specimens was ≤6. The experimentally measured values of E(η) were in a too narrow range of density to determine B(η) and c(η) accurately. It would be necessary to produce the foams in a sufficiently large density range at each concentration of filler and each loading mode. However, due to the technological requirement m 0 = 250 g ≈ const., the average density of each group of the selected specimens differed little from the common density ρ com = 224 kg/m 3 which was calculated as the average density of the 104 selected compression and tension specimens. The relative difference between ρ com and the average density of the selected compression specimens of each group was <3% and of the selected tension specimens, <5%. That permits us to assume c(η) ≈ b and calculate B(η) for each specimen of density ρ: where E(η) is the experimentally measured compression modulus. If there are M ≤ 5 selected compression specimens in a group, the average B(η), characterizing the whole group, can be calculated: Then, the normalized modulus is calculated as: In [9], isotropic neat NEOpolyol-380 PU foams of the same formulation and in the same mold as in the present study were produced. To compare the neat NEOpolyol-380 PU foams produced in the present study and in [9], the values of A and b of neat NEOpolyol-380 PU foams were calculated from the experimental data curves "E-ρ" and "σ-ρ" in [9], Table 2. Table 2. Parameters A and b of neat NEOpolyol-380 PU foams; densities 40 kg/m 3 ≤ ρ ≤ 600 kg/m 3 .

Mechanical Property
Compression Tension Drawing the b values from Table 2, the average A values were calculated for neat NEOpolyol-380 PU foams for the three groups of selected specimens in the present study, Table 3.  The slight differences in A values can be explained by different batches of chemicals and different shapes of compression specimens. No selection of specimens with similar characteristics of anisotropy was made in [9]. In general, good repeatability of the neat NEOpolyol-380 PU foams was identified, allowing us to assume c(η) ≈ b, to draw the b values from the Table 2 and to calculate the averaged and normalized moduli.
The other mechanical properties were normalized in a similar way. No values of parameters A and b were available for the elongation at break ε 11max for neat NEOpolyol-380 PU foams. Therefore, the experimental data of ε 11max of typical petrochemical PU foams [1] was combined with the ε 11max values acquired in the given investigation for neat NEOpolyol-380 PU foams (the selected tension specimens) and the parameters A and b of the best fitting model function, Equation (6), were determined. The density-independent Poisson's ratios were not normalized. Averaging of the ν 12 C , ν 32 C and ν 12 T values of N1 (N2 and N3) selected specimens from a certain block and at a certain loading mode was carried out to calculate the average Poisson's ratios at a certain concentration of the filler: Considering ρ com and b as constants, the uncertainty of a normalized modulus was estimated as ∆E = (ρ com ) b ∆B avE , of a normalized strength as ∆σ max = (ρ com ) b ∆B avσ , of a normalized stress at 10% strain as ∆σ 10% = (ρ com ) b ∆B avσ , of a normalized elongation at break as ∆ε 11max = (ρ com ) b ∆B avε and of a Poisson's ratio as ∆ν, where ∆B avE , ∆B avσ and ∆B avε are the standard deviations of B avE , B avσ and B avε values and ∆ν is the standard deviation of Poisson's ratio values.

Dependence of Mechanical Properties on Concentration of Filler
The dependence of the NEOpolyol-380 PU foams' averaged and normalized mechanical properties on the concentration of the filler of the selected specimens was analyzed and compared with the same properties calculated for all specimens (the selected + the excluded).
Several other elastic constants of the slightly monotropic NEOpolyol-380 PU foams were calculated at each concentration of filler, based on the linear elasticity theory [29] and using the experimentally determined ones: For strength and elongation at break in compression and in tension, it is valid that: When the selected compression specimens are nearly isotropic, the shear and bulk moduli can be estimated as follows: where E 1 , E 3 and ν 12 , ν 32 and ν 13 -elastic constants in compression.

XRD Analysis Results
The 5 wt.% Cloisite-30B dispersions made by (a) high shear mixing for 20 min and (b) sonication for 20 min gave similar XRD patterns, as shown in Figure 3, confirming similar efficiency for both methods. The "Cloisite-30B-NEOpolyol-380" dispersions for the production of the filled NEOpolyol-380 PU foams were prepared with high-shear mixing as it is a technically more convenient method (no ultrasound).

XRD Analysis Results
The 5 wt.% Cloisite-30B dispersions made by (a) high shear mixing for 20 min and (b) sonication for 20 min gave similar XRD patterns, as shown in Figure 3, confirming similar efficiency for both methods. The "Cloisite-30B-NEOpolyol-380" dispersions for the production of the filled NEOpolyol-380 PU foams were prepared with high-shear mixing as it is a technically more convenient method (no ultrasound).
The first diffraction peak shifted from an angle 2θ = 4.75° to 2θ = 2.38°, which corresponded to an increase in d-spacing (001) from 18.6 Å to 37.1 Å. The second diffraction peak corresponded to an angle 2θ ≈ 4.9°. The polyurethane chains grow during polymerization, which facilitates an expansion of the interlayer spacing and an exfoliation of nanoclay platelets in the polymer matrix. The nanoclay Cloisite-30B had not fully exfoliated and intercalation dominated, as indicated by the still visible diffraction peaks. Characteristic changes were observed in the diffraction patterns: (1) the angular position of the reflex 001 moved to smaller angles due to penetration of the macro chains into galleries and (2) the intensity of the diffraction peak decreased because of delamination of the nanoclay particles under the action of shear forces. The diffraction peaks of the dispersions shifted to the left, compared to those of pure Cloisite-30B, Figure 3. A change in d-spacing between the planes of the diffraction lattice was identified according to Bragg's law: d = nλ/(2sinθ), where the diffraction order n = 1, 2 and 3.
The first diffraction peak shifted from an angle 2θ = 4.75 • to 2θ = 2.38 • , which corresponded to an increase in d-spacing (001) from 18.6 Å to 37.1 Å. The second diffraction peak corresponded to an angle 2θ ≈ 4.9 • . The polyurethane chains grow during polymerization, which facilitates an expansion of the interlayer spacing and an exfoliation of nanoclay platelets in the polymer matrix. The nanoclay Cloisite-30B had not fully exfoliated and intercalation dominated, as indicated by the still visible diffraction peaks.

PU Foam Blocks
The relative difference between the target mass m 0 = 250 g = const. and actual mass m of each of the 7 NEOpolyol-380 PU foam blocks (244 g ≤ m ≤ 261 g) was estimated as ≤4%; therefore, the technological requirement m = m 0 = const. was considered as executed.
The density of the neat, free-rise NEOpolyol-380 PU foam of the given formulation, block No. 1, was measured as ρ 0 ≈ 145 kg/m 3 . If the apparent overall density of a block produced in a sealed mold is ρ sm ≈ 240 kg/m 3 , then the value of overpressure in the sealed mold p ov = ρ sm /ρ 0 = 240/145 ≈ 1.7 atm. The PU foams in the sealed mold are produced at a high overpressure, ensuring a nearly isotropic structure.
The average content of closed cells of the neat NEOpolyol-380 PU foam in block No. 1 was measured as 99%.

Gradient of Density
The density of section C-a differed little from the density of section C-b for all NEOpolyol-380 PU foam blocks. The relative difference in densities R < 1%; therefore, the gradient of density ρ' = δρ/δx 2 along axis OX 2 was considered as small in sections C-a and C-b. The light microscopy showed that a more rapid increase in density started at a distance~10-15 mm from the sides of blocks. Due to the square horizontal cross section of the mold, the foam blocks had a fourth order rotational symmetry C 4 around axis OX 3 , which permitted a zone of highly uniform density ( Figure 2, the green rectangles) to be outlined. The C 4 symmetry led to similar foaming conditions in locations (1) "1 Side" and "5 Side", (2) "1 Side'", "2 Intermediate", "4 Intermediate" and "5 Side" as well as (3) "2 Intermediate" and "4 Intermediate".

Density of Compression and Tension Specimens
The average density, standard deviation and coefficient of variation was estimated for compression specimens from section C-a as ρ av = 222.3 kg/m 3 ± 4.1 kg/m 3 (1.9%) and from section C-b as ρ av = 220.8 kg/m 3 ± 4.4 kg/m 3 (2.0%). Density was the smallest for specimens from locations 3 and 3 ("Central") of sections C-a and C-b. It increased for 1 kg/m 3 -4 kg/m 3 to the sides of a block (specimens at locations 1, 1 and 5, 5 ), Figure 4a-c.
block No. 1, was measured as ρ0 ≈ 145 kg/m . If the apparent overall density of a block produced in a sealed mold is ρsm ≈ 240 kg/m 3 , then the value of overpressure in the sealed mold pov = ρsm/ρ0 = 240/145 ≈ 1.7 atm. The PU foams in the sealed mold are produced at a high overpressure, ensuring a nearly isotropic structure.
The average content of closed cells of the neat NEOpolyol-380 PU foam in block No. 1 was measured as 99%.

Gradient of Density
The density of section C-a differed little from the density of section C-b for all NEOpolyol-380 PU foam blocks. The relative difference in densities R <1%; therefore, the gradient of density ρ' = δρ/δx2 along axis OX2 was considered as small in sections C-a and Cb. The light microscopy showed that a more rapid increase in density started at a distance ∼10-15 mm from the sides of blocks. Due to the square horizontal cross section of the mold, the foam blocks had a fourth order rotational symmetry C4 around axis OX3, which permitted a zone of highly uniform density ( Figure 2, the green rectangles) to be outlined. The C4 symmetry led to similar foaming conditions in locations (1) "1 Side" and "5 Side", (2) "1′ Side'", "2 Intermediate", "4 Intermediate" and "5′ Side" as well as (3) "2′ Intermediate" and "4′ Intermediate".

Density of Compression and Tension Specimens
The average density, standard deviation and coefficient of variation was estimated for compression specimens from section C-a as ρav = 222.3 kg/m 3 ± 4.1 kg/m 3 (1.9%) and from section C-b as ρav = 220.8 kg/m 3 ± 4.4 kg/m 3 (2.0%). Density was the smallest for specimens from locations 3 and 3′ ("Central") of sections C-a and C-b. It increased for 1 kg/m 3 -4 kg/m 3 to the sides of a block (specimens at locations 1, 1′ and 5, 5′), Figure 4a-c.  The density of the straight part of the tension specimens from sections T-a and T-b at locations 2 and 2 ("Middle") was in good correlation with the density of the compression specimens from locations 3 and 3 ("Central"). The relative density differences were ≤3.3%. The average density of the compression specimens from section C-a (C-b) was~8 kg/m 3 (~6 kg/m 3 ) less than the average density of the tension specimens from section T-a (T-b).

Mechanical Properties of NEOpolyol-380 PU Foams
At all concentrations of the filler, the general character of the "stress-strain" curves in compression and in tension remained similar to that of the neat NEOpolyol-380 PU foams. No stress maximum was detected in compression up to 10%, when loading was terminated. No visible signs of collapse were observed on the side surfaces of the tested specimens. The remaining strain of the compression specimens ≈ 1.5 years after the testing was measured as ≈3% (≈70% of the strain had recovered).
The tension specimens from section T-b had a lower density in the work zone compared to the ends, but for section T-a specimens, the density of the straight part was similar to that at the ends. Consequently, ≈90% of the section T-b specimens broke in the straight zone and ≈40% of the section T-a specimens. All tension specimens exhibited sufficient compression and shear resistance for gripping in the fixtures of the testing machine without supplementary appliances.

Poisson's Ratios and Density
When gripped in the fixtures of the testing machine, the tension specimens of the light-weight industrial PU foams broke prematurely at the ends. Iron fixtures [13] were glued to the ends of the specimens to facilitate load transfer to the work zone. Stress maximums were detected in compression below 10% and strength in compression was determined as the maximum compressive force divided by the initial cross-section of the specimen; ISO 844:2021(E).
The results of the mechanical testing of the industrial, monotropic PU foams showed (1) similar values of Poisson's ratios may correspond to different densities of foams and (2) the relationship E 3 /E 1 ≈ ν 31 /ν 13 was fulfilled, Table 4. While the moduli E 1 and E 3 are dependent on the foams' density, the ratio E 3 /E 1 depends only on the anisotropy of the foams' material.  The dependence of ν 31 , ν 32 , ν 12 and ν 13 on the degree of monotropy DM = E 3 /E 1 = ν 31 /ν 13 in compression is given in Figure 5. When DM → 1.0 (isotropic foams), ν 31 , ν 32 , ν 12 and ν 13 → ν = 0.33. The coefficients ν 12 and ν 13 decreased and coefficients ν 31 and ν 32 increased with an increase in DM which can be explained by an increasing orientation of polymeric struts in the rise direction OX 3 [1,23,30,31]. The experimental data confirmed that Poisson's ratios depend on the monotropy degree of the foams and do not depend directly on density. Within the limits of the linear elasticity theory, the statement remains valid for any cellular plastics, independent of their particular formulation and/or density [4,22,23]. The dependence of ν31, ν32, ν12 and ν13 on the degree of monotropy DM = E3/E1 = ν31/ν13 in compression is given in Figure 5. When DM → 1.0 (isotropic foams), ν31, ν32, ν12 and ν13 → ν = 0.33. The coefficients ν12 and ν13 decreased and coefficients ν31 and ν32 increased with an increase in DM which can be explained by an increasing orientation of polymeric struts in the rise direction OX3 [1,23,30,31]. The experimental data confirmed that Poisson's ratios depend on the monotropy degree of the foams and do not depend directly on density. Within the limits of the linear elasticity theory, the statement remains valid for any cellular plastics, independent of their particular formulation and/or density [4,22,23].

Selection of the Specimens of NEOpolyol-380 PU Foams
The analysis of the three experimental data sets of Poisson's ratios: ν 12 and ν 32 in compression and ν 12 in tension showed that the data of eight specimens were not fulfilling the criterion (4) (≈7% of 112 specimens in total). Namely, (a) in the compression data of three specimens: one from location 3 ("Central"), one from location 3 ("Central") and one from location 5 ("Side") and (b) in the tension data of five specimens: one from location 2 ("Middle") and four from location 3 ("Top"). These eight specimens are denoted as inappropriate. The data of 104 specimens (≈93% of 112 specimens) fulfilled criterion (4) and these specimens were denoted as appropriate.
Criterion (4) was not fulfilled by the Poisson's ratios of the compression specimens of the neat foams, block No. 1, the "Central" locations 3 and 3 , Table 5. The mechanical properties of the foams exhibited a slight degree of monotropy, DM:  Criterion (4) was not fulfilled by the Poisson's ratios of the "Side" specimen from location 5 of block No. 4, Table 6. Its mechanical properties exhibited a slight monotropy: If the mold happens to be placed askew during foaming, one or two of its corners are located above the others. However, the liquid reacting mixture maintains a horizontal level due to the action of gravitation. The free space, available for foaming above the level of the liquid, is determined by the distance to the lid, which is greatest in the elevated corner. Foam in the corner location 5 ("Side") has space to rise to a higher degree of monotropy than in the other locations. The selection of tension specimens from sections T-a and T-b identified-in four cases out of five-that criterion (4) was not fulfilled by the Poisson's ratios of the specimens from the "Top" location 3 of section T-b, blocks Nos. 1, 2, 3 and 7, Table 7. In this location, the straight part of the tension specimen was at the top of the rising foam, the closest to the CGRH, and the comparatively small values of ν 12 suggested a medium degree of monotropy.
The inappropriate value ν 12 T = 0.34 for the specimen from the "Middle" location of section T-a, block No. 2, Table 7 may have been caused by a local foaming defect. Of the eight inappropriate specimens, six (75%) belonged to the No. 1 block (the neat, unfilled block; η = 0.0%) and the No. 2 block (the lowest non-zero concentration η = 0.25%) which had the lowest viscosity of the liquid reacting mixture and the highest speed of rise of the mixture before reaching the lid of the mold (Figure 1). As a result, the monotropy degree of the foams in blocks Nos. 1 and 2 was the highest. The neat foams were the reference material when evaluating the effect of filling (Equations (23) and (24)); therefore, it was important to estimate their mechanical properties precisely. On the other hand, of the eight inappropriate specimens, six were from the "Central" and "Top" locations. At the free-rise stage, the central part of a block rises with the highest speed, because at the sides of a block, the reacting mixture sticks to the walls.
The average Poisson's ratios of the selected specimens over all the concentrations of filler were calculated in compression and in tension: ν 32av C = 0.34 ± 0.02 (4%), ν 12av C = 0.32 ± 0.02 (5%) and ν 12av T = 0.31 ± 0.01 (5%). (20) In general, when the values of Poisson's ratio are in a range 0.30 ≤ ν ≤ 0.33, PU foams exhibit an isotropy of structure and mechanical properties [1,2,4]. The values in Equation (20) identify a slight monotropy: With the averaged and normalized moduli E 3av C and E 1av C determined, the average monotropy degree of the 67 selected compression specimens was estimated: The value of DM av C identified nearly isotropic foams and was in good correspondence with the microscopy data of the same NEOpolyol-380 PU foam blocks [32]. Since the selected compression specimens are nearly isotropic, the shear and bulk moduli were estimated according to the Equations (16).

Dependence of the Mechanical Properties on Concentration of Filler
The elastic moduli, strength and stress at 10% strain, averaged and normalized at density ρ com = 224 kg/m 3 , and the averaged Poisson's ratios of the selected specimens are given in Figures 6 and 7 (continuous curves) for compression and tension, together with the trendlines of the results calculated for all specimens (dashed curves). The other calculated elastic constants (shear and bulk moduli) are given in Figure 8.
It can be seen that some data of the excluded specimens differs from the averaged data of the selected specimens ≈1.5-2 times; e.g., ν 12 in compression and E 1 in tension. The relative change R in moduli, stress at 10% strain and elongation at break due to filling was estimated according to the trendlines, e.g., for modulus E 1 in compression: where E 1fil -the highest E 1 value of the filled foams and E 10 -E 1 , the value of neat foams.
In the tension modulus, E 1 increased by ≈22% at η = 3 . . . 4% and decreased by 5%; the strength in tension σ 11max decreased by ≈16% and the elongation at break by ≈58% at η = 5.00%, compared to the neat foams. Poisson's ratios remained nearly constant at all concentrations, both in compression and in tension: ν 32av C ≈ 0.34, ν 12av C ≈ 0.32 and ν 12av T ≈ 0.31, which confirmed the isotropic structure of the foams. The selection of specimens mainly influenced the values of the mechanical properties of the neat foams and the foams with the low concentrations of filler: η = 0.25, 0.50 and 1.00%, see Figures 5 and 6. The neat PU foam is a reference material for the estimation of the effect of filling; therefore, an accurate evaluation of its mechanical properties is crucial. The relative adjustment, RA, caused by the relative change R in the selection of specimens, was calculated as: where R all is the relative change when data of all specimens is taken into account and R sel -the same for data of the selected specimens, Table 8.

Dependence of the Mechanical Properties on Concentration of Filler
The elastic moduli, strength and stress at 10% strain, averaged and normalized at density ρcom = 224 kg/m 3 , and the averaged Poisson's ratios of the selected specimens are given in Figures 6 and 7 (continuous curves) for compression and tension, together with the trendlines of the results calculated for all specimens (dashed curves). The other calculated elastic constants (shear and bulk moduli) are given in Figure 8.   The stiffness of the filled PU foams was higher than that of neat foams both in compression and tension. The stiffness of nanoclay platelets in compression is estimated as 175-265 GPa [33] and that of dry clay particles as 6.2 GPa [34] which is higher than the stiffness of the PU matrix at 2500 MPa [1,21,28]. Then, the rule of mixture predicts an increased stiffness for a "PU foam-nanoclay" composite. The increase in the stress at 10% strain in compression might be attributed to the creation of multiple crack sites and branches by the nanoparticles, which delay the propagation of fracture [12,[35][36][37].
In tension, the decrease in strength and elongation at break might be caused by a weakness of the "PU-nanoclay" interface in tension; thus, the nanoclay platelets act as the initiators of a crack. The platelets, when dispersed uniformly into the polymer, produce a huge number of interface regions as compared to microcomposites and the interphase can become a dominating factor determining the properties of the nanocomposite. It can be seen that some data of the excluded specimens differs from the averaged data of the selected specimens ≈1.5-2 times; e.g., ν12 in compression and E1 in tension. The relative change R in moduli, stress at 10% strain and elongation at break due to filling was estimated according to the trendlines, e.g., for modulus E1 in compression: R(E1) = ∆E1/E1 = (E1fil − E10)/E10; (23) where E1fil-the highest E1 value of the filled foams and E10-E1, the value of neat foams.

Conclusions
As estimated, ≈93% of the PU foam specimens fulfilled the criterion of similar anisotropy characteristics and ≈7% failed to fulfill it. Specimens from "Central" and "Top" locations did not fulfill the mentioned criterion because of the highest speed of PU foams' rise in the centre of the blocks, close to the CGRH and relatively far from the sides of the mold. The speed of rise being the highest in the centre of a block cannot be avoided without changing the technology. It is a systematic, predictable effect. Several specimens from the "Side" locations did not fulfill the criterion because of a technological flaw-a mold placed askew at foaming. It was a random, unpredictable effect which could be avoided by placing the mold in a precisely horizontal position.
The influence of the nanoclay filler Cloisite-30B on the mechanical properties of NEOpolyol-380 PU foams was estimated at filler concentrations of 0.00, 0.25, 0.50, 1.00, 2.00, 3.00 and 5.00% by the relative change in the foams' mechanical properties due to filling relative to the mechanical properties of unfilled, neat foams. It was shown that the selection of the mechanical testing specimens of foams, according to the criterion of similar anisotropy characteristics, reduced the influence of the structural anisotropy variations on the estimation of the foams' mechanical properties. The relative adjustment, provided in the estimation of the NEOpolyol-380 PU foams' mechanical properties by the selection of specimens, was ≈10-30%.
The benefit for practical applications of the criterion of similar anisotropy characteristics lies in a comparatively simple, efficient method for identifying and excluding mechanical testing specimens of PU foams with an unacceptably different structural anisotropy from those with a similar anisotropy. Further processing of the testing data of the excluded specimens can be avoided to save time and resources. In principle, the elaborated methodology is applicable to PU foams produced both in closed and open molds.
The filling of rigid NEOpolyol-380 PU foams with a density of 215-240 kg/m 3 with the nanoclay filler Cloisite-30B up to 5 wt.% from the mass of filled reacting mixture moderately improved the mechanical properties of the foams in compression and tension, due to the nanoclay not being fully exfoliated, as suggested by the XRD patterns. It may have been caused by the reduced efficiency of the organic modification of the Cloisite-30B filler's surface, because the production year of the filler was the year 2010, but it was added to the NEOpolyol-380 PU foams in the year 2020.
More research is necessary on normalization of the mechanical properties of anisotropic PU foams to a common density.