Polymer nanocomposite material and production method thereof

Abstract

[Problem] To provide a system capable of inputting an optimum amount of energy in a kneading process regardless of whether nanoparticles included in a polymer are organically modified. [Solution] This production method comprises: a charging step for charging nanoparticles into a polymer; and a kneading step for melt-kneading the nanoparticles into the polymer by inputting sufficient energy to form the dispersion state of the nanoparticles. In the charging step, the combination of the nanoparticles and the polymer is selected so that WPF / WFF > 0.9 is satisfied, and in the kneading step, the amount of energy to be input is determined so that σh / σc > 0.5. Here, WPF denotes adhesion work between the nanoparticle and the polymer, WFF denotes an aggregation work between the nanoparticles, σh denotes a shear stress, and σc denotes a crushing strength calculated by a Rumpf formula represented by the following formula (1). (In the formula, d represents a primary particle diameter, ε represents the porosity of an aggregate, and F represents an interparticle force.)

Description

Polymer nanocomposite material and its manufacturing method

[0001] The present invention relates to a polymer nanocomposite material and a method for producing the same.

[0002] Polymer nanocomposite materials, which contain nanoparticles embedded in polymers, are attracting attention as functional materials with superior mechanical, thermal, electrical, and optical properties compared to polymer materials alone. Due to these properties, polymer nanocomposite materials are expected to be applied to heat dissipation sheets, organic thin-film solar cells, optical devices, car bodies, etc.

[0003] One of the manufacturing methods for polymer nanocomposite materials is melt-kneading, in which polymers are heated and melted in a kneader and then mixed with nanoparticles through mechanical manipulation. To optimally express the functions and properties of polymer nanocomposite materials, a technique is required to uniformly disperse nanoparticles in the polymer.

[0004] For example, in nanohybrid materials intended for applications such as high refractive index materials, anti-reflection films, and transparent magnetic films, where transparency is important, the aggregate particle size must be approximately 1 / 10 or less of the visible light wavelength. However, in the melt-kneading process, if the affinity between the nanoparticles and the polymer is not well controlled, if sufficient kneading energy is not transmitted to the nanoaggregates, or if the amount of energy input is insufficient, the desired dispersion cannot be achieved.

[0005] In melt-kneading of nanoparticles, nanoparticles tend to aggregate due to their high surface energy, making dispersion of nanoparticles difficult. Factors that affect the material structure during melt-kneading include the residence time of the material in the kneader, the screw rotation speed, and the affinity between the polymer and the nanoparticles. In general, increasing the residence time reduces concentration unevenness, while increasing the screw rotation speed increases shear stress, promoting the disintegration of nanoparticle aggregates.

[0006] Furthermore, in order to promote dispersion of nanoparticles, it is desirable that the nanoparticles have a high affinity with the polymer.

[0007] Although this tendency has been recognized, no method for controlling the kneading process has been established.

[0008] In principle, if the affinity between the nanoparticles and the polymer is sufficiently high and sufficient shear force is applied to break down the agglomerates, it is possible to better disperse the nanoparticles by increasing the kneading time.

[0009] To control the optimum kneading conditions, both the optimum kneading time and good compatibility between the nanoparticles and the polymer are required.

[0010] As an index of affinity, the work of adhesion between nanoparticles and polymers, W ＰＦ and the cohesive work between nanoparticles W ＦＦ It has been proposed to focus on the following points (Non-Patent Document 1). ＰＦ / W ＦＦ By using this, it is possible to evaluate the wettability of the filler by the polymer, that is, the dispersibility of the filler (nanoparticles) in the polymer.

[0011] In addition, a method for synthesizing organically modified nanoparticles using supercritical hydrothermal synthesis has been proposed (Non-Patent Document 2). This synthesis method allows the surface of inorganic nanoparticles to be modified with any organic molecule, and by changing the organic molecule to be modified, it is possible to control the affinity between the polymer and the organically modified nanoparticles.

[0012] AS Prasad, Y. Wang, X. Li, A. Iyer, W. Chen, LC Brinson and LS Schadler, "Investigating the effect of surface modification on the dispersion process of polymer nanocomposites,", Nanocomposites, 6, 111 (2020)J. Zhang, S. Ohara, M. Umetsu, T. Naka, Y. Hatakeyama and T. Adschiri, "Colloidal ceria nanocrystals: A tailor-made crystal morphology in supercritical water," Adv. Mater., 19, 203 (2007).

[0013] In Non-Patent Document 1, the cohesive force σ ｃ However, when organically modified nanoparticles such as those described in Non-Patent Document 2 are handled, the method described in Non-Patent Document 1 may not be able to derive optimal kneading conditions, which may result in an excess or deficiency of the amount of energy input in the kneading step.

[0014] The present invention has been made in consideration of these problems, and aims to provide a system that can input an optimal amount of energy in the kneading process, regardless of whether the nanoparticles encapsulated in the polymer are organically modified or not.

[0015] The present inventors considered the interaction force caused by the modified chains of the nanoparticles and calculated the work of adhesion between the nanoparticles and the polymer (W ＰＦ / Cohesion work between nanoparticles W ＦＦ The combination of nanoparticles and polymers is selected so that the crushing strength σ ｃ Using the Rumpf equation (shear stress σ ｈ / Crushing strength σ ｃThe present inventors have found that the above-mentioned problems can be solved by determining the amount of energy input so that the value of (value of ) is greater than 0.5, and have completed the present invention. Specifically, the present invention provides the following.

[0016] The invention according to a first aspect includes a step of adding nanoparticles to a polymer, and a step of melt-kneading the nanoparticles into the polymer by adding energy necessary and sufficient to form a dispersed state of the nanoparticles. ＰＦ / W ＦＦ The combination of the nanoparticles and the polymer is selected so that σ > 0.9, and in the kneading step, ｈ / σ ｃ The present invention provides a method for producing a polymer nanocomposite material, in which the amount of input energy is determined so that W > 0.5. ＰＦ represents the work of adhesion between the nanoparticle and the polymer, and W ＦＦ denotes the cohesive work between nanoparticles, and σ ｈ denotes the shear stress, and σ ｃ indicates the crushing strength calculated by the Rumpf formula (1) below. (where d represents the primary particle diameter, ε represents the porosity of the aggregate, and F represents the interparticle force.)

[0017] The second aspect of the invention is the first aspect of the invention, and provides a method for selecting a combination of the nanoparticles and the polymer in the adding step so that the contact angle θ calculated by the following formula (2) is less than 37°.

[0018] A third aspect of the invention is the method according to the first or second aspect, wherein the energy input in the kneading step includes at least one selected from the group consisting of mechanical energy, thermal energy, vibration energy, electromagnetic induction energy, and electrical energy, which can be applied to the kneading process from the outside.

[0019] The invention according to a fourth feature is the invention according to any one of the first to third features, wherein the value of total input energy / cohesive energy, which is the value obtained by dividing the total energy input in the kneading step by the cohesive energy of the nanoparticles, is 10３ The above provides a method.

[0020] A fifth aspect of the invention provides a method according to any one of the first to fourth aspects of the invention, wherein the nanoparticles are organically modified nanoparticles in which organic molecules are bound to the surface of inorganic nanoparticles.

[0021] The sixth aspect of the invention provides a polymer nanocomposite material in which a polymer material and nanoparticles are combined, wherein the proportion of well-dispersed particles that have been crushed to a size 20 times or less the average particle size of single nanoparticles is 50 vol% or more, and the volume-based average particle size Dv50 of aggregates other than the well-dispersed particles is 100 nm or more and 500 nm or less.

[0022] A seventh aspect of the invention is the sixth aspect of the invention, which provides a polymer nanocomposite material in which the coefficient of variation of the aggregates is 1.5 or less.

[0023] The eighth aspect of the invention is the sixth or seventh aspect of the invention, and provides a polymer nanocomposite material produced by the production method of any one of the first to fifth aspects of the invention.

[0024] According to the present invention, it is possible to provide a system that can input an optimum amount of energy in the kneading step, regardless of whether the nanoparticles encapsulated in the polymer are organically modified or not.

[0025] Figure 1 is a schematic diagram showing the wetting state. Figure 2 is a schematic diagram showing the surface-modified nanoparticles approaching each other. Figure 3 is a schematic diagram showing the dispersion state. Figure 4 is a cross-sectional SEM image of CeO2 and C10-CeO2 / PS nanocomposite materials. Figure 5 is a cross-sectional TEM image of CeO2 and C10-CeO2 / PS nanocomposite materials. Figure 6 shows the aggregate size distribution of CeO2 and C10-CeO2 / PS nanocomposite materials. Figure 7 is a cross-sectional SEM image of different polymer species at different rotation speeds. Figure 8 is a cross-sectional TEM image of various polymer species. Figure 9 shows the aggregate size distribution of different polymer species at different rotation speeds. Figure 10 shows the effect of rotation speed on the aggregate occupancy. Figure 11 is a cross-sectional SEM image of PS at various particle concentrations. Figure 12 shows the aggregate size distribution of PS at various particle concentrations. Figure 13 shows the effect of particle concentration on the aggregate occupancy. Figure 14 shows potential curves for C10-CeO2 / (a) PP, (b) PS, and (c) PMMA. Figure 15 shows force curves for C10-CeO2 / (a) PP, (b) PS, and (c) PMMA. Figure 16 shows (a) potential and (b) force curves for the total C10-CeO2 for various polymer species. Figure 17 shows potential curves for (a) C8-SiO2, (b) ClC3-SiO2, and (c) NHClC3-SiO2 for different polymer species. Figure 18 shows force curves for (a) C8-SiO2, (b) ClC3-SiO2, and (c) NHClC3-SiO2 for different polymer species. Figure 19 shows a model of aggregate porosity. Figure 20 shows the analysis object and mesh (a) barrel, (b) disk. Figure 21 shows the shear stress distribution of PP over time during one rotation. Figure 22 shows the shear stress distribution of PP at each rotation. Figure 23 shows the shear stress distribution at each rotation speed for different polymer species. Figure 24 shows a structure formation map of polymer nanocomposite materials organized by affinity and the force acting on the particles (taking into account van der Waals forces and forces acting on the modified chains). Figure 25 shows a structure formation map of polymer nanocomposite materials organized by affinity and the force acting on the particles (taking into account only van der Waals forces).FIG. 26 shows the ratio of input energy to the cohesive energy of nanoparticles on the area ratio of the aggregates.

[0026] Specific embodiments of the present invention will be described in detail below, but the present invention is not limited to the following embodiments and can be implemented with appropriate modifications within the scope of the object of the present invention.

[0027] <Method for producing polymer nanocomposite material> The method according to this embodiment includes at least an introduction step of introducing nanoparticles into a polymer, and a kneading step of melt-kneading the nanoparticles into the polymer by introducing energy necessary and sufficient to form a dispersed state of the nanoparticles.

[0028] [Adding Step] The adding step is a step of adding nanoparticles to a polymer.

[0029] [Nanoparticles] The type of nanoparticles is not particularly limited, but it is preferable that the nanoparticles are organically modified nanoparticles in which inorganic nanoparticles are modified with organic molecules, because they are expected to be highly dispersed in a polymer and the method described in this embodiment allows an optimal amount of energy to be input in the kneading step. Organically modified nanoparticles can be obtained, for example, by the supercritical hydrothermal synthesis method described in Non-Patent Document 2.

[0030] The type of organic modifying group is not particularly limited, and examples thereof include an optionally substituted linear or branched alkyl group, an optionally substituted cyclic alkyl group, an optionally substituted aryl group, an optionally substituted aralkyl group, and an optionally substituted saturated or unsaturated heterocyclic group.

[0031] Examples of the substituent include a carboxy group, a cyano group, a nitro group, a halogen atom, an ester group, an amide group, a ketone group, a formyl group, an ether group, a hydroxyl group, an amino group, a sulfonyl group, -O-, -NH-, and -S-.

[0032] The organically modified nanoparticles may have one type of organic modifying group on the surface, or may have multiple types of organic modifying groups.

[0033] [Selection of Combination of Nanoparticles and Polymers] In the adding step,ＰＦ / W ＦＦ The combination of nanoparticles and polymers is selected so that W > 0.9, where W ＰＦ represents the work of adhesion between the nanoparticle and the polymer, and W ＦＦ denotes the cohesive work between nanoparticles.

[0034] W ＰＦ and W ＦＦ are expressed by the following equations (3) and (4), respectively.

[0035] In the formula, γ is the surface free energy, which can be obtained from measurements using the Owens-Wendt method. Among the subscripts, P indicates a polymer, F indicates a filler (nanoparticles), and among the superscripts, d indicates a dispersion component, and p indicates a polar component.

[0036] W ＰＦ Ya W ＦＦ are determined by the physical properties of the polymer and the filler, respectively, and the ratio thereof is an index showing the wettability of the polymer to the filler. ２ W in the case of nanoparticles ＰＦ / W ＦＦ and the value of the contact angle. The contact angle will be explained later. Quoted from Bharath Natarajan, Yang Li, Hua Deng, L. Catherine Brinson, and Linda S. Schadler, “Effect of Interfacial Energetics on Dispersion and Glass Transition Temperature in Polymer Nanocomposites”, Macromolecules 2013, 46, 2833-2841)

[0037] In Table 1, PMMA is polymethyl methacrylate, P2VP is poly(2-vinylpyridine), PS is polystyrene, and PEMA is polyethyl methacrylate.

[0038] FIG. 1 is a schematic diagram showing the wet state.ＰＦ / W ＦＦ The larger the value of W, the more easily the filler is wetted by the polymer, and the better the dispersibility of the filler, i.e., the nanoparticles, in the polymer. ＰＦ / W ＦＦ The value of is 0.9 or more, preferably 0.97 or more, more preferably 0.99 or more, even more preferably 0.998 or more, and even more preferably 1 or more.

[0039] The contact angle θ in FIG. 1 is expressed by the above-mentioned formula (2).

[0040] The smaller the value of θ, the more easily the filler is wetted by the polymer, and the better the dispersibility of the filler, i.e., the nanoparticles, in the polymer. θ<37°, preferably θ<20°, more preferably θ<11°, even more preferably θ<5°, and particularly preferably θ=0°.

[0041] [Kneading Step] The kneading step is a step of melt-kneading nanoparticles into a polymer by inputting energy necessary and sufficient to form a dispersed state of the nanoparticles.

[0042] The type of kneader is not particularly limited, and may be any of a single screw extruder, a twin screw extruder, and a batch kneader.

[0043] [σ ｈ / σ ｃ In the kneading process, σ ｈ / σ ｃ The amount of energy input is determined so that the ratio is adjusted to >0.5.

[0044] σ ｈ indicates shear stress and is expressed by the following equation (5).

[0045] In the formula, D is the barrel diameter of the kneader, N is the screw rotation speed, δ is the screw-to-barrel distance, γ (γ dotted with a dot) is the shear rate, and η is the viscosity of the nanocomposite.

[0046] σ ｃ indicates the crushing strength calculated by the Rumpf formula (1) above.

[0047] In the formula, d represents the primary particle diameter, ε represents the porosity of the aggregate, and F represents the interparticle force.

[0048] The interparticle force F is the sum of the van der Waals force acting between particles and the interaction force due to the modification chain. The van der Waals force f acting between particles i and j is ｉｊ ｖ is expressed as follows:

[0049] where A is the Hamaker constant of the particle in the molten polymer, H ｉｊ represents the center-to-center distance between particle i and particle j. Since the van der Waals force diverges as the interparticle distance becomes smaller, a cutoff distance is considered. For simplicity, in this specification, the critical contact distance (0.165 × 10 －９ When the surface separation is smaller than 1 / 2 m, the van der Waals force is assumed to be constant.

[0050] The interaction force due to the modified chains is explained in (1) J.B. Smitham et al., J. Chem. Soc. Farad. Trans. 1, 71 (1975) 285. (2) R. Evans et al., Colloid Polym. Sci., 255 (1977) 161. Figure 2 is a schematic diagram of surface-modified nanoparticles approaching each other. For simplicity, it is assumed herein that the modified chains are uniformly distributed on the surface. In this specification, two types of interaction force due to the modified chains are considered: a force based on mixing free energy and a force based on elastic energy. The mixing free energy can be considered when the modified chains interpenetrate as shown in Figure 2(a) and when, in addition to interpenetration, compression of the modified chains occurs as shown in Figure 2(b). The mixing free energy can be expressed as follows:

[0051] where L is the modification chain length, and v ｐis the molecular volume of the polymer, φ is the volume fraction of modified chains in a modified chain layer of thickness L (hereinafter referred to as the “modification rate”), and χ is the Flory-Huggins interaction parameter, which can be calculated using the following formula:

[0052] where α is a fitting parameter, set to 0.6 here, and V s is the molar volume per unit of polymer, δ d , δ p , δ h are the dispersion term, polar term, and hydrogen bond term of the Hansen solubility parameter, respectively, R is the gas constant, and T is temperature. The superscripts 1 and 2 indicate the modified chain and polymer, respectively.

[0053] The elastic energy is considered when the modified chain is compressed as shown in Figure 2(b), and the elastic energy generated by the elastic repulsion between particles due to the loss of conformational entropy of the modified chain acts as a repulsive force. The elastic energy V of the modified chain between particle i and particle j is ｉｊ ｅ is given as follows:

[0054] where ν ｎ is the number of modified chains per unit surface area of ​​the nanoparticle. The force based on the mixing free energy between two particles, f ｉｊ ｍ and the force based on elastic energy f ｉｊ ｅ are obtained by differentiating equations (7), (8), and (10), and are expressed as follows:

[0055] From the above, the interaction force due to the modification chain acting between particles i and j is expressed as follows:

[0056] For simplicity, in this specification, the interaction force due to the modified chain is calculated as the distance between the surfaces of the two particles (H ｉｊ -d) is 0.165 × 10 －９ If it is less than m, it is kept constant.

[0057] From the above, the interparticle force F acting on particle i is expressed as the sum of the van der Waals force and the interaction force due to the modification chain as follows:

[0058] FIG. 3 is a schematic diagram showing the dispersion state. ｈ / σ ｃ The larger the value of is, the better. ｈ / σ ｃ It is preferable that σ is greater than 0.5. ｈ / σ ｃ It is more preferable that σ is >1. ｈ / σ ｃ A value of >0.5 indicates that the particles are crushed and are easily dispersed. ｈ / σ ｃ <0.5 means that the particles are difficult to disperse. ｈ / σ ｃ is an index for distinguishing whether the mechanism of disintegration is rupture or erosion. The dispersion speed, average particle size, and particle size distribution of the aggregates differ depending on the mechanism of destruction.

[0059] The energy supplied to the kneader includes mechanical energy obtained from screw rotation, thermal energy supplied from the barrel (surroundings), and also energy groups that can be applied externally to the kneading process, such as vibration energy, electromagnetic induction energy, and electrical energy. The input mechanical energy is used to knead and transport the polymer, and further to disperse (disintegrate) aggregates, and a portion of it is converted into thermal energy (heat generation). It is thought that polymer decomposition can be caused not only by heat but also by shear stress.

[0060] [Correlation between Input Energy / Cohesion Energy and Structure] The input energy to a batch mixer is obtained by integrating the power P [W] required during mixing over time and dividing the result by the mass m [kg], and is defined by the following equation (16):

[0061] Here, N is the screw rotation speed [rpm], t is time [min], τ is torque [N·m], and m is mass [kg].

[0062] The influence of the rotation speed of the kneader and the kneading time can be organized as input energy, and the higher the affinity of the polymer, the more the dispersion progresses with a smaller input energy.

[0063] In addition, in the calculation of the input energy (energy consumption per unit extrusion rate) in the case of a continuous twin-screw extruder, for example, the input energy (specific energy) is defined as the energy consumption per unit extrusion rate and is expressed by the following formula (17).

[0064] In this formula, N is the screw rotation speed, Q is the discharge rate, and T is the screw torque.

[0065] <Polymer Nanocomposite Material> The polymer nanocomposite material according to this embodiment is a composite material of a polymer material and nanoparticles, and can be obtained by the above-described production method. As a novel functional material, the polymer nanocomposite material can be applied to heat dissipation sheets, organic thin-film solar cells, optical devices, automobile bodies, etc.

[0066] The proportion of well-dispersed particles that have been crushed to a size 20 times or less the average particle size of a single nanoparticle is 50 vol% or more, preferably 70 vol% or more, more preferably 90 vol% or more, even more preferably 95 vol% or more, and particularly preferably 97 vol% or more.

[0067] The volume-based average particle diameter Dv50 of the aggregates different from well-dispersed particles is 100 nm or more, and the average particle diameter Dv50 is 500 nm or less, preferably 450 nm or less, more preferably 400 nm or less, even more preferably 350 nm or less, and particularly preferably 300 nm or less.

[0068] The coefficient of variation of the aggregates is 1.5 or less, more preferably 1.2 or less, and even more preferably 1.0 or less.

[0069] In polymer nanocomposite materials, the proportion of well-dispersed particles, particle size of aggregates, and coefficient of variation are determined by image analysis using a scanning electron microscope (SEM) and a transmission electron microscope (TEM) using the following methods.

[0070] Sample preparation was performed by melt-molding the sample and sectioning it using a microtome. For melt-molding, the kneaded sample was placed in a silicone capsule with a diameter of 7 mm and a tip of 1.5 mm square, and then heated in a dryer for at least 1 hour. To prevent structural changes due to heating, the temperature was set 20°C lower than the kneading temperature. The melt-molded sample was fixed in the microtome, and a glass knife filled with distilled water was placed in a boat made of vinyl tape to collect 25 mm high and 6 mm wide sections on the knife stage. SEM samples were cut at a cutting speed of 50 mm / s to a cutting thickness of 500 nm, while TEM samples were cut at a cutting speed of 1.0 mm / s to a cutting thickness of 100 nm. The sample sections floating in the distilled water were collected on a TEM grid, thoroughly dried, and observed under a microscope. SEM samples were observed in backscattered electron imaging (BSE) mode at an accelerating voltage of 5 kV, and TEM samples in transmission electron imaging (TE) mode at an accelerating voltage of 200 kV.

[0071] The captured SEM images are analyzed using WinROOF, with 20 or more images being analyzed.

[0072] The details of the image analysis are as follows: (1) The image is converted to monochrome for binarization processing. (2) Background removal (49 pixels) is performed to remove noise in the image. (3) Binarization is performed using a single threshold value. The threshold value is set to a low value to prevent the omission of aggregates. In addition, hole filling processing is performed to identify aggregates. (4) Contraction processing is performed once. This is intended to smooth the boundaries. (5) Deletion processing (area threshold: 0.005) is performed to remove noise such as isolated points. (6) Shape feature processing is performed to calculate the area, circle equivalent diameter, and standard deviation of each aggregate. (7) Aggregate occupancy rate A A is calculated from the ratio of the aggregate area to the area of ​​the entire SEM image, and the coefficient of variation C v is calculated by dividing the standard deviation of aggregate diameters by the mean diameter Dv50.

[0073] Aggregate occupancy rate A obtained by image analysis A The proportion of well-dispersed particles can be calculated from the aggregate occupancy rate A A The smaller the value, the more progressed the kneading. The particle size of the aggregate can be calculated from the circle equivalent diameter obtained by image analysis. The coefficient of variation C is calculated by dividing the standard deviation of the aggregate size by the average size Dv50. v can be calculated.

[0074] The present invention will be specifically explained below with reference to examples, but the present invention is not limited to these examples.

[0075] <Test 1> W ＰＦ / W ＦＦ and σ ｈ / σ ｃ Example 1 Experimental Method Materials The nanoparticles used were unmodified CeO2 nanoparticles and decanoic acid-modified CeO2 nanoparticles (C10-CeO2) with an average particle size of 6 nm, synthesized by a supercritical hydrothermal method. The polymers used were polypropylene (PP, Mw=250,000), polystyrene (PS, Mw=192,000), and polymethyl methacrylate (PMMA, Mw=120,000).

[0076] (Preparation of composite materials) A batch mixer was used, with a particle concentration of 10 wt %, a mixing time of 10 minutes, and various rotation speeds. The temperature was set to 200°C for PP, and 230°C for PS and PMMA so that the torque of the pure polymers was the same.

[0077] (Structural analysis) The cross sections of the obtained samples were observed using a scanning electron microscope (SEM) and a transmission electron microscope (TEM). The SEM samples were observed in backscattered electron image (BSE) mode at an accelerating voltage of 5 kV, and the TEM samples were observed in transmission electron image (TE) mode at an accelerating voltage of 200 kV. More than 20 SEM images were analyzed using WinROOF Ver. 7.2.3 and WinROOF 2021.

[0078] After binarizing the aggregates, shape feature processing was performed to calculate the area, equivalent circle diameter, and standard deviation of each aggregate. Then, the aggregate occupancy rate A was calculated from the ratio of the aggregate area to the area of ​​the entire SEM image as an index of kneading.A The coefficient of variation C v The standard deviation of the aggregate diameter is the mean diameter d av The aggregate occupancy rate A was calculated by dividing by A The smaller the value, the more the kneading progressed.

[0079] [Results and Discussion] (Effect of surface modification on structure in PS) Figure 4 shows cross-sectional SEM images of unmodified CeO2 and C10-CeO2 polymer nanocomposite materials at a particle concentration of 10 wt% and a rotation speed of 60 rpm. The white areas are nanoparticles, and the black areas are polymers. With unmodified CeO2, aggregates larger than several tens of μm were observed, with many micro-sized aggregates. On the other hand, with C10-CeO2, micro-sized aggregates were observed, but relatively small aggregates of submicron size were also prevalent.

[0080] Figure 5 shows cross-sectional TEM images of unmodified CeO2 and C10-CeO2 polymer nanocomposite materials. Unmodified CeO2 was aggregated, and the size and shape of the particles themselves were not uniform. On the other hand, C10-CeO2 was observed to have nanoparticles existing as single particles, which suggests that it has high dispersibility. Furthermore, the size of the particles themselves was uniform and their shape was roughly spherical. This is thought to be due to the fact that C10-CeO2 was synthesized using the supercritical hydrothermal method, which resulted in the production of uniform particles.

[0081] Figure 6 shows the aggregate size distribution of unmodified CeO2 and C10-CeO2 at a particle concentration of 10 wt% analyzed from SEM images. av is the average diameter of the aggregates. d av is also called the median diameter, and is the number-based average particle diameter Dn50 at which the proportion of particles with a particle diameter of D50 or less is 50 vol%. v is the coefficient of variation. A A is the aggregate occupancy rate, which is the aggregate area relative to the total area of ​​the SEM image, and a small value indicates high dispersibility.

[0082] Compared to unmodified CeO2, C10-CeO2 had a peak on the smaller aggregate diameter side and a smaller coefficient of variation. Furthermore, the aggregate occupancy rate was smaller for C10-CeO2 than for unmodified CeO2, indicating that C10-CeO2 had higher dispersibility. This is thought to be due to the repulsive force of the modified chains resulting from the surface modification, which promoted the dispersion of the nanoparticles.

[0083] (Effect of Polymer Species on Structure at Various Rotational Speeds) Figure 7 shows cross-sectional SEM images of polymer nanocomposites containing C10-CeO2 at different rotational speeds and different polymer species. For the PMMA sample, mixing was impossible due to torque overload at speeds greater than 90 rpm. For the PP sample, large micro-sized aggregates were observed at a low rotational speed of 30 rpm. At 60 rpm, the number of large micro-sized aggregates decreased, while the number of aggregates increased. At speeds above 90 rpm, the number of large aggregates further decreased. For the PS sample, similar to the PP sample, large micro-sized aggregates were observed at 30 rpm. At 60 rpm, the number of submicron aggregates increased. Furthermore, the number of submicron aggregates further increased with increasing rotational speed. On the other hand, for the PMMA sample, many large micro-sized aggregates were observed at 30 and 60 rpm. From the above, good dispersion was observed for the PP and PS systems at rotational speeds above 60 rpm, while many aggregates were observed for the PMMA system.

[0084] Figure 8 shows cross-sectional TEM images of polymer nanocomposites containing C10-CeO2 with different polymer types at a rotation speed of 60 rpm. The black areas represent nanoparticles, and the white areas represent polymers. In the PP and PS samples, submicron-sized aggregates were observed, but many nanoparticles were present as single particles. In contrast, in the PMMA sample, micron-sized aggregates were observed, and single nanoparticles were present only near the interfaces of the aggregates. This result is consistent with the trends observed by SEM, demonstrating the influence of miscibility on nanoparticle dispersibility even at the nanoscale.

[0085] Figure 9 shows the aggregate size distribution of C10-CeO2 for different polymer types and rotation speeds. For the PP and PS samples, the distribution was broad and the average diameter was large at 30 rpm. At 60 rpm, the distribution narrowed, and at higher rotation speeds, the peak shifted toward smaller aggregate sizes. For the PMMA sample, the peak peak was large and the distribution was very broad at both rotation speeds. This is likely due to the lower affinity between PMMA and C10-CeO2 and the higher cohesion strength compared to PP and PS, which reduced the effect of rotation speed. Furthermore, the coefficient of variation and average diameter did not show a clear correlation with rotation speed. This is likely due to the progression of dispersion, which reduces the number of aggregates observable with SEM resolution, making it difficult to consider single particles and small aggregates.

[0086] Figure 10 shows the effect of rotation speed on the aggregate occupancy rate and SEM images of each polymer at 60 rpm. The white areas in the image are nanoparticle aggregates. For PP and PS, the aggregate occupancy rate was small, and the effect of rotation speed was also small. On the other hand, for PMMA, the aggregate occupancy rate was very large, and micro-sized aggregates were observed in the SEM image. Therefore, it was found that PMMA aggregates more than PP and PS.

[0087] (Effect of particle concentration on structure in PS) Figure 11 shows cross-sectional SEM images of polymer nanocomposites containing C10-CeO2 at various particle concentrations. The white areas are aggregates of nanoparticles, and the black areas are polymers. C F is the particle concentration. The higher the particle concentration, the greater the number of aggregates, and larger aggregates were observed.

[0088] Figure 12 shows the aggregate size distribution of C10-CeO2 at various particle concentrations in PS. As the particle concentration increased, the peak shifted to smaller aggregate sizes. Furthermore, at 2 wt% and 5 wt%, the average diameter, coefficient of variation, and aggregate occupancy rate did not change significantly, but at 10 wt%, the aggregate occupancy rate increased. At 15 wt%, a peak was observed at a position of several micrometers, and the average diameter, coefficient of variation, and aggregate occupancy rate were all large, indicating relatively low dispersibility. This is thought to be due to the broadening of the distribution caused by the high particle concentration.

[0089] Figure 13 shows the effect of particle concentration on the aggregate occupancy of C10-CeO2 in PS. The aggregate occupancy rate increased when the particle concentration was high. However, the change was smaller than when the polymer type was changed. This is thought to be because, while a high particle concentration reduces the distance between particles, increasing the likelihood of agglomeration, the presence of large aggregates and increased apparent viscosity increase the shear stress that causes the aggregates to break down. This suggests that the affinity between nanoparticles and polymers has a significant effect on dispersibility.

[0090] <Test 2> Calculation of crushing strength of surface-modified nanoparticles The dispersibility of nanoparticles during melt-kneading can be quantitatively evaluated by calculating the cohesive force of the nanoparticles, i.e., crushing strength. In this test, not only C10-CeO2, which was tested in Test 1, but also C8-SiO2, ClC3-SiO2, and NH2C3-SiO2, which were tested by Prasad et al., were examined.

[0091] Figure 14 shows potential curves for C10-CeO2 nanoparticles at various potentials for different polymer species, and Figure 15 shows force curves. The horizontal axis of the potential curve represents the particle center-to-center distance normalized by particle size, while the horizontal axis of the force curve represents the particle surface-to-surface distance. When the potential and force are greater than 0, it is predicted to be a dispersion system in which repulsive forces are active, while when they are less than 0, it is predicted to be an aggregate system in which attractive forces are active. van der Waals forces act as attractive forces, while elastic energy acts as repulsive forces. The mixing energy is bounded by χ = 0.5, where it acts as repulsive forces when χ is less than 0.5 and attractive when χ is greater than 0.5. The most stable interparticle distance occurs when the total energy is minimized. For both the potential and force curves, repulsive forces are active for PP and PS, resulting in larger minimum distances, while attractive forces are active for PMMA, resulting in smaller minimum distances. Furthermore, focusing on each potential, the van der Waals potential and elastic potential remain unchanged for each polymer species, while the mixing free energy is highest for PP and negative for PMMA. This indicates that the mixing free energy has a significant effect on dispersion and aggregation. Figure 16 shows the total potential curves and force curves for different polymer species. From the figure, it is predicted that PP and PS will disperse easily, while PMMA will aggregate easily, which is consistent with the trend of the χ-parameter.

[0092] Figure 17 shows the potential curves of modified SiO2 nanoparticles for various polymer species, and Figure 18 shows the force curves. For C8-SiO2 in Figure 18(a), the repulsive force was large for all polymer species, and the interparticle distance was also large. For ClC3-SiO2 in Figure 18(b), PS and PMMA had a large repulsive force and a large interparticle distance. On the other hand, PP had a large attractive force and a large interparticle distance. For NHClC3-SiO2 in Figure 18(c), the attractive force was large for all polymer species, and the interparticle distance was small, which did not match the trend of χ. This is due to the ν of C10-CeO2. n is high (4.97 modifiers / nm 2 ) On the other hand, the ν of silane-modified SiO2 n is relatively low (1 modifier / nm 2Therefore, we believe that the repulsive force due to the mixing free energy and elastic energy of the modified chains was not sufficiently obtained in the silane-modified SiO2.

[0093] Table 2 shows the porosity of C10-CeO2 and silane-modified SiO2 for each polymer type, Table 3 shows the adhesive force, and Table 4 shows the crushing strength. The porosity ε was calculated assuming that particles are arranged at equal intervals at the surface-to-surface distance within a two-dimensional square as shown in Figure 19. C10-CeO2 has a crushing strength of 10 times that of PMMA compared to PP and PS. 4 It was suggested that C10-CeO2 aggregates in PMMA at pressures of approximately kPa, and NH2C3-SiO2 aggregates in silane-modified SiO2 regardless of the polymer species.

[0094] <Test 3> Numerical analysis of shear stress The structure of polymer nanocomposite materials during melt-kneading depends not only on the cohesive force of nanoparticles but also on the shear stress applied to the nanoparticle aggregates. The shear stress within the device can be evaluated using equation (5), but in this test, in order to accurately evaluate the local shear stress distribution within the device, it was evaluated using a numerical simulation based on the finite element method.

[0095] [Numerical analysis method] Figure 20 shows the analysis object and mesh division. The analysis object was created based on the shape and dimensions of the kneader used in the experiment. The Mesh Superposition Technique (MST) was used, in which meshes for the barrel and disk were created separately and then superimposed for calculation. The analysis assumed the object was two-dimensional, and that the fluid was isothermal and incompressible, with the effects of fluid inertia and gravity negligible. Calculations were performed using POLYFLOW 2023R1 (ANSYS Inc.), a viscous fluid analysis software based on the finite element method.

[0096] The governing equations are the continuity equation in equation (18) and the equation of motion in equation (19).

[0097] Here, v is the fluid velocity, vbar (a horizontal line above v) is the velocity of the moving part, p is pressure, τ is the stress tensor, ρ is density, and t is time. H is a step function that solves the equation of motion outside the moving part inside the barrel, and assumes that the fluid velocity v and the moving part velocity vbar are equal inside the moving part. The stress tensor τ is expressed by equation (20).

[0098] where η is the viscosity and D is the deformation rate tensor defined by the following equation (21).

[0099] where ∇v is the velocity gradient tensor, (∇v) ｔ is the transpose tensor of the velocity gradient tensor. The shear velocity is expressed by the following equation (22).

[0100] Here, the operator tr represents the trace.

[0101] In this test, the Carreau model shown in the following equation (23) was used to represent the shear rate dependency of viscosity.

[0102] where η is viscosity, η ０ is the intrinsic viscosity, λ is the characteristic time, and n is the non-Newtonian viscosity index. The shear stress can be calculated using the viscosity η based on equation (20).

[0103] [Physical properties and calculation conditions] Table 5 shows the intrinsic viscosity η used in viscosity calculation. ０ , characteristic time λ, non-Newtonian viscosity index n, and density ρ. For intrinsic viscosity, values ​​with molecular weights close to those of the polymer species used in the experiments were quoted. For characteristic time and non-Newtonian viscosity index, experimental values ​​from previous research on each polymer species fitted with the Carreau model at each temperature were quoted.

[0104] The calculation conditions are shown in Table 6. The rotation speed was the same as that used in the experiment, and the calculation was performed up to six rotations of the disk with a total number of steps of 500. The maximum shear stress obtained was calculated by dividing the top 1% of all data and averaging it over time, taking into account the effect of singular points in the calculation.

[0105] [Calculation results] Figure 21 shows the change over time in the shear stress distribution of PP at a rotational speed of 60 rpm during one rotation. The shear stress was large mainly between the discs and between the disc and the barrel, and the shear stress was small from 0.12 s and 0.36 s when the discs were not meshing. This is thought to be because the velocity gradient was large where the discs were meshing, resulting in larger shear stress.

[0106] The shear stress distribution of PP at a rotation speed of 60 rpm after each rotation is shown in Figure 22. The shear stress distribution was similar after each rotation and did not change over time.

[0107] Figure 23 shows the shear stress distribution after six rotations at each rotation speed for different polymer types. For all polymer types, the shear stress increased as the rotation speed increased. Furthermore, the change in shear stress due to the polymer type was small. This coincides with the trend in the experimental results, where the torque for each polymer type was approximately equal at a rotation speed of 60 rpm during kneading.

[0108] Table 7 shows the maximum shear stress at each rotation speed for different polymer types. At all rotation speeds, the maximum shear stress values ​​were PP < PS < PMMA. In addition, the effect of rotation speed on maximum shear stress was also PP < PS < PMMA. This is thought to be because the viscosity values ​​were PP < PS < PMMA, and this was also the case in the high shear region. Furthermore, the calculation results of the crushing strength performed in <Test 2> showed that at all rotation speeds, the difference in maximum shear stress between each polymer type was smaller than the crushing strength, suggesting that the affinity between nanoparticles and polymers has a greater effect on dispersibility than the rotation speed.

[0109] <Test 4> Structure formation map of polymer nanocomposite material The dispersibility of nanoparticles was evaluated based on affinity and the force acting on the particles. Figure 24 shows a structure formation map of polymer nanocomposite material. The horizontal axis is the work of adhesion W between nanoparticles and polymers, which is an index of affinity. PF and the cohesive work between nanoparticles W FF Ratio of W PF / W FF W PF / WFF A value higher than 1 indicates high affinity. The vertical axis is the shear stress σ ｈ and crushing strength σ ｃ The ratio of σ ｈ / σ ｃ σ was used. ｈ was calculated from the analysis of the two-dimensional flow field using the viscous fluid analysis software POLYFLOW mentioned above. ｃ was calculated using the Rumpf formula (1).

[0110] In addition to the van der Waals force, the interaction force due to the modified chain was also considered for the interparticle force. ｈ / σ ｃ >0.5 is bursting dominance, σ ｈ / σ ｃ When the value is less than 0.5, dispersion proceeds by a mechanism called erosion control. In general, dispersion is promoted by bursting rather than erosion. In the case of C10-CeO2, when focusing on affinity, W is the most important factor for any polymer. PF / W FF On the other hand, when we focus on the force acting on the particles, PP and PS have σ ｈ / σ ｃ The system that explodes is larger than 0.5, PMMA is σ ｈ / σ ｃ The systems in which the erosion coefficient was less than 0.5 were found. This was consistent with the trend shown in Figure 2. Systems from previous studies (Non-Patent Documents 1 and 3) were also added to the map. The trends were consistent for all systems, demonstrating the validity of the map. (Non-Patent Documents) Non-Patent Document 3 SH Bumm et al., J. Elastomers Plast., 46, 527 (2014).

[0111] Comparative Example 1 The materials used in Example 1 and the materials shown in Table 8 below were evaluated according to the evaluation in Non-Patent Document 1. PF / W FF and σ ｈ / σ ｃ The relationship between is plotted.

[0112] The results are shown in Figure 25. The three polymers indicated by circles in the figure are located in the same place, but as can be seen from the SEM and TEM photographs in Figures 7 and 8, the aggregate diameter of PMMA is clearly larger than the others.

[0113] In Comparative Example 1, the crushing strength σ ｃ However, when organically modified nanoparticles are handled, the method of Comparative Example 1 may not be able to derive the optimal kneading conditions, which may result in an excess or deficiency of the amount of energy input in the kneading step.

[0114] From the above, it is possible to predict the structure of a wider range of polymer nanocomposite materials using a map organized by interaction forces that take into account affinity, van der Waals forces, and modified chains.

[0115] <Test 5> Correlation between input energy / cohesive energy and structure Figure 26 shows the relationship between the ratio of the energy input to the kneader and the cohesive energy of the nanoparticles, and the area ratio of the aggregates (equivalent to the size of the aggregates), for different polymers.

[0116] In this case, the cohesive energy also takes into account the interaction energy due to the modification chains in addition to the van der Waals energy. The vertical axis shows the total projected area of ​​the aggregate in the SEM image, and a smaller value means fewer particles of a size that can be resolved by SEM, and therefore a smaller aggregate size overall. Figure 26 shows that even with the same input energy, the aggregate size is large in the case of polymer-nanoparticles that are prone to aggregation (large cohesive energy), and that even with large cohesive energy, the aggregate size becomes smaller if the input energy is large.

[0117] Furthermore, Fig. 26 shows that the ratio of remaining aggregates in a polymer can be determined by the input energy. Fig. 26 shows that, regardless of the substance, dispersion will not occur unless the value of total input energy / cohesive energy is above a certain level. In other words, a kneading time that is too short is insufficient, and it is necessary to extend the kneading time until the value of total input energy / cohesive energy reaches the desired value.

[0118] To obtain a good dispersion state with the remaining aggregates being 3% or less, the total input energy / aggregation energy value should be set to 10 ３ It is desirable to have more than this.

[0119] On the other hand, although it also depends on the shear force / cohesion force, if the input energy is too large in the kneading dispersion operation for a system aimed at general dispersion, not only will it cause a decrease in productivity and an increase in the required power energy, but it may also cause breakage of the polymer, oxidative degradation, crushing of nanoparticles, etc.

[0120] Therefore, the upper limit of the value of total input energy / cohesive energy is not particularly limited, but if forced to do so, it is 10 ９ It is desirable that the following:

Claims

1. A method for producing a polymer by adding nanoparticles to a polymer, and a kneading process for melt-kneading the nanoparticles into the polymer by adding energy necessary and sufficient to form a dispersed state of the nanoparticles. ＰＦ / W ＦＦ A combination of the nanoparticles and the polymer is selected so that σ > 0.

9. ｈ / σ ｃ A method for producing a polymer nanocomposite material, wherein the amount of energy input is determined so that W > 0.

5. ＰＦ represents the work of adhesion between the nanoparticle and the polymer, and W ＦＦ denotes the cohesive work between nanoparticles, and σ ｈ denotes the shear stress, and σ ｃ indicates the crushing strength calculated by the Rumpf formula (1) below. (where d represents the primary particle diameter, ε represents the porosity of the aggregate, and F represents the interparticle force.) 2. The method according to claim 1, wherein in the adding step, the combination of the nanoparticles and the polymer is selected so that the contact angle θ calculated by the following formula (2) is less than 37°.

3. The manufacturing method according to claim 1, wherein the energy input in the kneading step includes at least one selected from the group consisting of mechanical energy, thermal energy, vibration energy, electromagnetic induction energy, and electrical energy, which can be externally applied to the kneading process.

4. The value of total input energy / cohesive energy, which is the sum of the energy input in the kneading step divided by the cohesive energy of the nanoparticles, is 10 ３ The manufacturing method according to claim 1 .

5. The method according to claim 1, wherein the nanoparticles are organically modified nanoparticles in which organic molecules are bound to the surface of inorganic nanoparticles.

6. A polymer nanocomposite material in which a polymer material and nanoparticles are combined, wherein the proportion of well-dispersed particles that have been crushed to a size 20 times or less the average particle size of single nanoparticles is 50 vol% or more, and the volume-based average particle size Dv50 of aggregates other than the well-dispersed particles is 100 nm or more and 500 nm or less.

7. The polymeric nanocomposite material according to claim 6, wherein the coefficient of variation of the aggregates is 1.5 or less.

8. A polymer nanocomposite material according to claim 6 or 7, produced by the production method according to any one of claims 1 to 5.

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