阅读说明：本技术 一种相变蓄能储热材料及其制备方法 (Phase-change energy-storage heat-storage material and preparation method thereof ) 是由 李金洪 崔爱铃 王桃 于 2021-08-13 设计创作，主要内容包括：本申请提供一种相变蓄能储热材料及其制备方法,该相变蓄能储热材料,用混合石蜡作为主贮热剂,用膨胀蛭石作为封装材料,用高分子聚合物作为包封支撑体；由于改性膨胀蛭石内部非均匀层状结构形成了丰富间隙,可以将大量混合石蜡填充进去,同时使用高分子聚合物,因其分子量大,支撑力度强,既防止了石蜡的泄露又可以使相变材料和石膏材料很好的连接在一起。另外,提供一种石膏基干混砂浆材料,将脱硫石膏熟料,粉煤灰,水泥,相变蓄能储热材料均匀混合即可制备得到；由于添加了相变蓄能储热材料,显著改善石膏基干混砂浆的蓄热调湿的能力,并且将脱硫石膏熟料和粉煤灰资源化利用,整体制备方法工艺简单,封装高效,尤其适合工业化大规模生产。(The application provides a phase-change energy-storage heat-storage material and a preparation method thereof, wherein the phase-change energy-storage heat-storage material takes mixed paraffin as a main heat storage agent, expanded vermiculite as a packaging material and high-molecular polymer as a packaging support body; because the internal non-uniform layer structure of the modified expanded vermiculite forms rich gaps, a large amount of mixed paraffin can be filled, and meanwhile, the high molecular polymer is used, so that the leakage of the paraffin is prevented, and the phase change material and the gypsum material can be well connected together. In addition, the gypsum-based dry-mixed mortar material is prepared by uniformly mixing desulfurized gypsum clinker, fly ash, cement and a phase-change energy-storage heat-storage material; due to the addition of the phase-change energy-storage heat-storage material, the heat storage and humidity adjustment capability of the gypsum-based dry-mixed mortar is remarkably improved, the desulfurized gypsum clinker and the fly ash are recycled, and the integral preparation method has the advantages of simple process and high packaging efficiency, and is particularly suitable for industrial large-scale production.)

1. The phase change energy storage and heat storage material is characterized by comprising the following raw materials: mixed paraffin is used as a main heat storage agent, expanded vermiculite is used as an encapsulating material, and high molecular polymer is used as an encapsulating support body;

wherein the mixed paraffin is prepared by mixing paraffin which is in a solid state and a liquid state at room temperature according to a proportion, heating the mixture to be completely melted at 50-60 ℃, and the weight ratio of the solid paraffin to the liquid paraffin is (3-5):1, wherein the melting point of the solid paraffin is 48-50 ℃, and the melting point of the liquid paraffin is lower than 20 ℃;

the high molecular polymer is selected from one or more of high-density polyethylene, polyvinyl alcohol and styrene-butadiene-styrene triblock copolymer.

2. A phase change energy storage and heat storage material as claimed in claim 1 wherein the weight ratio of the mixed paraffin, expanded vermiculite, high molecular weight polymer is (0.2-0.8): 1: (0.05-0.3).

3. The gypsum-based dry-mixed mortar material prepared from the phase-change energy-storage heat storage material as claimed in claim 1, which is characterized by comprising the following raw materials in parts by weight: 75-85 parts of desulfurized gypsum clinker, 0-5 parts of fly ash, 0-10 parts of cement and 5-30 parts of phase change energy storage heat storage material.

4. The gypsum-based dry-mixed mortar material according to claim 3, wherein the desulfurized gypsum clinker has an anhydrite (AIII gypsum) content of not more than 5 wt.%; dihydrate gypsum (DH) content not higher than 3 wt.%; the granularity of the desulfurized gypsum clinker is 100-400 meshes;

the fly ash is II-grade fly ash with the granularity of 300-450 meshes.

5. The gypsum-based dry-mixed mortar material according to claim 3, further comprising any one or more of a retarder, a binder, a water-reducing agent and a water-retaining agent;

75-85 parts of desulfurized gypsum clinker, 0-0.3 part of retarder, 0-1.5 parts of binder, 0-0.07 part of water reducer and 0-0.18 part of water-retaining agent.

6. The gypsum-based dry-mixed mortar material according to claim 5, wherein the retarder is selected from one or more of amino acids, protein retarders;

the binder is selected from one or more of redispersible latex powder, polyvinyl alcohol 2488 and polyvinyl alcohol 1788;

the water reducing agent is selected from one or more of a melamine resin water reducing agent, a polycarboxylic acid water reducing agent and a maleic anhydride water reducing agent;

the water retaining agent is selected from one or more of hydroxypropyl methyl cellulose ether, hydroxyethyl methyl cellulose ether and polyvinyl alcohol.

7. The method of claim 1 wherein the phase change energy storage heat storage material is prepared by a process comprising the steps of,

1) uniformly mixing the expanded vermiculite with supersaturated salt water, heating the mixture to more than 100 ℃, standing to room temperature, and gradually cooling to below 0 ℃ until the particle size d of the expanded vermiculite₅₀Less than or equal to 0.45 mu m to obtain expanded vermiculite powder;

2) filtering the expanded vermiculite powder, washing with deionized water to remove impurities, and drying to obtain modified expanded vermiculite;

3) heating solid paraffin to be completely melted, adding liquid paraffin according to a proportion, heating in a water bath, stirring for 2 hours, taking out, and standing at normal temperature for solidification to obtain mixed paraffin;

4) fully mixing and uniformly stirring modified expanded vermiculite and mixed paraffin, then maintaining for 10-60min under the conditions of constant temperature and constant pressure, filtering by using filter paper to obtain precipitate, namely the expanded vermiculite immersed in the mixed paraffin, drying to remove the mixed paraffin on the surface of the expanded vermiculite until no leakage trace exists on the surface of the expanded vermiculite, and then placing for 1d at room temperature;

5) and placing the expanded vermiculite packaged with the mixed paraffin into a high molecular polymer aqueous solution, uniformly stirring, and drying to constant weight to obtain the phase-change energy-storage heat-storage material.

8. The method of claim 7 wherein the phase change energy storage heat storage material is prepared by a process comprising the steps of,

in the step 1), the usage ratio of the expanded vermiculite to the supersaturated brine is as follows: 2g to 50g of expanded vermiculite is added into each liter of supersaturated salt water; the salt is an alkali metal salt.

9. The method of claim 7 wherein the phase change energy storage heat storage material is prepared by a process comprising the steps of,

the drying temperature in the step 2), the step 4) and the step 5) is 40-45 ℃, and the water bath temperature in the step 3) is 60-80 ℃.

10. The method of claim 7 wherein the phase change energy storage heat storage material is prepared by a process comprising the steps of,

the mass fraction of the high molecular polymer aqueous solution in the step 5) is 1-10%.

Technical Field

The invention belongs to the technical field of novel building materials, particularly relates to a phase-change energy-storage heat-storage material, and further provides a preparation method of the phase-change energy-storage heat-storage material suitable for industrial production.

Background

The cement concrete material is used as a building engineering material with the largest current consumption, the widest application range and the most economical efficiency, and makes irreplaceable contribution to the development of the human society. In recent years, with the continuous acceleration of the urbanization construction process of China, the house construction projects are increased day by day, and the problem of building energy consumption is highlighted. Gypsum is a porous building material, is sensitive to air humidity and temperature, and has good capacity of adjusting the environment humidity and temperature.

The phase change energy storage material is a substance which changes the state of a substance and can provide latent heat under the condition of constant temperature; the process of converting physical properties is called a phase transition process. At this point, the phase change material will absorb or release a large amount of latent heat.

The phase change material is organically combined with the gypsum base material to form the phase change functional decorative mortar by processing, and the phase change functional decorative mortar can be applied to the outer wall of the building in China as an environment-friendly and energy-saving building functional decorative material, so that the use comfort of the building in China can be effectively improved, and the comprehensive utilization rate of the energy of the outer wall of the building in China can be improved.

However, in the prior art, the mechanical strength of a gypsum product is greatly reduced after the phase change material is mixed into gypsum, and meanwhile, the problem that the phase change material is easy to leak exists.

Disclosure of Invention

The invention aims to provide a phase-change energy-storage heat-storage material which is composed of mixed paraffin, expanded vermiculite and high molecular polymer; because the inside inhomogeneous lamellar structure of expanded vermiculite has formed abundant clearance, can fill into a large amount of mixed paraffin, use high molecular polymer simultaneously, because its molecular weight is big, the support dynamics is strong, has both prevented revealing and can make phase change material and gypsum material fine link together, the effectual problem that slows down gypsum base phase change energy storage product mechanical strength and descend.

In order to achieve the purpose, the invention provides a phase-change energy-storage heat-storage material which is characterized by comprising the following raw materials: mixed paraffin is used as a main heat storage agent, expanded vermiculite is used as an encapsulating material, and high molecular polymer is used as an encapsulating support body;

wherein the mixed paraffin is prepared by mixing paraffin which is in a solid state and a liquid state at room temperature according to a proportion, heating the mixture to be completely melted at 50-60 ℃, and the weight ratio of the solid paraffin to the liquid paraffin is (3-5):1, wherein the melting point of the solid paraffin is 48-50 ℃, and the melting point of the liquid paraffin is lower than 20 ℃;

the high molecular polymer is selected from one or more of high-density polyethylene, polyvinyl alcohol and styrene-butadiene-styrene triblock copolymer.

In a preferred embodiment, the weight ratio of the mixed paraffin, the expanded vermiculite and the high molecular polymer is (0.2-0.8): 1: (0.05-0.3).

The invention also aims to provide a gypsum-based dry-mixed mortar material prepared from the phase-change energy-storage heat-storage material, which is prepared by uniformly mixing desulfurized gypsum clinker, fly ash, cement and the phase-change energy-storage heat-storage material; the phase-change energy-storage and heat-storage material is added, so that the heat storage and humidity adjustment capacity of the gypsum-based dry-mixed mortar is remarkably improved, the problem of poor mechanical property of the gypsum-based mortar is effectively solved, the desulfurized gypsum clinker and the fly ash are recycled, and the prepared gypsum-based dry-mixed mortar material is strong in mechanical property, low in cost, easy in obtaining of raw materials, simple in process and especially suitable for industrial large-scale production.

In order to achieve the purpose, the invention provides a gypsum-based dry-mixed mortar material which comprises the following raw materials in parts by weight: 75-85 parts of desulfurized gypsum clinker, 0-5 parts of fly ash, 0-10 parts of cement and 5-30 parts of phase change energy storage heat storage material.

In a preferred embodiment, the desulfurized gypsum clinker has an anhydrite (AIII gypsum) content of not more than 5 wt.%; dihydrate gypsum (DH) content not higher than 3 wt.%; the granularity of the desulfurized gypsum clinker is 100-400 meshes;

the fly ash is II-grade fly ash with the granularity of 300-450 meshes;

preferably, desulfurized gypsum clinker D₅₀Is 40-50 μm.

In a preferred embodiment, a gypsum-based dry mixed mortar material further comprises any one or more of a retarder, a binder, a water reducer and a water retention agent;

75-85 parts of desulfurized gypsum clinker, 0-0.3 part of retarder, 0-1.5 parts of binder, 0-0.07 part of water reducer and 0-0.18 part of water-retaining agent;

preferably 75-85 parts of desulfurized gypsum clinker, 0.05-0.2 part of retarder, 0.5-1.5 parts of binder, 0.02-0.06 part of water reducing agent and 0.05-0.15 part of water-retaining agent;

wherein the retarder is selected from one or more of amino acids and protein retarders;

the binder is selected from one or more of redispersible latex powder, polyvinyl alcohol 2488 and polyvinyl alcohol 1788;

the water reducing agent is selected from one or more of a melamine resin water reducing agent, a polycarboxylic acid water reducing agent and a maleic anhydride water reducing agent;

the water retaining agent is selected from one or more of hydroxypropyl methyl cellulose ether, hydroxyethyl methyl cellulose ether and polyvinyl alcohol;

preferably, the water retention agent is hydroxypropyl methyl cellulose ether with viscosity of 20000-100000 mpa.s.

The invention also aims to provide a preparation method of the phase-change energy-storage heat-storage material, which comprises the steps of firstly modifying expanded vermiculite by using supersaturated saline water and temperature difference, enabling the saline solution and different temperature changes to influence the pore structure of the expanded vermiculite, dissolving Mg ions in the expanded vermiculite by limiting the saline solution and the temperature changes, and increasing the interlayer spacing of the expanded vermiculite so as to improve the paraffin loading capacity; the mixed paraffin is packaged, and consists of solid paraffin and liquid paraffin, compared with single-state paraffin, the mixed paraffin is formed by fusing normal-temperature solid paraffin and liquid paraffin, has different heat storage performances, integrally shows a rising trend along with the increase of the number of carbon atoms, can improve the heat storage capacity of the phase-change material, is solid at normal temperature, and can effectively prevent leakage compared with liquid paraffin; and finally, the macromolecule solution is used as an encapsulation support body, so that the paraffin can be further prevented from leaking, and the phase-change material and the gypsum-based material can be effectively connected. The integral preparation method is simple, pollution-free, low in requirement on operators and easy to popularize.

In order to achieve the purpose, the invention provides a preparation method of a phase-change energy-storage heat-storage material, which is characterized in that,

1) uniformly mixing the expanded vermiculite with supersaturated salt water, heating the mixture to more than 100 ℃, standing to room temperature, and gradually cooling to below 0 ℃ until the particle size d of the expanded vermiculite₅₀Less than or equal to 0.45 mu m to obtain expanded vermiculite powder; alternatively, if the particle size d of the expanded vermiculite₅₀If the particle size of the expanded vermiculite is larger than 0.45 mu m, repeating the heating and cooling circulation process until the particle size of the expanded vermiculite meets the composite requirement;

2) filtering the expanded vermiculite powder, washing with deionized water to remove impurities, and drying to obtain modified expanded vermiculite;

3) heating solid paraffin to be completely melted, adding liquid paraffin according to a proportion, heating in a water bath, stirring for 2 hours, taking out, and standing at normal temperature for solidification to obtain mixed paraffin;

4) the preparation method comprises the steps of (1) uniformly stirring modified expanded vermiculite and mixed paraffin (fully mixing the paraffin when the paraffin is completely melted under the heating condition of 50-60 ℃), then maintaining the mixture for 10-60min under the conditions of constant temperature and constant pressure, immersing the mixed paraffin into pores of the expanded vermiculite under the action of capillary force and surface tension, filtering the mixture to obtain a precipitate, namely the expanded vermiculite immersed in the mixed paraffin, and drying the precipitate to remove the mixed paraffin on the surface of the expanded vermiculite until no paraffin trace leaks on the surface of the expanded vermiculite; then standing at room temperature for 1 d;

5) and placing the expanded vermiculite packaged with the mixed paraffin into a high molecular polymer aqueous solution, uniformly stirring, and drying to constant weight to obtain the phase-change energy-storage heat-storage material.

In a preferred embodiment, in the step 1), the dosage ratio of the expanded vermiculite to the supersaturated brine is that 2g to 50g of expanded vermiculite is added per liter of supersaturated brine; the salt is an alkali metal salt;

preferably, the alkali metal salt comprises a sodium salt or a lithium salt;

the drying temperature in the step 2), the step 4) and the step 5) is 40-45 ℃, and the water bath temperature in the step 3) is 60-80 ℃.

The mass fraction of the high molecular polymer aqueous solution in the step 5) is 1-10%, and the preparation method is to fully stir and dissolve the high molecular polymer in water.

Compared with the prior art, the phase-change energy-storage heat-storage material and the preparation method thereof have the following advantages:

1. the formula of the phase-change energy-storage heat-storage material only adopts mixed paraffin, expanded vermiculite, high-density polyethylene, polyvinyl alcohol and styrene-butadiene-styrene triblock copolymer, the raw materials are easy to obtain and purchase, and the cost is low, wherein the mixed paraffin is respectively selected from paraffin with melting points being liquid and solid at normal temperature, compared with single-state paraffin, the mixed paraffin is fused with normal-temperature solid paraffin and liquid paraffin, the two paraffin have different heat storage performances, and integrally shows a rising trend along with the increase of the number of carbon atoms, so that the heat storage capacity of the phase-change material can be improved, and the mixed paraffin is solid at normal temperature and can effectively prevent leakage compared with liquid paraffin; the expanded vermiculite has a typical non-uniform layered structure and rich gaps, Mg ions in the expanded vermiculite are dissolved out after treatment of saturated salt solution and temperature difference, the interlayer spacing of the expanded vermiculite is enlarged, the gap space is further increased, and the paraffin wax capacity is improved; the polymer solution has high molecular weight and strong supporting force, can be used as a propping agent to prevent paraffin leakage and can be used as a binder to well connect the phase-change material and the gypsum material together, thereby effectively slowing down the mechanical strength reduction of the gypsum-based phase-change energy storage product.

2. The desulfurized gypsum clinker is used as the main material, so that the resource utilization of desulfurized gypsum is realized, the cost is further reduced, the application range of the gypsum-based dry-mixed mortar is expanded, the prepared gypsum-based dry-mixed mortar has small drying shrinkage or hardening shrinkage, the material is prevented from drying and cracking, and the toughness of the material is improved.

3. The method has the advantages of simplified overall process, safety, low requirement on operators, suitability for large-scale production and capability of effectively reducing production cost and preparation difficulty.

Drawings

FIG. 1 is an electron microscope image of modified expanded vermiculite, and it can be seen that the expanded vermiculite has a typical non-uniform lamellar structure, and the close packing of lamellae forms rich pores to provide a large amount of packaging space for paraffin.

Fig. 2 is an electron microscope image of the expanded vermiculite after the mixed paraffin is packaged, and it can be seen that the mixed paraffin occupies the pores and the surface of the expanded vermiculite, which shows that the modified expanded vermiculite can effectively package the paraffin.

FIG. 3 is a curve showing the influence of the change of the amount of paraffin wax on the phase transition temperature and latent heat of phase transition of the compounded paraffin wax after DSC test, wherein 3-a is a melting process curve and 3-b is a solidification process curve.

Detailed Description

Unless otherwise specified, the technical means used in the examples are conventional means well known to those skilled in the art, and the raw materials used are commercially available.

Unless otherwise specifically stated, various raw materials, reagents, instruments, equipment and the like used in the present invention are commercially available or can be prepared by existing methods.

The retarder used in the following examples was spaghetti SICIT gypsum retarder PLAST RETARD PE, the water reducing agent was basf MELMENT F10, and the high molecular weight polymer was polyvinyl alcohol 2488.

The paraffin has two kinds, solid paraffin is from chemical reagent of national drug group limited company and has a melting point of 48-50 ℃, and the other liquid paraffin is from Beijing Fine chemical product limited company and has a melting point of less than 20 ℃.

The expanded vermiculite is from Hubei Lingshou county. Other raw materials and reagents are common commercial products.

In the present invention, the parts by weight may be in the units of μ g, mg, g, kg, etc. known in the art, or may be multiples thereof, such as 1/10, 1/100, 10, 100, etc.

Example 1

1. Preparation of composite phase-change energy-storage heat-storage material

(1) Crushing vermiculite to prepare expanded vermiculite with high expansion rate (screening by a 60-mesh sieve), cleaning the expanded vermiculite with deionized water, and mixing with NaCl supersaturated solution (the weight of the vermiculite is 20g/L) to obtain a mixed solution of the expanded vermiculite and water;

(2) placing the mixed solution of the expanded vermiculite and the water prepared in the step (1) on an electric heater (160 ℃), heating while stirring (periodically supplementing deionized water), cooling to room temperature after 8 hours, gradually cooling to-10 ℃, placing on an electric hot plate after 8 hours, cooling to below 0 ℃, and repeatedly circulating until the particle size d of the expanded vermiculite₅₀≤0.45μm；

(3) Filtering the vermiculite mixture prepared in the step (2) by using filter paper, and washing the vermiculite by using deionized water;

(4) the vermiculite on the filter paper is placed in an oven to dry until ready for use, at which time the expanded vermiculite has a pore size distribution of about 0.01 μm to 50 μm.

(5) Heating 400g of solid paraffin to be completely melted at the temperature of 80 ℃, adding 100g of liquid paraffin, stirring for 2 hours under the water bath heating condition of 50-60 ℃ until the paraffin is completely melted and fully mixed, taking out a beaker, cooling and solidifying the paraffin mixture in the air, and covering the mixture with a preservative film for later use.

(6) Adding expanded vermiculite nanosheets (vermiculite on dried filter paper in the step (4) in the treatment method of expanded vermiculite) into excessive mixed paraffin prepared in the step (5), fully and uniformly mixing, heating and filtering, and then maintaining for 20 minutes under the conditions of constant temperature (40 +/-2 ℃) and constant pressure (vacuum degree of-0.09 MPa to 0.01 MPa); under the action of capillary force and surface tension, the emulsified paraffin is immersed into the pores of the expanded vermiculite. The expanded vermiculite is then transferred to filter paper and the emulsified paraffin that leaks from the surface of the expanded vermiculite is removed in a drying oven above the melting point of the phase change material. The filter paper was changed continuously until no trace of leakage was observed, and then left at room temperature for 1 day to further remove the excess paraffin on the outside of the expanded vermiculite.

(7) Placing the mixture prepared in the step (6) into a polyvinyl alcohol solution (the mass fraction of the polyvinyl alcohol solution is 10%), wherein the weight ratio of the mixed paraffin, the expanded vermiculite and the high molecular polymer is 0.5: 1: 0.2, stirring evenly, and drying in an oven (45 ℃).

2. Preparation of gypsum-based plastering material

(1) Weighing the components according to the mass in the table 1;

(2) uniformly mixing cement and a composite phase-change energy-storage heat-storage material (comprising expanded vermiculite and emulsified paraffin) to obtain premixed powder;

(3) uniformly mixing the premixed powder with gypsum powder and fly ash;

(4) and adding a retarder, a water reducing agent, latex powder and cellulose ether, and uniformly mixing to obtain the gypsum-based plastering material.

3. Preparation of gypsum-based plastering mortar

The prepared gypsum-based plastering material is mixed with mixing water to prepare gypsum-based plastering mortar. Wherein, the dosage of the mixing water is determined according to a method of 7.4.2.1 'determination of water consumption of standard diffusivity' in the national standard GB/T28627-2012 plastering gypsum.

TABLE 1

Test example 1

And (3) testing the thermophysical properties of the solid-liquid compound paraffin by using a Differential Scanning Calorimeter (DSC) to determine the phase-change temperature and the phase-change latent heat of the solid-liquid compound paraffin. The DSC results of the compounded phase-change paraffin of solid paraffin and liquid paraffin in different mass ratios (solid-to-liquid ratio of 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%) are shown in fig. 3, and the specific phase-change parameters are detailed in table 2.

TABLE 2 phase transition parameters of compounded paraffins

It is obtained from the figure that the phase transition temperature and latent heat of the compound paraffin prepared by experiments are increased along with the increase of the solid paraffin content. According to the phase change temperature and the phase change latent heat value required by comprehensive practical operation, the solid paraffin doping amount is 80%, the phase change temperature of the prepared compound paraffin is 22.6 ℃, and the phase change latent heat is 168.2J/g. The invention makes the mass ratio of the solid paraffin to the liquid paraffin be 4: 1, taking the compound paraffin with the maximum latent heat value as a raw material.

Test example 2

The water retention rate of the gypsum-based slurry prepared by the formula in table 1 is tested according to the method specified in GB/T28627-2012 plastering Gypsum. The slurries of the examples and comparative examples were tested according to the standard method of national standard GB/T17669.3-1999 to prepare 40mm by 160mm test blocks, and the test blocks were cured at normal temperature (15-30 ℃) for 24 hours under the relative humidity of 50-70%, demolded, and then continuously cured to the specified age (T7 d) and dried to test the mechanical properties, and the test results are shown in Table 3.

TABLE 3

As can be seen from the above table, the desulfurized gypsum clinker added in comparative example 1 is increased by 25% compared to example 2, but the mechanical properties such as flexural strength and compressive strength are not as good as those of the composite material prepared by the present invention; compared with the prior art, the expanded vermiculite is directly adopted to replace the phase change energy storage heat storage material prepared by the method, and the mechanical property and the softening coefficient of the phase change energy storage heat storage material are obviously lower than those of the phase change energy storage heat storage material prepared by the method in the embodiment 2.

The foregoing descriptions of specific exemplary embodiments of the present invention have been presented for purposes of illustration and description. It is not intended to limit the invention to the precise form disclosed, and obviously many modifications and variations are possible in light of the above teaching. The exemplary embodiments were chosen and described in order to explain certain principles of the invention and its practical application to enable one skilled in the art to make and use various exemplary embodiments of the invention and various alternatives and modifications as are suited to the particular use contemplated. It is intended that the scope of the invention be defined by the claims and their equivalents.