Gypsum wallboard and method of making same

Abstract

Compositions for gypsum board are disclosed, comprising a mixture of a gypsum slurry and a pre-generated foam and a coalescing agent. The coalescing agent comprises one or more coalescing agents that are added to the composition singly, separately or in combination to change the size and distribution of the air bubbles in the foamed gypsum slurry. The resulting gypsum cores have increased nail pull resistance and an improved facer/gypsum core bond.

Claims

1. A foamed gypsum slurry composition, comprising: stucco; gauging water; a foam comprising foaming water, a foaming agent and air; a first coalescing agent having a first cloud point temperature; and a second coalescing agent having a second cloud point temperature that is different from the first cloud point temperature; wherein the foamed gypsum slurry composition has a mix temperature, and the first and second coalescing agents have a blended cloud point temperature that is lower than the mix temperature.

2. The foamed gypsum slurry composition of claim 1, wherein the blended cloud point temperature is lower than the mix temperature by about 5 F. to about 30 F.

3. The foamed gypsum slurry composition of claim 1, wherein the blended cloud point temperature is lower than the mix temperature by about 5 F. to about 10 F.

4. The foamed gypsum slurry of claim 1, wherein the first coalescing agent has a cloud point temperature of about 68 F., and the second coalescing agent has a cloud point temperature of about 110 F.

5. The foamed gypsum slurry of claim 1, wherein the first or second coalescing agent is a polyether block copolymer surfactant.

6. The foamed gypsum slurry of claim 5, wherein the polyether block copolymer surfactant is an ethylene oxide-propylene oxide block copolymer and/or reverse block copolymer.

7. The foamed gypsum slurry of claim 1, wherein the first or second coalescing agent is an alkoxylated alcohol surfactant.

8. The foamed gypsum slurry of claim 7, wherein the alkoxylated alcohol surfactant is a fatty alcohol alkoxylate.

9. The foamed gypsum slurry of claim 1, wherein the first and/or second coalescing agent has a delayed coalescing activity.

10. A method for making a foamed gypsum slurry composition, comprising the steps of: providing a gypsum slurry comprising stucco and gauging water; generating a foam comprising foam water, a foaming agent and air; introducing the foam to the gypsum slurry to form a foamed gypsum slurry having a mix temperature; adding a first coalescing agent to the foamed gypsum slurry, the first coalescing agent having a first cloud point temperature; and adding a second coalescing agent to the foamed gypsum slurry, the second coalescing agent having a second cloud point temperature that is different from the first cloud point temperature; wherein the first and second coalescing agents have a blended cloud point temperature that is lower than the mix temperature.

11. The method of claim 10, wherein the first and second coalescing agents have a blended cloud point temperature that is lower than the mix temperature by about 5 F. to about 30 F.

12. The method of claim 10, wherein the first and second coalescing agents have a blended cloud point temperature that is lower than the mix temperature by about 5 F. to about 10 F.

13. The method of claim 10, further comprising the steps of: determining the mix temperature of the foamed gypsum slurry; and adjusting the ratio of the first and second coalescing agents to provide a blended cloud point temperature that is lower that the mix temperature.

14. The method of claim 13, wherein the first and second coalescing agents have a blended cloud point temperature that is lower than the mix temperature by about 5 F. to about 30 F.

15. The method of claim 13, wherein the first and second coalescing agents have a blended cloud point temperature that is lower than the mix temperature by about 5 F. to about 10 F.

16. The method of claim 10, wherein the first coalescing agent has a cloud point temperature of about 68 F., and the second coalescing agent has a cloud point temperature of about 110 F.

17. The method of claim 10, wherein the first and second coalescing agents are added to the foamed gypsum slurry by mixing with a component of the composition selected from the group consisting of: the gypsum slurry, the gauging water, the foam water, the foaming agent, the foam, and combinations thereof.

18. The method of claim 17, wherein the first and second coalescing agents are added separately to the foamed gypsum slurry by mixing with different components of the composition.

19. The method of claim 10, further comprising the steps of: transferring the gypsum slurry from a mixer to a canister and to a boot; and introducing the foam to the gypsum slurry in the mixer or the canister; and wherein the first and second coalescing agents are added to the foamed gypsum slurry at a location selected from the group consisting of: the mixer, the canister, the boot, and combinations thereof.

20. The method of claim 19, wherein the first and second coalescing agents are added separately to the foamed gypsum slurry at different locations.

21. The method of claim 10, wherein the first or second coalescing agent is a polyether block copolymer surfactant.

22. The method of claim 21, wherein the polyether block copolymer surfactant is an ethylene oxide-propylene oxide block copolymer and/or reverse block copolymer.

23. The method of claim 10, wherein the first or second coalescing agent is an alkoxylated alcohol surfactant.

24. The method of claim 23, wherein the alkoxylated alcohol surfactant is a fatty alcohol alkoxylate.

25. A method for making a gypsum board, comprising the steps of: providing a gypsum slurry comprising stucco and water; generating a foam comprising water, a foaming agent and air; introducing the foam to the gypsum slurry to form a foamed gypsum slurry having a mix temperature; determining the mix temperature of the foamed gypsum slurry; adding a first coalescing agent to the foamed gypsum slurry, the first coalescing agent having a first cloud point temperature; adding a second coalescing agent to the foamed gypsum slurry, the second coalescing agent having a second cloud point temperature that is different from the first cloud point temperature, wherein the first and second coalescing agents are added in a ratio that provides a blended cloud point temperature that is lower that the mix temperature by about 5 F., to about 30 F.; applying the foamed gypsum slurry to a first facing material; applying a second facing material atop the foamed gypsum slurry to sandwich the foamed gypsum slurry between the first and second facing materials; forming the foamed gypsum slurry to a desired thickness; and drying the foamed gypsum slurry to form a board.

26. The method of claim 25, wherein the first and second coalescing agents are added in a ratio that provides a blended cloud point temperature that is lower that the mix temperature by about 5 F. to about 10 F.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIGS. 1A and 1B are SEM images showing the bubble structure of gypsum boards produced without and with coalescing agent, respectively;

(2) FIG. 2 is a data plot of the bubble diameter and total void area of the gypsum boards of FIGS. 1A and 1B;

(3) FIG. 3 is an SEM image showing the bubble structure of an ultra-light gypsum board produced with coalescing agent;

(4) FIG. 4 is a data plot of the bubble diameter and total void area of the gypsum board of FIG. 3;

(5) FIGS. 5A and 5B are SEM images showing the bubble structure of gypsum boards produced with coalescing agents having different cloud points;

(6) FIG. 6 is a data plot of the bubble diameter and total void area of the gypsum boards of FIGS. 5A and 5B;

(7) FIG. 7 is a data plot of the cloud points of blends of two different coalescing agents in varying ratios;

DETAILED DESCRIPTION OF THE INVENTION

(8) Compositions and methods for controlling the foam structure of a gypsum core are disclosed, that permit the weight of the gypsum board to be reduced while maintaining desirable board properties (e.g., nail pull resistance, humidified bond, deflection, etc.). The gypsum core composition comprises a mixture of a gypsum slurry, a pre-generated foam, and one or more coalescing agents. In a preferred embodiment, the pre-generated foam is formed using a stable soap. The bubble structure of the gypsum core is controlled by varying the ratio of the coalescing agent to the soap. In a further preferred embodiment, the bubble structure is controlled by varying the ratio between multiple coalescing agents and their ratios to the soap.

(9) Previous efforts to control the foam structure have been directed to the use of defoaming agents and the sensitivity of the defoaming agent to the temperature of the gypsum core composition. The use of weak defoaming agents, such as polyamines or chemistries based upon polydimethylsiloxane with aminoalkyl and polyether groups, is described in U.S. Pat. No. 8,016,961 to Martin et al., which is incorporated herein by reference in its entirety. Such defoaming agents tend to cause the bubbles to simply collapse rather than coalesce together. Consequently, the use of defoaming agents may require increased amounts of soap to compensate for the loss of air volume.

(10) In contrast to defoaming agents, coalescing agents tend to cause the bubbles to merge or fuse together into a larger bubble, which maintains the air volume (foam volume). Thus, the use of coalescing agents typically requires less soap compared to defoaming agents. The activity of the coalescing agent is affected by the temperature of the foamed gypsum slurry. Other process parameters may also affect the coalescing activity, including soap usage, foam weight (foam water and air), stiffening time, stucco particle size, fluidity (slump), water to stucco ratio, stucco impurities, and where the coalescing agent is added in the process.

(11) In general, coalescing agents react and destabilize the bubbles in the foamed gypsum slurry, coalescing them into larger ones, when the temperature of the slurry approaches the cloud point (T.sub.CP) of the coalescing agenti.e. the temperature at which the coalescing agent solution loses clarity. For purposes of the coalescing reaction, the operative mix temperature of the slurry is believed to be at or near the initial mix temperature of the foamed gypsum slurry, which is largely determined by the temperature of the stucco (generally ranging between about 130 F. to 210 F.) and the water temperature. Although the stucco reaction is exothermic and increases the mix temperature, almost all of the heat of the exothermic reaction is evolved after the board becomes solid and the bubbles can no longer coalesce. Thus, the operative mix temperature for coalescing activity is believed to be at or near the initial mix temperature of the foamed gypsum slurry, while the slurry is still fluid.

(12) It is generally desirable that the coalescing agent have a T.sub.CP that is lower than the mix temperature of the foamed gypsum slurry. If the mix temperature greatly exceeds the T.sub.CP, the coalescing agent may become too active and can result in paper blisters and blowsi.e. small and large areas where the paper has separated from the gypsum core.

(13) The mix temperature and other process parameters may change during a given day, week, or seasonally. Applicants have found that the cloud point of the coalescing agent may be adjusted by combining or blending multiple coalescing agents with different cloud points in varying ratios. This multiple coalescing agent system allows the coalescing reaction to be adjusted in situ during production, to quickly react to changes in the process parameters and provide increased flexibility to the manufacturing process. The coalescing agents may be added diluted or as is, separately or in tandem, and may introduced with different components of the composition and/or at different locations in the production process, such as by addition to the soap, foam water, gauging water, pulp water, to the mixer, canister, boot, slurry, and/or to the foam. The flexibility of changing the type, ratio, and introduction locations of the coalescing agents makes this process controllable and minimizes the risk of undesirable process issues such as blisters and blows or other quality issues. All these additions may be performed in situ to allow control of the foam structure in the gypsum core during the production process, although ex-situ preparations also are possible.

(14) Coalescing agents are available that have cloud points ranging from about 60 F. to about 140 F. (16 C. to 60 C.). By combining coalescing agents with different cloud points and varying their ratios, it is possible to adjust the cloud point of the coalescing agent or coalescing agent blend within this range. Thus, the cloud point may be optimized for the specific mix temperature, fluidity and other process parameters that may change during a given day, week, or seasonally.

(15) It is generally desirable to select coalescing agents that can be combined in varying ratios to adjust the blended T.sub.CP in a range that corresponds to the expected range of the operative mix temperature. The mix temperature is typically found to range from about 85 F. to about 120 F. The cloud point of the coalescing agent is preferably lower than or near the mix temperature.

(16) In one embodiment, the combination of coalescing agents comprises a first coalescing agent that has a T.sub.CP that is about 68 F. and a second coalescing agent that has a T.sub.CP that is about 110 F. The mix temperature of the gypsum slurry can be determined during production and the ratio of the coalescing agents can readily be adjusted in situ to vary the blended T.sub.CP between 68 F. and 110 F., as may be appropriate for the determined mix temperature. In a preferred embodiment, the coalescing agent has a blended T.sub.CP that is lower than the mix temperature by about 5 F. to 30 F., and more preferably by about 5 F. to 10 F.

(17) Applicants have found that controlling the ratio of coalescing agents to optimize the cloud point temperature relative to the mix temperature results in improved gypsum core void structures, nail pull resistance, and paper/gypsum core bonding. Board weight can be reduced while maintaining good board properties (nail pull, humidified bond, deflection, etc.). In addition, this adjustable coalescing agent system is much more flexible in reacting to parameter changes during the manufacturing process. By controlling the type, ratio, and introduction location of the coalescing agents or coalescing agent blend, the cloud point may be quickly and easily adjusted to achieve the desired bubble structure. This approach gives the ability to immediately react to variations in mix temperature, mix fluidity (slump) and other process parameters including, soap usage, foam weight, stiffening time, stucco particle size, water to stucco ratio, etc., by adjusting the amount and/or ratio of the coalescing agents to achieve the desired core structure and to reduce or eliminate the tendency to form blisters or blows, or other quality issues.

(18) This system also allows the manufacturing plants to use one soap type for all products and to use the coalescing agent only for products on an as needed basis. The amount of coalescing agent added to the soap (percentage of coalescing agent on soap) can be changed for each product to meet the physical property requirements for a given product type (i.e. strength, weight, etc.). Generally, the usage level of the coalescing agent on a soap basis can vary from plant to plant and it depends on process parameters such as mix fluidity, mix temperature, soap usage, setting time, type of stucco, the location where the foam is added, the location where the coalescing agent is added and other process factors. In one embodiment, the usage level of the coalescing agent can vary from 1% up to 25% on soap.

(19) The levels of coalescing agents or blends can be controlled through feed and control systems. The coalescing agents can be pre-blended in various ratios or added in a holding tank or mixing tank prior to addition to the foam, and can be introduced to the foam separately or in tandem, either diluted or as is. The coalescing agents can also be introduced at different entry locations in the manufacturing processe.g., added to the soap, foam water, gauging water, pulp water, to the mixer, boot, canister, slurry, and/or to the foam. Alternatively, the coalescing agents may be added directly to the foam at a later stage. All these additions may be done in situ in order to control the distribution of the foam bubbles in the gypsum core during the manufacturing process. Ex-situ methods are also possible.

(20) In a preferred embodiment, the coalescing agents have a delayed coalescing activity that takes place within the stiffening time of the mix, and not spontaneously. Thus, within a few seconds after the coalescing agent is mixed with the foamed slurry, the coalescing action starts and the size and distribution of the air voids in the core changes. For example, methods for delaying the action of a coalescing agent based on the mix temperature are known in the art, as described in U.S. Patent Publication No. 2012/0237756 to Lee et al., which is also incorporated herein in its entirety. The coalescing reaction does not happen immediately, but is time dependent and typically starts within a few seconds after the coalescing agent is mixed with the foamed slurry. The coalescing action continues until the mixture is set or stiff enough that it no longer allows the bubbles to coalesce.

(21) In one embodiment, the coalescing agent comprises a polyether block copolymer surfactant, such as are commercially available from BASF Corporation (Florham Park, N.J.). In a preferred embodiment, the coalescing agent is an ethylene oxide-propylene oxide block copolymer (i.e. EO/PO), and more preferably a reverse block copolymer (i.e. PO/EO). It is further preferred that the coalescing agent has an ethylene oxide (EO) or hydrophilic block content of from about 10 to about 50 wt %. In the case of a block copolymer, the EO content is preferably in the range of between about 20 to about 45 wt %, and in the case of a reverse block copolymer, the EO content is preferably in the range of between about 20 to about 45 wt %.

(22) In an alternative embodiment, the coalescing agent comprises an alkoxylated alcohol surfactant, such as a fatty alcohol alkoxylate. Exemplary alkoxylated alcohol surfactants are commercially available from BASF Corporation, and comprise the reaction product of linear and/or branched alcohol(s) and a mixture of propylene oxide and ethylene oxides, containing a mixed chain of propylene oxide and ethylene oxide terminated by a hydroxyl group. In a preferred embodiment, the alcohol contains 6 to 18 carbon atoms and the number of moles of lower alkylene oxide (2 or 3 carbon atoms) is from 3 to 12. In a particularly preferred embodiment, the alkoxylated alcohol surfactant comprises a C.sub.6-C.sub.10 fatty alcohol condensed with 6 to 12 moles of ethylene oxide and 3 moles of propylene oxide.

(23) In another embodiment, the coalescing agent has a hydrophilic-lipophilic balance of from about 1 to about 31, or about 1 to about 15. In the case of an EO/PO block copolymer, the hydrophilic-lipophilic balance is preferably in a range of between about 7 to about 15, and in the case of a reverse block copolymer, the hydrophilic-lipophilic balance is preferably in a range of between about 1 to about 7.

(24) In yet another embodiment, the coalescing agent has an average molecular weight of from about 1000 to about 4000. In the case of an EO/PO block copolymer, the average molecular weight is preferably in a range of between about 2000 to about 3500, and in the case of a reverse block copolymer, the average molecular weight is preferably in a range of between about 2000 to about 3500.

(25) The following examples and the techniques disclosed herein are included to demonstrate embodiments that have been found to function well in the practice of the invention, and thus can be considered to constitute preferred modes for its practice. However, those of skill in the art should, in light of the present disclosure, appreciate that many changes can be made in the specific embodiments which are disclosed and still obtain a like or similar result without departing from the scope of the invention.

EXAMPLE 1

(26) Gypsum board having improved nail pull strength was produced using coalescing agents. Foamed gypsum slurries were prepared and gypsum boards were formed in the laboratory, with and without a coalescing agent as set forth in Table I. Board 1 was a control board made with no coalescing agent. Board 2 was made with the coalescing agent Lumiten 4425 (BASF 8915). Additional components of the gypsum slurry include: a ball mill accelerator, BMA (National Gypsum Company); a retarder, Plast Retard L (SICIT 2000 SpA); a dispersant, Gypflow TF (Handy Chemicals); and a surfactant, Cedapal (Stepan Company).

(27) TABLE-US-00001 TABLE I Composition of Boards 1 and 2 Board 1 (control) Board 2 (4425) Stucco 700 g 700 g BMA 9.0 g 9.0 g Potash 0.2 g 0.2 g Dextrose 0.8 g 0.8 g Pulp 1.2 g 1.2 g Starch - Acid 13.0 g 13.0 g Modified Gypflow Dispersant 4.0 g 4.0 g Plast L 0.04 g 0.04 g Lumiten 4425 0 10.0% on soap Cedapal 0.41 g 0.39 g Water (total) 656.8 g 653.1

(28) The board weight and nail pull resistance of the resulting boards was measured as described in ASTM C 473 Standard Test Methods for Physical Testing of Gypsum Panel Products. The bubble structure of the gypsum cores was analyzed by scanning electron microscopy (SEM) at 50 magnification. The photographs of FIG. 1A (Board 1) and FIG. 1B (Board 2) are representative of the bubble structure of the gypsum cores, and correspond to an area of 5.0 mm.sup.2. The percentage of small bubbles in the gypsum core having a diameter less than 150 m (<150), the diameter of the bubbles at the mid-point of the size distribution (MP), the number of bubbles in the area of the photograph (Count), and the total area of air or void area of the gypsum core (VA) in the analyzed area (5.0 mm.sup.2) were measured and are shown in Table II. The bubble size distribution is shown in FIG. 2.

(29) TABLE-US-00002 TABLE II Bubble Structure Analysis of Boards 1 and 2 BW NP <150 MP VA (lb/msf) (lbf) (%) (m) Count (%) Board 1 1325 68 36 175 236 66.7 Board 2 1384 77 1 485 18 50.5

(30) The data in Table II and FIG. 2 shows that the presence of a coalescing agent reduces the number of small bubbles and increases the number or amount of large and discrete bubblesi.e. as shown by the substantial reduction in percentage of small bubbles (<150) and the increase in bubble size at the mid-point (MP).

(31) The data also shows that the coalescing agent does not act as a strong defoamer, but instead acts to coalesce the small bubbles into larger ones. The number of air bubbles in the control is dramatically reduced from 236 in the control to 18 with coalescing agent, whereas the void area (VA) is only reduced from 67% in the control to 50.5% with coalescing agent. Similarly, FIG. 2 shows that the presence of a coalescing agent results in a narrow distribution of larger bubbles in comparison to the control, which has a wide distribution of small and large bubbles. These changes in bubble structure produced by the coalescing agent also increases the width of the solid matrix between bubbles (as shown in FIG. 1B), which is believed to result in an increased nail pull resistance. Furthermore, this data shows that desirable core void structures and resulting board properties can be achieved using coalescing agents without increasing the amount of soap used in the system, as is generally required using defoaming agents.

EXAMPLE 2

(32) Gypsum board having reduced weight and increased nail pull resistance was produced by adjusting the relative concentration of coalescing agent. A foamed gypsum slurry was prepared as set forth in Table III, and gypsum boards formed as described in Example 2 above.

(33) TABLE-US-00003 TABLE III Composition of Board 3 Stucco 640 g BMA 13.0 g Phosphate 2.0 g Starch - Blend 15.0 g Gypflow Dispersant 10.0 g Plast L 0.04 g Lumiten 4426 15% on soap Cedapal 0.56 g Water (total) 800 g

(34) TABLE-US-00004 TABLE IV Bubble Structure Analysis of Board 3 BW NP <150 MP VA (lb/msf) (lbf) (%) (m) Count (%) Board 3 1233 83 1 570 21 58.1

(35) The board weight and nail pull resistance of the gypsum board (Board 3) was measured and the bubble structure of the gypsum core was analyzed by SEM, as described in Example 1 above. The bubble structure is shown in FIG. 3 and the resulting data shown in Table IV and FIG. 4. The data shows that the coalescing agent can be adjusted relative to the other components of the gypsum slurry to produce an ultra-light gypsum board (BW<1300 lb/msf), while increasing the nail pull resistance. Board 3 has a board weight of 1233 lb/msf and a nail pull resistance of 83 lbf, in comparison to the Board 1 control which has a board weight of 1325 lb/msf and a nail pull resistance of 68 lbf.

EXAMPLE 3

(36) The relationship between the cloud point and the mix temperature was investigated by preparing foamed gypsum slurries using coalescing agents with different cloud points, Lumiten 4425 (Board 4) and Lumiten 4426 (BASF 8938) (Board 5). The gypsum slurry had a mix temperature of 119 F., which was very high compared to the cloud point of Lumiten 4425 (T.sub.CP 68 F.). The high mix temperature resulted in a very aggressive coalescing action, which produced blisters and blows. To overcome the aggressive coalescing action, it was necessary to reduce the amount of coalescing agent to the point where it was insufficient to coalesce the small bubbles into large bubbles, as shown in FIG. 5A.

(37) Lumiten 4426 has a higher cloud point (T.sub.CP 87 F.) than Lumiten 4425, which permitted a four-fold increase in the amount of coalescing agent in the gypsum slurryenough to coalesce the small bubbles into large and discrete bubbles, as shown in FIG. 5B. The gypsum board produced using Lumiten 4426 (Board 5) exhibited a higher nail pull resistance and better paper/core bonding in comparison to Lumiten 4425 (Board 4), as shown in Table V. The bubble size distribution is shown in FIG. 6.

(38) TABLE-US-00005 TABLE V Bubble Structure Analysis of Boards 4 and 5 BW NP <150 MP VA (lb/msf) (lbf) (%) (m) Count (%) Board 4 1356 67 42 250 325 64.9 Board 5 1356 80 9 305 114 63.3

EXAMPLE 4

(39) The cloud point of the coalescing agent can be adjusted using varying combinations or blends of coalescing agents with different cloud points. Coalescing agents were prepared as 1% solutions in water of different blends of Lumiten 4426 and Lumiten 4425, containing 0%, 20%, 40%, 60% 80% and 100% Lumiten 4426 (with Lumiten 4425 as the remainder). The cloud point of the coalescing agents was determined by measuring the initial temperature at which the solution exhibits the first discernible change in opacity and begins to lose clarity, and the temperature at which the solution became fully opaque (i.e. when the thermometer bulb measuring the temperature of the solution in the middle of a beaker is no longer visible).

(40) TABLE-US-00006 TABLE VI Blended Coalescing Agent Cloud Point Initial Change In Coalescing Agent Blend Opacity ( F.) Fully Opaque ( F.) 100% Lumiten 4426 92 115 80% Lumiten 4426/20% 4425 87 97 60% Lumiten 4426/40% 4425 82 92 40% Lumiten 4426/60% 4425 79 91 20% Lumiten 4426/80% 4425 77 89 100% Lumiten 4425 78 88

(41) The cloud point results are shown in Table VI and FIG. 7. By combining Lumiten 4426 and Lumiten 4425 in different ratios, the cloud point of the coalescing agent can be continuously adjusted in a range between the T.sub.CP of Lumiten 4426 and the T.sub.CP of Lumiten 4425. Thus, it is possible to use either one coalescing agent or a combination of coalescing agents in gypsum core compositions. During production, the ratio of the coalescing agents can be changed in situ to adjust the cloud point, as may be required to accommodate changes in the mix temperature or other process parameters during production. In addition, the results show that it is possible to double the amount of coalescing agent without generating blisters or blows.

(42) While various embodiments have been described, it will be apparent to those of ordinary skill in the art that many more embodiments and implementations are possible within the scope of the invention. Accordingly, the invention is not to be restricted except in light of the attached claims and their equivalents.