Cellulose film electric heating material taking sugarcane residue as precursor and preparation method thereof
Cellulose films were prepared using sugarcane bagasse as a precursor, and tannic acid and carbon nanotubes were introduced to form a stable conductive network. This solved the problems of uneven conductive network and insufficient mechanical properties, and enabled the preparation of high-performance electrothermal materials suitable for flexible electronics and smart wearables.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN UNIV
- Filing Date
- 2026-04-03
- Publication Date
- 2026-06-09
AI Technical Summary
In existing technologies, the conductive network distribution of bagasse cellulose films is uneven, and it is difficult to balance mechanical strength and electrothermal stability, resulting in insufficient material performance.
Using sugarcane bagasse as a precursor, lignin-containing nanocellulose was prepared through a dissolution-regeneration-crosslinking technology. Organic additives tannic acid and conductive agents carbon nanotubes were introduced to form a stable conductive network. Combined with a LiCl/DMAc dissolution system, cellulose thin film electrothermal materials were prepared.
The material's mechanical strength and electrothermal stability have been improved, and the problem of uneven conductive network has been solved. The material has good water resistance and electrothermal properties, making it suitable for flexible electronics and smart wearables.
Abstract
Description
Technical Field
[0001] This invention belongs to the field of biomass value-added utilization, specifically relating to a cellulose film electrothermal material with sugarcane bagasse as a precursor and its preparation method. Background Technology
[0002] With the increasing global demand for sustainable development and green energy, the development of renewable, biodegradable, and functional bio-based materials has become a research hotspot. Sugarcane bagasse, a major byproduct of the sugar industry, is produced in huge quantities annually. If not effectively utilized, it not only wastes resources but also causes environmental problems. Sugarcane bagasse is rich in cellulose (approximately 40%-50%), making it an ideal precursor for preparing high-performance cellulose materials.
[0003] Traditional electrothermal materials mostly rely on non-renewable resources such as metals or carbon nanotubes, resulting in drawbacks such as high cost, complex processes, and poor biodegradability. Cellulose films have attracted attention due to their flexibility, biodegradability, and the ability to acquire conductivity through chemical or physical modification. Previous studies have extracted nanocellulose from sugarcane bagasse and prepared high-strength films using hot pressing or solution casting. Building upon this, by introducing conductive fillers (such as carbon nanotubes or metal nanoparticles) into the cellulose matrix, composite materials combining flexibility and electrothermal conversion functions can be constructed. For example, recent work reported a hybrid film using sugarcane bagasse cellulose as a substrate, incorporating carbon nanotubes and silver nanoparticles, which exhibited excellent electrothermal performance in wearable heaters.
[0004] However, existing technologies still face challenges such as uneven distribution of conductive networks and the difficulty in simultaneously achieving both mechanical strength and electrothermal stability of the thin film. Therefore, developing high-performance electrothermal thin films prepared using sugarcane bagasse cellulose as a precursor through green processes can not only increase the added value of agricultural waste but also provide environmentally friendly material solutions for fields such as flexible electronics and smart wearables. Summary of the Invention
[0005] To address the problems existing in the prior art, the present invention aims to provide a cellulose thin-film electrothermal material with sugarcane bagasse as a precursor and its preparation method. The present invention uses sugarcane bagasse as a precursor to prepare lignin-containing nanocellulose (LCNF), and introduces organic additives and conductive agents using a dissolution-regeneration-crosslinking technology to prepare a cellulose thin-film electrothermal material with good water resistance, mechanical properties and electrothermal properties, which greatly improves the utilization value of waste sugarcane bagasse.
[0006] The technical solution adopted in this invention is as follows: A method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor includes the following steps: Wash the sugarcane bagasse with clean water to remove the sugar and impurities, then dry it to obtain dried sugarcane bagasse. Then crush the dried sugarcane bagasse and sieve it. Take the sieve material to obtain the pretreated sugarcane bagasse. The pretreated sugarcane bagasse was mechanically stirred to obtain a lignin-containing nanocellulose product. The lignin-based nanocellulose product was washed until neutral, and then mixed with deionized water to prepare a lignin-containing nanocellulose suspension. A lignin-containing nanocellulose suspension was used to prepare a lignin-containing nanocellulose membrane. The lignin-containing nanocellulose membrane was mixed with an N,N-dimethylacetamide solution containing LiCl and reacted to obtain a lignin-containing nanocellulose solution. Tannic acid powder and carbon nanotubes were mixed evenly with the lignin-containing nanocellulose solution to obtain a reddish-brown solution. The cellulose film electrothermal material with sugarcane bagasse as a precursor was prepared by solution film formation using the reddish-brown solution.
[0007] Preferably, the dried sugarcane bagasse is crushed and passed through an 80-100 mesh sieve.
[0008] Preferably, when mechanically stirring the pretreated sugarcane bagasse to obtain a lignin-containing nanocellulose product, the stirring temperature is 30-80 ℃, the stirring speed is 500-800 rpm, and the stirring time is 2-4 h.
[0009] Preferably, the specific process of washing the lignin-based nanocellulose product to neutrality and then preparing a lignin-containing nanocellulose suspension with deionized water includes: After washing the lignin-based nanocellulose product to neutral, deionized water was added to adjust the suspension concentration to 0.5 wt%-1.0 wt%. The suspension was then sheared at 10,000-15,000 rpm for 30-60 min to achieve homogenization, thereby obtaining a lignin-containing nanocellulose suspension.
[0010] Preferably, the process of preparing a lignin-containing nanocellulose membrane from a lignin-containing nanocellulose suspension includes: A lignin-containing nanocellulose suspension is vacuum filtered to form a membrane, which is then peeled off. A clamping pressure of 10-15 MPa is applied to both sides of the peeled membrane, and the membrane is baked at 110-150 ℃ for 2-3 h under pressure to finally obtain the lignin-containing nanocellulose membrane.
[0011] Preferably, the lignin-containing nanocellulose membrane is mixed into an N,N-dimethylacetamide solution containing LiCl, and stirred at 110-130°C for 12-15 h, and then stirred at 25-50°C for 12-15 h to obtain a lignin-containing nanocellulose solution.
[0012] Preferably, the mass ratio of lignin-containing nanocellulose membrane, LiCl and N,N-dimethylacetamide solution is (2-5):(18-25):(188-200).
[0013] Preferably, the mass ratio of lignin-containing nanocellulose membrane, tannic acid and carbon nanotubes is (2-5):(5-10):(0.5-1).
[0014] The present invention also provides a cellulose film electrothermal material with sugarcane bagasse as a precursor, which is prepared by the preparation method of the present invention as described above.
[0015] Preferably, the cellulose film electrothermal material with sugarcane bagasse as a precursor has a resistance of 350~750 Ω / cm at room temperature. -2 At 36 V, the maximum temperature is 48~82 ℃; The cellulose film electrothermal material with sugarcane bagasse as a precursor has a water absorption rate of 20%-26% after 5 hours, and its tensile strength and toughness are 75-80 MPa and 3.6-4.0 MJ·m, respectively. -3 .
[0016] The present invention has the following beneficial effects: This invention prepares cellulose thin-film electrothermal materials using sugarcane bagasse as a precursor. First, the sugarcane bagasse is washed, dried, pulverized, sieved, and mechanically stirred to obtain a lignin-containing nanocellulose product. This product is then washed, formulated into a suspension, and used to prepare a lignin-containing nanocellulose membrane. During the preparation process, some lignin is retained, utilizing the residual lignin to impart antioxidant, UV absorption, and hydrophobic properties to the membrane, further enhancing the overall performance of the material. Subsequently, N,N-containing compounds containing LiCl are added to the membrane. Homogeneous dissolution of cellulose in a dimethylacetamide (DMAc) solution allows for complete dissociation of cellulose molecular chains, providing a uniform and stable reaction system for subsequent functional modification. Tannic acid powder is then added and mixed uniformly with carbon nanotubes. Finally, the target electrothermal material is prepared via a solution film-forming method. This approach uses agricultural waste, sugarcane bagasse, as raw material, effectively improving waste utilization, reducing raw material costs, and being more environmentally friendly. The LiCl / DMAc dissolution system achieves homogeneous dissolution of cellulose, avoiding the problem of uneven component dispersion. In this system, Cl... -Hydrogen bonds are formed with the hydroxyl groups of cellulose, disrupting the original hydrogen bond network and causing the cellulose molecular chains to separate and dissolve, providing a homogeneous reaction platform for subsequent functionalization modifications. The introduction of tannic acid (TA) and carbon nanotubes can construct a stable conductive network. Furthermore, tannic acid can improve the conductivity of Li... + Dispersion, avoid Li + Aggregation and precipitation ensure the stability and uniformity of the dissolved system, and strong interaction is formed with the cellulose matrix through π-π stacking, which helps carbon nanotubes form a stable and continuous conductive network. This gives the resulting film both good mechanical strength and electrothermal stability, solving the problems of uneven conductive network and difficulty in balancing mechanical and electrothermal properties in existing electrothermal materials. Moreover, the overall preparation process is simple, and the resulting material is lightweight, water-resistant, and has high electrothermal conversion efficiency, which can meet the application requirements of flexible electrothermal devices. Detailed Implementation
[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.
[0018] This invention uses bagasse as a precursor to prepare lignin-containing nanocellulose (LCNF). Organic additives and conductive agents are introduced using a dissolution-regeneration-crosslinking technology to prepare a cellulose film electrothermal material with good water resistance, mechanical properties and electrothermal properties, which greatly improves the utilization value of waste bagasse.
[0019] Specifically, the preparation process of the lignin-containing nanocellulose membrane prepared from waste sugarcane bagasse in this invention is as follows: Sugarcane bagasse was washed repeatedly with clean water to remove residual sugar and impurities, and then dried in a drying oven. The dried bagasse was then pulverized and passed through an 80-100 mesh sieve. The sieved material was mechanically stirred at 30-80 ℃ and 500-800 rpm for 2-4 h to obtain lignin-containing nanocellulose product (LCNFP). LCNFP was repeatedly washed until neutral, and then deionized water was added to adjust the suspension concentration to 0.5wt%-1.0wt%. The suspension was sheared at 10000-15000 rpm for 30-60 min to homogenize it, obtaining a lignin-containing nanocellulose suspension. A lignin-containing nanocellulose suspension is vacuum filtered in a sand core funnel with a polytetrafluoroethylene membrane to form a membrane. The peeled wet sheet (i.e. the membrane) is sandwiched between two polytetrafluoroethylene plates and baked at a clamping pressure of 10-15 MPa and 110-150 ℃ for 2-3 h to finally obtain a lignin-containing nanocellulose membrane (LCNF).
[0020] 18-25 g of lithium chloride (LiCl) was added to 188-200 g of N,N-dimethylacetamide (DMAc) solution and stirred until dissolved to obtain a DMAc solution containing LiCl. Then, 2-5 g of dried LCNF was added to the LiCl-containing DMAc solution. The mixture was first stirred at 110-130 °C for 12-15 h, and then stirred at 25-50 °C for 12-15 h to obtain a brown, dissolved lignin-containing nanocellulose solution. 5-10 g of tannic acid (TA) powder and 0.5-1 g of carbon nanotubes were added to the lignin-containing nanocellulose solution, and then stirred at 40-60 °C and 500-800 rpm for 2-4 h until homogeneous. The obtained reddish-brown solution was used to prepare the cellulose film electrothermal material with sugarcane bagasse as a precursor of the present invention by solution film formation method. Specifically, the reddish-brown solution was cast into a glass petri dish and dried at room temperature to obtain the brown cellulose film electrothermal material (i.e. the cellulose film electrothermal material with sugarcane bagasse as a precursor of the present invention).
[0021] Example 1 In this embodiment, lignin-containing cellulose nanofiber (LCNF) was prepared using bagasse as a precursor. Organic additives and conductive agents were introduced using a dissolution-regeneration-crosslinking technology to prepare a cellulose film electrothermal material with good water resistance, mechanical properties and electrothermal properties.
[0022] The preparation process of the lignin-containing nanocellulose membrane prepared from waste sugarcane bagasse in this embodiment is as follows: Sugarcane bagasse was washed with water to remove residual sugar and impurities, and then dried in a drying oven. The dried bagasse was pulverized and passed through an 80-mesh sieve. The sieved material was mechanically stirred at 30 ℃ and 500 rpm for 2 h to obtain lignin-containing nanocellulose product (LCNFP). LCNFP was washed until neutral, and then deionized water was added to adjust the suspension concentration to 0.5 wt%. The suspension was sheared at 10000 rpm for 30 min to homogenize it, obtaining a lignin-containing nanocellulose suspension. The lignin-containing nanocellulose suspension was vacuum filtered in a sand core funnel with a polytetrafluoroethylene (PTFE) membrane to form a membrane. The peeled wet sheet was sandwiched between two PTFE plates and baked at 110 ℃ for 2 h under a clamping pressure of 10 MPa to finally obtain a lignin-containing nanocellulose membrane (LCNF).
[0023] 18 g of lithium chloride (LiCl) was added to 188 g of N,N-dimethylacetamide (DMAc) solution and stirred until dissolved, yielding a DMAc solution containing LiCl. Then, 2 g of dried LCNF was added to the LiCl-containing DMAc solution. The mixture was stirred at 110 °C for 12 h, and then at 25 °C for 12 h, yielding a brown, dissolved lignin-containing cellulose nanoparticle solution. 5 g of tannic acid (TA) powder and 0.5 g of carbon nanotubes were added to the lignin-containing cellulose nanoparticle solution, and the mixture was stirred at 40 °C and 500 rpm for 2 h until homogeneous. The resulting reddish-brown solution was cast into a glass petri dish and dried at room temperature to obtain a brown cellulose thin-film electrothermal material.
[0024] Testing showed that the electrothermal material prepared in this embodiment has a resistance of 750 Ω / cm at room temperature. -2 At 36 V voltage and a maximum temperature of 48 ℃, the water absorption rate was 26% after 5 h, and the fracture strength and toughness were 80 MPa and 4.0 MJ·m, respectively. -3 .
[0025] Example 2 This invention uses bagasse as a precursor to prepare lignin-containing cellulose nanofiber (LCNF). By employing a dissolution-regeneration-crosslinking technology to introduce organic additives and conductive agents, a cellulose film electrothermal material with good water resistance, mechanical properties, and electrothermal properties is prepared, which greatly improves the utilization value of waste bagasse.
[0026] The lignin-containing cellulose solution process used in this embodiment is as follows: Sugarcane bagasse was washed with water to remove residual sugar and impurities, and then dried in a drying oven. The dried bagasse was pulverized and passed through a 90-mesh sieve. The sieved material was mechanically stirred at 50 °C and 600 rpm for 3 h to obtain lignin-containing nanocellulose product (LCNFP). LCNFP was washed until neutral, and then deionized water was added to adjust the suspension concentration to 0.7 wt%. The suspension was sheared at 12000 rpm for 45 min to homogenize it, obtaining a lignin-containing nanocellulose suspension. The lignin-containing nanocellulose suspension was vacuum filtered in a sintered funnel with a polytetrafluoroethylene (PTFE) membrane to form a membrane. The peeled wet sheet was sandwiched between two PTFE plates and baked at 130 °C for 2.5 h under a clamping pressure of 12 MPa to finally obtain a lignin-containing nanocellulose membrane (LCNF).
[0027] 21 g of lithium chloride (LiCl) was added to 192 g of N,N-dimethylacetamide (DMAc) solution and stirred until dissolved, yielding a DMAc solution containing LiCl. Then, 3.5 g of dried LCNF was added to the LiCl-containing DMAc solution. The mixture was stirred at 120 °C for 13 h, and then at 30 °C for 13 h, yielding a brown, dissolved lignin-containing cellulose nanoparticle solution. 8 g of tannic acid (TA) powder and 0.75 g of carbon nanotubes were added to the lignin-containing cellulose nanoparticle solution, and the mixture was stirred at 5 °C and 700 rpm for 3 h until homogeneous. The resulting reddish-brown solution was cast into glass petri dishes and dried at room temperature to obtain a brown cellulose thin-film electrothermal material.
[0028] Testing showed that the electrothermal material prepared in this embodiment has a resistance of 500 Ω / cm at room temperature. -2 At 36 V, the maximum temperature is 65 ℃, the water absorption rate is 23% after 5 h, and the fracture strength and toughness are 77 MPa and 3.8 MJ·m, respectively. -3 .
[0029] Example 3 This invention uses bagasse as a precursor to prepare lignin-containing cellulose nanofiber (LCNF). By employing a dissolution-regeneration-crosslinking technology to introduce organic additives and conductive agents, a cellulose film electrothermal material with good water resistance, mechanical properties, and electrothermal properties is prepared, which greatly improves the utilization value of waste bagasse.
[0030] The lignin-containing cellulose solution process used in this embodiment is as follows: Sugarcane bagasse was washed with clean water to remove residual sugar and impurities, and then dried in a drying oven. The dried bagasse was pulverized and passed through a 100-mesh sieve. The sieved material was mechanically stirred at 80 ℃ and 800 rpm for 4 h to obtain lignin-containing nanocellulose product (LCNFP). LCNFP was washed until neutral, and then deionized water was added to adjust the suspension concentration to 1.0 wt%. The suspension was sheared at 15000 rpm for 60 min to homogenize it, obtaining a lignin-containing nanocellulose suspension. The lignin-containing nanocellulose suspension was vacuum filtered in a sand core funnel with a polytetrafluoroethylene (PTFE) membrane to form a membrane. The peeled wet sheet was sandwiched between two PTFE plates and baked at 150 ℃ for 3 h under a clamping pressure of 15 MPa to finally obtain a lignin-containing nanocellulose membrane (LCNF).
[0031] 25 g of lithium chloride (LiCl) was added to 200 g of N,N-dimethylacetamide (DMAc) solution and stirred until dissolved, yielding a DMAc solution containing LiCl. Then, 5 g of dried LCNF was added to the LiCl-containing DMAc solution. The mixture was stirred at 130 °C for 15 h, and then at 50 °C for 15 h, yielding a brown, dissolved lignin-containing nanocellulose solution. 10 g of tannic acid (TA) powder and 1 g of carbon nanotubes were added to the lignin-containing nanocellulose solution, and the mixture was stirred at 60 °C and 800 rpm for 4 h until homogeneous. The resulting reddish-brown solution was cast into a glass petri dish and dried at room temperature to obtain a brown cellulose thin-film electrothermal material.
[0032] Tests showed that the electrothermal material prepared in this embodiment has a resistance of 350 Ω / cm at room temperature. -2 At 36 V, the maximum temperature is 82 ℃, the water absorption rate is 20% after 5 h, and the fracture strength and toughness are 75 MPa and 3.6 MJ·m, respectively. -3 .
[0033] In summary, the electrothermal material prepared by the method of this invention has a resistivity of 350~750 Ω / cm at room temperature. -2 Under voltages of 12–36 V, with a maximum temperature of 48–82 °C, a water absorption rate of 20%–26% after 5 hours, and a fracture strength and toughness of 75–80 MPa and 3.6–4.0 MJ·m, respectively. -3 It has good water resistance, mechanical properties and electrothermal properties.
[0034] The experimental results above demonstrate that the technical solution of this invention, using sugarcane bagasse as raw material, prepares lignin-containing nanocellulose through a mechanical method. Combined with the LiCl / DMAc dissolution and tannic acid blending modification approach, this not only fully utilizes the resource value of agricultural waste but also provides a new approach for the development of flexible, biodegradable electrothermal materials. This direction aligns with the requirements of green chemistry and the circular economy, and has broad prospects in fields such as smart wearables and flexible heaters.
[0035] Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.
[0036] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions made to the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the present invention. Furthermore, unless otherwise specified, all or part of any embodiment may be used in conjunction with all or part of any other embodiment.
Claims
1. A method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor, characterized in that, Includes the following steps: Wash the sugarcane bagasse with clean water to remove the sugar and impurities, then dry it to obtain dried sugarcane bagasse. Then crush the dried sugarcane bagasse and sieve it. Take the sieve material to obtain the pretreated sugarcane bagasse. The pretreated sugarcane bagasse was mechanically stirred to obtain a lignin-containing nanocellulose product. The lignin-based nanocellulose product was washed until neutral, and then mixed with deionized water to prepare a lignin-containing nanocellulose suspension. A lignin-containing nanocellulose suspension was used to prepare a lignin-containing nanocellulose membrane. The lignin-containing nanocellulose membrane was mixed with an N,N-dimethylacetamide solution containing LiCl and reacted to obtain a lignin-containing nanocellulose solution. Tannic acid powder and carbon nanotubes were mixed evenly with the lignin-containing nanocellulose solution to obtain a reddish-brown solution. The cellulose film electrothermal material with sugarcane bagasse as a precursor was prepared by solution film formation using the reddish-brown solution.
2. The method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 1, characterized in that, The dried sugarcane bagasse is crushed and passed through an 80-100 mesh sieve.
3. The method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 1, characterized in that, When mechanically stirring the pretreated sugarcane bagasse to obtain lignin-containing nanocellulose products, the stirring temperature is 30-80 ℃, the stirring speed is 500-800 rpm, and the stirring time is 2-4 h.
4. The method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 1, characterized in that, The specific process of washing the lignin-based nanocellulose product to neutrality and then preparing a lignin-containing nanocellulose suspension with deionized water includes: After washing the lignin-based nanocellulose product to neutral, deionized water was added to adjust the suspension concentration to 0.5 wt%-1.0 wt%. The suspension was then sheared at 10,000-15,000 rpm for 30-60 min to achieve homogenization, thereby obtaining a lignin-containing nanocellulose suspension.
5. The method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 1, characterized in that, The process of preparing a lignin-containing nanocellulose membrane from a lignin-containing nanocellulose suspension includes: A lignin-containing nanocellulose suspension is vacuum filtered to form a membrane, which is then peeled off. A clamping pressure of 10-15 MPa is applied to both sides of the peeled membrane, and the membrane is baked at 110-150 ℃ for 2-3 h under pressure to finally obtain the lignin-containing nanocellulose membrane.
6. The method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 1, characterized in that, The lignin-containing nanocellulose membrane was mixed into an N,N-dimethylacetamide solution containing LiCl, and stirred at 110-130℃ for 12-15 h, and then stirred at 25-50℃ for 12-15 h to obtain a lignin-containing nanocellulose solution.
7. A method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 1 or 6, characterized in that, The mass ratio of lignin-containing nanocellulose membrane, LiCl and N,N-dimethylacetamide solution is (2-5):(18-25):(188-200).
8. The method for preparing a cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 7, characterized in that, The mass ratio of lignin-containing nanocellulose membrane, tannic acid and carbon nanotubes is (2-5):(5-10):(0.5-1).
9. A cellulose thin-film electrothermal material using sugarcane bagasse as a precursor, characterized in that, The cellulose film electrothermal material is prepared by the preparation method described in any one of claims 1-8.
10. A cellulose thin-film electrothermal material using sugarcane bagasse as a precursor according to claim 9, characterized in that, The cellulose film electrothermal material with sugarcane bagasse as a precursor has a resistance of 350~750 Ω / cm at room temperature. -2 At 36V, the maximum temperature is 48~82℃; The cellulose film electrothermal material with sugarcane bagasse as a precursor has a water absorption rate of 20%-26% after 5 hours, and its tensile strength and toughness are 75-80 MPa and 3.6-4.0 MJ·m, respectively. -3 .