Cationic perylene bisimide dispersing agent as well as preparation method and application thereof
By utilizing the π-π interactions and hydrophilic side chain design of cationic perylene imide dispersants, the problem of high-concentration dispersion of carbon nanotube dispersants was solved, achieving efficient and stable carbon nanotube dispersion, maintaining its performance, and enhancing dispersion stability and functionality.
Patent Information
- Application Number
- CN202511526866.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-24
- Publication Date
- 2026-01-09
AI Technical Summary
Existing carbon nanotube dispersants cannot achieve high-concentration dispersion, and traditional methods may damage the electrical and thermal properties of carbon nanotubes.
A cationic perylene imide dispersant was used, which interacts with carbon nanotubes through a large conjugated structure and utilizes protonated polyethylene polyamine as a hydrophilic side chain to achieve high-concentration dispersion of carbon nanotubes in aqueous solution.
Achieving high-concentration dispersion of carbon nanotubes with relatively small dosage while maintaining their electrical and thermal properties, and enabling them to react with functional groups to enhance dispersion stability and separation ability.
Smart Images
Figure CN121293493A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of dispersants and nano-carbon materials technology, specifically relating to a cationic perylene imide dispersant, its preparation method, and its application. Background Technology
[0002] Carbon nanotubes are tubular nanostructures composed of carbon atoms, exhibiting single-walled, double-walled, and multi-walled forms. Their unique hexagonal honeycomb structure endows them with excellent mechanical, electrical, and thermal properties. Currently, carbon nanotubes are widely used in composite materials, electronic devices, energy storage materials, and sensors, demonstrating enormous application potential. However, due to the presence of van der Waals forces and π-π interactions, carbon nanotube bundles tend to entangle and aggregate, which not only affects the unique properties of individual carbon nanotubes but also significantly reduces their energy efficiency in subsequent applications. The key to solving this problem is to functionalize carbon nanotubes to obtain stable and uniform dispersions, ultimately achieving uniform composites of carbon nanotubes with other matrix materials.
[0003] Currently, methods for modifying carbon nanotubes mainly include covalent and non-covalent methods. Covalent methods introduce modifying groups onto the surface of carbon nanotubes through chemical reactions such as oxidation, amidation, and free radical addition. The high solubility, steric hindrance, and electrostatic interactions of these groups are utilized to achieve the exfoliation and dispersion of carbon nanotube bundles in solvents. However, the introduction of modifying groups inevitably disrupts the spline structure of carbon atoms. 2 Hybrid structures can negatively impact the electrical and thermal properties of carbon nanotubes. In contrast, non-covalent methods disperse carbon nanotube bundles by bonding surfactants to the surface of carbon nanotubes or by encapsulating them with polymers. This avoids disrupting the conjugated π-system of carbon nanotubes, preserving their inherent properties and offering better application prospects for carbon nanotube modification.
[0004] Currently, common carbon nanotube dispersants include traditional surfactants (CTAB, SDBS, etc.), conjugated organic compounds, polymers, and biomacromolecules. They can bind to carbon nanotubes through π-π interactions, dipole-dipole interactions, and other mechanisms. Taking π-π interactions as an example, the hydrophobic end of the dispersant binds to the carbon nanotubes through π-π interactions, while the solubilizing end interacts with solvent molecules, thereby achieving stable dispersion of carbon nanotubes. However, traditional surfactants cannot achieve high-concentration dispersion of carbon nanotubes; the insulating coating layer formed by some polymeric dispersants on the surface of carbon nanotubes can disrupt the formation of the conductive network of carbon nanotubes, increase interfacial contact resistance, and significantly affect the conductivity of carbon nanotubes; some novel fused-ring conjugated structure molecules are complex to synthesize, costly, and have limited practicality. Therefore, developing novel, efficient, and low-cost carbon nanotube dispersants is particularly important. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this invention provides a cationic perylene imide dispersant with a large conjugated structure and long hydrophilic side chains, which can achieve high concentration dispersion of carbon nanotubes with a relatively small dosage.
[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is: a cationic perylene imide dispersant, the molecular structure of which uses a fused ring of perylene tetrahydric anhydride as the conjugated center and a protonated polyethylene polyamine as the hydrophilic side group, having the chemical structural formula shown in (I):
[0007]
[0008] (I)
[0009] A method for preparing a cationic perylene imide dispersant includes the following steps:
[0010] (1) Perylene tetrahydric anhydride (PTCDA) and polyethylene polyamine (PEPA) were added to toluene solvent, refluxed, filtered, and washed to obtain the intermediate;
[0011] (2) Dissolve the intermediate in NaOH aqueous solution, stir at room temperature, filter, wash, and obtain the dispersant precursor;
[0012] (3) The obtained dispersant precursor was dissolved in formic acid by ultrasonication in a water bath. The resulting solution was added dropwise to isopropanol, allowed to stand, filtered, and washed to obtain a cationic perylene imide dispersant.
[0013] Further, in step (1), the molar ratio is perylene tetrahydric anhydride:polyethylene polyamine = 1:(10-12).
[0014] Furthermore, in step (1), the reflux reaction temperature is 120℃-140℃ and the reflux reaction time is 90h-100h.
[0015] Furthermore, in step (2), the concentration of the NaOH aqueous solution is 2M-3M, and the mixture is stirred at room temperature for 5-6 hours.
[0016] Further, in step (3), the volume ratio of formic acid to isopropanol is 1:(9-11).
[0017] This invention provides the application of a cationic perylene imide dispersant in the preparation of aqueous dispersions of carbon materials.
[0018] Further, the method includes the following steps: dissolving the cationic perylene imide dispersant in deionized water, adding a certain amount of carbon material, first performing preliminary dispersion by water bath ultrasound, and then performing ultrasound by an ultrasonic cell disruptor to obtain a perylene imide-carbon material aqueous dispersion.
[0019] Furthermore, the carbon material is selected from carbon nanotubes, graphene, or carbon black. Preferably, the carbon nanotubes are single-walled carbon nanotubes, double-walled carbon nanotubes, or multi-walled carbon nanotubes.
[0020] Further, by mass ratio, the ratio of cationic perylene imide dispersant to carbon material is 1:(1-3); in the perylene imide-carbon material aqueous dispersion, the concentration of carbon material is 0.5 mg·mL. -1 -40mg·mL -1 .
[0021] Compared with the prior art, the beneficial effects of the present invention are:
[0022] 1. This invention utilizes the large conjugated structure of perylene tetrahydric anhydride to conduct π-π interactions with carbon nanotubes. By grafting polyethylene polyamine onto the large conjugated center, amino-functionalized dispersant molecules are obtained. Furthermore, the hydrophilicity of the dispersant molecules is enhanced by protonation, ultimately achieving high-concentration dispersion of carbon nanotubes in aqueous solution.
[0023] 2. This invention discloses a cationic perylene imide dispersant composed of a large conjugated center and hydrophilic side chains. First, perylene tetrahydric anhydride possesses a highly conjugated structure, allowing it to bind with carbon nanotubes via π-π interactions. Second, the hydrophilic side chains contain abundant protonated amino groups, exhibiting good water solubility, enabling the dispersant molecules to be uniformly dispersed in water after binding with carbon nanotubes. Finally, the protonated amino groups in the molecular side chains can be deprotonated to obtain highly reactive amino groups, which can then react with functional groups such as epoxy, carbonyl, carboxyl, and sulfonic acid groups, thereby achieving the recovery and enrichment of rare and dispersed metal ions, heavy metal ions, etc.
[0024] 3. Compared with the prior art, the cationic perylene imide dispersant of the present invention has excellent dispersing ability for carbon nanotubes. When the mass ratio of dispersant to carbon nanotubes is 1:1, the highest dispersion concentration of carbon nanotubes can reach 40 mg·mL. -1 At a carbon nanotube concentration of 0.5 mg / mL -1 In a perylene imide-carbon nanotube aqueous dispersion, PBI dispersant can stably disperse carbon nanotubes at a mass ratio of 1:3 (PBI:MWCNTs). Attached Figure Description
[0025] Figure 1 The infrared spectra of the raw materials perylene tetrahydric anhydride (PTCDA), polyethylene polyamine (PEPA), and PBI dispersant precursor in Example 1 of this invention are shown.
[0026] Figure 2 In Example 2 of this invention, at a mass ratio of 1:3, 0.5 mg·mL -1Particle size distribution of peryleneimide-carbon nanotube aqueous dispersion.
[0027] Figure 3 In Example 2 of this invention, at a mass ratio of 1:3, 0.5 mg·mL -1 Zeta potential diagram of peryleneimide-carbon nanotube aqueous dispersion.
[0028] Figure 4 In Example 3 of this invention, at a 1:1 mass ratio, 40 mg·mL -1 Optical image of a diluted perylene imide-carbon nanotube aqueous dispersion.
[0029] Figure 5 The images show SEM images of the carbon nanotube aqueous dispersions before and after adding PBI dispersant on a silicon wafer in Example 4 of this invention, after drying.
[0030] Figure 6 In Example 6 of this invention, at a mass ratio of 1:2, 1 mg·mL -1 Optical image of the conductive coating obtained by drop coating and drying of perylene imide-carbon nanotube aqueous dispersion. Detailed Implementation
[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described more fully below in conjunction with specific embodiments. The described embodiments are only some, not all, of the embodiments of this invention. This invention can be implemented in other different forms. The following embodiments do not limit the invention in any way.
[0032] Unless otherwise specified, the raw materials and equipment used in this invention are all commonly used in the field.
[0033] A first aspect of this invention provides a cationic perylene imide dispersant (PBI dispersant) having the following chemical structural formula:
[0034]
[0035] Specifically, the molecular structure of the cationic perylene imide dispersant is based on a fused ring of perylene tetrahydric anhydride as the conjugated center and a protonated polyethylene polyamine as the hydrophilic side group. This PBI dispersant, with its fused ring conjugated structure of perylene tetrahydric anhydride as the main body, exhibits π-π interactions with carbon nanotubes. Perylene tetrahydric anhydride is modified using a polyamine rich in amino groups. Through a dehydration condensation reaction between the amino groups and the anhydride, long chains rich in amino groups are grafted onto both ends of the conjugated center. Under the action of formic acid, the amino groups are protonated, endowing the dispersant with excellent hydrophilicity.
[0036] A second aspect of this invention provides a method for preparing a cationic perylene imide dispersant, comprising the following steps:
[0037] (1) Add perylene tetrahydric anhydride and polyethylene polyamine to toluene solvent, reflux the reaction, filter, wash, and obtain intermediate;
[0038] (2) Dissolve the intermediate in NaOH aqueous solution, stir at room temperature, filter, wash, and obtain the dispersant precursor;
[0039] (3) The obtained dispersant precursor was dissolved in formic acid by ultrasonication in a water bath. The resulting solution was added dropwise to isopropanol, allowed to stand, filtered, and washed to obtain a cationic perylene imide dispersant.
[0040] In step (1), to avoid side reactions between perylene tetrahydric anhydride and polyethylene polyamine, an excess of polyethylene polyamine is used in the reaction, i.e., 1 molar amount of perylene tetrahydric anhydride corresponds to at least 10 molar amounts of polyethylene polyamine. Preferably, the molar ratio is perylene tetrahydric anhydride: polyethylene polyamine = 1:(10-12).
[0041] In step (2), the alkali treatment time should not be too long, and should be controlled at around 6 hours. Preferably, it is 5-6 hours.
[0042] In step (3), in order to fully protonate the amino group in the product dispersant precursor of step (2), the product dispersant precursor should be dissolved in formic acid under conditions of ultrasonication and stirring, preferably ultrasonication in a water bath. Secondly, after the dispersant solid is precipitated with isopropanol, in order to better collect the target dispersant, the solution should be allowed to stand until the layers appear before proceeding with the subsequent vacuum filtration operation.
[0043] A third aspect of this invention provides the application of a cationic perylene imide dispersant in the preparation of an aqueous dispersion of carbon materials.
[0044] The method includes the following steps: dissolving a cationic perylene imide dispersant in deionized water, adding a certain amount of carbon material, first performing preliminary dispersion by ultrasonication in a water bath, and then ultrasonicating with an ultrasonic cell disruptor to obtain a perylene imide-carbon material aqueous dispersion.
[0045] Preferably, when preparing the perylene imide-carbon material aqueous dispersion, the ultrasonic process is as follows: first, ultrasonicate in a water bath for 1-2 minutes, then in an ultrasonic cell disruptor in an ice-water bath environment at 350W, ultrasonicate for 3 seconds and stop for 3 seconds, for a period of 30 minutes to 3 hours.
[0046] Preferably, if the concentration of carbon material in the perylene imide-carbon material aqueous dispersion is greater than 5 mg·mL -1 The ultrasound time is 2-3 hours.
[0047] To further understand the present invention, the following examples illustrate the synthesis method and application of the cationic perylene imide dispersant (PBI dispersant) provided by the present invention. The scope of protection of the present invention is not limited by the following examples.
[0048] Example 1: Cationic perylene imide dispersant (PBI dispersant)
[0049] (a) Synthesis method
[0050] The synthesis route is as follows:
[0051]
[0052] (1) In a 100 mL round-bottom flask, add perylene tetrahydric anhydride (PTCDA) (1.000 g, 2.5 mmol) and 20 mL toluene, and sonicate in a water bath at 20 °C for 2 min. Then add a 275 g·mol⁻¹ of perylene tetrahydric anhydride. -1 Polyethylene polyamine (PEPA) (6.875 g, 25 mmol) was stirred evenly and then sonicated in a water bath for 10 min. It was then heated with an electric heating mantle and refluxed at 130 °C for 96 h. After the reaction mixture cooled to room temperature, it was filtered and then washed with ethanol to obtain a blackish-purple solid product, which was the intermediate.
[0053] (2) The obtained intermediate was added to 60 mL of 2 M NaOH aqueous solution and stirred at room temperature for 6 h. The mixture was filtered again and washed thoroughly with deionized water until the filtrate was colorless and neutral, resulting in a reddish-brown solid product, which is the precursor of the dispersant.
[0054] (3) Dissolve the obtained dispersant precursor in 20 mL of formic acid and sonicate and stir in a 20 °C water bath. Add the resulting solution dropwise to 200 mL of isopropanol to obtain a red flocculent precipitate. After standing, filter the solution after it separates into layers and wash it with isopropanol to obtain a brown solid product, which is the cationic perylene imide dispersant, labeled as PBI dispersant.
[0055] (II) Testing
[0056] Figure 1 The infrared spectra of the raw materials and the prepared dispersant precursor in this embodiment are provided by [the relevant source]. Figure 1 It can be seen that the perylene tetrahydric anhydride molecule has a molecular weight of 1770 cm⁻¹. -1 The strong absorption peak appearing at 1689 cm⁻¹ corresponds to the characteristic peak of the carbonyl stretching vibration in the acid anhydride. Compared to the starting material, this absorption peak completely disappears in the product dispersant precursor molecule, proving that the perylenetetraanic anhydride has reacted completely. The dispersant precursor at 1689 cm⁻¹... -1 -1692cm -1A new absorption peak appeared at the point, corresponding to the symmetrical absorption of C=O in the imide molecule, indicating that the dispersant precursor molecule contains a perylene imide structure.
[0057] Example 2: Carbon nanotube concentration was 0.5 mg / mL. -1 Perylene imide-carbon nanotube aqueous dispersion (mass ratio 1:3)
[0058] (I) Preparation method
[0059] 1. Dissolve the PBI dispersant prepared in Example 1 in a certain amount of deionized water to prepare a 5wt% reddish-brown PBI dispersant aqueous solution.
[0060] 2. Using a PBI dispersant to carbon nanotube ratio of 1:3, weigh 0.005 g of carbon nanotube powder and add 0.033 mL of a 5 wt% PBI dispersant aqueous solution. Dilute with deionized water to 10 mL and shake well. First, sonicate in a 20°C water bath for 1 min to initially disperse the powder. Then, sonicate in an ice-water bath using an ultrasonic cell disruptor at 350 W, pausing for 3 seconds after every 3 seconds of sonication, for a total of 30 min, to obtain a carbon nanotube concentration of 0.5 mg / mL. -1 Peryleneimide-carbon nanotube aqueous dispersion.
[0061] (II) Testing
[0062] Figure 2 The concentration of carbon nanotubes prepared was 0.5 mg·mL. -1 The particle size distribution of the perylene imide-carbon nanotube aqueous dispersion is shown. When the mass ratio of PBI dispersant to carbon nanotubes is 1:3, a very strong particle size distribution peak is observed, indicating that the carbon nanotubes are dispersed very uniformly. Although small peaks appear at larger sizes, their integrated area is very small and can be ignored, indicating that the PBI dispersant provided by this invention can disperse carbon nanotubes equivalent to three times its own mass.
[0063] Figure 3 The concentration of carbon nanotubes prepared was 0.5 mg·mL. -1 The zeta potential of the perylene imide-carbon nanotube aqueous dispersion was consistently around +31 mV, indicating that the dispersion system was relatively stable.
[0064] Example 3: Carbon nanotube concentration was 40 mg·mL -1 Peryleneimide-carbon nanotube aqueous dispersion (mass ratio 1:1)
[0065] (I) Preparation method
[0066] 1. Dissolve the PBI dispersant prepared in Example 1 in a certain amount of deionized water to prepare a 5wt% reddish-brown PBI dispersant aqueous solution.
[0067] 2. Using a PBI dispersant to carbon nanotube ratio of 1:1, weigh 0.400 g of carbon nanotube powder and add 8 mL of a 5 wt% PBI dispersant aqueous solution. Dilute with deionized water to 10 mL and shake well. First, sonicate in a 20°C water bath for 1 min to initially disperse the powder. Then, sonicate in an ice-water bath using an ultrasonic cell disruptor at 350 W, pausing for 3 seconds after every 3 seconds, for a total of 2 hours, to obtain a carbon nanotube concentration of 40 mg / mL. -1 Peryleneimide-carbon nanotube aqueous dispersion.
[0068] (II) Testing
[0069] Figure 4 To achieve a carbon nanotube concentration of 40 mg·mL⁻¹ at a PBI dispersant to carbon nanotube mass ratio of 1:1. -1 The perylene imide-carbon nanotube aqueous dispersion was diluted to 0.01 mg·mL⁻¹. -1 The Tyndall effect optical image, illuminated by a red laser pointer, clearly shows the optical path, indicating that the carbon nanotube aqueous dispersion exhibits colloidal behavior. The addition of a dispersant ensures that the carbon nanotubes are uniformly dispersed in water.
[0070] Example 4: Carbon nanotube concentration was 0.5 mg / mL -1 Peryleneimide-carbon nanotube aqueous dispersion (mass ratio 1:1)
[0071] (I) Preparation method
[0072] 1. Dissolve the PBI dispersant prepared in Example 1 in a certain amount of deionized water to prepare a 5wt% reddish-brown PBI dispersant aqueous solution.
[0073] 2. Using a PBI dispersant to carbon nanotube ratio of 1:1, weigh 0.005 g of carbon nanotube powder and add 0.1 mL of a 5 wt% PBI dispersant aqueous solution. Dilute with deionized water to 10 mL and shake well. First, sonicate in a 20°C water bath for 1 min to initially disperse the powder. Then, sonicate in an ice-water bath using an ultrasonic cell disruptor at 350 W, pausing for 3 seconds after every 3 seconds, for a total of 30 min, to obtain a carbon nanotube concentration of 0.5 mg / mL. -1 Peryleneimide-carbon nanotube aqueous dispersion.
[0074] (II) Testing
[0075] Figure 5To achieve a carbon nanotube concentration of 0.5 mg·mL at a PBI dispersant to carbon nanotube mass ratio of 1:1. -1 The SEM image of the perylene imide-carbon nanotube aqueous dispersion after it was dropped onto a silicon wafer and dried shows that the carbon nanotubes are stacked layer by layer and are uniformly distributed on the surface of the silicon wafer. In contrast, the carbon nanotubes without dispersant show entanglement and aggregation.
[0076] Example 5: Carbon nanotube concentration was 1 mg·mL -1 Peryleneimide-carbon nanotube aqueous dispersion (mass ratio 1:2)
[0077] Preparation method:
[0078] 1. Dissolve the PBI dispersant prepared in Example 1 in a certain amount of deionized water to prepare a 5wt% reddish-brown PBI dispersant aqueous solution.
[0079] 2. Using a PBI dispersant to carbon nanotube ratio of 1:2, weigh 0.010 g of carbon nanotube powder and add 0.1 mL of a 5 wt% PBI dispersant aqueous solution. Dilute with deionized water to 10 mL and shake well. First, sonicate in a 20°C water bath for 1 min to initially disperse the powder. Then, sonicate in an ice-water bath using an ultrasonic cell disruptor at 350 W, sonicating for 3 seconds followed by a 3-second pause, for a total of 30 min, to obtain a carbon nanotube concentration of 1 mg / mL. -1 Peryleneimide-carbon nanotube aqueous dispersion.
[0080] Example 6: Application of carbon nanotube aqueous dispersion prepared by PBI in conductive coatings
[0081] (a) Methods
[0082] The carbon nanotubes prepared in Example 5 were at a concentration of 1 mg·mL⁻¹. -1 Experiments were conducted on a perylene imide-carbon nanotube aqueous dispersion (PBI dispersant to carbon nanotube mass ratio of 1:2).
[0083] Use a pipette to draw 1 mL of carbon nanotubes with a concentration of 1 mg·mL⁻¹. -1 A peryleneimide-carbon nanotube aqueous dispersion was drop-coated onto a pre-cut 2.5cm × 2.5cm glass slide. The slide was then placed in a 120℃ oven and dried for 0.5 hours until all moisture was evaporated, thus obtaining the conductive coating.
[0084] (II) Testing
[0085] Figure 6 The optical image of the prepared conductive coating was obtained, and its conductivity was tested with a multimeter, which showed that its conductivity was 128.7 S / m.
[0086] The above embodiments are merely illustrative of several implementations of the present invention, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the invention patent. The scope of protection of this invention patent should be determined by the appended claims.
Claims
1. A cationic perylene imide dispersant, characterized in that, The molecular structure of the cationic perylene imide dispersant is based on a fused ring of perylene tetrahydric anhydride as the conjugated center and a protonated polyethylene polyamine as the hydrophilic side group, and has the chemical structural formula shown in (I): （I）。 2. The method for preparing a cationic perylene imide dispersant according to claim 1, characterized in that, The preparation method includes the following steps: (1) Add perylene tetrahydric anhydride and polyethylene polyamine to toluene solvent, reflux the reaction, filter, wash, and obtain intermediate; (2) Dissolve the intermediate in NaOH aqueous solution, stir at room temperature, filter, wash, and obtain the dispersant precursor; (3) The obtained dispersant precursor was dissolved in formic acid by ultrasonication in a water bath. The resulting solution was added dropwise to isopropanol, allowed to stand, filtered, and washed to obtain a cationic perylene imide dispersant.
3. The method for preparing a cationic perylene imide dispersant according to claim 2, characterized in that, In step (1), the molar ratio is perylene tetrahydric anhydride:polyethylene polyamine = 1:(10-12).
4. The method for preparing a cationic perylene imide dispersant according to claim 2, characterized in that, In step (1), the reflux reaction temperature is 120℃-140℃ and the reflux reaction time is 90h-100h.
5. The method for preparing a cationic perylene imide dispersant according to claim 2, characterized in that, In step (2), the concentration of the NaOH aqueous solution is 2M-3M, and the mixture is stirred at room temperature for 5-6 hours.
6. The method for preparing a cationic perylene imide dispersant according to claim 2, characterized in that, In step (3), the volume ratio of formic acid to isopropanol is 1: (9-11).
7. The application of the cationic perylene imide dispersant according to claim 1 in the preparation of aqueous dispersions of carbon materials.
8. The application according to claim 7, characterized in that, The method includes the following steps: dissolving a cationic perylene imide dispersant in deionized water, adding a certain amount of carbon material, first performing preliminary dispersion by ultrasonication in a water bath, and then ultrasonicating with an ultrasonic cell disruptor to obtain a perylene imide-carbon material aqueous dispersion.
9. The application according to claim 8, characterized in that, The carbon material is selected from carbon nanotubes, graphene, or carbon black.
10. The application according to claim 8, characterized in that, The mass ratio of cationic perylene imide dispersant to carbon material is 1:(1-3); the concentration of carbon material in the perylene imide-carbon material aqueous dispersion is 0.5 mg·mL. -1 -40mg·mL -1 .