Disclosure of Invention
In order to solve the technical problems, the invention provides an electrode plate and a lithium ion battery.
The invention adopts the following technical scheme:
An electrode plate comprises a current collector and an active material layer coated on the surface of the current collector; the active material layer comprises an active material and a conductive agent, wherein the conductive agent comprises an ion conductive agent and a carbon material conductive agent; wherein:
The ionic conductive agent is MxOy, and M is any one or more of Mg, al, si, ca, ti, zr;
The ratio of the oil absorption value to the specific surface area of the ionic conductive agent is not less than 0.8;
the mass ratio of the ion conductive agent to the carbon material conductive agent is 1.5-20.
In lithium ion batteries, electron conduction and ion conduction are generally accomplished by using carbon materials with high specific surface areas, and in fact, the two functions can be separated, especially in batteries made of pole pieces with high surface density and high compaction, and the ion conductivity is more important than the electron conductivity.
When only the carbon material conductive agent is used, side effects of electron conductivity are brought about while the ion conductivity function is completed, namely, redox is taken part in the anode and cathode, resulting in the loss of battery performance.
Therefore, the ionic conductive agent and the carbon material conductive agent are combined to be used as the conductive agent, the use amount of the carbon material conductive agent is reduced, and the influence of the conductive agent on the electrical property and the safety performance of the battery is improved.
The invention defines that the ratio of the oil absorption value and the specific surface area of the ion conductive agent is not less than 0.8.
When the ratio of the oil absorption value to the specific surface area is too low, one reason is that the specific surface area is large, which results in difficulty in processing the slurry in the battery material pulping process, and even if it can be processed, the slurry is easily unstable, resulting in difficulty in coating; another reason is that the oil absorption value is too low, and thus the effect as a conductive agent is lost.
Under the limiting ratio of the invention, the balance between the oil absorption value and the specific surface area value of the ionic conductive agent can be realized, so that the ionic conductive agent has an effective conductive effect and ensures the stability of the conductive paste.
The invention also defines that the mass ratio of the ion conductive agent to the carbon material conductive agent is 1.5-20.
When the mass ratio of the ion conductive agent to the carbon material conductive agent is too large, the ion conductive agent content is too large, and the carbon material content is too low, so that the resistivity of the pole piece is too high, the battery polarization is caused, the impedance is increased, and the heating is serious.
When the mass ratio of the ion conductive agent to the carbon material conductive agent is too small, the carbon material content is too high, resulting in an increase in the specific surface area of the pole piece, and an increase in side reactions, resulting in a loss of circulation or storage capacity.
Specifically, as one embodiment of the present invention, the mass ratio of the ion conductive agent to the carbon material conductive agent is 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 or a range composed of any two of these values.
Preferably, the mass ratio of the ion conductive agent to the carbon material conductive agent is 4-15.
Specifically, as an embodiment of the invention, in order to ensure the stability of the slurry and the proper oil absorption value and specific surface area on the premise that the ratio of the oil absorption value to the specific surface area of the ion conductive agent is more than 0.8, the oil absorption value of the ion conductive agent is 150-800 ml/100g, and the specific surface area of the ion conductive agent is 60-500 m 2/g.
More specifically, the ratio of the oil absorption value to the specific surface area of the ion conductive agent is 0.85, 0.9, 1, 1.5, 2,5, 6, 8, 10, 12, 15, 18, 20, 30, 40, 50, 60, 70, 80 or a range composed of any two of these values.
When the ratio of the oil absorption value to the specific surface is too large, the pores of the particles on the surface of the material are dense, the structure is complex to process, and the manufacturing cost is high.
Preferably, the ratio of the oil absorption value to the specific surface area of the ion conductive agent is 1.5-10.
More specifically, the ionic conduction agent has an oil absorption value of 150 ml/100g、200ml/100g、250ml/100g、300ml/100g、350ml/100g、400ml/100g、450ml/100g、500ml/100g、600ml/100g、700ml/100g、800ml/100g or a range composed of any two of these values.
The specific surface area of the ionic conductor is 60 m2/g、80m2/g、100m2/g、120m2/g、150m2/g、180m2/g、200m2/g、250m2/g、300m2/g、350m2/g、400m2/g、450m2/g、500m2/g or a range of any two of these values.
Specifically, as an embodiment of the present invention, the carbon material conductive agent includes one or more of carbon black, acetylene black, graphene, carbon nanotubes, ketjen black.
Specifically, as an embodiment of the present invention, the conductive agent accounts for 0.3-10% of the mass of the electrode sheet, based on 100% of the mass of the electrode sheet.
Specifically, as one embodiment of the present invention, the electrode sheet is a positive electrode sheet, the active material is a positive electrode active material, and the positive electrode active material is at least one selected from lithium cobaltate, lithium manganate, lithium iron phosphate, lithium nickel cobalt manganate, and nickel manganese spinel.
Specifically, as an embodiment of the present invention, the electrode sheet is a negative electrode sheet, the active material is a negative electrode active material, and the negative electrode active material is at least one selected from natural graphite, artificial graphite, mesophase carbon microspheres, lithium titanate, silicon alloy, tin alloy, and active lithium metal.
Specifically, as an embodiment of the present invention, the active material layer further includes a binder including a thermoplastic resin such as polyvinylidene fluoride, a copolymer of vinylidene fluoride, polytetrafluoroethylene, a copolymer of vinylidene fluoride-hexafluoropropylene, a copolymer of tetrafluoroethylene-perfluoroalkyl vinyl ether, a copolymer of ethylene-tetrafluoroethylene, a copolymer of vinylidene fluoride-trifluoroethylene, a copolymer of vinylidene fluoride-trichloroethylene, a copolymer of vinylidene fluoride-fluoroethylene, a copolymer of vinylidene fluoride-hexafluoropropylene-tetrafluoroethylene, thermoplastic polyimide, polyethylene, polypropylene, and the like; an acrylic resin; and one or more of styrene butadiene rubber.
On the other hand, the invention also provides a lithium ion battery, which comprises a positive electrode plate, a negative electrode plate, a diaphragm and electrolyte, wherein the positive electrode plate and/or the negative electrode plate are/is the electrode plate.
The electrode plate adopts the ionic conductive agent and the carbon material conductive agent to form the conductive agent in a combined way, and the ratio of the oil absorption value and the specific surface area of the ionic conductive agent and the mass ratio of the ionic conductive agent and the carbon material conductive agent are limited to form stable conductive slurry with good conductive effect, so that the electrode plate with low resistivity and the lithium ion battery with excellent high-temperature performance and cycle performance are obtained.
Detailed Description
The following description of the embodiments of the present invention will clearly and completely describe the technical solutions of the embodiments of the present invention, and it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments.
All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
Example 1
The preparation method of the lithium ion battery in the embodiment comprises the following steps:
1) Preparation of negative electrode sheet
Mixing the artificial graphite serving as the anode active material, the conductive agent and the styrene-butadiene rubber serving as the anode binder according to the mass ratio of 95:3:2, and dispersing the materials in deionized water to obtain anode slurry.
Coating the slurry on two sides of a copper foil, drying, calendaring and vacuum drying, and welding a nickel outgoing line by an ultrasonic welding machine to obtain the negative plate.
The conductive agent includes carbon black and Al 2O3, and the mass ratio of Al 2O3 to carbon black is 10, and the ratio of the oil absorption value of Al 2O3 to the specific surface area is 4.
3) Preparation of positive plate
Lithium iron phosphate, conductive carbon black Super-P and polyvinylidene fluoride (PVDF) as binders are uniformly mixed according to a mass ratio of 96:2:2, and then are dispersed in N-methyl-2-pyrrolidone (NMP) to obtain positive electrode slurry.
And uniformly coating the slurry on two sides of an aluminum foil, drying, calendaring and vacuum drying to obtain a positive electrode material layer, and welding an aluminum outgoing line by an ultrasonic welding machine to obtain the positive electrode plate.
4) Preparation of electrolyte:
ethylene Carbonate (EC) and diethyl carbonate (DEC) were mixed in a mass ratio of 1:1, and then lithium hexafluorophosphate (LiPF 6) was added to a molar concentration of 1.0mol/L.
5) And (3) battery assembly:
Placing a three-layer separator with the thickness of 20 mu m between the positive plate and the negative plate, and then assembling the positive plate, the negative plate and the separator into a soft-package battery core; and the shell is made of an aluminum plastic film material through packaging molding, and then the procedures of electrolyte injection, aging, formation, capacity division and the like are respectively carried out to prepare the lithium ion battery.
Example 2
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The mass ratio of Al 2O3 to carbon black was 8.
Example 3
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
the mass ratio of Al 2O3 to carbon black was 15.
Example 4
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The mass ratio of Al 2O3 to carbon black was 1.5.
Example 5
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
the mass ratio of Al 2O3 to carbon black was 4.
Example 6
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The mass ratio of Al 2O3 to carbon black was 16.
Example 7
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The mass ratio of Al 2O3 to carbon black was 20.
Example 8
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The ratio of the oil absorption value to the specific surface area of Al 2O3 was 1.5.
Example 9
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The ratio of the oil absorption value to the specific surface area of Al 2O3 was 5.
Example 10
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The ratio of the oil absorption value to the specific surface area of Al 2O3 was 10.
Example 11
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The ratio of the oil absorption value to the specific surface area of Al 2O3 was 0.8.
Example 12
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The ratio of the oil absorption value to the specific surface area of Al 2O3 was 12.
Example 13
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The conductive agent comprises carbon black and MgO, the mass ratio of MgO to carbon black is 10, and the ratio of the oil absorption value of MgO to the specific surface area is 4.
Example 14
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The conductive agent includes carbon black and SiO 2, and the mass ratio of SiO 2 to carbon black is 10, and the ratio of the oil absorption value of SiO 2 to the specific surface area is 4.
Example 15
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The conductive agent comprises carbon black and CaO, the mass ratio of the CaO to the carbon black is 10, and the ratio of the oil absorption value of the CaO to the specific surface area is 4.
Example 16
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The conductive agent comprises acetylene black and TiO 2, the mass ratio of TiO 2 to acetylene black is 10, and the ratio of the oil absorption value of TiO 2 to the specific surface area is 4.
Example 17
This example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The conductive agent comprises carbon nano tubes and ZrO 2, the mass ratio of the ZrO 2 to the carbon nano tubes is 10, and the ratio of the oil absorption value of the ZrO 2 to the specific surface area is 4.
Example 18
The preparation method of the lithium ion battery in the embodiment comprises the following steps:
1) Preparation of negative electrode sheet
Mixing the negative electrode active material artificial graphite, conductive carbon black Super-P and negative electrode binder styrene-butadiene rubber according to the mass ratio of 95:3:2, and dispersing the materials in deionized water to obtain negative electrode slurry.
Coating the slurry on two sides of a copper foil, drying, calendaring and vacuum drying, and welding a nickel outgoing line by an ultrasonic welding machine to obtain the negative plate.
3) Preparation of positive plate
Lithium iron phosphate, a conductive agent and a binder polyvinylidene fluoride (PVDF) are uniformly mixed according to a mass ratio of 96:2:2, and then dispersed in N-methyl-2-pyrrolidone (NMP) to obtain a positive electrode slurry.
And uniformly coating the slurry on two sides of an aluminum foil, drying, calendaring and vacuum drying to obtain a positive electrode material layer, and welding an aluminum outgoing line by an ultrasonic welding machine to obtain the positive electrode plate.
The conductive agent includes carbon black and Al 2O3, and the mass ratio of Al 2O3 to carbon black is 10, and the ratio of the oil absorption value of Al 2O3 to the specific surface area is 4.
4) Preparation of electrolyte:
ethylene Carbonate (EC) and diethyl carbonate (DEC) were mixed in a mass ratio of 1:1, and then lithium hexafluorophosphate (LiPF 6) was added to a molar concentration of 1.0mol/L.
5) And (3) battery assembly:
Placing a three-layer separator with the thickness of 20 mu m between the positive plate and the negative plate, and then assembling the positive plate, the negative plate and the separator into a soft-package battery core; and the shell is made of an aluminum plastic film material through packaging molding, and then the procedures of electrolyte injection, aging, formation, capacity division and the like are respectively carried out to prepare the lithium ion battery.
Example 19
The preparation method of the lithium ion battery in the embodiment comprises the following steps:
1) Preparation of negative electrode sheet
Mixing the artificial graphite serving as the anode active material, the conductive agent and the styrene-butadiene rubber serving as the anode binder according to the mass ratio of 95:3:2, and dispersing the materials in deionized water to obtain anode slurry.
Coating the slurry on two sides of a copper foil, drying, calendaring and vacuum drying, and welding a nickel outgoing line by an ultrasonic welding machine to obtain the negative plate.
The conductive agent includes carbon black and Al 2O3, and the mass ratio of Al 2O3 to carbon black is 10, and the ratio of the oil absorption value of Al 2O3 to the specific surface area is 4.
3) Preparation of positive plate
Lithium iron phosphate, a conductive agent and a binder polyvinylidene fluoride (PVDF) are uniformly mixed according to a mass ratio of 96:2:2, and then dispersed in N-methyl-2-pyrrolidone (NMP) to obtain a positive electrode slurry.
And uniformly coating the slurry on two sides of an aluminum foil, drying, calendaring and vacuum drying to obtain a positive electrode material layer, and welding an aluminum outgoing line by an ultrasonic welding machine to obtain the positive electrode plate.
The conductive agent includes carbon black and Al 2O3, and the mass ratio of Al 2O3 to carbon black is 10, and the ratio of the oil absorption value of Al 2O3 to the specific surface area is 4.
4) Preparation of electrolyte:
ethylene Carbonate (EC) and diethyl carbonate (DEC) were mixed in a mass ratio of 1:1, and then lithium hexafluorophosphate (LiPF 6) was added to a molar concentration of 1.0mol/L.
5) And (3) battery assembly:
Placing a three-layer separator with the thickness of 20 mu m between the positive plate and the negative plate, and then assembling the positive plate, the negative plate and the separator into a soft-package battery core; and the shell is made of an aluminum plastic film material through packaging molding, and then the procedures of electrolyte injection, aging, formation, capacity division and the like are respectively carried out to prepare the lithium ion battery.
Comparative example 1
This comparative example is substantially identical to example 1 except that the negative electrode conductive agent is only carbon black.
Comparative example 2
This comparative example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The mass ratio of Al 2O3 to carbon black was 1.
Comparative example 3
This comparative example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The mass ratio of Al 2O3 to carbon black was 21.
Comparative example 4
This comparative example is substantially identical to example 1, except that the negative electrode conductive agent is different, specifically:
The ratio of the oil absorption value to the specific surface area of Al 2O3 was 0.6.
Comparative example 5
The preparation method of the lithium ion battery in the comparative example comprises the following steps:
1) Preparation of negative electrode sheet
Mixing the negative electrode active material artificial graphite, conductive carbon black Super-P and negative electrode binder styrene-butadiene rubber according to the mass ratio of 95:3:2, and dispersing the materials in deionized water to obtain negative electrode slurry.
Coating the slurry on two sides of a copper foil, drying, calendaring and vacuum drying, and welding a nickel outgoing line by an ultrasonic welding machine to obtain the negative plate.
3) Preparation of positive plate
Lithium iron phosphate, conductive carbon black Super-P and polyvinylidene fluoride (PVDF) as binders are uniformly mixed according to a mass ratio of 96:2:2, and then are dispersed in N-methyl-2-pyrrolidone (NMP) to obtain positive electrode slurry.
And uniformly coating the slurry on two sides of an aluminum foil, drying, calendaring and vacuum drying to obtain a positive electrode material layer, and welding an aluminum outgoing line by an ultrasonic welding machine to obtain the positive electrode plate.
4) Preparation of electrolyte:
ethylene Carbonate (EC) and diethyl carbonate (DEC) were mixed in a mass ratio of 1:1, and then lithium hexafluorophosphate (LiPF 6) was added to a molar concentration of 1.0mol/L.
5) And (3) battery assembly:
Placing a three-layer separator with the thickness of 20 mu m between the positive plate and the negative plate, and then assembling the positive plate, the negative plate and the separator into a soft-package battery core; and the shell is made of an aluminum plastic film material through packaging molding, and then the procedures of electrolyte injection, aging, formation, capacity division and the like are respectively carried out to prepare the lithium ion battery.
The lithium ion batteries prepared in each example and comparative example were subjected to performance testing as follows:
description: the currents involved in the following test methods are all denoted xC, where x is a number, C is the nominal capacity of the battery, e.g. 0.5C is the nominal capacity 1Ah of the battery charge current 0.5 x 1 = 0.5a, and 6c is denoted 6 x 1 = 6A.
1. Four-probe pole piece resistor
① Taking a rolled pole piece sample, sticking a high-temperature adhesive tape with the thickness of 50 mu m on the surface of a pole piece dressing, and rolling the pole piece dressing back and forth for 5 times by using a roller with the weight of 2kg to ensure that the adhesive tape and the pole piece dressing are well stuck and smooth without bubbles;
② Stripping off the pole piece stuck on the high-temperature adhesive tape, and obtaining a sample with dressing stuck on the adhesive tape;
③ Cutting a plurality of small discs of the sample ② by using a sampler with the diameter of 14mm for testing;
④ Testing and recording the thickness of each small wafer in ③;
⑤ Aligning the four probes to the center of the small wafer, inputting information such as the diameter, the thickness and the like of a sample on equipment software, and adjusting a testing range and a current value on the equipment according to equipment prompt;
⑥ Clicking test to obtain the resistivity value of the tested sample.
2. First charge and discharge efficiency
① Charging process steps: charging at 0.05C for 60min at constant current; charging at 0.1C for 60min at constant current; charging for 120min at 0.2C;
② The volume-dividing process steps are as follows: constant-current and constant-voltage charging at 0.33C to 3.8v,0.05C cutoff; 0.33C is discharged to 2.0V;
③ First charge-discharge efficiency=0.33C discharge capacity/(0.05C charge capacity+0.1C charge capacity+0.2C charge capacity+0.33C constant current constant voltage charge capacity) ×100%.
3.6C constant current charging test and temperature test
① The temperature probes are respectively stuck to the surfaces of the positive electrode lug, the negative electrode lug and the battery and used for testing and recording the temperature of each position;
② Placing the battery in an environment of 25 ℃ for 3 hours;
③ Discharging constant current of 0.33C to 2.0V, and standing for 30min;
④ 6C constant current charging to 3.8V, and standing for 30min;
⑤ The 6C charge curve and the temperature change curve at each location were recorded.
4.55 ℃ Cycle test
① Placing the soft package battery in an environment of 55 ℃ for 3 hours;
② 1C constant-current constant-voltage charge to 3.8v,0.05C cutoff; standing for 30min;
③ Constant-current discharging to 2.0V at 1C; standing for 30min;
④ A loop step ②~③;
⑤ The cycle was repeated 500 times, and the discharge capacity of the 1 st time and the discharge capacity of the last time were recorded.
The capacity retention of the cycle is calculated as follows:
battery capacity retention (%) =last discharge capacity/first discharge capacity×100%.
Full electrical state high temperature storage at 5.60 DEG C
① Capacity test: placing at 25 ℃ for 3 hours; constant-current and constant-voltage charging at 0.33C to 3.8v, a 0.05C cut-off, standing for 30min; discharging constant current of 0.33C to 2.0V, and standing for 30min; cycling 3 times, recording an average capacity value C0;
② And (3) fully charging the battery: 0.33C0 constant-current and constant-voltage charging to 3.8V, and cutting off 0.05C;
③ After the full-charge battery is stored in the environment of 60 ℃ for 30 days, the battery is taken out to the environment of 25 ℃, and is discharged to 2.0V under constant current of 0.33C0, and the residual capacity is recorded.
The results of the performance tests of the respective examples and comparative examples are shown in tables 1 to 4.
Table 1 Experimental comparison of the mass ratios of different Al 2O3 and carbon black
As can be seen from the test results of examples 1-7 and comparative examples 1-3 in Table 1, the electrode plate provided by the invention has the advantages that the ionic conductive agent and the carbon material conductive agent are selected as the conductive agents, the ratio of the oil absorption value to the specific surface area of the ionic conductive agent is not less than 0.8, and when the mass ratio of the ionic conductive agent to the carbon material conductive agent is 1.5-20, the impedance of the prepared electrode plate is lower, and the lithium ion battery has better cycle performance and high-temperature performance.
Meanwhile, as shown by the test results of examples 1 to 7, when the mass ratio of the ion conductive agent to the carbon material conductive agent is 4 to 15, the battery performance is better.
As can be seen from the test results of comparative examples 1 to 3 and examples 1 to 7, when the mass ratio of the ion conductive agent to the carbon material conductive agent is less than 1.5, or only the carbon material conductive agent is used, the first charge-discharge efficiency of the battery is low, and the cycle capacity retention rate at 55 ℃ is also low; when the mass ratio of the ion conductive agent to the carbon material conductive agent is more than 20, the resistance of the pole piece is larger, so that the temperature of the battery exceeds 60 ℃ when the 6C battery is charged quickly, and the heating value is large.
Table 2 comparison of oil absorption values and specific surface area ratio experiments of different Al 2O3
From the test results of example 1, examples 8 to 12 and comparative example 4 in Table 2, it can be seen that the 6C constant current charge ratio is low when the ratio of the oil absorption value to the specific surface area of the ion conductive agent is too small.
Meanwhile, as can be seen from the test results of examples 1 and 8-12, the cost is relatively low when the ratio of the oil absorption value to the specific surface area of the ionic conductive agent is in the range of 1.5-10.
TABLE 3 experimental comparison of ion conductive agents of different materials
As can be seen from the test results of examples 1 and 13-17 in Table 3, for different types of MxOy ionic conductive agents and carbon material conductive agents, as long as the ratio of the oil absorption value to the specific surface area of the ionic conductive agent and the mass ratio of the ionic conductive agent to the carbon material conductive agent meet the corresponding conditions, the impedance of the obtained electrode plate is lower, and the difference between the battery cycle performance and the high-temperature performance is not large, so that the electrode plate has universality for different ionic conductive agent types and carbon material conductive agent types.
Table 4 experimental comparison of different anode and cathode formulation ratios
As can be seen from the test results of example 1, examples 18 to 19 and comparative example 5 in Table 4, the electrode sheet of the present invention can be used as a positive electrode sheet and/or a negative electrode sheet, and when the negative electrode conductive agent adopts the ionic conductive agent and the carbon material conductive agent, the first charge and discharge efficiency of the battery is optimized; when the positive electrode conductive agent adopts the ionic conductive agent and the carbon material conductive agent, the high-temperature storage performance of the battery is optimized; when the positive electrode and the negative electrode are made of ionic conductive agents and carbon material conductive agents, the battery performance is better.
Compared with the method which only uses carbon black as the conductive agent, the method can effectively reduce the influence of side reaction brought by the carbon black on the charge-discharge performance and the high-temperature performance of the battery, and is beneficial to obtaining the lithium ion battery with excellent high-temperature performance and cycle performance.
The invention has been further described with reference to specific embodiments, but it should be understood that the detailed description is not to be construed as limiting the spirit and scope of the invention, but rather as providing those skilled in the art with the benefit of this disclosure with the benefit of their various modifications to the described embodiments.