METHOD OF MANUFACTURING ARGYRODITE-TYPE SOLID ELECTROLYTE, ARGYRODITE-TYPE SOLID ELECTROLYTE, AND ALL-SOLID-STATE BATTERY COMPRISING THE SOLID ELECTROLYTE
20210242493 · 2021-08-05
Assignee
Inventors
- Dong Wook Shin (Gyeonggi-do, KR)
- Sun Ho Choi (Incheon, KR)
- Chan Hwi Park (Seoul, KR)
- Ji Yae Do (Seoul, KR)
- Seungwoo Lim (Seoul, KR)
- Gi Deok Kim (Seoul, KR)
Cpc classification
Y02P70/50
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
C01P2002/74
CHEMISTRY; METALLURGY
C01P2002/77
CHEMISTRY; METALLURGY
H01M10/0585
ELECTRICITY
Y02E60/10
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
C01P2002/72
CHEMISTRY; METALLURGY
H01M10/0525
ELECTRICITY
C01B25/14
CHEMISTRY; METALLURGY
International classification
C01B25/14
CHEMISTRY; METALLURGY
H01M10/0525
ELECTRICITY
Abstract
A method of manufacturing an argyrodite-type solid electrolyte, an argyrodite-type solid electrolyte, and an all-solid-state battery including the argyrodite-type solid electrolyte are provided. The method includes a first step of adding precursors represented by the following Formulas 1 and 2 into a polar aprotic solvent, followed by stirring to obtain a reaction solution; a second step of adding P.sub.2S.sub.5 into the stirred reaction solution, followed by further stirring to form a precipitate obtained as a result of the reaction in the reaction solution; and a third step of drying and heat-treating the reaction solution in which the precipitate is formed to obtain a solid electrolyte: [Formula 1] A.sub.2S [Formula 2] AX wherein A represents an alkali metal, and X represents an element of the halogen group.
Claims
1. A method of manufacturing an argyrodite-type solid electrolyte, comprising: a first step of adding precursors represented by the following Formulas 1 and 2 into a polar aprotic solvent, followed by stirring to obtain a reaction solution; a second step of adding P.sub.2S.sub.5 into the stirred reaction solution, followed by further stirring to form a precipitate obtained as a result of a reaction in the reaction solution; and a third step of drying and heat-treating the reaction solution in which the precipitate is formed to obtain a solid electrolyte:
A.sub.2S [Formula 1]
AX [Formula 2] wherein A represents an alkali metal, and X represents an element of the halogen group.
2. The method of claim 1, wherein the polar aprotic solvent has a nitrile group.
3. The method of claim 2, wherein the polar aprotic solvent having a nitrile group is acetonitrile.
4. The method of claim 1, wherein, in the first step, the precursors represented by Formulas 1 and 2 are at least partially dissolved in the solvent.
5. The method of claim 1, wherein, in the second step, after solvated P.sub.2S.sub.6.sup.2− is formed in the reaction solution, the P.sub.2S.sub.6.sup.2− is converted into solvated PS.sub.4.sup.3−, and a portion of the PS.sub.4.sup.3− forms amorphous A.sub.6PS.sub.5X as a precipitate along with A.sup.+, A.sub.2S, and AX.
6. The method of claim 5, wherein, in the second step, the reaction solution comprises a deposit including the precipitate and a supernatant above the deposit, and the reaction is performed until a fraction of PS.sub.4.sup.3− ions becomes higher than a fraction of P.sub.2S.sub.6.sup.2− ions in the supernatant, and a fraction of the precipitated A.sub.6PS.sub.5X becomes higher than a fraction of A.sub.2S in the deposit.
7. The method of claim 6, wherein the reaction is performed until a fraction of the precipitated A.sub.3PS.sub.4 becomes higher than a fraction of the A.sub.6PS.sub.5X in the deposit.
8. The method of claim 7, wherein, in the deposit, the A.sub.3PS.sub.4 has a fraction of 50 to 65%, the A.sub.6PS.sub.5X has a fraction of 25 to 35%, the A.sub.2S has a fraction of 5 to 15%, and the AX has a fraction of 1 to 10%.
9. The method of claim 5, wherein, in the third step, the amorphous A.sub.6PS.sub.5X is crystallized through heat treatment so that the amorphous A.sub.6PS.sub.5X is converted into A.sub.6PS.sub.5X having an argyrodite crystal phase.
10. The method of claim 5, wherein, in the second step, the remaining portion of the PS.sub.4.sup.3− precipitates into A.sub.3PS.sub.4 along with A.sup.+.
11. The method of claim 10, wherein, in the third step, A.sub.2S and AX are reacted with the A.sub.3PS.sub.4 precipitate and 3A.sup.+ and PS.sub.4.sup.3− remaining in the supernatant, and then crystallized to form A.sub.6PS.sub.5X having an argyrodite crystal phase.
12. A solid electrolyte comprising: 80 to 99.9% by weight or more of A.sub.6PS.sub.5X having an argyrodite crystal phase; and 0.1 to 20% by weight of A.sub.2S and/or AX, wherein A represents an alkali metal, X represents an element of the halogen group.
13. The solid electrolyte of claim 12, wherein the solid electrolyte has an ionic conductivity of 1.5 to 20 mS/cm.
14. The solid electrolyte of claim 12, wherein the A.sub.6PS.sub.5X is included at a content of 92 to 98% by weight, and the A.sub.2S and/or AX are included at a content of 2 to 8% by weight.
15. The solid electrolyte of claim 14, wherein the solid electrolyte has an ionic conductivity of 3 to 9 mS/cm.
16. A sulfide-based all-solid-state battery comprising a positive electrode, a solid electrolyte layer, and a negative electrode stacked in sequential order, wherein the solid electrolyte layer comprises the solid electrolyte defined in claim 12 and having a particle shape.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] The above and other objects, features and advantages of the present invention will become more apparent to those of ordinary skill in the art by describing in detail exemplary embodiments thereof with reference to the attached drawings, in which:
[0019]
[0020]
[0021]
[0022]
[0023]
[0024]
[0025]
[0026]
[0027]
[0028]
[0029]
[0030]
[0031]
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS
[0032] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings in order to describe the present invention in further detail. However, the present invention is not limited to the embodiments disclosed below and can be implemented in various forms. Throughout the specification, like elements have like reference numerals. In a case where it is stated that one layer is formed “on” another layer throughout the specification, this refers to the one layer being directly on the other layer or to a third layer being interposed between the one layer and the other layer.
[0033] Method of Manufacturing Solid Electrolyte Having Argyrodite Crystal Phase
[0034]
[0035] Referring to
A.sub.2S [Formula 1]
[0036] wherein A may represent an alkali metal, for example, Li or Na.
AX [Formula 2]
[0037] wherein A is as defined in Formula 1, and X may represent an element of the halogen group, for example, Cl, Br, or I.
[0038] The polar aprotic solvent is a solvent having a nitrile group, that is, a nitrile-based solvent. In this case, the polar aprotic solvent may be acetonitrile which is easily removed due to its relatively low boiling point.
[0039] In the first step, the stirring temperature and the stirring time may be set to temperature and time ranges in which the precursors represented by Formulas 1 and 2 may be at least partially dissolved in the solvent. As one example, the stirring time may be in a range of 0.5 to 1.5 hours, but the present invention is not limited thereto.
[0040] P.sub.2S.sub.5 may be added into the stirred reaction solution, followed by further stirring to form a precipitate obtained as a result of the reaction in the reaction solution (second step S20). The precipitate may be a reaction product. In this step, the solvent in the reaction solution may be identical to the solvent used in the first step, and another solvent may not be added. Also, P.sub.2S.sub.5 may be added in a solid phase that is not dissolved in other solvents.
[0041] [Reaction Scheme]
5A.sub.2S+P.sub.2S.sub.5+2AX.fwdarw.P.sub.2S.sub.6.sup.2−+2A.sup.++4A.sub.2S+2AX Step A:
P.sub.2S.sub.6.sup.2−+2A.sup.++4A.sub.2S+2AX.fwdarw.P.sub.2S.sub.7.sup.4−+4A.sup.++3A.sub.2S+2AX Step B:
P.sub.2S.sub.7.sup.4−+4A.sup.++3A.sub.2S+2AX.fwdarw.2PS.sub.4.sup.3−+6A.sup.++2A.sub.2S+2AX Step C:
2PS.sub.4.sup.3−+6A.sup.++2A.sub.2S+2AX.fwdarw.A.sub.6PS.sub.5X (amorphous solid)+PS.sub.4.sup.3−+3A.sup.++A.sub.2S+AX Step D:
[0042] wherein A is as defined in Formula 1, and X is as defined in Formula 2.
[0043] The formation of the precipitate may be explained from the above reaction scheme: Steps A to C may occur in the supernatant, and the precipitates formed in Step D may be solid electrolytes A.sub.6PS.sub.5X and A.sub.3PS.sub.4 in an amorphous state. Specifically, A.sub.2S(s) and P.sub.2S.sub.5(s) in the reaction solution may be slowly dissolved to form solvated P.sub.2S.sub.6.sup.2− (Step A), which is then converted into P.sub.2S.sub.7.sup.4− (Step B) and then into solvated PS.sub.4.sup.3− (Step C), a portion of PS.sub.4.sup.3− may form amorphous A.sub.6PS.sub.5X as a precipitate along with A.sup.+, A.sub.2S, and AX, and another portion of PS.sub.4.sup.3− may precipitate into A.sub.3PS.sub.4 along with A.sup.+.
[0044] Meanwhile, a deposit in the reaction solution may include the precipitate, and may include the precursors A.sub.2S and AX which are still not dissolved as well. However, in the first step, A.sub.2S and AX, which are not easily dissolved in the solvent as compared to P.sub.2S.sub.5, may be first added and dissolved in the solvent, and then reacted with P.sub.2S.sub.5 in the second step to more effectively form A.sub.6PS.sub.5X (an amorphous solid) as a reaction product of A.sub.2S, AX, and P.sub.2S.sub.5. Also, as the polar aprotic solvent is used, PS.sub.4.sup.3− serving as the product in the supernatant may be solvated and stabilized to increase a forward reaction rate as well.
[0045] In the second step, the reaction time and the reaction temperature may be adjusted so that a fraction of PS.sub.4.sup.3− ions becomes higher than a fraction of P.sub.2S.sub.6.sup.2− ions in the solvent of the reaction solution, that is, in the supernatant, and a fraction of the precipitated A.sub.6PS.sub.5X and a fraction of the A.sub.3PS.sub.4 become higher than a fraction of A.sub.2S in the deposit. Here, the fraction of the A.sub.3PS.sub.4 may be higher than the fraction of the A.sub.6PS.sub.5X. Specifically, in the deposit, the A.sub.3PS.sub.4 may have a fraction of 50 to 65%, the A.sub.6PS.sub.5X may have a fraction of 25 to 35%, the A.sub.2S may have a fraction of 5 to 15%, and the AX may have a fraction of 1 to 10%. More specifically, in the deposit, the A.sub.3PS.sub.4 may have a fraction of 55 to 60%, the A.sub.6PS.sub.5X may have a fraction of 27 to 33%, the A.sub.2S may have a fraction of 7 to 13%, and the AX may have a fraction of 2 to 7%. In addition, the reaction time and reaction temperature in the second step may be adjusted in a range where reaction products are not oxidized by the surrounding air to generate impurities. For example, the reaction temperature may be in a range of 20 to 65 Celsius degrees (° C.), specifically in a range of 25 to 60° C., and the total reaction time of the first and second steps may be in a range of 10 to 120 hours, specifically in a range of 20 to 100 hours, and more specifically in a range of 22 to 80 hours. Here, the fraction of P.sub.2S.sub.6.sup.2− ions and the fraction of PS.sub.4.sup.3− ions may be obtained from the relative areas of .sup.31P NMR peaks corresponding to P.sub.2S.sub.6.sup.2− and PS.sub.4.sup.3−. Also, the fraction of A.sub.2S, the fraction of A.sub.6PS.sub.5X, and the fraction of A.sub.3PS.sub.4 may be, for example, obtained from the relative areas of .sup.7A NMR (A represents an alkali metal) peaks for example, .sup.7Li or .sup.7Na NMR peaks which correspond to A.sub.2S, A.sub.6PS.sub.5X, and A.sub.3PS.sub.4.
[0046] Next, the reaction solution in which the precipitate is formed may be dried and heat-treated to obtain a solid electrolyte (third step S30). Specifically, the reaction solution may includes the supernatant and the deposit having the precipitate.
[0047] The drying step includes removing the solvent from the reaction solution in which the precipitate is formed. In this case, the solvent may be almost completely removed, but some of the solvent may not be removed. Some of the solvent which is not removed may be almost completely removed in the heat treatment step. This drying may be vacuum drying.
[0048] However, the solvent used in the first step and the second step may be a polar aprotic solvent. Because a polar protic solvent such as ethanol, etc. is not included in the solvent, the solvent in the solid electrolyte may not remain as an impurity after the drying and heat treatment steps.
[0049] In the heat treatment step, the A.sub.6PS.sub.5X (an amorphous solid) generated in the precipitate during the second step may be crystallized so that the A.sub.6PS.sub.5X can be obtained as the solid electrolyte. Also, A.sub.3PS.sub.4 present in the precipitate and 3A.sup.+ and PS.sub.4.sup.3− present in the supernatant may be further reacted with A.sub.2S and AX, and then crystallized to generate A.sub.6PS.sub.5X having an argyrodite crystal phase. The heat treatment may be performed at approximately 500 to 600° C. for 5 to 30 hours.
[0050] As described above in the second step, because the A.sub.6PS.sub.5X (amorphous solid) is formed at a high generation rate in the second step, the A.sub.6PS.sub.5X having an argyrodite crystal phase obtained in the third step may be obtained with high purity. Also, as previously described above, as acetonitrile is used as one example of the polar aprotic solvent, the solvent does remain as an impurity in the solid electrolyte, thereby improving the purity of the solid electrolyte as well. Also, the solid electrolyte obtained through the method consisting of the first to third steps may have a particle size of several micrometers for example 1 to 10 μm. This may result in an enhanced contact area with an active material in the all-solid-state battery, as will be described later.
[0051] The solid electrolyte obtained in this third step may contain 80% by weight or more of A.sub.6PS.sub.5X having an argyrodite crystal phase, and may contain 20% by weight or less of impurities, specifically the residual precursor A.sub.2S and/or AX. For example, the resulting product obtained in the third step may contain 80 to 99.9% by weight, specifically 90 to 99% by weight, and more specifically 92 to 98% by weight, 92 to 97% by weight, or 92 to 96% by weight of the argyrodite crystal phase. The impurities may be included at a content of 0.1 to 20% by weight, specifically 1 to 10% by weight, and more specifically 2 to 8% by weight, 3 to 8% by weight, or 4 to 8% by weight.
[0052] Also, the resulting product, that is, a sulfide-based solid electrolyte, obtained in the third step may have an ionic conductivity of 1.5 to 20 mS/cm, specifically 2 to 10 mS/cm, and more specifically 3 to 9 mS/cm, 3 to 5 mS/cm or 3 to 4 mS/cm.
[0053] All-Solid-State Battery
[0054]
[0055] Referring to
[0056] The solid electrolyte particles E may contain 80% by weight or more of A.sub.6PS.sub.5X having an argyrodite crystal phase, and contain 20% by weight or less of impurities, specifically the residual precursors A.sub.2S and/or AX. For example, the solid electrolyte particles E may contain 80 to 99.9% by weight, specifically 90 to 99% by weight, and more specifically 92 to 98% by weight, 92 to 97% by weight, or 92 to 96% by weight of the argyrodite crystal phase. The impurities may be included at a content of 0.1 to 20% by weight, specifically 1 to 10% by weight, and more specifically 2 to 8% by weight, 3 to 8% by weight, or 4 to 8% by weight. Also, the solid electrolyte particles E may have an ionic conductivity of 1.5 to 20 mS/cm, specifically 2 to 10 mS/cm, and more specifically 3 to 9 mS/cm, 3 to 5 mS/cm or 3 to 4 mS/cm.
[0057] The solid electrolyte particles E may be formed using a method described with reference to
[0058] The positive electrode active material particles AM may be one or more selected from the group consisting of Li.sub.1-xMPO.sub.4 (M=Fe, Mn or Ni, and 0≤x≤1), Li.sub.1-xMnO.sub.2 (0≤x≤1), LiCoO.sub.2, Li.sub.1-xNi.sub.aMn.sub.bCo.sub.cO.sub.2 (0≤x≤1, a+b+c=1, 0≤a≤1, 0≤b≤1, and 0≤c≤1), and Li.sub.1-xNi.sub.aCo.sub.bAl.sub.cO.sub.2 (0≤x≤1, a+b+c=1, 0≤a≤1, 0≤b≤1, and 0≤c≤1). The negative electrode active material particles CM may be carbon (C) such as graphite, etc. or metal particles such as, silicon (Si), or tin (Sn). Meanwhile, the conductive material particles C may be carbon black such as Ketjen black, acetylene black, or the like. However, the present invention is not limited thereto, and various materials used in the related art may be used as the positive electrode active material particles AM, the negative electrode active material particles CM, and the conductive material particles C.
[0059] Individual layers of the positive electrode 50, the solid electrolyte layer 60, and the negative electrode 70 may be stacked in sequential order by forming a slurry containing the corresponding particles, and subjecting the slurry to tape casting, screen printing, or electrostatic spraying. Thereafter, after the stacking is completed, the stacked layers may be pressed using one or more methods selected from the group consisting of hot pressing, roll pressing, and warm isostatic pressing (WIP).
[0060] Hereinafter, preferred examples are presented to aid in understanding the present invention. However, it should be understood that the following examples are merely intended to aid in understanding the present invention, and are not intended to limit the scope of the present invention.
Electrolyte Preparation Examples 1 to 12
[0061] (1) Generation of Reaction Solution
[0062] Li.sub.2S and LiCl were added into acetonitrile having a reaction temperature as mentioned in the following Table 1, and then stirred at 280 rpm for a reaction time as mentioned in the following Table 1 to obtain a reaction solution.
[0063] (2) Formation of Precipitate in Reaction Solution
[0064] P.sub.2S.sub.5 was added into the reaction solution, and stirred at 280 rpm for a reaction time as mentioned in the following Table 1 at the same temperature as the reaction temperature to form a precipitate in the reaction solution, thereby obtaining a mixture including a supernatant and a deposit including the precipitate. In this reaction, a molar ratio (i.e., Li.sub.2S:P.sub.2S.sub.5:LiCl) of the precursors was in a range of 5:1:2. Also, a concentration of the reaction solution to which all the Li.sub.2S, LiCl, and P.sub.2S.sub.5 were added was 0.06 M.
[0065] (3) Drying and Heat Treatment
[0066] After the reaction was completed, the reaction solution which is the mixture was vacuum-dried at 30° C. for 24 hours using a low-temperature trap device to volatilize the solvent from the reaction solution in which the precipitate was formed. Thereafter, the resulting product from which the solvent was volatilized was heat-treated at 550° C. for 10 to 24 hours to obtain a solid electrolyte.
Electrolyte Comparative Examples 1 and 2
[0067] An argyrodite solid electrolyte was obtained in the same manner as in Electrolyte Preparation Example 1, except that the reaction solution was stirred at 280 rpm for 24 hours after all the Li.sub.2S, P.sub.2S.sub.5, and LiCl were added into acetonitrile having a reaction temperature as mentioned in the following Table 1 one time.
TABLE-US-00001 TABLE 1 Reaction Reaction time after time after Total Reaction addition of addition reaction temperature Li.sub.2S and LiCl of P.sub.2S.sub.5 time Preparation 30° C. 1 minute 9 minutes 10 minutes Example 1 Preparation 10 minutes 50 minutes 1 hour Example 2 Preparation 1 hour 4 hours 5 hours Example 3 Preparation 1 hour 23 hours 24 hours Example 4 Preparation 1 hour 35 hours 36 hours Example 5 Preparation 1 hour 71 hours 72 hours Example 6 Preparation 1 hour 119 hours 120 hours Example 7 Preparation 40° C. 1 hour 23 hours 24 hours Example 8 Preparation 50° C. 1 hour 23 hours Example 9 Preparation 60° C. 1 hour 23 hours Example 10 Preparation 70° C. 1 hour 23 hours Example 11 Comparative 30° C. — — 24 hours Example 1 Comparative 50° C. — — 24 hours Example 2 Total reaction time = Reaction time after addition of Li.sub.2S and LiC1 + Reaction time after addition of P.sub.2S.sub.5
[0068]
[0069] Referring to
[0070] Referring to
[0071]
[0072] Referring to
[0073] Referring to
[0074]
[0075] Referring to
[0076] Referring to
[0077]
[0078] Referring to
[0079] Referring to
[0080]
[0081] Referring to
[0082] Referring to
[0083]
[0084] Also, the following Table 2 lists the crystal-phase fractions and ionic conductivities of the resulting products according to Preparation Example 1 to 7.
TABLE-US-00002 TABLE 2 Reaction Ionic temperature Reaction Crystal-phase fraction (% by weight) conductivity (° C.) time Li.sub.6PS.sub.5Cl Li.sub.2S Li.sub.4P.sub.2S.sub.6 LiCl Li.sub.3PO.sub.4 (mS/cm) Preparation 30 10 61.5 22.5 16.0 — — 0.41 Example 1 minutes Preparation 1 75.5 8.7 15.8 — — 1.1 Example 2 hour Preparation 5 83.5 8.4 8.2 — — 1.1 Example 3 hours Preparation 24 89.4 4.9 5.7 — — 1.5 Example 4 hours Preparation 36 90.8 7.2 — 2.0 — 2.1 Example 5 hours Preparation 72 84.2 11.3 — 4.6 — 2.0 Example 6 hours Preparation 120 80.2 14.0 — 5.8 — 1.9 Example 7 hours
[0085] Referring to
[0086]
[0087] Referring to
[0088] Specifically, it was assumed that 1 mole of Li.sub.2S and 1 mole of P.sub.2S.sub.5 were first reacted in the supernatant to generate 1 mole of Li.sup.2+P.sub.2S.sub.6.sup.2−, the Li.sup.2+P.sub.2S.sub.6.sup.2− was then reacted with 1 mole of Li.sub.2S to generate 1 mole of Li.sup.4+P.sub.2S.sub.7.sup.4−, and the Li.sup.4+P.sub.2S.sub.7.sup.4− was then reacted with 1 mole of Li.sub.2S to generate 2 moles of Li.sup.3+P.sub.2S.sub.4.sup.3−.
[0089] It was assumed that a portion of the Li.sup.3+P.sub.2S.sub.4.sup.3−, that is, the solvated Li.sub.3PS.sub.4, precipitated into crystalline Li.sub.3PS.sub.4, and the remaining Li.sup.3+P.sub.2S.sub.4.sup.3− precipitated into amorphous Li.sub.6PS.sub.5Cl along with dissolved Li.sub.2S and LiCl.
[0090]
[0091] Referring to
[0092]
TABLE-US-00003 TABLE 3 Reaction Total Ion temperature reaction Crystal-phase fraction (% by weight) Iconductivity (° C.) time (h) Li.sub.6PS.sub.5Cl Li.sub.2S Li.sub.4P.sub.2S.sub.6 LiCl Li.sub.3PO.sub.4 (mS/cm) Preparation 30 24 89.4 4.9 5.7 — — 1.5 Example 4 Preparation 30 36 90.8 7.2 — 2.0 — 2.1 Example 5 Preparation 40 24 90.7 7.2 — 2.1 — 2.4 Example 8 Preparation 50 95.1 4.8 — — — 3.4 Example 9 Preparation 60 93.0 4.0 — 1.0 1.9 3.2 Example 10 Comparative 30 88.6 5.1 6.3 — — 1.5 Example 1
[0093] Referring to
[0094] As described above, the argyrodite crystal-type solid electrolyte can be obtained with high purity using a solution synthesis according to the present invention.
[0095] While the invention has been shown and described with reference to certain exemplary embodiments thereof, it will be understood by those skilled in the art that various changes in forms and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.