Aromatic polyamide films for solvent resistant flexible substrates

Abstract

Films with optical transmittance of >80% between 400 and 750 nm and with coefficient of thermal expansion less than 20 ppm/ C. are prepared from aromatic polyamides that are soluble in polar organic solvents yet have glass transition temperatures >300 C. The films are cross-linked in the solid state by heating at elevated temperatures for short periods of time in the presence of multifunctional epoxides. Surprisingly, the optical and thermal properties of the films do not change significantly during the curing process. The temperature required for the crosslinking process to take place can be reduced by the presence of a few free, pendant carboxyl groups along the polyamide backbones. The films are useful as flexible substrates for electronic displays and photovoltaic devices.

Claims

1. A polymer solution capable of being made into transparent films; wherein the polymer solution comprises: (A) an aromatic copolyamide that is capable of being thermally cross-linked and having at least two repeat units of general formula (I) and (V): ##STR00025## wherein X represents the molar percentage of the repeat structure (I) and Y represents the molar percentage of the repeat structure (V) and wherein the copolyamide is soluble in polar organic solvents and can be solution cast into a clear film with a Tg higher than 300 C.; and Ar.sub.1 is selected from the group consisting of: ##STR00026## wherein p is 4, q is 3, and wherein R.sub.1, R.sub.2, R.sub.3, R.sub.4, R.sub.5 are selected from the group comprising hydrogen, halogen; alkyl groups; substituted alkyl groups; cyano groups; thioalkyl groups, alkoxy groups; substituted alkoxy groups; aryl groups; substituted aryl groups; alkyl ester groups; substituted alkyl ester groups; and combinations thereof, wherein G.sub.1 is selected from the group comprising a covalent bond; a CH.sub.2 group; a C(CH.sub.3).sub.2 group; a C(CF.sub.3).sub.2 group; and a C(CM.sub.3).sub.2 group, wherein M is selected from the group comprising a halogen; a CO group; an O atom; a S atom; a SO.sub.2 group; a Si (CH.sub.3).sub.2 group; a 9,9-bisphenylenefluorene group; a substituted 9,9-bisphenylenefluorene group; and an OZO group, wherein Z is selected from the group comprising a aryl group or substituted aryl group; a biphenyl group; a perfluorobiphenyl group; a 9,9-bisphenylenefluorene group; and a substituted 9,9-bisphenylenefluorene group, and wherein at least one of the Ar.sub.1 groups in at least one of the repeat units of (I) or at least one of the repeat units of (V) is selected from the group consisting of: ##STR00027## wherein Ar.sub.2 is selected from the group consisting of: ##STR00028## wherein p is 4, wherein R.sub.6, R.sub.7, R.sub.8 are selected from the group comprising hydrogen, halogens; alkyl groups; substituted alkyl groups; cyano groups; thioalkyl groups, alkoxy groups; substituted alkoxy groups; aryl groups; substituted aryl groups; alkyl ester groups; substituted alkyl ester groups; and combinations thereof, wherein G.sub.2 is selected from the group comprising a covalent bond; a CH.sub.2 group; a C(CH.sub.3).sub.2 group; a C(CF.sub.3).sub.2 group; and a C(CM.sub.3).sub.2 group, wherein M is selected from the group comprising a halogen; a CO group; an O atom; a S atom; a SO.sub.2 group; a Si(CH.sub.3).sub.2 group; a 9,9-bisphenylenefluorene group; a substituted 9,9-bisphenylenefluorene group; and an OZO group, wherein Z is selected from the group comprising a aryl group or substituted aryl group; a perfluorobiphenyl group; a 9,9-bisphenylenefluorene group; and a substituted 9,9-bisphenylenefluorene group, and wherein at least one of the Ar.sub.2 groups in at least one of the repeat units (I) is selected from the group consisting of: ##STR00029## and wherein Ar.sub.3 is selected from the group comprising: ##STR00030## wherein t is 0 to 3, g is 0 to 4, and s is 0 to 4, wherein R.sub.9, R.sub.10, R.sub.11 are selected from the group comprising hydrogen, halogens; alkyl groups; substituted alkyl groups; cyano groups; thioalkyl groups, alkoxy groups; substituted alkoxy groups; aryl groups; substituted aryl groups; alkyl ester groups; substituted alkyl ester groups; and combinations thereof, wherein G.sub.3 is selected from the group comprising a covalent bond; a CH.sub.2 group; a C(CH.sub.3).sub.2 group; a C(CF.sub.3).sub.2 group; and a C(CM.sub.3).sub.2 group, wherein M is selected from the group comprising a halogen; a CO group; an O atom; a S atom; a SO.sub.2 group; a Si(CH.sub.3).sub.2 group; a 9,9-bisphenylenefluorene group; a substituted 9,9-bisphenylenefluorene group; and an OZO group, wherein Z is selected from the group comprising a aryl group; substituted aryl group; a biphenyl group; a perfluorobiphenyl group; a 9,9-bisphenylenefluorene group; and a substituted 9,9-bisphenylenefluorene group; and, wherein at least one Ar.sub.3 group in at least one of the repeat units (V) is selected from: ##STR00031## and (B) a multifunctional epoxide selected from the group comprising the general structures (II), (III), and (IV): ##STR00032## wherein x>1 and R.sub.12 is selected from the group comprising ##STR00033## where the cyclic structure is selected from the group comprising ##STR00034## wherein n and n.sub.1>1 and R.sub.13 is an alkyl or aromatic group.

2. The polymer solution of claim 1, wherein the copolyamide contains multiple repeat units with structures (I) and (V).

3. The polymer solution of claim 1, wherein the copolyamide contains approximately 1 to approximately 10 mole % of the repeat unit containing at least one carboxyl group.

4. The polymer solution of claim 1, wherein the polymer solution may be cast into a film thickness with a thickness greater than approximately 4 m and less than approximately 100 m.

5. The polymer solution of claim 1, wherein the polymer solution may be cast into a film with a thickness approximately 10 m thick and has a transmittance of >85% at 550 nm.

6. The polymer solution of claim 1, wherein the polymer solution may be cast into a film that has an average coefficient of thermal expansion which is less than approximately 20 ppm/ C. between 25 C. and 250 C.

7. The polymer solution of claim 1, wherein the polymer solution is solution cast into a film that has a film transparency of >80% between 400 nm and 750 nm.

Description

DETAILED DESCRIPTION

(1) The present invention is directed toward transparent, solvent resistant films prepared from aromatic polyamides. The polyamides are prepared via a condensation polymerization of aromatic diamines and diacid chlorides in a polar solvent, where the hydrochloric acid generated in the reaction is trapped by a reagent like an alkylene oxide, a tertiary amine, or an inorganic base. Akylene oxides such as propylene oxide are preferred because their hydrogen chloride adducts can be easily removed by volatilization. The diamines and diacid chlorides must be selected so that the copolyamide remains in solution during the polymerization without the need for added inorganic salts. Rigid, linear diacid dichlorides such as terephthaloyl dichloride reduce solubility, but they increase the polymer glass transition temperature (Tg) and their use results in a lower film coefficient of thermal expansion (CTE). Non-linear, diacid dichlorides such as isophthaloyl dichloride slightly increase solubility, but they decrease the polymer glass transition temperature (Tg) and slightly increase the film coefficient of thermal expansion (CTE). Mixtures of these two monomers can be used to obtain the best combination of effects (Table 1). The most dramatic effects on polymer solubility can be achieved through the proper selection of the diamine components. Rigid monomers such as p-phenylenediamine reduce the polymer coefficient of thermal expansion (CTE) and increase the glass transition temperature (Tg), but they dramatically decrease solubility. Thus, they can only be used in very small amounts (<10 mol %). Flexible monomers containing ether linkages increase the polymer solubility, but they also increase the coefficient of thermal expansion (CTE). Thus, they cannot be used alone. However, a combination of the two types of monomers can be used to achieve the targeted properties. Diamines containing cardo units such as 9,9-bis(4-aminophenyl)fluorene (FDA) are unique in that they increase the polymer solubility and the Tg. Although their effect on coefficient of thermal expansion (CTE) is minimal when used in small amounts, the use of more than 30 mol % results in an increase in coefficient of thermal expansion (CTE) (Table 2). Diamines containing carboxyl groups such as 3,5-diaminobenzoic acid (DAB) and 4,4-diaminodiphenic acid (DADP) increase the polymer solubility, but only a limited amount (<10 mol %) can be used due to undesirable side effects. DADP is preferred because it increases solubility and reduces coefficient of thermal expansion (CTE). Particularly useful diamine monomers are those that contain twisted biphenyl structures such as 2,2-bis(trifluoromethyl)-4,4-diaminobiphenyl (PFMB) (Tables 1 and 2). Such monomers increase solubility while reducing film CTE and can be used alone. It is important that all the diamines must be handled carefully as they can undergo oxidation with the development of color. Their polymerizations also have to be carried out under a blanket of inert gas and at controlled low temperature in order to prevent their oxidation. Diamines that readily undergo oxidation such as p-phenylenediamine and m-phenylenediamine require special care, and must be used in very small amounts (>10 mol %). Diamines containing electron-withdrawing groups such as trifluoromethyl groups are much preferred as they are much more resistant to oxidation.

(2) The films, which display transparences >80% from 400 to 750 nm, can be prepared by casting procedures at temperatures below approximately 200 C. directly from the polymerization solutions if a volatile reagent such as propylene oxide is used to trap the hydrochloric acid by product. The adduct of the hydrochloride acid and the reagent is removed by evaporation along with the solvent during the film casting process. Alternatively, the polyamide may be first isolated by precipitation in a non-solvent. The film casting solution is then prepared by dissolving the polymer in a polar solvent. In either case, a multifunctional epoxide is added to the solution prior to casting. The epoxide must display minimum color. Colorless epoxides are much preferred. The minimum amount of epoxide is used that results is a film that displays solvent resistance after being heated at approximately 250 C. to approximately 280 C. for less than 30 minutes. The use of an excessive amount of epoxide results in a film that yellows when heated to elevated temperatures. The preferred amount on epoxide is 2 to 10 wt % of the weight of the polyamide. The most preferred amount is 4 to 6 wt %. The greater the number of epoxy groups in the multifunctional epoxide the smaller the amount that has to be used. The temperature required for the crosslinking process to take place can be lowered to approximately 250 C. or less by incorporating pendant carboxylic acid groups along the polymer backbone. This can be achieved through the use of a diamines containing carboxyl groups such as 3,5-diaminobenzoic acid and 4,4-diaminodiphenic acid. However, only a limited amount of these monomers can be used. An excessive amount of carboxyl groups results in a polymer that: 1) cannot be made solvent resistant even through the use of excess amounts of a multifunctional epoxides; 2) is moisture sensitive; and 3) displays too high a coefficient of thermal expansion (CTE) and 4) a reduced thermal stability. The preferred amount of the functionalized diamine is 1 to 10 mol % of the diamine mixture. The most preferred amount is 3 to 6 mol %. The greater the number of carboxyl groups in the diamine, the less the amount that is required to enhance the crosslinking process.

(3) The carboxyl group is unique in that it facilitates crosslinking with the epoxide without the development of color. It has been discovered that other functional groups that react with epoxy groups such as hydroxyl groups promote crosslinking, but at the expense of color development. Although not to be bound by theory, it is postulated that the carboxylic acid groups also catalyze the reaction of the epoxy groups with the amide linkages. Polyamides containing carboxyl groups will also undergo crosslinking without the presence of a multifunctional epoxide. However, in this case, the polymer must be heated to over 300 C. (Table 3).

(4) The curing process is carried out under reduced pressure or in an inert atmosphere so that no change in the film properties occurs. It is especially important that the process is carried out without any oxidative degradation that leads to the development of color. The films display coefficient of thermal expansion (CTE)<20 ppm/ C. as cast and do not need to be subjected to stretching.

(5) Representative and illustrative examples of the useful aromatic diacid dichlorides in the invention are:

(6) ##STR00018##

(7) Representative and illustrative examples of the useful aromatic diamines in the invention are:

(8) ##STR00019## ##STR00020##

(9) Representative and illustrative examples of the useful aromatic diamines with pendant free carboxylic acid groups in the invention are:

(10) ##STR00021##
The diamines may also be used in the form of their hydrochloride salts.

(11) Representative and illustrative examples of multifunctional compounds containing epoxy groups useful in the invention include triglycidyl isocyanate (TG), as shown below:

(12) ##STR00022## and others:

(13) ##STR00023## ##STR00024##

(14) Using the principles described herein one skilled in the art can design multiple polyamide structures that display the targeted properties. For example, the following are exemplary polymers that can be used in this invention: 1) about 50 to about 70 mol % TPC, about 30 to about 50 mol % IPC, about 90 to about 99 mol % PFMB, and about 1 to about 10 mol % 4, 4-diaminodiphenic acid (DADP); 2) about 50 to about 70 mol % TPC, about 25 to about 50 mol % IPC, about 90 to about 96 mol % PFMB, and about 4 to about 10 mol % 3, 5-diaminobenzoic acid (DAB); 3) about 100 mol % TPC, about 25 to about 85 mol % PFMB, about 15 to about 50 mol % 9, 9-bis(4-aminophenyl)fluorine (FDA), and about 1 to about 10 mol % DADP; and 4) about 100 mol % TPC, about 50 to about 85 mol % PFMB, about 15 to about 50 mol % FDA, and about 4 to about 10 mol % DAB.

(15) TABLE-US-00001 TABLE 1 Coefficient of thermal expansion (CTE) and glass transition temperature (Tg) of Films Prepared From Soluble TPC/IPC/PFMB Copolymers according to the general procedure in Example 2 TPC/IPC/PFMB CTE (ppm/ C.) Tg ( C.) 70/30/100 7.4 336 60/40/100 8.0 323 50/50/100 12.2 330 40/60/100 22.4 336 30/70/100 32.6 319 20/80/100 27.9 326 10/90/100 30.1 325 0/100/100 34.2 327

(16) TABLE-US-00002 TABLE 2 Coefficient of thermal expansion (CTE) and glass transition temperature (Tg) of Films Prepared From Soluble TPC/FDA/PFMB Copolymers according to the general procedure in Example 1 TPC/FDA/PFMB CTE (ppm/ C.) Tg ( C.) 100/20/80 5.8 365 100/30/70 5.1 370 100/50/50 13.1 391 100/70/30 18.3 406 100/80/20 26.7 404 100/90/10 33.2 410 100/100/0 >40 >410

EXAMPLES

Example 1

(17) This example illustrates the procedure for the preparation of a soluble copolymer from TPC, FDA and PFMB (70%/30%/100% mol ratio). For purposes of illustration, a representative film having mol ratios of (100%/20%/80% of TPC, FDA, and PFMB, respectively, is described below, but it should be understood that films having varying mol rations could be formed using the general procedure.

(18) To a 100 ml, four necked, round bottom flask, equipped with a mechanical stirrer, a nitrogen inlet and outlet, are added PFMB (1.0247 g, 3.2 mmol), FDA (0.02788 g, 0.8 mmol), and dried DMAc (20 ml) at room temperature under nitrogen. After the PFMB dissolves completely, TPC (0.8201 g 4.04 mmol) is added and the flask wall is washed with DMAc (5.0 ml) to remove any adhering TPC. The viscosity of the solution slowly increases until the mixture gels. After propylene oxide (0.5 g, 8.5 mmol) is added, the gel is broken up under stirring to form a viscous, homogenous solution. After the solution is stirred for another four hours, it is added to methanol to precipitate the copolymer, which is collected by filtration and dried under reduced pressure. The polymer is soluble in polar aprotic solvents.

Example 2

(19) This example illustrates the general procedure for the preparation of a soluble copolymer from TPC, IPC and PFMB. For purposes of illustration, a representative film having mol ratios of 70%/30%/100% of TPC, IPC, and PFMB, respectively is described. Below, but it should be understood that films having varying mol ratios could be formed using the general procedure.

(20) To a 250 ml, three necked, round bottom flask, equipped with a mechanical stirrer, a nitrogen inlet and an outlet, is added PFMB (3.2024 g, 0.01 mol) and dried DMAc (45 ml) at room temperature under nitrogen. After the PFMB dissolves completely, IPC (0.6395 g 0.003 mol) is added to the solution at room temperature under nitrogen, and the flask wall is washed with DMAc (1.5 ml). After 15 minutes, TPC (1.4211 g, 0.007) is added to the solution, and the flask wall is again washed with DMAc (1.5 ml). The viscosity of the solution increases until the mixture gels. After propylene oxide (1.4 g, 0.024 mol) is added, the gel is broken up with vigorous stirring to form a viscous, homogenous solution. The solution is added to methanol to precipitate the copolymer, which is collected by filtration and dried under reduced pressure. The polymer is soluble in polar aprotic solvents.

Comparative Example 1

(21) This example illustrates the deleterious effect on solubility of using excessive p-phenylenediamine in the preparation of the polyamides of this invention.

(22) To a 250 ml, three necked, round bottom flask equipped with a mechanical stirrer, a nitrogen inlet and outlet is added p-phenylenediamine (1.9465 g, 0.018 mol) and 3,5-diaminobenzoic acid (0.3043 g, 0.002 mol), dried N, N-dimethyl acetamide (60 ml) and propylene oxide (3.4 g). After the mixture is cooled under nitrogen to 10 C. with an ice/water bath, terephthaloyl chloride (4.0604 g, 0.02 mol) is added. A yellow polymer immediately precipitates from the solution. The polymer is insoluble in organic solvents.

Example 3

(23) This example illustrates the general procedure for the preparation of a solution containing a copolymer prepared of TPC, IPC and PFMB (70%/30%/100% mol ratio) containing 5 wt % triglycidyl isocyanate (TGI) (based on the weight of the polymer).

(24) To a 250 ml, three necked, round bottom flask, equipped with a mechanical stirrer, a nitrogen inlet and outlet, is added PFMB (3.2024 g, 0.01 mol), propylene oxide (1.4 g, 0.024 mol) and dried DMAc (45 ml). The solution is cooled to 10 C. in an ice/water bath. After the PFMB dissolves completely, IPC (0.6395 g, 0.003 mol) is added, and the flask wall is washed with DMAc (1.5 ml) to remove any adhering TPC. After 15 minutes, TPC (1.4211 g, 0.007 mol) is added, and the flask wall is again washed with DMAc (1.5 ml). The resulting viscous, homogenous solution is stirred at room temperature for another 4 hours. After triglycidyl isocyanate (TGI) (0.45 g) is added, the mixture is stirred for another two hours. The resulting solution can be cast directly into film. In an alternative procedure, the polymer solution is added to methanol to precipitate the polymer. The polymer is isolated by filtration, washed with methanol, and dried at 100 C. under reduced pressure. The dried polymer is then dissolved in DMAc to give a solution containing approximately 10 wt % solids. The solids concentration can be adjusted to obtain an optimum solution viscosity for the film casting process used. After triglycidyl isocyanate (TGI) is added, the solution is cast into film.

Example 4

(25) This example illustrates the procedure for the preparation of a solution containing a copolymer of TPC, IPC, DADP, and PFMB (70%/30%/3%/97% mol ratio) containing 5 wt % triglycidyl isocyanate (TGI) (based on the weight of the polymer).

(26) To a 250 ml, three necked, round bottom flask, equipped with a mechanical stirrer, a nitrogen inlet and outlet, are added PFMB (3.1060 g, 0.0097 mol), DADP (0.0817 g, 0.0003 mol), and dried DMAc (45 ml) at room temperature under nitrogen. After the PFMB dissolves completely, IPC (0.6091 g, 0.003 mol) is added, and the flask wall is washed with DMAc (1.5 ml) to remove any adhering IPC. After 15 minutes, TPC (1.4211 g, 0.007 mol) is added and the flask wall is again washed with DMAc (1.5 ml). The solution slowly gels. After propylene oxide (1.4 g, 0.024 mol) is added, the mixture is vigorously stirred to break up the gel and yield a viscous, homogenous solution. The mixture is stirred for another 4 hours at room temperature. After triglycidyl isocyanate (TGI) (0.45 g) is added, the mixture is stirred for another two hours. The resulting solution can be directly cast into film.

Example 5

(27) This example illustrates the procedure for the preparation of a solution containing a copolymer of TPC, IPC, DAB, and PFMB (75%/25%/5%/95% mol ratio) containing 5 wt % triglycidyl isocyanate (TGI) (based on the weight of the polymer).

(28) To a 250 ml, three necked, round bottom flask, equipped with a mechanical stirrer, a nitrogen inlet and outlet, are added PFMB (3.0423 g, 0.0095 mol), DAB (0.0761 g, 0.0005 mol), and dried DMAc (45 ml) at room temperature under nitrogen. After the PFMB dissolves completely, IPC (0.5076 g, 0.0025 mol) is added, and the flask wall is washed with DMAc (1.5 ml) to remove any adhering IPC. After 15 minutes, TPC (1.5227 g, 0.0075 mol) is added, and the flask wall is again washed with DMAc (1.5 ml). The solution slowly gels. After propylene oxide (1.4 g, 0.024 mol) is added, the mixture is vigorously stirred to break up the gel and yield a viscous, homogenous solution. The mixture is stirred for another 4 hours at room temperature. After triglycidyl isocyanate (TGI) (0.45 g) is added, the mixture is stirred for another two hours. The resulting solution can be directly cast into film.

Comparative Example 2

(29) The polymer is prepared according to the procedure described in Example 16 without the addition of TGI.

Comparative Example 3

(30) The polymer is prepared according to the procedure described in Example 17 without the addition of triglycidyl isocyanate (TGI).

Comparative Example 4

(31) The polymer is prepared according to the procedure described in Example 18 without the addition of triglycidyl isocyanate (TGI).

(32) Preparation and Characterization of Polymer Films

(33) Using techniques known to those skilled in the art, the solids content and viscosity of the polymer solution can be adjusted for optimum film formation. For the preparation of small films, the solutions are poured on a flat glass plate, and the film thickness is adjusted using a doctor blade. After drying under reduced pressure at 60 C. for several hours, the film is further dried at 200 C. under protection of a dry nitrogen flow for 1 hour. The film is cured by heating at a temperature between approximately 220 C. and approximately 280 C. under vacuum or in an inert atmosphere. The film can also be produced continuously by a roll-to-roll process.

(34) In one embodiment of this invention, the polymer solution is cast onto a reinforcing substrate like thin glass, silica or a microelectronic device. In this case, the process is adjusted so that the final polyamide film thickness is approximately 4 m or more. The film is used in place and not removed from the substrate in free standing form. In some cases, the substrate may have an irregular and/or porous surface, such that the solution may level or penetrate the surface. Alternatively, the polymer solution can be cast on a carrier film such as polyethylene terephthalate. After the film is formed, it is stripped from the carrier film and laminated to a substrate like thin glass.

(35) The coefficient of thermal expansion (CTE) and glass transition temperature (Tg) are determined with a thermal mechanical analyzer (TA Q 400 TMA). The thickness of the film is around 20 m, and the load strain is 0.05N. In one embodiment, the coefficient of thermal expansion (CTE) is less than approximately 20 ppm/ C., but it is understood that in other embodiments, the coefficient of thermal expansion (CTE) is less than approximately 15 ppm/ C., less than approximately 10 ppm/ C., and less than approximately 5 ppm/ C. It is to be understood that within these embodiments the coefficient of thermal expansion (CTE) can be less than approximately 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, or 5 ppm/ C. The experimentally derived coefficient of thermal expansion (CTE) are the average of the coefficient of thermal expansion (CTE) obtained from room temperature to about 250 C.

(36) Film transparency is measured by determining the transmittance of a 10 m thick film from 400 to 750 nm with a UV-Visible spectrometer (Shimadzu UV 2450).

(37) The solvent resistance of the film is determined by immersing it in a selected solvent from DMAc, N-methylpyrrolidone (NMP), dimethyl sulfoxide (DMSO), etc., for 30 minutes at room temperature. The film is considered solvent resistant if it is substantially free of surface wrinkles, swelling, or any other visible damage after immersion. The films are useful as substrates for flexible electronic devices.

(38) The curing conditions used for the example copolyamides and the properties of their cross-linked films are shown in Table 3. The Table data illustrate the relative mild curing conditions and the beneficial effects of free pendant carboxyl groups on the polyamide on the curing process.

(39) TABLE-US-00003 TABLE 3 Curing Conditions and Film Properties Comparative Comparative Comparative Example 3 Example 4 Example 5 Example 2 Example 3 Example 4 Curing 250 C. 240 C. 220 C. Cannot be 330 C. 330 C. Conditions 10 minutes 5 minutes 5 minutes cured 5 minutes 10 minutes Tg ( C.) 325 327 335 336 334 350 CTE 4.0 6.2 4.6 7.4 7.0 12.0 (ppm/ C.) T % at 400 82 83 83 82% 80% 81% nm Solvent Yes Yes Yes No Yes Yes resistance

(40) The embodiments have been described, hereinabove. It will be apparent to those skilled in the art that the above methods and apparatus may incorporate changes and modifications without departing from the general scope of this invention. It is intended to include all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof. Although the description above contains much specificity, this should not be construed as limiting the scope of the invention, but as merely providing illustrations of some of the embodiments of this invention. Various other embodiments and ramifications are possible within its scope.

(41) Furthermore, notwithstanding that the numerical ranges and parameters setting forth the broad scope of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as possible. Any numerical value, however, inherently contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements.