Method for the manufacture of lightweight foam materials from crystalline thermoplastic materials and the resultant products

This application is directed to light-weight and hard foam materials. The foams of this invention are prepared by extruding thermoplastic crystalline plastics in the presence of highly volatile organic liquids as the foaming agents. In accordance with the present method crystalline polyolefins, in the presence of polybutadiene, ethylenevinylacetate copolymers, ethylene-propylenes and/or ethylene-propylene terpolymer rubbers, and optionally radical formers such as suitable peroxides, azidene, sulfonyl azidene or the like, and inhibitors for radical decomposition, such as triallylcyanurate or an acrylate selected from the group consisting of trimethylolpropane-trimethacrylate, allyl-methacrylate, tetrahydrofurfurylmethacrylate, triethyleneglycol-dimethacrylate, polyethyleneglycol-dimethacrylate or the like, are converted into foam-like molded bodies by means of a highly volatile organic liquid foaming agent. The foaming agent is employed in an amount of from about 5 to about 30% by weight, based on the weight of the polyolefins. The foaming agent and the polyolefins are mixed in an extruder at a temperature of from about 180.degree. to about 280.degree. C., and at a pressure which is greater than the vapor pressure of the foaming agent. The mixture is subsequently extruded.

FIELD OF THE INVENTION 
The present invention relates to a method for manufacturing light-weight 
foams which are also hard or tough, from crystalline thermoplastic 
(synthetic) materials. In accordance with the method of the present 
invention, light-weight foams are prepared by extruding a mixture of 
crystalline synthetic materials in the presence of a highly volatile 
organic liquid as the foaming agent. 
BACKGROUND OF THE INVENTION 
The manufacture of foams by extrusion foaming is known. However, known 
extrusion processes lead to relatively heavy and soft foam materials. Such 
foam materials are of limited utility for many applications, and are 
unsuited for applications where a high resistance to mechanical influences 
is required. 
Light-weight foam materials prepared by extrusion foaming are disclosed by 
DE-AS 17 94 025. The foams disclosed by this reference are soft and 
flexible. One disadvantage associated with these foams lies in their 
inability to resist compression. Moreover, the method of preparation 
disclosed by the cited reference calls for the use of very large amounts 
of physical foaming agents. Thus, there are disadvantages associated with 
the properties of the foams disclosed by DE-AS 17 94 025, as well as with 
the method of foam preparation disclosed by this reference. 
It is an object of this invention to provide a light-weight foam material 
which is also hard or brittle. Thus, the foams which are the subject of 
this invention combine the advantages of known light-weight foams such as 
polyolefin foams, with the desirable hard or brittle properties of other 
materials such as wood. 
BRIEF DESCRIPTION OF THE INVENTION 
This invention provides light-weight, but hard foam materials. The foams of 
this invention are prepared by extruding thermoplastic crystalline 
plastics in the presence of highly volatile organic liquids as the foaming 
agents. In accordance with the present method crystalline polyolefins, in 
the presence of polybutadiene, ethylenevinylacetate copolymers, 
ethylenepropylenes and/or ethylene-propylene terpolymer rubbers, and 
optionally; 
(a) radical formers such as suitable peroxides, azidene, sulfonyl azidene 
or the like, and 
(b) inhibitors for radical decomposition, such as triallylcyanurate or an 
acrylate selected from the group consisting of 
trimethylolpropane-trimethacrylate, allyl-methacrylate, 
tetrahydrofurfuryl-methacrylate, triethyleneglycol-dimethacrylate, 
polyethyleneglycol-dimethacrylate or the like, are converted into 
foam-like molded bodies by means of a highly volatile organic liquid 
foaming agent. The foaming agent is employed in an amount of from about 5 
to about 30% by weight, based on the weight of the polyolefins. The 
foaming agent and the polyolefins are mixed in an extruder at a 
temperature of from about 180.degree. to about 280.degree. C., and at a 
pressure which is greater than the vapor pressure of the foaming agent. 
The mixture is subsequently extruded. 
In accordance with the method of this invention, polyolefin foam materials 
with specific bulk gravities of from about 30 to about 200 kg/m.sup.3 are 
obtained. Such light-weight foam materials, which are at the same time 
hard and brittle, have heretofore been unknown to the art. 
DETAILED DESCRIPTION OF THE INVENTION 
Suitable crystalline polyolefins for use in accordance with the present 
method are the isotactic polypropylenes. Preferably, the polypropylenes 
are foamed in the presence of a polybutadiene, wherein the polybutadiene 
is present in an amount corresponding to from about 2 to about 20% by 
weight of the polypropylene and polybutadiene mixture. The mixture is 
foamed at a temperature of from about 140.degree. to about 180.degree. C. 
Suitable polybutadienes include the 1,4-polybutadienes, as well as the 
liquid 1,2-polybutadienes having molecular weights of from about 500 to 
about 10,000 g/mol, and having a 1,2-content of at least 35%, and 
preferably having a 1,2-content of from about 80 to about 95%. Preferred 
polybutadienes have a molecular weight of from about 1,000 to about 3,000. 
When polybutadienes such as those described above are employed, the product 
polypropylene foam materials may be cross-linked by means of high-energy 
radiation, such as by electron ray or gamma ray irradiation. The 
1,2-content of the polybutadienes has an influence on the cross-linking; 
that is, the higher the 1,2-content of the polybutadienes, the lower are 
the radiation doses required for cross-linking the foam for the same 
amount of polybutadiene. For example, in order to cross-link by electron 
irradiation a foam with a polybutadiene content of 10% by weight (based on 
the weight of the polypropylene), wherein the polybutadiene has a 
molecular weight of 3000 g/mol, and a 1,2-content of 95%, a dose of 5 Mrad 
is sufficient. An Mrad is defined as 10 (kilojoules of radiation/kilograms 
of material irradiated). The cross-linked product will have a gel content 
of about 70%, as determined in boiling xylol. The cross-linking process 
yields a foam material which is both mechanically and chemically 
resistant. 
In general, radiation doses of from about 0.5 to about 20 Mrads may be 
successfully employed for cross-linking the foam material. The dose 
selected depends upon the degree of cross-linking desired and the ultimate 
properties desired for the final cross-linked product. The higher the 
degree of cross-linking, the harder and more brittle the foam material 
becomes. 
Preferably, the isotactic polypropylenes are foamed in the presence of from 
about 0.1 to about 5.0% by weight of radical formers, and from about 0.1 
to about 10.0% by weight of radical decomposition inhibitors. 
Highly volatile organic liquids are suitable for use as the foaming agents 
of the present invention. Thus suitable foaming agents include highly 
volatile hydrocarbons, fluorocarbons, chlorocarbons, fluorochlorocarbons 
or the like. The foaming agents are employed in amounts corresponding to 
from about 5 to about 30% and preferably from about 10 to about 15% by 
weight, based on the weight of the polyolefin components. The foaming 
agent must be highly soluble in the polymer, and must be retained by the 
expanding polymer during the foaming process. This is particularly 
important for the manufacture of light-weight foam materials. If the 
necessary amount of foaming agent is not held fast and retained by the 
polyolefin mixture during the foaming process, although light-weight 
products are obtained for a short time after leaving the extruder, they 
collapse upon cooling down. This may be the reason that in the process 
described in DE-AS 17 94 025 relatively large amounts of foaming agent are 
required. The process disclosed by this reference requires about four- to 
five-times the amount of foaming agent, than is employed in accordance 
with the method of this invention. The use of small amounts of foaming 
agent called for by the present method lowers the overall cost of 
manufacturing the light-weight foam products of this invention. 
It is possible to foam crystalline polyolefins, such as the preferred 
isotactic polypropylenes, in the presence of polybutadienes by employing 
volatile solvents as foaming agents. It may be desirable, however, to 
modify the extrusion foaming process of this invention such that a mixture 
of high-molecular weight and branched polyolefins are obtained during the 
process, along with a simultaneous increase in the presence of 
low-molecular weight polyolefin components. Such mixtures are produced by 
reactions initiated by adding radical formers to the other reaction 
components, i.e., the crystalline polyolefin and the polybutadiene. Such 
radical formers include the peroxides, azides, sulfonyl azides and the 
like. When polypropylene is employed as the crystalline polyolefin, a 
further component must be added to the reaction mixture which prevents 
radical decomposition. Suitable radical decomposition inhibitors include 
acrylates such as trimethylolpropane-trimethacrylate, allyl-methacrylate, 
tetrahydrofurfuryl-methacrylate, triethyleneglycol-dimethacrylate, 
polyethyleneglycol-dimethacrylate and the like, as well as 
triallylcyanurate, or polybutadiene. The preferred polybutadiene is a 
1,2-polybutadiene having at least about a 35% 1,2-content. Inhibitors are 
recommended for use not only with the preferred isotactic polypropylenes, 
but also for use with other crystalline polyolefins, such as the 
polyethylenes. 
As a result of the use of the radical formers discussed above, radicals are 
formed on the polyolefin chains which are made to recombine only in part 
with other polyolefin chains. In this manner, an increase in the molecular 
weight of the polyolefins is achieved. The process is carried out only to 
the extent that a maximum of 5% by weight of gel components which are 
insoluble in boiling xylol are produced. Moreover, through the use of 
suitable reaction mixtures part of the polyolefin, and in particular the 
polypropylene, is decomposed such that a mixture of polyolefins is 
obtained. This mixture contains a broad distribution of branched and 
straight-chain polyolefins ranging from low-molecular weight to 
high-molecular weight polyolefin components. Such mixtures are described 
in Examples 1 to 6. 
Due to the branching, the molecular-weight distributions cannot be 
precisely determined. For the polypropylenes of Example 5, however, the 
molecular weight distribution spans a range of from about 1,000 to 
4,000,000 gm/mol, with a maximum between about 100,000 and about 200,000. 
About 4.1% by weight of the modified polypropylene of Example 5 had a 
molecular weight of from about 1,100,000 and about 9,000,000 gm/mol. Prior 
to the modification, only 0.05 weight % of the polypropylene had a 
molecular weight of from about 1,100,000 to about 2,000,000 gm/mol. In the 
low-molecular region, the weight share of the polypropylene of Example 5 
with a molecular weight of from about 600 to about 30,000 gm/mol was 
21.8%. The unmodified polypropylene, however, had only 11.9% by weight in 
the range of from about 3,700 to about 30,000 gm/mol. 
When radical former is not employed, it is preferred to employ polyolefins 
with a broad distribution of molecular weights. Broad molecular weight 
distributions are readily obtained by mixing polypropylenes of different 
molecular weights, as disclosed by Examples 7 and 8. It is also possible 
to employ polypropylenes which are commercially available in the form of a 
distribution of polypropylenes of various molecular weights. The use of 
such commercially available polypropylenes is disclosed by Example 9. 
However, under the same extrusion conditions, a finished foam material 
having a coarser pore pattern is obtained through the use of such 
commercially available polypropylenes, as compared to foam materials 
prepared from polypropylene mixtures prepared by mixing polypropylenes of 
different molecular weights. 
As shown by Example 10, it is necessary in all cases to use a polybutadiene 
and/or ethylenevinylacetate copolymer or ethylene-propylene or 
ethylene-propylene terpolymer rubber component. Preferably they are 
employed in amounts of 2 to 20 weight % relative to the weight of the 
polypropylene component. 
During the foaming process, the high-molecular polyolefins form a framework 
which prevents the forming foam from collapsing. The low-molecular weight 
components insure that the physical foaming agents are sufficiently 
soluble in the polyolefins. This facilitates the extrusion foaming process 
due to the fact that the extrusion can take place at temperatures lower 
than those employed by comparable processes. As low-molecular weight 
components, the 1,2-polybutadienes, in particular, fulfill this task with 
surprisingly good success. 
It is advisable to add the supplemental substances such as 
1,2-polybutadiene, between the charging opening of the extruder and about 
15 D. The preferred addition is made between 2 D and 5 D, i.e., through an 
inlet positioned at a length measured from the charging opening of between 
2 times and 5 times the diameter of the screw. 
In accordance with the method of this invention, lightweight polyolefin 
foam materials with specific bulk gravities below about 200 kg/m.sup.3 can 
be obtained through direct gas application, by means of customary machines 
such as single- or twin-screw extruders, or the so-called tandem systems. 
Through the modification of the starting materials described above, a 
considerable reduction in the amount of foaming agents employed is 
accomplished. Additionally, customary substances such as metal powders, 
pigments, azodicarbonamide and sodium bicarbonate with citric acid can be 
used as nucleation agents (pore regulators). 
The invention will be described further with reference to the following 
examples.

EXAMPLE 1 
100 parts by weight isotactic polypropylene with a density of 0.90, and a 
melting index MFI 230.degree. C./2.16 kg; 16 to 20 g/10 min are mixed with 
0.5 parts by weight azodicarbonamide, as the pore regulator, as well as 
with 0.8 parts by weight .alpha.,.alpha.'-bis (t-butylperoxy)p-isopropyl 
benzene, a radical former. The mixture is extruded at the rate of 10 kg of 
material per hour (10 kg/h) by a twin screw extruder (D=34, L (length)=38 
D), whereby beyond 5 D a liquid 1,2-polybutadiene with a molecular weight 
of 3000 g/mol is added at the rate of 0.4 kg/h. The temperature of the 
melt at the injection point is advantageously between about 180.degree. 
and about 220.degree. C. 
Beyond 15 D, monofluorotrichloromethane is injected at the rate of 0.8 kg/h 
into the melted polypropylene, which is at a temperature of about 
240.degree. C. 
During this process, the pressure must be higher than the vapor pressure of 
the monofluorotrichloromethane at the operating temperature of about 
240.degree. C. After the monofluorotrichloromethane has been added to the 
melt, the latter is cooled down in the extruder to 135.degree. C. After 
leaving the nozzle, the product foams up and produces a foam material with 
a specific bulk gravity of 100 kg/m.sup.3. 
EXAMPLES 2-6 
In accordance with the procedure of Example 1, foam materials with specific 
bulk gravities of from 30 to 200 kg/m.sup.3 are obtained employing the 
polypropylene of Example 1, in the formulations set forth in Examples 2-6 
of Table I. 
TABLE I 
__________________________________________________________________________ 
Specific Bulk Gravity 
Example 
Radical Former 
Nucleation 
Additive 
Foaming Agent 
of the Foam (Kg/m.sup.3) 
__________________________________________________________________________ 
2 0.4 wt. % .alpha.-.alpha.' 
0.5 wt % 
4 wt % Poly- 
5 wt % mono- 
200 
Bis(t-butylperoxy) 
Azodicarbon- 
butadiene, 
fluorotrichloro- 
p-diisopropylben- 
amide Molecular wt 
methane 
zene 3000 
3 0.6 wt % .alpha.-.alpha.' 
0.5 wt % 
4 wt % Poly- 
8 wt % mono- 
100 
Bis(t-butylperoxy) 
Azodicarbon- 
butadiene, 
fluorotrichloro- 
p-diisopropylben- 
amide Molecular wt 
methane 
zene 3000 
4 0.8 wt % .alpha.-.alpha.' 
0.5 wt % 
6 wt % Poly- 
10 wt % mono- 
50 
Bis(t-butylperoxy) 
Azodicarbon- 
butadiene, 
fluorotricarbon- 
p-diisopropylben- 
amide Molecular wt 
methane 
zene 3000 
5 0.8 wt % .alpha.-.alpha.' 
0.5 wt % 
5 wt % Poly- 
15 wt % mono- 
30 
Bis (t-butylperoxy) 
Azodicarbon- 
butadiene, 
fluorotrichloro- 
p-diisopropylben- 
amide Molecular wt 
methane and tri- 
zene 3000 fluorotrichloro- 
ethane (1:1) 
6 0.8 wt % .alpha.-.alpha.' 
0.5 wt % 
7 wt % Poly- 
15 wt % mono- 
30 
Bis(t-butylperoxy) 
Azodicarbon- 
butadiene, 
fluorotrichloro- 
p-diisopropylben- 
amide Molecular wt 
methane and tri- 
zene 3000 fluorotrichloro- 
ethane (1:1) 
__________________________________________________________________________ 
The foams produced by this method having a specific bulk gravity of 50 
kg/m.sup.3 can withstand a compression load of 47 N/cm.sup.2. Such foams 
are deformed by only about 2 mm, and break down above 47 N/cm.sup.2. N 
refers to one Newton or 10.sup.5 dynes. 
Gal-chromatography examination of the polypropylene of Example 5 showed the 
presence of 4.1 weight % polypropylene with a molecular weight in the 
range of 1,100,000 to 9,000,000 gm/mol. The starting polypropylene 
reactant contained less than 0.05 weight % polypropylene with a molecular 
weight above about 1,100,000 gm/mol. The weight average of the molecular 
weight of the starting polypropylene was 200,000 gm/mol. The weight 
average of the molecular weight of the modified polypropylene was 236,000 
gm/mol. 
EXAMPLE 7 
30 parts by weight of a polypropylene with an average molecular weight of 
200,000 gm/mol are mixed with 40 parts by weight of a polypropylene with 
an average molecular weight of 400,000 gm/mol, as well as with 20 parts by 
weight of a polypropylene with an average molecular weight of 640,000 
gm/mol, and 10 parts by weight of a propylene with an average molecular 
weight of 800,000 gm/mol; 0.2 parts by weight azodicarbonamide is added to 
this mixture. 
The mixture is extruded at the rate of 10 kg/h via a twin-screw extruded 
(D=34, L=28 D), where beyond 5 D, liquid 1,2-polybutadiene with a 
molecular weight of 3000 g/mol is added at the rate of 1 kg/h. 
Beyond 15 D, monofluorotrichloromethane and trifluorotrichloroethane (mixed 
1:1) are injected at the rate of 1.4 kg/h into the melted polypropylene at 
a temperature of about 250.degree. C. During this process, the pressure in 
the melt must be higher than the vapor pressure of the 
monofluorotrichloromethane, at a temperature of about 250.degree. C. After 
the monofluorotrichloromethane/trifluorotrichloroethane mixture has been 
added to the melt, the latter is cooled in the extruder down to about 
155.degree. C. 
After leaving the nozzle, the product foams up and yields a foam material 
with a specific bulk gravity of 40 kg/m.sup.3. 
The foam material produced in this manner can be crosslinked with electron 
rays at a dose of 6 Mrad to the extent that the gel content in boiling 
xylol is 80%. 
EXAMPLE 8 
30 parts by weight of a polypropylene with an average molecular weight of 
200,000 gm/mol are mixed with 40 parts by weight of a polypropylene with 
an average molecular weight of 400,000 gm/mol, as well as with 30 parts by 
weight of a polypropylene with an average molecular weight of 800,000 
gm/mol. 0.2 parts by weight of azodicarbonamide is added to this mixture. 
The mixture is extruded at the rate of 10 kg/h via a twin-screw extruder 
(D=34, L=28 D). Beyond 5 D, liquid 1,2-polybutadiene with a molecular 
weight of 3000 g/mol is added at the rate of 1 kg/h. Beyond 15 D, 
monofluorotrichloromethane and trifluorotrichloroethane (mixed 1:1) are 
injected into the melted polypropylene at a rate of 1.4 kg/h, which is at 
a temperature of about 250.degree. C. The pressure of the melt must be 
higher than the vapor pressure of the monofluorotrichloromethane at a 
temperature of about 250.degree. C. After the 
monofluorotrichloromethane/trifluorotrichloroethane mixture has been 
added, the melt is cooled in the extruder down to 155.degree. C. After 
leaving the nozzle, the product foams up, and yields a foam material with 
a specific bulk gravity of 40 kg/m.sup.3. 
EXAMPLE 9 
100 parts by weight of a polypropylene with an average molecular weight of 
400,000 gm/mol is reacted with 0.2 parts by weight azodicarbonamide. 
The mixture is extruded at the rate of 10 kg/h, via a twin-screw extruder 
(D=34, L=28 D). Beyond 5 D, liquid 1,2-polybutadiene with a molecular 
weight of 3000 g/mol is added at the rate of 1 kg/h. Beyond 15 D, 1.4 kg/h 
of monofluorotrichloromethane and trifluorotrichloroethane (mixed 1:1) are 
injected into the melted polypropylene which is at about 250.degree. C. 
The pressure in the melt must be higher than the vapor pressure of the 
monofluorotrichloromethane at a temperature of about 250.degree. C. After 
the monofluorotrichloromethane/trifluorotrichloroethane mixture has been 
added, the melt is cooled down to 155.degree. C. in the extruder. After 
leaving the nozzle, the product foams up and yields a foam material with a 
specific bulk gravity of 40 kg/m.sup.3. 
EXAMPLE 10 
The polypropylene mixture of Example 8 was extruded under the same 
conditions as described in Example 8, but without the addition of 
polybutadiene. The foam material obtained had a specific bulk weight of 
only about 650 kg/m.sup.3. 
EXAMPLES 11-13 
Following the procedure of Example 9, foam materials having specific bulk 
weights of 80 and 100 kg/m.sup.3 are obtained by employing the 
formulations of Examples 11-13. 
TABLE II 
__________________________________________________________________________ 
Weight % and Average Specific Bulk 
Molecular Weight Foaming 
Gravity of the 
Example 
of the Polypropylene 
Nucleation 
Additive Agent Foam (Kg/m.sup.3) 
__________________________________________________________________________ 
11 30 wt % 200 kg/mol 
0.2 wt % 
2 parts by 
15 wt % 
100 
40 wt % 400 kg/mol 
Azodicarbon- 
weight, poly- 
monofluoro- 
30 wt % 800 kg/mol 
amide butadiene, 
trichloro- 
molecular wt 
methane and 
3000 g/mol 
trifluoro- 
trichloro- 
ethane (1:1) 
12 as per Example 11 
0.2 wt % 
5 parts by 
15 wt % 
80 
Azodicarbon- 
weight, poly- 
monofluoro- 
amide butadiene, 
trichloro- 
molecular wt 
methane and 
3000 g/mol 
trifluoro- 
trichloro- 
ethane (1:1) 
13 as per Example 11 
0.2 wt % 
20 parts by 
15 wt % 
100 
Azodicarbon- 
weight, monofluoro- 
amide ethylene- 
trichloro- 
propylene- 
methane and 
copolymer (EPM) 
trifluoro- 
trichloro- 
ethane (1:1) 
__________________________________________________________________________ 
EXAMPLE 14 
100 parts by weight polyethylene (density 0.96; melting index MFI 
190.degree. C./5 kg; 4 g/10 min) are mixed with 0.5 parts by weight 
azodicarbonamide, a pore regulator, as well as with 0.1 parts by weight 
dicumylperoxide, a radical former. The mixture is extruded at the rate of 
10 kg/h in a twin-screw extruder (D=34, L=28 D), where beyond 5 D a liquid 
polybutadiene with a molecular weight of 3000 g/mol is added at the rate 
of 0.4 kg/h. 
Beyond 15 D, monofluorotrichloromethane is injected into the melted 
polyethylene which is at a temperature of approximately 200.degree. C. at 
the rate of 1.4 kg/h. The pressure in the melt must be higher than the 
vapor pressure of the monofluorotrichloromethane at a temperature of 
200.degree. C. After the monofluorotrichloromethane has been added to the 
melt, the latter is cooled in the extruder down to 90.degree. C. After 
leaving the nozzle, the product foams up and yields a foam material with a 
specific bulk gravity of 50 kg/m.sup.3. 
EXAMPLES 15-18 
Table III sets forth the specific bulk gravities of foams obtained by 
employing the polyethylene of Example 14 and the formulations of Examples 
15-18. The preparative procedure followed is that of Example 14. 
TABLE III 
__________________________________________________________________________ 
Specific Bulk Gravity 
Example 
Radical Former 
Nucleation 
Additive 
Foaming Agent 
of the Foam (Kg/m.sup.3) 
__________________________________________________________________________ 
15 0.2 wt % 0.2 wt % 
-- 10 wt % mono- 
80 
dicumylperoxide 
azodicarbon- fluorotrichloro- 
amide methane 
16 0.1 wt % 0.2 wt % 
0.2 wt % 
18 wt % mono- 
30 
dicumylperoxide 
azodicarbon- 
polybutadiene 
fluorotrichloro- 
amide molecular 
methane 
weight 3000 
17 0.05 wt % 
0.2 wt % 
0.6 wt % 
14 wt % mono- 
50 
dicumylperoxide 
azodicarbon- 
polybutadiene 
fluorotrichloro- 
amide molecular 
methane 
weight 3000 
18 0.2 wt % 0.2 wt % 
0.1 wt % 
8 wt % mono- 
100 
dicumylperoxide 
azodicarbon- 
polybutadiene 
fluorotrichloro- 
amide molecular 
methane 
weight 3000 
__________________________________________________________________________ 
This invention has been described in terms of specific embodiments set 
forth in detail herein. It should be understood, however, that these are 
by way of illustration only and that the invention is not necessarily 
limited thereto. Modifications and variations will be apparent from this 
disclosure and may be resorted to without departing from the spirit of 
this invention, as those skilled in the art will readily understand. 
Accordingly, such variations and modifications of the disclosed 
embodiments are considered to be within the scope of this invention and 
the following claims.