The present invention relates to a polymer including a fullerene core and a plurality of prepolymer units. Each of the prepolymer units is linked to a carbon atom of the core by a moiety independently selected from the group consisting of --O--(C.dbd.O)--NH--, --NH--(C.dbd.O)--NH--, --0--(C.dbd.S)--NH--, and --N--(C.dbd.S)--NH--.

BACKGROUND OF THE INVENTION 
Fullerenes are a class of carbon molecules having an even number of carbon 
atoms arranged in the form of a closed hollow cage, typically spheroid, 
wherein the carbon-carbon bonds define a polyhedral structure. 
Fullerene monolayers have been described. See, e.g., K. Chen, et al. J. Am. 
Chem. Soc., 115 (1993) 1193 (the self-assembled monolayer (SAM) of 
covalently bonded fullerenes on (MeO).sub.3 Si(CH.sub.2).sub.3 NH.sub.2 
-modified oxide surfaces), and in W. B. Calwell, et al. Langmuir, 9 (1993) 
1945 (SAM on HS(CH.sub.2)NH.sub.2 -modified gold surfaces). 
Similarly, some fullerenes with relatively small functional groups or 
addends such as amido, alkoxy, and halides have been described. See, e.g., 
U.S. Pat. No. 5,177,248; European Application No. 546,718 (treatment of 
unfunctionalized fullerenes with trifluoromethanesulfonic acid and 
nucleophiles to form alkoxylated fullerenes); European Application No. 
575,129 (treatment of unfunctionalized fullerenes with sulfuric acid to 
form sulfated fullerenes). 
However, few macromolecules have been attached to fullerenes. K. L. Wooley, 
et al. (J. Am. Chem. Soc., 115 (1993) 9836) attached two dendritic (highly 
branched, fan-shaped) polyphenylethers to a bifunctionalized fullerene 
with an ether linkage. A broad mixture of products with between 1 and 10 
polystyrene chains attached was obtained from reacting unfunctionalized 
fullerenes with living polystyrene (carbon-carbon linkage) (E. T. 
Samulski, et al., Chem. Mater., 4 (1992) 1153). Unfunctionalized fullerene 
have also been grafted with some cross-linking to an amine-containing 
linear polymer (carbon-nitrogen linkage) (A. O. Patil, et al., Polymer 
Bull., 30 (1993) 187). 
SUMMARY OF THE INVENTION 
One aspect of the present invention relates to a polymer which contains at 
least one fullerene core and a plurality of prepolymer units bonded to the 
fullerene core. More specifically, each of the prepolymer units is linked 
to a carbon atom of the core by a linking moiety M.sup.1 in the manner of 
F--M.sup.1 --P, wherein F represents the fullerene core, P represents one 
of the prepolymer units, and M.sup.1 is independently selected from the 
group consisting of --O--(C.dbd.O)--NH--, --NH--(C.dbd.O)--NH--, 
--O--(C.dbd.S)--NH--, and --NH--(C.dbd.S)--NH--; a carbon atom of the core 
being bonded to the left-terminal oxygen or nitrogen atom of M.sup.1 and 
the right-terminal nitrogen atom of M.sup.1 being bonded to a carbon atom 
of each of the prepolymer units. Thus, the embodiments of the invention 
include polyurethane fullerene polymers, polythiourethane fullerene 
polymers, polyurea fullerene polymers, polythiourea fullerene polymers, 
and mixed polymers, e.g., poly(urea-urethane) fullerene polymers. The 
polymers derive from the multiplicity of prepolymer units which are bonded 
to the fullerene core, and each prepolymer unit may in addition be 
connected end-to-end to another prepolymer unit. 
The term "fullerene core" refers to a fullerene, such as C.sub.60, 
C.sub.70, C.sub.76, C.sub.80, C.sub.84, or C.sub.120, which may be 
substituted with an alkyl, alkoxy, aryl, or organocarboxy group of between 
1 and 20 carbon atoms, and which may also be functionalized with amino, 
hydroxy or other groups not bonded to a prepolymer unit. The term "a 
plurality of prepolymer units" or the like in this disclosure is meant to 
include between 2 and 32. Examples include ranges such as 2-24, 2-16, 
4-12, and 6-10; or numbers such as 6, 7, and 10, where the number or range 
is an average number of, e.g., prepolymer units per fullerene core. This 
number or range is determined by methods well-known to those skilled in 
the art; an example of such a method is provided below in Example 4. One 
preferred embodiment of this invention has an average of 6 prepolymer 
units per C.sub.60, with a relatively narrow distribution range. One 
embodiment of this invention has a polydispersity of 1.45. 
The prepolymer unit P may have, for example, the formula --R.sup.1 
--M.sup.2 --R.sup.2 --M.sup.3 --R.sup.3 --X, wherein R.sup.1 and R.sup.3 
are each, independently, a hydrocarbon moiety of 1 to 20 carbon atoms, 
which is bonded to the right-terminal nitrogen atom of M.sup.1 and 
M.sup.3, respectively. M.sup.2 is selected from the group consisting of 
--NH--(C.dbd.O)--O--, --NH--(C.dbd.O)--NH--, --NH--(C.dbd.S)--O--, and 
--NH--(C.dbd.S)--NH--. As indicated by the formula, the left-terminal 
nitrogen atom of M.sup.2 is bonded to the right-terminal carbon atom of 
R.sup.1, and so on. R.sup.2 is a polymeric moiety selected from the group 
consisting of poly(tetramethylene oxide), poly(ethylene oxide), 
poly(butadiene), poly(isoprene), poly(hydrogenated butadiene), 
poly(hydrogenated isoprene), polyester, polyethylene, polycarbonate, 
polyamide, polyurethane, polyurea, polyanhydride, polyimide, polyacrylate, 
polymethacrylate, and polysiloxane. M.sup.3 is independently selected from 
the group consisting of --O--(C.dbd.O)--NH--, --NH--(C.dbd.O)--NH--, 
--O--(C.dbd.S)--NH--, and --NH--(C.dbd.S)--NH--. X is a moiety selected 
from the group consisting of --NH--(C.dbd.O)--O--, --NH--(C.dbd.O)--NH--, 
--NH--(C.dbd.S)--O--, --NH--(C.dbd.S)--NH--, --N.dbd.C.dbd.O, and 
--N.dbd.C.dbd.S. X may also be selected from --NH--(C.dbd.O)--O--Y, 
--NH--(C.dbd.O)--NH--Y, --NH--(C.dbd.S)--O--Y, and --NH--(C.dbd.S)--NH--Y, 
wherein Y is hydrogen, or a hydrocarbon moiety of 1 to 20 carbon atoms. 
The hydrocarbon moiety mentioned in this disclosure may be substituted or 
unsubstituted; saturated or unsaturated; acylic, cyclic, or polycyclic. 
Note that the orientation of each of the above moieties is understood to 
be that as drawn. Preferred embodiments include those where M.sup.1 and 
M.sup.3 are both --O--(C.dbd.O)--NH--, and M.sup.2 is 
--NH--(C.dbd.O)--O--and X is --NH--(C.dbd.O)--O-- or 
--NH--(C.dbd.O)--O--Y; where M.sup.1 and M.sup.3 are both 
--O--(C.dbd.S)--NH--, and M.sup.2 is --NH--(C.dbd.S)--O-- and X is 
--NH--(C.dbd.S)--O-- or --NH--(C.dbd.S)--O--Y; where R.sup.1 and R.sup.3 
are each 4,4'-methylene diphenyl; where X is --N.dbd.C.dbd.O or 
--N.dbd.C.dbd.S; or where R.sup.1 is 4,4'-methylene diphenyl, R.sup.2 is a 
polymeric moiety of poly(tetramethylene oxide), and R.sup.3 is 4,4' 
methylene diphenyl. In another embodiment, X is preferably 
--NH--(C.dbd.O)--O--, --NH--(C.dbd.O)--NH--, --NH--(C.dbd.S)--O--, or 
--NH--(C.dbd.S)--NH--, where a second fullerene core is bonded to X; or is 
--N.dbd.C.dbd.O, --N.dbd.C.dbd.S, --NH--(C.dbd.O)--O--Y, 
--NH--(C.dbd.O)--NH--Y, --NH--(C.dbd.S)--O--Y, or --NH--(C.dbd.S)--NH--Y. 
An example of the polymer described in the preceeding paragraph is a sole 
fullerene core with a plurality of prepolymer units bonded thereto; in 
other words, the fullerene core is not linked to other fullerene cores. In 
another embodiment, a fullerene core is linked to at least one other core, 
e.g., via a prepolymer unit. In this latter case, moiety X is 
--NH--(C.dbd.O)--O--, --NH--(C.dbd.O)--NH--, --NH--(C.dbd.S)--O--, or 
--NH--(C.dbd.S)--NH--, and the right-terminal oxygen or nitrogen atom of X 
is bonded to a carbon atom of the second fullerene core. The first 
fullerene core may be thus linked to a plurality of satellite fullerene 
cores, which in turn may also be linked to additional fullerene cores. 
As will be described in more detail below, methods of preparing such 
polymers are also within the invention. 
Prepolymer units increase the intermolecular interaction among functional 
groups bonded to either the same or different fullerene cores; thus 
polymers of the present invention are not only suitable for the 
manufacture of viscosity modifiers and other rheological applications, but 
also serve as superior crosslinking agents for the preparation of polymer 
networks and for the manufacture of elastomers, as well as other polymer 
applications known to those skilled in the art. 
Other features and advantages of the present invention will be apparent 
from the following description of the preferred embodiments, and also from 
the appending claims.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
The present invention relates to fullerene derivatives which include one or 
more fullerene cores and at least two, and preferably three or more, 
prepolymer units linked to each fullerene core. The prepolymer units are 
linked to the fullerene cores via the linking moieties 
--O--(C.dbd.O)--NH--, --NH--(C.dbd.O)--NH--, --O--(C.dbd.S)--NH--, and 
--NH--(C.dbd.S)--NH--. These moieties are identical to those found in 
urethane, urea, thiourethane, and thiourea, respectively. 
The present invention includes a polymer containing a fullerene core not 
linked to other fullerene cores. As an example, each C.sub.60 core on 
average is linked to at least two prepolymer units, wherein a carbon atom 
of the core is bonded to, e.g., the left-terminal oxygen of the linking 
moiety --O--(C.dbd.O)--NH--. In this example, the right-terminal nitrogen 
of the linking moiety is bonded to a carbon atom of a prepolymer unit. 
A prepolymer unit can be a simple hydrocarbon moiety of the formula 
--C.sub.n H.sub.2n+1, where n .dbd.2-100. A prepolymer unit can also be a 
large hydrocarbon group (substituted or unsubstituted) of at least 25 
carbon atoms, and can contain polymeric or repeating moieties, or both. 
The prepolymer unit can also be a complex macromolecule of over 200 carbon 
atoms (e.g., over 400 carbon atoms). For example, a complex prepolymer 
unit may contain several linking moieties which connect individual 
hydrocarbon moieties to each other, or to polymeric segments. The linking 
moieties within the prepolymer unit may be, for example, 
--O--(C.dbd.O)--NH--, --NH--(C.dbd.O)--NH-- or --NH--(C.dbd.O)--O--, or 
any other moieties which are different from the linking moieties which 
connect prepolymer units to fullerene cores. The polymeric segments may 
contain one or more repeating units, and may contain one or more types of 
monomers. An example of a polymeric segment is a poly(tetramethylene 
oxide) segment with more than 40 repeating units. As with other 
embodiments of the invention, the prepolymer units linked to any single 
fullerene core may be the same or different, and may be linked by the same 
or different linking moieties. Persons of skill in the art will be able to 
determine whether a composition of more similar fullerene polymers or a 
mixture of varied fullerene polymers is more appropriate for a particular 
application. 
In addition to the prepolymer units, the fullerene core may have 
functionalities such as hydroxyl or amino, or substitutions such alkoxy or 
alkyl, which are not linked to a prepolymer unit, e.g., C.sub.60 
(--OH).sub.6-8 [--O--(C.dbd.O)--NH--(n-dodecyl)].sub.6, and the polymer 
(3) prepared in Example 3 below. Methods of preparing polyfunctionalized 
fullerenes, e.g., polyhydroxylated, polyaminohydroxylated, and 
polyaminated fullerenes, are described, for example, in U.S. Pat. No. 
5,177,248 (hydroxy), and U.S. Pat. No. 5,294,732 (amino, hydroxy, and 
aminohydroxy). Additional methods can be found in L. Y. Chiang, et al., J. 
Chem. Soc., Chem. Comm. (1992) 1791; L. Y. Chiang, et al., J. Am. Chem. 
Soc., 115 (1993) 5453; L. Y. Chiang, et al., J. Am. Chem. Soc., 114 (1992) 
10154; and L. Y. Chiang, et al., J. Org. Chem., 59 (1994) 3960. Methods of 
preparing substituted fullerene cores are described, for example, in 
European Application No. 0 546 718 and in U.S. Pat. No. 5,177,248. 
The present invention also includes a polymer made of linked fullerene 
cores. For example, a fullerene core has a plurality of prepolymer units 
which are each (i) linked at one end to that core and (ii) linked at the 
other end to "end-capping" fullerene cores. In this example, both linkages 
are via one or more of the above-described linking moieties. In a somewhat 
different embodiment, one or more of the prepolymer units are not 
end-capped by fullerene cores. The end-capping fullerene cores may have 
additional functional groups, substitutions, or even additional prepolymer 
units, attached to them. 
The present invention also includes two fullerene cores connected by more 
than one prepolymer unit. In one example, two fullerene cores may be 
connected to each other by more than one prepolymer unit, with the 
distance between the two fullerene cores being no more than approximately 
one prepolymer unit. In another example, two fullerene cores can be 
connected by a linear (end-to-end) or branched formation of two or more 
prepolymer units, with the distance between two fullerene cores being 
approximately 1.5 or 2 (or more) prepolymer units. The intervening linking 
moieties between such linear or branched prepolymer units may be any 
moiety. As noted above, the prepolymer units may be the same or different. 
The present invention also includes a fullerene core which is crosslinked 
to more than one other fullerene core. For example, each fullerene core 
might be bonded to an average of 4-8 other fullerene cores to form an 
extended, continuous polymer network. A second fullerene core may be 
selected, independently from the first fullerene core, from C.sub.60, 
C.sub.70, C.sub.76, C.sub.80, C.sub.84, and C.sub.120. Furthermore, the 
second fullerene core may be polyfunctionalized or substituted as 
described above, in addition to being linked to prepolymer units. 
The present invention also encompasses processes for the attachment of a 
plurality of polymeric arms to a fullerene core. This process includes 
obtaining a polyfunctionalized fullerene having functional groups 
independently selected from amino and hydroxy, obtaining a polymeric 
reagent having a functional group selected from isocyanate and 
thioisocyanate, reacting fullerene with the polymeric reagent, and 
separating the reaction product from the reaction mixture. 
The term "polyfunctionalized fullerene" is meant to include a fullerene 
having between 2 and 32 functional groups, independently selected from the 
group consisting of amino and hydroxy. For example, the nitrogen atom of 
an amino group is bonded to a carbon atom of the fullerene; similarly, the 
oxygen atom of the hydroxy group is bonded to a carbon atom of the 
fullerene. Examples of polyfunctionalized fullerenes include C.sub.60 
(--OH).sub.10-12, C.sub.60 (--OH).sub.14-15, C.sub.60 (--OH).sub.18-20, 
C.sub.60 (--OH).sub.10-12 (NH.sub.2).sub.6-8, C.sub.60 
(--NH.sub.2).sub.10-12 and C.sub.70 (--OH).sub.24. 
The term "a functional group selected from" in "a polymeric reagent having 
a functional group selected from the group consisting of isocyanate and 
thioisocyanate" is meant to include a reagent having one or more 
functional groups, e.g., one, two, or three, which are independently 
selected from the group consisting of isocyanate and thioisocyanate. 
Examples include alkyl and aryl diisocyanates and dithiocyanates. 
In one such process, the mole ratio of the hydroxyl and amino groups on the 
fullerene to the thioisocyanate and isocyanate groups on the polymeric 
reagent is between 1:2 and 1:20 (e.g., 1:10). In another such process, the 
mole ratio of the groups on the fullerene to the groups on the polymeric 
reagent is between 10:1 and 1:1. In the present invention, mole ratios are 
understood to encompass measurements or amounts within twenty percent of 
the designated ratio. In another embodiment, the present invention further 
includes adding a substituted or unsubstituted alcohol after the reacting 
step. Examples include (i) an alcohol having between 1 and 20 carbon atoms 
such as 1-dodecanol or 2,2'-dichloroethanol, and (ii) a polyfunctionalized 
hydrocarbon such as fullerene which is polyaminated, 
polyaminohydroxylated, or polyhydroxylated, such as C.sub.60 (-13 
OH).sub.6-8. The present invention includes the products produced by 
processes disclosed herein, and the processes, according to the methods 
described herein, to make the products disclosed herein. In addition, the 
present invention includes final products made from products disclosed 
herein. 
Polymeric arms or addends include both a linking moiety and one or more 
macromolecular substituents or prepolymer units. The polymeric chains or 
polymeric arms may be radially arranged with respect to the geometric 
center of the core; they may be spaced evenly across the surface to form a 
three-dimensional star polymer, or they may be grouped, for example, near 
opposite poles. 
The polymeric reagents of this invention include the reaction products of 
(a) an alkyl or aryl isocyanate compound, or an alkyl or aryl 
thioisocyanate compound, such 4,4'-methylene diphenyl diisocyanate or 
4,4'-methylene diphenyl dithiocyanate, and (b) a polyalcohol, e.g., a 
diol, e.g., poly(tetramethylene oxide) glycol, poly(ethylene oxide)glycol, 
poly(butadiene) diol, poly(isoprene) diol, poly(hydrogenated butadiene) 
diol, poly(hydrogenated isoprene) diol, polyester diol, polyethylene diol, 
polycarbonate diol, polyamide diol, polyurethane diol, polyurea diol, 
polyanhydride diol, polyimide diol, polyacrylate diol, polymethacrylate 
diol, polysiloxane diol, and mixtures thereof. In one preferred 
embodiment, the diol is poly(tetramethylene oxide) glycol. The isocyanate 
compound is 4,4'-methylene diphenyl isocyanate in another preferred 
embodiment. Note that an excess of the diisocyanate or dithioisocyanate 
polymeric reagent is preferably used in a mole ratio of (number of 
hydroxyl and amino groups) to (number of isocyanate and thiocyanate 
groups) between 1:2 and 1:20 to form non-crosslinked polymers. The 
polymeric reagents are thiocyanate or isocyanate prepolymers. 
A hydrocarbon moiety as in, for example, R.sub.1, R.sub.2, and X, refers to 
substituted, e.g., halogenated, or unsubstituted moieties, having between 
1 and 20 carbon atoms, saturated or unsaturated, acylic, cyclic, or 
polycyclic. Nonlimiting examples include n-dodecyl, methylene diphenyl, 
napthyl, and polyethylene. 
One embodiment of the present invention is the final reaction product of 
(A) an alcohol having between 1 and 20 carbon atoms and (B) the reaction 
product of (i) a polyfunctionalized fullerene and (ii) the polymeric 
reagent being the reaction product of (a) 4,4'-methylene diphenyl 
diisocyanate or 4,4'-methylene diphenyl dithiocyanate and (b) a diol 
selected from the group consisting of poly(tetramethylene oxide) glycol, 
poly(ethylene oxide)glycol, poly(butadiene) diol, poly(isoprene) diol, 
poly(hydrogenated butadiene) diol, poly(hydrogenated isoprene) diol, 
polyester diol, polyethylene diol, and polycarbonate diol. 
A preferred embodiment of this invention is the final reaction product of 
(a) 1-dodecanol and (b) the reaction product of (i) polyhydroxylated 
fullerenes and (ii) the polymeric reagent being the reaction product of 
4,4'-methylene diphenyl diisocyanate and poly(tetramethylene oxide)glycol, 
wherein the mole ratio of hydroxy groups on said polyhydroxylated 
fullerenes to isocyanate groups on said polymeric reagent is between 1:2 
and 1:20, e.g., 1:10, to form said reaction product of (i) and (ii). 
Another preferred embodiment of this invention is the reaction product of 
(i) polyhydroxylated fullerenes and (ii) the prepolymer reaction product 
of 4,4'-methylene diphenyl diisocyanate and poly(tetramethylene 
oxide)glycol, wherein the mole ratio of hydroxy groups on the 
polyhydroxylated fullerenes to isocyanate groups on the prepolymer 
reaction product is between 10:1 and 1:1 to form said polymer. 
Without further elaboration, it is believed that one skilled in the art 
can, based on the description herein, utilize the present invention to its 
fullest extent. The following specific embodiments are, therefore, to be 
construed as merely illustrative, and not limitative of the remainder of 
the disclosure in any way. All references cited herein are hereby 
incorporated by reference. 
EXAMPLE 1 
A four-necked reaction vessel (500 mL) equipped with a stainless-steel 
stirrer was charged with 4,4'-methane diphenyl diisocyanate (MDI, 11.9 g) 
and poly(tetramethylene oxide) glycol (PTMO, M.sub.n =2,000, 47.6 g). The 
reagent mixture was stirred at 60-60.degree. C. under N.sub.2 for a period 
of 4h. At the end of reaction, the unreacted 4,4'-methane diphenyl 
diisocyanate was removed from reaction product by washing 5.times.50 mL 
with acetonitrile (5 times, 50 mL each time) under N.sub.2. Acetonitrile 
washings were removed by syringe. Drying under vacuum yielded 
diisocyanate-capped urethane polyether prepolymer (1) (46.3 g). 
EXAMPLE 2 
Preparation of the diisocyanate prepolymer 2 was carried out by the 
reaction of poly(tetramethylene oxide) glycol (PTMO) with 4,4'-methane 
diphenyl diisocyanate (MDI, 2.0 equiv.) in CDCl.sub.3 at 60.degree. C. 
under N.sub.2 for 10 hours. The average molecular weight of 
poly(tetramethylene oxide) glycol was determined by gel permeation 
chromatography (GPC) calibrated with a PTMO standard to be M.sub.n =2,000 
and M.sub.w =4,500 with a polydispersity of 2.25. The progress of the 
reaction monitored by the decreasing intensity of the infrared band at 
3480 cm.sup.-1, corresponding to the hydroxyl absorption. 
EXAMPLE 3 
The condensation reaction between the prepolymer 2 and polyfunctionalized 
fullerene 1 was performed in a mixture of anhydrous THF and DMF (3:1) at 
60.degree. C. under N.sub.2 for 16 h. To completely eliminate the 
cross-linking reaction, an excess of diisocyanated urethane polyether 
prepolymers 2 (10 equiv. of isocyanate for each hydroxy on fullerenol) was 
used. 
After 16 hours, the mixture was allowed to react further with 1-dodecanol. 
Bis(1-dodecanoxy) poly(urethane ether) 4, (the byproduct resulting from 
the reaction of 1-dodecanol with the unreacted prepolymer 2, was removed 
by repeated precipitation of the final product from the THF solution into 
methanol, followed by washing with a mixture of THF and methanol. The 
corresponding C.sub.60 urethane polyether star-polymer 3 was isolated as 
soluble, highly viscous brownish-red semi-solids in high yield (more than 
15 times the weight of the starting fullerenol was obtained). 
As anticipated, the infrared spectrum of the star-polymer product 3 closely 
resembled that of bis(1-dodecanoxy) poly(urethane ether) prepolymer 4, 
showing the disappearance of a band at 2272 cm.sup.-1 corresponding to the 
isocyanate absorption, as well as the disappearance of a baud at 3550 
cm.sup.-1 hydroxyl absorptions. The conversion of isocyanate functional 
groups into urethanes moieties was evident through an observation of a 
band at 3300 cm.sup.-1 and a strong band at 1733 cm.sup.-1 corresponding 
to the urethanic --NH-- and carbonyl absorptions, respectively. 
EXAMPLE 4 
The molecular weight of star-polymer 3 was determined mainly by its GPC 
spectrum (using toluene as eluent) and confirmed by the light scattering 
measurements. In the GPC study, the spectrum was calibrated by the 
polystyrene standards. To ensure and examine the suitability and accuracy 
of calibration by the linear styrene oligomers, two star model compounds 
were synthesized. Compound 5 contained three urethane polyether arms and 
compound 6 contained four urethane polyether arms. These model compounds 
were obtained by the reaction of the diisocyanated urethane polyether 
prepolymer 2 with triethanolamine or pentaerythritol, respectively, 
following by quenching with 1-dodecanol. 
The GPC spectra of oligomers 5 and 6 indicated an average molecular weight 
of M.sub.n 9,260 (M.sub.w 15,200 with a polydispersity of 1.64) and 
M.sub.n 12,600 (M.sub.w 20,300 with a polydispersity of 1.61), 
respectively. These data are consistent with a material having roughly 
three and four times, respectively, the molecular weight of 
bis(1-dodecanoxy) poly(urethane ether) 4 (M.sub.n 2,600 and M.sub.w with a 
polydispersity of 2.11). Thus, the average molecular weight of 3 was 
determined to be M.sub.n 18,000 and M.sub.w 26,100, which corresponds to a 
fullerenol-based star polymer with an average of six urethane polyether 
arms. 
Most significantly, the polydispersity (1.45) of 3 is notably narrower than 
that of the single polymer chain 4 (2.11). The only way to increase the 
number of polymer arms randomly bonded to a star polymer without 
increasing the polydispersity is to restrict the number of polymer arms to 
a fairly narrow, uniform distribution. The phenomena occurs in both the 
model polymer 5 (polydispersity equals 1.64) and 6 (polydispersity equals 
1.61), both with a structure containing a fixed number of polymer arms. 
The GPC data also demonstrated that the polydispersity value of the star 
polymers having a fixed number of polymer arms tends to be lower than that 
of the parent polymer arm alone. 
EXAMPLE 5 
The average number of repeating tetramethylene PTMO units in structures 3, 
4, 5, and 6 was also determined by .sup.1 H NMR spectroscopic study. The 
chemical shift of two types of aromatic protons in the MDI-derived 
urethane moieties can be readily identified at .gamma. 7.08 (d, J=10 Hz) 
and 7.28 (d, J=10 Hz). The intensity of each group of peaks corresponds to 
8 protons in one polymer arm as shown in Scheme I. Therefore, the value of 
integration ratio between these aromatic protons and the oxygenated 
methylene protons (at .gamma.3.40) or the non-oxygenated methylene protons 
(at .gamma. 1.62) in the PTMO moieties allows an accurate estimation of 
the average molecular weight of PTMO. As a result, each PTMO segment was 
found to contain 42 tetramethylene repeating units. This indicates an 
average molecular weight in poly(urethane ether) 4 for each polymer arm as 
3,920 or 3,790 Daltons, respectively, which is between M.sub.n (2,600) and 
M.sub.w (5,450) of 4. Furthermore, this analysis results in the 
determination of the average molecular weight of 3 as 2.4.times.10.sup.4 
Dalton. 
EXAMPLE 6 
One unexpected physical property of star polymer 3 is its unusual thermal 
behavior at low temperatures. Although the molecular weight of 3 is 6 
times that of the linear poly(urethane ether) 4, the glass transition 
temperature (T.sub.g) of 3 was found to be -67.degree. C., only slightly 
higher than that of 4 (-71.degree. C.), 5 (-70.degree. C.), and 6 
(-69.degree. C.) calculated from the DSC (differential scanning 
calorimetry) profiles. There was a systematic, gradual increase in the 
glass transition temperature from the linear structure of 4 to 5 
(three-armed star) and 6 (four-armed star) and then to the six-armed star 
polymer 3. 
EXAMPLE 7 
With respect to the PTMO chain softening temperature, all four polymers 
were found to turn into a paste-like material upon heating in a similar 
temperature range at 21.degree. C. (34.3 J/g), 22.degree. C. (45.3 J/g), 
23.degree. C. (43.5 J/g), and 23.degree. C. (42.7 J/g) for 3, 4, 5, and 6, 
respectively. All four polymers also showed similar thermal properties in 
the recrystallization of oligomeric PTMO chains after heating. While the 
linear polymer 4 had a more intense recrystallization transition at 
-25.degree. C. (45.0 J/g), the other star polymers 3, 5, and 6 exhibited 
only a moderate to weak transition at -31.degree. C., -29.degree. C., and 
-31.degree. C., respectively. These profiles indicate that each polymer 
arm on the C.sub.60 molecule reacts independently to temperature 
fluctuations in a manner similar to the parent linear polymer 4. Due to 
the star shape of 3, 5, and 6, the ability of polymer arms to 
recrystallize decreases significantly. 
EXAMPLE 8 
A four-necked reaction vessel (500 mL) equipped with a stainless-steel 
stirrer was charged with 4,4'-methane diphenyl diisocyanate (MDI, 11.9 g) 
and poly(tetramethylene oxide) glycol (PTMO, M.sub.n =2,000, 47.6 g). The 
reagent mixture was stirred at 60.degree.-60.degree. C. under N.sub.2 for 
a period of 4h. At the end of reaction, the unreacted 4,4'-methane 
diphenyl diisocyanate was removed from reaction product by washing 
5.times.50 mL with acetonitrile (5 times, 50 mL each time) under N.sub.2. 
Acetonitrile washings were removed by syringe. Drying under vacuum yielded 
diisocyanate-capped urethane polyether prepolymer (46.3 g). 
A reaction flask A (250 mL) connected with a condenser and an inert gas 
bubbler was charged with diisocyanate-capped urethane polyether prepolymer 
(25 g), anhydrous tetrahydrofuran (90 mL, distilled over sodium), and 
dimethylformamide (10 mL, dried over molecular sieves). The mixture was 
stirred at ambient temperature until complete resolution of 
isocyanate-capped urethan polyether prepolymer. In a separate reaction 
flask B (50 mL), polyhydroxylated fullerene derivatives (fullerenols, 
1.5g) was dissolved in dimethylformamide (25 mL) and the solution was 
dried over 4.ANG. molecular sieves for 2 days. The fullerenol solution in 
flask B was then added into the reaction flask A. The resulting mixture 
was stirred at 60.degree.-65.degree. C. for 16h under N.sub.2. The 
solution became a gel within 5 hours of reaction. The solvent was allowed 
to evaporate slowly under N.sub.2 to afford a rubbery film. The film was 
suspended in methanol and treated briefly in a ultrasonic bath at ambient 
temperature for 30 minutes. Removal of methanol and drying under vacuum at 
60.degree. C. yielded the product fullerenol-crosslinked polyurethane 
networks (23 g). 
EXAMPLE 9 
The preparation of polymer-networks was carried out by the treatment of 
fullerenol 1, C.sub.60 (OH).sub.10-12, with diisocyanated urethane 
polyether prepolymer 2 (1.0 equiv. of isocyanate to each hydroxy on 
fullerenol) in a mixture of anhydrous THF and DMF (3:1) at 60.degree. C. 
under N.sub.2 for 16 hours. Diisocyanated prepolymer 2 was prepared by the 
reaction of poly(tetramethylene oxide) glycol (PTMO) with 4,4'-methane 
diphenyl disocyanate (MDI, 2.0 equiv.) in CDCl.sub.3 at 60.degree. C. 
under N.sub.2. The average molecular weight of poly(tetramethylene oxide) 
glycol used was determined to be M.sub.n 2,000 and M.sub.w 4,500 with a 
polydispersity of 2.25. Prior to the isocyanate-hydroxyl condensation 
reaction, the fullerenol was predried under vacuum at 60.degree. C. for 
24h. Water was removed from the reaction medium by drying the DMF-THF 
solution over molecular sieves (4.ANG.) for 2 days. Progress of the 
reaction was monitored by the decreasing intensity of the hydroxyl 
absorption band at 3480 cm.sup.-1. Gradual gel formation was observed 
during the first few hours of reaction. At the end of the reaction, the 
residual isocyanate functionalities were quenched with methanol under 
ultrasonic treatment. After the solvent evaporation and the subsequent 
drying in vacuum, the corresponding [C.sub.60 ] fullerenol cross-linked 
polyurethane 7 was isolated as a thick, free-standing film. 
The infrared spectrum of the cross-linked fullerenol polyurethane product 7 
showed the disappearance of a band around 2272 cm.sup.-1 corresponding to 
the isocyanate absorption and the sharp decrease of hydroxyl absorptions 
centered at 3550 cm.sup.-1. The conversion of isocyanate functions into 
urethanes was evident through an observation of a band at 3300 cm.sup.-1. 
The conversion of isocyanate functions into urethanes was evident through 
an observation of a band at 3300 cm.sup.-1 and strong band at 1733 
cm.sup.-1 corresponding to the urethanic --NH-- and carbonyl absorptions, 
respectively. 
EXAMPLE 10 
The thermal behavior of highly cross-linked polyurethane 7 at low 
temperatures is remarkable. To facilitate the correlation of physical 
properties of 7 to its linear polymer version, bis(1-dodecanoxy) 
poly(urethane ether) 4 was synthesized from the reaction of 1-dodecanol 
(2.0 equiv.) with the diisocyanate prepolymer 2 at 60.degree. C. 
Interestingly, the glass transition temperature of 7 was found to be 
-70.degree. C., very similar to that of 4 (-71.degree. C.), as shown in 
the DSC profiles. Thermal properties of both the PTMO chain softening 
behavior and recrystallization of 7 upon heating at 7.degree. C. and 
-32.degree. C., respectively, were detected at temperatures much lower 
than those of 4 at 22.degree. C. and -25.degree. C. respectively. These 
observations suggest that each polyurethane chain chemically attached on 
C.sub.60 molecules in polymer network 7 behaves independently under 
temperature fluctuation. 
EXAMPLE 11 
The thermal mechanical properties of 7 were studied using a flat-point 
probe. An enlargement of the polymer's dimension was observed at an onset 
temperature of -70.degree. C. which is consistent with its glass 
transition temperature. This thermogram contained by a region with nearly 
constant polymer dimensions at temperatures between -33.degree. C. and 
-20.degree. C., where the recrystallization transition of 7 occurs. The 
PTMO chain softening transition at roughly 5.degree. C. induced a sharp 
increase in polymer dimension before the linear thermal expansion at 
higher temperatures. Furthermore, the thermal penetration of polymer film 
by probe under a constant force of was not appeared until temperature 
reaching about 191.degree. C. 
EXAMPLE 12 
A reaction flask A (250 mL) equipped with a condenser and an inert gas 
bubbler was charged with diisocyanate-capped urethane polyether prepolymer 
(25 g, excess) or monoisocyanate-capped urethane polyether prepolymer 25g, 
anhydrous tetrahydrofuran (90 mL, distilled over sodium), and 
dimethylformamide (10 mL, dried over 4.ANG. molecular sieves for 2 days. 
The fullerenol solution in flask B was then added to the reaction flask A 
at ambient temperature. The resulting mixture was stirred at 
60.degree.-65.degree. C. for 16h under N.sub.2. At the end of reaction, 
1-dodecanol (4.0 g) was added to form the urethan functionalities at each 
isocyanate-capped prepolymer chain-end while temperature was maintained at 
60.degree. C. After 1h, the reaction products were washed repeatedly with 
a mixture of methanol and tetrahydrofuran (3:1) and dried under vacuum at 
60.degree. C. Fullerene-based star-shaped poly(urethane-ether) was 
obtained as a dark-brown semi-solid (2.3 g). 
Other Embodiments 
From the above description, one skilled in the art can easily ascertain the 
essential characteristics of the present invention, and without departing 
form the spirit and scope thereof, can make various changes and 
modifications of the invention to adapt it to various usages and 
conditions. Thus, other embodiments are also within the claims.