Studies have demonstrated versatility of PMR approach for tailor making polyimide matrix resins with side range of flow characteristics. By simply adjusting molar ratio of reactants in monomer mixture, resins having flow values of as much as 20% can be achieved

Serafini, T. T.

Vannucci, R. D.

English

NASA Technical Reports Server

20 
15 
9 10 
i-n LU
0 
1.0	 1.2	 1.4	 1.6	 1.8	 2.0 
MOLES OF DIMETHYL ESTER, n
July 1975	 B75-1.0137 
NASA TECH BRIEF 
Lewis Research Center 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield, Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Office, NASA, Code KT, Washington, D.C. 20546. 
Tailor Making High Performance 
Graphite Fiber Reinforced PMR Polyimides 
.
The effectiveness of the in situ polymerization of 
monomer reactants (PMR) approach for preparing high 
temperature fiber-reinforced polyimide composites for use 
at 589 K (600°F) has been demonstrated (see Notes) In 
the PMR approach, the reinforcing fibers are impregnated 
with a solution containing a mixture of the following 
monomers: (a) a dimethyl ester of an aromatic tetra-
carboxylic acid, (b) an aromatic diamine, and (c) the 
monomethyl ester of a dicarboxylic acid. The molar ratio 
of a:b:c is n:(n+l):2. The monomers are essentially 
nonreactive at room temperature but react in situ at 
elevated temperatures forming thermally stable poly-
imides. 
The polyimide matrix resin having the best overall 
balance of properties at 589 K (600°F) is prepared from a 
mixture of dimethyl ester of 3,3'-4,4'. 
benzo phenone te tra-carboxylic acid, 4,4'-methylene 
diamine and the monomethyl ester of 5-norbornene .2,3-
dicarboxylic acid in which n = 2.087. This resin exhibited 
lower flow values (3%) than normally obtained with 
epoxy resins (as much as 24%). 
Recent studies have demonstrated the versatility of the 
PMR approach for tailor making polyimide matrix resins 
with a wide range of flow characteristics (see figure). By 
simply adjusting the molar ratio of the reactants in the 
monomer mixture, resins having flow values of as much as 
20% can be achieved. Moreover, the higher flow value 
PMR resins have use temperatures up to 561 K (5500F), 
which is nearly 366 K (200°F) above the use temperature 
for epoxies. For example, after 600 hours exposure at 561 
K (550°F), graphite fiber reinforced laminates made from 
these high flow PMR polyimides exhibited excellent 
strength and weight retention (70-78% strength retention 
and less than 4% composite weight loss). 
Notes: 
1. This process can be applied to the fabrication of 
compressor fan blades, guide vanes and cowls for jet 
engines, as well as centrifugal impellers and other 
aerospace or commercial structures requiring high 
quality, high temperature resin matrix composite con-
struction. 
2. The PMR polyimides were previously described in 
NASA Tech Briefs 71-10442, "Thermally Stable Poly-
imides from Solutions of Monomeric Reactants," and 
73 . 10014, "Technique for the Polymerization of 
Monomers for PPQ/Graphite Fiber Composites." 
3. Further information about this process is available in 
the following reports: 
NASA TM-X-71616 (N74-34960), Tailor Making 
High Performance Graphite Fiber Reinforced PMR 
Polyimides 
NASA TN-D-6877 (N72-29598), Addition Type 
Polyimides from Solutions of Monomeric React-
ants 
Copies may be obtained at cost from: 
Aerospace Research Applications Center 
Indiana University 
400 East Seventh Street 
Bloomington, Indiana 47401 
Telephone: 812.337.7833 
Reference: B75-10137 
4. Specific technical questions may be directed to: 
Technology Utilization Officer 
Lewis Research Center 
21000 Brookpark Road 
Cleveland, Ohio 44135 
Reference: B75-10137
(continued overleaf) 
This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Patent Status: 
NASA has decided not to apply for a patent. 
Source: T.T. Serafini and R.D. Vannucci

Lewis Research Center
(LEW- 12416)
. 
is 
. 
B75-10137	 Category 04


Tailor making high performance graphite fiber reinforced PMR polyimides

Studies performed to demonstrate the feasibility of using the polymerization of monomer reactants (PMR) approach to tailor make processable polyimide matrix resins are described. Monomeric reactant solutions containing the dimethyl ester of 3,3',4,4' -benzophenonetetracarboxylic acid, 4, 4' -methylenedianiline and the monomethyl ester of 5-norbornene-2, 3-dicarboxylic acid were used to impregnate Hercules HTS graphite fiber. Six different monomeric reactant stoichiometries were studied. The processing characteristics and elevated temperature mechanical properties of the PMR polyimide/HTS graphite fiber composites are described

NASA TECHNICAL NASATMX-71616
MEMORANDUM
--_ (_'5A-TS-Z-71616) IA[_CR _AKING HiGH N7;-34960
_ F-_FOEM_NC_- G_A_BI °_; ?!BEP ?EINFO_CED P_
r_m _6_I_I=ES (NASA) 13 o _C $3.(9
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G3/18 51163
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TAILORMAKINGHIGHPERFORMANCE
GRAPHITEFIBERREINFORCEDPMRPOLYIMIDES
by T. T. Serafini and R. D. Vannucci '..x
Lewm Research Center "
Cleveland, Ohio 44135
TECHNICAL PAPER proposed for presentationat .-
ThirtielhA.-:',ualReinforcedPlasticComposites
, Conference sponsored by the Society of the Plastics Industry
" Washipgton, D C., February 4-7, 1975
1974026847
https://ntrs.nasa.gov/search.jsp?R=19740026847 2020-03-23T02:43:34+00:00Z
TAILOR MAKING HIGH PERFORMANCE
GRAPHITE FIBER REINFORCED PMR POLYIMIDES
by T. T. Serafim and R. D. Vannucci
Lewis Research Center
, ABSTRACT
Studies performed to demonstrate the feasibility of using the
polymerization of monomer reactants (PMR) approach to "tailor
make" p:'ocessable polyimide matrLx resins are described. Mono-
meric reactant solutions containing the dimethyl ester of 3, 3'. 4.4' -
benzophenonetetracarboxylic acid, 4, 4'-methylenedianilhle and the
monomethyl ester of 5-norbornene-2, 3-dicarboxylic acid were used
to impregnate Hercules HTS graphite fiber. Six different monomeric
reactant stoichiometries were studied. The processing characteris-
tics and elevated temperature mechanical properties of the PMR
polyimide/HTS graphite fiber composites are described.
INTRODUCTION
The resins currently being used as matrices in the vast majority
of advanced fiber composites are epoxy resins. Fiber reinforced
epoxy resins can easily be processed into a variety of hardware items.
However, the upper use temperature of epoxies is limited to a max-
imum of 350 ° F. In addition, the elevated temperature mechanical
properties of graphite fiber/epoxs, composites are degraded during
long-term exposure of the composites to humid environments.
Therefore, a matrix resin needs to be developed which has the pro-
cessability of epoxies, higher use temperatures than epoxies and
greater moisture resistance than epoxies.
Prior studies conducted in our laboratories (refs. 1 to 3) and else-
where (ref. 4) have demonstrated the effectiveness of PMR (iv situ polym-
erization of monomer reactant_ on the surface of remforcin,._ fibers)
1974026847-002
methodol,)gy for preparing high temperature reststant llber reinforced
l:olymer alatrix composites. These earher studies (refs. 1 to 4} were
concerned with the development of composites for continuous use in air
at 600 ° F. Theretore, monomer compositions and st_tch_ometrles
were selected which would lead to addnlon-type polyim_des hawng the
best over-all balance of processabihty and thermo-oxldatlve stability.
The trade-off between processing charactermt_cs and thermo-oxldative
stability necessitated using monomer compositions and stoichlometries
which provided lower flow characteristics than normally obtained from
epoxy resins. The _tudies reported In reference 2 showed that PMR
methodology is a facile method tor introducing molecuiar structural
variations into the polymer matrix. The monomer composlt:ons and
stoichimetries previously studied provided a fairly broad range of pro-
perties together with moderate varmtlons in flow charactermtics.
Therefore, it is hypothesized that the PMR approach can be used to
select monomer compositions and or stmchiometr_es which provide
higher flow polyimides for use at temperatures well above the upper
use temperature of epoxy resins.
This report describes a study to establish the vahdlty of the afore-
said hypothesis. If the hypothesis is proven to be correct, then it
should be possible to use the laMR approach for the "'tailor making" of
polyimide matrices-
Composites were fabricated from Hercules HTS graphne fiber and
PI based on the monomers 5-norborene-2.3-d_carboxyhc acid mono-
methyl ester (NE), dimethyl ester of 3, 3". 4.4"-benzophenonetetracar-
boxylic acid (BTDE) and 4, 4' -methylened_amlL_e (MDA;. Form-
ulated molecular weights (FMW) m the range of 1000 to 1500 were in-
vestigated. Resin flow characteristics and composite properties were
determined. Composite mechamcal properties were determined at
room temperature, 450 ° and 550 ° F. Composite weight loss and me-
chanical properties retention eharactermtics as a function of exposure
time and elevated temperature were also determined.
1974026847-003
EXPERIMENTAL PROC EDURE
Monomeric Reactant Solutions
The monomers used in tills study are shown in table [ The mono-
methyl ester of 5-norbornene -2.3-dlcarboxylic acid (NE) and 4.4:-
methylenedianiline (MDA) were obtained from commercml sources.
The dimethyl ester of 3, 3', 4, 4'-benzophenonetetracarboxylic acid (BTDE)
was synthezised by refluxing a suspension of 3, 3". 4.4" -benzophenonetetra-
carboxylic dianhydriae (96.6 g, 3, 00>,10 "1 mole) m anhydrous methanol
(1"/0 ml) until the solid had dissolved (2 to 3 hr) and then for an additional
hour, resulting in a 50 weight percent BTDE/methanol solution. Reac-
tant solutions were prepared at a solids loading of 50 weight percent in
methanol. The stoichiometry ol the reactants was governed by the de-
sired formulated molecular weight.
Composite Fabricatmn
Prepreg tapes were made by drum winding and impregnating Her-
cules HTS graphite fiber with the various solutions of monomer_c reac-
tants to yield prepregs that centained 45.5 percent monomers and 54.5
percent fiber by weight. The prepreg. _ made from monomer solutions
were air dried on the drum at room temperature for 1 hour
and then 2 hours at 120 ° F to reduce the solvent content to approximately
10 percent by weight. After this treatment, the prepregs remained flex-
ible, but not tacky. The prepreg tapes were then removed irom the drum,
cut into 3 by 10 inch plies and stacked unidirectionally, 9 plie_ thick, into
a preforming mold. The stacked prepreg was staged at 400 ° F for 2 hours
under an applied pressure of 0.3 psi. Composites were then molded by
placing the staged prepreg into a matched metal die preheated to _00 ° F.
Follcwing a dwell time, which ranged from 45 to 90 seconds, 1000 psi was
applied for 60 minutes. After curing, the coml_]sltes were post-cured by
placing them directly into a 600 ° F oven for 16 hours. Resin floyd,was de-
termined by weight difference prior to final cure and after the cure with
resin flash removed.
1974026847-004
Composite Testing
Prior to specimen preparati_)nall laminates were inspected using
the ultrasonic C zcan technique (ref.5). Flexural strength tests were
performed using a 3 point loading fixturewith a fixed span of 2 inches.
The thicknesses of the laminates ranged from 0.070 inch to 0.090 inch.
The resultant span/depth ratio used ranged from 22 to 28. The rate of
center loading/or fiexural testingwas 0.05 inch/rain. Interlaminar
shear strength tests were conducted at a constant span/depth ratio of 5.
Elevated temperature tests were performed in an environmental heat-
ing chamber. For the flexuraland shear tests the load was applied
after a 15 minute soak at the testtemperature. Forced convection air
ovens were used for the long-term isothermal exposure at 450° and
550° F. Composite weight measurements were made throughout the
exposure time period. The at1 change rate was I00 cubic centimeters
per minute.
The properties data presented are averages of 3 or more testsat
eac_ ,_ondition.Fiber content was determined for alllaminates and
ranged from 53 to 65 volume percent. For flexuraltests allresults
were normalized to 55 volume percent fiber.
RESULTS AND DISCUSSION
The monomeric reactant stoichiometrles used in thlsstudy are glven
in table II. The number of moles of the monomeric reactants m each of
the monomeric solutionswas governed by the following ratio:
n:(n+l):2
Where n, (n + I) and 2 are the number of moles of BTDE, MDA and
NE, respectively. The formulated molecular weight (FMW) given in the
table is considered to be the average molecular weight of the imidized
prepolymer that could have been formed ffamide-acid prepolymer had
been synthesized. The equation for FMW is:
1974026847-005
FMW = n l%9_VBTDE+ (n+ I)MWMD A
+ 2 MWNE - 2(n +1) MWH20 + MWcH30 H (1)
where MWBTDE, MWMD A etc. are the molecular weights of the in-
dicated reactants and by-products. It is now common practice to de-
note the stoichiometry of a PMR resin made from BTDE, MDA and
NE as PMR FMW/100. For example, PMR 15 denotes the polyimide
prepared from BTDE, MDA and NE with the stoichiometry adjusted
so that the FMW = 1500.
The effect of FMW on percent resin flow is shown in figure 1. It
can be seen that the resin flow increased significantly (from 3 to 20
percent) as the FMW was decreased from 1500 to 1000. These results
clearly show that the resin flow characteristics of PMR polymides can
be varied over a wide range or "tailor made" to meet specific require-
ments. It is important to note that ultrasonic C scan examination of the
laminates revealed them to be void free. The resin flow results show
the sensitivity of resin flow to imide ring content. As the number of
imide rings was decreased by 33 percent (from 6 rings to 4) in going
from PMR 15 to PMR 10, the resin flow increased by nearly 600 percent.
Figure 2 shows the variation of percent resin weight loss as a func-
tion of matrix FMW for PMR/HTS graphite fiber composites after expo-
sure in air for 600 hours at 450 ° and 550 ° F. The results show that all
of the PMR composites exhibited excellent thermo-oxidative stability
(TOS) at 450 ° F. The resin weight loss at 450°F for the higher resin
flow PMR compositions (PMR 10 to PMR 13) was less than 2 percent.
At 550 ° F the resin weight loss of PMR compositions in the FMW range
of 1000 to 1400 was appreciably higher than for PMR 15. Earlier studies
(ref. 2) identified PMR 15 as the PMR polyimide matrix resin possessing
the best over-all balance of processing characteristics and 600 ° F TOS.
The superior TOS of PMR 15 at temperatures in the range of 550 ° to
600 ° F can be attributed to the low alicyclic content of PMR 15 as shown
in table II. The percentage of alicyclic ,naterial is given by the follow-
ing equation:
1974026847-006
21MWNE - (MWcooH MWcoocH3) ] "_ 100
Percent alicyclic (2)
Fh_/
Where MWcooH a_',d MWcoocH3 are the molecular weights of car-
boxyl and methyl ester groups, respectively.
The resin flow and weight retention data presented in figures 1 and
2 support the hypothesis that the PMR approach can be used to select
monome-:- stGichiometrles which provide high flow PMR polyimides for
use at temperatures above the use temperature for epoxy resins. Iso-
thermal gravimetric analysis data are not sufficient to permit specifi-
cation of a material's upper use temperature. It is more important to
consider the material's retention of mechanic_.l p,-operties after extended
exposure at elevated temperatures and to compare these data to design
requirements.
The variation of composite flexural strength for the various PMR
compositions reinforced w_th Hercules HTS graphite fiber as a function
of FMW is shown in figure 3. Results are shown for specimens tested
at room temperature and at 450 ° and 550 ° F after short-term (15 min)
exposure in air at the indicated test temperature.
The room temperature flexural stre,,gth ranged from 223 000 psi
at an FMW of 1000 to 200 000 psi at an FMW of 1500. It is important
to note that at 450 ° and 550 ° F the composites exhibited excellent re-
tention of ro,.m temperature flexural stre,_th throughout the FMW
range i_vestlgated. The retention levels at 450 ° F ranged from 75 to
88 percent and at 550 ° F from 70 to 78 percent. In contrast the highest
retention level at 350 ° F for graphite fiber/epoxy composites is gen-
erally considered to be 55 percent.
It can be seen in figure 3 that the room temperature, 450 ° and
550 ° F properties decreased as FMW was increased. The influence
of matrix modulus and ultimate strength on composite flexural strength
was discussed in reference 6. Because the cure of PMR polym_ides
involves a complex addition reaction of the alicyclic chain-ends result-
ing in chain extension and cross-linking, resin matrices having decreased
cross-link densities, and therefore, decreased moduli result from in-
creases in FMW. The room temperature results reflect the effect of
1974026847-007
matrix modulus. The 450 ° and 550 ° F results reflect the combined
effects of matrtx modulus and temperature.
Figure 4 shows the varmtion c_f room temperature. 450 ° and
550 ° F (short-ti.,ne) interlammar shear strength (ILSS) with FMW.
It was pointed out in reference 6 that composde ILSS Is strongly
influenced by the modulus, proportional limit strain and ultimate
strength of the matrix. Therefore. it can be speculated that the
variation of ILSS with FMW at any given temperature reflects the
net effect of the various matrix propertms. The more important
point to be made is that the composites retained a h_gh level of
ILSS at 450 ° and 550 ° F throughout the range of FMW investi-
gated. The ranges for tht. retention levels at 450 ° and 550 ° F
were 66 to 75 percent and 57 to 61 percent, respectively.
Figures 5 and 6 show the variation of flexural strength and
ILSS, respectively, with exposure time (maximum of 600 hours)
for PMR 10 graphite f_ber composites exposed and tested at 450 °
and 550 ° F. Data showing the effects of isathermal exposure on
flexural strength and ILSS were also collected for the PMR graphite
fiber composites made from the other FMW compositions. It can
be seen in figures 5 and 6 that the PMX 10 composites exhibited
excellent retention of mechanical properties throughout the 600 hour
exposure time. Similar retentmn characteristms were displayed
by the other graphite fiber reilfforced PMR compositions.
In figure 7 the short-time (15 rain) elevated temperature proper-
ties are compared with the long-time (600 hr) elevated temperature
properties over the ra,lge of FMW. The data from the tests conducted
at 450 ° F are shown in figures 7a and 7b for flexural strength and
ILSS, respectively. Figures 7c and 7d show the results from the tests
conducted at 550 ° F.
The comparisons presented m figure 7 clearly illustrate the
superior elevated temperature properties retentmn characteristics of
the PMR polyimide matmx resins at temperatures up to 550 ° F. With
tl'e exception of the data from the FMW composltmns of 1000 and 1100
the short-time and h)ng-time data for a gwen prope, ty and temperature
are quite comparable. By comparing figure 7awlth figure 7b it can
also be seen thai the 450 ° and 550 ° F propt ctms do not differ appreciably.
1974026847-008
The mechanical property data, together with the resip flow and
weight retention characteristics have, in our opinion, established
the validity oi the hypothesis that the PMR app-.'oach can be used to
"tailor make" high flew polyimides with higher use temperatures than
epoxy resins.
C ONC L UDING RE MARKS
Tke in situ polymerization of monomer re ctants (PMR) approach
can be used to "tailor make" fiber reinforced addition-type polyimides
ha_ing specified resin flow characteristics and excellent retention of
mechanical properties after Icng-term exposure in air in the 450 ° to
5._C° F temperature range. By adjusting the monomeric reactant stoi-
chiometry the resin flow characteristics can be varied over a wide
range and in this way a product can be achieved which meets specific
requirements. The PMR compositions investigated in this study pro-
vided flow values in the range of 3 to 20 percent. After 600 hours of
exposure at 450 ° or 550 ° F the composite properties determined at the
exposure temperature were comparable to the short-time elevated
temperature properties. The short-time elevated temperature pro-
perties_ in turn, compared favorably with room temperature proper-
ties.
The excellent processability and thermo-oxidative stability Gf high
flow PMR polyimides suggests that these materials have excellent po-
tential as matrix resins both within and above the use temperature
range of epoxy resins.
i
1974026847-009
9RE FE RENC ES
1. Serafini, T. T. ; Delvigs, P. ; and Lightsey, G. R. : Thermally
Stable Polyimides from Solutions of Monomeric Reactants.
J. appl. Polym. Sci., vol. 16, no. 4, Apr. 1972, pp. 905o915.
2. Delvigs, Peter; Serafini, Tito T. ; and Lightsey, George R. :
Addition-Type Polyimides from Solutions of Monomer Reactants.
NASA TN D-6877, 1972.
3. Serafini, T. T. ; Delvigs, P. ; and Vannucci, R. D. : In Sltu
Polymerization of Monomers for Polyphenylquinoxaline/Graphite
Fiber Composites. The Wide World of Reinforced Plastics,
Proc. 29th Soc. Plastics Industry Conf., Washington, D.C.,
Feb. 5-8, 1974, pp. 16-A,1 to 16-A,6.
4. Cavano, P. J. : Resin/Graphite Fiber Composites. (TRW-ER-7581F,
TRW Equipment Labs. ; NASA Contract NAS3-15829. ) NASA
CR-121275, 1974.
5. Ultrasonic Immersion Tests. Nondestructive Testing Handbook,
Vol. 2, Sec. 46, R. C. McMaster, ed., Ronald Press Co., 1963.
6. Chamis, C. C.; Hanson, M. P. ; and Serafini, T. T. : Criteria for
Selectlng Resin Matrices for Improved Composite Strength.
Rei_dorced Plastics - Ever New, Proc. 28th Soc. Plastics Industry
Conf., Washington, D.C., Feb. 6-9, 1973, pp. 12-C, 1 to 12-C, 12.
1974026847-010
TABLE I. - MONOMERS USED FOR POLYIMIDE SYNTHESIS
Structure Name Abbreviati()n__
O
C -OMe
Mo,_omethvl ester of 5-norbornene- 'L! 2, 3-dlcarbo:yhe acid
. C-OH
E,
O
O O
il p
MeO-C O C-OMe
C Dimethyl ester of 3,3', 4,4' -benzophenone- BTDE
• tetracarboxylic acid
HO-C C-OH
N H
0 0
_D
_q
H2N CH 4, 4'-Methvlenedmmhne MDA!
TABLE II. - MONOMER STOICHIO/vIETRY
Formulated Moles of BTI)E,a Percent
molecular (n) ahcyelic
we,ght content !
I000 1 054 9.20
II00 1 260 8.37
1200 1.465 7 67
1300 1. 672 _, 08
1400 1. 880 6.57
1500 2.087 6.13 ]
aMolar ratio of BTDE/MDA/NE equals
n:(n+l):2
1974026847-011
, "_ _o _- _,._'_
,_ _ E '_ "_, _
_-58 ,,.,85 =
_o _o_
I :_ '" _1 _"
cKi
IN33_3d'MO]_NIS3_ ISd 'HlgN:I_IIS]','anx]]_
1974026847-012
220x103
_ 180 _ 4500 F
6 o5500F
x I L I I I I
_- o loo 2oo 3oo 4oo _oo 6oo 7oo
TIME.HR
Ftgure 5. - Flexu,al strength of FMVV10OOPt,IRPI/I-ffSgraphite hber compos-
ttesexposedand testedat 450o and 5500F.
14)103
_g
L,q (_.
cc_
--8 o5500E
_- 6 1 I I I I I I
0 100 200 300 400 5UO 600 700
'4:) TIME, HRN
Figure6 - Interlammar shear strength of FMW1000PMRPI/HTSgraph,rehber
t composlte_exposedand testedat 450° and 5500F.
,,
200)(103 O 15MIN EXPOSURE
_I I I I I I i I I I I I
qa_4500F FLEXURALSTRENGTH. (b,5500F FLEXURALSTRENGTH.
[-- 15MIN EXPOSURE
_z_ o r-- A 15MIN EXPOSIIRE
6I- 600HREXPOS,'RE
_ 41 I _I I I I L I J I I I
z_ I000 II00 1200 1300 _400 1500 lO00 II00 1200 130{3 1400 1500
FORMULATEDMOLECULARWEIGHT
(c)4500INTERLAt'41NARSHEARSTRENGTH, (d) 5500F INTFP'^ 'qhAR SHEARSTRENGTH.
Figure1. - Long-timeJndshort ume elevatedtemperature properhesof PMRPI/HTSoraph_tehl}er
composites.
1974026847-013


Tailor making high performance graphite fiber reinforced PMR polyimides

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