A Review on Polymer Nanofibers by Electrospinning and Their Applications in Nanocomposites
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been successfully electrospun into ultrane bers in recent years mostly in solvent solution and some in melt form. Potential
When the diameters of polymer ber materials areshrunk from micrometers (e.g. 10100 mm) to sub-
deformations while being cohesive enough to supportthe stresses developed during pulling can be made into
echnospinning [29,49], etc. have been used to prepare polymernanobers in recent years. The drawing is a processmicrons or nanometers (e.g. 1010 10010 mm),there appear several amazing characteristics such asvery large surface area to volume ratio (this ratio for ananober can be as large as 103 times of that of amicrober), exibility in surface functionalities, andsuperior mechanical performance (e.g. stiness and ten-sile strength) compared with any other known form ofthe material. These outstanding properties make thepolymer nanobers to be optimal candidates for manyimportant applications. A number of processing techni-ques such as drawing , template synthesis [45,108],phase separation , self-assembly [104,161], electro-
nanobers through drawing. The template synthesis, asthe name suggests, uses a nanoporous membrane as atemplate to make nanobers of solid (a bril) or hollow(a tubule) shape. The most important feature of thismethod may lie in that nanometer tubules and brils ofvarious raw materials such as electronically conductingpolymers, metals, semiconductors, and carbons can befabricated. On the other hand, the method cannot makeone-by-one continuous nanobers. The phase separa-tion consists of dissolution, gelation, extraction using adierent solvent, freezing, and drying resulting in ananoscale porous foam. The process takes relativelyprocessing, structure and property characterization, applications, and modeling and simulations. Information of those polymerstogether with their processing conditions for electrospinning of ultrane bers has been summarized in the paper. Other issuesregarding the technology limitations, research challenges, and future trends are also discussed.
# 2003 Elsevier Ltd. All rights reserved.
1. Introduction make one-by-one very long single nanobers. However,only a viscoelastic material that can undergo strongpaper, a comprehensive review is presented on the researches an
applications based on such bers specically their use as reinforcement in nanocomposite development have been realized. In this
d developments related to electrospun polymer nanobers includingA review on polymer nanotheir applications
Zheng-Ming Huanga,*, Y.-Z. ZhanaDepartment of Engineering Mechanics, Tongji
bDivision of Bioengineering, National University ofcNanoscience and Nanotechnology Initiative, National UnivdDepartment of Mechanical Engineering, National Unive
Received 21 January 2003; received in rev
Electrospinning has been recognized as an ecient technique
Composites Science and Ters by electrospinning andnanocomposites
, M. Kotakic, S. Ramakrishnab,c,d
ersity, 1239 Siping Road, Shanghai, PR China
apore, 10 Kent Ridge Crescent 119260, Singapore
of Singapore, 10 Kent Ridge Crescent 119260, Singapore
f Singapore, 10 Kent Ridge Crescent 119260, Singapore
orm 7 April 2003; accepted 8 April 2003
the fabrication of polymer nanobers. Various polymers have
logy 63 (2003) 22232253
www.elsevier.com/locate/compscitechever, similarly to the phase separation the self-assemblyis time-consuming in processing continuous polymernanobers. Thus, the electrospinning process seems to
0266-3538/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved.doi:10.1016/S0266-3538(03)00178-7
* Corresponding author. Tel.: +86-21-65985373; fax: +86-21-
E-mail address: [email protected] (Z.-M. Huang).similar to dry spinning in ber industry, which can
long period of time to transfer the solid polymer intothe nano-porous foam. The self-assembly is a process inwhich individual, pre-existing components organizethemselves into desired patterns and functions. How-
pump. A high-voltage dc current was connected to the the term Electrospinning, as at 18 October 2002).
nce abe the only method which can be further developed formass production of one-by-one continuous nanobersfrom various polymers.Although the term electrospinning, derived from
electrostatic spinning, was used relatively recently (inaround 1994), its fundamental idea dates back morethan 60 years earlier. From 1934 to 1944, Formalaspublished a series of patents , describing anexperimental setup for the production of polymer la-ments using an electrostatic force. A polymer solution,such as cellulose acetate, was introduced into the electriceld. The polymer laments were formed, from thesolution, between two electrodes bearing electricalcharges of opposite polarity. One of the electrodes wasplaced into the solution and the other onto a collector.Once ejected out of a metal spinnerette with a smallhole, the charged solution jets evaporated to becomebers which were collected on the collector. The poten-tial dierence depended on the properties of the spin-ning solution, such as polymer molecular weight andviscosity. When the distance between the spinneretteand the collecting device was short, spun bers tendedto stick to the collecting device as well as to each other,due to incomplete solvent evaporation.In 1952, Vonnegut and Neubauer were able to pro-
duce streams of highly electried uniform droplets ofabout 0.1 mm in diameter . They invented a simpleapparatus for the electrical atomization. A glass tubewas drawn down to a capillary having a diameter in theorder of a few tenths of millimeter. The tube was lledwith water or some other liquid and an electric wireconnected with a source of variable high voltage (510kV) was introduced into the liquid. In 1955, Drozininvestigated the dispersion of a series of liquids intoaerosols under high electric potentials . He used aglass tube ending in a ne capillary similar to the oneemployed by Vonnegut and Neubauer. He found thatfor certain liquids and under proper conditions, theliquid was issued from the capillary as a highly dis-persed aerosol consisting of droplets with a relativelyuniform size. He also captured dierent stages of thedispersion. In 1966, Simons patented an apparatus forthe production of non-woven fabrics of ultra thin andvery light in weight with dierent patterns using elec-trical spinning . The positive electrode wasimmersed into the polymer solution and the negativeone was connected to a belt where the non-woven fabricwas collected. He found that the bers from low visc-osity solutions tended to be shorter and ner whereasthose from more viscous solutions were relatively con-tinuous. In 1971, Baumgarten made an apparatus toelectrospin acrylic bers with diameters in the range of0.051.1 microns . The spinning drop was suspendedfrom a stainless steel capillary tube and maintainedconstant in size by adjusting the feed rate of an infusion
2224 Z.-M. Huang et al. / Composites ScieFig. 1. (a) Comparison of the annual number of scientic publications
since the term of electrospinning was introduced in 1994. (b) Pub-
lication distributions around the world based on (a). (Data analysis of
publications was done using the SciFinder Scholar search system withcapillary tube whereas the bers were collected on agrounded metal screen.Since 1980s and especially in recent years, the elec-
trospinning process essentially similar to that describedby  has regained more attention probably due in partto a surging interest in nanotechnology, as ultranebers or brous structures of various polymers withdiameters down to submicrons or nanometers can beeasily fabricated with this process. A survey of openpublications related with electrospinning in the past 10years is given in Fig. 1(a), whereas those publicationdistributions all over the world are shown in Fig. 1(b).These literature data were obtained based on a Sci-Finder Scholar search system. The data clearly demon-strated that the electrospinning has attracted increasingattentions recently. Up to date, it is generally believedthat nearly one hundred dierent polymers, mostly dis-solved in solvents yet some heated into melts, have beensuccessfully spun into ultrane bers using this tech-nique (though only half of them have been found by usfrom the open literature, see subsequently). Strangelyenough, although the electrospinning process has shownpotential promising and has existed in the literature forquite several decades, its understanding is still very lim-ited. In this paper, a systematic review is made on theresearches and developments related to electrospunpolymer nanobers including processing, structure and
nd Technology 63 (2003) 22232253
tage supplier, a capillary tube with a pipette or needle ofsmall diameter, and a metal collecting screen. In the
in the electrospinning chamber .spinning.
nce aFig. 2. Schematic diagram to show polymer nanobers by electro-electrospinning process a high voltage is used to createan electrically charged jet of polymer solution or meltout of the pipette. Before reaching the collecting screen,the solution jet evaporates or solidies, and is collectedas an interconnected web of small bers [29,49]. Oneelectrode is placed into the spinning solution/melt andthe other attached to the collector. In most cases, thecollector is simply grounded, as indicated in Fig. 2. Theelectric eld is subjected to the end of the capillary tubethat contains the solution uid held by its surface ten-sion. This induces a charge on the surface of the liquid.Mutual charge repulsion and the contraction of thesurface charges to the counter electrode cause a forcedirectly opposite to the surface tension . As theintensity of the electric eld is increased, the hemi-spherical surface of the uid at the tip of the capillarytube elongates to form a conical shape known as theTaylor cone . Further increasing the electric eld, acritical value is attained with which the repulsive elec-trostatic force overcomes the surface tension and thecharged jet of the uid is ejected from the tip of theTaylor cone. The discharged polymer solution jetundergoes an instability and elongation process, whichallows the jet to become very long and thin. Meanwhile,the solvent evaporates, leaving behind a charged poly-mer ber. In the case of the melt the discharged jetsolidies when it travels in the air.So far, we have found in the open literature that more
than fty dierent polymers have been successfullyelectrospun into ultra ne bers with diameters rangingfrom
Polymers to have been electrospun in solution form
No. Polymer Detailsa Solvent o tion Perspective applications
1 Nylon6,6, PA-6,6  Formic acid Protective clothing
2 Polyurethanes, PU  Dimethyl formamide Protective clothing
 Dimethylformamide Electret lter
3 Polybenzimidazole, PBI  Dimethyl accetamide Protective clothing
 nanober reinforced
4 Polycarboate, PC  Dimethyl formamide:tetrahydrofuran (1:1) Protective clothing
 Dichlormethane Sensor, lter
Mw=60,000  Chloroform, tetrahydrofuran
MI=810 g/10 min
 Dimethylformamide:tetrahydrofuran (1:1) Electret lter
6 Polyacrylonitrile, PAN  Dimethyl formamide 0 N/10-5m3
 Dimethyl formamide
 Dimethyl formamide Carbon nanober
 Dimethyl formamide
 Dimethyl formamide
7 Polyvinil alcohol, PVA Mn=65,000  Distilled water 1
 Distilled water 1
Mn=150,000  1
8 Polylactic acid, PLA poly(d, l-lactic acid) Mw =109,000
Dimethyl formamide Membrane for prevention
of surfery induced-adhesion
poly(l-lactic acid) Mw =100,000
Methylene chloride and dimethyl
Sama as above
poly(l-lactic acid) Mn =150,000g/mol 
Dichlormethane w Sensor, Filter
Mw=205 kDa  Drug delivery system
9 Polyethylene-co-vinyl acetate, PEVA Mw=60.4kDa  Drug delivery system
10 PEVA/PLA PEVA/PLA=50/50  Drug delivery system
(continued on next page)
Table 1 (continued)
No. Polymer Detailsa Solvent o tion Perspective applications
11 Polymethacrylate (PMMA) /
010% TAN  Dimethyl formamide : toluene (1:9)
12 Polyethylene oxide, PEO 2,000,000 g/mol  Distilled water 1
Mw =400,000  Distilled water 1
Mw =400,000  Distilled water 1
Mw =9105 g/mol  Distilled water and ethanol or NaCl 4 Distilled water, distilled water and
chloroform, distilled water and
Mw=1,000,000  Distilled water:ethanol (3:2) w Microelectronic wiring,
Mw=300,000  Distilled water, chloroform, acetone,
 Ethanol 1
Mn=58,000  1
Mn=100,000  1
 Isopropyle alcohol+water, Electret lter
 Isopropanol:water (6:1)
M=300 K  Isopropanol:water (6:1) 1
M=100 K to 2 M  Chloroform 5 %
13 Collagen-PEO Puried collagen, nominal molecular
weight 900 kD 
Hydrochloric acid 2 Wound healing, tissue engineering,
PEO: Mn=900,000  Hydrochloric acid (pH =2.0) w Wound healing, tissue engineering
14 Polyaniline (PANI) /PEO blend  Chloroform Conductive ber
 Camphorsulfonic acid w Conducting ber
Pan: Mw=120,000 Da, PEO: Mw=900,000Da,
Pan/HCSA /PEO: 1150 wt.%
Chloroform 4 Conducting ber
15 Polyaniline (PANI)/ Polystyrene (PS)  Chloroform Conductive ber
 Camphorsulfonic acid w Conductive ber
16 Silk-like polymer with bronectin
 Formic acid 8 t.% Implantable device
17 Polyvinylcarbazole Mw =1,100,000 g/mol  Dichlormethane 5 Sensor, lter
(continued on next page)
Table 1 (continued)
No. Polymer Detailsa Solvent o tion Perspective applications
18 Polyethylene Terephtalate, PET Mw=10,00020,000 g/mol
Dichlormethane and triuoracetic w
 Dichloromethane:triuoroacetic acid (1:1)
19 polyacrylic acid-polypyrene
Mw=50,000 g/mol  Dimethyl formamide Optical sensor
20 Polystyrene, PS Mw=190,000  Tetrahydrofuran, dimethylformamide,
CS2(carbon disulde), toluene,
M=200 kDa  Methylethylketone Enzymatic biotransformation
 Chloroform, dimethylformamide 5
M=280,000  Dimethylformamide (Flat ribbons)
Mw=280,000  Tetrahydrofuran Catalyst, lter
Mw=280,000/Mw=28,000: 90/1  Tetrahydrofuran Catalyst, lter
Mw=280,000/Mw=28,000 : 50/50  Tetrahydrofuran Catalyst, lter
Mw=280,000/Mw=2,430;90/10  Tetrahydrofuran Catalyst, lter
21 Polymethacrylate, PMMA Mw=540,000  Tetrahydrofuran, acetone, chloroform
22 Polyamide, PA  Dimethylacetamide Glass ber lter media
23 Silk/PEO blend Mw(PEO)=900,000 g/mol  Silk aqueous solutions 8 .% Biomaterial scaolds
24 poly vinyl phenol, PVP Mw=20,000, 100,000
Tetrahydrofuran , t./vol.) Antimicrobial agent
25 Polyvinylchloride, PVC [100,101] Tetrahydrofuran/dimethylformamide=100/0,
80/20, 60/40, 50/50, 40/60, 20/80, 0/100 (vol.%)
26 Cellulose acetate, CA  Acetone, acetic acid, dimethylacetamide . Membrane
27 Mixture of PAA-PM (polyacrylic acid
poly (pyrene methanol) ) and
 Dimethylformamide Optical sensor
28 Polyvinil alcohol (PVA)/Silica, PVA: Mn=86,000, silica content (wt.%):
0, 22, 34, 40, 49, 59 
(continued on next page)
Table 1 (continued)
No. Polymer Detailsa Solvent Co tion Perspective applications
29 Polyacrylamide, PAAm Mn=5,000,000  11
30 PLGA PLGA(PLA/PGA)=(85/15)  Tetrahydrofuran:dimethylformamide (1:1) 1 g Scaold for tissue engineering
31 Collagen  Hexauoro-2-propanol Scaold for tissue engineering
32 Polycaprolactone, PCL  Chloroform:methanol (3:1) toluene:methanol
(1:1), and dichloromethane:methanol (3:1)
33 Poly(2-hydroxyethyl methacrylate),
M=200,000  Ethanol:formic acid (1:1), ethanol 12, /
34 Poly(vinylidene uoride) , PVDF M=107,000  Dimethylformamide:dimethylacetamide (1/1) 20 (Flat ribbons)
35 Polyether imide, PEI  Hexauoro-2-propanol 10 (Flat ribbons)
36 Polyethylene gricol, PEG M=10 K  Chloroform 0.5 %
37 nylon-4,6, PA-4,6  Formic acid 10 Transparent composite
38 Poly(ferrocenyldimethylsilane), PFDMS Mw=87,000 g/mol  Tetrahydrofuran:dimethylformamide (9:1) 30
39 Nylon6 (PA-6) /montmorillonnite (Mt) Mt content=7.5 wt.%  Hexa-uoro-isopropanol (HFIP),
HFIP/dimethylformamide: 95/5 (wt%)
40 poly(ethylene-co-vinyl alcohol) Vinyl alcohol repeat unit: 5671 mol%
Isopropanol/water: 70/30 (%v/v) 2.5 /v Biomedical
41 Polyacrylnitrile (PAN) / TiO2  Photovoltaic and
42 Polycaprolactone (PCL) / metal Metals: gold, ZnO,  ZnO: cosmetic use
43 Polyvinyl pyrrolidone, PVP 
44 Polymetha-phenylene isophthalamide 
a Details possibly include: (a) reference, (b) molecular weight, and (c) content of each polymer in co-polymer/blend/composite.
16, 20 w
tone/DMAc (dimethylacetamide),  recognized thatviscosities between 1.2 and 10.2 poises were applicable.
side that range, th be elec-pun into bers at , eitherfew bers could highersity solution or ropletsto too low vis se twoples clearly dem y rangedierent polym able isrent.s long as a polym nano-, ideal targets wo eters ofbers be consiste e berace be defect-fre nd (3)inuous single na wever,arches so far have gets areo means easily acne of the most d with
electrospinning is the ber diameter. Since nanobers arelted from evapor olymer
has been recognized that during the traveling of a solu-
Deitzel et al. pointed out that the ber diameterincreased with increasing polymer concentration accord-ing t p . Demir et afoun was proportioncube ation . Anothmete diameter to a rem
Mw=4.6104  270
Fig. 3. PLLA nanobers with dierent diameters and pores .
nce and Technology 63 (2003) 22232253Several researchers investigated spinnibility of dierentpolymers. For instance,  found for electrospinningof aqueous poly(ethylene oxide) (PEO) dissolved inethanol-to-water solutions that viscosities in the rangeof 120 poises and surface tension between 35 and 55dynes/cm were suitable for ber formation. At viscos-ities above 20 poises, electrospinning was prohibitedbecause of the instability of ow caused by the highcohesiveness of the solution. Droplets were formedwhen the viscosity was too low (
whereas the concentration done at the high temperature
Fig. 5. SEM photographs of electrospun nanobers from dierent polymer concentration solutions .was 21.2 wt.%. Unfortunately, Demir et al. did notcompare the viscosity values of the two concentrationsolutions which were electrospun at two dierent tem-peratures.Another problem encountered in electrospinning is
that defects such as beads Fig. 4,  and pores Fig. 3)may occur in polymer nanobers. It has been found thatthe polymer concentration also aects the formation ofthe beads. Fong  recognized that higher polymerconcentration resulted in fewer beads. In their experi-ments with PEO polymer, the polymer concentrationsof 14.5 wt.% were used. The resulting ber membraneswere visualized under SEM, and dierent bermorphologies were captured, as shown in Fig. 5, inwhich the lowest viscosity, 13 centipoise, correspondedto 1 wt.% PEO concentration, whereas the highestviscosity, 1250 centipoise, corresponded to 4 wt.% con- Fig. 4. AFM image of electrospun PEO nanobers with beads .extent is the applied electrical voltage. In general, ahigher applied voltage ejects more uid in a jet, resultingin a larger ber diameter .Further challenge with current electrospinning lies in
the fact that the ber diameters obtained are seldomuniform. Not many reports have been given towardsresolving this problem. A useful attempt was recentlymade by . While electrospinning polyurethanenanobers, they recognized that the ber diametersobtained from the polymer solution at a high (70 C)temperature were much more uniform than those atroom temperature. The mechanisms involved, however,were not fully understood. It should be noted that theviscosity of the polyurethane solution with the sameconcentration at some higher temperature was sig-nicantly lower than that at room temperature. Thehighest polymer concentration which could be electro-spun into bers was 12.8 wt.% at room temperature,
centration. It should be realized that with the 4 wt.%PEO concentration the beads were not reported tocompletely disappear. Instead, the bead diameters, ifany, at higher concentrations were even larger. Theshape of the beads changed from spherical to spindle-like when the polymer concentration varied from low tohigh levels.Doshi & Reneker  pointed out that by reducing
surface tension of a polymer solution, bers could beobtained without beads. This might be correct in somesense, but should be applied with caution. It has beenrecognized by [48,105] that the surface tension seemsmore likely to be a function of solvent compositions,but is negligibly dependent on the polymer concen-
Z.-M. Huang et al. / Composites Science and Technology 63 (2003) 22232253 2231
uniform diameters around 700 nm . solution and high shear forces induced by the spinning
Fig. 6. SEM photographs of PEO nanobers electrospun under dierent electrical potentials .Furthermore, adding some ller material into a poly-mer solution can also result in bers free of beads. Zonget al. realized this while electrospinning biodegradablePLDA polymers . They found that with 1 wt.% saltaddition, the resulting nanobers were bead-free. Theyargued that the addition of salts resulted in a highercharge density on the surface of the solution jet duringthe electrospinning, bringing more electric charges tothe jet. As the charges carried by the jet increased,higher elongation forces were imposed to the jet underthe electrical eld, resulting in smaller bead and thinnerber diameters. This, however, does not imply that ahigher applied electrical eld could result in fewer beadsand smoother nanobers. In fact, Deitzel et al. investi-gated the inuence of electrical charge, which wasapplied for electrospinning, on the morphology of PEOnanobers . They reported that with the increase ofthe electrical potential the resulting nanobers becamerougher. Their results are shown in Fig. 6.. Ko et al.  dispersed carbon SWNTs (singlewall nanotubes) in polyacrylonitrile solution that waselectrospun into ultrane bers. In this way, the nano-composite brils were obtained. They characterized thestructure, composition, and physical properties of theresulting nanocomposite brils. Park et al. dispersed thecarbon SWNTs of 1.21.6 nm in diameter and 3 mmlong in a polyimide (CP2) solution for electrospinning.The resulting ultrane bers had diameters rangedfrom 500 nm to 2 mm. Unfortunately, no mechanicalbehavior of these bers or comparison between theproperties of them and pure polymer nanobers hasbeen reported.The idea of incorporating nanoscale llers into poly-
mer solution to electrospin composite nanobers hasbeen extended to prepare a composite solution oforganic and inorganic materials for electrospinning. Anumber of research groups have tried to yield dierentsuch nanobers in recent years, in making Poly-tration. Dierent solvents may contribute dierent sur-face tensions. However, not necessarily a lower surfacetension of a solvent will always be more suitable forelectrospinning. In their work with CA (cellulose ace-tate) polymer, Liu & Hsieh chose acetone, dimethylace-tamide (DMAc), and mixture of both as solvents. Theacetone used had a surface tension value of 23.7 dyne/cm lower than that of the DMAc, which was 32.4 dyne/cm. While no bers but only beads were obtained fromusing theDMAc solvent alone, the electrospinning of 5 and8 wt.%CA in acetone also showed to generate short berswith diameters around 1 mm and a beads on the stringmorphology. However, by using the mixture solvent with aratio of 2 (acetone) to 1 (DMAc), Liu & Hsieh yielded CAnanobers free of beads in a range of concentrations 1525wt.%. In a solvent of 10:1 acetone: DMAc, a 15 wt.% CAsolution generated bers with very smooth surfaces and
2.3. Composite nanobers
Carbon nanotubes (CNT) possess several uniquemechanical, electronic, and other kinds of character-istics. For instance, single carbon nanotube has a mod-ulus as high as several thousands of GPa and a tensilestrength of several tens of GPa . Unfortunately,carbon nanotubes are dicult to be aligned when theyare used as reinforcement in composite fabrication. Theresulting nanocomposite cannot exhibit the mechanicalproperties as much as one would expect. Thus, severalresearch groups have tried to incorporate CNTs intopolymer nanobers produced through electrospinning[89,119]. The spinning process is expected to align CNTsor their bundles along the ber direction due to combi-nation of dielectrophoretic forces caused by dielectric orconductivity mismatch between CNTs and the polymer
2232 Z.-M. Huang et al. / Composites Science and Technology 63 (2003) 22232253
behind the technique has not been explained in detail so
collected since the overfast take-up speed will break theber jet. The reason why a perfect alignment is dicult
Fig. 7. A schematic rotating collector for electrospun ultrane bers.
nce acaprolactone/gold or ZnO , Polyacrylnitrile (PAN)/TiO2 , PVA/Silica , and Nylon6/montmor-illonite (Mt)  ultrane bers, respectively. It deservesspecial mentioning that a signicant eort was madevery recently by  who used sol-gel processing andelectrospinning technique to prepare alumina-borate/PVA composite nanobers. These bers were then cal-cined at above 1000 C into alumina-borate ultranebers. In their processing, the aqueous PVA solutionwas rst prepared by dissolving PVA powder in distilledwater, which was then added to the aluminium acetatestabilized with boric acid. The mixture solution waselectrospun into the alumina-borate/PVA compositenanobers. It was found that at temperatures higherthan 1000 C the PVA decomposed, leaving the alu-mina-borate alone. In this way, the continuous (non-woven) ceramic ultrane bers were obtained. Evi-dently, the technique needs to be extensively explored sothat other kinds of ceramic or metal nanobers can beprepared through electrospinning.
2.4. Fiber alignment
Most nanobers obtained so far are in non-wovenform, which can be useful for relatively small number ofapplications such as ltration [3,60], tissue scaolds ,implant coating lm , and wound dressing .However, as we understand from traditional ber andtextile industry, only when continuous single nanobersor uniaxial ber bundles are obtained can their applica-tions be expanded into unlimited. Nevertheless, this is avery tough target to be achieved for electrospun nano-bers, because the polymer jet trajectory is in a verycomplicated three-dimensional whipping way causedby bending instability rather than in a straight line.Eorts are believed to be being made in various researchgroups all over the world. Up to date, however, there isno continuous long nanober yarn obtained and thepublications related to aligned nanobers are very lim-ited. Following ve techniques are some possible meanswhich have been attempted to align electrospun nano-bers.
2.4.1. A cylinder collector with high rotating speedIt has been suggested that by rotating a cylinder col-
lector Fig. 7) at a very high speed up to thousands ofrpm (round per minute), electrospun nanobers couldbe oriented circumferentially. Researchers from VirginiaCommonwealth University [11,113] have used this tech-nique to obtain aligned electrospun poly(glycolic acid)(PGA) (at 1000 rpm rotating speed) and type I collagen(4500 rpm rotating speed) bers. The results are shownin Fig. 8. As can be seen from the gure, their pre-liminary trials were less successful. The ber alignmentswere achieved only to some extent. As the mechanism
Z.-M. Huang et al. / Composites Scieto achieve can be attributed to the fact that the chaosmotions of polymer jets are not likely to be consistentand are less controllable.
2.4.2. An auxiliary electrode/electrical eldUS Patent 4689186  disclosed a method to fabri-
cate tubular products for blood vessel prosthesis andurinary and bile duct applications. The unique featureof this invention is that deposited bers can be cir-cumferentially oriented substantially by employing anauxiliary electrical eld. Following Bornats idea, a pre-liminary trial has been carried out in our laboratoryusing a set-up as depicted schematically in Fig. 9(a). Theber collection device was a Teon tube of 4 mm indiameter, rotating at a speed of 1165 rpm above thecharged grid. The PLAPCL copolymer was given apositive charge of +12 kV. The auxiliary electrode(grid) made of a plurality of connected aluminum foilstrips in 5 mm width, 30 mm long, and 5 mm apart, wasplaced 8 cm away from the collection mandrel andcharged to 8 kV. The alignment eect with and with-out the auxiliary electrical elds can be seen from thecomparison shown in Fig. 10. The gure clearlydemonstrates that the auxiliary electrical eld devicesubstantially improved the ber alignment.In another US Patent 5024789  also for the pro-
duction of tubular structures, it was reported that byfar, some intuitive conjectures are given as follows.When a linear speed of the rotating cylinder surface,which serves as a ber take-up device, matches that ofevaporated jet depositions, the bers are taken up onthe surface of the cylinder tightly in a circumferentialmanner, resulting in a fair alignment. Such a speed canbe called as an alignment speed. If the surface speed ofthe cylinder is slower than the alignment speed, ran-domly deposited bers will be collected, as it is the fastchaos motions of jets determine the nal depositionmanner. On the other hand, there must be a limitrotating speed above which continuous bers cannot be
nd Technology 63 (2003) 22232253 2233
as-spun nanobers are almost all attracted to and can distances is due to varying repulsive forces related to
nce aFig. 8. Aligned collagen  a
2234 Z.-M. Huang et al. / Composites ScieA  electrospun nanobers.
nd Technology 63 (2003) 22232253Fig. 9. Aligning electrospun bers with an auxiliary electrical eld.asymmetrically placing rotating and charged mandrelbetween two charged plates [Fig. 9(b)], electrospunultrane bers with larger diameter could be orientedcircumferentially to the longitudinal axis of the tubularstructure. However, small diameter bers remainedrandomly oriented.
2.4.3. A thin wheel with sharp edgeA signicant advancement in collecting aligned elec-
trospun nanobers has been recently made by ,who described a novel approach to position and alignindividual nanobers on a tapered and grounded wheel-like bobbin as shown in Fig. 11(a). The tip-like edgesubstantially concentrates the electrical eld so that the
be continuously wound on the bobbin edge of therotating wheel. It has been demonstrated that with thisapproach polyethylene oxide nanobers with diametersranging from 100 to 400 nm were in alignment with apitch (the distance between two bers) varies from 1 to 2mm [Fig. 11(b)]. It was explained that before reachingthe electrically grounded target the nanobers retainsucient residual charges to repel each other. Thisinuences the morphology of ber depositions. As aresult, once a nanober is attached to the wheel tip, itwill exert a repulsive force on the next ber attracted tothe tip. This repulsion from one another results in aseparation between the deposited nanobers asobserved [Fig. 11(b)]. The variation in the separation
which is equivalent to a rotating speed as high as 1070
aluminum frame and observed under an optical micro-
wooden frame. Fig. 13 shows SEM pictures of the bers
nce aFig. 10. Comparison between polymer [a copolymer of PLAPCL (75:2
Z.-M. Huang et al. / Composites Scienober depositions: (a) without and (b) with an auxiliary electrical eld.
nd Technology 63 (2003) 22232253 2235rpm. Unfortunately, no reports on the relationshipbetween alignments and dierent rotating speeds wereprovided. Even so, this paper has initiated a useful rou-tine towards fabrication and collection of uniaxiallyaligned polymer nanober yarns.
2.4.4. A frame collectorIn order to obtain an individual nanober for the
purpose of experimental characterizations, we veryrecently developed another approach to ber alignmentby simply placing a rectangular frame structure underthe spinning jet [Fig. 12(a)]. Fig. 12(b) shows typicalalignments of electrospun PEO bers collected with an
obtained using the wooden frame and the aluminumframe respectively with the same frame inclination angle() of 60. As can be seen from the gure, the aluminumframe resulted in much better alignments than the woo-den frame. Further work was done by rotating a multi-frame structure on which the electrospun PEO nano-bers could be continuously deposited, as demonstratedin Fig. 14. More investigation is under going to under-stand the alignment characteristics in terms of varyingthe shape and size of frame rods, the distance betweenthe frame rods, and the inclination angle of a singleframe (which will be useful in determining how manysides would be best suitable to construct a polygonalnanober diameters and residual charges. It should benoted that they collected their aligned bers with a lin-ear velocity of 22 m/s at the tip of the wheel collector,
scope. We have noticed that dierent frame materialsresult in dierent ber alignments. For example, thealuminum frame favors better ber alignments than a
Fig. 11. (a) A set up used to collect uniaxial nanobers, (b) PEO bers thus obtained .
using a multiple eld technique [Fig. 16(a)] the polymer not the focus in this paper, the technique proposed
Fig. 12. Aligned as-spun PEO nan
frame structure. Fig. 15. Aligned electrospun nylon 6 ultrane bers .
nce and Technology 63 (2003) 22232253obers by a frame method.wherein suggests a promising strategy through control-ling electrical elds to achieve ber alignment, andhence is worthy of further study.
Fig. 14. Continuous as-spun nanobers deposited on a rotating multi-2.4.5. Other approachesFong et al.  obtained some aligned nylon 6 bers
by rapidly oscillating a grounded frame within theelectrospun polymer jets. The ber alignments areshown in Fig. 15. Unfortunately, no detail of theirframe has been reported in the open literature yet. Inanother approach by , it was demonstrated that by
jet, which is usually in chaotic oscillating motion duringtraveling towards the collection target, can be straigh-tened to some extent. In this way one may control thedeposition of electrospun polymer nanobers and evencollects nicely aligned ber yarns. Based on the multipleeld technique, macroscopically oriented bers werecollected [Fig. 16(b)]. Although the ber alignment was
Fig. 13. Comparison of ber alignments between using (a) a wooden frame, and (b) an aluminum frame.2236 Z.-M. Huang et al. / Composites Scie
merits which cannot be shared by traditional (microber)
tionship characterization of such nanocomposites is
point bending, double torsion, and tear tests were per-
membranes were cured at room temperature. Tensile
nce a3. Composite application
One of the most important applications of traditional(micro-size) bers, especially engineering bers such ascarbon, glass, and Kevlar bers, is to be used as rein-forcements in composite developments . With thesereinforcements, the composite materials can providesuperior structural properties such as high modulus andstrength to weight ratios, which generally cannot beachieved by other engineered monolithic materialsalone. Needless to say, nanobers will also eventuallynd important applications in making nanocomposites.This is because nanobers can have even bettermechanical properties than micro bers of the samematerials, and hence the superior structural propertiesof nanocomposites can be anticipated. Moreover, nano-ber reinforced composites may possess some additional
Fig. 16. (a) A multiple eld technique, a
Z.-M. Huang et al. / Composites Sciebelieved to be useful, but is unfortunately not muchavailable in the literature. Kim & Reneker  investi-gated the reinforcing eect of electrospun nanobers ofpolybenzimidazole (PBI) in an epoxy matrix and in arubber matrix. The PBI polymer was electrospun intonon-woven fabric sheets, which were treated with aque-ous sulfuric acid and other procedures for compositefabrication . Eight to 32 plies of the fabric sheetswere cut and folded to t a compression mold, and werelater impregnated with the epoxy resin before being putinto an elevated temperature and vacuum oven for cur-ing. The rubber matrix was mixed with the choppedber fabrics which were made by cutting the non-wovennanober sheets into 0.5 cm squares, and was compres-sion molded into composite samples. Fiber contents of315% by weight were determined by extracting thebers from the uncured mixture with toluene. Tensile, 3-
) aligned PEO ber yarn obtained .
nd Technology 63 (2003) 22232253 2237composites. For instance, if there is a dierence in refrac-tive indices between ber and matrix, the resulting com-posite becomes opaque or nontransparent due to lightscattering. This limitation, however, can be circumventedwhen the ber diameters become signicantly smaller thanthe wavelength of visible light .Perhaps the majority work in the current literature on
nanober composites is concerned with carbon nano-ber or nanotube reinforcements. These nanobers ornanotubes are generally not obtained through electro-spinning. Several comprehensive reviews have summar-ized the researches done until very recently on thesecomposites [5,98,112,150]. On the other hand, so farpolymer nanobers made from electrospinning havebeen much less used as composite reinforcements. Onlylimited researchers have tried to make nanocompositesreinforced with electrospun polymer nanobers. Infor-mation on the fabrication and structure-property rela-
formed for the epoxy and rubber nanocomposites,respectively. As the tested samples were in normaldimensions, relevant testing standards were followed. Itwas found that with increasing content of bers, thebending Youngs modulus and the fracture toughness ofthe epoxy nanocomposite were increased marginally,whereas the fracture energy increased signicantly. Forthe rubber nanocomposite, however, the Youngs mod-ulus was ten times and the tear strength was twice aslarge as that of the unlled rubber material.Bergshoef and Vancso fabricated a nanocomposite
using electrospun Nylon-4,6 nanober non-wovenmembranes and an epoxy matrix . After electrospin-ning, the membranes were washed with ethanol anddried at room temperature and atmospheric pressure,and then were impregnated with the epoxy resin bydipping them into the diluted resin. The composite lmsamples were obtained after the resin impregnated
yet. For instance, it is well known that the interfacebonding between a polymer ber and a dierent poly-
have been steadily extended especially in recent years.
nce atests were conducted for the composite as well as themonolithic matrix lms. It was reported that both thestiness and strength of the composite were signicantlyhigher than those of the reference matrix lm althoughthe ber content was low. It is noted that Bergshoef &Vancso determined the ber content by using an ele-mental analysis and a thermal analysis. In the rst ana-lysis, the nitrogen content of the pure bers, thereinforced matrix, and the monolithic resin were deter-mined. Assuming weight additivity, the ber content inthe composite thus obtained was 3.9% by weight. In theother analysis, the melt enthalpy of the nylon used inthe composite was determined by DSC, which yielded aber weight fraction of 4.6%.In addition to the stiness and strength improve-
ment, researchers also tried to modify other mechanicalbehavior of composites by using electrospun ultranepolymer bers. For instance, the very high surface tovolume ratio of these bers may be suitable for theimprovement of the interlaminar toughness of a highperformance composite laminate, which is an impor-tant issue in applications. A US patent was recentlyissued to Dzenis & Reneker  who proposed usingpolymer nanobers in between laminas of a laminate toimprove delamination resistance. They arranged PBInanobers at the interfaces between plies of the lami-nate without a substantial reduction for the in-plainproperties and an increase in weight and/or ply thickness.It was reported that by incorporating electrospun PBInanobers of 300500 nm diameters in-between a uni-directional composites made of graphite/epoxy prepregsof T2G190/F263, Mode I critical energy release rate GIcincreased by 15%, while an increase of 130% in the ModeII critical energy release rate GIIc was observed.Up to date, the polymer composites reinforced with
electrospun nanobers have been developed mainly forproviding some outstanding physical (e.g. optical andelectrical) and chemical properties while keeping theirappropriate mechanical performance. For instance, inthe report by , the epoxy composite with electrospunnylon 4,6 nanobers of 30200 nm diameters exhibiteda characteristic transparency due to the ber sizessmaller than the wavelength of visible light. It is alsonoted that single wall carbon nanotube (SWNT) rein-forced polyimide composite in the form of nanobrouslm was made by electrospinning to explore a potentialapplication for spacecrafts . Carbon nanobers forcomposite applications can also be manufactured fromprecursor polymer nanobers [24,40]. Such kind ofcontinuous carbon nanober composite also has poten-tial applications as lters for separation of small parti-cles from gas or liquid, supports for high temperaturecatalysts, heat management materials in aircraft andsemiconductor devices, as well as promising candidatesas small electronic devices, rechargeable batteries, and
2238 Z.-M. Huang et al. / Composites Sciemer matrix is generally poor. How to modify thisbonding for polymer nanober polymer matrix compo-sites seems to have not been touched at all, althoughthere are a vast number of publications on this topic fortraditional brous composites in the literature. Fur-thermore, little work has been done on the modelingand simulation of the mechanical properties of nano-ber composites. Although many micromechanics mod-els have been developed for predicting the stiness andstrength of brous composites , whether they arestill applicable to nanober composites needs to be ver-ied . Compared with its counterpart for traditionalbrous composites, one of the main barriers to theimplementation of such work for nanober compositesis that one does not know the mechanical behavior ofsingle polymer nanobers.Several reasons can be attributed to the less develop-
ment of electrospun polymer nanober reinforced com-posites. First of all, not sucient quantity of uniaxialand continuous nanobers has been obtained and couldbe used as reinforcements. It is well known from com-posite theory and practice that the superior structuralproperties can be achieved only when bers are arran-ged in pre-determined directions such as in unidirec-tional laminae, multidirectional laminates, woven orbraided fabric reinforced composites. To make thesecomposites, continuous ber bundles are necessary. Thenon-woven or randomly arranged nanober mats, ascollected to date from electrospinning, generally cannotresult in a signicant improvement in the mechanicalproperties of the composites with their reinforcement.Another reason may be that polymers yielding thesebers are generally considered as less suitable for struc-tural enhancement. Although carbon nanobers areprincipally achievable from post-processing of electro-spun precursor polymer nanobers such as poly-acrylonitrile (PAN) nanobers [23,40,156], these bersseem to have not been obtained in large quantity ofcontinuous single yarns yet. Thus, extensive work bothfrom the standpoint of nanober composite science(fabrication, characterization, modeling and simulation)and from industrial base (applications) viewpoint isnecessary in the future.
4. Other applications
In addition to composite reinforcement, other appli-cation elds based on electrospun polymer nanobersDue to limited number of papers published in theopen literature, many important issues relevant tonanocomposites reinforced with electrospun polymernanobers have essentially not been taken into account
nd Technology 63 (2003) 22232253
was estimated that future ltration market would be up easily trapped in the electrospun nanobrous struc-
Fig. 17. Application elds targeted by US patents on electrospun nanobers.
Fig. 18. Potential applications of electrospun polymer nanobers.One of the best representatives in this regard is shownby relevant US patents, in which most applications arein the eld of ltration systems and medical prosthesismainly grafts and vessels. Other applications whichhave been targeted include tissue template, electro-magnetic shielding, composite delamination resistance,and liquid crystal device. A schematic diagram illus-trating these patent applications is shown in Fig. 17.More extended or perspective application areas aresummarized in Fig. 18. It should be realized that mostof these applications have not reached their industrylevel, but just at a laboratory research and developmentstage. However, their promising potential is believed tobe attracting attentions and investments from academia,governments, and industry all over the world.
4.1. Filtration application
Filtration is necessary in many engineering elds. It
to US $700b by the year 2020 . Fibrous materialsused for lter media provide advantages of high l-tration eciency and low air resistance . Filtrationeciency, which is closely associated with the berneness, is one of the most important concerns for thelter performance Fig. 19). In the industry, coalescinglter media are studied to produce clean compressedair. These media are required to capture oil droplets assmall as 0.3 micron. It is realized that electrospinning isrising to the challenge of providing solutions for theremoval of unfriendly particles in such submicronrange. Since the channels and structural elements of alter must be matched to the scale of the particles ordroplets that are to be captured in the lter, one directway of developing high ecient and eective ltermedia is by using nanometer sized bers in the lterstructure . In general, due to the very high surfacearea to volume ratio and resulting high surface cohe-sion, tiny particles of the order of
or structures. Examples include: bone, dentin, collagen,
have been proposed for a number of soft tissue pros- absorption and dermal delivery.
nce atured lters and hence the ltration eciency can beimproved. There is one major manufacturer of electro-spun products in the world, Freudenberg Nonwovens,which has been producing electrospun lter media froma continuous web feed for ultra high eciency ltrationmarkets for more than 20 years [65,127]. This is per-haps one of the earliest commercial businesses relevantto electrospinning.Recently, a US patent  has disclosed a method for
making a dust lter bag which constitutes a plurality oflayers including a carrier material layer and a nanobernonwoven tissue layer. Nanobers for applications inpulse-clean cartridges for dust collection and in cabinair ltration of mining vehicles have been discussed .Polymer nanobers can also be electrostatically chargedto modify the ability of electrostatic attraction of parti-cles without increase in pressure drop to furtherimprove ltration eciency. In this regard, the electro-spinning process has been shown to integrate the spin-ning and charging of polymer into nanobers in onestep [3,152].In addition to fullling the more traditional purpose
in ltration, the nanober membranes fabricated fromsome specic polymers or coated with some selectiveagents can also be used as, for example, molecular l-ters. For instance, such lters can be applied to thedetection and ltration of chemical and biologicalweapon agents .
4.2. Biomedical application
From a biological viewpoint, almost all of the humantissues and organs are deposited in nanobrous forms
Fig. 19. The eciency of a lter increases with decrease in ber diameter.
2240 Z.-M. Huang et al. / Composites Scietheses applications such as blood vessel, vascular,breast, etc. [8,12,70,109,110,128,142. In addition, elec-trospun biocompatible polymer nanobers can also bedeposited as a thin porous lm onto a hard tissue pros-thetic device designed to be implanted into the humanbody [4,1618]. This coating lm with gradient brousstructure works as an interphase between the prostheticdevice and the host tissues, and is expected to ecientlyreduce the stiness mismatch at the tissue/device inter-phase and hence prevent the device failure after theimplantation.
4.2.2. Tissue templateFor the treatment of tissues or organs in malfunction
in a human body, one of the challenges to the eld oftissue engineering/biomaterials is the design of idealscaolds/synthetic matrices that can mimic the structureand biological functions of the natural extracellurlarmatrix (ECM). Human cells can attach and organizewell around bers with diameters smaller than those ofthe cells . In this regard, nanoscale brous scaoldscan provide an optimal template for cells to seed,migrate, and grow. A successful regeneration of biolo-gical tissues and organs calls for the development ofbrous structures with ber architectures benecial forcell deposition and cell proliferation. Of particularinterest in tissue engineering is the creation of repro-ducible and biocompatible three-dimensional scaoldsfor cell ingrowth resulting in bio-matrix composites forvarious tissue repair and replacement procedures.Recently, people have started to pay attention to mak-ing such scaolds with synthetic biopolymers and/orbiodegradable polymer nanobers [16,46,73]. It isbelieved that converting biopolymers into bers andnetworks that mimic native structures will ultimatelyenhance the utility of these materials as large diameterbers do not mimic the morphological characteristics ofthe native brils.
4.2.3. Wound dressingPolymer nanobers can also be used for the treatment
of wounds or burns of a human skin, as well as designedfor haemostatic devices with some unique character-istics. With the aid of electric eld, ne bers of bio-degradable polymers can be directly sprayed/spun ontothe injured location of skin to form a brous mat dres-sing Fig. 20), which can let wounds heal by encouragingthe formation of normal skin growth and eliminate theformation of scar tissue which would occur in a tradi-tional treatment [25,82,111,137]. Non-woven nano-brous membrane mats for wound dressing usually havepore sizes ranging from 500 nm to 1 mm, small enoughto protect the wound from bacterial penetration viaaerosol particle capturing mechanisms. High surfacearea of 5100 m2/g is extremely ecient for uid
nd Technology 63 (2003) 22232253cartilage, and skin. All of them are characterized by wellorganized hierarchical brous structures realigning innanometer scale. As such, current research in electro-spun polymer nanobers has focused one of their majorapplications on bioengineering. We can easily nd theirpromising potential in various biomedical areas. Someexamples are listed later.
4.2.1. Medical prosthesesPolymer nanobers fabricated via electrospinning
biotic drug Mefoxin. Preliminary eciency of this
delivery in the form of nanobers is still in the early protective clothing.
nce a4.2.4. Drug delivery and pharmaceutical compositionDelivery of drug/pharmaceuticals to patients in the
most physiologically acceptable manner has alwaysbeen an important concern in medicine. In general, thesmaller the dimensions of the drug and the coatingmaterial required to encapsulate the drug, the better thedrug to be absorbed by human being. Drug deliverywith polymer nanobers is based on the principle thatdissolution rate of a particulate drug increases withincreasing surface area of both the drug and the corre-sponding carrier if needed. Kenawy et al. investigateddelivery of tetracycline hydrochloride based on thebrous delivery matrices of poly (ethylene-co-vinylace-tate), poly(lactic acid), and their blend . In anotherwork by , bioabsorbable nanober membranes ofpoly(lactic acid) targeted for the prevention of surgery-induced adhesions, ware also used for loading an anti-
Fig. 20. Nanobers for wound dressing (www.electrosols.com).
Z.-M. Huang et al. / Composites Sciestage exploration, a real delivery mode after productionand eciency have yet to be determined in the future.
4.2.5. CosmeticsThe current skin care masks applied as topical
creams, lotions or ointments may include dusts or liquidsprays which may be more likely than brous materialsto migrate into sensitive areas of the body such as thenose and eyes where the skin mask is being applied tothe face. Electrospun polymer nanobers have beenattempted as a cosmetic skin care mask for the treat-ment of skin healing, skin cleansing, or other ther-apeutical or medical properties with or without variousadditives . This nanobrous skin mask with verysmall interstices and high surface area can facilitatefar greater utilization and speed up the rate oftransfer of the additives to the skin for the fullestpotential of the additive. The cosmetic skin maskfrom the electrospun nanobers can be applied gentlyand painlessly as well as directly to the three-dimen-sional topography of the skin to provide healing orcare treatment to the skin.
4.3. Protective clothing application
The protective clothing in military is mostly expectedto help maximize the survivability, sustainability, andcombat eectiveness of the individual soldier systemagainst extreme weather conditions, ballistics, andNBC (nuclear, biological, and chemical) warfare .In peace ages, breathing apparatus and protectiveclothing with the particular function of against chemi-cal warfare agents such as sarin, soman, tabun andmustard gas from inhalation and absorption throughthe skin become special concern for combatants inconicts and civilian populations in terrorist attacks.Current protective clothing containing charcoal absor-bents has its limitations in terms of water permeability,extra weight-imposed to the article of clothing. Assuch, a lightweight and breathable fabric, which ispermeable to both air and water vapor, insoluble in allsolvents and highly reactive with nerve gases and otherdeadly chemical agents, is desirable. Because of theirgreat surface area, nanober fabrics are capable of theneutralization of chemical agents and without impe-dance of the air and water vapor permeability to theclothing . Electrospinning results in nanobers laiddown in a layer that has high porosity but very smallpore size, providing good resistance to the penetrationof chemical harm agents in aerosol form . Pre-liminary investigations have indicated that compared toconventional textiles the electrospun nanobers presentboth minimal impedance to moisture vapor diusionand extremely eciency in trapping aerosol particles[59,61,127], as well as show strong promises as ideal
nd Technology 63 (2003) 22232253 2241nanober membrane compared with bulk lm wasdemonstrated. Ignatious & Baldoni  described elec-trospun polymer nanobers for pharmaceutical compo-sitions, which can be designed to provide rapid,immediate, delayed, or modied dissolution, such assustained and/or pulsatile release characteristics. As thedrug and carrier materials can be mixed together forelectrospinning of nanobers, the likely modes of thedrug in the resulting nanostructed products are: (1) drugas particles attached to the surface of the carrier whichis in the form of nanobers, (2) both drug and carrierare nanober-form, hence the end product will be thetwo kinds of nanobers interlaced together, (3) theblend of drug and carrier materials integrated into onekind of bers containing both components, and (4) thecarrier material is electrospun into a tubular form inwhich the drug particles are encapsulated. The modes(3) and (4) may be preferred. However, as the drug
tube material is coated on the nanober template, and
on the surface are generally chosen. The upper hor-izontal tangent of the lower ber is taken as a reference,
urethanes, Estane and Pellethane . They found that
nce a4.4. Electrical and optical application
Conductive nanobers are expected to be used in thefabrication of tiny electronic devices or machines suchas Schottky junctions, sensors and actuators. Due to thewell-known fact that the rate of electrochemical reac-tions is proportional to the surface area of the electrode,conductive nanobrous membranes are also quite sui-table for using as porous electrode in developing highperformance battery [116,166]. Conductive (in terms ofelectrical, ionic and photoelectric) membranes also havepotential for applications including electrostatic dis-sipation, corrosion protection, electromagnetic inter-ference shielding, photovoltaic device, etc. [130,131].Waters et al.  reported to use electrospun nano-
bers in the development of a liquid crystal device ofoptical shutter which is switchable under an electric eldbetween a state in which it is substantially transparentto incident light and a state in which it is substantiallyopaque. The main part of this liquid crystal device con-sisted of a layer of nanobers permeated with a liquid-crystal material, having a thickness of only few tensmicrons. The layer was located between two electrodes,by means of which an electric eld could be appliedacross the layer to vary the transmissivity of the liquidcrystal/nanober composite. It is the ber size used thatdetermines the sensitivities of the refractive index dif-ferences between the liquid crystal material and thebers, and consequently governs the transmissivity ofthe device. Obviously nanoscale polymer bers arenecessary in this kind of devices.
4.5. Other functional application
Nanobers from polymers with piezoelectric eectsuch as polyvinylidene uoride will make the resultantnanobrous devices piezoelectric . Electrospunpolymer nanobers could also be used in developingfunctional sensors with the high surface area of nano-bers facilitating the sensitivity. Poly(lactic acid co gly-colic acid) (PLAGA) nanober lms were employed asa new sensing interface for developing chemical andbiochemical sensor applications [93,94]. Highly sensitiveoptical sensors based on uorescent electrospun poly-mer nanober lms were also recently reported[101,154,155]. Preliminary results indicate the sensitiv-ities of nanober lms to detect ferric and mercury ionsand a nitro compound (2,4-dinitrotulene, DNT) are twoto three orders of magnitude higher than that obtainedfrom thin lm sensors.Nanoscale tubes made from various materials
including carbon, ceramics, metals, and polymers areimportant in many industry elds. Ultrane bers pre-pared from electrospinning can be used as templates todevelop the various nanotubes [9,71]. In general, the
2242 Z.-M. Huang et al. / Composites Scieand the vertical distance above this reference is con-sidered to be the exact diameter of the upper nanober. Fig. 21 shows the nanober structures observedthrough SEM, TEM and AFM. AFM can also be usedto characterize the roughness of bers. The roughnessvalue is the arithmetic average of the deviations ofheight from the central horizontal plane given in termsof millivolts of measured current .Another geometric parameter is porosity. The poros-
ity and pore size of nanober membranes are importantfor applications of ltration, tissue template, protectiveclothing, etc. [102,127,169]. The pore size measurementcan be conducted by, for example, a capillary owporometer [102,127,143]. Schreuder-Gibson et al. com-pared the pore sizes of membranes electrospun fromNylon 6,6, FBI (polybenzimidazole), and two poly-
1 1the nanotube is formed once the template is removedthrough thermal degradation or solvent extraction. Forthis purpose, the template nanober must be stableduring the coating and be degradable or extractablewithout destructing the coating layer. By using PLA[poly(l-lactide)] nanobers, Bognitzki et al. obtainedpolymer [PPX, or poly(p-xylylene)], composite of poly-mer (PPX) and metal (aluminum), and metal (alumi-num) nanotubes respectively through chemical vapordeposition (CVD) coating and physical vapor deposi-tion (PVD) coating and then thermal degradation. Thewall thickness of the tubes was in the range of 0.11mm . Hou et al. employed the similar procedure.However, both PA [poly (tetramethylene adipamide)]and PLA nanober of smaller diameters were used astemplates and thinner nanotubes were achieved .
5.1. Geometrical characterization
Geometric properties of nanobers such as ber dia-meter, diameter distribution, ber orientation and bermorphology (e.g. cross-section shape and surfaceroughness) can be characterized using scanning electronmicroscopy (SEM), eld emission scanning electronmicroscopy (FESEM), transmission electron micro-scopy (TEM) and atomic force microscopy (AFM)[32,102,114,140]. The use of TEM does not require thesample in a dry state as that of SEM. Hence, nanoberselectrospun from a polymer solution can be directlyobserved under TEM. An accurate measurement of thenanober diameter with AFM requires a rather preciseprocedure. The bers appear larger than their actualdiameters because of the AFM tip geometry . For aprecise measurement, two bers crossing to each other
nd Technology 63 (2003) 22232253
of the macromolecules in a nanober, and can be char-
had no time to crystallize and hence it could only have
measure both the moisture vapor transport and the air
bers were investigated by [116,156]. Norris et al.
nce aNylon 6,6 could be electrospun into a very ne mem-brane with extremely small pore throat sizes (with amean ow pore diameter of 0.12 mm) which were muchsmaller than the average ber diameters. FBI alsoexhibited pore sizes (0.20 mm) smaller than the electro-spun ber sizes. However, the Estane1 and Pellethane1
exhibited mean pore sizes which were signicantlyhigher, with average ow pore diameters of 0.76 and 2.6mm, respectively .
5.2. Chemical Characterization
Molecular structure of a nanober can be character-ized by Fourier tranform infra red (FTIR) and nuclearmagnetic resonance (NMR) techniques [72,73]. If twopolymers were blended together for the fabrication ofnanobers, not only the structure of the two materialscan be detected but also the inter-molecular interactioncan be determined. In the case of a collagen and PEOblend used for electrospinning of nanobers, the NMRspectrum showed a new phase structure which wascaused by the hydrogen bond formation between theether oxygen of PEO and the protons of the amino andhydroxyl groups in collagen .Supermolecular structure describes the conguration
Fig. 21. (a) SEM of PLLA nanobers (), (b) TEM of elastin-mimeti
Z.-M. Huang et al. / Composites Sciean amorphous supermolecular structure. It should benoted that polymer crystallization does occur duringelectrospinning when the polymer is in a molten form,see a subsequent discussion. Since the supermolecularstructure changed during the electrospinning the transi-tion points of the polymers also changed. One of themwas lower than the normal melting point due to defectsexisting in crystallization while drying.Surface chemical properties can be determined by
XPS, water contact angle measurement, and FTIRATR analyses.  measured the atomic percentage ofuorine in PMMA-TAN blend. It was shown that theatomic percentage of uorine in the near surface regionof the electrospun bers was about double the atomicpercentage in a bulk polymer. Surface chemical proper-ties of nanober can also be evaluated by its hydro-philicilty, which can be measured by the water contactangle analysis of the nanober membrane surface.
5.3. Physical characterization
Air and vapor transport properties of electrospunnanobrous mats have been measured using an appara-tus called dynamic moisture vapor permeation cell(DMPC) [58,60]. This device has been designed to
tide bers (bar represents 3.3 mm) (), and (c) AFM of polyurethane
nd Technology 63 (2003) 22232253 2243acterized by optical birefringence [16,22,104], wide-angle X-ray diraction (WAXD), small angle X-rayscattering (SAXC) and dierential scanning calorimeter(DSC) [16,169]. Fong & Reneker  studied thebirefringence of the styrenebutadienestyrene (SBS)triblock copolymer nanobers with diameters around100 nm under an optical microscope. The occurrence ofbirefringence reects the molecular orientation. Zonget al.  noticed that the electrospun PLLA bersquenched below 0 C resulted in amorphous berstructure. After drying the electrospun nanobers atroom temperature, they found that melting point tran-sitions appeared at two peaks by DSC. It was explainedthat during electrospinning of this polymer molecule
permeability (convective gas ow) of continuous lms,fabrics, coated textiles and open foams and battings.Schreuder-Gibson & Gibson compared electrospunnanobrous nonwovens of a thermoplastic poly-urethane with the corresponding meltblown nonwovens.Average pore size of the electrospun nonwovens was 4100 times smaller than that of the meltblown nonwovens,resulting in an increase in air ow resistance by as much as156 times. However, no signicant dierence has beenfound for the breathability, or moisture vapor diusionresistances of the two nonwovens . Crosslinking thebers of the electrospun membrane signicantly decreasesliquid transport through the membrane.Electrical transport properties of electrospun nano-
acterization of an individual nanober is a challenge for
resulting tenacity was 2.9 g/day. The mean elongation at
with an AFM tip while keeping the other end xed. Yu
nce ameasured the conductivity of the electrospun non-woven ultra-ne ber mat of polyaniline doped withcamphorsulfonic acid blended with PEO (polyethyleneoxide). As the non-woven mat was highly porous andthe ll factor of the bers was less than that of a castlm, the measured conductivity seemed to be lower thanthat of the bulk . Wang et al. measured the con-ductivities of PAN (polyacrylonitrile) nanobers beforeand after carbonized using a digital electrometer withtwo neighboring contacts of 4 mm distance. The elec-trospinning was conducted carefully and briey so thatthere was only one continuous ber deposited across thetwo neighboring contacts. The PAN ber (before car-bonized) exhibited a resistance which was beyond theupper limit of the electrometer, whereas the graphitiza-tion of the PAN nanober led to a sharp increase inconductivity to around 490 S/m .Kim & Lee  characterized the thermal prop-
erties of nanobers of pure PET [poly (ethylene ter-ephthalate)] and PEN [poly(ethylene naphthalate)]polymers and PET/PEN blends obtained in melt form.They found that the electrospinning of polymers resul-ted in increase of crystallinity and decrease of Tg (glasstransition temperature) and Tc (crystallization peaktemperature) of PET and PEN. The crystalline meltingpeak temperatures (Tm) of PET and PEN were almostthe same before and after electrsopinnning. On theother hand, not only Tg and Tc but also Tm of the elec-trospun PET/PEN nanobers were lower than those ofthe bulk. The change in thermal properties of electro-spun neat polyesters was primarily resulted fromdecrease of molecular weight after the electrospinningby thermal as well as mechanical degradation. However,the change in those of PET/PEN blends was attributedto exchange reactions of PET and PEN in melt blends.
5.4. Mechanical characterization
Mechanical tests of nanobrous nonwoven mem-branes can be performed using conventional testingtechniques [75,100102,113,127]. When the membranesare collected on a static collector screen, no anisotropyin the in-plane tensile behavior seems to have beenreported. Fig. 22 shows typical stressstrain curves of aPLLA nanobrous mat obtained by  for tissueengineering applications. It has been found the tensilestrength of nanobrous mat was similar to that of anatural skin. However, when the membranes wereobtained from a rotating drum, Lee et al. found that theelectrospun nonwoven mats had dierent properties indierent directions [100,101]. The ber orientationdepended on the linear velocity of the drum surface andother electrospinning parameters.Due to very small dimension, the mechanical char-
2244 Z.-M. Huang et al. / Composites Sciethe existing test techniques. The established methodsand standards for determining the mechanical beha-viour of conventional bers are inadequate in the caseof manipulation or testing of nanobers. This is prob-ably one of the main reasons why articles addressing themechanical tests of single nanobers are rare in the lit-erature.  described a cantilever technique tomeasure the tenacity of a single electrospun PAN(polyacrylonitrile) ultrane ber. A cantilever consistingof a 30 mm glass ber was glued at one end onto amicroscope slide and a 15 mm nylon ber was attachedat the free end of the glass ber. The electrospun testber was glued with epoxy resin to the free end of thenylon ber. A part of the same ber was cut anddeposited on a SEM specimen holder for diametermeasurement using SEM. As the sample ber wasstretched with a computer controlled Instron model5569, the deection of the cantilever was measuredunder light microscopy using a calibrated eyepiece. Achart was used to convert the deections into actualvalues of ber tenacity. The elongation-to-break ofelectrospun PAN bers was estimated using a caliper. Itwas reported that the electrospun PAN bers with adiameter of 1.25 mm and length of 10 mm exhibitedfailure at 0.4 mm deection at 41 mg of force and the
Fig. 22. Tensile stressstrain curves of nanobrous membranes elec-
trospun from PLGA ().
nd Technology 63 (2003) 22232253break of the same ber was 190% with a standarddeviation of 16%.No report in the open literature has been found on the
tensile test of a single polymer nanober yet. On theother hand, signicant eorts have been made to char-acterize the mechanical specically tensile properties ofsingle carbon nanotubes. The methods used wherein canalso be applicable for the measurement of tensile prop-erties of single electrospun polymer nanobers.Due to nanometer specimens, the mechanical mea-
surements for carbon nanotubes reported so far wereconducted in terms of AFM, SEM, or TEM. obtained the bending strength and Youngs modulus ofa carbon nanotube by deecting one end of the tube
and ne jets are drawn from the vertices . Accord-ing to Taylor, the formation of ne threads from vis-
the Taylors cone angle should be 33.5 instead of 49.3 . called whipping instability, mainly by the bending
nce acous liquid drops in an electric eld is due to themaximum instability of the liquid surface induced bythe electrical forces. Taylor also has shown that a vis-cous uid exists in equilibrium in an electric eld whenit has the form of a cone with a semi-vertical angle,=49.3 . In other words, a uid jet is developedwhen a semi-vertical cone angle attains =49.3. Such acone is now well known as the Taylors cone. The Tay-lors cone angle has been independently veried by  who experimentally observed that the semi-verticalcone angle just before jet formation is about 50. It isnoted that a recent publication by  pointed out that
et al.  successfully used AFM cantilever tips tomeasure the tensile properties of individual multi-wallcarbon nanotubes via a SEM. They designed a nano-manipulator so that the carbon nanotube could bemanipulated in three dimensions inside the SEM, andwas attached to the tips of the AFM . Veryrecently, Demczyk et al.  directly measured the ten-sile strength and elastic modulus of multiwalled carbonnanotubes under TEM by using a tensile testing devicefabricated through a microfabrication technique. It isexpected that the similar techniques can be applied tounderstand the mechanical properties of single nanobers.
6. Modeling and simulation
6.1. Modeling of electrospinning process
The electrospinning process is a uid dynamics relatedproblem. In order to control the property, geometry,and mass production of the nanobers, it is necessary tounderstand quantitatively how the electrospinning pro-cess transforms the uid solution through a millimeterdiameter capillary tube into solid bers which are fourto ve orders smaller in diameter. When the appliedelectrostatic forces overcome the uid surface tension, theelectried uid forms a jet out of the capillary tip towardsa grounded collecting screen. The process consists of threestages : (a) jet initiation and the extension of the jetalong a straight line, (b) the growth of whipping instabilityand further elongation of the jet, whichmay or may not beaccompanied with the jet branching and/or splitting and(c) solidication of the jet into nanobers.
6.1.1. Jet initiationThe basic principles for dealing with the electrospin-
ning jet uids were developed by . Taylorshowed that ne jets of various monomeric liquids canbe drawn from conducting tubes by electrostatic forces.As the potential of the conducting tube rises, the ori-ginally planar uid meniscus becomes nearly conical
Z.-M. Huang et al. / Composites ScieAnother issue related with the initiation of the jet isthe strength of the electrostatic eld required. Tayloralso showed that the critical voltage Vc (expressed inkilovolts) at which the maximum jet uid instabilitydevelops is given by 
0:117R ; 1
where H is the distance between the electrodes (thecapillary tip and the collecting screen), L is the length ofthe capillary tube, R is the radius of the tube, and issurface tension of the uid (units: H, L, and R in cm, in dyn per cm). In spinning, the ow beyond thespinneret is mainly elongational. Hendricks et al. also calculated the minimum spraying potential of asuspended, hemispherical, conducting drop in air as
where r is the jet radius. If the surrounding medium isnot air but a nonconductive liquid immiscible with thespinning uid, drop distortion will be greater at anygiven electric eld and, therefore, the minimum spinningvoltage will be reduced . This means that if theelectrospinning process is encapsulated in vacuum, therequired voltage will be lower.
6.1.2. Jet thinningUnderstanding of jet thinning is not yet complete.
But, it is clear now that uid instabilities occur duringthis stage. From the conventional viewpoint, when theelectried jet uid accelerates and thins along its trajec-tory, the radial charge repulsion results in splitting ofthe primary jet into multiple sub-jets in a process knownas splaying. The nal ber size seemed to be mainlydetermined by the number of subsidiary jets developed.Recent studies, however, have demonstrated that
the key role in reducing the jet diameter from a micro-meter to a nanometer is played by a nonaxisym-metric or whipping instability, which causes bendingand stretching of the jet in very high frequencies[69,70,123,133,134]. Shin et al. [69,70,133] investigatedthe stability of electrospinning PEO (polyethyleneoxide) jet using a technique of asymptotic expansionfor the equations of electrohydrodynamics in powers ofthe aspect ratio of the perturbation quantity, which wasthe radius of the jet and was assumed to be small. Aftersolving the governing equations thus obtained, theyfound that the possibility for three types of instabilitiesexists. The rst is the classical Rayleigh instability,which is axisymmetric with respect to the jet centerline.The second is again an axisymmetric instability, whichmay be referred to as the second axisymmetricinstability. The third is a nonaxisymmetric instability,
nd Technology 63 (2003) 22232253 2245
cm), m is the mass ow rate (gram/sec) at the moment rent literature, simulation of textile nonwoven fabrics is
nce aforce. Keeping all the other parameters unchanged, theelectric eld strength will be proportional to theinstability level. Namely, when the eld is the lowest,the Rayleigh instability occurs, whereas the bending (orwhipping) instability corresponds to the highest eld. Shin et al. have also experimentally observed thatthe phenomenon of so-called inverse cone in whichthe primary jet was thought to be split into multiplejets is actually caused by the bending instability. Athigher resolution and with shorter electronic cameraexposure time, the inverse cone is not due to splittingbut as a consequence of small lateral uctuations in thecenterline of the jet. Some similar phenomena wererecognized earlier by  through their theoretical andexperimental work. Both research groups have foundthe non-splitting phenomenon using PEO solutionswith relatively low weight concentration (of 2% and6%).However, as the jet uid driven by the electric forces
is unstable during its trajectory towards the collectingscreen, branching and/or splitting from the primary jetshould be possible. In fact, using more advancedexperimental set-ups, the phenomena of branching andsplitting have been re-realized by a number of researchgroups.  captured a splaying event during the elec-trospinning of 10 wt.% PEO solution.  recognizedthat branching and splitting occurred from the primaryjet in electrospinning a number of polymer solutionssuch as HEMA [poly(2-hydroxethyl methacrylate)], PS(polystyrene), PVDF [poly(vinylidene uoride)], andPEI [poly(ether imide)], with weight concentrations ofmore than 10%.  theoretically investigated theexcitation conditions of both axisymmetric and non-axisymmetric perturbations of an electrically chargedjet. The linearized problem was analyzed in terms of thesurface frozen charge approximation. Their solutionsindicate that there is a possibility of stability control ofa moving electried jet in the longitudinal electric eld.By adjusting electric intensity and liquid properties, theaxisymmetric mode instability usually causing the jetdecay on drops can be reduced considerably, and theincrements of nonaxisymmetric modes m=1 and m=2are increased where m is the azimuthal wave number.They showed that the nonaxisymmetric mode could leadto the longitudinal splitting into two of the initial jet.Regarding the uid jet diameter,  noticed that as
viscosity of the polymer solvent increased, the spinningdrop changed from approximately hemispherical toconical. By using equi-potential line approximation cal-culation, Baumgarten obtained an expression to calcu-late the radius r0 of a spherical drop (jet) as follows
where " is the permittivity of the uid (in coulombs/volt-:
2246 Z.-M. Huang et al. / Composites Sciewhere r0 is to be calculated, k is a dimensionless para-meter related with the electric currents, is electric con-ductivity (amp/volt cm), and is density (g/cm3).Spivak et al.  formulated an electrohydro-
dynamic model of steady state electrospinning in asingle jet, taking into account inertial, hydrostatic,viscous, electric, and surface tension forces. A one-dimensional dierential equation for the jet radius, as afunction of the distance from the jet tip towards thecollecting plate, was derived by averaging physicalquantities over the jet cross-section. They comparedtheir theoretical jet radii at various distances up to 60%of the whole jet trajectory with their measured results.Reasonably good agreement was reported.
6.1.3. Jet solidicationYarin et al.  derived a quasi-one-dimensional
equation to describe the mass decrease and volumevariation of the uid jet due to evaporation and solidi-cation, by assuming that there is no branching orsplitting from the primary jet. With an initial weightconcentration of 6% and other processing parameters,they calculated that the cross-sectional radius of the dryber was 1.31103 times of that of the initial uid jet.Although the solidication rate varied with polymerconcentration was implemented, the other issues such ashow this rate varies with electrostatic eld, gap distance,etc. and how to control the porous dimension and dis-tribution during the solidication have not been clearlyaddressed.
6.2. Modeling of nanobrous preform
The mechanical performance of nanober preforms isof interest in applications such as semi-permeablemembranes, lters, protective clothing, and tissue engi-neering. For instance, the nanober scaold templateshould be designed to be structurally biocompatiblewith the host tissue. This will be possible when thestructureproperty relationship of the scaolds has beenclearly understood.Challenges in the modeling of mechanical properties
of nanoscale nonwoven scaolds (lms) include thedetermination of the nano-ber orientation distribu-tions in the scaolds, the measurement of the coecientof friction of the nanobers, and the specication of thecondition under which the ber slippage occurs. Inaddition to the mechanical behavior, the geometricproperties of nanobrous preforms such as pore shape,pore size and pore size distribution, free volume or voi-dage and surface area are also important for applica-tions. In tissue engineering, for instance, theseproperties inuence to a great extent the cell seeding andgrowth eciency. While no modeling work has beenfound for any nanobrous nonwoven fabric in the cur-
nd Technology 63 (2003) 222322530
xed volume V at a constant temperature T. Suppose erties were calculated as ensemble averages of functions
nce aexpected to provide a starting point for researches inthis area. Simulation of the mechanical properties ofcommon textile nonwoven fabrics has been carried outmainly using the Finite Element approach [2,103]. Ingeneral, the nite displacements in the non-woven fabricstructure must be taken into account [13,14]. Morecomplexity lies in the fact that the friction and slippageoccur between the bers. These two phenomena aresomewhat contradictory, but both exist during the fab-ric deformation. In the Finite Element simulation, theber web is usually considered as an assembly of singlenode at ber ends and paired nodes where they are incontact with one another.Abdel-Ghani and Davies  proposed a model to
simulate the non-woven fabric geometry by assumingthat the non-woven fabric can be decomposed intolayers one above another. Each layer was considered asa random network of bers. The areas formed betweenintersecting or overlapping bers in a particular layerconstituted the pores in the media. A Monte Carlomethod was used to produce random line networks torepresent a layer. Methods of describing the line networkwere reviewed in their work. A variation in diameters ofbers was considered in the simulation to representpractical ber materials. An analysis of networks waspresented and results for distributions of pore area,perimeter, and hydraulic radii were computed.
6.3. Modeling of single nanober
Due to its extremely small diameter, experimentalcharacterization for the mechanical properties of a sin-gle nanober is dicult with the current techniques.So, a possible way to understand the macroscopiccharacteristics of the nanober is through a molecularcomputer simulation. Molecular simulation of a systemis to determine its macroscopic properties using themicroscopic model which has been constructed todescribe the main interactions between the particleswhich make the system . It has been widely used inpolymer science and engineering to rationalize themolecular structure, function, and interaction of thepolymer material. As the simulation is based on atomsand molecules, almost all the thermodynamic, struc-tural, and transport properties of the material can besimulated.There are two kinds of molecular simulation techni-
ques. One is the purely stochastic Monte Carlo method,which randomly samples the congurational space andwhich generally leads to static properties such as surfaceenergy, density, etc. Another is the deterministic molec-ular dynamics method, which produces trajectories inthe congurational space and leads to both static anddynamic properties. Let us assume that we have a sys-tem made of a xed number of particles N occupying a
Z.-M. Huang et al. / Composites Sciethat we would like to calculate the equilibrium value Aof a quantity A (e.g. the potential energy function) ofthe system, where A=A(rN) with rN referring to the setof position vectors of the particles (r1, r2, . . ., rN).According to statistical mechanics, A is given by
exp U rN dr1 . . . drN 4where =1/(kT). k is the Boltzmann constant. Z is thecongurational integral dened as
Z . . .
exp U rN dr1 . . . drN 5
U(rN) is the intermolecular potential function of thesystem. Due to the 3N-dimensional character (sincedri=dxidyidzi) of the integrals (4) and (5), it is not pos-sible to evaluate them using standard numerical techni-ques such as a Gaussian procedure (in practice, a systemcontains quite a lot of atoms, i.e. N can be rather large).Thus, the Monte Carlo method becomes attractivelyfeasible. For each conguration ri
N accepted, the inte-grand of Eq. (4) is evaluated. Several million congur-ations are generally needed to obtain statisticallymeaningful averages. Suppose m is the total number ofcongurations. The result of the Monte Carlo eval-uation of integral (4) is given by
where Ai=A(riN), ri
N being the set of position vectorsafter