Critical Surface Tension, Surface Free Energy, Contact Angles with Water, and Hansen Solubility Parameters for Various Polymers

Name(1) CAS #(2) γc(3) γS(4) dγ/dt(5) θWY(6) θWA(7) θWR(8) W (9) δ(10) δD(11) δP(12) δH(13) Ro(14)
Amorphous fluoropolymer (Teflon AF) - - - - - 117.5 90.3 27.1 - - - - -
  5.67(5) 3.42(5) 9.13(5)
Epoxies - 44.5 45.3 - 54.0 87.5 - - 24.1 19.2 10.9 9.6 11.1
  0.71(2) 4.21(6) -(1) 3.54(2) 2.53(13) 2.37(13) 2.66(13) 3.98(13)
Nylon 7,7 - 43.0 - - - 70.0 - - - - - - -
  -(1) -(1)
Nylon 8,8 - 34.0 - - - 86.0 - - - - - - -
  -(1) -(1)
Nylon 9,9 - 34.0 - - - 86.0 - - - - - - -
  -(1) -(1)
Nylon 10,10 - 32.0 - - - 94.0 - - - - - - -
  -(1) -(1)
Polyacetylene (polyethyne) - - 51.5 - 72.0 - - - - - - - -
  0.71(2) -(1)
Polybutylene isophthalate - - 47.8 -0.080(c) - - - - - - - - -
  -(1)
Poly(dimethylaminoethyl methacrylate) - - 36.0 - - - - - - - - - -
  -(1)
Poly(heptadecafluorooctyl methacrylate) - - 15.3 - - - - - - - - - -
  -(1)
Poly(heptafluoroisopropyl acrylate) - - 14.0 - - - - - - - - - -
  -(1)
Poly(heptafluoroisopropyl methacrylate) - - 15.0 - - - - - - - - - -
  -(1)
Poly(hexachlorobutadiene) - - 41.5 - - - - - - - - - -
  -(1)
Poly(hexafluoropropylene) - 16.9 15.9 - 112.0 - - - - - - - -
  0.96(3) 2.67(4) -(1)
Poly(4-methyl pentene-1) - - 25.0 - - - - - - - - - -
  -(1)
Polymethylphenylsilylene - - 43.7 - - - - - - - - - -
  0.57(2)
Poly(nonafluoroisobutyl acrylate) - - 14.0 - - - - - - - - - -
  -(1)
Polyoctyl methacrylate - 23.5 - - - - - - - - - - -
  -(1)
Polyphenyl methacrylate - 35.0 - - - - - - - - - - -
  -(1)
Poly(phosphazene) - 16.5 15.8 - - - - - - - - - -
  -(1) 0.35(2)
Polypropylene (PP) (a) 30.5 30.2 -0.058(b) 94.9 107.3 89.0 20.2 18.0 17.7 2.9 1.2 6.2
  1.50(3) 2.77(32) 5.29(11) 7.75(15) 5.73(6) 2.72(6) 0.46(2) 2.80(2) 1.71(2) 1.76(2)
Polypropylene isophthalate - - 49.3 -0.083(c) - - - - - - - - -
  -(1)
Polytetramethylene oxide - - 32.8 - - - - - - - - - -
  1.27(2)
Polyurethanes - - 37.5 - 77.5 83.1 35.5 47.4 22.8 18.8 10.0 8.2 9.8
  4.01(11) 7.52(8) 14.2(9) 16.3(9) 21.7(9) 1.53(11) 2.54(11) 3.09(11) 3.48(11)
Polyvinyl butyrate - - 31.1 -0.070(c) - - - - - - - - -
  -(1)
Polyvinyl decanoate - - 28.9 -0.062(c) - - - - - - - - -
  -(1)
Polyvinyl dodecanoate - - 29.1 -0.063(c) - - - - - - - - -
 
Polyvinyl hexadecanoate - - 30.9 -0.066(c) - - - - - - - - -
  -(1)
Polyvinyl hexanoate - - 28.9 -0.063(c) - - - - - - - - -
  -(1)
Polyvinyl octanoate - - 28.7 -0.061(c) - - - - - - - - -
  -(1)
Polyxylylene (parylene) - - 46.3 - - - - - - - - - -
  -(1)
Thermoplastic polyolefin (TPO) - - 30.9 - - 101.5 79.0 22.5 - - - - -
  3.45(11) 3.54(2) 7.07(2) 3.54(2)
Ethyl methacrylate (EMA) 97-63-2 - 42.0 - - 74.0 - - - - - - -
  1.06(2) -(1)
Eicosane 112-95-8 - 28.9 -0.0833(c) - - - - - - - - -
  -(1)
Hexatriacontane 630-06-8 20.6 22.8 -0.066(c) 108.2 109.0 - - - - - - -
  1.30(6) 5.03(9) 4.03(2) -(1)
2-Hydroxyethyl methacrylate (HEMA, ethylene glycol monoacrylate) 867-77-9 - 56.8 - - 59.0 - - - - - - -
  1.20(2) -(1)
Poly n-propyl methacrylate 2210-79-9 32.0 33.2 -0.065(c) - - - - - - - - -
  -(1) -(1)
Aluminum foil (f) 7429-90-5 - 41.2 - 81.3 - - - - - - - -
  2.47(2) 4.60(2) - - - - - - - -
Paraffin 8002-74-2 24.8 27.9 -0.060(c) 109.3 108.5 96.0 11.0 - - - - -
  6.53(3) 3.96(12) 1.84(2) 2.12(2) -(1) -(1)
Polychlorotrifluoroethylene (PCTFE) 9002-83-9 30.8 30.7 -0.067(c) 90.0 104.0 72.0 32.0 16.5 15.6 2.5 4.7 5.8
  1.34(4) 3.79(7) -(1) 0.00(2) 7.07(2) 7.07(2) 2.10(3) 1.46(3) 2.44(3) 1.56(3)
Polytetrafluoroethylene (PTFE) 9002-84-0 19.4 21.8 -0.058(c) 109.4 108.9 96.0 14.3 16.7 16.2 1.8 3.4 3.9
  1.49(8) 3.24(35) 5.70(17) 7.06(8) 8.72(3) 10.6(3) -(1) -(1) -(1) -(1)
Polyvinylidene chloride (PVDC, Saran) 9002-85-1 40.2 43.7 - 80.0 - - - 23.1 19.0 9.6 9.0 5.8
  3.89(4) 2.81(9) -(1) 1.98(2) 0.64(2) 1.70(2) 2.62(2)
Polyvinyl chloride (PVC) 9002-86-2 37.9 40.1 - 83.2 91.9 75.3 - 20.0 16.8 8.9 6.1 8.5
  7.05(11) 3.66(22) 10.3(8) 7.88(3) -(1) 1.65(5) 1.95(5) 1.78(5) 3.94(5)
Polyethylene (PE) 9002-88-4 31.6 33.5 -0.057(b) 94.9 97.2 83.1 13.9 17.6 16.8 3.8 3.8 6.6
  2.05(21) 3.02(62) 6.96(27) 5.80(26) 10.7(9) 8.66(9) 0.88(7) 1.94(7) 2.52(7) 2.84(7)
Polyacrylamide 9003-05-8 34.3 52.3 - - - - - - - - - -
  4.60(2) -(1)
Polybutadiene 9003-17-2 29.3 45.9 -0.144(d) 96.0 - - - 18.0 17.5 2.3 3.4 6.6
  3.79(3) 3.89(2) -0.110(e) 1.41(2) -(1) -(1) -(1) -(1)
Polyvinyl acetate (PVA) 9003-20-7 35.3 38.5 -0.066(b) 60.6 - - - 25.7 20.9 11.3 9.7 13.7
  2.08(3) 2.75(14) -(1) -(1) -(1) -(1) -(1)
Polyisobutylene (PIB, butyl rubber) 9003-27-4 27.0 33.2 -0.064(b) - 112.1 - - 17.1 16.4 1.7 4.7 7.9
  0.00(2) 3.21(10) -(1) 1.26(6) 2.15(6) 2.08(6) 2.46(6)
Polyisoprene (PIP) 9003-31-0 - 32.3 - - - - - 18.4 18.1 2.4 2.3 10.3
  1.53(3) 2.32(3) 1.40(3) 2.66(3) 3.40(3)
Polyethyl acrylate (PEA) 9003-32-1 34.0 35.1 -0.070(c) - - - - - - - - -
  1.41(2) 1.47(6)
Polyvinyl pyrrolidone (PVP) 9003-39-8 - 46.0 - - - - - - - - - -
  3.61(2)
Polyethyl methacrylate (PEMA) 9003-42-3 32.8 34.0 -0.070(c) - - - - 20.0 17.5 8.5 4.7 9.6
  0.90(4) 2.50(7) 1.34(3) 0.62(3) 3.82(3) 1.99(3)
Poly n-butyl acrylate 9003-49-0 29.5 32.8 -0.070(c) - - - - - - - - -
  2.12(2) 1.82(3)
Polystyrene (PS) 9003-53-6 34.0 38.3 -0.072(b) 85.3 88.5 81.8 10.0 23.9 22.8 5.8 4.3 12.7
  4.27(18) 5.23(32) 6.08(8) 5.75(15) 3.86(4) 2.65(3) -(1) -(1) -(1) -(1)
Acrylonitrile butadiene styrene (ABS) 9003-56-9 38.5 42.0 - 89.7 72.0 - - 19.2 17.0 5.7 6.8 9.4
  -(1) 4.70(8) -(1) -(1) 0.92(2) 4.17(2) 0.49(2) 2.19(2)
Poly 2-ethylhexyl acrylate 9003-77-4 31.0 29.7 -0.070(c) - - - - - - - - -
  -(1) 0.71(2)
Cellulose acetate (CA) 9004-35-7 37.5 41.1 - 54.5 - - - 23.5 17.1 13.1 9.4 10.6
  2.12(2) 3.37(5) -(1) 1.58(4) 4.41(4) 3.81(4) 2.96(4)
Cellulose acetate butyrate (CAB) 9004-36-8 - 34.0 - - - - - 22.2 17.2 13.8 2.8 12.6
  -(1) -(1) -(1) -(1) -(1)
Ethyl cellulose 9004-57-3 - 30.3 - - 84.5 - - 20.4 19.0 5.6 4.9 7.9
  2.40(2) -(1) 1.56(2) 1.84(2) 1.41(2) 2.83(2)
Nitrocellulose (cellulose nitrate) 9004-70-0 - 42.7 - - 54.7 20.0 34.7 23.5 16.2 14.1 9.5 10.7
  4.10(3) 11.0(3) 22.5(3) 12.1(3) 1.06(2) 0.85(2) 1.06(2) 1.13(2)
Polymethylphenylsiloxane 9005-12-3 - 26.1 - - - - - - - - - -
  -(1)
Cellophane 9005-81-6 - 45.4 - - - - - 28.5 16.1 18.5 14.5 9.3
  -(1) -(1) -(1) -(1) -(1)
Nylon 6,10 9008-66-6 - 40.5 - - 71.0 - - - - - - -
  -(1) -(1)
Polychloroprene 9010-98-4 38.0 40.9 -0.086(b) - - - - - - - - -
  0.00(2) 3.63(7)
Polymethyl methacrylate (PMMA, acrylic, plexiglas) 9011-14-7 37.5 41.8 -0.076(b) 69.1 74.7 54.2 18.4 21.3 17.9 10.1 5.4 11.0
  4.68(12) 3.63(38) 6.08(17) 10.2(8) 5.44(2) 1.98(2) 1.37(5) 4.46(5) 3.73(5) 4.63(5)
Poly iso-butyl methacrylate (PIBMA) 9011-15-8 - 30.9 -0.060(b) - - - - 20.0 18.3 4.9 6.3 9.4
  0.00(2) 2.11(3) 0.93(3) 5.12(3) 2.10(3)
Cellulose triacetate 9012-09-3 48.8 - - - - - - - - - - -
  -(1)
Polydimethylsiloxane (PDMS) 9016-00-6 20.1 20.4 -0.048(b) 107.8 107.0 69.1 39.3 - - - - -
  3.17(7) 1.54(26) 8.78(3) 4.44(9) 7.10(7) 3.73(7)
Poly(2-hydroxyethyl methacrylate) 24249-16-5 37.0 - - - - - - - - - - -
  -(1)
Polycarbonate (PC) 24936-68-3 44.0 42.3 -0.060(c) 81.3 84.0 68.0 16.0 22.2 19.6 8.8 5.7 10.2
  2.83(2) 5.32(7) 5.77(3) -(1) -(1) -(1) 1.75(3) 2.58(3) 1.04(3) 4.06(3)
Nylon 6,12 24936-74-1 - 67.0 - - - - - - - - - -
  -(1)
Nylon 12 24937-16-4 37.1 39.3 - - 72.4 56.5 20.5 22.2 18.5 8.1 9.1 6.3
  8.63(2) 3.02(3) 5.37(3) -(1) -(1) -(1) -(1) -(1) -(1)
Polyvinylidene fluoride (PVDF) 24937-79-9 31.6 31.5 - 86.0 93.4 91.0 1.0 23.2 17.0 12.1 10.2 4.1
  5.83(5) 5.29(13) 4.00(3) 1.98(2) -(1) -(1) -(1) -(1) -(1) -(1)
Nylon 4 24938-56-5 - 48.5 - - - - - - - - - -
  -(1)
Polyepichlorohydrin 24969-06-0 35.0 43.2 - - - - - - - - - -
  0.00(2) -(1)
Polyoxymethylene (POM, polyacetal, polymethylene oxide) 24969-26-4 37.0 38.6 - 74.5 79.0 54.0 25.0 - - - - -
  1.41(2) 5.68(3) -(1) -(1) -(1) -(1)
Polytrifluoroethylene 24980-67-4 26.5 26.5 - 92.0 - - - - - - - -
  3.99(3) 2.79(7) -(1)
Polyvinyl fluoride (PVF) 24981-14-4 32.7 36.4 - 82.5 88.6 - - - - - - -
  4.66(4) 4.07(14) 3.54(2) -(1)
Poly a-methyl styrene 25014-31-7 - 38.7 -0.058(b) - - - - - - - - -
  -(1)
Polyacrylonitrile (PAN) 25014-41-9 47.0 46.8 - - - - - 27.4 21.7 14.1 9.1 10.9
  4.24(2) 6.62(4) -(1) -(1) -(1) -(1)
Polyvinyl proprionate 25035-84-1 - 34.0 -0.072(c) - - - - - - - - -
  -(1)
Ethylene-propylene-diene-monomer (EPDM) 25038-36-2 - 32.5 - 91.0 - - - - - - - -
  4.31(2) -(1)
Nylon 6 (polycaprolactum, aramid 6) 25038-54-4 43.9 45.4 - - 65.5 42.4 26.8 20.3 17.0 3.4 10.6 5.1
  2.42(3) 3.52(6) 4.27(7) -(1) -(1) -(1) -(1) -(1) -(1)
Polyethylene terephthalate (PET) 25038-59-9 39.0 44.0 -0.065(c) 72.0 73.0 54.5 20.0 20.8 18.7 6.3 6.7 6.5
  5.71(11) 3.85(28) 6.33(17) 7.32(17) 5.77(8) 11.0(8) 1.25(8) 2.03(8) 2.80(8) 3.36(8)
Polyimide (PI) 25038-81-7 - 43.8 - 71.5 79.9 48.0 31.3 - - - - -
  6.80(4) 2.07(6) 5.01(8) 12.2(8) 10.4(8)
Fluorinated ethylene polypropylene (FEP) 25067-11-2 19.1 18.5 - 105.7 112.7 98.5 14.8 19.6 19.0 4.0 3.0 4.0
  1.27(2) 2.25(7) 4.54(6) 5.03(4) 5.28(4) 1.31(3) -(1) -(1) -(1) -(1)
Polymethacrylonitrile (PMAN) 25067-61-2 39.0 42.3 - - - - - 23.7 17.2 14.4 7.6 3.8
  -(1) 3.08(3) -(1) -(1) -(1) -(1)
Polybenzyl methacrylate (PBMA) 25085-83-0 36.0 - - - - - - - - - - -
  -(1)
Poly(hexyl methacrylate) 25087-17-6 27.5 30.0 -0.062(c) - - - - - - - - -
  -(1) 0.00(2)
Polymethyl acrylate (PMA) 25087-26-7 38.0 39.8 -0.070(c) - - - - - - - - -
  4.24(2) 2.21(9)
Polyvinyl ethyl ether (polyethoxyethylene) 25104-37-4 - 36.0 - - - - - - - - - -
  -(1)
Polyphenylene oxide (PPO) 25134-01-4 47.0 46.0 - - - - - 19.3 16.9 8.9 2.7 11.7
  -(1) -(1) -(1) -(1) -(1) -(1)
Polysulfone (PSU) 25135-51-7 42.1 44.9 - 75.0 66.0 - - 21.5 18.5 8.5 7.0 9.4
  1.48(2) 2.47(2) -(1) -(1) 2.17(3) 2.61(3) 1.12(3) 1.69(3)
Polyethersulfone (PES) 25154-01-2 - 47.0 - 68.5 - - - 21.0 18.3 8.2 6.4 6.3
  -(1) 0.71(2) 0.91(6) 3.10(6) 2.33(6) 2.61(6)
Poly t-butyl methacrylate (PtBMA) 25189-00-9 18.1 30.5 -0.059(b) 108.1 - - - - - - - -
  -(1) 0.00(2) -(1)
Polytetrahydrofuran (PTHF) 25190-06-1 - 31.9 - - - - - - - - - -
  0.00(2)
Poly(L-alanine) 25191-17-7 - 45.2 - - - - - - - - - -
  -(1)
Polyvinyl alcohol (PVOH) 25213-24-5 37.0 44.2 - 51.0 - - - 25.2 14.7 14.1 14.9 10.5
  -(1) 6.56(4) -(1) 2.51(4) 2.13(4) 2.18(4) 1.38(4)
Polyethylene oxide (PEO, PEG, polyethylene glycol) 25322-68-3 43.0 43.1 -0.095(c) 63.0 - - - - - - - -
  -(1) 2.07(16) -(1)
Polypropylene glycol (PPG, polypropylene oxide) 25322-69-4 32.0 30.6 -0.079(b) - - - - - - - - -
  -(1) 2.36(7)
Nylon 11 25587-80-8 35.6 34.0 - - 82.0 - - 20.5 17.0 4.4 10.6 5.1
  4.40(8) -(1) 9.90(2) -(1) -(1) -(1) -(1)
Poly n-butyl methacrylate (PnBMA) 25608-33-7 29.8 33.1 -0.059(b) 91.0 - - - 18.4 16.0 6.2 6.6 9.5
  1.94(3) 2.70(12) -(1) -(1) -(1) -(1) -(1)
Polystearyl methacrylate 25639-21-8 20.8 36.3 - - - - - - - - - -
  -(1) -(1)
Nylon 2 (polyglycine) 25718-94-9 - 50.1 - - - - - - - - - -
  -(1)
Poly 2-ethylhexyl methacrylate 25719-51-1 - 28.8 -0.062(c) - - - - - - - - -
  -(1)
Polylauryl methacrylate 25719-52-2 21.3 32.8 - - - - - - - - - -
  -(1) -(1)
Polybutylene terephthalate (PBT) 26062-94-2 - 46.3 - - 84.0 - - - - - - -
  0.51(5) 0.00(2)
Polyphenylene sulfide (PPS) 26125-40-6 38.0 46.8 - 80.3 - - - 19.8 18.7 5.3 3.7 6.7
  -(1) 3.29(3) 1.53(3) -(1) -(1) -(1) -(1)
Aramid (Kevlar) 26125-61-1 - 45.7 - - 63.7 - - - - - - -
  1.76(3) 3.54(2)
Phenoxy resin 26402-79-9 - 43.0 - - - - - - - - - -
  -(1)
Polyetheretherketone (PEEK) 29658-26-2 - 42.1 - 91.0 85.0 55.0 30.0 - - - - -
  -(1) -(1) -(1) -(1) -(1)
Nafion 31175-20-9 - - - - 90.5 - - - - - - -
  4.80(4)
Nylon 6,6 32131-17-2 42.2 44.3 -0.065(c) 67.6 69.3 40.9 27.6 25.8 17.2 9.9 16.5 4.4
  4.50(12) 3.62(18) 4.94(7) 2.91(5) -(1) -(1) 1.11 1.10 6.80 1.24
Polyetherimide (PEI) 61128-46-9 - - - 76.5 - - - 19.8 17.7 6.0 6.4 4.8
  12.0(2) 1.07(5) 1.14(5) 2.43(5) 1.70(5)
Polydiethylsiloxane (PDES) 63148-61-8 - 25.7 -0.073(c) - - - - - - - - -
  -(1)
Polyvinyl butyral 63148-65-2 28.0 38.0 - - - - - 24.6 19.1 9.5 12.2 10.0
  -(1) -(1) 0.92(3) 4.50(3) 1.65(3) 1.53(3)
Polyvinyl formal 63450-15-7 39.0 - - - - - - - - - - -
  -(1)

(a) Atactic PP CAS #9003-08-0; isotactic PP CAS #25085-53-4.To top of page

(b) S. Wu, J. Macromol. Sci., C10, 1 (1974).To top of page

(c) S. Wu, in Polymer Handbook, 3rd Ed., J. Brandrup and E.H. Immergut, eds., Wiley-Interscience, New York, NY, 1989, p. VI: 414-426.To top of page

(d) Polybutadiene data for carboxyl end group; S. Wu, in Polymer Handbook, 3rd Ed., J. Brandrup and E.H. Immergut, eds., Wiley-Interscience, New York, NY, 1989, p. VI: 414-426.To top of page

(e) Polybutadiene data for methyl ester end group; S. Wu, in Polymer Handbook, 3rd Ed., J. Brandrup and E.H. Immergut, eds., Wiley-Interscience, New York, NY, 1989, p. VI: 414-426.To top of page

(f) Aluminum foil, while obviously not a polymer, is included due to its widespread use in package converting and other industries.To top of page

(1) Names which are most widely used to describe the material or family of materials (e.g., polyurethanes and epoxies) at hand are preferred here. Commonly used acronyms and synonyms are also shown.To top of page

(2) CAS (Chemical Abstract Series) numbers are shown where available. In a number of instances, more than one CAS number is assigned to a given polymer — in some cases the details and nuances of these divergences are not at all clear. We have tried to reference the CAS number which appears to have the widest use with reference to the solid state properties of the given polymer.To top of page

(3) γc: Critical surface tension in mJ/m2 (equivalent to dynes/cm), generally determined by the Zisman method (regression of the cosine of the contact angle), or by the wetting tension method (using solutions of 2-ethoxyethanol and formamide, per ASTM Std. D-2578).To top of page

(4) γs: Surface free energy in mJ/m2 (equivalent to dynes/cm), as measured, estimated, and calculated by a wide variety of methods and theories.To top of page

(5) dγ/dt: Change in surface energy in mJ/m2 (equivalent to dynes/cm) per degree Kelvin (or Celsius). To top of page

(6) θWY: Equilibrium (or Young's) contact angle with water, in degrees.To top of page

(7) θWA: Advancing contact angle with water, in degrees.To top of page

(8) θWR: Retreating contact angle with water, in degrees.To top of page

(9)W: Contact angle hysteresis (difference between advancing and retreating) with water, in degrees.To top of page

(10) δ: Total Hansen solubility parameter (square root of the sum of squares of the average values for dispersion, polar, and hydrogen bonding components), in MPa1/2 (equivalent to joules/cubic centimeter; 2.0455 x (cal/cc)1/2) @ 20-25oC (293.15-298.15 K). All data from Hansen Solubility Parameters: A User's Handbook, 2nd Ed., C.M. Hansen, CRC Press, Boca Raton, FL, 2007.To top of page

(11) δD: Hansen dispersion solubility parameter, in MPa1/2 (equivalent to joules/cubic centimeter; 2.0455 x (cal/cc)1/2) @ 20-25oC (293.15-298.15 K). All data from Hansen Solubility Parameters: A User's Handbook, 2nd Ed., C.M. Hansen, CRC Press, Boca Raton, FL, 2007.To top of page

(12) δP: Hansen polar solubility parameter, in MPa1/2 (equivalent to joules/cubic centimeter; 2.0455 x (cal/cc)1/2) @ 20-25oC (293.15-298.15 K). All data from Hansen Solubility Parameters: A User's Handbook, 2nd Ed., C.M. Hansen, CRC Press, Boca Raton, FL, 2007.To top of page

(13) δH: Hansen hydrogen bonding solubility parameter, in MPa1/2 (equivalent to joules/cubic centimeter; 2.0455 x (cal/cc)1/2) @ 20-25oC (293.15-298.15 K). All data from Hansen Solubility Parameters: A User's Handbook, 2nd Ed., C.M. Hansen, CRC Press, Boca Raton, FL, 2007.To top of page

(14) Ro: Interaction radius. All data from Hansen Solubility Parameters: A User's Handbook, 2nd Ed., C.M. Hansen, CRC Press, Boca Raton, FL, 2007.To top of page