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)
Cellulose triacetate 9012-09-3 48.8 - - - - - - - - - - -
  -(1)
Nafion 31175-20-9 - - - - 90.5 - - - - - - -
  4.80(4)
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)
Polybenzyl methacrylate (PBMA) 25085-83-0 36.0 - - - - - - - - - - -
  -(1)
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)
Poly(2-hydroxyethyl methacrylate) 24249-16-5 37.0 - - - - - - - - - - -
  -(1)
Polyoctyl methacrylate - 23.5 - - - - - - - - - - -
  -(1)
Polyphenyl methacrylate - 35.0 - - - - - - - - - - -
  -(1)
Polyvinyl formal 63450-15-7 39.0 - - - - - - - - - - -
  -(1)
Poly(heptafluoroisopropyl acrylate) - - 14.0 - - - - - - - - - -
  -(1)
Poly(nonafluoroisobutyl acrylate) - - 14.0 - - - - - - - - - -
  -(1)
Poly(heptafluoroisopropyl methacrylate) - - 15.0 - - - - - - - - - -
  -(1)
Poly(heptadecafluorooctyl methacrylate) - - 15.3 - - - - - - - - - -
  -(1)
Poly(phosphazene) - 16.5 15.8 - - - - - - - - - -
  -(1) 0.35(2)
Poly(hexafluoropropylene) - 16.9 15.9 - 112.0 - - - - - - - -
  0.96(3) 2.67(4) -(1)
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)
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)
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)
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)
Poly(4-methyl pentene-1) - - 25.0 - - - - - - - - - -
  -(1)
Polydiethylsiloxane (PDES) 63148-61-8 - 25.7 -0.073(c) - - - - - - - - -
  -(1)
Polymethylphenylsiloxane 9005-12-3 - 26.1 - - - - - - - - - -
  -(1)
Polytrifluoroethylene 24980-67-4 26.5 26.5 - 92.0 - - - - - - - -
  3.99(3) 2.79(7) -(1)
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)
Polyvinyl octanoate - - 28.7 -0.061(c) - - - - - - - - -
  -(1)
Poly 2-ethylhexyl methacrylate 25719-51-1 - 28.8 -0.062(c) - - - - - - - - -
  -(1)
Eicosane 112-95-8 - 28.9 -0.0833(c) - - - - - - - - -
  -(1)
Polyvinyl decanoate - - 28.9 -0.062(c) - - - - - - - - -
  -(1)
Polyvinyl hexanoate - - 28.9 -0.063(c) - - - - - - - - -
  -(1)
Polyvinyl dodecanoate - - 29.1 -0.063(c) - - - - - - - - -
 
Poly 2-ethylhexyl acrylate 9003-77-4 31.0 29.7 -0.070(c) - - - - - - - - -
  -(1) 0.71(2)
Poly(hexyl methacrylate) 25087-17-6 27.5 30.0 -0.062(c) - - - - - - - - -
  -(1) 0.00(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)
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)
Poly t-butyl methacrylate (PtBMA) 25189-00-9 18.1 30.5 -0.059(b) 108.1 - - - - - - - -
  -(1) 0.00(2) -(1)
Polypropylene glycol (PPG, polypropylene oxide) 25322-69-4 32.0 30.6 -0.079(b) - - - - - - - - -
  -(1) 2.36(7)
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)
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)
Polyvinyl hexadecanoate - - 30.9 -0.066(c) - - - - - - - - -
  -(1)
Thermoplastic polyolefin (TPO) - - 30.9 - - 101.5 79.0 22.5 - - - - -
  3.45(11) 3.54(2) 7.07(2) 3.54(2)
Polyvinyl butyrate - - 31.1 -0.070(c) - - - - - - - - -
  -(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)
Polytetrahydrofuran (PTHF) 25190-06-1 - 31.9 - - - - - - - - - -
  0.00(2)
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)
Ethylene-propylene-diene-monomer (EPDM) 25038-36-2 - 32.5 - 91.0 - - - - - - - -
  4.31(2) -(1)
Poly n-butyl acrylate 9003-49-0 29.5 32.8 -0.070(c) - - - - - - - - -
  2.12(2) 1.82(3)
Polylauryl methacrylate 25719-52-2 21.3 32.8 - - - - - - - - - -
  -(1) -(1)
Polytetramethylene oxide - - 32.8 - - - - - - - - - -
  1.27(2)
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)
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)
Poly n-propyl methacrylate 2210-79-9 32.0 33.2 -0.065(c) - - - - - - - - -
  -(1) -(1)
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)
Cellulose acetate butyrate (CAB) 9004-36-8 - 34.0 - - - - - 22.2 17.2 13.8 2.8 12.6
  -(1) -(1) -(1) -(1) -(1)
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)
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)
Polyvinyl proprionate 25035-84-1 - 34.0 -0.072(c) - - - - - - - - -
  -(1)
Polyethyl acrylate (PEA) 9003-32-1 34.0 35.1 -0.070(c) - - - - - - - - -
  1.41(2) 1.47(6)
Poly(dimethylaminoethyl methacrylate) - - 36.0 - - - - - - - - - -
  -(1)
Polyvinyl ethyl ether (polyethoxyethylene) 25104-37-4 - 36.0 - - - - - - - - - -
  -(1)
Polystearyl methacrylate 25639-21-8 20.8 36.3 - - - - - - - - - -
  -(1) -(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)
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 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)
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)
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)
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)
Poly a-methyl styrene 25014-31-7 - 38.7 -0.058(b) - - - - - - - - -
  -(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)
Polymethyl acrylate (PMA) 25087-26-7 38.0 39.8 -0.070(c) - - - - - - - - -
  4.24(2) 2.21(9)
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)
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)
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)
Aluminum foil (f) 7429-90-5 - 41.2 - 81.3 - - - - - - - -
  2.47(2) 4.60(2) - - - - - - - -
Poly(hexachlorobutadiene) - - 41.5 - - - - - - - - - -
  -(1)
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)
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)
Ethyl methacrylate (EMA) 97-63-2 - 42.0 - - 74.0 - - - - - - -
  1.06(2) -(1)
Polyetheretherketone (PEEK) 29658-26-2 - 42.1 - 91.0 85.0 55.0 30.0 - - - - -
  -(1) -(1) -(1) -(1) -(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)
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)
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)
Phenoxy resin 26402-79-9 - 43.0 - - - - - - - - - -
  -(1)
Polyethylene oxide (PEO, PEG, polyethylene glycol) 25322-68-3 43.0 43.1 -0.095(c) 63.0 - - - - - - - -
  -(1) 2.07(16) -(1)
Polyepichlorohydrin 24969-06-0 35.0 43.2 - - - - - - - - - -
  0.00(2) -(1)
Polymethylphenylsilylene - - 43.7 - - - - - - - - - -
  0.57(2)
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)
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)
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)
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)
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
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)
Poly(L-alanine) 25191-17-7 - 45.2 - - - - - - - - - -
  -(1)
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)
Cellophane 9005-81-6 - 45.4 - - - - - 28.5 16.1 18.5 14.5 9.3
  -(1) -(1) -(1) -(1) -(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)
Aramid (Kevlar) 26125-61-1 - 45.7 - - 63.7 - - - - - - -
  1.76(3) 3.54(2)
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)
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)
Polyvinyl pyrrolidone (PVP) 9003-39-8 - 46.0 - - - - - - - - - -
  3.61(2)
Polybutylene terephthalate (PBT) 26062-94-2 - 46.3 - - 84.0 - - - - - - -
  0.51(5) 0.00(2)
Polyxylylene (parylene) - - 46.3 - - - - - - - - - -
  -(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)
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)
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)
Polybutylene isophthalate - - 47.8 -0.080(c) - - - - - - - - -
  -(1)
Nylon 4 24938-56-5 - 48.5 - - - - - - - - - -
  -(1)
Polypropylene isophthalate - - 49.3 -0.083(c) - - - - - - - - -
  -(1)
Nylon 2 (polyglycine) 25718-94-9 - 50.1 - - - - - - - - - -
  -(1)
Polyacetylene (polyethyne) - - 51.5 - 72.0 - - - - - - - -
  0.71(2) -(1)
Polyacrylamide 9003-05-8 34.3 52.3 - - - - - - - - - -
  4.60(2) -(1)
2-Hydroxyethyl methacrylate (HEMA, ethylene glycol monoacrylate) 867-77-9 - 56.8 - - 59.0 - - - - - - -
  1.20(2) -(1)
Nylon 6,12 24936-74-1 - 67.0 - - - - - - - - - -
  -(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