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)
Thermoplastic polyolefin (TPO) - - 30.9 - - 101.5 79.0 22.5 - - - - -
  3.45(11) 3.54(2) 7.07(2) 3.54(2)
Polyxylylene (parylene) - - 46.3 - - - - - - - - - -
  -(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)
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 pyrrolidone (PVP) 9003-39-8 - 46.0 - - - - - - - - - -
  3.61(2)
Polyvinyl formal 63450-15-7 39.0 - - - - - - - - - - -
  -(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)
Polyvinyl ethyl ether (polyethoxyethylene) 25104-37-4 - 36.0 - - - - - - - - - -
  -(1)
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)
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 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)
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)
Polytrifluoroethylene 24980-67-4 26.5 26.5 - 92.0 - - - - - - - -
  3.99(3) 2.79(7) -(1)
Polytetramethylene oxide - - 32.8 - - - - - - - - - -
  1.27(2)
Polytetrahydrofuran (PTHF) 25190-06-1 - 31.9 - - - - - - - - - -
  0.00(2)
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)
Polystearyl methacrylate 25639-21-8 20.8 36.3 - - - - - - - - - -
  -(1) -(1)
Poly(phosphazene) - 16.5 15.8 - - - - - - - - - -
  -(1) 0.35(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)
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)
Polyphenyl methacrylate - 35.0 - - - - - - - - - - -
  -(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)
Polyoctyl methacrylate - 23.5 - - - - - - - - - - -
  -(1)
Poly(nonafluoroisobutyl acrylate) - - 14.0 - - - - - - - - - -
  -(1)
Polymethylphenylsilylene - - 43.7 - - - - - - - - - -
  0.57(2)
Polymethylphenylsiloxane 9005-12-3 - 26.1 - - - - - - - - - -
  -(1)
Poly(4-methyl pentene-1) - - 25.0 - - - - - - - - - -
  -(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)
Polylauryl methacrylate 25719-52-2 21.3 32.8 - - - - - - - - - -
  -(1) -(1)
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)
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)
Poly(2-hydroxyethyl methacrylate) 24249-16-5 37.0 - - - - - - - - - - -
  -(1)
Poly(hexafluoropropylene) - 16.9 15.9 - 112.0 - - - - - - - -
  0.96(3) 2.67(4) -(1)
Poly(hexachlorobutadiene) - - 41.5 - - - - - - - - - -
  -(1)
Poly(heptafluoroisopropyl methacrylate) - - 15.0 - - - - - - - - - -
  -(1)
Poly(heptafluoroisopropyl acrylate) - - 14.0 - - - - - - - - - -
  -(1)
Poly(heptadecafluorooctyl methacrylate) - - 15.3 - - - - - - - - - -
  -(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)
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)
Polyetheretherketone (PEEK) 29658-26-2 - 42.1 - 91.0 85.0 55.0 30.0 - - - - -
  -(1) -(1) -(1) -(1) -(1)
Polyepichlorohydrin 24969-06-0 35.0 43.2 - - - - - - - - - -
  0.00(2) -(1)
Poly(dimethylaminoethyl methacrylate) - - 36.0 - - - - - - - - - -
  -(1)
Polybutylene terephthalate (PBT) 26062-94-2 - 46.3 - - 84.0 - - - - - - -
  0.51(5) 0.00(2)
Polybenzyl methacrylate (PBMA) 25085-83-0 36.0 - - - - - - - - - - -
  -(1)
Poly(L-alanine) 25191-17-7 - 45.2 - - - - - - - - - -
  -(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)
Polyacrylamide 9003-05-8 34.3 52.3 - - - - - - - - - -
  4.60(2) -(1)
Polyacetylene (polyethyne) - - 51.5 - 72.0 - - - - - - - -
  0.71(2) -(1)
Phenoxy resin 26402-79-9 - 43.0 - - - - - - - - - -
  -(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)
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)
Nylon 10,10 - 32.0 - - - 94.0 - - - - - - -
  -(1) -(1)
Nylon 9,9 - 34.0 - - - 86.0 - - - - - - -
  -(1) -(1)
Nylon 8,8 - 34.0 - - - 86.0 - - - - - - -
  -(1) -(1)
Nylon 7,7 - 43.0 - - - 70.0 - - - - - - -
  -(1) -(1)
Nylon 6,12 24936-74-1 - 67.0 - - - - - - - - - -
  -(1)
Nylon 6,10 9008-66-6 - 40.5 - - 71.0 - - - - - - -
  -(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)
Nylon 4 24938-56-5 - 48.5 - - - - - - - - - -
  -(1)
Nylon 2 (polyglycine) 25718-94-9 - 50.1 - - - - - - - - - -
  -(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)
Nafion 31175-20-9 - - - - 90.5 - - - - - - -
  4.80(4)
2-Hydroxyethyl methacrylate (HEMA, ethylene glycol monoacrylate) 867-77-9 - 56.8 - - 59.0 - - - - - - -
  1.20(2) -(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)
Ethylene-propylene-diene-monomer (EPDM) 25038-36-2 - 32.5 - 91.0 - - - - - - - -
  4.31(2) -(1)
Ethyl methacrylate (EMA) 97-63-2 - 42.0 - - 74.0 - - - - - - -
  1.06(2) -(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)
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)
Cellulose triacetate 9012-09-3 48.8 - - - - - - - - - - -
  -(1)
Cellulose acetate butyrate (CAB) 9004-36-8 - 34.0 - - - - - 22.2 17.2 13.8 2.8 12.6
  -(1) -(1) -(1) -(1) -(1)
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)
Cellophane 9005-81-6 - 45.4 - - - - - 28.5 16.1 18.5 14.5 9.3
  -(1) -(1) -(1) -(1) -(1)
Aramid (Kevlar) 26125-61-1 - 45.7 - - 63.7 - - - - - - -
  1.76(3) 3.54(2)
Amorphous fluoropolymer (Teflon AF) - - - - - 117.5 90.3 27.1 - - - - -
  5.67(5) 3.42(5) 9.13(5)
Aluminum foil (f) 7429-90-5 - 41.2 - 81.3 - - - - - - - -
  2.47(2) 4.60(2) - - - - - - - -
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)
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)
Polyvinyl octanoate - - 28.7 -0.061(c) - - - - - - - - -
  -(1)
Polyvinyl hexanoate - - 28.9 -0.063(c) - - - - - - - - -
  -(1)
Polyvinyl dodecanoate - - 29.1 -0.063(c) - - - - - - - - -
 
Polyvinyl decanoate - - 28.9 -0.062(c) - - - - - - - - -
  -(1)
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)
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)
Poly a-methyl styrene 25014-31-7 - 38.7 -0.058(b) - - - - - - - - -
  -(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(hexyl methacrylate) 25087-17-6 27.5 30.0 -0.062(c) - - - - - - - - -
  -(1) 0.00(2)
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)
Poly 2-ethylhexyl methacrylate 25719-51-1 - 28.8 -0.062(c) - - - - - - - - -
  -(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)
Poly t-butyl methacrylate (PtBMA) 25189-00-9 18.1 30.5 -0.059(b) 108.1 - - - - - - - -
  -(1) 0.00(2) -(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)
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)
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 proprionate 25035-84-1 - 34.0 -0.072(c) - - - - - - - - -
  -(1)
Polyvinyl hexadecanoate - - 30.9 -0.066(c) - - - - - - - - -
  -(1)
Polyvinyl butyrate - - 31.1 -0.070(c) - - - - - - - - -
  -(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)
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)
Poly n-propyl methacrylate 2210-79-9 32.0 33.2 -0.065(c) - - - - - - - - -
  -(1) -(1)
Polymethyl acrylate (PMA) 25087-26-7 38.0 39.8 -0.070(c) - - - - - - - - -
  4.24(2) 2.21(9)
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)
Poly 2-ethylhexyl acrylate 9003-77-4 31.0 29.7 -0.070(c) - - - - - - - - -
  -(1) 0.71(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)
Polyethyl acrylate (PEA) 9003-32-1 34.0 35.1 -0.070(c) - - - - - - - - -
  1.41(2) 1.47(6)
Polydiethylsiloxane (PDES) 63148-61-8 - 25.7 -0.073(c) - - - - - - - - -
  -(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)
Poly n-butyl acrylate 9003-49-0 29.5 32.8 -0.070(c) - - - - - - - - -
  2.12(2) 1.82(3)
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
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)
Polypropylene isophthalate - - 49.3 -0.083(c) - - - - - - - - -
  -(1)
Polypropylene glycol (PPG, polypropylene oxide) 25322-69-4 32.0 30.6 -0.079(b) - - - - - - - - -
  -(1) 2.36(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)
Polybutylene isophthalate - - 47.8 -0.080(c) - - - - - - - - -
  -(1)
Eicosane 112-95-8 - 28.9 -0.0833(c) - - - - - - - - -
  -(1)
Polychloroprene 9010-98-4 38.0 40.9 -0.086(b) - - - - - - - - -
  0.00(2) 3.63(7)
Polyethylene oxide (PEO, PEG, polyethylene glycol) 25322-68-3 43.0 43.1 -0.095(c) 63.0 - - - - - - - -
  -(1) 2.07(16) -(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)

(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