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)
Cellophane 9005-81-6 - 45.4 - - - - - 28.5 16.1 18.5 14.5 9.3
  -(1) -(1) -(1) -(1) -(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)
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
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)
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)
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)
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)
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)
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)
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)
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)
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)
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 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)
Cellulose acetate butyrate (CAB) 9004-36-8 - 34.0 - - - - - 22.2 17.2 13.8 2.8 12.6
  -(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)
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)
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)
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)
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)
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)
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)
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)
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 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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
Polyvinyl pyrrolidone (PVP) 9003-39-8 - 46.0 - - - - - - - - - -
  3.61(2)
Polyvinyl proprionate 25035-84-1 - 34.0 -0.072(c) - - - - - - - - -
  -(1)
Polyvinyl octanoate - - 28.7 -0.061(c) - - - - - - - - -
  -(1)
Polyvinyl hexanoate - - 28.9 -0.063(c) - - - - - - - - -
  -(1)
Polyvinyl hexadecanoate - - 30.9 -0.066(c) - - - - - - - - -
  -(1)
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 dodecanoate - - 29.1 -0.063(c) - - - - - - - - -
 
Polyvinyl decanoate - - 28.9 -0.062(c) - - - - - - - - -
  -(1)
Polyvinyl butyrate - - 31.1 -0.070(c) - - - - - - - - -
  -(1)
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)
Polystearyl methacrylate 25639-21-8 20.8 36.3 - - - - - - - - - -
  -(1) -(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)
Poly n-propyl methacrylate 2210-79-9 32.0 33.2 -0.065(c) - - - - - - - - -
  -(1) -(1)
Poly(phosphazene) - 16.5 15.8 - - - - - - - - - -
  -(1) 0.35(2)
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 a-methyl styrene 25014-31-7 - 38.7 -0.058(b) - - - - - - - - -
  -(1)
Poly(4-methyl pentene-1) - - 25.0 - - - - - - - - - -
  -(1)
Polymethyl acrylate (PMA) 25087-26-7 38.0 39.8 -0.070(c) - - - - - - - - -
  4.24(2) 2.21(9)
Polylauryl methacrylate 25719-52-2 21.3 32.8 - - - - - - - - - -
  -(1) -(1)
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(hexyl methacrylate) 25087-17-6 27.5 30.0 -0.062(c) - - - - - - - - -
  -(1) 0.00(2)
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)
Polyethylene oxide (PEO, PEG, polyethylene glycol) 25322-68-3 43.0 43.1 -0.095(c) 63.0 - - - - - - - -
  -(1) 2.07(16) -(1)
Poly 2-ethylhexyl methacrylate 25719-51-1 - 28.8 -0.062(c) - - - - - - - - -
  -(1)
Poly 2-ethylhexyl acrylate 9003-77-4 31.0 29.7 -0.070(c) - - - - - - - - -
  -(1) 0.71(2)
Polyethyl acrylate (PEA) 9003-32-1 34.0 35.1 -0.070(c) - - - - - - - - -
  1.41(2) 1.47(6)
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)
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(dimethylaminoethyl methacrylate) - - 36.0 - - - - - - - - - -
  -(1)
Polydiethylsiloxane (PDES) 63148-61-8 - 25.7 -0.073(c) - - - - - - - - -
  -(1)
Polychloroprene 9010-98-4 38.0 40.9 -0.086(b) - - - - - - - - -
  0.00(2) 3.63(7)
Polybutylene terephthalate (PBT) 26062-94-2 - 46.3 - - 84.0 - - - - - - -
  0.51(5) 0.00(2)
Polybutylene isophthalate - - 47.8 -0.080(c) - - - - - - - - -
  -(1)
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 acrylate 9003-49-0 29.5 32.8 -0.070(c) - - - - - - - - -
  2.12(2) 1.82(3)
Polybenzyl methacrylate (PBMA) 25085-83-0 36.0 - - - - - - - - - - -
  -(1)
Poly(L-alanine) 25191-17-7 - 45.2 - - - - - - - - - -
  -(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)
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)
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 4 24938-56-5 - 48.5 - - - - - - - - - -
  -(1)
Nylon 2 (polyglycine) 25718-94-9 - 50.1 - - - - - - - - - -
  -(1)
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)
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)
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)
Eicosane 112-95-8 - 28.9 -0.0833(c) - - - - - - - - -
  -(1)
Cellulose triacetate 9012-09-3 48.8 - - - - - - - - - - -
  -(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) - - - - - - - -

(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